bluuebunny/crossref_metadata_2025 huggingface dataset:
Sharing Teaching Ideas: A Formula for Factoring
Authors: Meeks Roebuck Kay I.
Published: November 2020

At a recent meeting of mathematics and science teachers, three colleagues were discussing the algebra courses at their high schools. The major topic of conversation was the amount of time to be devoted to solving quadratic equations by factoring. The three were concerned that by devoting the large number of class days necessary for students to gain proficiency at factoring by inspection or grouping, they were left without sufficient time to work with the students on other important concepts. The teachers agreed that they were stuck in a no-win situation; they accepted and supported the idea expressed in the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) that less time should be devoted to solving equations by factoring, yet other mathematics teachers within their schools would expect students to be proficient at factoring when they leave algebra.
Implementing the Assessment Standards for School Mathematics: Using the Assessment of Students' Learning to Reshape Teaching
Authors: Wilcox Sandra K. , Zielinski Ronald S.
Published: November 2020

Asessment. should serve as the essential link among curriculum, teaching, and learning. In traditional practice, however, assessment is used by teachers primarily to assign grades at the end of a unit of instruction and to distinguish the students who are successful from those who are not. This practice stands in stark contrast to the conceptualization of assessment reflected in the Standards documents of the National Council of Teachers of Mathematics (1989, 1991, 1995). When used in a broader and more constructive manner, assessment can help teachers gain better insights into students' understandings, including their misconceptions and partially integrated ideas. Further, assessment can be a powerful tool to help teachers monitor the effectiveness of their own teaching, judge the usefulness of learning tasks, and shape their ongoing instructional decisions.
The Pyramid Question: A Problem–Solving Adventure
Authors: McClintock Ruth M.
Published: November 2020

Good teachers know that a good question can launch a discovery journey through conjecture, research, serendipitous encounters, proof, answers, and new questions. The importance of a problem-solving approach to investigating and understanding mathematics is underscored by the fourth grade-level standard in NCTM's Curriculum and Evaluation Standards for School Mathematics (NCTM 1989).
Activities: More Functions of a Toy Balloon
Authors: Coes Loring
Published: November 2020

Like all teachers, I am constantly looking for economical but memorable activities that illustrate important ideas in mathematics. Toy balloons, inexpensive and entertaining, offer some interesting opportunities to connect algebra and geometry. In the following activities, students can measure the speed of a released balloon and investigate the subtle relationship between the volume of a sphere and its surface area. In addition, the activities can prompt a rich and revealing discussion about why the experimental results are not the same as those we would expect theoretically.
A Singular Function: A Problem-Solving Parable
Authors: Bosch Peter Vanden
Published: November 2020

The Boss looked up from Fran's resume and sized her up. “You're not an engineer? What's operations research?“
Projects
Authors: Stenglein Sharon
Published: November 2020

For all students to succeed in learning more mathematics, content and instruction must change. Access to all will be open when teachers are prepared to assist all students with learning rich, contextual mathematics in a standards-based classroom. In Minneapolis-Saint Paul, Minnesota, Project Open Access, funded primarily by the National Science Foundation (NSF), attempts to meet the needs of teachers who are ready for professional development that will support them in reaching this goal. The intent of the project is to increase the readiness of large numbers of teachers to implement one of the new curriculum projects for middle or high school mathematics that have been funded by the NSF.
Sharing Teaching Ideas: What Day Is It?
Authors: Ferguson Donna K.
Published: November 2020

“What Day Is It?” is a multidisciplinary project encompassing English, history, public speaking, and mathematics. Because this activity involves several disciplines, it allows students to expelience success in my classroom even if mathematics is not their strength. It also helps the students realize that mathematics is integrated into every part of everyday living.
National Council of Teachers of Mathematics: Choices and Challenges
Authors: Burrill Gail
Published: November 2020

Life has changed enormously since I grew up in Fisher, Minnesota. Over the years, we faced many challenges and made choices that helped us meet those challenges as we kept up with changes in agriculture, manufacturing, transportation, entertainment, and education.
Creating a Learning Environment for Geometric Reasoning
Authors: Perham Arnold E. , V. C. S. , Perham Bernadette H. , Perham Faustine L.
Published: November 2020

Geometry teachers can introduce the theorems of Euclidean geometry in various ways. Complementing the standbys of the past, namely, compass-and-straightedge constructions and manipulatives, are geometry-construction software, spreadsheets, and programmable graphing calculators.
Sharing Teaching Ideas: Table Tennis, Anyone? Using Ping-Pong to Teach the Coordinate Plane
Authors: Foshay John D. , Wells Wendy L.
Published: November 2020

During a first-year-algebra class, tenth- and eleventh-grade students, overhearing the sounds of a Ping-Pong game from downstairs, voiced a strong desire to play. This incident led the authors to stumble onto the idea of using Ping-Pong to teach coordinate geometry. From this inquiry by interested students came the idea of using a Ping-Pong table as the visual anchor on which to situate the coordinate plane.
Solutions to Calendar
Authors: McLoughlin John Grant
Published: November 2020

Problems 1–24 and 30 were contributed by Victor G. Feser, University of Mary, 7500 University Drive, Bismarck, ND 58504-9652. Problem 25 appears in Madachy's Mathematical Recreations by JosephS. Madachy (New York: Dover Publications, 1979). Problems 26–29 were submitted by Larry Cusick and Agnes Tuska, both of California State University—Fresno, 5245 North Backer Avenue, Fresno, CA 93740.
Implementing the Professional Standards for Teaching Mathematics: From the General to the Particular: Knowing Our Own Students as Learners of Mathematics
Authors: Ball Deborah Loewenberg
Published: November 2020

“Knowledge of students” is a core domain of professional knowledge. According to the Professional Standards for Teaching Mathematics (NCTM 1991), both initial and continuing professional education should offer teachers opportunities to develop understandings about these topics:
Projects
Authors: Stenglein Sharon
Published: November 2020

The time is ripe to strengthen the mathematics capacity of inner-city high schools, creating wider access to powerful and exciting mathematics courses for public high school students in America's cities. A particular national weakness is that a significant percent of urban secondary schools offer no calculus course. Access and availability to a curriculum comparable to that offered in virtually every suburban and private high school is denied these students.
The Euler Line and Nine-Point-Circle Theorems
Authors: Eccles Frank M.
Published: November 2020

A train of ideas leading to the application of a particular transformation, a dilation, to the proofs of both the Euler line and nine–point–circle theorems, to help introduce students to the important role that functions can play in the field of geometry.
Connecting Research to Teaching: Cooperative Learning in Mathematics
Authors: Leikin Roza , Zaslavsky Orit
Published: November 2020

How can the teacher best organize and manage the classroom during cooperative work so that discipline prone problems do not arise, interaction between students primarily involves task, and pupils still have sufficient freedom to contribute and to participate in the group discussion?
Connecting Research to Teaching: A Problem-Based Approach to Mathematics Instruction
Authors: Erickson Dianne K.
Published: November 2020

The way in which teachers approach mathematics instruction determines to a large extent the mathematics, thinking strategies, and dispositions that our students develop. Hiebert and others describe one of the essential principles for instruction focused on building understanding in mathematics: “Make the subject problematic.” Instruction ought to allow “students to wonder why things are, to inquire, to search for solutions, and to resolve incongruities. It means that both curriculum and instruction should begin with problems, dilemmas, and questions for students” (1996, 12).
Ten Lessons From the Proof of Fermat's Last Theorem
Authors: Kahan Jeremy
Published: November 2020

The proof of Fermat's last theorem establishes the truth of an old mathematical conjecture in ways that are beyond the understanding of most students and their teachers. Yet the lessons from the proof process can help teachers and their students gain insight into constructing mathematics.
A Mathematical Study of the Game Twenty-Four Points
Authors: Shi Yixun
Published: November 2020

The game “twenty-four-points” was my favorite when I was a child because I was thrilled to find myself capable of “figuring numbers out right and fast.” Teachers also appreciate it because of its effectiveness in improving children's ability to do mental arithmetic.
Sharing Teaching Ideas: I Found Sinusoids in My Gas Bill
Authors: Schloemer Cathy G.
Published: November 2020

With the current emphasis on real-world mathematics applications, many recent trigonometry textbooks include examples of sinusoidal functions for which students are required to find a model. These examples typically refer to the height of a person above the ground as a function of length of time riding on a Ferris wheel or to the number of hours of daylight in a U.S. city as a function of the day of the year. Unfortunately, as real-world as these examples are, many students still reject them as artificial and contrived. Complaints of “I'll never do this in my adult life” and “Who cares how high the Ferris wheel rider is?” are common among the eleventh- and twelfth-grade students that I teach.
Media Clips: January 2000
Authors: Westegaard Susanne
Published: November 2020

We welcome and encourage submissions to this department, which will comprise resources that teachers can use immediately or file away for future use. The assignments generated by these entries may range from starters for an entire class to fullblown projects for optional individual pursuit. Each lesson, though, should help convince our students that mathematics is useful, current, and newsworthy. Please send submissions to “Media Clips,” Mathematics Teacher, 1906 Association Drive, Reston, VA 20191-9988.
Chaotic Behavior in the Classroom
Authors: Iovinelli Robert C.
Published: November 2020

During a meeting of our school's Mu Alpha Theta chapter, several students were having a lively debate about chaos theory. They were interpreting chaos as frenzy, disorder, confusion, and even bedlam. I asked them, “Has anyone taken the time to research the subject?” With sheepish grins, they said, “No.” One student immediately went to the classroom resource library and began to browse. The others quickly followed.
Getting to the Root of the Problem
Authors: Bosch Peter Vanden
Published: November 2020

Many processes depend on finding the roots of a function—the places at which the value of the function is zero. We might consider tuning a radio to a station to be a matter of finding the value for which the static function is zero. The cruise control on a car is constantly trying to zero the difference between its speed and some desired speed. The process of finding a root is a special case of inverting the function, which is seldom an easy problem.
Finger Math in Geometry
Authors: Warkentin Don R.
Published: November 2020

To gesture or not to gesture; is that really the question? Try out my technique in your geometry classrooms. You may be pleased to learn that the careful and conscious use of finger math will reinforce meaning for many of your mathematics students.
Connecting Research to Teaching: Using Data-Collection Devices to Enhance Students' Understanding
Authors: Lapp Douglas A. , Flora Cyrus Vivian
Published: November 2020

While working with high school students at a Mathematics, Physics, and Advanced Technology Exploration Day, we observed an activity in which students tried to reproduce a distance-time graph by walking. They used a Calculator-Based Ranger (CBR) to collect data about their distance from a motion detector and to generate a distance-time graph in real time. During the activity, the students clearly did not understand the distance information that the given graph was conveying.
Connecting Research to Teaching: The Challenges of Implementing Innovation
Authors: Edwards Barbara S.
Published: November 2020

Several years ago, I attended a workshop that introduced high school and college teachers to new pedagogical techniques that could “revolutionize the teaching of mathematics.” I returned from the workshop energized by what I had seen and determined to reform my ways forever. The reality of implementing these new ideas, however, hit me when my first attempt to introduce an innovative activity failed miserably with my students. Somehow, the results that my students produced were nothing like those demonstrated in the workshop. In an attempt to fix the problem, I sought help from my colleagues, only to hear discouraging words and an assurance that “those kinds of things” never really work anyway. I slowly slipped back to my old way of teaching.
Implementing the Assessment Standards: The Myth of Objectivity in Mathematics Assessment
Authors: Romagnano Lew
Published: November 2020

Awide array of alternatives to traditional quiz-and-test assessment of students' mathematical understanding has been proposed in the last decade (e.g., Stenmark [1991]; NCTM [1995]; Greer et al. [1999]). Adding open-ended problems, performance tasks, writing assignments, and portfolios to teachers' assessment repertoires is important, these documents argue, because “assembling evidence from a variety of sources is more likely to yield an accurate picture of what each student knows and is able to do” (NCTM 2000, p. 24).
Tunja Sequences as Examples of Employing Students' Powers to Generalize
Authors: Mason John H.
Published: November 2020

Students initially come to lessons ready to specialize and to generalize, to imagine and to express, to conjecture and to convince. They need only a few days in school to discover whether those powers can be used there. Since the use of these powers by each student is essential if mathematics is going to be appreciated rather than simply trained, seeking ways in which these powers can be employed in every lesson is vital.
Pierre Varignon and the Parallelogram Theorem
Authors: Oliver Peter N.
Published: November 2020

A brief biography of Pierre Varignon (1654–1722), French academician of the era of Newton and Liebniz, who furnished the first rigorous proof of the Parallelogram Theorem.
Sharing Teaching Ideas: Seven Wonders of the Ancient and Modern Quadratic World
Authors: Taylor Sharon E. , Mittag Kathleen Cage
Published: November 2020

After teaching algebra for many years in both high school and college, we noticed that our students were still having trouble understanding the concepts derived from the fundamental theorem of algebra. With the increased emphasis on multiple representations—graphical, numerical, and algebraic, we decided to design a classroom activity that examined solving quadratic equations by using a variety of methods.
The Mayan Zeros
Authors: McNeill Sheila A.
Published: November 2020

The Maya, one of only two cultures to invent a zero concept, used various glyphs as their symbol for zero.
Projects: The National Math Trail
Authors: Foletta Gina
Published: November 2020

During the past few school years, teachers and students across the country have been taking virtual walks along the National Math Trail, which can be found at www.nationalmathtrail.org. The K–12 Internet-based project invites students and teachers to submit community-based mathematics problems, along with photographs, illustrations, audio or video content, or Web pages. These submissions are posted to the National Math Trail map throughout the year. International submissions are also being solicited, and appropriate maps are created.
Sound Off!: Why Do So Many Students Perform So Poorly in Higher-Level Mathematics
Authors: Risher Kathryn
Published: November 2020

As high school mathematics teachers, my colleagues and I face this sad reality on a daily basis. After years of experience instructing teenagers in algebra, geometry, trigonometry, and calculus, we have recognized a number of forces that impede the success of high school students in higher-level mathematics courses. Many students and their parents either fail to recognize these forces or refuse to face them.
Paper Folding and Conic Sections
Authors: Smith Scott G.
Published: November 2020

One sign of a good problem is that it offers multiple revelations during its investigation. Another is that it can be approached mathematically in more than one way. Three related problems that meet both those criteria involve paper folding and conic sections. Each problem can be demonstrated easily with a sheet of wax paper or emulated by a geometry drawing program like The Geometer's Sketchpad, yet each contains interesting mathematics whose properties are established in nontrivial ways.
Sharing Teaching Ideas: Calculator Cryptography
Authors: Hall Matthew
Published: November 2020

Allowing students to participate in real-world applications of mathematics enables them to advance their own understanding of mathematical topics. Furthermore, most mathematics teachers would agree with NCTM's statement that “students' engagement with, and ownership of, abstract mathematical ideas can be fostered through technology” (NCTM 2000, p. 25). However, finding real applications becomes increasingly difficult as students progress into higher forms of mathematics like algebra. One topic that I have found particularly effective in demonstrating the importance of algebra and the use of technology is cryptography, or the encoding and decoding of messages.
Activities for Students: Geoboard Areas: Students' Remarkable Ideas
Authors: Utley Juliana , Wolfe John
Published: November 2020

Geometry class can be a lot of fun. An animated discussion with the students was unfolding.
Media Clips: May 2004
Authors: Vennebush G. Patrick
Published: November 2020

“Media Clips” aims to offer readers contemporary, authentic applications of quantitative reasoning that are based on print or electronic media. We encourage submissions, which may include questions as well as clips. We especially welcome examples of flawed quantitative reasoning. Clips may be in text or graphic format, and clip sources may be either print or electronic media. Submissions must include a complete citation of the source along with the full text of the cited material. If possible, submissions should also include a copy of the actual clip. Please send submissions to “Media Clips,” Mathematics Teacher, 1906 Association Drive, Reston, VA 20191-1502.
Building Mathematical Maturity in Calculus: Teaching Implicit Differentiation through a Review of Functions
Authors: Hare Angela , Phillippy Doug
Published: November 2020

Identifies characteristics of mathematically maturity at the calculus level and provides a project focusing on implicit differentiation that is designed to build students' mathematical maturity by helping them connect calculus concepts with prerequisite material. Gives prelesson assignment and lesson outline with examples of student responses that indicate weak understanding of problems and their probable reasoning. Solutions are included.
New Worlds to Conquer
Authors: Francis Richard L.
Published: November 2020

Still undiscovered areas of mathematical problem solving. Prime numbers and subset groups are discussed, including Mersenne and Fermat primes.
Delving Deeper: A Tale Of Two Theorems
Authors: Lu Jitan , Scacalossi Raymond
Published: November 2020

This month's offering consists of two articles. Jitan Lu shows that a triangle is determined by its three angle bisectors. Then Raymond Scacalossi describes an incident in his Advanced Placement calculus class where a student–invented method that seemed implausible turned out to be valid.
Sound Off!: How the Nation's Largest City Is Managing One of Its Severest Math Teacher Shortages
Authors: Posamentier Alfred S. , Coppin Joyce R.
Published: November 2020

Imagine the daunting task of having to hire about a thousand math teachers before the start of the school year—and during one of our nation's worst math teacher shortages in memory. That task is precisely what the New York City Department of Education had to do before the start of school in September 2003, and the situation was about the same for the school year beginning in September 2004. The result has left the school system with a relatively inexperienced math teacher force. Current estimates show that more than 50 percent of the certified math teachers in New York City have less than four years of teaching experience. So what has the school system done to meet this seemingly unending situation? What will be done to continue to curb this shortage? And what ought to be considered for the future?
Activities for Students: Using Statistics to Check on Elvis
Authors: Schabel Carmen
Published: November 2020

Elvis, a Welsh corgi, has captured the attention of the mathematics community because of his owner's claim that this cute dog knows calculus. In the May 2003 issue of the College Mathematics Journal, Tim Pennings writes that his dog Elvis chooses a path that is “remarkably” close to the optimal path (in terms of time) when a tennis ball is thrown from the water's edge at point A to a point B in the water (Pennings 2003, p. 181). See the figure on sheet 1. Elvis runs along the shore from point A to D and then dives into the water and swims to the ball at point B. Since Elvis can run faster than he can swim, the quickest route to the ball is different from the shortest route to the ball (swimming from A to B). The quickest route to fetch the ball involves a combination of running along the shore and swimming in the water.
Trigonometry Saves Engineer's Time
Authors: Rule Sean D.
Published: November 2020

There is a story behind the unusual title of this article. My most memorable teacher, Richard Crouse of the University of Delaware, had a lasting impact on the way I learned and teach mathematics. During the problem-solving course I took with Professor Crouse, we learned many ways to reach students, and to this day I use those strategies. Crouse was a frequent contributor to this journal, and his last article, “Linear Function Saves Carpenter's Time,” published in May 1990, was yet another example of how he got students to “think outside the box.” Sadly, Crouse lost a battle with cancer in 2000.
Grandfather Tang Goes to High School
Authors: Johnson Iris DeLoach
Published: November 2020

Grandfather Tang's Story (Tompert 1990) has been read in many elementary and middle school classrooms in which students engage in mathematical discoveries of simple geometric terms and relationships. In the middle grades it is possible to engage in more sophisticated investigations, which include reasoning about fractions, percents, and powers of 2. Middle school students may also engage in informal proof to show “that there are in fact just thirteen possible convex polygons that can be made from the seven Tangram pieces” (Bradford 2002, p. 4). Because “the tangram is a versatile manipulative” that can support more mathematics than originally meets the eye (Thatcher 2001, p. 394), it is time to seek a place for this story in high school mathematics classes.
Connecting Research to Teaching: A Study of Note Taking and Its Impact on Student Perception of Use in a Geometry Classroom
Authors: Walmsley Angela L. E. , Hickman Aaron
Published: November 2020

In the Paideia Program, Mortimer Adler (1984) states that “the activity of the mind is occasioned or initiated by wonder, sustained by interest and excitement, and reinforced by the pleasure inherent in the activity itself and by delight in its success” (p. 47). Yet, in many mathematics classrooms, the teaching methods used are contrary to each piece of Adler's statement. More specifically, teachers insist on note-taking strategies that bind and inhibit the curiosity and creativity of students. Most of these strategies involve copying main points word for word from the board, copying theorems from the book word for word, or possibly matching words with their definitions on a worksheet. One might question whether these styles of note taking are effective in fostering genuine understanding and prolonged retention of the material being taught.
Nature and origin of large-scale and intrasalt deformation within the Wieliczka salt mine, Poland
Authors: ROWAN Mark G. , KRZYWIEC Piotr , BUKOWSKI Krzysztof , PRZYBYŁO Jerzy
Published: November 2020

The Wieliczka salt mine, near Kraków in southern Poland, is a world-famous historical and modern destination for both geoscientists and tourists. Despite numerous publications, there is still a lack of consensus on the nature and origin of the large-scale folds as well as whether the small-scale structures represent tectonic or soft-sediment deformation. In this preliminary work, we offer new ideas on both aspects. At the large scale, we emphasize the mechanical stratigraphy of the layered evaporite sequence, which comprises a thin basal weak layer, a thin strong unit, a thicker weak layer, and a thicker strong unit. We suggest that the inclined to recumbent folds and thrusts formed tectonically due to overthrust shear between the basal detachment and the overriding Carpathian frontal thrust, with different structural styles decoupled by the thick weak layer. At the small scale, we suggest that there was early extension directed toward the east to north-east, followed by contraction vergent toward the north. We infer that there was early, syndepositional gravity gliding down a topographic slope dipping into the coeval Gdów depocenter to the east, and that subsequent north-directed Carpathian shortening generated the small-scale contractional structures as the larger folds were developing
ON THE REALISTIC STRESS SPACE OF SOLIDS (CONTINUED)
Authors: LIU SHU-I  ,   北京钢铁工业学院
Published: November 2020

A general theory on the realistic stress space of solids was formulated in a previous paper. In this paper, the bell stress spaces of several metals are compared, the concept of "efficiency of plastic deformation" is introduced and formulated, and the locus of deformation is discussed in connection with the theory of bell stress space. The main concepts of this paper are:Because the concept of strength of solids is associated with the stress state, it is difficult to bring out the concrete meaning of strength by a brief definition. Inasmuch as the volume of the closed stress space is a complete and concrete measure of the fracture strength and the limit of strain-hardened elastic strength in all stress states, we are inclined to define this volume as strength. This is not just a matter of definition; the important point is that the size and shape of the closed space actually reflect the physical and mechanical aspects of strength, and it gives one a clear impression about what is meant by strength.The concept of "efficiency of plastic deformation" arises from the fact that one may raise the internal potential energy of a solid infinitely without causing plastic deformation if the stress state is not favourable. This efficiency is the ratio of plastic distortion energy to the sum of elastic and plastic strain energies. It may be formulated, by simple arguments, as a function of octahedral shear strain and a stress state parameter c=θ/τ, where θ is the average normal stress and τ the octahedral shear stress. It increases with increasing strain and decreases with increasing hydrostatic stress, and it is actually measured by the length and the direction cotangent (c) of the position vector with respect to the hydrostatic axis.A process of deformation can hardly be well understood without knowing its locus of deformation in relation to the limiting surfaces of the stress space. By the theory of bell stress space and experimental measurements, such locus can be located. A locus for strip rolling is presented. It is interesting to note that there is a natural tendency for continuous processes of deformation to turn towards the [111] direction in order to make the total strain energy of the system a minimum.
THE FORMATION OF σ-PHASE IN A MODIFIED 18/8 STAINLESS STEEL
Authors: CHUANG Yü-CHIH  , LI YO-KO  ,   中国科学院金属研究所
Published: November 2020

The formation of σ-phase in a 18% Cr 11% Ni 2.6% Mo 0.8% Ti stainless steel has been investigated. Microscopic and X-ray examinations showed that the formationσf σ-phase from δ-ferrite was accompanied by the formation of austenite, the reaction being most rapid at 850℃The formation of a caused a marked decrease in Izod value and a slight increase in hardness. The σ-phase and its detrimental effects can be removed by a re-solution treatment at 1100℃.
THE RADIATIVE CORRECTIONS TO THE SCATTERING OF ELECTRONS AND POSITRONS
Authors: KING SING-NAN  ,   中国科学院物理研究所
Published: November 2020

With the Mφller's theory of scattering between the electrons and the Dirac's hole theory, Bhabha has obtained the formula for the scattering of the electrons and the positrons. The experimental evidence of this phenomenon was discovered by Ho (何泽慧), and she has studied this phenomenon by means of the β+-radioactivity of the β+ sources such as Mn52, and F18 in the cloud chamber. The comparison of the theory and the experiment was done (see reference [2], [3], [4], [5] and [6].) by Ho, O. Ritter et al, R. R. Roy and L. Groven, G. R. Hoke and A. Ashkin et al.The purpose of the present work is to show the effect of the radiative corrections to the scattering of the electrons and the positrons by the method in the quantum electrodynamics developed by S. Tomonaga, J. Schwinger, R. P. Feynman and F. J. Dyson.In the above-mentioned electron and positron scattering experiments, the contributions to the scattering cross-section are mostly due to the positrons of low energies (about 0.1 to 0.2 Mev). In this energy range, the exchange effect in Bhabha's theory is small. In this work for the radiative corrections to the scattering of the electrons and the positrons, we have neglected this exchange effect. The ratio of the correction of the scattering cross-section due to the radiative corrections to the scattering cross-section of Bhabha's theory at this energy range does not exceed 1%. For experiments of the low energy positrons and of the higher energy positrons (e.g positrons with energies of 0.5 Mev to 1 Mev as in the experiment of Ashkin et al) with small exchanges of energy between the electrons and the positrons during scattering, our calculation is adequate. But for positrons of higher energies and with large exchanges during scattering, our calculation should be improved by considering the exchange effect.
AN APPROXIMATE SOLUTION OF TORSION PROBLEM OF PRISM WITH SMALL HOLE
Authors: LI YU-CHANG  ,   南昌第一中学
Published: November 2020

In this paper, a method of superposition in given for the determination of approximate stress function of prisin with small hole in torsion. The approximate stress function consists of two parts. The first part is the solution of torsion problem for a simply connected region bounded by the exterior boundary of the given prism. The second part is the solution of Von-Neumann problem in the exterior region of the small hole.The boundary value of second part on the small hole is determined so that the superposition of these two solution gives free boundary condition on the surface of hole. It can be shown that the effect of second solution are concentrated in around the neighbourhood of the small hole.
SEDIMENTATION MOTION OF SAND PARTICLES IN MOVING WATER (Ⅰ)——THE RESISTANCE OK A SMALL SPHERE MOVING IN NON-UNIFORM FLOW
Authors: TSAI SHU-TANG  ,   中国科学院力学研究所
Published: November 2020

In hydraulics, when we deal with the problem of sand particles moving relative to the surrounding water, Stokes' formula of resistance has usually been used to render the velocity of sedimentation of the particles. But such an approach has not been proved rigorously, and its accuracy must be carefully considered. In this paper, we discuss the problem of a sphere moving in a non-uniform flow field, on the basis of the fundamental theory of hydrodynamics. We introduce two assumptions: i)the diameter of the sphere is much smaller than the linear dimension of the flow field, ii) the velocity of the sphere relative to surrounding water is very small. Usnig these two assumptions, we solve the linearized Navier-Stokes' equations and equations of continuity by the method of Laplace transform, and finally we obtain a formula for the resistance acting on a, sphere moving in a non-uniform flow field.
SEDIMENTATION MOTION OF SAND PARTICLES IN MOVING WATER (Ⅱ)——SEDIMENTATION OF SAND PARTICLES IN LAMINAR FLOW
Authors: TSAI SHU-TANG  ,   中国科学院力学研究所
Published: November 2020

In dealing with the problem of sand particles moving relative to the surrounding water, Stokes' formula of resistance has usually been used to render the velocity of sedimentation of the particles. But such an approach has not been proved rigorously, and its accuracy must be carefully examined. In the previous paper, we gave the resistance acting on a sphere moving in a non-uniform flow field. In this paper, we assume the concentration of sand particles to be very small, and using the previously obtained formula for the resistance, we establish the general equations of motion of laminar flow of sand particles and water. Then, we discuss the sedimentation motion of sand particles for laminar flow in an open channel.Finally, we find that the component of relative velocity parallel to the main stream is not equal to zero. Thereby, we obtain the error in the position of sedimentation as calculated by means of the usual simplified assumption. This error in position is proportional to the depth of water, and is independent of the size of sand particles. In general, it is not a negligible quantity.
EFFECT OF SURFACE RECOMBINATION ON THE PHOTOCONDUCTIVE SPECTRUM OF n-TYPE GERMANIUM (Ⅰ)
Authors: TANG TING-YUAN  , KAO KUO-YU  ,   中国科学院应用物理研究所
Published: November 2020

A method of measuring photoconductive spectra is described in detail, and results of measurement made on n-type germanium are presented. It is found that the shape of the photoconductive spectra is dependent on the surface treatment of the sample.
THE DEVELOPMENT OF RECRYSTALLIZATION TEXTURE OF COLD-ROLLED COPPER STRIPS
Authors: YEN MING-KAO  , CHOU PANG-HSIN  ,   中国科学院应用物理研究所
Published: November 2020

The rolling texture of electrolytic copper after a reduction of thickness 88.7% can be described as (110) [112], (112) [111] and a texture (3,6,11) [533]. During annealing at lower temperature, the recrystallization texture was found to be (100) [001] + (358) [352] plus a (122) [212] texture which is a twin position with respect to (100) [001] texture. Together with the raising of the annealing temperature, a decrease of (358) [352] texture and on increase of (100) [001] texture was observed. When annealing temperature reached to 900℃, a nearly perfect cubic texture was developed.During annealing at higher temperature (900℃), grains having (100) [001] oriention appeared first. Then, an overall "recrystallization in situ" took place and the (100) [001] grains tended to grow selectively at the expense of the others. Finally, a concentrated (100) [001] texture was produced.The geometric relationship between the rolling texture and the recrystallization texture was investigated. In general, the change from the rolling texture to the recrystallization texture may be suggested as a rotation of 45°, 22°, 38° about a common [111] axis. The ideal pole-figures, constructed according to the above relationship were found to be in good agreement with the experimental results.It was found that the different rate of heating and the different annealing procedures produced no signeficant effect on the final recrystallization texture. The temperature of annealing, however, was the main factor contributing to the development of the recrystallization texture.
THE EXCITATION OF NUCLEI BY ELECTRONS AND X-RAYS
Authors: HO KUO-CHU  ,   南开大学
Published: November 2020

The theory of the excitation of nuclei by electrons of intermediate energy has been studied. Cross sections for the excitation of nuclei due to the interaction of the electromagnetic field of the electron with the electric dipole, qua-drupole, and with the magnetic dipole and quadrupole moments of the nucleus have been evaluated explicitly in terms of these moments.A relationship between the electro-excitation cross section and corresponding X-ray excitation cross section is established. This relationship is independent of all properties of the nucleus except for the change in the energy, angular momentum and parity involved in the transition.The predictions of the theory are compared with the experimental measurements in the excitation of In115. It is found that no definite information about the nuclear levels is obtained by this comparison because of insufficient precise experimental results. Measurements which would lead to information about the properties of the nuclear states are suggested.
MECHANISM OF CARBON DIFFUSION PEAK IN F. C. C. IRON-NICKEL ALLOYS
Authors: WU TZU-LIANG  , WANG CHI-MIN  ,   中国科学院冶金陶瓷研究所
Published: November 2020

An internal friction peak induced by carbon diffusion has been observed in f. c. c. iron-nickel alloys. At a vibrational frequency of 1.4 cycles per sec., the peak occurs at about 500°K. This peak arises from the preferential rotation of the axes of carbon pairs existed in the specimen under the influence of an alternating load. These carbon pairs were formed by the interaction between the substitutional carbon atoms and their neighboring interstitial carbon atoms. Based upon this mechanism and considering the possible redistribution of the carbon atoms amongst the frozen-in vacancies in the specimen during the course of internal friction measurement, an equation bearing the quantitative relationship between the peak height and the carbon concentration has been derived. The energy of vacancy formation as well as the binding energy of the carbon pairs have been determined.The characteristics of the carbon diffusion peak in f. c. c. metals are: (1) The internal friction curve is not symmetric with respect to the peak position, the internal friction on the high temperature side being smaller than on the low temperature side. (2) The T′Qmax-1 product varies with the peak temperature T′; the lower the peak temperature, the higher the T′Qmax-1 product. (3) The peak temperature T′ drifts with the carbon concentration as well as the quench temperature of the specimen. Either an increase of the carbon concentration or a raise of the quench temperature tends to shift the peak position toward a lower temperature. These characteristics are interpreted in terms of the carbon pair theory as given in the text.
THE PROCESS OF DECOMPOSITION OF MARTENSITE DURING THE FIRST STAGE OF TEMPERING
Authors: SZE SHIH-YUAN  ,   南京大学
Published: November 2020

The process of decomposition of supersaturated tetragonal martensite during the first stage of tempering is investigated by considering the characteristics of motion of a carbon atom from one interstitial position to another within the martensite matrix. It is evident that not all the carbon atoms take part simultaneously in the process of precipitation, some remain in solution for a longer time, others shorter, some mobile, others stationary. By assuming that each transition from one state of motion to another has a definite probability, which is independant of time and carbon concentration but dependant on temperature and the nature of crystalline matrix, it can be shown that an isothermal decomposition curve can be expressed as a series with exponential terms, the coefficients of which are related to the distribution of carbon atoms in different states of motion. The agreement between this expression and the existing experimental data is satisfactory. The general tendancy of the variation of the coefficients with temperature is just what should be expected.
Generation and control of photo-excited thermal currents in triple degenerate topological semimetal MoP with circularly polarized ultrafast light pulses
Authors: Jiazila Hasaien  , Zhu Ke-Jia , Sun Fei , Wu Yan-Ling , Shi You-Guo , Zhao Ji-Min ,   Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China,   School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China,   Songshan Lake Materials Laboratory, Dongguan 523808, China
Published: November 2020

Ultrafast spectroscopy is a powerful method to generate and control topological phase transitions and spin-polarized electrical currents in topological quantum materials. These light-induced novel physical properties originate from the topologically nontrivial states of Dirac and Weyl fermions. The topological semimetal molybdenum phosphide (MoP) exhibits double and triple degenerate points in the momentum space. We present the preliminary results of spin-polarized electrical currents and optical response investigations of MoP. We design and construct an experimental setup to perform the photocurrent generation and control by circularly polarized light in topological insulator Bi2Se3. The results compare well with those reported, which confirms the validity and reliability of our experimental setup. Further, we conduct the photocurrent experiment on MoP by using 400 nm laser pulses for excitation and successfully detect the current signals at different sample positions. We attribute the observed currents to photo-induced thermal currents (not the photo current associated with the triple degenerate topological properties), which facilitates generating and controlling photocurrents in MoP in the future investigation. Our thermal current investigations are of essence for further exploring the photocurrents in various types of topological quantum materials.
Theoretical study of nonlinear multi-exciton dynamics in coupled molecular chains
Authors: Fu Xiao-Qian , Lü Si-Yuan , Wang Lu-Xia ,   Physics Department, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
Published: November 2020

Details of exciton dynamics in dye aggregates and supra-molecular complexes are substantially important for the functionality of molecular based opto-electronic devices. There are intensive theoretical studies of the multi-exciton dynamics in quantum dot structures but much less in molecular systems. Multiple excitons can be produced in molecular chains as well as two-dimensional and three-dimensional aggregates under an excitation of ultrafast strong laser pulse. According to the dipole arrangements of molecular chains, the coupled molecular chains are designed as H-H, H-J and J-H types of dipole configurations. In the scheme of density matrix theory, the dynamic processes of multiple excitons of different configurations are investigated by solving the quantum master equation through using the approximate dipole-dipole and expectation values of interest. The equations of motion for expectation values of interest governing the respective density operator are used to describe the temporal evolution of the multi-exciton states. It is found that the exciton energy band can be formed in the energy representation, and the multiple excitons are delocalized in the aggregates. The excitons represent different temporal evolutions excited by different resonant excitations. Compared with single-chain systems, double-chain systems have different degrees of blue shift or red shift due to interchain coupling. In the H-H type of aggregate, the electron population is lower if the double-molecule chain is simultaneously excited by the resonance frequency of a single molecule; the electron population increases to a certain extent if the frequency of the field is higher than the vibration frequency of a single molecule. The band width and the energy levels of the multiple excitons vary for different configurations of coupled molecular chains, and the wave packets show their own characters in these energetic levels. In the H-H type of aggregate, exciton state has priority to occupy the high-order energy level. The width of the exciton band of H-J type is significantly narrower than that of H single or H-H double chain configuration, because the Coulomb interaction of the inter-stranded dipole moment makes the whole energy low. In the J-H aggregates, the exciton states are more stable from the energy point of view, and the exciton energy band is wide because of the large Coulomb interaction. The energy of exciton state can be transferred via the interchain coupling, no matter which chain is excited. The transfer period directly correlates with the nearest interchain coupling.