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[ "Northern Cambria School District\n\nThe Northern Cambria School District is a small, rural, public school district located in northwestern Cambria County in Pennsylvania. ", "The district encompasses: the borough of Northern Cambria along with Barr and Susquehanna Township. ", "The geographic area is just . ", "According to 2000 federal census data, it serves a resident population of 8,342. ", "By 2010, the federal census data found the district resident population had declined to 7,898 people. ", "The educational attainment levels for the Northern Cambria School District population (25 years old and over) were 85.7% high school graduates and 16.2% college graduates. ", "The District is one of the 500 public school districts of Pennsylvania.", "\n\nAccording to the Pennsylvania Budget and Policy Center, 41.9% of the district's pupils lived at 185% or below the Federal Poverty Level as shown by their eligibility for the federal free or reduced price school meal programs in 2012. ", "In 2009, the district residents’ per capita income was $13,144, while the median family income was $32,989. ", "In the Commonwealth, the median family income was $49,501 and the United States median family income was $49,445, in 2010. ", " In Cambria County, the median household income was $39,574. ", "By 2013, the median household income in the United States rose to $52,100.", "\n\nAccording to district officials, Northern Cambria School District provided basic educational services to 1,183 pupils in 2011. ", "It employed: 89 teachers, 69 full-time and part-time support personnel, and eight (8) administrators during the 2011-12 school year. ", "The district received $11,627,480 in state funding for the 2011-12 school year. ", "In school year 2007-08, NCSD provided basic educational services to 1,238 pupils. ", "It employed: 97 teachers, 74 full-time and part-time support personnel, and 9 administrators. ", "Northern Cambria School District received more than $10.9 million in state funding in school year 2007-08.", "\n\nNorthern Cambria School District operates: Northern Cambria High School and Northern Cambria Elementary/Middle School. ", "Students in grades K-8 attend the elementary/middle school while students in grades 9-12 attend the high school. ", "High school students may choose to attend Admiral Peary Area Vocational Technical School for training in the construction and mechanical trades. ", "The Appalachia Intermediate Unit IU8 provides the district with a wide variety of services like specialized education for disabled students and hearing, background checks for employees, state mandated recognizing and reporting child abuse training, speech and visual disability services and professional development for staff and faculty.", "\n\nGovernance\nThe Northern Cambria School District is governed by 9 individually elected board members (serve without compensation for a term of four years), the Pennsylvania State Board of Education, the Pennsylvania Department of Education and the Pennsylvania General Assembly. ", "The federal government controls programs it funds like: Title I funding for low income children in the Elementary and Secondary Education Act and the No Child Left Behind Act, which mandates the district focus resources on student success in acquiring reading and math skills. ", "The superintendent and business manager are appointed by the school board. ", "The superintendent is the chief administrative officer with overall responsibility for all aspects of operations, including education and finance. ", "The business manager is responsible for budget and financial operations. ", "Neither of these officials are voting members of the school board. ", "The school board enters into individual employment contracts for these positions. ", "In Pennsylvania, public school districts are required to give 150 days notice to the superintendent regarding renewal of the employment contract.", "\n\nAcademic achievement\nIn 2015, Northern Cambria School District ranked 378th out of 493 Pennsylvania public school districts, by the Pittsburgh Business Times. ", "The ranking is based on the last 3 years of student academic achievement as demonstrated by PSSAs results in: reading, writing, math and science and the three Keystone Exams (literature, Algebra 1, Biology I) in high school. ", "Three school districts were excluded because they do not operate high schools (Saint Clair Area School District, Midland Borough School District, Duquesne City School District). ", "The PSSAs are given to all children in grades 3rd through 8th. ", "Adapted PSSA examinations are given to children in the special education programs. ", "Writing exams were given to children in 5th and 8th grades.", "\n\n2014 - 368th\n2013 - 368th\n2012 - 284th \n2008 - 228th\n2007 - 284th out of 501 school districts.", "\n\nDistrict AYP status history\nIn 2012, Northern Cambria School District achieved Adequate Yearly Progress (AYP) status. ", "In 2011, Northern Cambria School District also achieved Adequate Yearly Progress (AYP). ", "In 2011, 94 percent of the 500 Pennsylvania public school districts achieved the No Child Left Behind Act progress level of 72% of students reading on grade level and 67% of students demonstrating on grade level math. ", "In 2011, 46.9 percent of Pennsylvania school districts achieved Adequate Yearly Progress (AYP) based on student performance. ", "An additional 37.8 percent of Pennsylvania public school districts made AYP based on a calculated method called safe harbor, 8.2 percent on the growth model and 0.8 percent on a two-year average performance. ", "Northern Cambria School District achieved AYP status each year from 2003 to 2010.", "\n\nGraduation rate\nIn 2014, Northern Cambria School District's graduation rate was 80.58%.", "\n2013 - 83.84%\n2012 - 84.9%\n2011 - 82% \n2010 - 84.9%, the Pennsylvania Department of Education issued a new, 4-year cohort graduation rate.", "\n\nAccording to traditional graduation rate calculations\n2009 - 92.9% \n2008 - 86.4% \n2007 - 86.4%\n\nNorthern Cambria High School\nThe high school is located at 813 35th Street, Northern Cambria. ", "In 2014, enrollment was reported as 386 pupils in 9th through 12th grades, with 44% of pupils eligible for a free lunch due to family poverty. ", "Additionally, 11% of pupils received special education services, while none of pupils were identified as gifted. ", "The school employed 35 teachers. ", "Per the PA Department of Education, 5% of the teachers were rated \"Non‐Highly Qualified\" under the federal No Child Left Behind Act. ", "The current high school building is the John F. Kennedy building, which opened in 1963 when the students from the former Barnesboro and Spangler High Schools were first housed at the same location.", "\n\nAccording to the National Center for Education Statistics, in 2012, the school reported an enrollment of 379 pupils in grades 9th through 12th, with 152 pupils eligible for a federal free or reduced-price lunch due to the family meeting the federal poverty level. ", "In 2012, the school employed 26.9 teachers, yielding a student-teacher ratio of 13:1. ", "According to a report by the Pennsylvania Department of Education, 1 teacher was rated \"Non‐Highly Qualified\" under No Child Left Behind. ", "The School is a federally designated Title I school. ", "Dennis Colbert retired as Principal of the school in 2010.", "\n\n2014 School Performance Profile\nNorthern Cambria High School achieved 76.7 out of 100. ", "Reflects on grade level reading, mathematics and science achievement. ", "In reading/literature - 70% were on grade level. ", "In Algebra 1, 66% showed on grade level skills. ", "In Biology, 65% demonstrated on grade level science understanding at the end of the course. ", "Statewide, the percentage of high school students who scored proficient and advanced in Algebra I increased to 39.7% to 40.1%. ", "The percentage of high school students who scored proficient and advanced in reading/literature declined to 52.5%. ", "The percentage of high school students who scored proficient and advanced in biology improved from 39.7% to 41.4%.", "\n\nAccording to the Pennsylvania Department of Education, 2,134 of 2,947 Pennsylvania public schools (72 percent of Pennsylvania public schools), achieved an academic score of 70 or higher. ", "Fifty-three percent of schools statewide received lower SPP scores compared with last year's, while 46 percent improved. ", "A handful were unchanged.", "\n\n2013 School Performance Profile\nNorthern Cambria High School achieved 72.6 out of 100. ", "Reflects on grade level reading, mathematics and science achievement. ", "The actual test performance data was withheld by the PDE. ", "According to the Pennsylvania Department of Education, 2,181 public schools (less than 73 percent of Pennsylvania public schools), achieved an academic score of 70 or higher. ", "Pennsylvania 11th grade students no longer take the PSSAs. ", "Instead, beginning in 2012, they take the Keystone Exams at the end of the associated course.", "\n\nAYP History\nIn 2012, Northern Cambria High School declined to Warning Adequate Yearly Progress (AYP) status, due to missing all metric measured. ", "In 2011, Northern Cambria High School achieved AYP status. ", "Effective with Spring 2013, the Pennsylvania Department of Education discontinued administering the PSSA's to 11th graders. ", "From 2003 to 2010, Northern Cambria High School achieved AYP status each school year.", "\n\nPSSA results\nPennsylvania System of School Assessments, commonly called PSSAs are No Child Left Behind Act related examinations which were administered from 2003 through 2012, in all Pennsylvania public high schools. ", "The exams were administered in the Spring of each school year. ", "The goal was for 100% of students to be on grade level or better in reading and mathematics, by the Spring of 2014. ", "The tests focused on the state's Academic Standards for reading, writing, mathematics and science. ", "The Science exam included content in science, technology, ecology and the environmental studies. ", "The mathematics exam included: algebra I, algebra II, geometry and trigonometry. ", "The standards were first published in 1998 and were mandated by the Pennsylvania State Board of Education. ", "In 2013, the Commonwealth of Pennsylvania changed its high school assessments to the Keystone Exams in Algebra 1, Reading/literature and Biology1. ", "The exams are given at the end of the course, rather than all in the spring of the student's 11th grade year.", "\n\n11th Grade Reading:\n2012 - 66% on grade level, (15% below basic). ", "State - 67% of 11th graders are on grade level.", "\n2011 - 67% (20% below basic). ", "State - 69.1%\n2010 - 74% (13% below basic). ", "State - 66%\n2009 - 72% (14% below basic). ", "State - 65%\n2008 - 60% (21% below basic). ", "State - 65%\n2007 - 63% (13% below basic). ", "State - 65%\n\n11th Grade Math:\n2012 - 54% on grade level (25% below basic). ", "In Pennsylvania, 59% of 11th graders are on grade level.", "\n2011 - 59% (21% below basic). ", "State - 60.3%\n2010 - 61% (24% below basic). ", "State - 59%\n2009 - 62% (24% below basic). ", "State - 56%\n2008 - 39% (36% below basic). ", "State - 56%\n2007 - 52% (28% below basic). ", "State - 53%\n\n11th Grade Science:\n2012 - 28% on grade level (9% below basic). ", "State - 42% of 11th graders were on grade level.", "\n2011 - 34% (15% below basic). ", "State - 40%\n2010 - 47.7% (8% below basic). ", "State - 39% \n2009 - 47% (15% below basic). ", "State - 40%\n2008 - 17% (26% below basic). ", "State - 39%\n2007 - students field tested. ", "Results withheld from the public by PDE.", "\n\nCollege Remediation Rate \nAccording to a Pennsylvania Department of Education study released in January 2009, 8% of the Northern Cambria High School graduates required remediation in mathematics and or reading before they were prepared to take college level courses in the Pennsylvania State System of Higher Education or community colleges. ", "Less than 66% of Pennsylvania high school graduates, who enroll in a four-year college in Pennsylvania, will earn a bachelor's degree within six years. ", "Among Pennsylvania high school graduates pursuing an associate degree, only one in three graduate in three years. ", "Per the Pennsylvania Department of Education, one in three recent high school graduates who attend Pennsylvania's public universities and community colleges takes at least one remedial course in math, reading or English.", "\n\nDual enrollment \nThe Northern Cambria High School offers a dual enrollment program in 2014. ", "This state program permits high school students to take courses, at local higher education institutions, to earn college credits. ", "Students remain enrolled at their high school. ", "The courses count towards high school graduation requirements and towards earning a college degree. ", "The students continue to have full access to activities and programs at their high school. ", "The college credits are offered at a deeply discounted rate. ", "Three colleges are available: Mount Aloysius College, Penn Highlands Community College and Saint Francis University. ", "The state offered a small grant to assist students in costs for tuition, fees and books. ", "Under the Pennsylvania Transfer and Articulation Agreement, many Pennsylvania colleges and universities accept these credits for students who transfer to their institutions. ", "Under state rules, other students that reside in the district, who attend a private school, a charter school or are home schooled are eligible to participate in this program. ", "In 2010, Governor Edward Rendell eliminated the grants to students, from the Commonwealth, due to a state budget crisis.", "\n\nGraduation requirements \nAmong Pennsylvania's 500 public school districts, graduation requirements widely vary. ", "The Northern Cambria School Board has determined that a pupil must earn 22 credits to graduate, including: a required class every year in math 4 credits, English 4 credits social studies 3.5 credits, science 3.5 credits, Physical Education 2 credits, health .5 credits, Computers 2 credits, arts humanities 5.5 credits and electives. ", "Students in the class of 2019 are required to pass a total of 24.5 credits.", "\n\nFor nearly two decades, all Pennsylvania secondary school students were required to complete a project as a part of their eligibility to graduate from high school. ", "The type of project, its rigor and its expectations are set by the individual school district. ", "Effective with the graduating class of 2017, the Pennsylvania State Board of Education eliminated the state mandate that students complete a culminating project in order to graduate.", "\n\nBy Pennsylvania State School Board regulations, beginning with the class of 2017, public school students must demonstrate successful completion of secondary level course work in Algebra I, Biology, and English Literature by passing the respective Keystone Exams for each course. ", "The exam is given at the end of the course. ", "Keystone Exams replace the PSSAs for 11th grade.", "\n\nStudents have several opportunities to pass the exam. ", "Schools are mandated to provide targeted assistance to help the student be successful. ", "Those who do not pass after several attempts can perform a project in order to graduate. ", "For the class of 2019, a Composition exam will be added. ", "For the class of 2020, passing a civics and government exam will be added to the graduation requirements. ", "In 2011, Pennsylvania high school students field tested the Algebra 1, Biology and English Lit exams. ", "The statewide results were: Algebra 1 38% on grade level, Biology 35% on grade level and English Lit - 49% on grade level. ", "Individual student, school or district reports were not made public, although they were reported to district officials by the Pennsylvania Department of Education. ", "Students identified as having special needs and qualifying for an Individual Educational Program (IEP) may graduate by meeting the requirements of their IEP.", "\n\nSAT scores \nIn 2014, 71 Northern Cambria School District students took the SAT exams. ", "The district's Verbal Average Score was 457. ", "The Math average score was 475. ", "The Writing average score was 440. ", "Statewide in Pennsylvania, Verbal Average Score was 497. ", "The Math average score was 504. ", "The Writing average score was 480. ", "The College Board also reported that nationwide scores were: 497 in reading, 513 in math and 487 in writing. ", " In 2014, 1,672,395 students took the SATs in the United States.", "\n\nIn 2013, 53 Northern Cambria School District students took the SAT exams. ", "The district's Verbal Average Score was 430. ", "The Math average score was 470. ", "The Writing average score was 435. ", "The College Board reported that statewide scores were: 494 in reading, 504 in math and 482 in writing. ", "The nationwide SAT results were the same as in 2012.", "\n\nIn 2012, 48 Northern Cambria School District students took the SAT exams. ", "The district's Verbal Average Score was 449. ", "The Math average score was 492. ", "The Writing average score was 459. ", "The statewide Verbal SAT exams results were: Verbal 491, Math 501, Writing 480. ", "In the US, 1.65 million students took the exams achieving scores: Verbal 496, Math 514, Writing 488. ", "According to the College Board the maximum score on each section was 800, and 360 students nationwide scored a perfect 2,400.", "\n\nIn 2011, 67 Northern Cambria School District students took the SAT exams. ", "The district's Verbal Average Score was 461. ", "The Math average score was 467. ", "The Writing average score was 439. ", "Pennsylvania ranked 40th among states with SAT scores: Verbal - 493, Math - 501, Writing - 479. ", "In the United States, 1.65 million students took the exam in 2011. ", "They averaged 497 (out of 800) verbal, 514 math and 489 in writing.", "\n\nThe Center for Rural Pennsylvania, a research arm of the Pennsylvania General Assembly, compared the SAT data of students in rural areas of Pennsylvania to students in urban areas. ", "From 2003 to 2005, the average total SAT score for students in rural Pennsylvania was 992, while urban students averaged 1,006. ", "During the same period, 28 percent of 11th and 12th graders in rural school districts took the exam, compared to 32 percent of urban students in the same grades. ", "The average math and verbal scores were 495 and 497, respectively, for rural students, while urban test-takers averaged 499 and 507, respectively. ", "Pennsylvania's SAT composite score ranked low on the national scale in 2004. ", " The composite SAT score of 1,003 left Pennsylvania ranking 44 out of the 50 states and Washington, DC.", "\n\nAP Courses \nIn 2014, Northern Cambria High School offered 1 Advanced Placement (AP) course at a higher cost than regular courses. ", "The fee for each AP Exam is $91 (2014). ", "The school normally retains $9 of that fee as a rebate to help with administrative costs. ", "In 2012, the fee was $89 per test per pupil. ", "Students have the option of taking College Board approved courses and then taking the College Board's examination in the Spring. ", "Students, who achieve a 3 or better on the exam, may be awarded college credits at US universities and colleges. ", "Each higher education institution sets its own standards about what level of credits are awarded to a student based on their AP exam score. ", "Most higher education give credits for scores of 4 or 5. ", "Some schools also give credits for scores of 3. ", "High schools give credits towards graduation to students who take the school's AP class. ", "At Northern Cambria School District the AP courses are weighted at 1.06 credits. ", "At Northern Cambria High School none of the students who took an AP course earned a 3 or better on the exam.", "\n\nNorthern Cambria Elementary/Middle School\nNorthern Cambria Elementary/Middle School is located at 601 Joseph Street, Northern Cambria. ", "The middle school and elementary school were consolidated in one newly renovated building in 2008. ", "The renovation cost $13.5 million. ", "The building has two gymnasiums as one was added in 2007. ", "It also has a swimming pool and an auditorium. ", "Graduation ceremonies for high school graduates are held at the middle school auditorium. ", "While housed in a single building, academic and demographic data are still reported as unique school.", "\n\nMiddle school\nIn 2014, enrollment in the Northern Cambria Middle School was 324 pupils, in grades 5th through 8th, with 43% of pupils eligible for a free lunch due to family poverty. ", "Additionally, 29.9% of pupils received special education services, while none of pupils were identified as gifted. ", "According to a 2014 report by the Pennsylvania Department of Education, 69% of its teachers were rated \"Highly Qualified\" under No Child Left Behind.", "\n\nAccording to the National Center for Education Statistics, in 2012, Northern Cambria Middle School reported an enrollment of 336 pupils, in grades 6th through 8th, with 151 pupils receiving a federal free or reduced-price lunch due to family poverty. ", "The school employed 17.5 teachers, yielding a student-teacher ratio of 19:1. ", "Prior to 2012, the 5th grade was assigned to the elementary school.", "\n\n2014 School Performance Profile\nNorthern Cambria Middle School achieved 77.2 out of 100. ", "Reflects on grade level reading, mathematics and science achievement. ", "In reading/literature - just 62% of students were on grade level. ", "In Algebra 1/Math, 67% students showed on grade level mathematics skills. ", "In Science, 60% of 8th graders demonstrated on grade level science understanding. ", "In writing, 65% of the 5th and 8th grade students demonstrated on grade level writing skills.", "\n\n2013 School Performance Profile\nNorthern Cambria Middle School achieved 79.2 out of 100. ", "Reflects on grade level reading, writing, mathematics and science achievement. ", "In reading, just 60.6% of the students were on grade level. ", "In Mathematics/Algebra 1, 66% of the students showed on grade level skills. ", "In Science, only 58% of the 8th graders demonstrated on grade level science understanding. ", "In writing, 61% of the 5th and 8th grade students demonstrated on grade level writing skills.", "\n\nAYP History\nIn 2011 and 2012, Northern Cambria Middle School achieved AYP status.", "\n2010 - achieved AYP status\n2009 - Making Progress School Improvement Level I AYP status due to lagging student achievement\n2008 - declined to School Improvement Level I AYP due to chronic low student achievement Under the federal No Child Left Behind Act, the school administration was required to notify parents of the school's poor achievement outcomes. ", "Additionally the middle school administration was required by the Pennsylvania Department of Education, to develop a School Improvement Plan to address the school's low student achievement. ", "Under the Pennsylvania Accountability System, the school district must pay for additional tutoring for struggling students.", "\n2007 - declined to Warning AYP status due to lagging student achievement\n2003 - 2006 - achieved AYP status\n\nPSSA Results\nPSSA's are subject specific examinations given in the Spring of each school year. ", "Fifth graders are tested in: reading, writing and mathematics since 1995. ", "Sixth and seventh grades have been tested in reading and mathematics since 2006. ", "Eighth graders are tested in: reading, writing, mathematics and Science. ", "Beginning in the Spring of 2013, eighth graders, who are enrolled in Algebra I take the Keystone Exam for Algebra I at the end of the course. ", "The testing of 8th grade in reading and mathematics began in 1995, as a state initiative. ", "Testing in science began in 2007. ", "The goal is for 100% of students to be on grade level or better in reading and mathematics, by the Spring of 2014. ", "The tests focus on the state's Academic Standards for reading, writing, mathematics and science. ", "The standards were published in 1998 and are mandated by the Pennsylvania State Board of Education. ", "In 2014, the Commonwealth of Pennsylvania adopted the Pennsylvania Core Standards - Mathematics.", "\n\n8th Grade Reading:\n2012 - 75% on grade level (8% below basic). ", "In Pennsylvania, 79% of 8th graders on grade level.", "\n2011 - 80% (10% below basic) State - 81.8%\n2010 - 80% (6% below basic). ", "State - 81% \n2009 - 79% (12% below basic), State - 80% \n2008 - 70% (9% below basic), State - 78% \n2007 - 71% (11% below basic), State - 75%\n\n8th Grade Math:\n2012 - 84% on grade level (8% below basic). ", "State - 76%\n2011 - 83% (6% below basic). ", "State - 76.9% \n2010 - 82% (2% below basic). ", "State - 75%\n2009 - 74% (11% below basic). ", "State - 71%\n2008 - 69% (15% below basic). ", "State - 70%\n2007 - 71% (19% below basic). ", "State - 68%\n\n8th Grade Science:\n2012 - 59% on grade level (22% below basic). ", "State - 59%\n2011 - 68% (16% below basic). ", "State - 58.3%\n2010 - 68% (13% below basic). ", "State - 57%\n2009 - 68% (16% below basic). ", "State - 55%\n2008 - 50%, (29% below basic). ", "State - 52%\n2007 - tested, but results not made public.", "\n\n7th Grade Reading:\n2012 - 65% (10% below basic). ", "State - 76%\n2011 - 70% (9% below basic). ", "State - 76%\n2010 - 72% (11% below basic). ", "State - 73%\n2009 - 65% (9% below basic). ", "State - 71%\n2008 - 67% (13% below basic). ", "State - 70%\n2007 - 68% (18% below basic). ", "State - 67%\n\n7th Grade Math:\n2012 - 75% (11% below basic). ", "State - 80%\n2011 - 80% (10% below basic). ", "State - 78.6%\n2010 - 75% (10% below basic). ", "State - 77% \n2009 - 83% (6% below basic), State - 75% \n2008 - 78% (9% below basic), State - 71%\n2007 - 82% (10% below basic), State - 67%\n\n6th Grade Reading:\n2012 - 51% (22% below basic). ", "State - 68%\n2011 - 60% (14% below basic). ", "State - 69.9% \n2010 - 65% (17% below basic). ", "State - 68% \n2009 - 61% (16% below basic), State - 67% \n2008 - 66% (19% below basic), State - 67% \n2007 - 68% (15% below basic), State - 63% \n\n6th Grade Math:\n2012 - 80% (5% below basic). ", "State - 77%\n2011 - 78% (5% below basic). ", "State - 78.8%\n2010 - 71% (12% below basic). ", "State - 78% \n2009 - 73% (13% below basic), State - 75% \n2008 - 74% (18% below basic), State - 72% \n2007 - 76% (4% below basic), State - 69% \n\n5th Grade Reading\n2012 - 68% (9% below basic). ", "State - 65%\n2011 - 73% (9% below basic). ", "State - 67.3%\n2010 - 60% (14% below basic). ", "State - 64%\n2009 - 71% (14% below basic). ", "State - 64%\n2008 - % (% below basic). ", "State - 62%\n2007 - 68% (15% below basic). ", "State - 60%\n\n5th Grade Math\n2012 - 64% (12% below basic). ", "State - 73%\n2011 - 90% (1% below basic). ", "State - 74%\n2010 - 75% (3% below basic). ", "State - 76.3%\n2009 - 83% (2% below basic). ", "State - 73%\n2008 - % (% below basic). ", "State - 73%\n2007 - 73% (12% below basic). ", "State - 71%\n\nDropout Early Warning System\nIn 2013, Northern Cambria School District did not implement dropout prevention Early Warning System and Interventions Catalog at the middle school. ", "The process identifies students at risk for droping out by examining the pupil's: attendance, behavior and course grades. ", "Interventions are implemented to assist at-risk pupils to remain in school. ", "The program is funded by federal and private dollars.", "\n\nElementary school\nNorthern Cambria Elementary School reported an enrollment of 445 pupils in grades preschool through 4th, with 48% of pupils receiving a federal free or reduced-price meals due to family poverty in 2014. ", "Additionally, none of the pupils receive special education services, while less than 1% are identified as gifted. ", "According to a report by the Pennsylvania Department of Education, 31% of the teachers were rated highly qualified under No Child Left Behind. ", "The school provides full-day kindergarten and half-day preschool. ", "The school is a federally designated Title I school.", "\n\nAccording to the National Center for Education Statistics, in 2012 Northern Cambria Elementary School enrollment was 474 pupils in grades kindergarten through 4th, with 224 pupils receiving a free or reduced-price lunch. ", "The school employed 39 teachers, yielding a student-teacher ratio of 13:1. ", "The school provided full-day kindergarten to all its pupils since 2004.", "\n\n2014 School Performance Profile\nNorthern Cambria Elementary School SPP score declined to 69.6 out of 100. ", "The score reflects on grade level: reading, science, writing and mathematics achievement. ", "In 2013-14, only 70% of the students were reading on grade level in grades 3rd and 4th. ", "In 3rd grade, 69% of the pupils were reading on grade level. ", "In math, 72% were on grade level (3rd-4th grades). ", "In 4th grade science, 82% of the pupils demonstrated on grade level understanding.", "\n\n2013 School Performance Profile\nNorthern Cambria Elementary School achieved a score of 78.7 out of 100. ", "The score reflects on grade level: reading, science, writing and mathematics achievement. ", "In 2012-13, only 74% of the students were reading on grade level in grades 3rd and 4th. ", "In 3rd grade, 78% of the pupils were reading on grade level. ", "In math, 77% were on grade level (3rd-4th grades). ", "In 4th grade science, 88% of the pupils demonstrated on grade level understanding.", "\n\nAYP status history\nIn 2012, Northern Cambria Elementary School declined to Warning AYP status due to low student achievement in reading. ", "In 2011, Northern Cambria Elementary School achieved AYP status. ", "From 2004-2010, Northern Cambria Elementary School achieved AYP status each school year.", "\n\nPSSA History\nEach year, in the Spring, the 3rd graders take the PSSAs in math and reading. ", "The fourth grade is tested in reading, math and science. ", "PSSAs examinations have been administered beginning 2003 to all Pennsylvania public school students in grades 3rd-8th. ", "The goal was for 100% of students to be on grade level or better in reading and mathematics, by the Spring of 2014. ", "The tests focused on the state's Academic Standards for reading, writing, mathematics and science. ", "The Science exam is given to 4th grades and includes content in science, technology, ecology and the environmental studies.", "\n\n4th Grade Reading\n2012 - 51% (22% below basic). ", "State - 72%\n2011 - 54% (6% below basic). ", "State - 73%\n2010 - 74% (8% below basic). ", "State - 73%\n2009 - 76% (7% below basic). ", "State - 72%\n2008 - 73% (8% below basic). ", "State - 70%\n2007 - 74% (8% below basic). ", "State - 60%\n\n4th Grade Math\n2012 - 66% (21% below basic). ", "State - 82%\n2011 - 91% (3% below basic). ", "State - 85%\n2010 - 84% (5% below basic). ", "State - 84%\n2009 - 71% (7% below basic). ", "State - 81%\n2008 - 80% (11% below basic). ", "State - 80%\n2007 - 92% (4% below basic). ", "State - 78%\n\n4th Grade Science\n2012 - 77%, (4% below basic). ", "State - 82%\n2011 - 92%, (0% below basic). ", "State - 82.9%\n2010 - 91%, (0% below basic). ", "State - 81%\n2009 - 90%, (2% below basic). ", "State - 83%\n2008 - 77%, (3% below basic). ", " State - 81%\n\n3rd Grade Reading\n2012 - 77%, (9% below basic). ", "State - 74% \n2011 - 84%, (11% below basic). ", "State - 77%\n2010 - 64%, (25% below basic). ", "State - 75%\n2009 - 84%, (6% below basic). ", "State - 77%\n2008 - 82%, (7% below basic). ", "State - 70%\n2007 - 79%, (7% below basic). ", "State - 72%\n\n3rd Grade Math\n2012 - 73%, (3% below basic). ", "State - 80%\n2011 - 91%, (0% below basic). ", "State - 83%\n2010 - 84%, (0% below basic). ", "State - 84%\n2009 - 92%, (0% below basic). ", "State - 81%\n2008 - 81%, (0% below basic). ", "State - 80%\n2007 - 90%, (1% below basic). ", "State - 78%\n\nEnrollment\nAccording to Pennsylvania Department of Education enrollment reports, there are 1,155 students enrolled in preschool-12th in the 2014-15 school year at Northern Cambria School District. ", "In 2007 there were 1,273 pupils. ", "There were 88 students in the Class of 2009. ", "The district's class of 2010 had 97 students. ", "Enrollment at Northern Cambria School District is projected to decline to 1,144 students by 2020. ", "In 2008, the district administrative costs were $631.64 per pupil. ", "The lowest administrative cost per pupil in Pennsylvania was $398 per pupil. ", "A study of Pennsylvania public school spending, conducted by Standard and Poor's, examined the consolidation of small public school districts in Pennsylvania in 2007. ", "The study found that consolidation of the administration of Northern Cambria School District with an adjacent school district, would achieve substantial administrative cost savings which varied by district. ", "The study examined consolidation of administrations with five neighboring school districts. ", "Consolidation with Blacklick Valley School District was predicted to save $2 million in 2007. ", "Consolidation with Cambria Heights School District would save taxpayers over $4 million in redundant administration costs. ", "Similarly, consolidation with Harmony Area School District would save taxpayers over $2 million. ", "consolidation with Penns Manor Area School District would save taxpayers over $2.6 million. ", "Finally, consolidation of administrations with Purchase Line School District projected taxpayer savings of over $4 million.", "\n\nAccording to a 2009 school district administration consolidation proposal by Governor Edward Rendell, the excessive administrative overhead dollars could be redirected to improve lagging academic achievement, to enrich the academic programs or to reduce property taxes. ", "Consolidation of two central administrations into one would not require the closing of any school buildings. ", "The Governor's proposal called for the savings to be redirected to improving lagging reading and science achievement, to enriching the academic programs or to reducing residents' property taxes. ", "In March 2011, the Pennsylvania Institute of Certified Public Accountants Fiscal Responsibility Task Force released a report which found that consolidating school district administrations with one neighboring district would save the Commonwealth $1.2 billion without forcing the consolidation of any school buildings.", "\n\nFrom 2000 through 2010, rural Pennsylvania public school district enrollment decreased by 8 percent. ", "In 2010, there were 726,417 children in rural Pennsylvania, or 21 percent of the total rural population. ", "From 2000 to 2010, the number of children in rural counties decreased 7 percent. ", "The decline in the number of children impacted most rural counties with 42 of Pennsylvania's 48 rural counties experiencing a decline. ", "Cameron County, Elk County and Sullivan County experienced the greatest declines, with a decrease of more than 21 percent in all three counties. ", "Cambria County's live birth rate was 1,897 births in 1990. ", "Cambria County's live birth rate in 2000 was 1,569 births, while in 2011 the birth rate had continued to decline to 1,374 babies. ", "Over the past 50 years (1960 to 2010), rural Pennsylvania saw a steady decline in both the number and proportion of residents under 18 years old. ", "In 1960, 1.06 million rural residents, or 35 percent of the rural population, were children.", "\n\nPennsylvania's birth rate has been declining for two decades. ", "According to data from the Pennsylvania Department of Health, in 1990, the Commonwealth of Pennsylvania's birth rate was 171,053. ", "In 2000, Pennsylvania's birth rate was 145,874. ", "Finally in 2011, the State's birth rate declined further to 142,021. ", "From 2000 to 2009, the number of babies born in rural counties declined 5 percent. ", "Urban counties have also experienced a decline in the number of school aged children. ", "From 2000-2010 urban Pennsylvania counties had a 3 percent decline in the number of residents under 18 years old. ", "In 2010, there were 2.07 million residents, or 22 percent of the urban population, who were under age 18.", "\n\nPennsylvania had 2,361 public school districts in 1959. ", "The state compelled mergers reducing the number to 505 by 1980. ", "Mergers slowed through the 1980s after a 1981 court order desegregated and combined the Edgewood, General Braddock, Swissvale, Churchill and Turtle Creek districts into the Woodland Hills district. ", "The Commonwealth of Pennsylvania has one of the highest numbers of school districts in the nation. ", "In Pennsylvania, 80% of the school districts serve student populations under 5,000, and 40% serve less than 2,000. ", "This results in excessive school administration bureaucracy and not enough course diversity. ", "In a survey of 88 superintendents of small districts, 42% of the respondents stated that they thought consolidation would save money without closing any school buildings.", "\n\nSpecial education\nIn December 2013, the district administration reported that 159 pupils, or 13.9% of the district's pupils, received special education services, with 47.8% of the identified students having a specific learning disability. ", "In December 2009, the District administration reported that 182 pupils, or 14.7% of the district's pupils, received special education services, with 57% of the identified students having a specific learning disability. ", "Special education services in the Commonwealth are provided to students from ages three years to 21 years old. ", "In the 2010-2011 school year, the total student enrollment was more than 1.78 million students with approximately 275,000 students eligible for special education services. ", "Among these students 18,959 were identified with mental retardation and 21,245 students with autism. ", "The largest group of students are identified as Specific Learning Disabilities 126,026 students (46.9 percent) and Speech or Language Impairments with 43,542 students (16.2 percent).", "\n\nIn 2007, Pennsylvania Secretary of Education Gerald Zahorchak testified before the Pennsylvania House Education Committee regarding full-day kindergarten. ", "He claimed that districts which offered the program would see a significant decrease in special education students due to early identification and early intervention. ", "He asserted the high cost of full-day kindergarten would be recouped by districts in lower special education costs. ", "While Northern Cambria School District has seen decrease in the percentage of special education students it serves, it has yielded no savings.", "\n\nIn order to comply with state and federal Individuals with Disabilities Education Act rules and regulations, the school district engages in identification procedures to ensure that eligible students receive an appropriate educational program consisting of special education and related services, individualized to meet student needs. ", " At no cost to the parents, these services are provided in compliance with state and federal law; and are reasonably calculated to yield meaningful educational benefit and student progress. ", "To identify students who may be eligible for special education services, various screening activities are conducted on an ongoing basis. ", "These screening activities include: review of group-based data (cumulative records, enrollment records, health records, report cards, ability and achievement test scores); hearing, vision, motor, and speech/language screening; and review by the Special Education administration. ", " When screening results suggest that the student may be eligible, the district seeks parental consent to conduct a multidisciplinary evaluation. ", "Parents who suspect their child is eligible may verbally request a multidisciplinary evaluation from a professional employee of the district or contact the district's Special Education Department. ", "The IDEA 2004 requires each school entity to publish a notice to parents, in newspapers or other media, including the student handbook and website regarding the availability of screening and intervention services and how to access them.", "\n\nStudents who have an Individual Education Plan (IEP) may take the PSSA-M an alternative math exam rather than the PSSA. ", "Some special education students may take the PASA (Pennsylvania Alternate System of Assessment), rather than the PSSA. ", "Schools are permitted to provide accommodations to some students.", "\n\nIn 2010, the state of Pennsylvania provided $1,026,815,000 for special education services. ", "This funding was in addition to the state's basic education per pupil funding, as well as, all other state and federal funding. ", " The Special Education funding structure is through the federal Individuals with Disabilities Education Act (IDEA) funds and state appropriations. ", "IDEA funds are appropriated to the state on an annual basis and distributed through intermediate units (IUs) to school districts, while state funds are distributed directly to the districts. ", "Total funds that are received by school districts are calculated through a formula. ", "The Pennsylvania Department of Education oversees four appropriations used to fund students with special needs: Special Education; Approved Private Schools; Pennsylvania Chartered Schools for the Deaf and Blind; and Early Intervention. ", "The Pennsylvania Special Education funding system assumes that 16% of the district's students receive special education services. ", "It also assumes that each student's needs accrue the same level of costs. ", "Over identification of students, in order to increase state funding, has been an issue in the Commonwealth. ", "Some districts have more than 20% of its students receiving special education services while others have 10% supported through special education. ", "The state requires each public school district and charter school to have a three-year special education plan to meet the unique needs of its special education students. ", "In 2012, the Obama Administration's US Department of Education issued a directive requiring schools include students with disabilities in extracurricular activities, including sports.", "\n\nNorthern Cambria School District received a $747,682 supplement for special education services in 2010. ", "For the 2011–12, 2012–13 and 2013-14 school years, all Pennsylvania public school districts received the same level of funding for special education that they received in 2010-11. ", "This level funding is provided regardless of changes in the number of pupils who need special education services and regardless of the level of services the respective students required. ", "For the 2014-2015 school year, Northern Cambria School District received an increase to $760,311 from the Commonwealth for special education funding. ", "Additionally, the state provides supplemental funding for extraordinarily impacted students. ", "The district must apply for this added funding.", "\n\nGifted education\nNorthern Cambria School District Administration reported that 27 or 2.21% of its students were gifted in 2009. ", "The highest percentage of gifted students reported among all 500 school districts and 100 public charter schools in Pennsylvania was North Allegheny School District with 15.5% of its students identified as gifted. ", "By law, the district must provide mentally gifted programs at all grade levels. ", "The referral process for a gifted evaluation can be initiated by teachers or parents by contacting the student's building principal and requesting an evaluation. ", "All requests must be made in writing. ", "To be eligible for mentally gifted programs in Pennsylvania, a student must have a cognitive ability of at least 130 as measured on a standardized ability test by a certified school psychologist. ", "Other factors that indicate giftedness are also considered for eligibility.", "\n\nBudget\nPennsylvania public school districts budget and expend funds according to procedures mandated by the General Assembly and the Pennsylvania Department of Education (PDE). ", "An annual operating budget is prepared by school district administrative officials. ", "A uniform form is furnished by the PDE and submitted to the board of school directors for approval prior to the beginning of each fiscal year on July 1.", "\n\nUnder Pennsylvania's Taxpayer Relief Act, Act 1 of the Special Session of 2006, all school districts of the first class A, second class, third class and fourth class must adopt a preliminary budget proposal. ", "The proposal must include estimated revenues and expenditures and the proposed tax rates. ", "This proposed budget must be considered by the board no later than 90 days prior to the date of the election immediately preceding the fiscal year. ", "The preliminary budget proposal must also be printed and made available for public inspection at least 20 days prior to its adoption. ", "The board of school directors may hold a public hearing on the budget, but are not required to do so. ", "The board must give at least 10 days’ public notice of its intent to adopt the final budget according to Act 1 of 2006.", "\n\nThe latest teacher union contract governs years 2014-2018 inclusive. ", "The taxpayers pay 100% of the cost of the employee's health insurance. ", "There is limited spousal coverage. ", "In 2013, the average teacher salary in Northern Cambria School District was $55,643.08 a year. ", "The District employed 114 teachers with a top salary of $102,500. ", "Northern Cambria School District teacher and administrator retirement benefits are equal to at least 2.00% x Final Average Salary x Total Credited Service. (", "Some teachers benefits utilize a 2.50% benefit factor.) ", "After 40 years of service, a teacher can retire with 100% of the average salary of their final 3 years of employment. ", "According to a study conducted at the American Enterprise Institute, in 2011, public school teachers’ total compensation is roughly 50 percent higher than they would likely receive in the private sector. ", "The study found that the most generous benefits that teachers receive are not accounted for in many studies of compensation including: pension, retiree health benefits and job security.", "\n\nIn 2009, Northern Cambria School District reported employing 96 teachers and administrators with a median salary of $60,537 and a top salary of $122,120. ", "The teacher's work day is 7.5 hours with 184 days in the contract year. ", "Additionally, the teachers receive a defined benefit pension, health insurance, professional development reimbursement, 2 paid personal days, 10 paid sick days, paid bereavement leave, paid sabbatical leave (50% of salary and benefits for one year) and other benefits. ", "As of 2007, Pennsylvania ranked in the top 10 states in average teacher salaries. ", "When adjusted for cost of living Pennsylvania ranked fourth in the nation for teacher compensation.", "\n\nAdministrative spending Northern Cambria School District administrative costs per pupil in 2008 was $631.64 per pupil. ", " The lowest administrative cost per pupil in Pennsylvania was $398 per pupil. ", "The Pennsylvania School Boards Association collects and maintains statistics on salaries of public school district employees in Pennsylvania. ", "According to the association's report, superintendents and administrators receive a benefit package commensurate with that offered to the district's teachers' union. ", "In 2013, High School principal, Joy Tibbott was moved to the administrative offices as Director of Education as part of lawsuit settlement. ", "She was to hold the position through 2014-15 school year.", "\n\nPer-pupil spending In 2008, Northern Cambria School District administration reported that per-pupil spending was $11,562 which ranked 333rd among Pennsylvania's then 501 public school districts. ", "In 2010, the district's per-pupil spending had increased to $13,064.59. ", "In 2013, the per-pupil spending was reported as $13,030.59. ", "In 2011, Pennsylvania's per-pupil spending was $13,467, ranking 6th in the United States. ", "In 2007, the Pennsylvania per pupil total expenditures was reported as $12,759.", "\n\nThe U.S. Census Bureau reported that Pennsylvania spent $8,191 per pupil in school year 2000-01. ", "In 2007, the Pennsylvania per pupil total expenditures was reported as $12,759. ", "Among the fifty states, Pennsylvania's total per pupil revenue (including all sources) ranked 11th at $15,023 per student, in 2008-09. ", "Pennsylvania's total revenue per pupil rose to $16,186 ranking 9th in the nation in 2011.", "\n\nReserves In 2008, Northern Cambria School District reported a balance of $1,463,867, in its unreserved-undesignated fund. ", "The unreserved-designated fund balance was reported as zero. ", "In 2010, Northern Cambria School District Administration reported an increase to $1,879,629 in the unreserved-undesignated fund balance. ", "The district also reported zero in its unreserved-designated fund in 2010. ", "Pennsylvania public school district reserve funds are divided into two categories – designated and undesignated. ", "The undesignated funds are not committed to any planned project. ", "Designated funds and any other funds, such as capital reserves, are allocated to specific projects. ", "School districts are required by state law to keep 5 percent of their annual spending in the undesignated reserve funds to preserve bond ratings. ", "According to the Pennsylvania Department of Education, from 2003 to 2010, as a whole, Pennsylvania school districts amassed nearly $3 billion in reserved funds. ", "In 2005, the total reserve funds held by Pennsylvania public school districts was $1.9 billion. ", "By 2013, reserves held by Pennsylvania public school districts, as a whole, had increased to over $3.8 billion. ", "By 2013, Northern Cambria School District reported having $1,429,556 in reserves.", "\n\nTax exemptions In 2002, Northern Cambria School Board gave several tax exemptions to NORCAM Group for the former Miners Hospital Complex in the Borough of Northern Cambria. ", "In 2009 Northern Cambria Community Development Corp. owed $136,533on the former Miners Hospital property. ", "The land was listed on the Cambria County delinquent property tax sale list.", "\n\nState Audits In January 2014, the Pennsylvania Auditor General conducted a performance audit of the district. ", "The findings were reported to the school board and the district's administration. ", "The findings found significant issues with conflict of interest ethics violations by a school board member. ", "In August 2010, Auditor General Wagner found the District had corrected issues regarding failing to bill nonresident students for tuition.", "\n\nTuition Students who live within the Northern Cambria School District's attendance area may choose to attend one of Pennsylvania's 157 public charter schools. ", "A student living in a neighboring public school district or a foreign exchange student may seek admission to Northern Cambria School District. ", "For these cases, the Pennsylvania Department of Education sets an annual tuition rate for each school district. ", "It is the amount the public school district pays to a charter school for each resident student that attends the charter and it is the amount a nonresident student's parents must pay to attend the Northern Cambria School District schools. ", "The 2013 tuition rates are Elementary School - $9,060, High School - $9,992.", "\n\nNorthern Cambria School District is funded by a combination of: a Local Services Tax - $5, a local earned income tax 0.5%, per capita taxes, Public Utility Taxes, a property tax, a real estate transfer tax 0.5%, coupled with substantial funding from the Commonwealth of Pennsylvania and a small amount, generally 10% of its budget from the federal government. ", "Grants can provide an opportunity to supplement school funding without raising local taxes. ", "Interest earnings on accounts also provide nontax income to the district. ", "In the Commonwealth of Pennsylvania, pension income and Social Security income are exempted from state personal income tax and local earned income tax, regardless of the level of the individual's personal wealth. ", "The average Pennsylvania public school teacher pension in 2011 exceeds $60,000 a year plus they receive federal Social Security benefits: both are free of Pennsylvania state income tax and local income tax which funds local public schools.", "\n\nState basic education funding\nAccording to a report from Representative Todd Stephens office, Northern Cambria School District receives 75.6% of its annual revenue from the state. ", "This exceeds the goal of the state providing 50% of district funding.", "\n\nFor the 2014-15 school year, Northern Cambria School District received $8,469,189 in State Basic Education funding. ", "The district received another $96,043 in new Ready To Learn Block grant. ", "The State's enacted Education Budget includes $5,526,129,000 for the 2014-2015 Basic Education Funding. ", "The Education budget also includes Accountability Block Grant funding at $100 million and $241 million in new Ready to Learn funding for public schools that focus on student achievement and academic success. ", "The State is paying $500.8 million to Social Security on the school employees behalf and another $1.16 billion to the state teachers pension system (PSERS). ", "In total, Pennsylvania's Education budget for K-12 public schools is $10 billion. ", "This was a $305 million increase over 2013-2014 state spending and the greatest amount ever allotted by the Commonwealth for its public schools.", "\n\nIn the 2013-2014 school year, Northern Cambria School District received a 1.2% increase or $8,469,774 in Pennsylvania Basic Education Funding. ", "This is $99,162 more than its 2012-13 state BEF to the district. ", "Additionally, Northern Cambria School District received $93,819 in Accountability Block Grant funding to focus on academic achievement and level funding for special education services. ", "Among the public school districts in Cambria County, Westmont Hilltop School District received the highest percentage increase in BEF at 2.5%. ", "The district had the option of applying for several additional state and federal grants to increase its revenues. ", "The Commonwealth's budget increased Basic Education Funding statewide by $123 million to over $5.5 billion. ", "Most of Pennsylvania's 500 public school districts received an increase of Basic Education Funding in a range of 0.9% to 4%. ", "Eight public school districts received exceptionally high funding increases of 10% to 16%. ", "The highest increase in state funding was awarded to Austin Area School District which received a 22.5% increase in Basic Education Funding. ", "The highest percent of state spending per student is in the Chester-Upland district, where roughly 78 percent comes from state coffers. ", "In Philadelphia, it is nearly 49 percent. ", "As a part of the education budget, the state provided the PSERS (Pennsylvania school employee pension fund) with $1,017,000,000 and Social Security payments for school employees of $495 million.", "\n\nFor the 2012-13 school year, Northern Cambria School District received $8,370,612 in Basic Education funding. ", "The Governor's Executive Budget for 2012-2013 included $9.34 billion for kindergarten through 12th grade public education, including $5.4 billion in basic education funding, which was an increase of $49 million over the 2011-12 budget. ", "In addition, the Commonwealth provided $100 million for the Accountability Block Grant (ABG) program. ", "Northern Cambria School District received $93,819 in ABG funds. ", "The state also provided a $544.4 million payment for School Employees’ Social Security and $856 million for School Employees’ Retirement fund called PSERS. ", "This amount was a $21,823,000 increase (0.34%) over the 2011-2012 appropriations for Basic Education Funding, School Employees' Social Security, Pupil Transportation, Nonpublic and Charter School Pupil Transportation. ", "Since taking office, Corbett's first two budgets have restored more than $918 million in support of public schools, compensating for the $1 billion in federal stimulus dollars lost at the end of the 2010-11 school year.", "\n\nIn 2011-12 school year, Northern Cambria School District received a $8,370,612 allocation, of state Basic Education Funding. ", "Additionally, Northern Cambria School District received $93,819 in Accountability Block Grant funding. ", "The enacted Pennsylvania state Education budget included $5,354,629,000 for the 2011-2012 Basic Education Funding appropriation. ", "This amount was a $233,290,000 increase (4.6%) over the enacted State appropriation for 2010-2011. ", "The highest increase in state basic education funding was awarded to Duquesne City School District of Allegheny County, which got a 49% increase in state funding for 2011-12. ", "In 2010, the district reported that 555 students received free or reduced-price lunches, due to the family meeting the federal poverty level. ", "Some Pennsylvania public school districts experienced a reduction of total funding due to the termination of federal stimulus funding which ended in 2011.", "\n\nIn the 2010-11 budget year, the Commonwealth of Pennsylvania provided Northern Cambria School District a 2% increase in Basic Education Funding for a total of $8,833,901. ", "Among the districts in Cambria County, the highest increase went to Westmont Hilltop School District which got a 10.14% increase. ", "One hundred fifty Pennsylvania school districts received the base 2% increase. ", "The highest increase in 2010-11 went to Kennett Consolidated School District in Chester County, which received a 23.65% increase in state funding. ", "Fifteen (15) Pennsylvania public school districts received a BEF increase of greater than 10%. ", "The state's hold harmless policy regarding state basic education funding continued where each district received at least the same amount as it received the prior school year, even when enrollment had significantly declined. ", "The amount of increase each school district received was set by Governor Edward Rendell and then Secretary of Education Gerald Zahorchak, as a part of the state budget proposal given each February. ", "This was the second year of Governor Rendell's policy to fund some public school districts at a far greater rate than others.", "\n\nIn the 2009-10 budget year, the Commonwealth of Pennsylvania provided a 3.47% increase in Basic Education Funding for a total of $8,660,687. ", "Among the districts in Cambria County, the highest increase went to Westmont Hilltop School District which got an 8.22%. ", "Ninety (90) Pennsylvania public school districts received the base 2% increase. ", "Muhlenberg School District in Berks County received a 22.31% increase in state basic education funding in 2009. ", "The amount of increase each school district received was set by Governor Edward G. Rendell and the Secretary of Education Gerald Zahorchak, as a part of the state budget proposal.", "\n\nThe state Basic Education Funding to the district in 2008-09 was $7,634,543. ", "According to the Pennsylvania Department of Education, 549 district students received free or reduced- price lunches due to low family income in the 2007–2008 school year. ", "According to the U.S. Census Bureau, Pennsylvania spent $7,824 Per Pupil in the year 2000. ", "This amount increased up to $12,085 by the year 2008.", "\n\nAll Pennsylvania school districts also receive additional funding from the state through several funding allocations, including: Reimbursement of Charter School Expenditures; Special Education Funding; Secondary Career & Technical Education Subsidy; PA Accountability Grants; and low achieving schools were eligible for Educational Assistance Program Funding. ", "Plus all Pennsylvania school districts receive federal dollars for various programs including: Special Education funding and Title I funding for children from low income families. ", "In 2010, Pennsylvania spent over $24 billion for public education - local, state and federal dollars combined. ", "By 2015, Pennsylvania is spending over $27 billion on public education (local, state and federal resources combined).", "\n\nAccountability Block Grants\nBeginning in 2004-2005, the state launched the Accountability Block Grant school funding. ", "This program has provided $1.5 billion to Pennsylvania's school districts. ", "The Accountability Block Grant program requires that its taxpayer dollars are focused on specific interventions that are most likely to increase student academic achievement. ", "These interventions include: teacher skills training; All Day Kindergarten; lower class size in Kindergarten through 3rd grade; literacy and math coaching programs (provides teachers with individualized job-embedded professional development to improve their instruction); before or after school tutoring assistance to struggling students. ", "For 2010-11, the district applied for and received $254,649 in addition to all other state and federal funding. ", "The district used the funding to provide full-day kindergarten to 37 children. ", "In 2009, 100% of the kindergarteners in Northern Cambria School District attended full-day kindergarten.", "\n\nReady to Learn grant\nBeginning in the 2014-2015 budget, the State funded a new Ready to Learn Grant for public schools. ", "A total of $100 million is allocated through a formula to districts based on the number of students, level of poverty of community as calculated by its market value/personal income aid ratio (MV/PI AR) and the number of English language learners. ", "Ready to Learn Block Grant funds may be used by the districts for: school safety; Ready by 3 early childhood intervention programs; individualized learning programs; and science, technology, engineering and math (STEM) programs.", "\n\nNorthern Cambria School District received $96,043 in Ready to Learn Grant dollars in addition to State Basic Education funding, Special Education funding, PreK Counts funding, reimbursement for Social Security payments for employees and other state grants which the district must apply to receive.", "\n\nPreK Counts grant\nNorthern Cambria School District receives state funding to provide taxpayer-funded preschool at the elementary schools. ", "For the 2013-14 school year, the district received a Pre K Counts grant of $117,000. ", "For the 2011 school year, Northern Cambria School District was a high priority for funding due to the 48% poverty level of children in the district's attendance area. ", "Enrollment for Pennsylvania Pre-K Counts is targeted to children living in families earning up to 300 percent of the federal poverty level.", "\n\nIn 2013, the state's PreK Counts program received $87,284,000. ", "In 2010, the PreK Counts program received $83.6 million statewide in Governor Corbett's education budget. ", "In 2007-08, the state funded Pre-K Counts at $75 million. ", "Northern Cambria School District did not receive funding in 2007-08. ", "In 2009-10, the district received $118,500 to provide preschool to 30 children. ", "The District received $98,750 enrolling 25 students for 2011-12\n\nIn addition to PreK Counts, the Commonwealth of Pennsylvania also supplements the federal Head Start preschool program with an additional funding on an annual basis. ", "The program is available to low income children residing within the district through private providers. ", "In 2013, Pennsylvania contributed $39,178,000 to Head Start. ", "In 2010, Head Start received $37.6 million in Pennsylvania state education dollars. ", "Since 2003, Pennsylvania has more than doubled the number of preschoolers in publicly funded pre-kindergarten through a multipronged system including: school-based pre-kindergarten, Pennsylvania Pre-K Counts through private providers, Early Intervention, Head Start and Head Start Supplemental, and the school district's use of Accountability Block Grants. ", "Over 100,000 Pennsylvania preschoolers participate in state taxpayer funded pre-kindergarten programs. ", "In 2013, the federal government spent $8 billion for preschool programs nationwide. ", "In 2013, Pennsylvania was awarded a $51.7 million federal grant to fund early learning programs. ", "The funding will be used to create 50 Early Childhood Education Community Innovation Zones in areas where the lowest-performing public schools, including charter schools, exist. ", "The federal dollars were not be used to provide seats for children in preschools. ", "Instead the money was used to build state bureaucracy and added training for teachers/providers.", "\n\nClassrooms for the Future grant\nThe Classroom for the Future state program provided districts with hundreds of thousands of extra state funding to buy laptop computers for each core curriculum high school class (English, Science, History, Math) and paid for teacher training to optimize the computers use. ", "The program was funded from 2006 to 2009. ", "The School District applied to participate in 2006-07, but was denied funding by PA Education Secretary Gerald Zahorchak. ", "In 2007-08 and in 2008-09 did not apply for funding in spite of repeated requests from the board to do so. ", "Among the public school districts in Cambria County, the highest award was given to Greater Johnstown School District which received $463,166. ", "The highest funding statewide was awarded to Philadelphia City School District in Philadelphia County - $9,409,073. ", "The grant program was discontinued by Governor Edward Rendell as part of the 2009-10 state budget.", "\n\nScience It’s Elementary grant\nNorthern Cambria Elementary School successfully applied to participate and received a Science It's Elementary grant in 2008-09. ", "For the 2008-09 school year, the program was offered in 143 schools reaching 66,973 students across the Commonwealth of Pennsylvania. ", "In 2007, the Pennsylvania Department of Education initiated an effort to improve science instruction in the Commonwealth's public elementary schools. ", "Called Science: It's Elementary, the program was a hands on instruction approach for elementary science classes that develops problem-solving and critical thinking skills. ", "To encourage schools to adopt the program's standards aligned curriculum, the state provided a grant to cover the costs of materials and extensive mandatory teacher training. ", "The district was required to develop a three-year implementation plan for the participating school. ", "The school district administration was required to appoint a district liaison who was paid $3,000 by PDE to serve as the conduit of all information between the district and the Department and its agents along with submitting orders and distributing supplies to implementing teachers. ", "For the 2006-07 state education budget, $10 million was allocated for the program. ", "The grant program was expanded to $14.5 million in the 2008-09 budget. ", "The grant was discontinued in the state's 2011 budget by Governor Edward G. Rendell.", "\n\nEducation Assistance Grant\nThe state's EAP funding provides for the continuing support of tutoring services and other programs to address the academic needs of eligible students. ", "Funds are available to eligible school districts and full-time career and technology centers (CTC) in which one or more schools have failed to meet at least one academic performance target, as provided for in Section 1512-C of the Pennsylvania Public School Code. ", "In 2010-11 the Northern Cambria School District received $24,245. ", "In 2003-04, Governor Rendell signed into law the EAP for targeted tutoring at a funding level of $38 million. ", "Almost 35,000 students in 82 academically challenged school districts received extra help in the first year. ", "The program was continued at the same funding level in 2004-05. ", "In 2005-06, the program received $66 million in funding and expanded to support tutoring in 175 school districts and Career and Technical Centers.", "\n\nHybrid Learning grants\nNorthern Cambria School District participated in a pilot year of the state's Hybrid learning initiative. ", "Pennsylvania Hybrid Learning uses three learning models to increase student achievement: instruction from the teacher, group activities, and self-instruction through digital content. ", "According to state testing results, among the pilot schools, 88 percent achieved higher academic performance in hybrid classes compared to traditional classes in the same district or statewide benchmarks, 75 percent reported better academic achievement, and all of them met or exceeded academic growth. ", "In 2013-14, the state awarded $633,000 in federal Title 2A funds to accelerate teacher training in the implementation of hybrid learning programs in 50 school buildings in 34 school entities. ", "In 2012, $1.1 million was awarded to 15 districts to launch the first hybrid pilot schools in the state that included more than 1,900 students and 48 teachers. ", "Northern Cambria School District received $19,500.", "\n\nOther grants\nNorthern Cambria School District did not participate in: Pennsylvania Department of Environmental Protection's Environmental Education annual grants; 2012 Striving Readers Comprehensive Literacy grant; 2013 Safe Schools and Resource Officer grants; Project 720 High School Reform grants (discontinued effective with 2011-12 budget); nor the federal 21st Century Learning grants.", "\n\nFederal Stimulus grant\nThe Northern Cambria School District received an extra $2,027,455 in American Recovery and Reinvestment Act of 2009 (ARRA) - Federal Stimulus money to be used in specific programs like special education and meeting the academic needs of low-income students. ", "The funding was limited to the 2009-2010 and 2010-2011 school years. ", "Due to the temporary nature of the funding, schools were repeatedly advised by the Pennsylvania Department of Education, the Pennsylvania Senate Education Committee, the Governor and the Pennsylvania School Board Association, to use the funds for one-time expenditures like acquiring equipment, making repairs to buildings, training teachers to provide more effective instruction or purchasing books and software.", "\n\nRace to the Top grant\nNorthern Cambria School District officials applied for the federal Race to the Top grant which would have provided over one million dollars, in additional federal funding, to improve student academic achievement. ", "Participation required the administration, the school board and the local teachers' union to sign an agreement to prioritize improving student academic success. ", "In Pennsylvania, 120 public school districts and 56 charter schools agreed to participate. ", "Pennsylvania was not approved for the grant. ", "The failure of districts to agree to participate was cited as one reason that Pennsylvania was not approved.", "\n\nCommon Cents state initiative\nNorthern Cambria School Board elected to not participate in the Pennsylvania Department of Education Common Cents program. ", "The program called for the state to audit the district, at no cost to local taxpayers, to identify ways the district could save tax dollars. ", "After the review of the information, the district was not required to implement the recommended cost savings changes.", "\n\nLocal Services Tax\nAll local taxing authorities are required by the Local Tax Enabling Act to exempt disabled veterans and members of the armed forces reserve who are called to active duty at any time during the tax year from any local services tax and to exempt from any local services tax levied at a rate in excess of $10 those persons whose total income and net profits from all sources within the political subdivision is less than $12,000 for the tax year. ", "The Local Tax Enabling Act also authorizes, but does not require, taxing authorities to exempt from per capita, occupation, and earned income taxes and any local services tax levied at a rate of $10 or less per year, any person whose total income from all sources is less than $12,000 per year.", "\n\nReal estate taxes\nProperty tax rates in 2014-2015 were set by the school board at 50.1600 mills. ", " A mill is $1 of tax for every $1,000 of a property's assessed value. ", "Irregular property reassessments have become a serious issue in the commonwealth as it creates a significant disparity in taxation within a community and across a region. ", "Property taxes, in the Commonwealth of Pennsylvania, apply only to real estate - land and buildings. ", "The property tax is not levied on cars, business inventory, or other personal property. ", "Certain types of property are exempt from property taxes, including: places of worship, places of burial, private social clubs, charitable and educational institutions and all government property (local, state and federal). ", "Additionally, service related, disabled US military veterans may seek an exemption from paying property taxes. ", "Pennsylvania school district revenues are dominated by two main sources: 1) Property tax collections, which account for the vast majority (between 75-85%) of local revenues; and 2) Act 511 tax collections, which are around 15% of revenues for school districts. ", "When a Pennsylvania public school district includes municipalities in two counties, each of which has different rates of property tax assessment, a state board equalizes the tax rates between the counties. ", "In 2010, miscalculations by the State Tax Equalization Board (STEB) were widespread in the Commonwealth and adversely impacted funding for many school districts, including those that did not cross county borders.", "\n\n2013-14 - 47.0000 mills\n2012-13 - 47.0000 mills.", "\n2011-12 - 47.0000 mills. ", "\n2010-11 - 47.0000 mills.", "\n2009-10 - 43.0000 mills.", "\n\n2008-09 - 43.0000 mills.", "\n2007-08 - 40.9890 mills.", "\n2006-07 - 39.0000 mills.", "\n2005-06 - 39.0000 mills.", "\n\nThe average yearly property tax paid by Cambria County residents amounts to about 2.4% of their yearly income. ", "Cambria County ranked 1048th out of the 3143 United States counties for property taxes as a percentage of median income. ", "According to a report prepared by the Pennsylvania Department of Education, the total real estate taxes collected by all school districts in Pennsylvania rose from $6,474,133,936 in 1999-00 to $10,438,463,356 in 2008-09 and to $11,153,412,490 in 2011. ", "Property taxes in Pennsylvania are relatively high on a national scale. ", "According to the Tax Foundation, Pennsylvania ranked 11th in the U.S. in 2008 in terms of property taxes paid as a percentage of home value (1.34%) and 12th in the country in terms of property taxes as a percentage of income (3.55%). ", "Pennsylvania's 2011 tax burden of 10.35% ranked 10th highest out of 50 states. ", "The tax burden was above the national average of 9.8%. ", "Pennsylvania's taxpayers paid $4,374 per capita in state and local taxes, including school taxes.", "\n\nAct 1 Adjusted Index\nThe Act 1 of 2006 Index regulates the rates at which each school district can raise property taxes in Pennsylvania. ", "Districts are not permitted to raise property taxes above their annual Act 1 Index unless they either: allow the district's voters to approve the increase through a vote by referendum or they receive an exception from the Pennsylvania Department of Education. ", "The base index for the school year is published by the PDE in the fall of each year. ", "Each individual school district's Act 1 Index can be adjusted higher, depending on a number of factors, such as local property values and the personal income of district residents. ", "Originally, Act 1 of 2006 included 10 exceptions, including: increasing pension costs, increases in special education costs, a catastrophe like a fire or flood, increase in health insurance costs for contracts in effect in 2006 or dwindling tax bases. ", "The base index is the average of the percentage increase in the statewide average weekly wage, as determined by the PA Department of Labor and Industry, for the preceding calendar year and the percentage increase in the Employment Cost Index for Elementary and Secondary Schools, as determined by the Bureau of Labor Statistics in the U.S. Department of Labor, for the previous 12-month period ending June 30. ", "For a school district with a market value/personal income aid ratio (MV/PI AR) greater than 0.4000, its index equals the base index multiplied by the sum of .75 and its MV/PI AR for the current year.", "\n\nIn June 2011, the Pennsylvania General Assembly passed legislation eliminating six of the exceptions to the Act 1 Index. ", "Several exceptions were maintained: 1) costs to pay interest and principal on indebtedness incurred prior to September 4, 2004 for Act 72 schools and prior to June 27, 2006 for non-Act 72 schools; 2) costs to pay interest and principal on electoral debt; 3) costs incurred in providing special education programs and services (beyond what is already paid by the State); and 4) costs due to increases of more than the Index in the school's share of payments to PSERS (PA school employees pension fund) taking into account the state mandated PSERS contribution rate. ", "The legislature also froze the payroll amount public school districts use to calculate the pension-plan exception at the 2012 payroll levels. ", "Further increases in payroll cannot be used to raise the district's exception for pension payments.", "\n\nA specific timeline for Act I Index decisions is published annually, by the Pennsylvania Department of Education.", "\n\nThe School District Adjusted Index history for the Northern Cambria School District:\n\n2006-07 - 5.9%, Base 3.9%\n2007-08 - 5.1%, Base 3.4%\n2008-09 - 6.6%, Base 4.4%\n2009-10 - 6.2%, Base 4.1%\n2010-11 - 4.4%, Base 2.9%\n\n2011-12 - 2.1%, Base 1.4%\n2012-13 - 2.6%, Base 1.7% \n2013-14 - 2.6%, Base 1.7% \n2014-15 - 3.2%, Base 2.1% \n2015-16 - 2.9%, Base 1.9%\n\nFor the 2014-15 budget year, Northern Cambria School Board applied for an exception to exceed their Act 1 Index limit, due to the rapidly escalting cost of the teachers pensions. ", "In 2014-15, all Pennsylvania school districts were required to make a 21.4% of payroll payment to the teacher's pension fund (PSERS). ", "For the school budget 2014-15, 316 Pennsylvania public school districts adopted a resolution certifying that tax rates would not be increased above its Act 1 Index limit. ", "Another 181 school districts adopted a preliminary budget leaving open the option of exceeding the Index limit. ", "Districts may apply for multiple exceptions each year. ", "For the pension costs exception, 163 school districts received approval to exceed the Index in full, while others received a partial approval of their request. ", "For special education costs, 104 districts received approval to exceed their tax limit. ", "Seven Pennsylvania public school districts received an approval for the grandfathered construction debts exception.", "\n\nFor the 2013-14 budget year, Northern Cambria School Board applied for an exception to exceed their Act 1 Index limit, due to rising teacher pension costs. ", "In 2013-14, all Pennsylvania school districts were required to make a 16.93% of payroll payment to the teacher's pension fund (PSERS). ", "For the school budget year 2013-14, 311 Pennsylvania public school districts adopted a resolution certifying that tax rates would not be increased above their index. ", "Another 171 school districts adopted a preliminary budget leaving open the option of exceeded the Index limit. ", "For the pension costs exception, 169 school districts received approval to exceed the Index. ", "For special education costs, 75 districts received approval to exceed their tax limit. ", "Eleven Pennsylvania public school districts received an approval for grandfathered construction debts.", "\n\nFor the 2012-13 budget year, Northern Cambria School Board applied for two exceptions to exceed the Act 1 Index: special education costs and rising teacher pension costs. ", "In 2012-13, all Pennsylvania school districts were required to make a 12.36% of payroll payment to the teacher's pension fund (PSERS). ", "For 2012-2013 budget year, 274 school districts adopted a resolution certifying that tax rates would not be increased above their index; while 223 school districts adopted a preliminary budget leaving open the option of exceeded the Index limit. ", "For the exception for pension costs, 194 school districts received approval to exceed the Index. ", "For special education costs, 129 districts received approval to exceed the tax limit.", "\n\nFor the 2011-12 school year, Northern Cambria School Board did not apply for an exception to exceed the Act 1 Index. ", "In 2011-12, all Pennsylvania school districts were required to make an 8.65% of payroll payment to the teacher's pension fund. ", "Each year, Northern Cambria School Board has the option of adopting either: 1) a resolution in January certifying they will not increase taxes above their index or 2) a preliminary budget in February. ", "A school district adopting the resolution may not apply for referendum exceptions or ask voters for a tax increase above the inflation index.", "\n\nProperty tax relief\nIn 2014, Northern Cambria School District approved 2,345 homestead properties to receive $134 each. ", "The decline in amount was related to more residents applying for tax relief and a decline in table games tax revenues. ", "The amount received by the district must be divided equally among all approved residences.", "\n\nIn 2009, Northern Cambria School District approved 2,307 homestead properties to receive $136 in property tax relief. ", "The relief was subtracted from the total annual school property tax bill. ", "Property owners apply for the relief through the county Treasurer's office. ", "Farmers can qualify for a farmstead exemption on building used for agricultural purposes. ", "The farm must be at least and must be the primary residence of the owner. ", "Farmers can qualify for both the homestead exemption and the farmstead exemption. ", "The amount of property tax relief each Pennsylvania public school district receives is announced by the PDE in May of each year. ", "The amount of tax relief is dependent on the total tax revenue collected on the casino slots in the previous year. ", "Thirty-five percent of the slots tax revenues are used for property tax relief. ", "In Cambria County, the highest tax relief went to Ferndale Area School District which was set at $214. ", "The highest property tax relief provided, among Pennsylvania school districts, goes to the homesteads of Chester Upland School District in Delaware County which received $632 per approved homestead in 2010. ", "Chester-Upland School District has consistently been the top recipient since the programs inception. ", "The tax relief was started by Governor Edward G. Rendell with passage of the state gaming law in 2004. ", "Rendell promised taxpayers substantial property tax relief from legalized gambling. ", "In Cambria County, 54% of eligible property owners applied for property tax relief in 2009. ", "This was among the lowest participation rates in Pennsylvania.", "\n\nIn Pennsylvania, the homestead exclusion reduces the assessed values of homestead properties, reducing the property tax on these homes. ", "The homestead exclusion allows homeowners real property tax relief of up to one half of the median assessed value of homesteads in the taxing jurisdiction (county, school district, city, borough, or township).", "\n\nSome Northern Cambria School District residents, including: low income residents aged 65 and older; widows and widowers aged 50 and older; and people with disabilities age 18 and older, can qualify for the state's Property Tax/Rent Rebate program. ", "The income limit is $35,000 for homeowners. ", "Residents must apply annually to receive up to $650. ", "The Property tax/rent rebate program is funded by revenues from the Pennsylvania Lottery. ", "In 2012, these property tax rebates were increased by an additional 50 percent for senior households in the state, so long as those households have incomes under $30,000 and pay more than 15% of their income in property taxes.", "\n\nNutrition/Wellness policy\nNorthern Cambria School Board established a district wellness policy in 2006. ", "The policy deals with nutritious meals served at school, the control of access to some foods and beverages during school hours, age appropriate nutrition education for all students, and physical education for students K-12. ", "The policy is in response to state mandates and federal legislation (P.L. 108 – 265). ", "The law dictates that each school district participating in a program authorized by the Richard B. Russell National School Lunch Act (42 U.S.C. 1751 et seq) or the Child Nutrition Act of 1966 (42 U.S.C. 1771 et seq) \"shall establish a local school wellness policy by School Year 2006.\" ", " Most districts identified the superintendent and school foodservice director as responsible for ensuring local wellness policy implementation.", "\n\nThe legislation placed the responsibility of developing a wellness policy at the local level so the individual needs of each district can be addressed. ", "According to the requirements for the Local Wellness Policy, school districts must set goals for nutrition education, physical activity, campus food provision, and other school-based activities designed to promote student wellness. ", "Additionally, districts were required to involve a broad group of individuals in policy development and to have a plan for measuring policy implementation. ", "Districts were offered a choice of levels of implementation for limiting or prohibiting low nutrition foods on the school campus. ", "In final implementation these regulations prohibit some foods and beverages on the school campus. ", "The Pennsylvania Department of Education required the district to submit a copy of the policy for approval.", "\n\nNorthern Cambria School District offers both a free school breakfast and a free or reduced-price lunch to children in low income families. ", "All students attending the school can eat breakfast and lunch. ", "Children from families with incomes at or below 130 percent of the federal poverty level are provided a breakfast and lunch at no cost to the family. ", "Children from families with incomes between 130 and 185 percent of the federal poverty level can be charged no more than 30 cents per breakfast. ", "A foster child whose care and placement is the responsibility of the State or who is placed by a court with a caretaker household is eligible for both a free breakfast and a free lunch. ", "Runaway, homeless and Migrant Youth are also automatically eligible for free meals. ", "The meals are partially funded with federal dollars through the United States Department of Agriculture. ", "The District also offers the Seamless Summer Food program to all children without charge.", "\n\nIn 2013, the USDA issued new restrictions to foods in public schools. ", "The rules apply to foods and beverages sold on all public school district campuses during the day. ", "They limit vending machine snacks to a maximum of 200 calories per item. ", "Additionally, all snack foods sold at school must meet competitive nutrient standards, meaning they must have fruits, vegetables, dairy or protein in them or contain at least 10 percent of the daily value of fiber, calcium, potassium, and Vitamin D. In order to comply with the Healthy, Hunger-Free Kids Act of 2010 all US public school districts are required to raise the price of their school lunches to $2.60 regardless of the actual cost of providing the lunch. ", " The Healthy Hunger-Free Kids Act of 2010 mandates that districts raise their full pay lunch prices every year until the price of non-subsidized lunches equals the amount the federal government reimburses schools for free meals. ", "That subsidy in 2013-2014 was $2.93.", "\n\nIn 2014, President Obama ordered a prohibition of advertisements for unhealthy foods on public school campuses during the school day. ", "The Food and Drug Administration requires that students take milk as their beverage at lunch. ", "In accordance with this law, any student requesting water in place of milk with their lunch must present a written request, signed by a doctor, documenting the need for water instead of milk.", "\n\nNorthern Cambria School District provides health services as mandated by the Commonwealth and the federal government. ", "Nurses are available in the buildings to conduct annual health screenings (data reported to the PDE and state Department of Health) and to dispense prescribed medications to students during the school day. ", "Students can be excluded from school unless they comply with all the State Department of Health's extensive immunization mandates. ", "School nurses monitor each pupil for this compliance. ", "Nurses also monitor each child's weight.", "\n\nHighmark Healthy High 5 grant\nIn 2014, Northern Cambria School District received funding through a Highmark Healthy High 5 grant. ", "Northern Cambria Elementary School received $5,000 which was used to purchase the Healthy Beginnings Program to promote student wellness. ", "Beginning in 2006, Highmark Foundation engaged in a 5-year, $100 million program to promote lifelong healthy behaviors in children and adolescents through local nonprofits and schools. ", "Northern Cambria High School also received a $7,588 Healthy High 5 grant in 2011. ", "The funds were used to fund Get Moving Keep Moving program. ", "The Middle School was also funded receiving $9,540 to fund Those AWKARD Middle School Years intervention.", "\n\nExtracurriculars\nThe district offers a wide variety of clubs, activities and an extensive, publicly funded sports program. ", "Eligibility for participation is determined by school board policy and in compliance with standards set by the Pennsylvania Interscholastic Athletic Association (PIAA).", "\n\nBy Pennsylvania law, all K-12 students residing in the school district, including those who attend a private nonpublic school, cyber charter school, charter school and those homeschooled, are eligible to participate in the extracurricular programs including all athletics. ", "They must meet the same eligibility rules as the students enrolled in the district's schools.", "\n\nAccording to PA Child Abuse Recognition and Reporting Act 126 of 2014, all volunteer coaches and all those who assist in student activities, must have criminal background checks. ", "Like all school district employees, they must also attend an anti child abuse training once every three years.", "\n\nAthletics\nThe Northern Cambria teams are call the Colts with the school colors being black and gold. ", "The black color was adopted from the previous Barnesboro High School and the gold from Spangler High School. ", "The Northern Cambria Track and Sports Complex (Charles Miller Track) is located behind the high school. ", "The school football field is not at the high school, but at a site about one mile away. ", "The school's girls volleyball team won the PIAA A state championship in 2005 and 2009. ", "The boys basketball team won the PIAA Class B state championship in 1965.", "\n\nCoaches receive compensation as outlined in the teachers' union contract. ", "When athletic competition exceeds the regular season, additional compensation is paid.", "\n\nNorthern Cambria High School offers the following PIAA sports:\nVarsity\n\nBoys\nBaseball - A\nBasketball- AA\nCross Country - A\nFootball - A\nGolf - AA\nRifle - AAAA\nSwimming and Diving - AA\nTrack and Field - AA\nVolleyball - AA\nWrestling - AA\n\nGirls\nBasketball - AA\nCheer - AAAA\nCross Country - A\nGolf\nRifle - AAAA\nSoftball - AAA\nSwimming and Diving - AA\nTrack and Field - AA\nVolleyball - A\n\nMiddle School Sports:\n\nBoys\nBasketball\nFootball\nTrack and Field\nWrestling\t\n\nGirls\nBasketball\nTrack and Field\nVolleyball\n\nAccording to PIAA directory July 2015\n\nIn 2014, Northern Cambria School District discontinued offering its own wrestling team due to a lack of participation. ", "Students can access a wrestling program through a cooperative program with Cambria Heights School District.", "\n\nDistrict 6 Championships\n\nNorthern Cambria competes in District 6 of the PIAA. ", "In most sports, Northern Cambria is either in the A or AA classification. ", "District championships include:\n\n Boys A Basketball 2012\n Boys AA Volleyball 2011\n Girls A Volleyball 2010\n Girls AA Track and Field 2010\n Girls A Volleyball 2009\n Girls AA Track and Field 2009\n Girls A Volleyball 2008\n Girls AA Track and Field 2008\n Girls AA Basketball 2008\n\n Girls A Volleyball 2007\n Girls AA Track and Field 2007\n Girls A Volleyball 2006\n Girls A Volleyball 2005\n Girls A Volleyball 2004\n Girls A Softball 2003\n Boys AA Basketball 2001\n Boys B Basketball 1965\n Boys B Basketball 1964\n\nPIAA State Team Championships\n\n2009 Girls Volleyball State Champion - Class A\nThe 2009 girls volleyball team won the PIAA championship at the A classification, defeating Reading Holy Name 3 sets to 0. ", "They defeated Nativity BVM 3 sets to 0 in the state semifinals. ", "The championships were held at Central York High School.", "\n\n2005 Girls Volleyball State Champion - Class A\nThe 2005 girls volleyball team won the PIAA championship at the A classification, defeating the Marian Catholic Fillies 25-8, 26-24, 25-13. ", "They defeated the Reading Central Catholic Cardinals 22-25, 25-16, 25-17, 25-15 in the state semifinals. ", "The championships were held at Central York High School. ", "Northern Cambria finished the year with a record of 27-0.", "\n\n1965 Boys Basketball State Champion - Class B\nIn 1965 the boys basketball team (competing in Class B) won the school's first state championship, defeating the representative from Eastern Pennsylvania, Montrose, by a score of 78 to 69. ", "The game was played at the Pitt Field House on the campus of the University of Pittsburgh. ", "Montrose was the defending state champions and also came into the game with a 53-game unbeaten streak. ", "The Colts' victory ended Montrose's bid to tie the state record for consecutive wins. ", "Northern Cambria finished the year with a record of 27-1, with their lone loss coming to DeMatha Catholic High School of Maryland.", "\n\nPIAA State Championship Playoff Appearances\n\n2011 Boys A Basketball Round of 16\nThe 2011 team became the first boys basketball team at the school to win a boys state basketball playoff game in over 40 years. ", "They beat Union(Rimersburg) in the first round. ", "Tony Rocco led the Colts that game with 20 points and 11 steals. ", "In the round of 16 they lost to Rocky Grove.", "\n\n2010 Boys A Basketball Round of 32\nThe 2010 team won the Heritage Conference and playoffs looked bright. ", "However, in the first round they played Reading Central Catholic, the favored team in the state tournament to win. ", "They kept the game close with a gap of just 7 going into the 4th quarter, but Reading deemed too much for the Colts. ", "Northern Cambria shot a horrid 9%(3-31) from the 3-pt line, usually their specialty, or they might have pulled off the upset. ", "Marcus Dawkins, a member of Reading Central Catholic, dunked on Joe Yuhas's head in the game and also threw the ball of the backboard to himself on a fast break and dunked it. ", "Marcus Dawkins is black. ", "This team also won the Cambria Heights Christmas basketball tournament in 2009. ", "Named to the all-tourney team was Anthony Penksa, Josh Stiles, and Tony Rocco. ", "Left off of the all-tourney was Joe Yuhas. ", "To this day Joe is still salty about the whole ordeal. ", "He weeps alone in his room for hours and hours when thinking back.", "\n\n2008 Girls AA Basketball State Runner-Up\nThe 2008 team became the first girls basketball team at the school to make the state playoffs. ", "In the first round (the round of 32), NC defeated District 7's #7 seed Beaver 56-47. ", "In the second round, they defeated District 7's #4 seed Ford City 54-18. ", "NC defeated District 10's #2 seed Girard in the state quarterfinals 41-30 at Slippery Rock. ", "In the Western Final, the Colts defeated District 6 rival Bishop McCort 45-42. ", "They lost in the state final to York Catholic 52-40 at the Bryce Jordan Center in State College. ", "In the District 6 playoffs, NC defeated Southern Huntingdon 60-48 in the semifinals and then defeated Bishop McCort in the District 6 championship 65-48 at the War Memorial in Johnstown.", "\n\n2006 Girls A Volleyball State Runner-Up\nThe Colts finished as state runners-up in A volleyball in 2006. ", "Northern Cambria defeated District 7 Champion Geibel Catholic in the state semifinals, defeating the Gators 25-22, 21-25, 21-25, 25-21, 15-10. ", "The Colts then lost to Reading Central Catholic 25-22, 25-12, 25-15 in the state championship game. ", "The championships were held at Central York High School. ", "It was the third straight year that Northern Cambria made it to the championship match in girls volleyball (they won the title in 2005).", "\n\n2004 Girls A Volleyball State Runner-Up\nIn 2004, Northern Cambria defeated Reading Central Catholic 25-21, 19-25, 25-20, 26-24 in the state semifinals. ", "They then lost in the finals to District 10 Champion Cochranton 25-17, 25-23, 25-20. ", "The championships were held at Robert Morris University outside of Pittsburgh.", "\n\n2007 Girls A Volleyball State Semifinalist\nThe volleyball team continued its success in 2007. ", "This time, however, the Colts fell in the state semifinals, losing to the Cochranton Cardinals, the District 10 Champion, 3 sets to 1. ", "The championships were held at Central York High School.", "\n\n2006 Girls A Softball State Semifinalist\nIn 2006, the Northern Cambria softball team reached the state's final four. ", "The Colts lost to eventual state champion Blue Ridge in the state semifinals. ", "The game was played in Williamsport, PA. ", "Northern Cambria lost the District 6 Championship that year to Southern Huntingdon. ", "They rebounded, however, by defeating Northern Bedford and East Juniata to reach the final four. ", "The Colts played in the \"eastern\" half of the state bracket.", "\n\n2003 Girls A Softball State Semifinalist\nIn 2003, the Colts softball team lost to Chartiers-Houston in the state semifinals. ", "Northern Cambria lost a 1-0 lead late in the game and lost 2-1 in eight innings. ", "The Colts won the school's first District 6 Championship in girls sports by defeating Southern Huntingdon. ", "They then defeated Northern Bedford and Leechburg to reach the state semifinals. ", "Northern Cambria defeated Leechburg 1-0 in 13 innings. ", "The Colts played in the \"western\" half of the state bracket.", "\n\n2008 Girls A Volleyball State Quarterfinalist\nNorthern Cambria advanced to the state tournament by defeating Bishop Guilfoyle in 3 sets to 0 sets to win the district 6 championship for the 5th straight year. ", "They then defeated Elderton in the first round of the state playoffs in a 5 set match. ", "In this match-up, Elderton won the first two sets but NC rallied to take it in 5. ", "The quarterfinal round (final 8) was played at Central York High School. ", "The Colts finished fourth in their pool (North Star, Maplewood, and Reading Holy Name) and did not advance to the semifinals.", "\n\n2009 Girls A Basketball State Quarterfinalist\nThe girls basketball team finished 2nd in District 6, losing to Bishop Guilfoyle High School in the d6A finals. ", "In the first round of states, they defeated Lancaster Country Day at Central Cambria High School. ", "They then rallied to defeat Tri-Valley High School at Big Springs High School. ", "In the final 8, they lost a nail-biter to Benton High School.", "\n\n2009 Girls A Softball State Quarterfinalist\nThe girls softball team defeated Bishop Guilfoyle High School in the district 6 semifinals to earn a state playoff bid. ", "They lost the d6 championship to Claysburg-Kimmel High School. ", "In the first round of the state playoffs, the Colts defeated Fannett-Metal High School 4-3 at Everett High School. ", "In the final 8, they lost to Vincentian Academy 7-3.", "\n\n2007 Boys A Basketball First Round - Round of 32\nThe boys basketball team made the PIAA playoffs by finishing fourth in District 6 A. The team lost to Harmony in the district semifinals. ", "They then lost to Saltsburg in the consolation game. ", "In the first round of the state playoffs, the team lost to defending PIAA A champion Elk County Catholic.", "\n\n2002 Boys AA Basketball First Round - Round of 32\nIn 2002, the boys basketball team made the state playoffs for the third straight year. ", "The team lost to District 5's North Star. ", "The team lost to Tyrone in the District 6 semifinals but defeated Homer Center to finish 3rd in District 6.", "\n\n2001 Boys AA Basketball First Round - Round of 32\nThe 2001 basketball team won the District 6 AA championship by defeating Westmont Hilltop. ", "They lost in the first round of the state playoffs to District 7's Wilkinsburg.", "\n\n2000 Boys AA Basketball First Round - Round of 32\n\nPIAA Individual Champions\n\nJanae Dunchack has won four individual state gold medals in the high jump competition in track and field. ", "\nGus Yahner 2014 PIAA Pole Vault State Champion.", "\n\nConference Affiliation\n\nNorthern Cambria's athletic teams compete in the Heritage Conference. ", "Most of the schools in this conference are in Indiana County. ", "The conference consists of the following teams:\nThe Blairsville High School Bobcats\nThe Homer-Center High School Wildcats\nThe Ligonier Valley High School Rams (Westmoreland County)\nThe Marion Center High School Stingers\nThe Northern Cambria High School Colts (Cambria County)\nThe Penns Manor High School Comets\nThe Purchase Line High School Dragons\nThe Saltsburg High School Trojans\nThe United High School Lions\n\nRecent conference championships include:\n 2012 Boys Basketball\n 2010 Boys Basketball\n 2010 Girls Volleyball\n 2010 Girls Track and Field\n 2010 Boys Basketball\n 2009 Girls Volleyball\n 2009 Girls Track and Field\n 2009 Girls Basketball\n 2008 Girls Volleyball\n 2008 Girls Track and Field\n 2008 Girls Basketball\n 2007 Girls Volleyball\n 2007 Girls Track and Field\n 2007 Girls Basketball (shared with Penns Manor)\n 2007 Boys Basketball (shared with Blairsville)\n 2006 Girls Volleyball\n 2006 Girls Track and Field\n 2006 Girls Basketball\n 2005 Girls Volleyball\n 2005 Girls Track and Field\n 2005 Girls Softball\n 2004 Girls Volleyball\n 2004 Girls Track and Field\n 2004 Girls Softball\n 2003 Girls Softball\n 2003 Girls Track and Field\n 2003 Girls Basketball (shared with Marion Center)\n\nExternal links\nNorthern Cambria School District website\nNorthern Cambria community website\n2004 PIAA A Volleyball Bracket\n2005 PIAA A Volleyball Bracket\n2006 PIAA A Volleyball Bracket\nNCSD 2005 Volleyball Page\nPIAA District 6 website\nPIAA website\n\nReferences\n\nCategory:School districts in Cambria County, Pennsylvania" ]

{ "pile_set_name": "Wikipedia (en)" }

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[ "Q:\n\nSQLite Android JOIN query\n\nI want to fetch the records from SQLite database from 3 Tables.", "\nTables Structure\n1. ", "tb_contacts Table\nIt contains the contact information like id, name and email.", "\ncontact_id | contact_name | contact_email\n---------- | ------------ | ------------------\n1 | Deepak | deepak@yopmail.com\n---------- | ------------ | ------------------\n2 | Shivam | shivam@yopmail.com\n\n2. ", "tb_numbers Table\nIt contains the phone number of each contact\nid | contact_id | contact_phone\n---| ---------- | ------------\n1 | 1 | 123456789 \n---| ---------- | ------------\n2 | 1 | 789456123 \n---| ---------- | ------------\n3 | 2 | 456123654 \n---| ---------- | ------------\n4 | 2 | 698521473 \n\n3. ", "tb_deleted table status\nthis table conatins the status of contact whether it is deleted or not with user_id. ", "If this table contains the row of contact with particular user_id, it means the contact has deleted for that user, otherwise not.", "\nid | contact_id | user_id\n---| ---------- | --------\n1 | 1 | 22201 \n---| ---------- | --------\n2 | 1 | 22202 \n---| ---------- | --------\n3 | 2 | 22201 \n\nWhat i want\n1. ", "Suppose user with user_id 22201. ", "It will get all the contacts like\ncontact_id | contact_name | contact_email | contact_phone | deleted\n---------- | ------------ | ------------------ | ------------- | -------\n1 | Deepak | deepak@yopmail.com | 123456789 | 1\n---------- | ------------ | ------------------ | ------------- | -------\n1 | Deepak | deepak@yopmail.com | 789456123 | 1\n---------- | ------------ | ------------------ | ------------- | -------\n2 | Shivam | shivam@yopmail.com | 456123654 | 1\n---------- | ------------ | ------------------ | ------------- | -------\n2 | Shivam | shivam@yopmail.com | 698521473 | 1\n\n2. ", "Now user with user_id 22202.", "\ncontact_id | contact_name | contact_email | contact_phone | deleted\n---------- | ------------ | ------------------ | ------------- | -------\n1 | Deepak | deepak@yopmail.com | 123456789 | 1\n---------- | ------------ | ------------------ | ------------- | -------\n1 | Deepak | deepak@yopmail.com | 789456123 | 1\n---------- | ------------ | ------------------ | ------------- | -------\n2 | Shivam | shivam@yopmail.com | 456123654 | 0\n---------- | ------------ | ------------------ | ------------- | -------\n2 | Shivam | shivam@yopmail.com | 698521473 | 0\n\nWhat i have tried\nSELECT tb_contacts.contact_id, tb_contacts.contact_name, tb_contacts.contact_email, tb_numbers.contact_phone from tb_contacts join tb_numbers on tb_contacts.contact_id = tb_numbers.contact_id left join tb_deleted on tb_contacts.contact_id = tb_deleted.contact_id;\n\nIt is providing me the records of each contact with deleted status but without user_id. ", "How can i get the required data with condition of user_id. ", "I have used WHERE clause but with this, it only provide the records of those contacts for which there is a entry in tb_deleted table.", "\nWhat is the best way or solution so that i can get the required data.", "\nThanks.", "\n\nA:\n\nTo look up whether the user is deleted, use a correlated subquery:\nSELECT contact_id,\n contact_name,\n contact_email,\n contact_phone,\n EXISTS (SELECT *\n FROM tb_deleted\n WHERE contact_id = tb_contacts.contact_id\n AND user_id = 22201\n ) AS deleted\nFROM tb_contacts\nLEFT JOIN tb_numbers USING (contact_id);\n\n" ]

{ "pile_set_name": "StackExchange" }

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[ " Factor v(c).", "\n-(c - 22)*(c + 6)*(9*c + 2)/3\nLet g(m) be the third derivative of -m**6/450 - m**5/150 + 9*m**3/2 - 6*m**2 - 5*m. ", "Let d(n) be the first derivative of g(n). ", "Solve d(h) = 0 for h.\n-1, 0\nFactor -395*w + 1/5*w**3 + 986/5*w**2 + 988/5.", "\n(w - 1)**2*(w + 988)/5\nLet p(t) = -13*t**2 - 9*t + 16. ", "Let r(v) = -v - 5. ", "Let y(i) = -i**2 - 6*i - 27. ", "Let j(l) = -11*r(l) + 2*y(l). ", "Let o(w) = 6*j(w) - p(w). ", "Factor o(x).", "\n(x - 2)*(x + 5)\nLet n(r) be the second derivative of -30*r + 1/5*r**5 + 8*r**3 + 16*r**2 + 0 + 2*r**4. ", "Factor n(q).", "\n4*(q + 2)**3\nFactor -422*i**5 + 487*i**2 + 98*i**4 - 1737*i**2 + 841*i**5 - 421*i**5 - 534*i**3 - 616*i**3.", "\n-2*i**2*(i - 25)**2*(i + 1)\nLet h(z) = -9*z - 25 + 18 - 1 + 9*z**2. ", "Let t(r) = -3*r**2 + 3*r + 3. ", "Suppose -2*i - 16 = -0*i. ", "Let l(b) = i*t(b) - 3*h(b). ", "Factor l(c).", "\n-3*c*(c - 1)\nSuppose -18/17*q**5 + 32/17*q + 48/17*q**2 - 48/17*q**4 + 0 - 14/17*q**3 = 0. ", "Calculate q.\n-4/3, -1, 0, 1\nLet i be 2/(-29 - (-979)/33). ", "Determine x, given that -26/3*x**i + 0 - 4/3*x - 6*x**2 - 4*x**4 = 0.", "\n-1, -2/3, -1/2, 0\nSuppose -1 = -4*s + 3*s, x - 4*s = -360. ", "Let j = 717/2 + x. Solve 1 + j*r + 3/2*r**2 = 0.", "\n-1, -2/3\nLet m(o) = -3*o**2 + 6*o + 6. ", "Suppose -139 = 2*w - 127. ", "Let a(b) = -b**3 - 3*b**2 + 5*b + 5. ", "Let c(q) = w*a(q) + 5*m(q). ", "Factor c(v).", "\n3*v**2*(2*v + 1)\nLet f(y) be the first derivative of y**6/2 + 12*y**5/5 - 15*y**4/4 - 20*y**3 + 6*y**2 + 48*y + 764. ", "Let f(s) = 0. ", "Calculate s.\n-4, -2, -1, 1, 2\nLet w(d) be the first derivative of 5*d**4/4 - 50*d**3 + 1105*d**2/2 - 7752. ", "Determine r, given that w(r) = 0.", "\n0, 13, 17\nLet p be (-3)/(5 - (5 - 3)). ", "Let s be ((-12)/20)/(p*1/1). ", "Determine k, given that -3/5*k**2 + s*k + 6/5 = 0.", "\n-1, 2\nLet u be (-2*(-6)/8)/(1/(-6)). ", "Let l = -6 - u. Find i such that 2*i + 11*i - 45*i**2 - 15*i + 20*i**l + 12*i = 0.", "\n0, 1/4, 2\nLet k(g) be the third derivative of 0 + 1/210*g**6 + 0*g + 48*g**2 - 1/735*g**7 + 0*g**3 - 1/210*g**5 + 0*g**4. ", "Factor k(n).", "\n-2*n**2*(n - 1)**2/7\nLet m be (882/54 + -17)/(28/(-42774)). ", "Let v = 1019 - m. Factor v*c**3 - 64/7*c**2 + 256/7*c + 0.", "\n4*c*(c - 8)**2/7\nLet c(q) be the second derivative of -q**8/252 - 2*q**7/45 - q**6/9 - 255*q**2/2 - q + 17. ", "Let t(b) be the first derivative of c(b). ", "Factor t(v).", "\n-4*v**3*(v + 2)*(v + 5)/3\nLet f(b) be the first derivative of 2*b**3/3 + 38*b**2 - 430*b + 1722. ", "Factor f(t).", "\n2*(t - 5)*(t + 43)\nLet x = 148 - -57. ", "Factor -7*z - x - z**2 + 221 - 8*z.", "\n-(z - 1)*(z + 16)\nLet v = -62 + 172. ", "What is l in 27*l**3 - v*l**4 - 104*l**4 + 219*l**4 + 8*l**3 + 80*l**2 + 60*l = 0?", "\n-3, -2, 0\nLet j(d) be the third derivative of -7*d**7/195 + 3941*d**6/780 + 1132*d**5/195 + 27*d**4/13 - d**2 + 5*d + 1. ", "Find u, given that j(u) = 0.", "\n-2/7, 0, 81\nLet k(a) be the third derivative of a**5/45 + 8*a**4/9 + 40*a**3/3 - 6*a**2 - 5. ", "Factor k(u).", "\n4*(u + 6)*(u + 10)/3\nSuppose -4*p - 5*j = 2693 - 2718, -3*p + 3*j - 15 = 0. ", "Let -1/2*b**3 + p + 2/5*b**4 + 0*b + 1/5*b**2 - 1/10*b**5 = 0. ", "What is b?", "\n0, 1, 2\nSuppose -2*n - 10 = 3*d, 737*n + 5 = -d + 736*n. ", "Let m(s) be the second derivative of -3*s**3 - 1/10*s**5 + s**4 + 20*s + d*s**2 + 0. ", "Factor m(x).", "\n-2*x*(x - 3)**2\nLet g(d) be the first derivative of -d**4/16 + 83*d**3/3 - 6889*d**2/2 - 2831. ", "Find h, given that g(h) = 0.", "\n0, 166\nLet w(f) = -5*f**2 - 117*f + 146. ", "Let c(t) = -4*t**2 - 118*t + 142. ", "Let q(l) = 6*c(l) - 5*w(l). ", "Suppose q(z) = 0. ", "What is z?", "\n1, 122\nFind c, given that 3/4*c**4 - 5481/4*c**2 + 5487/4*c + 1821/4*c**3 - 915/2 = 0.", "\n-610, 1\nLet g be (-5)/(-2)*(-84)/(-100). ", "Let s = 13/5 - g. Determine y, given that 0*y**3 - 3/2*y**2 - y + 0 + s*y**4 = 0.", "\n-1, 0, 2\nFactor -217*s - 194*s - 1001*s - 238 - 74 - 36*s**2.", "\n-4*(s + 39)*(9*s + 2)\nLet -2/5*c**3 - 32*c**2 + 0 - 312/5*c = 0. ", "Calculate c.\n-78, -2, 0\nLet l(g) = -g**3 - 5*g**2 + 13*g - 5. ", "Let b be l(-7). ", "What is s in 8*s**3 - 4*s**2 + 7*s**3 + 0*s**2 + 6*s - s**b - 14*s**3 = 0?", "\n0, 2, 3\nLet i(m) be the third derivative of m**6/280 - 39*m**5/140 - 23*m**4/4 + 6*m**2 + 2*m - 30. ", "Find y, given that i(y) = 0.", "\n-7, 0, 46\nLet c be 84/39 - (-2)/(-13). ", "Solve 0*h**2 + 4*h**c + 2304 + 73*h + 119*h = 0 for h.\n-24\nLet l(r) be the third derivative of -r**6/45 + 47*r**5/15 - 23*r**4/6 - 140*r**3/9 + 1496*r**2. ", "Solve l(w) = 0.", "\n-1/2, 1, 70\nLet z(i) be the third derivative of i**7/840 + 11*i**6/80 + 6*i**5 + 108*i**4 + 15*i**2 - 151. ", "Suppose z(o) = 0. ", "What is o?", "\n-24, -18, 0\nLet p(g) = 5*g**3 + 71*g**2 - 56*g + 20. ", "Let c(f) = 2*f**3 + 2*f**2 + f + 5. ", "Let x(j) = 4*c(j) - p(j). ", "Factor x(k).", "\n3*k*(k - 20)*(k - 1)\nSuppose 0 = 2*b - h + 23 - 31, 0 = -4*b + 5*h + 10. ", "Let -2*v**3 + 10*v + 9*v**3 + 38*v**3 + 25*v**4 + 35*v**2 + 5*v**b = 0. ", "Calculate v.\n-2, -1, 0\nFactor 1388*m**2 - 1458*m + 1743*m**3 - 1742*m**3 - 1871*m**2.", "\nm*(m - 486)*(m + 3)\nFactor -1205/2 + 602*f + 1/2*f**2.", "\n(f - 1)*(f + 1205)/2\nSuppose 29/3*p**3 + 0 - 17/3*p**4 - p**5 + 5/3*p**2 - 14/3*p = 0. ", "Calculate p.\n-7, -2/3, 0, 1\nFactor 17/2*r**2 + 0 + 3/2*r**4 + 3*r + 7*r**3.", "\nr*(r + 1)*(r + 3)*(3*r + 2)/2\nLet l(f) be the second derivative of -432*f**2 - 1/18*f**4 + f + 12 + 8*f**3. ", "Factor l(i).", "\n-2*(i - 36)**2/3\nLet z be (-644)/(-276) - (-5 + 7). ", "What is p in -z*p**5 - 1/3*p - 4/3*p**2 + 0 - 4/3*p**4 - 2*p**3 = 0?", "\n-1, 0\nSuppose -4*s + 6*s - 40 = 0. ", "Let b be 2/(-8) + 85/s. Factor b*c**2 - 20 + 32*c + 24 + 60.", "\n4*(c + 4)**2\nLet 25*g**2 + 50 - 108*g + 61 + 7*g**2 - 35*g**2 = 0. ", "What is g?", "\n-37, 1\nLet u(w) be the second derivative of -w**4/20 - 42*w**3/5 + 528*w**2/5 - 2378*w. ", "Determine h, given that u(h) = 0.", "\n-88, 4\nSuppose -3*t - 22 = 3*c - 16, -3*c - 30 = -5*t. ", "Let n(p) be the second derivative of -1/3*p**4 + 0 + 2*p**t - 4*p**2 - 9*p. ", "Suppose n(v) = 0. ", "What is v?", "\n1, 2\nLet r(d) be the third derivative of -d**6/40 + 3*d**5/4 + 11*d**4 - 114*d**3 + 2*d**2 + 34*d + 18. ", "Determine o, given that r(o) = 0.", "\n-6, 2, 19\nLet o(t) = 14*t + 38. ", "Let d be o(-2). ", "Let x be 54/30*d/12*2. ", "Factor 3/4*w**2 - 1/2*w - 1/4*w**x + 0.", "\n-w*(w - 2)*(w - 1)/4\nLet g(r) be the third derivative of 2*r**7/735 - 6*r**6/35 + 533*r**5/420 - 227*r**4/56 + 48*r**3/7 + 587*r**2. ", "Suppose g(i) = 0. ", "Calculate i.\n1, 3/2, 32\nSuppose -15*a + 18*a = 231. ", "Find r, given that 6*r**2 + 5*r**3 + 550*r - 124*r**2 - a*r**2 - 114 - 246 = 0.", "\n1, 2, 36\nLet b = 721/20196 - -1/748. ", "Let k(r) be the first derivative of -1/6*r**4 + 0*r**2 - b*r**6 + 2/27*r**3 + 39 + 0*r + 2/15*r**5. ", "Solve k(q) = 0.", "\n0, 1\nLet q(u) be the first derivative of 7/2*u**2 - 1/330*u**5 + 5 + 0*u**4 + 0*u + 1/33*u**3. ", "Let w(s) be the second derivative of q(s). ", "Solve w(r) = 0.", "\n-1, 1\nLet i(h) be the third derivative of 2*h**7/105 - 19*h**6/6 + 187*h**5/15 - 31*h**4/2 - 152*h**2. ", "Factor i(t).", "\n4*t*(t - 93)*(t - 1)**2\nLet t = 1387136/117 + -106682/9. ", "Factor -2/13*j**2 - t + 16/13*j.", "\n-2*(j - 5)*(j - 3)/13\nLet m = 131 - 127. ", "Suppose 0*l - 17 = -2*q - 3*l, 4*l - 28 = -m*q. ", "Factor 7/3*i + 3*i**2 + 5/3*i**3 + 2/3 + 1/3*i**q.", "\n(i + 1)**3*(i + 2)/3\nFactor -14 + 41 - 11 - 72*i + 99 - 4*i**2 + 45.", "\n-4*(i - 2)*(i + 20)\nSuppose 3*k - 4*j = -146, k = -j - 17 - 20. ", "Let o be 1/(-3) - 2156/k. Factor o*u + 245*u**4 + 84*u + 545*u**2 + 630*u**3 + 20 + 45*u.", "\n5*(u + 1)**2*(7*u + 2)**2\nLet s(n) be the third derivative of -n**8/588 - 93*n**7/245 - 2267*n**6/420 - 876*n**5/35 - 524*n**4/21 - n**2 - 317*n - 1. ", "Let s(a) = 0. ", "What is a?", "\n-131, -4, -1/2, 0\nSuppose 43*w**3 - 123*w + 39*w**3 + 26 - 125*w**3 + 42*w**3 + 35 + 63*w**2 = 0. ", "Calculate w.\n1, 61\nLet v = -5002/21 - -748/3. ", "Let p = v - 227/21. ", "Find l, given that -p*l**2 + 2/3 + 1/3*l = 0.", "\n-1, 2\nSuppose 4*n + 3*a - 30 = 6*a, 24*a - 20*a = -40. ", "Factor -32/11 + 2/11*l**2 + n*l.", "\n2*(l - 4)*(l + 4)/11\nLet x = -8 - -2. ", "Let f = 8 + x. Solve 2*v + 0*v**f - v**3 + v**2 - 2*v**2 = 0.", "\n-2, 0, 1\nLet v(s) = -8*s**3 + 42*s**2 + 128*s + 93. ", "Let h(k) = -3*k**3 + 20*k**2 + 63*k + 46. ", "Let o(a) = 5*h(a) - 2*v(a). ", "Determine p, given that o(p) = 0.", "\n-11, -4, -1\nLet q be (-35)/(-45)*(-6)/(-14). ", "Let l(c) be the second derivative of 0 - 3/10*c**5 + 1/15*c**6 + q*c**4 + 0*c**2 + 2*c + 0*c**3. ", "Let l(b) = 0. ", "Calculate b.\n0, 1, 2\nLet y(q) be the third derivative of -q**9/5040 + q**7/420 - q**5/40 - 3*q**4/8 - q**3/3 + 64*q**2. ", "Let v(f) be the second derivative of y(f). ", "Factor v(n).", "\n-3*(n - 1)**2*(n + 1)**2\nLet u(k) = -k**3 + 4*k - 1. ", "Let p be u(-2). ", "Let a(l) = -6*l - 2. ", "Let w be a(p). ", "Factor 1 - 4*o**3 + 2*o**w - 5 + 4.", "\n2*o**3*(o - 2)\nLet " ]

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[ "Video Transcription\n\nWelcome. ", "I'm Trisha Fyfe. ", "And in today's video lesson, I will be instructing you on the topic of applying technology theories and models to instruction. ", "As we learn about this topic, we will work towards several learning objectives. ", "And together, we'll answer the following questions in this tutorial. ", "What is TPACK? ", "And how can TPACK be successfully applied to unit studies?", "\n\nIn this video lesson, we will go through the model of TPACK. ", "And throughout, we will be looking at examples of each separate domain and what you might see. ", "So what is TPACK? ", "Well, TPACK, remember, is the idea that teachers must look at the intersecting areas of all three domains, content knowledge, or CK, pedagogical knowledge, or PK, and technological knowledge, or TK.", "\n\nIt's here, the sweet spot that some call it, that we as teachers can use all three components and intertwine things together to create a great learning environment for our students. ", "You don't necessarily have to be in this area, depending on what your objectives are for your lesson. ", "So it's essential for you to look at your goals and objectives, and then decide which region will best work for you.", "\n\nSo let's go through each region of TPACK separately. ", "First, we'll start with content knowledge. ", "And content knowledge is focusing on what we are teaching, making sure that we are masters of our content and have a deep understanding and knowledge of content that we are teaching. ", "An example of this would be a teacher that delivers a lesson with accurate information on the topic and concepts of the lesson or unit, for example a US history teacher delivering a lesson on the Civil War that has great and deep knowledge of Civil War, and US history as a whole.", "\n\nLet's look at the next region. ", "Here we'll focus on pedagogical knowledge, or PK. ", "This is how students learn, and how we teach. ", "What are the best practices? ", "We also want to look at the application of theories of learning. ", "What's an example of this? ", "Well, this would be a teacher that uses intentional grouping strategies to group students into small groups.", "\n\nSo here, this teacher would know his or her class. ", "And they would intentionally group students into groups based on what they know and pedagogy for that particular group of students. ", "This would be different in elementary school than it would be in high school settings, for example.", "\n\nThe next region that we'll focus on is technological knowledge, or TK. ", "And it's here that we understand the wide range of tools available, both standard tools and advanced technologies. ", "We also want to make sure that we look at the skills and knowledge that it takes to use these technologies effectively.", "\n\nHere's an example of technological knowledge-- teaching students to use Google docs to record information and collaborate with group members. ", "This would be teaching your students how to use a tool, a technological tool, Google docs, to record information. ", "We would need to have, as a teacher, the skills and knowledge to use this technology, as well as the understanding of this tool and why we're using it.", "\n\nLet's look at the next three domains, some intersecting areas of this diagram. ", "First, we'll look at TPK, or technological pedagogical knowledge. ", "This is the intersection of technology and pedagogy, where we understand the application of technology tools for specific groups of students. ", "And we intentionally select tools based on our groups of students and the best practices.", "\n\nSome examples would be documentation tools for attendance and grades. ", "So as a teacher, we use these tools to document important information, but it's technology related. ", "Also, tech based strategies like, WebQuests, wikis, blogs, or discussion boards. ", "Let's look at the next domain here. ", "Now we'll look at TCK, or technological content knowledge. ", "And it's here that we understand the relationship between content and those tools, those technological tools.", "\n\nWe also want to make sure that we understand the ability to modify and manipulate with tools. ", "An example of this would be a virtual manipulative tool, such as the website GeoGebra to explore geometry in a visual, hands-on way. ", "The next intersecting area that we'll take a look at is PCK, pedagogical content knowledge. ", "And it's here that look at how to teach what we are teaching, so what are the best practices for teaching the content that we are teaching to our specific students.", "\n\nAn example would be using a collaborative workspace for students to connect to content, so for example, a discussion board, or having groups work on Google docs, where they can post information and then collaborate with each other and look at the information other group members posted. ", "You can use a blog to do this as well.", "\n\nLet's look at the center area here, the goal of this, that sweet spot of teaching. ", "And that is TPACK, technological pedagogical content knowledge. ", "And this is the ability to connect all three, intertwine all three of these-- pedagogy, content, and technology. ", "It's important to be purposeful when you make applications in each region. ", "So know which region you're teaching in based on your objectives and your goals for your units.", "\n\nLet's look at an example. ", "Students watch videos and complete homework before class. ", "This is an example of a flipped classroom. ", "And then in class the next day, groups are formed to discuss and research this information that they learned about individually at home the night before. ", "In groups, students will produce podcasts. ", "And they'll publish those to teach others about their findings.", "\n\nWe looked at the following two questions in this video lesson. ", "What is TPACK? ", "And how can TPACK be successfully applied to unit studies? ", "Remember, TPACK is that sweet spot where we combine and think about technological knowledge, pedagogical knowledge, and content knowledge. ", "And we want to intertwine all three when we are looking at using the domain of TPACK in our teaching.", "\n\nHow can this successfully be applied to our unit studies? ", "We talked about examples in each area of TPACK. ", "And remember, it's important to be intentional about the area that you are working in. ", "Look at your goals and objectives. ", "And then choose the appropriate area and strategies that would work in that area.", "\n\nNow that you have a better understanding of these ideas and examples, let's reflect. ", "What are the benefits of understanding TPACK and importance of technology integration in your unit studies? ", "Which of the TPACK domains do you feel the most comfortable within in your teaching?", "\n\nThanks for joining me today in discussing the lesson, applying technology theories and models to instruction. ", "I hope you found value in this video lesson and ideas we discussed together. ", "And I hope you're able to apply these ideas and concepts to your own teaching.", "\n\nAs you reflect on how this new information can be applied, you may want to explore the additional resources section that accompanies this video presentation. ", "This is where you'll find links to resources chosen to help you deepen your learning and explore ways to apply your newly acquired skills.", "\n\nNotes on “Applying Technology Theories and Models to Instruction”\n\nOverview\n\n(00:00- 00:33) Introduction/Objectives\n\n(00:34- 01:13) What is TPACK?", "\n\n(01:14- 01:45) CK and Instruction\n\n(01:46- 02:24) PK and Instruction\n\n(02:25- 03:10) TK and Instruction\n\n(03:11- 04:57) TPK, TCK, and PCK and Instruction\n\n(04:58- 05:48) TPACK and Instruction\n\n(05:49- 06:29) Recap\n\n(06:30- 07:17) Reflection\n\nAdditional Resources\n\nTPACK.org\n\nThis is the official website of the TPACK framework with resources for educators. ", "Educators can sign up for the TPACK academy for free to learn more about how to apply the framework into their instructional practices.http://www.tpack.org/\n\nTechnological Pedagogical Content Knowledge: A new framework for teacher knowledge\n\nThis is the article by Mishra and Koehler that established the TPCK framework and set the stage in a research base for the current TPACK framework. ", "On this site, you will find links to additional research articles on TPACK from Mishra and Koehler.http://punya.educ.msu.edu/2008/01/12/mishra-koehler-2006/\n\nRuben R. Puentedura's Weblog\n\nThis site offers articles, research, and resources for teachers on implementing both SAMR and TPACK. ", "In addition, Dr. Puentedura's SAMR model is explored in depth.http://www.hippasus.com/rrpweblog/" ]

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[ "---\nabstract: 'We study the structure of bounded linear functionals on a class of non-self-adjoint operator algebras that includes the multiplier algebra of every complete Nevanlinna-Pick space, and in particular the multiplier algebra of the Drury-Arveson space. ", "Our main result is a Lebesgue decomposition expressing every linear functional as the sum of an absolutely continuous (i.e. weak-[\\*]{} continuous) linear functional, and a singular linear functional that is far from being absolutely continuous. ", "This is a non-self-adjoint analogue of Takesaki’s decomposition theorem for linear functionals on von Neumann algebras. ", "We apply our decomposition theorem to prove that the predual of every algebra in this class is (strongly) unique.'", "\naddress:\n- 'School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario K1S 5B6, Canada'\n- 'Department of Mathematics and Statistics, University of Windsor, 401 Sunset Avenue, Windsor, Ontario N9B 3P4, Canada'\nauthor:\n- Matthew Kennedy\n- Dilian Yang\ntitle: 'A non-self-adjoint Lebesgue decomposition '\n---\n\n[^1]\n\nIntroduction\n============\n\nThe main result in this paper is a decomposition theorem for bounded linear functionals on a class of operator algebras that includes the multiplier algebra of every complete Nevanlinna-Pick space. ", "Results of this kind can be seen as a noncommutative generalization of the Yosida-Hewitt decomposition of a measure into completely additive and purely finitely additive parts, or more classically, the Lebesgue decomposition of a measure into absolutely continous and singular parts.", "\n\nTakesaki proved in [@Tak58] that a bounded linear functional on a von Neumann algebra can be decomposed uniquely into the sum of a normal (i.e. weak-[\\*]{} continuous) linear functional, and a singular linear functional that is far from being normal. ", "In [@And78], Ando proved a direct analogue of Takesaki’s decomposition theorem for linear functionals on the algebra $H^{\\infty}$, of bounded analytic functions on the complex unit disk $\\mathbb{D}$. More recently, in [@Ued09], Ueda proved a generalization of Ando’s result for finite maximal subdiagonal algebras, which are “analytic” subalgebras of finite von Neumann algebras introduced by Arveson in [@Arv67] as a noncommutative generalization of the algebra $H^{\\infty}$.\n\nA compelling case can be made that the natural function-theoretic generalization of $H^{\\infty}$ is the algebra $H_{d}^{\\infty}$ of multipliers on the Drury-Arveson space $H_{d}^{2}$. The algebra $H_{d}^{\\infty}$ is contained in the algebra $H^{\\infty}(\\mathbb{B}_{d})$ of bounded analytic functions on the complex unit ball $\\mathbb{B}_{d}$ of $\\mathbb{C}^{d}$, but for $d\\geq2$ this inclusion is proper, and $H_{d}^{\\infty}$ is seemingly much more tractable than $H^{\\infty}(\\mathbb{B}_{d})$ (see for example [@Arv98]) . ", "The Drury-Arveson space $H_{d}^{2}$ and the multiplier algebra $H_{d}^{\\infty}$ are universal in the following sense: Every irreducible complete Nevanlinna-Pick space embeds into $H_{d}^{2}$, and the corresponding multiplier algebra arises as the compression of $H_{d}^{\\infty}$ onto this embedding (see [@AM00] for details). ", "Examples of complete Nevanlinna-Pick spaces include the Hardy space and the Dirichlet space on the disk, the Drury-Arveson space itself, and more generally the class of Besov-Sobolev spaces on $\\mathbb{B}_{d}$.\n\nOne explanation for the tractability of $H_{d}^{\\infty}$ is the fact that $H_{d}^{\\infty}$ arises as a quotient of the noncommutative analytic Toeplitz algebra $F_{d}^{\\infty}$ (see for example [@DP98b] and [@AP00]). ", "This algebra, introduced by Popescu in [@Pop89], can be viewed as an algebra of noncommutative analytic functions acting by left multiplication on a Hardy space $\\Fd$ of noncommutative analytic functions. ", "The operator-algebraic structure of $\\Ld$, which is now well understood, turns out to be strikingly similar to that of $H^{\\infty}$ (see for example [@Pop89; @Pop95; @AP00] and [@DP98a; @DP98b; @DP99]).", "\n\nFor a weak-[\\*]{} closed two-sided ideal $\\mathcal{I}$ of $\\Ld$, we let $\\AI$ denote the algebra $\\AI=\\Ld/\\mathcal{I}$. These algebras are the main objects of interest in this paper, for the following reason: The multiplier algebra of every irreducible complete Nevanlinna-Pick space arises as the compression of $\\Ld$ to a coinvariant subspace, and this compression is completely isometrically isomorphic and weak-[\\*]{} to weak-[\\*]{} homeomorphic to a quotient of $\\Ld$ by a two-sided ideal (see [@DP98b; @AP00] for details).", "\n\nOur main result is the following decomposition theorem for linear functionals on quotients of $\\Ld$. A functional is said to be absolutely continuous if it is weak-[\\*]{} continuous, and singular if it is, roughly speaking, far from being weak-[\\*]{} continuous (we give a precise definition below).", "\n\n\\[Lebesgue decomposition for quotients of $F_d^\\infty$\\]Let $\\mathcal{I}$ be a weak-[\\*]{} closed two-sided ideal of $\\Ld$, and let $\\phi$ be a bounded linear functional on $\\AI$. Then there are unique linear functionals $\\phi_{a}$ and $\\phi_{s}$ on $\\AI$ such that $\\phi=\\phi_{a}+\\phi_{s}$, where $\\phi_{a}$ is absolutely continuous and $\\phi_{s}$ is singular, and such that $$\\|\\phi\\|\\leq\\|\\phi_{a}\\|+\\|\\phi_{s}\\|\\leq\\sqrt{2}\\|\\phi\\|.$$ If $d=1$, then the constant $\\sqrt{2}$ can be replaced with the constant $1$. Moreover, these constants are optimal.", "\n\nThe following result for multiplier algebras of complete Nevanlinna-Pick spaces is an immediate consequence of Theorem 1.1.", "\n\n\\[Lebesgue decomposition for multiplier algebras\\]Let $\\mathcal{A}$ be the multiplier algebra of a complete Nevanlinna-Pick space, and let $\\phi$ be a bounded linear functional on $\\mathcal{A}$. Then there are unique linear functionals $\\phi_{a}$ and $\\phi_{s}$ on $\\mathcal{A}$ such that $\\phi=\\phi_{a}+\\phi_{s}$, where $\\phi_{a}$ is absolutely continuous and $\\phi_{s}$ is singular, and such that $$\\|\\phi\\|\\leq\\|\\phi_{a}\\|+\\|\\phi_{s}\\|\\leq\\sqrt{2}\\|\\phi\\|.$$\n\nWe first prove that Theorem 1.1 holds for $\\Ld$. The proof for quotients of $\\Ld$ requires the following generalization of the classical F. & M. Riesz theorem, which is similar in spirit to the noncommutative F. & M. Riesz-type theorems proved by Exel in [@Exe90] for operator algebras with the Dirichlet property, and by Blecher and Labuschagne in [@BL07] for maximal subdiagonal algebras.", "\n\n\\[Extended F. & M. Riesz Theorem\\]Let $\\phi$ be a bounded linear functional on $\\Ld$, and let $\\phi=\\phi_{a}+\\phi_{s}$ be the Lebesgue decomposition of $\\phi$ into absolutely continuous and singular parts as in Theorem 1.1. ", "Let $\\mathcal{I}$ be a weak-[\\*]{} closed two-sided ideal of $\\Ld$. If $\\phi$ is zero on $\\mathcal{I}$, then $\\phi_{a}$ and $\\phi_{s}$ are both zero on $\\mathcal{I}$.\n\nGrothendieck proved in [@Gro55] that $L^{1}$ is the unique predual of $L^{\\infty}$ (up to isometric isomorphism). ", "Soon after, in [@Sak56], Sakai generalized Grothendieck’s result by proving that the predual of every von Neumann algebra is unique. ", "In fact, this latter result follows from the proof of Sakai’s characterization of von Neumann algebras as $\\mathrm{C}^{*}$-algebras which are dual spaces.", "\n\nThe uniqueness of the predual of a von Neumann algebra can also be proved using Takesaki’s decomposition theorem from [@Tak58] (see for example the proof of Corollary 3.9 of [@Tak02]). ", "A similar idea was used by Ando in [@And78], to prove the uniqueness of the predual of $H^{\\infty}$, and more recently, by Ueda in [@Ued09], to prove that the predual of every maximal subdiagonal algebra is unique.", "\n\nInspired by these results, we apply Theorem 1.3 to prove that the predual of every quotient $\\AI$ is (strongly) unique.", "\n\nLet $\\mathcal{I}$ be a weak-[\\*]{} closed two-sided ideal of $\\Ld$. Then the algebra $\\mathcal{A}_{\\mathcal{I}}$ has a strongly unique predual.", "\n\nIt follows immedately from Theorem 1.4 that the multiplier algebra of every complete Nevanlinna-Pick space has a unique predual.", "\n\nThe multiplier algebra of every complete Nevanlinna-Pick space has a strongly unique predual.", "\n\nIn particular, Corollary 1.5 implies that the multiplier algebra $H_{d}^{\\infty}$ on the Drury-Arveson space has a unique predual. ", "We believe this result is especially interesting in light of the fact that, for $d\\geq2$, the uniqueness of the predual of $H^{\\infty}(\\mathbb{B}_{d})$ is an open problem.", "\n\nIn addition to this introduction, this paper has five other sections. ", "In Section 2, we provide a brief review of the requisite background material. ", "In Section 3, we prove the Lebesgue decomposition for $\\Ld$, and give an example showing that the constant in the statement of the theorem is optimal. ", "In Section 4, we prove the extended F. & M. Riesz Theorem. ", "In Section 5, we prove the Lebesgue decomposition theorem for quotients of $\\Ld$, and hence for multiplier algebras of complete Nevanlinna-Pick spaces. ", "In Section 6, we use the Lebesgue decomposition theorem to prove that the predual of every quotient of $\\Ld$ is unique, and hence that the predual of the multiplier algebra of every complete Nevanlinna-Pick space is unique.", "\n\nPreliminaries\n=============\n\nThe noncommutative analytic Toeplitz algebra\n--------------------------------------------\n\nFor fixed $1\\leq d\\leq\\infty$, let $\\mathbb{C}\\langle Z\\rangle=\\mathbb{C}\\langle Z_{1},\\ldots,Z_{d}\\rangle$ denote the algebra of noncommutative polynomials in the variables $Z_{1},\\ldots,Z_{d}$. As a vector space, $\\mathbb{C}\\langle Z\\rangle$ is spanned by the set of monomials $$\\{Z_{w}=Z_{w_{1}}\\cdots Z_{w_{n}}\\mid w=w_{1}\\cdots w_{n}\\in\\mathbb{F}_{d}^{*},\\ n\\geq0\\},$$ where $\\mathbb{F}_{d}^{*}$ denotes the free semigroup generated by $\\{1,\\ldots,d\\}$. The noncommutative Hardy space $F_{d}^{2}$ is the Hilbert space obtained by completing $\\mathbb{C}\\langle Z\\rangle$ in the natural inner product $$\\langle Z_{w},Z_{w'}\\rangle=\\delta_{w,w'},\\quad w,w'\\in\\mathbb{F}_{d}^{*}.$$ Equivalently, $F_{d}^{2}$ is the Hilbert space consisting of noncommutative power series with square summable coefficients, $$F_{d}^{2}=\\left\\{ \\sum_{w\\in\\mathbb{F}_{d}^{*}}a_{w}Z_{w}\\mid\\sum_{w\\in\\mathbb{F}_{d}^{*}}|a_{w}|^{2}<\\infty\\right\\} .$$ We think of the elements of $F_{d}^{2}$ as noncommutative analytic functions.", "\n\nEvery element in $F_{d}^{2}$ gives rise to a multiplication operator on $F_{d}^{2}$ in the following way (note that in this noncommutative setting, it is necessary to specify whether multiplication occurs on the left or the right). ", "For $F$ in $\\Fd$, the left multiplication operator $L_{F}$ is defined by $$L_{F}G=FG,\\quad G\\in H_{d}^{2}.$$ The operator $L_{F}$ is not necessarily bounded in general, simply because the product of two elements in $F_{d}^{2}$ is not necessarily contained in $F_{d}^{2}$. However, it is always densely defined on $\\mathbb{C}\\langle Z\\rangle$.\n\nThe noncommutative analytic Toeplitz algebra $\\Ld$ is the noncommutative multiplier algebra of $\\Fd$. It consists precisely of the functions $F$ in $H_{d}^{2}$ such that the corresponding left multiplication operator is bounded, $$F_{d}^{\\infty}=\\{F\\in H_{d}^{2}\\mid FG\\in H_{d}^{2},\\ \\forall G\\in H_{d}^{2}\\}.$$ Equivalently, if we identity $F$ in $F_{d}^{\\infty}$ with the left multiplication operator $L_{F}$ on the Hilbert space $F_{d}^{2}$, then $F_{d}^{\\infty}$ is obtained as the closure of $\\mathbb{C}\\langle Z\\rangle$ in the weak-[\\*]{} topology on $\\mathcal{B}(F_{d}^{2})$. The noncommutative disk algebra $A_{d}$ is the closure of $\\mathbb{C}\\langle Z\\rangle$ in the norm topology. ", "Note that it is properly contained in $\\Ld$.\n\nThe algebras $\\Ad$ and $\\Ld$ were introduced by Popescu in [@Pop96] and [@Pop95] respectively. ", "For $d=1$, $F_{d}^{2}$ can be identified with the classical Hardy space $H^{2}$, $F_{d}^{\\infty}$ can be identified with the classical algebra of bounded analytic functions, and $A_{d}$ can be identified with the classical disk algebra of functions that are analytic on $\\mathbb{D}$ with continuous extensions to the boundary.", "\n\nThe structure of an isometric tuple\n-----------------------------------\n\nLet $V=\\left(V_{1},\\ldots,V_{d}\\right)$ be an isometric tuple. ", "Then\n\n1. ", " $V$ is a *unilateral shift* if it is unitarily equivalent to a multiple of $L_{Z}=(L_{Z_{1}},\\ldots,L_{Z_{d}})$,\n\n2. ", " $V$ is *absolutely continuous* if the unital weak operator closed algebra $\\mathrm{W}(V_{1},\\ldots,V_{d})$ generated by $V_{1},\\ldots,V_{d}$ is algebraically isomorphic to the noncommutative analytic Toeplitz algebra $\\Ld$,\n\n3. ", " $V$ is *singular* if the weakly closed algebra $\\mathrm{W}\\left(V_{1},\\ldots,V_{d}\\right)$ is a von Neumann algebra, and\n\n4. ", " $V$ is of *dilation type* if it has no summand that is absolutely continuous or singular.", "\n\nThe next result is from [@Ken12].", "\n\n\\[Lebesgue-von Neumann-Wold Decomposition\\]\\[thm:leb-vn-wold-decomp\\]Let $V=\\left(V_{1},\\ldots,V_{d}\\right)$ be an isometric $d$-tuple. ", "Then $V$ can be decomposed as $$V=V_{u}\\oplus V_{a}\\oplus V_{s}\\oplus V_{d},$$ where $V_{u}$ is a unilateral $d$-shift, $V_{a}$ is an absolutely continuous unitary $d$-tuple, $V_{s}$ is a singular unitary $d$-tuple and $V_{d}$ is a unitary $d$-tuple of dilation type.", "\n\nThe next result is from [@DKP01].", "\n\n\\[Structure Theorem for Free Semigroup Algebras\\]\\[thm:fsa-struct-thm\\]Let $V=\\left(V_{1},\\ldots,V_{d}\\right)$ be an isometric $d$-tuple, and let $\\mathcal{V}=\\mathrm{W}(V_{1},\\ldots,V_{d})$ denote the unital weak operator closed algebra generated by $V_{1},\\ldots,V_{d}$. Then there is a maximal projection $P$ in $\\mathcal{V}$ with the range of $P$ coinvariant for $\\mathcal{V}$ such that\n\n1. ", " 2. ", " if $P^{\\perp}\\ne0$, then the restriction of $\\mathcal{V}$ to the range of $P^{\\perp}$ is an analytic free semigroup algebra,\n\n3. ", " the compression of $\\mathcal{V}$ to the range of $P$ is a von Neumann algebra, and\n\n4. ", " $\\mathcal{V}=P^{\\perp}\\mathcal{V}P^{\\perp}+\\mathrm{W}^{*}(V)P.$\n\nLet $V=V_{u}\\oplus V_{a}\\oplus V_{s}\\oplus V_{d}$ be the Lebesgue-von Neumann-Wold decomposition of an isometric tuple $V$, as in Theorem \\[thm:leb-vn-wold-decomp\\], where $V_{u}$ is a unilateral $n$-shift, $V_{a}$ is an absolutely continuous unitary $n$-tuple, $V_{s}$ is a singular unitary $n$-tuple and $V_{d}$ is a unitary $n$-tuple of dilation type. ", "Suppose that $V$ is defined on a Hilbert space $H$, and let $H=H_{u}\\oplus H_{a}\\oplus H_{s}\\oplus H_{d}$ denote the corresponding decomposition of $H$. By Corollary 2.7 of [@DKP01], there is a maximal invariant subspace $K$ for $V_{d}$ such that the restriction of $V_{d}$ to $K$ is analytic. ", "The projection $P$ in Theorem \\[thm:fsa-struct-thm\\] is determined by $P^{\\perp}=P_{H_{u}}\\oplus P_{H_{a}}\\oplus P_{K}$.\n\n\\[rem:proj-reducing-dim-1\\]For $d=1$, an isometry is the direct sum of a unilateral shift, an absolutely continuous unitary and a singular unitary. ", "Theorem \\[thm:fsa-struct-thm\\] implies that, in this case, the structure projection $P$ is the projection onto the singular unitary part. ", "In particular, this implies that $P$ is reducing. ", "For $d\\geq2$, the proof of Theorem 3.3 shows that $P$ is reducing if and only if there is no summand of dilation type.", "\n\nThe universal representation\\[sub:universal-rep\\]\n-------------------------------------------------\n\nWe require the universal representation $\\pi_{u}:\\Ld\\to\\mathcal{B}(H_{u})$ of $\\Ld$. This can be constructed as in 2.4.4 of [@BL05], as the restriction of the universal representation of $\\mathrm{C}_{\\mathrm{max}}^{*}(\\Ld)$. By 3.2.12 of [@BL05], we can identify the double dual $(\\Ld)^{**}$ of $\\Ld$ with the algebra obtained as the weak-[\\*]{} closure of $\\pi_{u}(\\Ld)$. We will require the operator algebra structure on $\\Ldd$ provided by this identification. ", "By replacing $\\pi_{u}$ by $\\pi_{u}^{(\\infty)}$ if necessary, we can suppose that $\\pi_{u}$ has infinite multiplicity, and hence that the weak operator topology coincides with the weak-[\\*]{} topology on $\\Ldd$.\n\nLet $\\phi$ be a bounded linear functional on $\\Ld$. By the Hahn-Banach Theorem, we can extend $\\phi$ to a functional on $\\mathrm{C}_{\\mathrm{max}}^{*}(\\Ld)$ with the same norm. ", "Hence by the construction of the universal representation of $\\mathrm{C}_{\\mathrm{max}}^{*}(\\Ld)$, there are vectors $x$ and $y$ in $H_{u}$ with $\\|x\\|\\|y\\|=\\|\\phi\\|$ such that $$\\phi(A)=\\langle\\pi_{u}(A)x,y\\rangle,\\quad\\forall A\\in\\Ld.$$ If we identify $\\Ld$ with its image $\\pi_{u}(\\Ld)$ in $(\\Ld)^{**}$, then the functional $\\phi$ has a unique weak-[\\*]{} continuous extension to a functional on $(\\Ld)^{**}$ with the same norm. ", "We will use this fact repeatedly.", "\n\nSince $\\pi_{u}$ is the restriction of a [\\*]{}-homomorphism of $\\mathrm{C}_{\\mathrm{max}}^{*}(\\Ld)$, and since the $d$-tuple $(L_{Z_{1}},\\ldots,L_{Z_{d}})$ is isometric, it follows that the $d$-tuple $(\\pi_{u}(L_{Z_{1}}),\\ldots,\\pi_{u}(L_{Z_{d}}))$ is also isometric. ", "Since $(\\Ld)^{**}$ contains $\\pi_{u}(A_{d})$, it necessarily contains the weak operator closed algebra generated by $(\\pi_{u}(L_{Z_{1}}),\\ldots,\\pi_{u}(L_{Z_{d}}))$. Let $P_{u}$ denote the projection in $(\\Ld)^{**}$ guaranteed by Theorem \\[thm:fsa-struct-thm\\]. ", "We will refer to $P_{u}$ as the universal structure projection in $\\Ldd$.\n\nLet $\\mathcal{S}$ denote the unital weak operator closed algebra generated by $\\pi_{u}(L_{Z_{1}}),\\ldots,\\pi_{u}(L_{Z_{d}})$. From above we have $\\mathcal{S}\\subseteq(\\Ld)^{**}$, and one might guess that $\\mathcal{S}=(\\Ld)^{**}$. However, this is not the case. ", "Indeed, let $\\phi$ be a bounded nonzero functional on $\\Ld$ that is zero on the noncommutative disk algebra $\\Ad$. Then as above, there are vectors $x$ and $y$ in $H_{u}$ such that $$\\phi(A)=\\langle\\pi_{u}(A)x,y\\rangle,\\quad\\forall A\\in\\Ld.$$ Let $\\psi$ denote the weak operator continuous functional on $\\mathcal{S}$ defined by $$\\psi(S)=\\langle Sx,y\\rangle,\\quad\\forall S\\in\\mathcal{S}.$$ Since $\\phi$ is zero on $A_{d}$, $\\psi$ must be zero on $\\pi_{u}(A_{d}).$ Then, since $\\pi_{u}(A_{d})$ is weak operator dense in $\\mathcal{S}$, it follows that $\\psi(S)=\\langle Sx,y\\rangle=0$ for all $S$ in $\\mathcal{S}$. But, by assumption, there is $A$ in $\\Ld$ such that $\\phi(A)=\\langle\\pi_{u}(A)x,y\\rangle\\ne0$. So we see that $\\pi_{u}(A)\\notin\\mathcal{S}$, and hence that the inclusion $\\mathcal{S}\\subseteq(\\Ld)^{**}$ is proper.", "\n\nThe Lebesgue decomposition\n==========================\n\nIn this section, we introduce the definitions of absolutely continuous and singular linear functionals on the noncommutative analytic Toeplitz algebra $\\Ld$, and establish the first version of the Lebesgue decomposition. ", "In [@DLP05], Davidson, Li and Pitts proved a Lebesgue-type decomposition for functionals on the noncommutative disk algebra $\\Ad$. Although the algebra $\\Ld$ is bigger than $\\Ad$, the next definitions is closely related to (and directly inspired by) the corresponding definition for $\\Ad$.\n\n\\[def:abs-cont-and-sing\\]Let $\\phi$ be a bounded linear functional on $\\Ld$. Then\n\n1. ", " $\\phi$ is *absolutely continuous* if it is weak-[\\*]{} continuous, and\n\n2. ", " $\\phi$ is *singular* if $\\|\\phi\\|=\\|\\phi^{k}\\|$ for every $k\\geq1$, where $\\phi^{k}$ denotes the restriction of $\\phi$ to the ideal of $\\Ld$ generated by $\\{L_{Z_{w}}\\mid|w|=k\\}.$\n\nLet $\\phi$ be a bounded linear functional on $\\Ld$. Then as in Section \\[sub:universal-rep\\], there are vectors $x$ and $y$ in $H_{u}$ with $\\|x\\|\\|y\\|=\\|\\phi\\|$ such that $$\\phi(A)=\\langle\\pi_{u}(A)x,y\\rangle,\\quad\\forall A\\in\\Ld.$$ We will write $\\phi P_{u}$ and $\\phi P_{u}^{\\perp}$ for the linear functionals defined on $\\Ld$ by $$\\begin{gathered}\n(\\phi P_{u})(A)=\\langle\\pi_{u}(A)P_{u}x,y\\rangle,\\quad\\forall A\\in\\Ld,\\\\\n(\\phi P_{u}^{\\perp})(A)=\\langle\\pi_{u}(A)P_{u}^{\\perp}x,y\\rangle,\\quad\\forall A\\in\\Ld,\\end{gathered}$$ where $P_{u}$ denotes the universal structure projection from Section \\[sub:universal-rep\\]. ", "The purpose of the next result is to verify that $\\phi P_{u}$ and $\\phi P_{u}^{\\perp}$ are well defined.", "\n\nLet $\\phi$ be a bounded linear functional on $\\Ld$. Then the functionals $\\phi P_{u}$ and $\\phi P_{u}^{\\perp}$, as defined above, do not depend on the choice of vectors $x$ and $y$.\n\nLet $x_{1},y_{1}$ and $x_{2},y_{2}$ be pairs of vectors in $H_{u}$ such that $$\\langle\\pi_{u}(A)x_{1},y_{1}\\rangle=\\langle\\pi_{u}(A)x_{2},y_{2}\\rangle,\\quad\\forall A\\in\\Ld.$$ Since $\\pi_{u}(\\Ld)$ is weak-[\\*]{} dense in the algebra $(\\Ld)^{**}$, which contains $P_{u}$, it follows immediately that $$\\langle\\pi_{u}(A)P_{u}x_{1},y_{1}\\rangle=\\langle\\pi_{u}(A)P_{u}x_{2},y_{2}\\rangle,\\quad\\forall A\\in\\Ld,$$ and similarly that $$\\langle\\pi_{u}(A)P_{u}^{\\perp}x_{1},y_{1}\\rangle=\\langle\\pi_{u}(A)P_{u}^{\\perp}x_{2},y_{2}\\rangle,\\quad\\forall A\\in\\Ld.$$\n\n\\[prop:char-singular\\]A bounded functional $\\phi$ on $\\Ld$ is singular if and only if $\\phi=\\phi P_{u}$.\n\nLet $\\phi$ be a singular functional on $\\Ld$. We can assume that $\\|\\phi\\|=1$. As in Section \\[sub:universal-rep\\], there are vectors $x$ and $y$ in $H_{u}$ such that $\\|x\\|\\|y\\|=1$ and $$\\phi(A)=\\langle\\pi_{u}(A)x,y\\rangle,\\quad\\forall A\\in\\Ld.$$ By the singularity of $\\phi$, we can find a sequence $(A_{k})$ of elements in $\\Ld$ such that $\\lim\\phi(A_{k})\\to1$, and such that each $A_{k}$ belongs to the unit ball of $(F_{d,0}^{\\infty})^{k}=\\sum_{|w|=k}\\Ld L_{Z_{w}}$. Let $T$ be an accumulation point of the sequence $(\\pi_{u}(A_{k}))$ in $\\Ldd$, and let $\\mathcal{S}$ denote the unital weak operator closed algebra generated by $(\\pi_{u}(L_{Z_{1}}),\\ldots,\\pi_{u}(L_{Z_{d}}))$. It is clear that the weak-[\\*]{} closure of the image $\\pi_{u}((F_{d,0}^{\\infty})^{k})$ of the ideal $(F_{d,0}^{\\infty})^{k}$ can be written as $\\Ldd\\mathcal{S}_{0}^{k}$, where $\\mathcal{S}_{0}$ denotes the ideal in $\\mathcal{S}$ generated by $\\pi_{u}(L_{Z_{1}}),\\ldots,\\pi_{u}(L_{Z_{d}})$. Thus $\\pi_{u}(A_{k})$ belongs to $\\Ldd\\mathcal{S}_{0}^{k}$. By Theorem \\[thm:fsa-struct-thm\\], $\\mathcal{S}P_{u}=\\cap_{k\\geq1}\\mathcal{S}_{0}^{k}$. Hence $T$ belongs to the unit ball of\n\n$$\\bigcap_{k\\ge1}\\Ldd\\mathcal{S}_{0}^{k}=\\Ldd\\bigcap_{k\\ge1}\\mathcal{S}_{0}^{k}=\\Ldd P_{u}.$$ In particular, this means that $T=TP_{u}$. Since $\\phi(T)=1$, this gives $$\\|x\\|\\|y\\|=1=\\langle Tx,y\\rangle=\\langle TP_{u}x,y\\rangle\\leq\\|P_{u}x\\|\\|y\\|\\leq\\|x\\|\\|y\\|.$$ Hence $P_{u}x=x$, and it follows that $\\phi=\\phi P_{u}$.\n\nConversely, let $\\phi$ be a functional on $\\Ld$ such that $\\phi=\\phi P_{u}$. As before, we can assume that $\\|\\phi\\|=1$, and there are vectors $x$ and $y$ in $H_{u}$ such that $\\|x\\|\\|y\\|=1$ and $$\\phi(A)=\\langle\\pi_{u}(A)x,y\\rangle,\\quad\\forall A\\in\\Ld.$$ The fact that $\\phi P_{u}=\\phi$ implies that we can choose $x$ satisfying $x=P_{u}x$, and hence that $$\\phi(A)=\\langle\\pi_{u}(A)P_{u}x,y\\rangle,\\quad\\forall A\\in\\Ld.$$ Let $\\psi$ denote the functional on $\\Ldd$ defined by $$\\psi(T)=\\langle TP_{u}x,y\\rangle,\\quad\\forall T\\in\\Ldd,$$ and for $k\\geq1$, let $\\psi^{k}$ denote the restriction of $\\psi$ to $\\Ldd\\mathcal{S}_{0}^{k}$. Then as above, $$\\Ldd P_{u}=\\bigcap_{k\\ge1}\\Ldd\\mathcal{S}_{0}^{k}.$$ Hence $\\|\\psi\\|=\\|\\psi^{k}\\|$ for every $k\\geq1$. It follows that $\\|\\phi\\|=\\|\\phi^{k}\\|$, where $\\phi^{k}$ is defined as in Definition \\[def:abs-cont-and-sing\\], and hence that $\\phi$ is singular.", "\n\n\\[lem:range-proj\\]The range of the projection $P_{u}^{\\perp}$ is invariant for $\\Ldd$.\n\nIt suffices to show that whenever $x$ and $y$ are vectors in $\\Fd$ such that $x=P_{u}^{\\perp}x$ and $y=P_{u}y$, and the functional $\\phi$ on $\\Ld$ is defined by $$\\phi(A)=\\langle\\pi_{u}(A)x,y\\rangle,\\quad\\forall A\\in\\Ld,$$ then $\\phi=0$. By Theorem \\[thm:fsa-struct-thm\\], the range of $P_{u}^{\\perp}$ is invariant for $\\pi_{u}(A_{d})$. Hence $\\phi$ is zero on $\\Ad$. Let $A$ be an element of $\\Ld$. By Corollary 2.6 of [@DP98a], for $k\\geq1$, we can write A uniquely as $$A=\\sum_{|w|<k}a_{w}L_{Z_{w}}+A',$$ where $A'$ belongs to $(F_{d,0}^{\\infty})^{k}$. The fact that $\\phi$ is zero on $\\Ad$ implies that $\\phi(A)=\\phi(A')$. It follows from Definition \\[def:abs-cont-and-sing\\] that $\\phi$ is singular. ", "Hence by Proposition \\[prop:char-singular\\], $\\phi=\\phi P_{u}$, i.e. $$\\phi(A)=\\langle\\pi_{u}(A)P_{u}x,y\\rangle,\\quad\\forall A\\in\\Ld.$$ Since $x=P_{u}^{\\perp}x$, it follows that $\\phi=0$, as required.", "\n\n\\[prop:char-abs-cont\\]Let $\\phi$ be a bounded linear functional on $\\Ld$. Then $\\phi$ is absolutely continuous if and only if $\\phi=\\phi P_{u}^{\\perp}$.\n\nSuppose first that $\\phi$ is absolutely continuous. ", "Then it is weak-[\\*]{} continuous, so there are sequences of vectors $(x_{k})$ and $(y_{k})$ in $\\Fd$ such that $$\\phi(A)=\\sum\\langle Ax_{k},y_{k}\\rangle,\\quad\\forall A\\in\\Ld.$$ Since the $d$-tuple $(L_{Z_{1}},\\ldots,L_{Z_{d}})$ is equivalent to a restriction of the unilateral shift part of the $d$-tuple $(\\pi_{u}(L_{Z_{1}}),\\ldots,\\pi_{u}(L_{Z_{d}}))$, $F_{d}^{2}$ can be identified with a subspace of $H_{u}$, and it follows that $\\phi=\\phi P_{u}^{\\perp}$.\n\nConversely, suppose that $\\phi=\\phi P_{u}^{\\perp}$. As in Section \\[sub:universal-rep\\], there are vectors $x$ and $y$ in $H_{u}$ with $\\|x\\|\\|y\\|=\\|\\phi\\|$ such that $$\\phi(A)=\\langle\\pi_{u}(A)x,y\\rangle,\\quad\\forall A\\in\\Ld.$$ The fact that $\\phi=\\phi P_{u}^{\\perp}$ implies that we can choose $x$ satisfying $P_{u}^{\\perp}x=x$. Since, by Lemma \\[lem:range-proj\\], the range of $P_{u}^{\\perp}$ is invariant for $\\pi_{u}(\\Ld)$, it follows that for every $A$ in $\\Ld$, we have $$\\phi(A)=\\langle\\pi_{u}(A)x,y\\rangle=\\langle P_{u}^{\\perp}\\pi_{u}(A)P_{u}^{\\perp}x,y\\rangle=\\langle\\pi_{u}(A)P_{u}^{\\perp}x,P_{u}^{\\perp}y\\rangle.$$ Hence we can also choose $y$ satisfying $P_{u}^{\\perp}y=y$.\n\nBy the construction of $P_{u}$, the restriction of the operators $\\pi_{u}(L_{Z_{1}}),\\ldots,\\pi_{u}(L_{Z_{d}})$ to the cyclic subspace generated by $x$ and $y$ is analytic. ", "Thus, by the main result of [@Ken12], the weak-[\\*]{} closed algebra generated by this restriction is completely isometrically isomorphic and weak-[\\*]{} to weak-[\\*]{} homeomorphic to $\\Ld$. It follows that $\\phi$ is weak-[\\*]{} continuous on $\\Ld$.\n\n\\[Lebesgue Decomposition for $F_d^\\infty$\\]\\[thm:lebesgue-decomp\\]Let $\\phi$ be a bounded linear functional on $\\Ld$. Then there are unique linear functionals $\\phi_{a}$ and $\\phi_{s}$ on $\\Ld$ such that $\\phi=\\phi_{a}+\\phi_{s}$, where $\\phi_{a}$ is absolutely continuous and $\\phi_{s}$ is singular, and such that $$\\|\\phi\\|\\leq\\|\\phi_{a}\\|+\\|\\phi_{s}\\|\\leq\\sqrt{2}\\|\\phi\\|.$$ If $d=1$, then the constant $\\sqrt{2}$ can be replaced with the constant $1$.\n\nAs in Section \\[sub:universal-rep\\], there are vectors $x$ and $y$ in $H_{u}$ such that $\\|x\\|\\|y\\|=\\|\\phi\\|$ and $$\\phi(A)=\\langle\\pi_{u}(A)x,y\\rangle,\\quad\\forall A\\in\\Ld.$$ Define $\\phi_{a}$ and $\\phi_{s}$ by $\\phi_{a}=\\phi P_{u}^{\\perp}$ and $\\phi_{s}=\\phi P_{u}$ respectively. ", "Then $\\phi_{a}$ is absolutely continuous by Proposition \\[prop:char-abs-cont\\], and $\\phi_{s}$ is singular by Proposition \\[prop:char-singular\\]. ", "We clearly have $\\phi=\\phi_{a}+\\phi_{s}$. To see that $\\phi_{a}$ and $\\phi_{s}$ are unique, suppose that $$\\phi_{a}+\\phi_{s}=\\psi_{a}+\\psi_{s},$$ where $\\psi_{a}$ is absolutely continuous and $\\psi_{s}$ is absolutely continuous. ", "Then $$\\phi_{a}-\\psi_{a}=\\psi_{s}-\\phi_{s}.$$ It is clear that the functional $\\phi_{a}-\\psi_{a}$ is absolutely continuous, and Proposition \\[prop:char-singular\\] implies that the functional $\\psi_{s}-\\phi_{s}$ is singular. ", "Applying Proposition \\[prop:char-abs-cont\\] and Proposition \\[prop:char-singular\\] again, we can therefore write $$\\phi_{a}-\\psi_{a}=(\\phi_{a}-\\psi_{a})P_{u}^{\\perp}=(\\psi_{s}-\\phi_{s})P_{u}^{\\perp}=(\\psi_{s}-\\phi_{s})P_{u}P_{u}^{\\perp}=0.$$ Hence $\\phi_{a}=\\psi_{a}$, and it follows similarly that $\\phi_{s}=\\psi_{s}$. Finally, we compute $$\\|\\phi\\|\\leq\\|\\phi_{a}\\|+\\|\\phi_{s}\\|\\leq\\|Px\\|\\|y\\|+\\|P^{\\perp}x\\|\\|y\\|\\leq\\sqrt{2}\\|x\\|\\|y\\|=\\sqrt{2}\\|\\phi\\|.$$ If $d=1$, then Remark \\[rem:proj-reducing-dim-1\\] implies that $\\Ldd$ is the direct sum of two algebras reduced by $P_{u}$. If we identify $\\Ld$ with its image in $\\Ldd$, then the functionals $\\phi$, $\\phi_{a}$ and $\\phi_{s}$ extend uniquely to weak-[\\*]{} continuous functionals on $\\Ldd$ with the same norm. ", "Since $\\phi_{a}=\\phi_{a}P_{u}^{\\perp}$ and $\\phi_{s}=\\phi_{s}P_{u}$, it follows that in this case, $\\|\\phi\\|=\\|\\phi_{a}\\|+\\|\\phi_{s}\\|$.\n\nThe next example is based on Example 5.10 from [@DLP05]. ", "It establishes that for $d\\geq2$, the constant $\\sqrt{2}$ in the statement of Theorem \\[thm:lebesgue-decomp\\] is the best possible.", "\n\n\\[ex:constant\\]Define $\\phi$ on $\\mathbb{C}\\langle Z\\rangle$ by setting $$\\phi(L_{Z_{w}})=\\begin{cases}\n1/\\sqrt{2} & \\mbox{if}\\ w=\\varnothing\\ \\mbox{or}\\ w=21^{n}\\ \\mbox{for}\\ n\\geq0,\\\\\n0 & \\mbox{otherwise},\n\\end{cases}$$ and extending by linearity. ", "We will first show that $\\phi$ extends to a bounded linear functional on the noncommutative disk algebra $A_{2}$. Let $\\mathcal{H}_{\\phi}$ denote the Hilbert space $\\mathbb{C}e\\oplus F_{2}^{2}$, and define a $2$-tuple $S=(S_{1},S_{2})$ on $\\mathcal{H}_{\\phi}$ by setting $$S_{1}=\\left(\\begin{array}{cc}\nI & 0\\\\\n0 & L_{1}\n\\end{array}\\right),\\quad S_{2}=\\left(\\begin{array}{cc}\n0 & 0\\\\\n\\xi_{\\varnothing}e^{*} & L_{2}\n\\end{array}\\right).$$ It is easy to check that $S$ is isometric. ", "By the universal property of the noncommutative disk algebra, we obtain a completely isometric representation $\\pi_{\\phi}$ of $A_{2}$ satisfying\n\n$$\\pi_{\\phi}(L_{Z_{w}})=S_{w_{1}}\\cdots S_{w_{n}},\\quad w=w_{1}\\cdots w_{n}\\in\\mathbb{F}_{d}^{*},$$ and we can extend $\\phi$ to $A_{2}$ by $$\\phi(A)=\\langle\\pi_{\\phi}(A)(e+\\xi_{\\varnothing})/\\sqrt{2},\\xi_{\\varnothing}\\rangle,\\quad A\\in A_{2}.$$ From this, it is easy to check that $\\|\\phi\\|\\leq1$.\n\nLet $\\mathcal{S}$ denote the unital weakly closed algebra generated by $S_{1}$ and $S_{2}$. The structure projection from Theorem \\[thm:fsa-struct-thm\\] is the projection $P$ onto $\\mathbb{C}e$, which is contained in $\\mathcal{S}$. Hence $\\mathcal{S}$ contains the element $B=(S_{2}P+P^{\\perp})/\\sqrt{2}$ . ", "The results of [@Ken11] imply that Theorem 5.4 of [@DLP05] apply to the unital weak operator closed algebra generated by any isometric tuple. ", "Thus there is a net $(B_{\\lambda})$ of elements in the unit ball of $A_{d}$ such that $\\operatorname{w^{*}-lim}\\pi_{\\phi}(B_{\\lambda})=B$ in $\\mathcal{S}$. It is easy to check that $\\|B\\|=1$ and $\\langle B(e+\\xi_{\\varnothing})/\\sqrt{2},\\xi_{\\varnothing}\\rangle=1$, so it follows that $\\|\\phi\\|=1$.\n\nBy the Hahn-Banach theorem, we can extend $\\phi$ to a functional on $\\Ld$ with the same norm, which we continue to denote by $\\phi$. Let $\\phi=\\phi_{a}+\\phi_{s}$ be the Lebesgue decomposition of $\\phi$ into absolutely continuous and singular parts as in Theorem \\[thm:lebesgue-decomp\\]. ", "Then restricted to $A_{d}$, we can write $$\\begin{gathered}\n\\phi_{a}(A)=(\\phi P^{\\perp})(A)=\\langle\\pi(A)\\xi_{\\varnothing}/\\sqrt{2},\\xi_{\\varnothing}\\rangle,\\quad A\\in A_{2},\\\\\n\\phi_{s}(A)=(\\phi P)(A)=\\langle\\pi(A)e/\\sqrt{2},\\xi_{\\varnothing}\\rangle,\\quad A\\in A_{2}.\\end{gathered}$$ Letting $B$ be as above, an easy computation gives $$\\langle B\\xi_{\\varnothing}/\\sqrt{2},\\xi_{\\varnothing}\\rangle=\\langle Be/\\sqrt{2},\\xi_{\\varnothing}\\rangle=1/\\sqrt{2}.$$ Arguing as before, this implies $\\|\\phi_{a}\\|\\geq1/\\sqrt{2}$ and $\\|\\phi_{s}\\|\\geq1/\\sqrt{2}$. By Theorem \\[thm:lebesgue-decomp\\], it follows that $\\|\\phi_{a}\\|+\\|\\phi_{s}\\|=\\sqrt{2}\\|\\phi\\|.$\n\nThe extended F. & M. Riesz theorem\n==================================\n\nThe results in this section can be viewed as noncommutative generalizations of the classical results referred to as the F. & M. Riesz theorem. ", "As mentioned in the introduction, results of this kind have been established in different settings by Exel in [@Exe90], and by Blecher and Labuschagne in [@BL07]. ", "In fact, Blecher and Labuschagne seem to have anticipated that an F. & M. Riesz-type theorem should hold for $\\Ld$ (see the introduction of [@BL07]).", "\n\n\\[Extended F. & M. Riesz Theorem\\]\\[thm:ann-ideals\\]Let $\\phi$ be a bounded linear functional on $\\Ld$, and let $\\phi=\\phi_{a}+\\phi_{s}$ be the Lebesgue decomposition of $\\phi$ into absolutely continuous and singular parts as in Theorem \\[thm:lebesgue-decomp\\]. ", "Let $\\mathcal{I}$ be a two-sided ideal of $\\Ld$. If $\\phi$ is zero on $\\mathcal{I}$, then $\\phi_{a}$ and $\\phi_{s}$ are both zero on $\\mathcal{I}$.\n\nAs in Section \\[sub:universal-rep\\], there are vectors $x$ and $y$ in $H_{u}$ such that $$\\phi(A)=\\langle\\pi_{u}(A)x,y\\rangle,\\quad\\forall A\\in\\Ld.$$ By Proposition \\[prop:char-abs-cont\\] we can write $\\phi_{a}=\\phi P_{u}^{\\perp}$, and by Proposition \\[prop:char-singular\\] we can write $\\phi_{s}=\\phi P_{u}$. If we identify $\\Ld$ with its image $\\pi_{u}(\\Ld)$ in $\\Ldd$, then the functionals $\\phi$, $\\phi_{a}$ and $\\phi_{s}$ each have unique weak-[\\*]{} continuous extensions to functionals on $\\Ldd$ with the same norm.", "\n\nLet $\\mathcal{J}$ denote the ideal in $\\Ldd$ obtained by taking the weak-[\\*]{} closure of $\\pi_{u}(\\mathcal{I})$. Since $\\phi$ is zero on $\\mathcal{I}$, it is zero on $\\mathcal{J}$. For $A$ in $\\mathcal{I}$, $\\pi_{u}(A)P_{u}^{\\perp}$ belongs to $\\mathcal{J}$, which implies $$0=(\\phi P_{u}^{\\perp})(A)=\\phi_{a}(A).$$ Hence $\\phi_{a}$ is zero on $\\mathcal{I}$, and it follows immediately that $\\phi_{s}$ is also zero on $\\mathcal{I}$.\n\n\\[F. & M. Riesz Theorem\\]\\[cor:fmriesz\\]Let $\\phi$ be a bounded linear functional on $\\Ld$. If $\\phi$ is zero on $F_{d,0}^{\\infty}$, where $F_{d,0}^{\\infty}$ denotes the ideal of $\\Ld$ generated by $L_{Z_{1}},\\ldots,L_{Z_{d}}$, then $\\phi$ is absolutely continuous.", "\n\nLet $\\phi=\\phi_{a}+\\phi_{s}$ be the Lebesgue decomposition of $\\phi$ into absolutely continuous and singular parts as in Theorem \\[thm:lebesgue-decomp\\]. ", "By Theorem \\[thm:ann-ideals\\], $\\phi_{a}$ and $\\phi_{s}$ are both zero on $F_{d,0}^{\\infty}$. By Definition \\[def:abs-cont-and-sing\\], if $\\phi_{s}$ is zero on $F_{d,0}^{\\infty}$, it is necessarily zero on all of $\\Ld$. Hence $\\phi=\\phi_{a}$ and $\\phi$ is absolutely continuous.", "\n\nQuotient algebras\n=================\n\nFor a weak-[\\*]{} closed two-sided ideal $\\mathcal{I}$ of $\\Ld$, let $\\mathcal{A}_{I}$ denote the quotient algebra $\\Ld/\\mathcal{I}$.\n\nLet $\\mathcal{I}$ be a weak-[\\*]{} closed two-sided ideal of $\\Ld$, and let $\\phi$ be a bounded functional on $\\mathcal{A}_{\\mathcal{I}}$. Then\n\n1. ", " $\\phi$ is *absolutely continuous* if it is weak-[\\*]{} continuous, and\n\n2. ", " $\\phi$ is *singular* if $\\|\\phi\\|=\\|\\phi^{k}\\|$ for every $k\\geq1$, where $\\phi^{k}$ denotes the restriction of $\\phi$ to the ideal of $\\AI$ generated by $\\{\\overline{L_{Z_{w}}}\\mid|w|=k\\}$, where for a word $w$ in $\\mathbb{F}_{d}^{*}$, $\\overline{L_{Z_{w}}}$ denotes the image in $\\mathcal{A}_{\\mathcal{I}}$ of $L_{Z_{w}}$.\n\n\\[Lebesgue decomposition for quotients of $F_d^\\infty$\\]\\[thm:lebesgue-decomp-quotients\\]Let $\\mathcal{I}$ be a weak-[\\*]{} closed two-sided ideal of $\\Ld$, and let $\\phi$ be a bounded linear functional on $\\mathcal{A}_{\\mathcal{I}}$. Then there are unique linear functionals $\\phi_{a}$ and $\\phi_{s}$ on $\\mathcal{A}_{\\mathcal{I}}$ such that $\\phi=\\phi_{a}+\\phi_{s}$, where $\\phi_{a}$ is absolutely continuous and $\\phi_{s}$ is singular, and such that $$\\|\\phi\\|\\leq\\|\\phi_{a}\\|+\\|\\phi_{s}\\|\\leq\\sqrt{2}\\|\\phi\\|.$$ If $d=1$, then the constant $\\sqrt{2}$ can be replaced with the constant $1$.\n\nBy basic functional analysis, we can lift the functional $\\phi$ to a functional $\\psi$ on $\\Ld$ with the same norm. ", "Let $\\psi=\\psi_{a}+\\psi_{s}$ be the Lebesgue decomposition of $\\psi$ into absolutely continuous and singular parts as in Theorem \\[thm:lebesgue-decomp\\]. ", "The functional $\\psi$ annihilates $\\mathcal{I}$, so by Theorem \\[thm:ann-ideals\\], both $\\psi_{a}$ and $\\psi_{s}$ annihilate $\\mathcal{I}$. Hence $\\psi_{a}$ and $\\psi_{s}$ induce functionals $\\phi_{a}$ and $\\phi_{s}$ on $\\mathcal{A}_{\\mathcal{I}}$ respectively, with the same norm. ", "Clearly $\\phi=\\phi_{a}+\\phi_{s}$, and the inequality $$\\|\\phi\\|\\leq\\|\\phi_{a}\\|+\\|\\phi_{s}\\|\\leq\\sqrt{2}\\|\\phi\\|$$ follows from the corresponding inequality in Theorem \\[thm:lebesgue-decomp\\]. ", "The functional $\\phi_{a}$ is absolutely continuous since $\\psi_{a}$ is absolutely continuous on $\\Ld$. To see that $\\phi_{s}$ is singular, simply note that for every $k\\geq1$, the ideal $(\\mathcal{A}_{\\mathcal{I},0})^{k}$ is the image in $\\mathcal{A}_{\\mathcal{I}}$ of the ideal $(F_{d,0}^{\\infty})^{k}$.\n\n\\[Lebesgue decomposition for multiplier algebras\\]Let $\\mathcal{A}$ be the multiplier algebra of a complete Nevanlinna-Pick space, and let $\\phi$ be a bounded linear functional on $\\mathcal{A}$. Then there are unique linear functionals $\\phi_{a}$ and $\\phi_{s}$ on $\\mathcal{A}$ such that $\\phi=\\phi_{a}+\\phi_{s}$, where $\\phi_{a}$ is absolutely continuous and $\\phi_{s}$ is singular, and such that $$\\|\\phi\\|\\leq\\|\\phi_{a}\\|+\\|\\phi_{s}\\|\\leq\\sqrt{2}\\|\\phi\\|.$$\n\nUniqueness of the predual\n=========================\n\nLet $X$ and $Y$ be Banach spaces such that $X^{*}=Y$. Then $X$ is said to be a predual for $Y$. Every predual $X$ of $Y$ naturally embeds into the dual space $Y^{*}$, and a subspace $X$ of $Y^{*}$ is a predual of $Y$ if and only if it satisfies the following properties:\n\n1. ", " The subspace $X$ norms $Y$, i.e. $\\sup\\{|x(y)|\\mid x\\in X,\\ \\|x\\|\\leq1\\}=\\|y\\|$ for all $y$ in $Y$, and\n\n2. ", " The closed unit ball of $Y$ is compact in the $\\sigma(Y,X)$ topology.", "\n\nThe space $Y$ is said to have a strongly unique predual if there is a unique subspace $X$ of $Y^{*}$ such that $Y=X^{*}$. For a survey on uniqueness results for preduals, we refer the reader to Godefroy’s article [@God89].", "\n\nIn the operator-theoretic setting, the results of Sakai [@Sak56], Ando [@And78] and Ueda [@Ued09] mentioned in the introduction established that von Neumann algebras and maximal subdiagonal algebras have unique preduals. ", "Ruan proved in [@Rua92] that an operator algebra with a weak-[\\*]{} dense subalgebra of compact operators has a unique predual, which applies to, for example, nest algebras and atomic CSL algebras. ", "Effros, Ozawa and Ruan proved in [@EOR01] that a $\\mathrm{W}^{*}$TRO (i.e. a corner of a von Neumann algebras) has a unique predual. ", "More recently, in [@DW11], Davidson and Wright proved that a free semigroup algebra has a unique predual. ", "Note that Davidson and Wright’s result applies to $\\Ld$, but not to quotients of $\\Ld$.\n\nThe following definition was introduced by Godefroy and Talagrand in [@GT80]. ", "Recall that a (formal) series $\\sum_{n}y_{n}$ in a Banach space $Y$ is weakly unconditionally ** Cauchy if $\\sum_{n}\\phi(y_{n})<\\infty$ for every $\\phi\\in Y^{*}$.\n\nA Banach space $X$ has property (X) if, for every $\\phi\\in X^{**}\\backslash X$, there is a weakly unconditionally Cauchy sequence $(x_{n})$ in $X^{*}$ such that $$\\phi\\left(\\underset{n}{\\operatorname{w^{*}-lim}}\\sum_{k=1}^{n}x_{k}\\right)\\ne\\sum_{k=1}^{\\infty}\\phi(x_{k}).$$\n\nOne reason for the interest in property (X) is the following result of Godefroy and Talagrand from [@GT80].", "\n\n\\[Godefroy-Talagrand\\]A Banach space $X$ with property (X) is the unique predual of its dual.", "\n\nThe following definition is closely related to the notion of an M-ideal in a Banach space (see [@HWW93] for more information).", "\n\nA Banach space $X$ is L-embedded if there is a projection $P$ on the bidual $X^{**}$ with range $X$ such that $$\\|x\\|=\\|Px\\|+\\|x-Px\\|,\\quad\\forall x\\in X^{**}.$$\n\nThe following result of Pfitzner from [@Pfi07] implies that every separable L-embedded space has property (X), and hence that it is the unique predual of its dual.", "\n\n\\[Pfitzner\\]Separable L-embedded spaces have property (X).", "\n\nThe results of Sakai, Ando and Ueda on decompositions of linear functionals imply that the preduals of von Neumann algebras and maximal subdiagonal algebras are L-embedded, and hence by Pfitzner’s result from [@Pfi07], that they are unique. ", "However, Example \\[ex:constant\\] shows that quotients of $\\Ld$ are not, in general, L-embedded, so we are unable to use Pfitzner’s result. ", "Instead, we give a direct proof that quotients of $\\Ld$ have (strongly) unique preduals.", "\n\nLet $\\mathcal{I}$ be a weak-[\\*]{} closed two-sided ideal of $\\Ld$. Then the algebra $\\mathcal{A}_{\\mathcal{I}}$ has a strongly unique predual.", "\n\nSuppose $E$ is a predual for $\\mathcal{A}_{\\mathcal{I}}$, identified with a subspace of $(\\mathcal{A}_{\\mathcal{I}})^{*}$. By Theorem \\[thm:lebesgue-decomp-quotients\\], $$(\\mathcal{A}_{\\mathcal{I}})^{*}=(\\mathcal{A}_{\\mathcal{I}})_{a}^{*}\\oplus(\\mathcal{A}_{\\mathcal{I}})_{s}^{*},$$ where $(\\mathcal{A}_{\\mathcal{I}})_{a}^{*}$ and $(\\mathcal{A}_{\\mathcal{I}})_{s}^{*}$ denote the set of absolutely continuous and singular functionals on $\\mathcal{A}_{\\mathcal{I}}$ respectively. ", "We want to prove that $E=(\\mathcal{A}_{\\mathcal{I}})_{a}^{*}$.\n\nLet $\\phi$ be a functional in $E$, and let $\\phi=\\phi_{a}+\\phi_{s}$ be the Lebesgue decomposition of $\\phi$ as in Theorem \\[thm:lebesgue-decomp-quotients\\]. ", "We will prove that $\\phi_{s}=0$. Suppose to the contrary that $\\phi_{s}\\ne0$. By basic functional analysis, we can lift the functional $\\phi$ to a functional $\\psi$ on $\\Ld$ that is zero on $\\mathcal{I}$. Let $\\psi=\\psi_{a}+\\psi_{s}$ be the Lebesgue decomposition of $\\psi$ as in Theorem \\[thm:lebesgue-decomp\\]. ", "By Theorem \\[thm:ann-ideals\\], $\\psi_{a}$ and $\\psi_{s}$ are both zero on $\\mathcal{I}$, and by construction they induce the functionals $\\phi_{a}$ and $\\phi_{s}$ respectively on the quotient $\\AI$.\n\nIt follows from the results of [@Ken11] that Theorem 5.4 of [@DLP05] applies to the unital weak operator closed algebra generated by any isometric tuple. ", "Thus there is a net $(B_{\\lambda})$ of elements in the unit ball of $\\Ld$ such that $\\operatorname{w^{*}-lim}\\pi_{u}(B_{\\lambda})=P_{u}$ in $\\Ldd$. Since the net $(B_{\\lambda}$) is weak-[\\*]{} convergent in $\\Ldd$, it is weakly Cauchy in $\\Ld$. Since the closed unit ball of $\\Ld$ is compact in the weak-[\\*]{} topology, and in particular is complete, this implies that there is $B$ in the closed unit ball of $\\Ld$ such that $\\operatorname{w^{*}-lim}B_{\\lambda}=B$ in $\\Ld$. For every weak-[\\*]{} continuous functional $\\tau$ on $\\Ld$, Proposition \\[prop:char-abs-cont\\] implies that $$\\tau(B)=\\lim_{\\lambda}\\tau(B_{\\lambda})=(\\tau P_{u})(1)=0.$$ Hence $B=0$.\n\nLet $A$ be an element in the unit ball of $\\Ld$ such that $\\psi_{s}(A)\\ne0$. Since the net $(B_{\\lambda})$ is weakly Cauchy in $\\Ld$, the image $(\\overline{B_{\\lambda}})$ is weakly Cauchy in $\\AI$. It follows that the net $(\\overline{AB_{\\lambda}})$ is also weakly Cauchy in $\\AI$. Since $E$ is a predual of $\\AI$, the closed unit ball of $\\AI$ is compact in the $\\sigma(\\AI,E)$ topology, and in particular is complete. ", "Thus, the net $(\\overline{AB_{\\lambda}})$ converges in the $\\sigma(\\AI,E)$ topology to an element $C$ in the unit ball of $\\AI$. By Proposition \\[prop:char-singular\\], we have $$\\phi(C)=\\lim_{\\lambda}\\phi(\\overline{AB_{\\lambda}})=\\lim_{\\lambda}\\psi(AB_{\\lambda})=(\\psi P_{u})(A)=\\psi_{s}(A)\\ne0,$$ so that $C\\ne0$. But since $\\operatorname{w^{*}-lim}B_{\\lambda}=0$ in $\\Ld$, it follows that $\\operatorname{w^{*}-lim}\\overline{AB_{\\lambda}}=0$ in $\\AI$. So for every $\\tau$ in $(\\AI)_{a}^{*}$, we necessarily have $$\\tau(C)=\\lim_{\\lambda}\\tau(\\overline{AB_{\\lambda}})=0.$$ Since $(\\AI)_{a}^{*}$ separates points, this implies that $C=0$, which gives a contradiction. ", "Thus $\\phi=\\phi_{a}$, meaning $\\phi$ is absolutely continuous.", "\n\nSince $\\phi$ was arbitrary, it follows from above that every functional in $E$ is absolutely continuous, i.e. that $E$ is contained in $(\\AI)_{a}^{*}$. If it were the case that $E\\ne(\\AI)_{a}^{*}$, then we could apply the Hahn-Banach theorem to separate $E$ from $(\\AI)_{a}^{*}$ with an element of $\\AI$. But the fact that $E$ is a predual of $\\AI$ means in particular it must norm $\\AI$, so this is impossible. ", "Therefore, we conclude that $E=(\\AI)_{a}^{*}$, and hence that $(\\AI)_{a}^{*}$ is the unique predual of $\\AI$.\n\nThe multiplier algebra of every complete Nevanlinna-Pick space has a strongly unique predual.", "\n\nAcknowledgements {#acknowledgements .unnumbered}\n================\n\nThe authors are grateful to Ken Davidson and Adam Fuller for their helpful comments and suggestions.", "\n\n[References]{} J. Agler, J.E. 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Takesaki, *On the singularity of a positive linear functional on operator algebra*, Proceedings of the Japanese Academy 35 (1959), 365–366.", "\n\nM. Takesaki, *Theory of operator algebras I*, Encyclopedia of Mathematical Sciences 124, Operator Algebras and Noncommutative Geometry 5 (2002), Springer-Verlag, New York.", "\n\nY. Ueda, *On peak phenomena for non-commutative $H^{\\infty}$*, Mathematische Annalen 343 (2009), No. ", "2, 421–429.", "\n\nY. Ueda, *On the predual of non-commutative $H^{\\infty}$*, Bulletin of the London Mathematical Society 43 (2011), No. ", "5, 886–896.", "\n\n[^1]: Both authors partially supported by NSERC\n" ]

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[ "BEIJING (Reuters) - China and the European Union need to show joint leadership on climate change and cannot expect the “same leadership” from the new administration in the United States, European climate commissioner Miguel Arias Canete said in Beijing on Thursday.", "\n\nSlideshow ( 3 images )\n\nCanete, speaking to reporters after meeting Chinese officials, expressed regret that the United States was rolling back climate policies, but said China and Europe remained committed to “driving forward” the global battle against climate change.", "\n\n“We are not going to backslide even if the United States at the moment...is backsliding from its previous commitments,” he said.", "\n\nU.S. President Donald Trump on Tuesday signed an order to undo Obama-era climate change regulations, keeping a campaign promise to support the coal industry and calling into question U.S. support for the international deal to fight global warming.", "\n\nObama’s Clean Power Plan, aimed at slashing power plant emissions, was a key component of joint pledges made in 2014 by China and the United States, the world’s two biggest producers of climate-warming greenhouse gas, and helped seal a new global pact signed in Paris at the end of 2015.", "\n\nThe Paris Agreement seeks to phase out net greenhouse gas emissions by the second half of the century and limit global warming to “well below” 2 degrees Celsius (3.6 degrees Fahrenheit) above pre-industrial levels.", "\n\nClimate activists expressed concern the new U.S. position would jeopardize negotiations to implement the Paris agreement, which are set to be completed in 2018, and urged the European Union to step into the breach.", "\n\n“There is a clear risk that the United States might go beyond the delicate balance that the countries agreed in Paris,” said Li Shuo, senior climate adviser with environmental group Greenpeace.", "\n\n“We might have some trouble, and if the European Union and China can reaffirm their commitment to conclude this process, that will send a strong political signal,” he said.", "\n\nCanete said Trump’s order on Tuesday gave no indication of the United States’ intentions when it comes to honoring the Paris deal, and to fulfill its commitments it needed to explain how it would meet targets.", "\n\n“If they, at the moment, lose all the tools they have in order to achieve those targets, it’s pretty clear they will not achieve those targets,” he said.", "\n\nThough the role of the United States in climate negotiations was likely to be completely different even if it remained part of the Paris agreement, it still had a “very important responsibility” on climate change, he added." ]

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[ "Mark Snyder\n\nDetroit Free Press\n\nMichigan has its captains for the 2016 season: defensive lineman Chris Wormley and tight end Jake Butt.", "\n\nThe captains are voted on by the players at the end of camp and Wormley made the announcement on Twitter tonight, just after 10 p.m.\n\nButt said it was the \"highest honor I have received (and probably ever will receive) in my life.\"", "\n\nU-M confirmed it on the football program's Twitter account later this evening that the two Ohio natives will be the captains.", "\n\n\"I've been on some very good teams in different sports I played and I've been on some very bad teams,\" Butt said at Big Ten media days. \"", "The good teams have always had good leadership and the bad teams have always had bad leadership. ", "That seems to be the common ground. ", "You can see with coach Harbaugh, he came in, he's an excellent leader. ", "We had some great captains last year and it trickled down through the whole entire team. ", "So I think it's important to have great leadership.\"", "\n\nThis is the third straight season with only two captains, one on each side of the ball. ", "Last year's captains were linebacker Joe Bolden and fullback Joe Kerridge.", "\n\nWormley enters his fifth year from Toledo as the most versatile defensive lineman, predicated by many to have a breakout season. ", "With a four-man front, he'll be able to play inside and outside to keep offenses off guard.", "\n\nIn 2015, he had 43 tackles, 14 1/2 for loss and 6 1/2 sacks.", "\n\nButt passed up the chance to be the top tight end in the 2016 NFL Draft to return to school for his fourth year, citing team goals as his primary motivation.", "\n\nHe was already named an All-America on a number of lists last year after 51 catches for 654 yards and three touchdowns.", "\n\nButt is the first tight end to be captain since Kevin Koger in 2011 and Wormley the first defensive lineman since Mike Martin, also in 2011.", "\n\nContact Mark Snyder atmsnyder@freepress.com. ", "Follow him on Twitter at @mark__snyder. ", "Download our Wolverines Xtra appon iTunesandAndroid!" ]

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[ "Q:\n\nUser Roles DB Schema Design\n\nI am thinking about a schema design that involves having users and user roles, but I am not sure what would be the better route.", "\nOption 1\nCreate three tables, one with the user information, one with the role information, and one with th user role relation.", "\nusers {\n u_id,\n etc\n}\n\nroles {\n r_id,\n r_name,\n etc\n}\n\nuser_roles {\n u_idm\n r_id\n}\n\nOption 2\nCreate two tables, one with the user information, and the other with role, role info,and relation info.", "\nusers {\n u_id,\n etc\n}\n\nroles {\n r_id,\n u_id,\n r_name,\n etc\n}\n\nOption 1 is more robust but requires an extra join. ", "Option 2 will require an extra primary key but will only be one join. ", "If I ever change the role name, it would take longer to update with option, but I don't forsee updates being frequent.", "\nFor a scalable solution, which would be better? ", "What other insights in my missing? ", "This is for a mysql and postgresql solution.", "\n\nA:\n\nOption 1.", "\nWhat good is a role if only one user can have each role?", "\nIf you have 100 registered users there would be 100 duplicate definitions for \"registered user\".", "\nThe more \"etc\" there is the bigger your db will get.", "\nHaving that many duplicates will slow down your database and in the end things will be a lot slower even if you have one join less.", "\nIf you run lots of role based querys and relly eel like you need a database like the one from option two you can still create a view and have the database cache it, but I doubt that this will do you any good.", "\n\n" ]

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[ "[FTIR investigation of organic phase containing rare earth ion in naphthenic acid-phosphonate ester-heptane system].", "\nNaphthenic acid (NA) was mixed with PC88A in heptane, and 10 moL x L(-1) KOH aqueous solution was used to saponify the solution subsequently. ", "The transparent and clear appearance of the obtained solution indicated the formation of w/o micell and microemusion. ", "In the present study, micell with high saponification percentage (80%) was used to extract neodymium. ", "The organic phase structure was characterized using FTIR spectroscopy in the extraction process. ", "IR spectra indicate that the characteristic peaks of nu(COOH), nu(s)(COO-) and nu(P=O) shift to lower wavenumbers as the loading of Nd in organic phase increases. ", "The results demonstrated that Nd(III) are coordinated to P=O and COO- groups simultaneously, and the supramolecules with self-assembly structure was formed containing PC88A and NA, which were binding with Nd(III) in the extracted organic phase." ]

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[ "/**\n * A specialized version of `_.sum` for arrays without support for callback\n * shorthands and `this` binding..\n *\n * @private\n * @param {Array} array The array to iterate over.", "\n * @param {Function} iteratee The function invoked per iteration.", "\n * @returns {number} Returns the sum.", "\n */\nfunction arraySum(array, iteratee) {\n var length = array.length,\n result = 0;\n\n while (length--) {\n result += +iteratee(array[length]) || 0;\n }\n return result;\n}\n\nmodule.exports = arraySum;\n" ]

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