diff --git "a/reference_files/sentence-test.new_wiki.txt" "b/reference_files/sentence-test.new_wiki.txt" --- "a/reference_files/sentence-test.new_wiki.txt" +++ "b/reference_files/sentence-test.new_wiki.txt" @@ -45,15 +45,11 @@ The Mother See of Holy Etchmiadzin operates two seminaries, the Gevorkian Theolo Over a 6-year course of simultaneous study, students receive both a bachelor's degree and a master's degree in Theology. Over a 6-year course of simultaneous study, students receive both a bachelor's degree and a master's degree in Theology . The Great House of Cilicia operates one seminary, the Seminary of Antelias at Bikfaya , Lebanon. -Armenian - religious minorities and human rights groups also expressed serious concern over the amendments, with human rights activist Stepan Danielian stating "the Armenian Apostolic Church today wants to have a monopoly on religion". +Armenian. religious minorities and human rights groups also expressed serious concern over the amendments, with human rights activist Stepan Danielian stating "the Armenian Apostolic Church today wants to have a monopoly on religion". In 2009 , further constitutional amendments were drafted that would make it a crime for non-traditional religious groups to proselytize on adherents of the Apostolic Church. -Armenian -religious minorities and human rights groups also expressed serious concern over the amendments, with human rights activist Stepan Danielian stating "the Armenian Apostolic Church today wants to have a monopoly on religion". -Armenian -religious minorities and human rights groups also expressed serious concern over the amendments, with human rights activist Stepan Danielian stating "the Armenian Apostolic Church today wants to have a monopoly on religion". The Armenian Church defines religious groups operating outside its domain as "sects" and, in the words of spokesman Bishop Arshak Khachatrian, considers that "their activities in Armenia are nothing but a denial of the creed of the Armenian Apostolic Church, which is considered the national religion of the Armenian people". -Armenian -religious minorities and human rights groups also expressed serious concern over the amendments, with human rights activist Stepan Danielian stating "the Armenian Apostolic Church today wants to have a monopoly on religion". +Armenian.religious minorities and human rights groups also expressed serious concern over the amendments, with human rights activist Stepan Danielian stating "the Armenian Apostolic Church today wants to have a monopoly on religion". +Armenian.religious minorities and human rights groups also expressed serious concern over the amendments, with human rights activist Stepan Danielian stating "the Armenian Apostolic Church today wants to have a monopoly on religion". The Armenian Church defines religious groups operating outside its domain as "sects" and, in the words of spokesman Bishop Arshak Khachatrian, considers that "their activities in Armenia are nothing but a denial of the creed of the Armenian Apostolic Church, which is considered the national religion of the Armenian people". +Armenian.religious minorities and human rights groups also expressed serious concern over the amendments, with human rights activist Stepan Danielian stating "the Armenian Apostolic Church today wants to have a monopoly on religion". Due to the Bolshevik revolution and the subsequent annexation of Armenia by the U.S.S.R ., all functioning religious institutions in Armenia and NKAO were closed down, and their clergymen either exiled or shot. Due to the Bolshevik revolution and the subsequent annexation of Armenia by the U.S.S.R., all functioning religious institutions in Armenia and NKAO were closed down, and their clergymen either exiled or shot. Due to the Bolshevik revolution and the subsequent annexation of Armenia by the U.S.S.R., all functioning religious institutions in Armenia and NKAO were closed down, and their clergymen either exiled or shot. @@ -314,8 +310,7 @@ In the extreme south a major transform fault separates Tierra del Fuego from the Across the 1,000 km (620 mi) wide Drake Passage lie the mountains of the Antarctic Peninsula south of the Scotia Plate which appear to be a continuation of the Andes chain.[citation needed] Across the 1,000 km (620 mi) wide Drake Passage lie the mountains of the Antarctic Peninsula south of the Scotia Plate which appear to be a continuation of the Andes chain.[citation needed] Parts of the Sunsás Orogen in Amazonian craton disappeared from the surface of earth being overrided by the Andes. -Parts of the Sunsás Orogen in Amazonian craton disappeared from the surface of earth being overrided by the Andes. - The Sierras de Córdoba , where the effects of the ancient Pampean orogeny can be observed, owe their modern uplift and relief to the Andean orogeny in the Tertiary. +Parts of the Sunsás Orogen in Amazonian craton disappeared from the surface of earth being overrided by the Andes.. The Sierras de Córdoba , where the effects of the ancient Pampean orogeny can be observed, owe their modern uplift and relief to the Andean orogeny in the Tertiary. Parts of the Sunsás Orogen in Amazonian craton disappeared from the surface of earth being overrided by the Andes. Further south in southern Patagonia the onset of the Andean orogeny caused the Magallanes Basin to evolve from being an extensional back-arc basin in the Mesozoic to being a compressional foreland basin in the Cenozoic. Further south in southern Patagonia the onset of the Andean orogeny caused the Magallanes Basin to evolve from being an extensional back-arc basin in the Mesozoic to being a compressional foreland basin in the Cenozoic. @@ -416,8 +411,7 @@ Alternative sources of labour, such as indentured servitude, failed to provide a The Atlantic Slave Trade was the result of, among other things, labour shortage, itself in turn created by the desire of European colonists to exploit New World land and resources for capital profits. The last recorded slave ship to land on American soil was the Clotilde, which in 1859 illegally smuggled a number of Africans into the town of Mobile, Alabama. The last survivor of the voyage was Cudjoe Lewis, who died in 1935 . - -The last country to ban the Atlantic slave trade was Brazil in 1831 . +.The last country to ban the Atlantic slave trade was Brazil in 1831 . In Brazil slavery itself however did not end until 1888 , which was the last country in the Americas to end involuntary servitude. However, a vibrant illegal trade continued to ship large numbers of enslaved people to Brazil and also to Cuba until the 1860s, when British enforcement and further diplomacy finally ended the Atlantic trade. In 1870 Portugal ended the last trade route with the Americas where the last country to import slaves was Brazil. Africans played a direct role in the slave trade, selling their captives or prisoners of war to European buyers. @@ -577,14 +571,12 @@ The DASH diet (high in nuts, fish, fruits and vegetables, and low in sweets, red Insufficient physical activity ( defined as less than 5 x 30 minutes of moderate activity per week, or less than 3 x 20 minutes of vigorous activity per week ) is currently the fourth leading risk factor for mortality worldwide. Insufficient physical activity (defined as less than 5 x 30 minutes of moderate activity per week, or less than 3 x 20 minutes of vigorous activity per week) is currently the fourth leading risk factor for mortality worldwide. In 2008, 31.3% of adults aged 15 or older (28.2% men and 34.4% women) were insufficiently physically active. - -The risk of ischemic heart disease and diabetes mellitus is reduced by almost a third in adults who participate in 150 minutes of moderate physical activity each week (or equivalent). + .The risk of ischemic heart disease and diabetes mellitus is reduced by almost a third in adults who participate in 150 minutes of moderate physical activity each week (or equivalent). In addition, physical activity assists weight loss and improves blood glucose control, blood pressure, lipid profile and insulin sensitivity . High dietary intakes of saturated fat, trans-fats and salt, and low intake of fruits, vegetables and fish are linked to cardiovascular risk, although whether all these associations are a cause is disputed. The World Health Organization attributes approximately 1.7 million deaths worldwide to low fruit and vegetable consumption. Frequent consumption of high-energy foods, such as processed foods that are high in fats and sugars, promotes obesity and may increase cardiovascular risk. - - There is evidence that higher consumption of sugar is associated with higher blood pressure and unfavorable blood lipids , and sugar intake also increases the risk of diabetes mellitus. +. There is evidence that higher consumption of sugar is associated with higher blood pressure and unfavorable blood lipids , and sugar intake also increases the risk of diabetes mellitus. High consumption of processed meats is associated with an increased risk of cardiovascular disease, possibly in part due to increased dietary salt intake. Total fat intake does not appear to be an important risk factor . Worldwide, dietary guidelines recommend a reduction in saturated fat . @@ -593,8 +585,7 @@ Benefits from replacement with polyunsaturated fat appears greatest; however, su Replacement of saturated fats with carbohydrates does not change or may increase risk. Benefits from replacement with polyunsaturated fat appears greatest; however, supplementation with omega-3 fatty acids (a type of polysaturated fat) does not appear to have an effect. The relationship between alcohol consumption and cardiovascular disease is complex, and may depend on the amount of alcohol consumed . Drinking at low levels without episodes of heavy drinking may be associated with a reduced risk of cardiovascular disease . - - Overall alcohol consumption at the population level is associated with multiple health risks that exceed any potential benefits. +. Overall alcohol consumption at the population level is associated with multiple health risks that exceed any potential benefits. There is a direct relationship between high levels of alcohol consumption and risk of cardiovascular disease. Drinking at low levels without episodes of heavy drinking may be associated with a reduced risk of cardiovascular disease. The relationship between alcohol consumption and cardiovascular disease is complex , and may depend on the amount of alcohol consumed. In addition, the review suggested that a low-salt diet may be harmful in those with congestive heart failure . @@ -631,17 +622,13 @@ If a fe male has diabetes, she is more likely to develop heart disease than a ma Cardiovascular disease affects low- and middle-income countries even more than high-income countries. Policies that have resulted in increased socio-economic inequalities have been associated with greater subsequent socio-economic differences in cardiovascular disease implying a cause and effect relationship . There is relatively little information regarding social patterns of cardiovascular disease within low- and middle-income countries, but within high-income countries low income and low educational status are consistently associated with greater risk of cardiovascular disease. - - The Commission on Social Determinants of Health recommended that more equal distributions of power, wealth, education, housing, environmental factors, nutrition, and health care were needed to address inequalities in cardiovascular disease and non-communicable diseases. - - The Commission on Social Determinants of Health recommended that more equal distributions of power, wealth, education, housing, environmental factors, nutrition, and health care were needed to address inequalities in cardiovascular disease and non-communicable diseases. +. The Commission on Social Determinants of Health recommended that more equal distributions of power, wealth, education, housing, environmental factors, nutrition, and health care were needed to address inequalities in cardiovascular disease and non-communicable diseases. +. The Commission on Social Determinants of Health recommended that more equal distributions of power, wealth, education, housing, environmental factors, nutrition, and health care were needed to address inequalities in cardiovascular disease and non-communicable diseases. Cardiovascular disease affects low- and middle-income countries even more than high-income countries. There is relatively little information regarding social patterns of cardiovascular disease within low- and middle-income countries, but within high-income countries low income and low educational status are consistently associated with greater risk of cardiovascular disease. Policies that have resulted in increased socio-economic inequalities have been associated with greater subsequent socio-economic differences in cardiovascular disease implying a cause and effect relationship . - - The Commission on Social Determinants of Health recommended that more equal distributions of power, wealth, education, housing, environmental factors, nutrition, and health care were needed to address inequalities in cardiovascular disease and non-communicable diseases. - - The Commission on Social Determinants of Health recommended that more equal distributions of power, wealth, education, housing, environmental factors, nutrition, and health care were needed to address inequalities in cardiovascular disease and non-communicable diseases. +. The Commission on Social Determinants of Health recommended that more equal distributions of power, wealth, education, housing, environmental factors, nutrition, and health care were needed to address inequalities in cardiovascular disease and non-communicable diseases. +. The Commission on Social Determinants of Health recommended that more equal distributions of power, wealth, education, housing, environmental factors, nutrition, and health care were needed to address inequalities in cardiovascular disease and non-communicable diseases. Coronary heart diseases are 2 to 5 times more common among middle-aged men than women. Coronary heart diseases are 2 to 5 times more common among middle-aged men than women. Estrogen may have protective effects through glucose metabolism and hemostatic system, and may have direct effect in improving endothelial cell function. @@ -796,12 +783,10 @@ On some U.S. military uniforms, flag patches are worn on the right shoulder , fo Since the Stars and Stripes are mounted with the canton closest to the pole, that section stayed to the right, while the stripes flew to the left . Several US military uniforms, such as flight suits worn by members of the United States Navy, have the flag patch on the left shoulder. Following the reopening of the National Museum of American History on November 21, 2008 , the flag is now on display in a special exhibition, "The Star-Spangled Banner: The Flag That Inspired the National Anthem," where it rests at a 10 degree angle in dim light for conservation purposes. -In 1907 Eben Appleton , New York stockbroker and grandson of Lieutenant Colonel George Armistead -(the commander of Fort McHenry during the 1814 bombardment) lent the Star Spangled Banner Flag to the Smithsonian Institution, and in 1912 he converted the loan to a gift. +In 1907 Eben Appleton , New York stockbroker and grandson of Lieutenant Colonel George Armistead.(the commander of Fort McHenry during the 1814 bombardment) lent the Star Spangled Banner Flag to the Smithsonian Institution, and in 1912 he converted the loan to a gift. Following the reopening of the National Museum of American History on November 21, 2008, the flag is now on display in a special exhibition, "The Star-Spangled Banner: The Flag That Inspired the National Anthem," where it rests at a 10 degree angle in dim light for conservation purposes . a 10 degree angle in dim light for conservation purposes. -In 1907 Eben Appleton, New York stockbroker and grandson of Lieutenant Colonel George Armistead -(the commander of Fort McHenry during the 1814 bombardment) lent the Star Spangled Banner Flag to the Smithsonian Institution, and in 1912 he converted the loan to a gift. +In 1907 Eben Appleton, New York stockbroker and grandson of Lieutenant Colonel George Armistead.(the commander of Fort McHenry during the 1814 bombardment) lent the Star Spangled Banner Flag to the Smithsonian Institution, and in 1912 he converted the loan to a gift. The flag is displayed at half-staff (half-mast in naval usage) as a sign of respect or mourning . President Dwight D. Eisenhower issued the first proclamation on March 1, 1954 , standardizing the dates and time periods for flying the flag at half-staff from all federal buildings, grounds, and naval vessels; other congressional resolutions and presidential proclamations ensued. President Dwight D. Eisenhower issued the first proclamation on March 1, 1954, standardizing the dates and time periods for flying the flag at half-staff from all federal buildings, grounds, and naval vessels; other congressional resolutions and presidential proclamations ensued. @@ -1316,8 +1301,7 @@ Istanbul (/ˌɪstænˈbuːl/ or /ˌiːstɑːnˈbuːl/; Turkish: İstanbul [isˈt Istanbul is a transcontinental city in Eurasia, straddling the Bosphorus strait between the Sea of Marmara and the Black Sea . Its commercial and historical center lies on the European side and about a third of its population lives on the Asian side . Istanbul is one of the world's most populous cities and ranks as world's 6th-largest city proper and the largest European city. -Its commercial and historical center lies on the European side and about a third of its population lives on the Asian side. - The city is the administrative center of the Istanbul Metropolitan Municipality (coterminous with Istanbul Province) , both hosting a population of around 14 million residents. +Its commercial and historical center lies on the European side and about a third of its population lives on the Asian side.. The city is the administrative center of the Istanbul Metropolitan Municipality (coterminous with Istanbul Province) , both hosting a population of around 14 million residents. Founded under the name of Byzantium on the Sarayburnu promontory around 660 BCE, the city developed to become one of the most significant in history. After its reestablishment as Constantinople in 330 CE , it served as an imperial capital for almost 16 centuries, during the Roman and Byzantine (330–1204 and 1261–1453), the Latin (1204–1261), and the Ottoman (1453–1922) empires. After its reestablishment as Constantinople in 330 CE, it served as an imperial capital for almost 16 centuries, during the Roman and Byzantine (330–1204 and 1261–1453), the Latin (1204–1261), and the Ottoman (1453–1922) empires. @@ -1646,8 +1630,7 @@ Since the 1970s there has been deregulation of some industries, like banking, tr Since the 1970s there has been deregulation of some industries, like banking, trucking, airlines and telecommunications which resulted generally in more competition and lower prices.[citation needed] According to Cato Institute , an American libertarian think-tank, some industries deregulation of aspects of an industry were offset by more ambitious regulations elsewhere that hurt consumers, the electricity industry being a prime example. Since the 1970s there has been deregulation of some industries, like banking, trucking, airlines and telecommunications which resulted generally in more competition and lower prices.[citation needed] According to Cato Institute, an American libertarian think-tank, some industries deregulation of aspects of an industry were offset by more ambitious regulations elsewhere that hurt consumers, the electricity industry being a prime example. For example, in banking, Cato Institute believes some deregulation allowed banks to compete across state lines, increasing consumer choice, while an actual increase in regulators and regulations forced banks to do business the way central government regulators commanded, including making loans to individuals incapable of repaying them, leading eventually to the financial crisis of 2007–2008 .[unreliable source?] -Some argue that government standardisation in areas from commodity market, inspection and testing procurement bidding, Building codes, professional and vocational education, trade certification, safety, etc. are necessary.[citation needed] Emmanuelle Auriol and Michel Benaim write about the "comparative -benefits" of decentralization versus government regulation in the setting of standards. +Some argue that government standardisation in areas from commodity market, inspection and testing procurement bidding, Building codes, professional and vocational education, trade certification, safety, etc. are necessary.[citation needed] Emmanuelle Auriol and Michel Benaim write about the "comparative.benefits" of decentralization versus government regulation in the setting of standards. They find that while there may be a need for public regulation if public safety is at stake , private creation of standards usually is better because "regulators or 'experts' might misrepresent consumers' tastes and needs." They find that while there may be a need for public regulation if public safety is at stake, private creation of standards usually is better because "regulators or 'experts' might misrepresent consumers' tastes and needs." As long as companies are averse to incompatible standards, standards will be created that satisfy needs of a modern economy. They find that while there may be a need for public regulation if public safety is at stake, private creation of standards usually is better because "regulators or 'experts' might misrepresent consumers' tastes and needs." As long as companies are averse to incompatible standards , standards will be created that satisfy needs of a modern economy. @@ -1764,14 +1747,10 @@ Theorists believe that local representative authorities with actual discretionar Theorists believe that local representative authorities with actual discretionary powers are the basis of decentralization that can lead to local efficiency, equity and development .” Columbia University's Earth Institute identified one of three major trends relating to decentralization as: "increased involvement of local jurisdictions and civil society in the management of their affairs, with new forms of participation, consultation, and partnerships." Columbia University's Earth Institute identified one of three major trends relating to decentralization as: "increased involvement of local jurisdictions and civil society in the management of their affairs, with new forms of participation, consultation, and partnerships ." -Diversity -Norman L. Johnson writes that diversity plays an important role in decentralized systems like ecosystems, social groups, large organizations, political systems. -Diversity - Norman L. Johnson writes that diversity plays an important role in decentralized systems like ecosystems, social groups, large organizations, political systems. -Diversity -Norman L. Johnson writes that diversity plays an important role in decentralized systems like ecosystems, social groups, large organizations, political systems. -Diversity -Norman L. Johnson writes that diversity plays an important role in decentralized systems like ecosystems, social groups, large organizations, political systems. +Diversity.Norman L. Johnson writes that diversity plays an important role in decentralized systems like ecosystems, social groups, large organizations, political systems. +Diversity. Norman L. Johnson writes that diversity plays an important role in decentralized systems like ecosystems, social groups, large organizations, political systems. +Diversity.Norman L. Johnson writes that diversity plays an important role in decentralized systems like ecosystems, social groups, large organizations, political systems. +Diversity .Norman L. Johnson writes that diversity plays an important role in decentralized systems like ecosystems, social groups, large organizations, political systems. Decentralized is defined as a property of a system where the agents have some ability to operate "locally.” An OECD study quotes Chanchal Kumar Sharma as stating: "a true assessment of the degree of decentralization in a country can be made only if a comprehensive approach is adopted and rather than trying to simplify the syndrome of characteristics into the single dimension of autonomy, interrelationships of various dimensions of decentralization are taken into account." Measuring the amount of decentralization, especially politically, is difficult because different studies of it use different definitions and measurements . @@ -1787,18 +1766,14 @@ In his 1910 The History of Nations Henry Cabot Lodge wrote that Persian king Dar Yildiz Atasoy writes this process has been going on “since the Stone Age” through not just chiefdoms and states, but empires and today’s “hegemonic core states”. In his 1910 The History of Nations Henry Cabot Lodge wrote that Persian king Darius I (550-486 BCE) was a master of organization and “for the first time in history centralization becomes a political fact.” Christopher K. Chase-Dunn and Thomas D. Hall review other works that detail these cycles, including works which analyze the concept of core elites which compete with state accumulation of wealth and how their "intra-ruling-class competition accounts for the rise and fall of states" and of their phases of centralization and decentralization. -Conflict resolution - Economic and/or political decentralization can help prevent or reduce conflict because they reduce actual or perceived inequities between various regions or between a region and the central government. -Conflict resolution -Economic and/or political decentralization can help prevent or reduce conflict because they reduce actual or perceived inequities between various regions or between a region and the central government. +Conflict resolution. Economic and/or political decentralization can help prevent or reduce conflict because they reduce actual or perceived inequities between various regions or between a region and the central government. +Conflict resolution.Economic and/or political decentralization can help prevent or reduce conflict because they reduce actual or perceived inequities between various regions or between a region and the central government. Dawn Brancati finds that political decentralization reduces intrastate conflict unless politicians create political parties that mobilize minority and even extremist groups to demand more resources and power within national governments. Brancati holds that decentralization can promote peace if it encourages statewide parties to incorporate regional demands and limit the power of regional parties. - -It has been called the "new public management" which has been described as decentralization, management by objectives, contracting out, competition within government and consumer orientation. +.It has been called the "new public management" which has been described as decentralization, management by objectives, contracting out, competition within government and consumer orientation. Government decentralization has both political and administrative aspects. Its decentralization may be territorial , moving power from a central city to other localities, and it may be functional, moving decision-making from the top administrator of any branch of government to lower level officials, or divesting of the function entirely through privatization. - Its decentralization may be territorial, moving power from a central city to other localities, and it may be functional, moving decision-making from the top administrator of any branch of government to lower level officials, or divesting of the function entirely through privatization. -It has been called the "new public management" which has been described as decentralization, management by objectives, contracting out, competition within government and consumer orientation. + Its decentralization may be territorial, moving power from a central city to other localities, and it may be functional, moving decision-making from the top administrator of any branch of government to lower level officials, or divesting of the function entirely through privatization. .It has been called the "new public management" which has been described as decentralization, management by objectives, contracting out, competition within government and consumer orientation. It may be associated with pluralistic politics and representative government , but it also means giving citizens, or their representatives, more influence in the formulation and implementation of laws and policies. It may be associated with pluralistic politics and representative government, but it also means giving citizens, or their representatives, more influence in the formulation and implementation of laws and policies . Depending on the country, this may require constitutional or statutory reforms , the development of new political parties, increased power for legislatures, the creation of local political units, and encouragement of advocacy groups. @@ -1826,10 +1801,8 @@ While centralization, especially in the governmental sphere, is widely studied a The meaning of decentralization may vary in part because of the different ways it is applied. Concepts of decentralization have been applied to group dynamics and management science in private businesses and organizations, political science, law and public administration, economics and technology. Concepts of decentralization have been applied to group dynamics and management science in private businesses and organizations, political science, law and public administration, economics and technology . The word "centralization" came into use in France in 1794 as the post-French Revolution French Directory leadership created a new government structure. -The word "decentralization" came into usage in the 1820s. "Centralization" entered written English in the first third of the 1800s; -mentions of decentralization also first appear during those years. -"Centralization" entered written English in the first third of the 1800s ; -mentions of decentralization also first appear during those years. +The word "decentralization" came into usage in the 1820s. "Centralization" entered written English in the first third of the 1800s;.mentions of decentralization also first appear during those years. +"Centralization" entered written English in the first third of the 1800s ;.mentions of decentralization also first appear during those years. In the mid-1800s Alexis de Tocqueville wrote that the French Revolution began with " a push towards decentralization...[but became,]in the end, an extension of centralization. " In 1863 retired French bureaucrat Maurice Block wrote an article called “Decentralization” for a French journal which reviewed the dynamics of government and bureaucratic centralization and recent French efforts at decentralization of government functions. [but became,]in the end, an extension of centralization." In 1863 retired French bureaucrat Maurice Block wrote an article called “Decentralization” for a French journal which reviewed the dynamics of government and bureaucratic centralization and recent French efforts at decentralization of government functions. Ideas of liberty and decentralization were carried to their logical conclusions during the 19th and 20th centuries by anti-state political activists calling themselves "anarchists", "libertarians," and even decentralists . @@ -1846,8 +1819,7 @@ Leopold Kohr, author of the 1957 book The Breakdown of Nations—known for its s Discussing the books in a later interview, Toffler said that industrial-style, centralized, top-down bureaucratic planning would be replaced by a more open, democratic, decentralized style which he called “anticipatory democracy.” Futurist John Naisbitt's 1982 book “Megatrends” was on The New York Times Best Seller list for more than two years and sold 14 million copies. Daniel Bell's The Coming of Post-Industrial Society discussed the need for decentralization and a “comprehensive overhaul of government structure to find the appropriate size and scope of units”, as well as the need to detach functions from current state boundaries, creating regions based on functions like water, transport, education and economics which might have “different ‘overlays’ on the map.” Alvin Toffler published Future Shock (1970) and The Third Wave (1980) . Futurist John Naisbitt's 1982 book “Megatrends” was on The New York Times Best Seller list for more than two years and sold 14 million copies. Naisbitt’s book outlines 10 “megatrends”, the fifth of which is from centralization to decentralization. -Analysis of operations - Project and program planners must assess the lowest organizational level at which functions can be carried out efficiently and effectively. +Analysis of operations. Project and program planners must assess the lowest organizational level at which functions can be carried out efficiently and effectively. Training for both national and local managers and officials is necessary, as well as technical assistance in the planning, financing, and management of decentralized functions. Training for both national and local managers and officials is necessary, as well as technical assistance in the planning, financing, and management of decentralized functions. The appropriate balance of centralization and decentralization should be studied. @@ -1857,8 +1829,7 @@ There is no one blueprint for decentralization since it depends on the initial s Decentralization ideally happens as a careful, rational, and orderly process, but it often takes place during times of economic and political crisis , the fall of a regime and the resultant power struggles. Decentralization usually is conscious process based on explicit policies. However, it may occur as " silent decentralization " in the absence of reforms as changes in networks, policy emphasize and resource availability lead inevitably to a more decentralized system. - -A variation on this is "inadvertent decentralization", when other policy innovations produce an unintended decentralization of power and resources. +.A variation on this is "inadvertent decentralization", when other policy innovations produce an unintended decentralization of power and resources. In both China and Russia , lower level authorities attained greater powers than intended by central authorities. Decentralization may be uneven and " asymmetric " given any one country's population, political, ethnic and other forms of diversity. In many countries, political, economic and administrative responsibilities may be decentralized to the larger urban areas, while rural areas are administered by the central government. @@ -2077,8 +2048,7 @@ A mediterranean sea of the Atlantic, with limited water exchange between the two While Tacitus called it Mare Suebicum after the Germanic people called the Suebi, the first to name it the Baltic Sea (Mare Balticum) was the eleventh-century German chronicler Adam of Bremen . Adam of Bremen himself compared the sea with a belt , stating that it is so named because it stretches through the land as a belt (Balticus, eo quod in modum baltei longo tractu per Scithicas regiones tendatur usque in Greciam). On this basis, a related hypothesis holds that the name originated from this Indo-European root via a Baltic language such as Lithuanian. - -Some Swedish historians believe the name derives from the god Balder of Nordic mythology. +.Some Swedish historians believe the name derives from the god Balder of Nordic mythology. It is possible that Pliny refers to an island named Basilia ("kingdom" or "royal") in On the Ocean by Pytheas. At the time of the Roman Empire, the Baltic Sea was known as the Mare Suebicum or Mare Sarmaticum. Tacitus in his AD 98 Agricola and Germania described the Mare Suebicum, named for the Suebi tribe, during the spring months, as a brackish sea where the ice broke apart and chunks floated about. @@ -2211,38 +2181,11 @@ The role of the parentheses in the definition is to ensure that any formula can This property is known as unique readability of formulas . For example, some authors use colons or full stops instead of parentheses, or change the places in which parentheses are inserted. a proof of unique readability . -A less common convention is Polish notation , in which one writes - - - -→ - - -{\displaystyle \rightarrow } - -, - - - -∧ - - -{\displaystyle \wedge } - -, and so on in front of their arguments rather than between them. +A less common convention is Polish notation , in which one writes ....→...{\displaystyle \rightarrow }.., ....∧...{\displaystyle \wedge }.., and so on in front of their arguments rather than between them. This convention allows all punctuation symbols to be discarded. Polish notation is compact and elegant, but rarely used in practice because it is hard for humans to read it. Polish notation is compact and elegant , but rarely used in practice because it is hard for humans to read it. -The definitions above use infix notation for binary connectives such as - - - -→ - - -{\displaystyle \to } - -. +The definitions above use infix notation for binary connectives such as ....→...{\displaystyle \to }... English sentences like "everyone loves someone" can be formalized by first-order logic formulas like ∀x∃y L(x,y). English sentences like "everyone loves someone" can be formalized by first-order logic formulas like ∀x∃y L(x,y) . Using just the two quantifiers ∀ and ∃ and the loving relation symbol L, but no logical connectives and no function symbols (including constants), formulas with 8 different meanings can be built. @@ -2256,67 +2199,9 @@ For example, one common rule of inference is the rule of substitution . If t is a term and φ is a formula possibly containing the variable x, then φ[t/x] (often denoted φ[x/t]) is the result of replacing all free instances of x by t in φ. The substitution rule states that for any φ and any term t, one can conclude φ[t/x] from φ provided that no free variable of t becomes bound during the substitution process. ( If some free variable of t becomes bound, then to substitute t for x it is first necessary to change the bound variables of φ to differ from the free variables of t.) -The intended replacement can be obtained by renaming the bound variable x of φ to something else, say z , so that the formula after substitution is - - - -∃ -z -( -z -= -x -+ -1 -) - - -{\displaystyle \exists z(z=x+1)} - -, which is again logically valid. -If t is the term "x + 1", the formula φ[t/y] is - - - -∃ -x -( -x -= -x -+ -1 -) - - -{\displaystyle \exists x(x=x+1)} - -, which will be false in many interpretations. The problem is that the free variable x of t became bound during the substitution. The intended replacement can be obtained by renaming the bound variable x of φ to something else, say z, so that the formula after substitution is - - - -∃ -z -( -z -The intended replacement can be obtained by renaming the bound variable x of φ to something else, say z , so that the formula after substitution is - - - -∃ -z -( -z -= -x -+ -1 -) - - -{\displaystyle \exists z(z=x+1)} - -, which is again logically valid. +The intended replacement can be obtained by renaming the bound variable x of φ to something else, say z , so that the formula after substitution is ....∃.z.(.z.=.x.+.1.)...{\displaystyle \exists z(z=x+1)}.., which is again logically valid. +If t is the term "x + 1", the formula φ[t/y] is ....∃.x.(.x.=.x.+.1.)...{\displaystyle \exists x(x=x+1)}.., which will be false in many interpretations. The problem is that the free variable x of t became bound during the substitution. The intended replacement can be obtained by renaming the bound variable x of φ to something else, say z, so that the formula after substitution is ....∃.z.(.z +The intended replacement can be obtained by renaming the bound variable x of φ to something else, say z , so that the formula after substitution is ....∃.z.(.z.=.x.+.1.)...{\displaystyle \exists z(z=x+1)}.., which is again logically valid. The substitution rule demonstrates several common aspects of rules of inference. It is entirely syntactical ; one can tell whether it was correctly applied without appeal to any interpretation. It has (syntactically defined) limitations on when it can be applied , which must be respected to preserve the correctness of derivations. @@ -2381,104 +2266,19 @@ Unlike first-order logic, for which only one semantics is studied, there are sev The combination of additional quantifiers and the full semantics for these quantifiers makes higher-order logic stronger than first-order logic. The most commonly employed semantics for second-order and higher-order logic is known as full semantics . In particular, the (semantic) logical consequence relation for second-order and higher-order logic is not semidecidable; there is no effective deduction system for second-order logic that is sound and complete under full semantics. -However, the compactness theorem can be used to show that connected graphs are not an elementary class in first-order logic, and there is no formula φ(x,y) of first-order logic, in the logic of graphs, that expresses the idea that there is a path from x to y. Connectedness can be expressed in second-order logic , however, but not with only existential set quantifiers, as - - - - -Σ - -1 - - -1 - - - - -{\displaystyle \Sigma _{1}^{1}} - - also enjoys compactness. +However, the compactness theorem can be used to show that connected graphs are not an elementary class in first-order logic, and there is no formula φ(x,y) of first-order logic, in the logic of graphs, that expresses the idea that there is a path from x to y. Connectedness can be expressed in second-order logic , however, but not with only existential set quantifiers, as .....Σ..1...1.....{\displaystyle \Sigma _{1}^{1}}.. also enjoys compactness. For example, in computer science, many situations can be modeled as a directed graph of states ( nodes ) and connections (directed edges). There are also more subtle limitations of first-order logic that are implied by the compactness theorem . -However, the compactness theorem can be used to show that connected graphs are not an elementary class in first-order logic, and there is no formula φ(x,y) of first-order logic, in the logic of graphs, that expresses the idea that there is a path from x to y. Connectedness can be expressed in second-order logic, however, but not with only existential set quantifiers, as - - - - -Σ - -1 - - -1 - - - - -{\displaystyle \Sigma _{1}^{1}} - - also enjoys compactness. +However, the compactness theorem can be used to show that connected graphs are not an elementary class in first-order logic, and there is no formula φ(x,y) of first-order logic, in the logic of graphs, that expresses the idea that there is a path from x to y. Connectedness can be expressed in second-order logic, however, but not with only existential set quantifiers, as .....Σ..1...1.....{\displaystyle \Sigma _{1}^{1}}.. also enjoys compactness. For example, in computer science, many situations can be modeled as a directed graph of states (nodes) and connections ( directed edges ) There are also more subtle limitations of first-order logic that are implied by the compactness theorem . -Connectedness can be expressed in second-order logic, however, but not with only existential set quantifiers, as - - - - -Σ - -1 - - -1 - - - - -{\displaystyle \Sigma _{1}^{1}} - - also enjoys compactness. +Connectedness can be expressed in second-order logic, however, but not with only existential set quantifiers, as .....Σ..1...1.....{\displaystyle \Sigma _{1}^{1}}.. also enjoys compactness. There are also more subtle limitations of first-order logic that are implied by the compactness theorem. For example, in computer science, many situations can be modeled as a directed graph of states ( nodes ) and connections (directed edges). For example, in computer science, many situations can be modeled as a directed graph of states (nodes) and connections ( directed edges ) Validating such a system may require showing that no " bad " state can be reached from any "good" state. -However, the compactness theorem can be used to show that connected graphs are not an elementary class in first-order logic, and there is no formula φ(x,y) of first-order logic, in the logic of graphs, that expresses the idea that there is a path from x to y. Connectedness can be expressed in second-order logic, however, but not with only existential set quantifiers, as - - - - -Σ - -1 - - -1 - - - - -{\displaystyle \Sigma _{1}^{1}} - - also enjoys compactness. -However, the compactness theorem can be used to show that connected graphs are not an elementary class in first-order logic, and there is no formula φ(x,y) of first-order logic, in the logic of graphs, that expresses the idea that there is a path from x to y. Connectedness can be expressed in second -order logic, however, but not with only existential set quantifiers, as - - - - -Σ - -1 - - -1 - - - - -{\displaystyle \Sigma _{1}^{1}} - - also enjoys compactness. +However, the compactness theorem can be used to show that connected graphs are not an elementary class in first-order logic, and there is no formula φ(x,y) of first-order logic, in the logic of graphs, that expresses the idea that there is a path from x to y. Connectedness can be expressed in second-order logic, however, but not with only existential set quantifiers, as .....Σ..1...1.....{\displaystyle \Sigma _{1}^{1}}.. also enjoys compactness. +However, the compactness theorem can be used to show that connected graphs are not an elementary class in first-order logic, and there is no formula φ(x,y) of first-order logic, in the logic of graphs, that expresses the idea that there is a path from x to y. Connectedness can be expressed in second -order logic, however, but not with only existential set quantifiers, as .....Σ..1...1.....{\displaystyle \Sigma _{1}^{1}}.. also enjoys compactness. Second-order logic with full semantics is more expressive than first-order logic. For example, it is possible to create axiom systems in second-order logic that uniquely characterize the natural numbers and the real line. The cost of this expressiveness is that second-order and higher-order logics have fewer attractive metalogical properties than first-order logic. @@ -2532,17 +2332,13 @@ There are many deductive systems for first-order logic which are both sound (all Although the logical consequence relation is only semidecidable , much progress has been made in automated theorem proving in first-order logic. First-order logic also satisfies several metalogical theorems that make it amenable to analysis in proof theory, such as the Löwenheim–Skolem theorem and the compactness theorem. Although the logical consequence relation is only semidecidable, much progress has been made in automated theorem proving in first-order logic. - - No first-order theory , however, has the strength to uniquely describe a structure with an infinite domain, such as the natural numbers or the real line. +. No first-order theory , however, has the strength to uniquely describe a structure with an infinite domain, such as the natural numbers or the real line. First-order logic is the standard for the formalization of mathematics into axioms and is studied in the foundations of mathematics. - -Peano arithmetic and Zermelo–Fraenkel set theory are axiomatizations of number theory and set theory, respectively, into first-order logic. +.Peano arithmetic and Zermelo–Fraenkel set theory are axiomatizations of number theory and set theory, respectively, into first-order logic. Axioms systems that do fully describe these two structures (that is, categorical axiom systems) can be obtained in stronger logics such as second-order logic . First-order logic is the standard for the formalization of mathematics into axioms and is studied in the foundations of mathematics . - - Peano arithmetic and Zermelo–Fraenkel set theory are axiomatizations of number theory and set theory, respectively, into first-order logic. - -Peano arithmetic and Zermelo–Fraenkel set theory are axiomatizations of number theory and set theory, respectively, into first-order logic. +. Peano arithmetic and Zermelo–Fraenkel set theory are axiomatizations of number theory and set theory, respectively, into first-order logic. +.Peano arithmetic and Zermelo–Fraenkel set theory are axiomatizations of number theory and set theory, respectively, into first-order logic. Axioms systems that do fully describe these two structures (that is, categorical axiom systems) can be obtained in stronger logics such as second-order logic. Axioms systems that do fully describe these two structures (that is, categorical axiom systems) can be obtained in stronger logics such as second-order logic. A predicate takes an entity or entities in the domain of discourse as input and outputs either True or False. @@ -2993,10 +2789,8 @@ Ayurveda M.D (Ayu) (Ayurveda vachaspati) is a master's degree accepted by Univer The medical education in Taiwan is usually 7 years (6-year learning plus 1-year internship) in duration, starting right after high schools. The medical education in Taiwan is usually 7 years (6-year learning plus 1-year internship) in duration, starting right after high schools. The first 2 years in the 7-year system is composed of basic sciences and liberal art courses. - -Taiwan’s medical education began in 1897 and is over 100 years old now. - -Taiwan’s medical education began in 1897 and is over 100 years old now. +.Taiwan’s medical education began in 1897 and is over 100 years old now. +.Taiwan’s medical education began in 1897 and is over 100 years old now. The Thai medical education is 6 years system, consisting of 1 year in basic-science, 2 years in pre-clinical training, and 3 years for clinical training. The Thai medical education is 6 years system, consisting of 1 year in basic-science, 2 years in pre-clinical training, and 3 years for clinical training. The Thai medical education is 6 years system, consisting of 1 year in basic-science, 2 years in pre-clinical training, and 3 years for clinical training. @@ -3636,8 +3430,7 @@ In short, most winning candidates have won the endorsement of the applicable "ma In short, most winning candidates have won the endorsement of the applicable "major"-party convention; nearly all of the rest have won with a "professionally managed" primary-election campaign ; and successful minor-party candidates are almost without exception major-party figures like Lowell Weicker whose minor parties disappear after that success. A Connecticut Party, which Weicker founded, became nominally the leading major party, and state law was changed during his administration to provide that in a situation such as his win, the top "three" parties in the governor's race all became major parties . In short, most winning candidates have won the endorsement of the applicable "major"-party convention; nearly all of the rest have won with a "professionally managed" primary-election campaign; and successful minor-party candidates are almost without exception major-party figures like Lowell Weicker whose minor parties disappear after that success. -Connecticut retained land -extending across the northern part of present-day Ohio, called the Connecticut Western Reserve . +Connecticut retained land.extending across the northern part of present-day Ohio, called the Connecticut Western Reserve . The Western Reserve section was settled largely by people from Connecticut , and they brought Connecticut place names to Ohio. Agreements with Pennsylvania and New York extinguished the land claims by Connecticut within its neighbors, creating the Connecticut Panhandle. In 1786, Connecticut ceded territory to the U.S. government that became part of the Northwest Territory . @@ -3802,30 +3595,8 @@ Thus they would write f−1[B] and f−1[b] for the preimage of a set and a sing Use of f(A) to denote the image of a subset A ⊆ X is consistent so long as no subset of the domain is also an element of the domain . That is, the value of x is obtained by first applying f to x to obtain y = f(x) and then applying g to y to obtain z = g(y) . The notation can be memorized by reading the notation as "g of f" or "g after f" . -The composition - - - -g -∘ -f - - -{\displaystyle g\circ f} - - is only defined when the codomain of f is the domain of g . -In the notation - - - -g -∘ -f - - -{\displaystyle g\circ f} - -, the function on the right, f, acts first and the function on the left, g acts second, reversing English reading order . +The composition ....g.∘.f...{\displaystyle g\circ f}.. is only defined when the codomain of f is the domain of g . +In the notation ....g.∘.f...{\displaystyle g\circ f}.., the function on the right, f, acts first and the function on the left, g acts second, reversing English reading order . The overriding of f: X → Y by g: W → Y (also called overriding union ) is an extension of g denoted as (f ⊕ g): (X ∪ W) → Y. Its graph is the set-theoretical union of the graphs of g and f|X \ W. Thus, it relates any element of the domain of g to its image under g, and any other element of the domain of f to its image under f. Overriding is an associative operation; it has the empty function as an identity element. The overriding of f: X → Y by g: W → Y (also called overriding union) is an extension of g denoted as (f ⊕ g): (X ∪ W) → Y . The overriding of f: X → Y by g: W → Y (also called overriding union) is an extension of g denoted as (f ⊕ g): (X ∪ W) → Y. Its graph is the set-theoretical union of the graphs of g and f|X \ W. Thus, it relates any element of the domain of g to its image under g, and any other element of the domain of f to its image under f. Overriding is an associative operation ; it has the empty function as an identity element. @@ -3848,101 +3619,10 @@ Despite that, many authors drop the specification of the domain and codomain , e Despite that, many authors drop the specification of the domain and codomain, especially if these are clear from the context. (with different domain) is not considered the same function, even though the formulas defining f and g agree, and similarly with a different codomain. So in this example many just write f(x) = 4 − x . -Sometimes, the maximal possible domain is also understood implicitly: a formula such as - - - - -f -( -x -) +Sometimes, the maximal possible domain is also understood implicitly: a formula such as .....f.(.x.) To define a function, sometimes a dot notation is used in order to emphasize the functional nature of an expression without assigning a special symbol to the variable. To define a function, sometimes a dot notation is used in order to emphasize the functional nature of an expression without assigning a special symbol to the variable. -For instance, - - - - -a -( -⋅ - -) - -2 - - - - - - {\displaystyle \scriptstyle a(\cdot )^{2}} - - stands for the function - - - - -x -↦ -a - -x - -2 - - - - - -{\displaystyle \textstyle x\mapsto ax^{2}} - -, - - - - - -∫ - -a - - - -⋅ - - -f -( -u -) -d -u - - - -{\displaystyle \scriptstyle \int _{a}^{\,\cdot }f(u)du} - - stands for the integral function - - - - -x -↦ - -∫ - -a - - -x - - -f -( -u -) +For instance, .....a.(.⋅..)..2...... {\displaystyle \scriptstyle a(\cdot )^{2}} .. stands for the function .....x.↦.a..x..2......{\displaystyle \textstyle x\mapsto ax^{2}}.., ......∫..a....⋅...f.(.u.).d.u....{\displaystyle \scriptstyle \int _{a}^{\,\cdot }f(u)du}.. stands for the integral function .....x.↦..∫..a...x...f.(.u.) To define a function, sometimes a dot notation is used in order to emphasize the functional nature of an expression without assigning a special symbol to the variable. To define a function, sometimes a dot notation is used in order to emphasize the functional nature of an expression without assigning a special symbol to the variable . Functions that send integers to integers, or finite strings to finite strings, can sometimes be defined by an algorithm, which gives a precise description of a set of steps for computing the output of the function from its input. @@ -4033,16 +3713,7 @@ If (x, y) are the Cartesian coordinates of a point, then (−x, y) are the coord Likewise, (x, −y) are the coordinates of its reflection across the first coordinate axis ( the X-axis ). If (x, y) are the Cartesian coordinates of a point, then (−x, y) are the coordinates of its reflection across the second coordinate axis ( the Y-axis ), as if that line were a mirror. Likewise, (x, −y) are the coordinates of its reflection across the first coordinate axis (the X-axis) . -In more generality, reflection across a line through the origin making an angle - - - - θ - - -{\displaystyle \theta } - - with the x-axis, is equivalent to replacing every point with coordinates (x, y) by the point with coordinates (x′,y′), where +In more generality, reflection across a line through the origin making an angle .... θ ...{\displaystyle \theta }.. with the x-axis, is equivalent to replacing every point with coordinates (x, y) by the point with coordinates (x′,y′), where The standard orientation, where the xy-plane is horizontal and the z-axis points up (and the x- Once the x- and y-axes are specified, they determine the line along which the z-axis should lie, but there are two possible directions on this line. The standard orientation, where the xy-plane is horizontal and the z-axis points up (and the x- and the y-axis form a positively oriented two-dimensional coordinate system in the xy-plane if observed from above the xy-plane) is called right-handed or positive. @@ -4058,205 +3729,10 @@ Many observers see Figure 8 as "flipping in and out" between a convex cube a nd Many observers see Figure 8 as "flipping in and out" between a convex cube and a concave "corner" . Again, there is an ambiguity caused by projecting the three-dimensional coordinate system into the plane. Thus the "correct" way to view Figure 8 is to imagine the x-axis as pointing towards the observer and thus seeing a concave corner. -where - - - - -i - -= - - -( - - - -1 - - - - -0 - - - -) - - - - -{\displaystyle \mathbf {i} ={\begin{pmatrix}1\\0\end{pmatrix}}} - -, and - - - - -j - -= - - -( - - - -0 - - - - -1 - - - -) - - - - -{\displaystyle \mathbf {j} ={\begin{pmatrix}0\\1\end{pmatrix}}} - - are unit vectors in the direction of the x-axis and y-axis respectively, generally referred to as the standard basis (in some application areas these may also be referred to as versors). -where - - - - -i - -= - - -( - - - -1 - - - - -0 - - - -) - - - - -{\displaystyle \mathbf {i} ={\begin{pmatrix}1\\0\end{pmatrix}}} - -, and - - - - -j - -= - - -( - - - -0 - - - - -1 - - - -) - - - - -{\displaystyle \mathbf {j} ={\begin{pmatrix}0\\1\end{pmatrix}}} - - are unit vectors in the direction of the x-axis and y-axis respectively, generally referred to as the standard basis (in some application areas these may also be referred to as versors ) -where - - - - -i - -= - - -( - - - -1 - - - - -0 - - - -) - - - - -{\displaystyle \mathbf {i} ={\begin{pmatrix}1\\0\end{pmatrix}}} - -, and - - - - -j - -= - - -( - - - -0 - - - - -1 - - - -) - - - - -{\displaystyle \mathbf {j} ={\begin{pmatrix}0\\1\end{pmatrix}}} - - are unit vectors in the direction of the x-axis and y-axis respectively, generally referred to as the standard basis (in some application areas these may also be referred to as versors). -Similarly, in three dimensions, the vector from the origin to the point with Cartesian coordinates - - - -( -x -, -y -, -z -) - - -{\displaystyle ( x,y,z )} - - can be written as: +where .....i..=...(....1.....0....).....{\displaystyle \mathbf {i} ={\begin{pmatrix}1\\0\end{pmatrix}}}.., and .....j..=...(....0.....1....).....{\displaystyle \mathbf {j} ={\begin{pmatrix}0\\1\end{pmatrix}}}.. are unit vectors in the direction of the x-axis and y-axis respectively, generally referred to as the standard basis (in some application areas these may also be referred to as versors). +where .....i..=...(....1.....0....).....{\displaystyle \mathbf {i} ={\begin{pmatrix}1\\0\end{pmatrix}}}.., and .....j..=...(....0.....1....).....{\displaystyle \mathbf {j} ={\begin{pmatrix}0\\1\end{pmatrix}}}.. are unit vectors in the direction of the x-axis and y-axis respectively, generally referred to as the standard basis (in some application areas these may also be referred to as versors ) +where .....i..=...(....1.....0....).....{\displaystyle \mathbf {i} ={\begin{pmatrix}1\\0\end{pmatrix}}}.., and .....j..=...(....0.....1....).....{\displaystyle \mathbf {j} ={\begin{pmatrix}0\\1\end{pmatrix}}}.. are unit vectors in the direction of the x-axis and y-axis respectively, generally referred to as the standard basis (in some application areas these may also be referred to as versors). +Similarly, in three dimensions, the vector from the origin to the point with Cartesian coordinates ....(.x.,.y.,.z.)...{\displaystyle ( x,y,z )}.. can be written as: There is no natural interpretation of multiplying vectors to obtain another vector that works in all dimensions, however there is a way to use complex numbers to provide such a multiplication. In a two dimensional cartesian plane, identify the point with coordinates (x, y) with the complex number z = x + iy . Here, i is the imaginary unit and is identified with the point with coordinates (0, 1) , so it is not the unit vector in the direction of the x-axis. @@ -4300,115 +3776,10 @@ Choosing a Cartesian coordinate system for a three-dimensional space means choos Choosing a Cartesian coordinate system for a three-dimensional space means choosing an ordered triplet of lines (axes) that are pair-wise perpendicular, have a single unit of length for all three axes and have an orientation for each axis. Choosing a Cartesian coordinate system for a three-dimensional space means choosing an ordered triplet of lines (axes) that are pair-wise perpendicular , have a single unit of length for all three axes and have an orientation for each axis. As in the two-dimensional case, each axis becomes a number line . -A Euclidean plane with a chosen Cartesian system is called a Cartesian plane. Since Cartesian coordinates are unique and non-ambiguous, the points of a Cartesian plane can be identified with pairs of real numbers; that is with the Cartesian product - - - - - -R - - -2 - - -= - -R - -× - -R - - - -{\displaystyle \mathbb {R} ^{2}=\mathbb {R} \times \mathbb {R} } - -, where - - - - -R - - - -{\displaystyle \mathbb {R} } - - is the set of all reals. - Since Cartesian coordinates are unique and non-ambiguous, the points of a Cartesian plane can be identified with pairs of real numbers ; that is with the Cartesian product - - - - - -R - - -2 - - -= - -R - -× - -R - - - -{\displaystyle \mathbb {R} ^{2}=\mathbb {R} \times \mathbb {R} } - -, where - - - - -R - - - -{\displaystyle \mathbb {R} } - - is the set of all reals. +A Euclidean plane with a chosen Cartesian system is called a Cartesian plane. Since Cartesian coordinates are unique and non-ambiguous, the points of a Cartesian plane can be identified with pairs of real numbers; that is with the Cartesian product ......R...2...=..R..×..R....{\displaystyle \mathbb {R} ^{2}=\mathbb {R} \times \mathbb {R} }.., where .....R....{\displaystyle \mathbb {R} }.. is the set of all reals. + Since Cartesian coordinates are unique and non-ambiguous, the points of a Cartesian plane can be identified with pairs of real numbers ; that is with the Cartesian product ......R...2...=..R..×..R....{\displaystyle \mathbb {R} ^{2}=\mathbb {R} \times \mathbb {R} }.., where .....R....{\displaystyle \mathbb {R} }.. is the set of all reals. In the same way, the points any Euclidean space of dimension n be identified with the tuples ( lists ) of n real numbers, - Since Cartesian coordinates are unique and non-ambiguous , the points of a Cartesian plane can be identified with pairs of real numbers; that is with the Cartesian product - - - - - -R - - -2 - - -= - -R - -× - -R - - - -{\displaystyle \mathbb {R} ^{2}=\mathbb {R} \times \mathbb {R} } - -, where - - - - -R - - - -{\displaystyle \mathbb {R} } - - is the set of all reals. + Since Cartesian coordinates are unique and non-ambiguous , the points of a Cartesian plane can be identified with pairs of real numbers; that is with the Cartesian product ......R...2...=..R..×..R....{\displaystyle \mathbb {R} ^{2}=\mathbb {R} \times \mathbb {R} }.., where .....R....{\displaystyle \mathbb {R} }.. is the set of all reals. The concept of Cartesian coordinates generalizes to allow axes that are not perpendicular to each other, and/or different units along each axis . In that case, each coordinate is obtained by projecting the point onto one axis along a direction that is parallel to the other axis (or, in general, to the hyperplane defined by all the other axes). In such an oblique coordinate system the computations of distances and angles must be modified from that in standard Cartesian systems, and many standard formulas (such as the Pythagorean formula for the distance) do not hold (see Affine plane). @@ -4593,32 +3964,24 @@ New deposits are reported to be in southern Mongolia, and in 2009 , new deposits New deposits are reported to be in southern Mongolia , and in 2009, new deposits of tin were discovered in Colombia, by the Seminole Group Colombia CI, SAS. New deposits are reported to be in southern Mongolia, and in 2009, new deposits of tin were discovered in Colombia , by the Seminole Group Colombia CI, SAS. New deposits are reported to be in southern Mongolia, and in 2009, new deposits of tin were discovered in Colombia, by the Seminole Group Colombia CI, SAS . - -Most of the world's tin is traded on the London Metal Exchange (LME) , from 8 countries, under 17 brands. - -Most of the world's tin is traded on the London Metal Exchange (LME), from 8 countries, under 17 brands . - -Most of the world's tin is traded on the London Metal Exchange (LME), from 8 countries, under 17 brands. +.Most of the world's tin is traded on the London Metal Exchange (LME) , from 8 countries, under 17 brands. +.Most of the world's tin is traded on the London Metal Exchange (LME), from 8 countries, under 17 brands . +.Most of the world's tin is traded on the London Metal Exchange (LME), from 8 countries, under 17 brands. It is not clear which of these companies include tin smelted from the mine at Bisie, Democratic Republic of the Congo, which is controlled by a renegade militia and produces 15,000 tonnes. a renegade militia and produces 15,000 tonnes. The ten largest companies produced most of the world's tin in 2007. It is not clear which of these companies include tin smelted from the mine at Bisie, Democratic Republic of the Congo, which is controlled by a renegade militia and produces 15,000 tonnes . It is not clear which of these companies include tin smelted from the mine at Bisie, Democratic Republic of the Congo , which is controlled by a renegade militia and produces 15,000 tonnes. - -Most of the world's tin is traded on the London Metal Exchange (LME) , from 8 countries, under 17 brands. +.Most of the world's tin is traded on the London Metal Exchange (LME) , from 8 countries, under 17 brands. Tin is unique among other mineral commodities by the complex "agreements" between producer countries and consumer countries dating back to 1921. -The earlier agreements tended to be somewhat informal and sporadic; they led to the "First International Tin Agreement" in 1956, the first of a -continuously numbered series that essentially collapsed in 1985. +The earlier agreements tended to be somewhat informal and sporadic; they led to the "First International Tin Agreement" in 1956, the first of a.continuously numbered series that essentially collapsed in 1985. Through this series of agreements, the International Tin Council (ITC) had a considerable effect on tin prices. However, the buffer stockpile was not sufficiently large, and during most of those 29 years tin prices rose, sometimes sharply, especially from 1973 through 1980 when rampant inflation plagued many world economies. Tin is unique among other mineral commodities by the complex "agreements" between producer countries and consumer countries dating back to 1921. -The earlier agreements tended to be somewhat informal and sporadic ; they led to the "First International Tin Agreement" in 1956, the first of a -continuously numbered series that essentially collapsed in 1985. -The earlier agreements tended to be somewhat informal and sporadic; they led to the "First International Tin Agreement" in 1956, the first of a -continuously numbered series that essentially collapsed in 1985 . +The earlier agreements tended to be somewhat informal and sporadic ; they led to the "First International Tin Agreement" in 1956, the first of a.continuously numbered series that essentially collapsed in 1985. +The earlier agreements tended to be somewhat informal and sporadic; they led to the "First International Tin Agreement" in 1956, the first of a.continuously numbered series that essentially collapsed in 1985 . Through this series of agreements, the International Tin Council (ITC) had a considerable effect on tin prices. -The earlier agreements tended to be somewhat informal and sporadic; they led to the "First International Tin Agreement" in 1956, the first of a -continuously numbered series that essentially collapsed in 1985. +The earlier agreements tended to be somewhat informal and sporadic; they led to the "First International Tin Agreement" in 1956, the first of a.continuously numbered series that essentially collapsed in 1985. Before the modern era, in some areas of the Alps , a goat or sheep's horn would be sharpened and a tin panel would be punched out using the alphabet and numbers from one to nine. Before the modern era , in some areas of the Alps, a goat or sheep's horn would be sharpened and a tin panel would be punched out using the alphabet and numbers from one to nine. Before the modern era, in some areas of the Alps, a goat or sheep's horn would be sharpened and a tin panel would be punched out using the alphabet and numbers from one to nine . @@ -4788,10 +4151,8 @@ Radcliffe is now the Radcliffe Institute for Advanced Study in Women's Studies a Second-wave feminists viewed popular culture as sexist , and created pop culture of their own to counteract this. Australian artist Helen Reddy's song "I Am Woman" played a large role in popular culture and became a feminist anthem; Reddy came to be known as a "feminist poster girl" or a "feminist icon". Second-wave feminists viewed popular culture as sexist, and created pop culture of their own to counteract this. -Australian artist Helen Reddy's song "I Am Woman" played a large role in popular culture and became a feminist anthem; Reddy came to be known as a "feminist poster girl" or a "feminist icon". -"One project of second wave feminism was to create 'positive' images of women, to act as a counterweight to the dominant images circulating in popular culture and to raise women's consciousness of their oppressions." - -"One project of second wave feminism was to create 'positive' images of women , to act as a counterweight to the dominant images circulating in popular culture and to raise women's consciousness of their oppressions." +Australian artist Helen Reddy's song "I Am Woman" played a large role in popular culture and became a feminist anthem; Reddy came to be known as a "feminist poster girl" or a "feminist icon". ."One project of second wave feminism was to create 'positive' images of women, to act as a counterweight to the dominant images circulating in popular culture and to raise women's consciousness of their oppressions." +."One project of second wave feminism was to create 'positive' images of women , to act as a counterweight to the dominant images circulating in popular culture and to raise women's consciousness of their oppressions." In June 1967 Jo Freeman attended a "free school'" course on women at the University of Chicago led by Heather Booth and Naomi Weisstein. In June 1967 Jo Freeman attended a "free school'" course on women at the University of Chicago led by Heather Booth and Naomi Weisstein . She invited them to organize a woman's workshop at the then-forthcoming National Conference of New Politics (NCNP) , to be held over Labor Day weekend 1967 in Chicago. @@ -5201,15 +4562,11 @@ It was released on July 29, 2015 , It was released on July 29, 2015, and addresses shortcomings in the user interface first introduced with Windows 8. On September 30, 2014 , Microsoft announced Windows 10 as the successor to Windows 8.1. Windows 10 is said to be available to update from qualified Windows 7 with SP1 and Windows 8.1 computers from the Get Windows 10 Application (for Windows 7, Windows 8.1) or Windows Update (Windows 7). - -Microsoft updates Xbox One's OS every month , and these updates can be downloaded from the Xbox Live service to the Xbox and subsequently installed, or by using offline recovery images downloaded via a PC. +.Microsoft updates Xbox One's OS every month , and these updates can be downloaded from the Xbox Live service to the Xbox and subsequently installed, or by using offline recovery images downloaded via a PC. Xbox OS is an unofficial name given to the version of Windows that runs on the Xbox One. - -Microsoft updates Xbox One's OS every month, and these updates can be downloaded from the Xbox Live service to the Xbox and subsequently installed, or by using offline recovery images downloaded via a PC. - - Xbox One's system also allows backward compatibility with Xbox 360, and the Xbox 360's system is backwards compatible with the original Xbox. - -Microsoft updates Xbox One's OS every month, and these updates can be downloaded from the Xbox Live service to the Xbox and subsequently installed, or by using offline recovery images downloaded via a PC . +.Microsoft updates Xbox One's OS every month, and these updates can be downloaded from the Xbox Live service to the Xbox and subsequently installed, or by using offline recovery images downloaded via a PC. +. Xbox One's system also allows backward compatibility with Xbox 360, and the Xbox 360's system is backwards compatible with the original Xbox. +.Microsoft updates Xbox One's OS every month, and these updates can be downloaded from the Xbox Live service to the Xbox and subsequently installed, or by using offline recovery images downloaded via a PC . Microsoft releases security patches through its Windows Update service approximately once a month (usually the second Tuesday of the month), although critical updates are made available at shorter intervals when necessary. Microsoft releases security patches through its Windows Update service approximately once a month (usually the second Tuesday of the month), although critical updates are made available at shorter intervals when necessary. In versions of Windows after and including Windows 2000 SP3 and Windows XP , updates can be automatically downloaded and installed if the user selects to do so. @@ -5267,10 +4624,8 @@ Rice was domesticated in southern China later on. They were cultivated around 2500 BC . These species were subsequently widely cultivated in the Yellow River basin (7,500 years ago). On the African continent, three areas have been identified as independently developing agriculture: the Ethiopian highlands, the Sahel and West Africa. - -Many grinding stones are found with the early Egyptian Sebilian and Mechian cultures and evidence has been found of a neolithic domesticated crop-based economy dating around 7,000 BP . - -Unlike the Middle East, this evidence appears as a "false dawn" to agriculture, as the sites were later abandoned, and permanent farming then was delayed until 6,500 BP with the Tasian and Badarian cultures and the arrival of crops and animals from the Near East. + .Many grinding stones are found with the early Egyptian Sebilian and Mechian cultures and evidence has been found of a neolithic domesticated crop-based economy dating around 7,000 BP . +.Unlike the Middle East, this evidence appears as a "false dawn" to agriculture, as the sites were later abandoned, and permanent farming then was delayed until 6,500 BP with the Tasian and Badarian cultures and the arrival of crops and animals from the Near East. On the African continent, three areas have been identified as independently developing agriculture: the Ethiopian highlands, the Sahel and West Africa . By contrast, Agriculture in the Nile River Valley is thought to have developed from the original Neolithic Revolution in the Fertile Crescent. During the next millennia it would transform the small and mobile groups of hunter-gatherers that had hitherto dominated human pre-history into sedentary (here meaning non-nomadic) societies based in built-up villages and towns. @@ -5584,8 +4939,7 @@ At its four th and last session, held on 24–25 July 1945 in Zagreb, ZAVNOH pro Croat partisans were unique in having the highest numbers of local Jews in their ranks of any other European resistance,[citation needed] and in early 1943 they took steps to establish ZAVNOH (National Anti-Fascist Council of the People's Liberation of Croatia) to act as a parliamentary body for all of Croatia – the only one of its kind in occupied Europe. Croat partisans were unique in having the highest numbers of local Jews in their ranks of any other European resistance,[citation needed] and in early 1943 they took steps to establish ZAVNOH (National Anti-Fascist Council of the People's Liberation of Croatia) to act as a parliamentary body for all of Croatia – the only one of its kind in occupied Europe. Croatian Partisans were integral to overall Yugoslav Partisans; by the end of 1943 Croatia proper, with 24% of the Yugoslav population, provided more Partisans than Serbia, Montenegro, Slovenia and Macedonia combined which collectively accounted for 59% of the Yugoslav population. - -In the liberated territories of Croatia after the war, Croatian Partisans proclaimed the Democratic Republic which was referred to by Winston Churchill as "the Croatian miracle." +.In the liberated territories of Croatia after the war, Croatian Partisans proclaimed the Democratic Republic which was referred to by Winston Churchill as "the Croatian miracle." This change was partly due to the decision of a key Croatian Peasant Party member, Božidar Magovac, to join the Partisans in June 1943, and partly due to the surrender of Italy. In 1941-42, the majority of Partisans in Croatia were Serbs, but by October 1943 the majority were Croats. In 1941-42, the majority of Partisans in Croatia were Serbs , but by October 1943 the majority were Croats. @@ -5819,8 +5173,7 @@ The state legislature authorized the California Geological Survey to officially From 1892–7 Theodore Solomons made the first attempt to map a route along the crest of the Sierra. Men of the survey, including William H. Brewer, Charles F. Hoffmann and Clarence King , explored the backcountry of what would become Yosemite National Park in 1863. The Valley and Mariposa Grove were ceded to California in 1866 and turned into a state park. - -Yosemite Valley was first protected by the federal government in 1864 . +.Yosemite Valley was first protected by the federal government in 1864 . John Muir perceived overgrazing by sheep and logging of Giant Sequoia to be a problem in the Sierra. Muir successfully lobbied for the protection of the rest of Yosemite National Park: Congress created an Act to protect the park in 1890 . The Valley and Mariposa Grove were added to the Park in 1906 . @@ -6287,8 +5640,7 @@ Numerous colleges and universities are located in Manhattan, including Columbia The name "Manhattan" derives from the word Manna-hata , as written in the 1609 logbook of Robert Juet, an officer on Henry Hudson's yacht Halve Maen (Half Moon). The name "Manhattan" derives from the word Manna-hata, as written in the 1609 logbook of Robert Juet , an officer on Henry Hudson's yacht Halve Maen (Half Moon). The word "Manhattan" has been translated as " island of many hills " from the Lenape language. -The word "Manhattan" has been translated as "island of many hills" from the Lenape language. -The United States Postal Service prefers that mail addressed to Manhattan use "New York, NY" rather than "Manhattan, NY". +The word "Manhattan" has been translated as "island of many hills" from the Lenape language. .The United States Postal Service prefers that mail addressed to Manhattan use "New York, NY" rather than "Manhattan, NY". The area that is now Manhattan was long inhabited by the Lenape Native Americans . In 1524, Florentine explorer Giovanni da Verrazzano – sailing in service of King Francis I of France – was the first European to visit the area that would become New York City. He entered the tidal strait now known as The Narrows aboard his ship La Dauphine and named the land around Upper New York Harbor "New Angoulême", in reference to the family name of King Francis I that was derived from Angoulême in France; he sailed far enough into the harbor to sight the Hudson River, which he referred to in his report to the French king as a "very big river"; and he named the Bay of Santa Margarita – what is now Upper New York Bay – after Marguerite de Navarre , the elder sister of the king. @@ -6410,8 +5762,7 @@ The school took the name the Western University of Pennsylvania, or WUP, and was Due to the historical nature of various sites around Pitt's buildings, the Commonwealth of Pennsylvania has placed historical markers outside the Allegheny Observatory, Posvar Hall, Salk Hall, Stephen Foster Memorial, and the William Pitt Union. Due to the historical nature of various sites around Pitt's buildings, the Commonwealth of Pennsylvania has placed historical markers outside the Allegheny Observatory, Posvar Hall, Salk Hall, Stephen Foster Memorial, and the William Pitt Union. Another state historical marker has been placed to highlight the significance of Pitt's involvement in the archaeological excavation at the Meadowcroft Rockshelter in Avella, Pennsylvania. - -In addition, a Pennsylvania Historical Marker has been placed on campus near the Cathedral of Learning to mark the significance of the University of Pittsburgh itself. +.In addition, a Pennsylvania Historical Marker has been placed on campus near the Cathedral of Learning to mark the significance of the University of Pittsburgh itself. Another state historical marker has been placed to highlight the significance of Pitt's involvement in the archaeological excavation at the Meadowcroft Rockshelter in Avella, Pennsylvania . In addition, the Pittsburgh History and Landmarks Foundation has designated the following Pitt buildings as Pittsburgh Historic Landmarks: Allegheny Observatory, Allen Hall, Alumni Hall, Bellefield Hall, Chancellor's Residence, Cathedral of Learning, the Cathedral of Learning interior rooms, Gardner Steel Conference Center, Heinz Memorial Chapel, Thaw Hall, Salk Hall, Schenley Quadrangle residence halls, Stephen Foster Memorial, the University Child Development Center, and the William Pitt Union. In addition, the Pittsburgh History and Landmarks Foundation has designated the following Pitt buildings as Pittsburgh Historic Landmarks: Allegheny Observatory, Allen Hall, Alumni Hall, Bellefield Hall, Chancellor's Residence, Cathedral of Learning, the Cathedral of Learning interior rooms, Gardner Steel Conference Center, Heinz Memorial Chapel, Thaw Hall, Salk Hall, Schenley Quadrangle residence halls, Stephen Foster Memorial, the University Child Development Center, and the William Pitt Union. @@ -6539,10 +5890,8 @@ The campus is adjacent to Schenley Plaza, the main branch of the Carnegie Public The main campus is within walking distance of many recreational, cultural, and educational institutions in the Oakland neighborhood. The campus is adjacent to Schenley Plaza, the main branch of the Carnegie Public Library, the Carnegie Museums of Natural History and Art and the Carnegie Music Hall, as well as portions of Carnegie Mellon University . From January to November 2012, the U.S. added approximately 151,000 jobs per month on average. - -Each month, The Hamilton Project examines the "jobs gap," which is the number of jobs that the U.S. economy needs to create in order to return to pre-recession employment levels while also absorbing the people who enter the labor force each month. - - Each month , The Hamilton Project examines the "jobs gap," which is the number of jobs that the U.S. economy needs to create in order to return to pre-recession employment levels while also absorbing the people who enter the labor force each month. +.Each month, The Hamilton Project examines the "jobs gap," which is the number of jobs that the U.S. economy needs to create in order to return to pre-recession employment levels while also absorbing the people who enter the labor force each month. +. Each month , The Hamilton Project examines the "jobs gap," which is the number of jobs that the U.S. economy needs to create in order to return to pre-recession employment levels while also absorbing the people who enter the labor force each month. Job creation would have to average 208,000 per month to close the gap by 2020; 320,000 by 2017; or 472,000 by mid-2015. Job creation would have to average 208,000 per month to close the gap by 2020; 320,000 by 2017; or 472,000 by mid-2015. By this measure, the 2008-2009 recession was considerably worse than the five other U.S. recessions from 1970 to present. @@ -7250,8 +6599,7 @@ The major virtues they identified include wisdom / knowledge; courage; humanity; The major virtues they identified include wisdom / knowledge ; courage; humanity; justice; temperance; and transcendence. On April 26, 2012, the results of a study which tested their subjects' pro-social sentiments were published in the Social Psychological and Personality Science journal in which non-religious people had higher scores showing that they were more inclined to show generosity in random acts of kindness, such as lending their possessions and offering a seat on a crowded bus or train. On April 26, 2012, the results of a study which tested their subjects' pro-social sentiments were published in the Social Psychological and Personality Science journal in which non-religious people had higher scores showing that they were more inclined to show generosity in random acts of kindness, such as lending their possessions and offering a seat on a crowded bus or train. -His conclusion is that a " complex relationship " exists between religiosity and homicide "with some -dimensions of religiosity encouraging homicide and other dimensions discouraging it". +His conclusion is that a " complex relationship " exists between religiosity and homicide "with some.dimensions of religiosity encouraging homicide and other dimensions discouraging it". A 2005 study by Gregory S. Paul published in the Journal of Religion and Society stated that, "In general, higher rates of belief in and worship of a creator correlate with higher rates of homicide, juvenile and early adult mortality, STD infection rates, teen pregnancy, and abortion in the prosperous democracies," and "In all secular developing democracies a centuries long-term trend has seen homicide rates drop to historical lows" with the exceptions being the United States (with a high religiosity level) and "theistic" Portugal. [d] In a response, Gary Jensen builds on and refines Paul's study. A 2005 study by Gregory S. Paul published in the Journal of Religion and Society stated that, "In general, higher rates of belief in and worship of a creator correlate with higher rates of homicide, juvenile and early adult mortality, STD infection rates, teen pregnancy, and abortion in the prosperous democracies," and "In all secular developing democracies a centuries long-term trend has seen homicide rates drop to historical lows" with the exceptions being the United States (with a high religiosity level) and "theistic" Portugal.[d] In a response, Gary Jensen builds on and refines Paul's study. Philosopher David Hume stated that, "the greatest crimes have been found, in many instances, to be compatible with a superstitious piety and devotion ; Hence it is justly regarded as unsafe to draw any inference in favor of a man's morals, from the fervor or strictness of his religious exercises, even though he himself believe them sincere." @@ -7298,12 +6646,10 @@ Even though we have a sense of responsibility to pursue moral purposes,[accordin Moral self-licensing attempts to explain this phenomenon and proposes that self-image security increases our likelihood to engage in immoral behaviour. Even though we have a sense of responsibility to pursue moral purposes,[according to whom?] we still, at least occasionally, engage in immoral behaviour. Stimulation of the VMPC by transcranial magnetic stimulation, has been shown to inhibit the ability of human subjects to take into account intent when forming a moral judgment. -According to this investigation, TMS did not disrupt participants' ability to make any moral -judgment. +According to this investigation, TMS did not disrupt participants' ability to make any moral.judgment. On the contrary, moral judgments of intentional harms and nonharms were unaffected by TMS to either the RTPJ or the control site; presumably, however, people typically make moral judgments of intentional harms by considering not only the action's harmful outcome but the agent's intentions and beliefs . Alternatively, following TMS to the RTPJ, moral judgments might be made via an abnormal processing route that does not take belief into account. -So why -were moral judgments of intentional harms not affected by TMS to the RTPJ ? +So why.were moral judgments of intentional harms not affected by TMS to the RTPJ ? The development of modern morality is a process closely tied to sociocultural evolution . The development of modern morality is a process closely tied to sociocultural evolution. Some evolutionary biologists, particularly sociobiologists , believe that morality is a product of evolutionary forces acting at an individual level and also at the group level through group selection (although to what degree this actually occurs is a controversial topic in evolutionary theory). @@ -7388,15 +6734,13 @@ Adolf Hitler had hoped to conquer the country in just one day, but his forces me The Dutch army was finally forced to capitulate on 15 May 1940 , following Hitler's bombing Rotterdam on 14 May and threatening to bomb other Dutch cities. Some 80,000 civilians were made homeless and 900 were killed; a relatively low number given that many had fled the city because of the warfare and bombing going on in Rotterdam since the start of the invasion three days earlier. In 1898 , the 45-metre (148-foot) high-rise office building the White House (in Dutch Witte Huis) was completed, at that time the tallest office building in Europe. - - In the first decades of the 20th century , some influential architecture in the modern style was built in Rotterdam. +. In the first decades of the 20th century , some influential architecture in the modern style was built in Rotterdam. In 1898, the 45-metre (148-foot) high-rise office building the White House (in Dutch Witte Huis) was completed, at that time the tallest office building in Europe. Notable are the Van Nelle fabriek (1929) a monument of modern factory design by Brinkman en Van der Vlugt , the Jugendstil clubhouse of the Royal Maas Yacht Club designed by Hooijkaas jr. The Van Nelle Factory has since 2014 the status of UNESCO World Heritage Site. In 1898 , the 45-metre (148-foot) high-rise office building the White House (in Dutch Witte Huis) was completed, at that time the tallest office building in Europe. In 1898, the 45-metre (148-foot) high-rise office building the White House (in Dutch Witte Huis) was completed, at that time the tallest office building in Europe. - - In the first decades of the 20th century , some influential architecture in the modern style was built in Rotterdam. +. In the first decades of the 20th century , some influential architecture in the modern style was built in Rotterdam. Notable are the Van Nelle fabriek (1929) a monument of modern factory design by Brinkman en Van der Vlugt , the Jugendstil clubhouse of the Royal Maas Yacht Club designed by Hooijkaas jr. The Van Nelle Factory has since 2014 the status of UNESCO World Heritage Site. Feyenoord, founded in 1908 and the dominant of the three professional clubs, has won fourteen national titles since the introduction of professional football in the Netherlands. @@ -7406,8 +6750,7 @@ It won the European Cup (current Champions league) as the first Dutch club in 19 Feyenoord , founded in 1908 and the dominant of the three professional clubs, has won fourteen national titles since the introduction of professional football in the Netherlands. In November 2008 Rotterdam was chosen as the host of the Grand Départ of the 2010 Tour de France. Germany's Düsseldorf had previously also expressed interest in hosting. - -Rotterdam won the selection over the Dutch city of Utrecht . +.Rotterdam won the selection over the Dutch city of Utrecht . The Amaury Sport Organization (ASO) , organizer of the Tour de France, said in a statement on its web site that it chose Rotterdam because, in addition to it being another big city, like London, to showcase the use of bikes for urban transportation, it provided a location well positioned considering the rest of the route envisioned for the 2010 event. The Amaury Sport Organization (ASO), organizer of the Tour de France, said in a statement on its web site that it chose Rotterdam because, in addition to it being another big city, like London, to showcase the use of bikes for urban transportation, it provided a location well positioned considering the rest of the route envisioned for the 2010 event. Rotterdam's swimming tradition started with Marie Braun aka Zus (sister) Braun , who was coached to a Gold medal at the 1928 Amsterdam Olympics by her mother Ma Braun, and 3 European titles 3 years later in Paris. @@ -7415,12 +6758,10 @@ a Gold medal at the 1928 Amsterdam Olympics by her mother Ma Braun, and 3 Europe Rotterdam's swimming tradition started with Marie Braun aka Zus (sister) Braun, who was coached to a Gold medal at the 1928 Amsterdam Olympics by her mother Ma Braun , and 3 European titles 3 years later in Paris. In her career as 14 time national champ , she broke 6 world records. Ma Braun later also coached the Rotterdam born, three-times Olympic champion Rie Mastenbroek during the Berlin Olympics in 1936. -Airport -Much smaller than the international hub Schiphol Airport, Rotterdam The Hague Airport (formerly known as Zestienhoven) is the third largest airport in the country, behind Schiphol Airport and Eindhoven Airport. +Airport.Much smaller than the international hub Schiphol Airport, Rotterdam The Hague Airport (formerly known as Zestienhoven) is the third largest airport in the country, behind Schiphol Airport and Eindhoven Airport. Located north of the city, it has shown a very strong growth over the past five years, mostly caused by the growth of the low-cost carrier market. For business travelers, Rotterdam The Hague Airport offers advantages in terms of rapid handling of passengers and baggage. Environmental regulations make further growth uncertain. -Airport -Much smaller than the international hub Schiphol Airport, Rotterdam The Hague Airport (formerly known as Zestienhoven) is the third largest airport in the country, behind Schiphol Airport and Eindhoven Airport . +Airport.Much smaller than the international hub Schiphol Airport, Rotterdam The Hague Airport (formerly known as Zestienhoven) is the third largest airport in the country, behind Schiphol Airport and Eindhoven Airport . For business travelers, Rotterdam The Hague Airport offers advantages in terms of rapid handling of passengers and baggage. Environmental regulations make further growth uncertain. 'Rotterdam' is divided into a northern and a southern part by the river Nieuwe Maas , connected by (from west to east): the Beneluxtunnel; the Maastunnel; the Erasmusbrug ('Erasmus Bridge'); a subway tunnel; the Willemsspoortunnel ('Willems railway tunnel'); the Willemsbrug ('Willems Bridge'); the Koninginnebrug ('Queen's Bridge'); and the Van Brienenoordbrug ('Van Brienenoord Bridge'). The former railway lift bridge De Hef ('the Lift') is preserved as a monument in lifted position between the Noordereiland ('North Island') and the south of Rotterdam. @@ -7434,20 +6775,16 @@ The former railway lift bridge De Hef ('the Lift') is preserved as a monument in 'Rotterdam' is divided into a northern and a southern part by the river Nieuwe Maas, connected by (from west to east): the Beneluxtunnel; the Maastunnel; the Erasmusbrug ('Erasmus Bridge'); a subway tunnel; the Willemsspoortunnel ('Willems railway tunnel'); the Willemsbrug ('Willems Bridge'); the Koninginnebrug ('Queen's Bridge'); and the Van Brienenoordbrug ('Van Brienenoord Bridge'). Rotterdam was gradually rebuilt from the 1950s through to the 1970s. In the 1990s, the Kop van Zuid was built on the south bank of the river as a new business centre. - -Rotterdam was voted 2015 European City of the Year by the Academy of Urbanism. - -Rotterdam was voted 2015 European City of the Year by the Academy of Urbanism . +.Rotterdam was voted 2015 European City of the Year by the Academy of Urbanism. +.Rotterdam was voted 2015 European City of the Year by the Academy of Urbanism . It remained quite windy and open until the city councils from the 1980s on began developing an active architectural policy. In the 1990s, the Kop van Zuid was built on the south bank of the river as a new business centre. - -Rotterdam was voted 2015 European City of the Year by the Academy of Urbanism. +.Rotterdam was voted 2015 European City of the Year by the Academy of Urbanism. It remained quite windy and open until the city councils from the 1980s on began developing an active architectural policy. Daring and new styles of apartments, office buildings and recreation facilities resulted in a more ' livable ' city centre with a new skyline. Rotterdam was gradually rebuilt from the 1950s through to the 1970s. Furthermore, Rotterdam has the Dutch headquarters of Allianz, Maersk, Petrobras, Samskip, Louis Dreyfus Group and Aon . - -It is also home to the regional headquarters of chemical company LyondellBasell, commodities trading company Glencore, pharmaceutical company Pfizer , logistics companies Stolt-Nielsen, electrical equipment company ABB Group and consumer goods company Procter & Gamble. +.It is also home to the regional headquarters of chemical company LyondellBasell, commodities trading company Glencore, pharmaceutical company Pfizer , logistics companies Stolt-Nielsen, electrical equipment company ABB Group and consumer goods company Procter & Gamble. Nowadays, well-known companies with headquarters in Rotterdam are consumers goods company Unilever , asset management firm Robeco, energy company Eneco, dredging company Van Oord, oil company Shell Downstream, terminal operator Vopak,commodity trading company Vitol and architecture firm Office for Metropolitan Architecture. Nowadays, well-known companies with headquarters in Rotterdam are consumers goods company Unilever, asset management firm Robeco, energy company Eneco, dredging company Van Oord, oil company Shell Downstream , terminal operator Vopak,commodity trading company Vitol and architecture firm Office for Metropolitan Architecture. the Lijnbaan (the first set of pedestrian streets of the country, opened in 1953), the Hoogstraat, the Coolsingel with the city hall, and the Weena, which runs from the Central Station to the Hofplein (square). @@ -7476,8 +6813,7 @@ The city also has its own China Town at the (West-) Kruiskade , close to the cen Rotterdam features some urban architecture projects, nightlife, and many summer festivals celebrating the city's multicultural population and identity, such as the Caribbean-inspired "Summer Carnival", the Dance Parade, Rotterdam 666, the Metropolis pop festival and the World Port days . This resulted in the disappearance of the major music venues Nighttown and WATT and smaller stages such as Waterfront, Exit, and Heidegger . In the years 2005–2011 the city struggled with venues for popmusic.[citation needed] Many of the venues suffered severe financial problems. - -There are also the International Film Festival in January, the Poetry International Festival in June, the North Sea Jazz Festival in July, the Valery Gergiev Festival in September, September in Rotterdam and the World of the Witte de With. +.There are also the International Film Festival in January, the Poetry International Festival in June, the North Sea Jazz Festival in July, the Valery Gergiev Festival in September, September in Rotterdam and the World of the Witte de With. Chromatic aberration is caused by the dispersion of the lens material—the variation of its refractive index, n, with the wavelength of light. Since, from the formulae above, f is dependent upon n, it follows that light of different wavelengths is focused to different positions. Chromatic aberration of a lens is seen as fringes of colour around the image . It can be minimised by using an achromatic doublet (or achromat) in which two materials with differing dispersion are bonded together to form a single lens. @@ -8062,13 +7398,10 @@ In those languages, function calls are normally embedded in expressions (e.g., a Other languages, such as C and Lisp , do not distinguish between functions and subroutines. Procedure calls either behave syntactically as statements (e.g., a print procedure may be called as if x > 0 then print(x) or are explicitly invoked by a statement such as CALL or GOSUB (e.g. call print(x)). The earliest computers and microprocessors, such as the Small-Scale Experimental Machine and the RCA 1802 , did not have a single subroutine call instruction. - -Subroutines could be implemented, but they required programmers to use the call sequence —a series of instructions—at each call site. +.Subroutines could be implemented, but they required programmers to use the call sequence —a series of instructions—at each call site. This allows arbitrarily deep levels of subroutine nesting , but does not support recursive subroutines. - -Subroutines could be implemented, but they required programmers to use the call sequence— a series of instructions —at each call site. - -Machines before the mid 1960s—such as the UNIVAC I, the PDP-1, and the IBM 1130—typically use a calling convention which saved the instruction counter in the first memory location of the called subroutine. +.Subroutines could be implemented, but they required programmers to use the call sequence— a series of instructions —at each call site. +.Machines before the mid 1960s—such as the UNIVAC I, the PDP-1, and the IBM 1130—typically use a calling convention which saved the instruction counter in the first memory location of the called subroutine. In many early computers, the program instructions were entered into memory from a punched paper tape . The name subroutine library originally meant a library, in the literal sense, which kept indexed collections of such tapes or card decks for collective use . A similar approach was used in computers whose main input was through punched cards . @@ -8082,8 +7415,7 @@ At any moment, the stack contains only the private data of the calls that are cu Indeed, the call stack mechanism can be viewed as the earliest and simplest method for automatic memory management . When stack-based procedure calls were first introduced, an important motivation was to save precious memory.[citation needed] With this scheme, the compiler does not have to reserve separate space in memory for the private data ( parameters, return address, and local variables ) of each procedure Because of the ways in which programs were usually assembled from libraries, it was (and still is) not uncommon to find programs that include thousands of subroutines, of which only a handful are active at any given moment.[citation needed] For such programs, the call stack mechanism could save significant amounts of memory. Indeed, the call stack mechanism can be viewed as the earliest and simplest method for automatic memory management. - -To reduce that overhead, many modern compilers try to delay the use of a call stack until it is really needed .[citation needed] For example, the call of a procedure P may store the return address and parameters of the called procedure in certain processor registers, and transfer control to the procedure's body by a simple jump. +.To reduce that overhead, many modern compilers try to delay the use of a call stack until it is really needed .[citation needed] For example, the call of a procedure P may store the return address and parameters of the called procedure in certain processor registers, and transfer control to the procedure's body by a simple jump. This overhead is most obvious and objectionable in leaf procedures or leaf functions , which return without making any procedure calls themselves. This overhead is most obvious and objectionable in leaf procedures or leaf functions, which return without making any procedure calls themselves . If procedure P returns without making any other call , the call stack is not used at all. @@ -8405,10 +7737,8 @@ They can be designed by making a hanging-chain model, which will act as a catena The role of a structural engineer today involves a significant understanding of both static and dynamic loading, and the structures that are available to resist them. A structural engineer will typically have a four or five year undergraduate degree, followed by a minimum of three years of professional practice before being considered fully qualified. A structural engineer will typically have a four or five year undergraduate degree, followed by a minimum of three years of professional practice before being considered fully qualified. - -Structural engineers are licensed or accredited by different learned societies and regulatory bodies around the world (for example, the Institution of Structural Engineers in the UK). - -Another international organisation is IABSE (International Association for Bridge and Structural Engineering). +.Structural engineers are licensed or accredited by different learned societies and regulatory bodies around the world (for example, the Institution of Structural Engineers in the UK). +.Another international organisation is IABSE (International Association for Bridge and Structural Engineering). Structural engineering dates back to 2700 B.C.E. when the step pyramid for Pharaoh Djoser was built by Imhotep, the first engineer in history known by name. Structural engineering dates back to 2700 B.C.E. when the step pyramid for Pharaoh Djoser was built by Imhotep, the first engineer in history known by name. Pyramids were the most common major structures built by ancient civilizations because the structural form of a pyramid is inherently stable and can be almost infinitely scaled (as opposed to most other structural forms, which cannot be linearly increased in size in proportion to increased loads). @@ -8494,27 +7824,7 @@ The design of a column must check the axial capacity of the element, and the buc The design of a column must check the axial capacity of the element, and the buckling capacity. Its capacity depends upon its geometry, material, and the effective length of the column , which depends upon the restraint conditions at the top and bottom of the column. Its capacity depends upon its geometry, material, and the effective length of the column, which depends upon the restraint conditions at the top and bottom of the column. -The effective length is - - - -K -∗ -l - - -{\displaystyle K*l} - - where - - - -l - - -{\displaystyle l} - - is the real length of the column. +The effective length is ....K.∗.l...{\displaystyle K*l}.. where ....l...{\displaystyle l}.. is the real length of the column. The capacity of a column to carry axial load depends on the degree of bending it is subjected to , and vice versa. a complex non-linear relationship. The capacity of a column to carry axial load depends on the degree of bending it is subjected to, and vice versa.