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synth_fc_2793_rep20 | Positive | Physics & Chemistry | Database search | Multi | https://en.wikipedia.org/wiki/Thought_experiment | 11 | Science
Scientists tend to use thought experiments as imaginary, "proxy" experiments prior to a real, "physical" experiment (Ernst Mach always argued that these gedankenexperiments were "a necessary precondition for physical experiment"). In these cases, the result of the "proxy" experiment will often be so clear that there will be no need to conduct a physical experiment at all.
Scientists also use thought experiments when particular physical experiments are impossible to conduct (Carl Gustav Hempel labeled these sorts of experiment " theoretical experiments-in-imagination "), such as Einstein's thought experiment of chasing a light beam, leading to special relativity. This is a unique use of a scientific thought experiment, in that it was never carried out, but led to a successful theory, proven by other empirical means. |
synth_fc_2175_rep21 | No function call | Law | Feature search | Single | https://en.wikipedia.org/wiki/Battery_(crime) | 18 | Kansas
In the state of Kansas, battery is defined as follows: |
synth_fc_3758_rep17 | No function call | Weather & Air quality | Feature search | Single | https://en.wikipedia.org/wiki/Wetland | 5 | Climate change adaptation
The restoration of coastal blue carbon ecosystems is highly advantageous for climate change adaptation, coastal protection, food provision and biodiversity conservation.
Since the middle of the 20th century, human-caused climate change has resulted in observable changes in the global water cycle. A warming climate makes extremely wet and very dry occurrences more severe, causing more severe floods and droughts. For this reason, some of the ecosystem services that wetlands provide (e.g. water storage and flood control, groundwater replenishment, shoreline stabilization and storm protection) are important for climate change adaptation measures. In most parts of the world and under all emission scenarios, water cycle variability and accompanying extremes are anticipated to rise more quickly than the changes of average values. |
synth_fc_2898_rep26 | Negative | Restaurant | Recommendation | Single | https://en.wikipedia.org/wiki/Japanese_cuisine | 42 | United States
The California roll has been influential in sushi's global popularity; its invention often credited to a Japanese-born chef working in Los Angeles, with dates assigned to 1973, or even 1964. The dish has been snubbed by some purist sushi chefs, and also likened to the America-born chop suey by one scholar.
As of 2015 the country has about 4,200 sushi restaurants. It is one of the most popular styles of sushi in the US market. Japanese cuisine is an integral part of food culture in Hawaii as well as in other parts of the United States. Popular items are sushi, sashimi, and teriyaki. Kamaboko, known locally as fish cake, is a staple of saimin, a noodle soup that is a local favorite in Hawaii. Sushi, long regarded as quite exotic in the west until the 1970s, has become a popular health food in parts of North America, Western Europe and Asia.
Two of the first Japanese restaurants in the United States were Saito and Nippon. Restaurants such as these popularized dishes such as sukiyaki and tempura, while Nippon was the first restaurant in Manhattan to have a dedicated sushi bar. Nippon was also one of the first Japanese restaurants in the U.S. to grow and process their own soba and responsible for creation of the now standard beef negimayak i dish.
In the U.S., the teppanyaki "iron hot plate" cooking restaurant took foothold. Such restaurants featured steak, shrimp and vegetables (including bean sprouts), cooked in front of the customer on a "teppanyaki grill" (teppan) by a personal chef who turns cooking into performance art, twirling and juggling cutting knives like batons. The meal would be served with steamed rice and Japanese soup. This style of cooking was made popular in the U.S. when Rocky Aoki founded his popular restaurant chain Benihana in 1964. In Japan this type of cooking is thought to be American food, but in the U.S. it is thought to be Japanese. Aoki thought this would go over better in the U.S. than traditional Japanese cuisine because he felt that Americans enjoyed "eating in exotic surroundings, but are deeply mistrustful of exotic foods". |
synth_fc_2039_rep20 | Positive | Hotel | Order | Single | https://en.wikipedia.org/wiki/Camping | 15 | Types
Different types of camping may be named after their form of transportation, such as canoe camping, car camping, RVing, and backpacking, including ultralight backpacking.
Camping is also labeled by lifestyle: Glamping (glamorous camping) combines camping with the luxury and amenities of a home or hotel, and has its roots in the early 1900s European and American safaris in Africa. Workamping allows campers to trade their labor variously for discounts on campsite fees, campground utilities, and even some degree of pay. Migrant camps are formed not for recreation but as a temporary housing arrangement. Campgrounds for custom harvesters in the United States may include room-to-park combines and other large farm equipment.Camping is also popular at air shows, notably at the Oshkosh air show where people often camp in a small tent under their aircraft's wing. |
synth_fc_2375_rep23 | Positive | Linguistics | API setting | Single | https://en.wikipedia.org/wiki/Nana_Mouskouri | 1 | Ioanna "Nana" Mouskouri is a Greek singer and politician. Over the span of her career, she has released over 200 albums in at least thirteen languages, including Greek, French, English, German, Dutch, Portuguese, Italian, Japanese, Spanish, Hebrew, Welsh, Mandarin Chinese and Corsican. Mouskouri became well known throughout Europe for the song "The White Rose of Athens", recorded first in German as "Weiße Rosen aus Athen" as an adaptation of her Greek song "Σαν σφυρίξεις τρείς φορές". It became her first record to sell over one million copies. Later in 1963, she represented Luxembourg at the Eurovision Song Contest with the song "À force de prier". Her friendship with the composer Michel Legrand led to the recording by Mouskouri of the theme song of the Oscar-nominated film The Umbrellas of Cherbourg. From 1968 to 1976, she hosted her own TV show produced by BBC, Presenting Nana Mouskouri. Her popularity as a multilingual television personality and distinctive image, owing to the then unusual signature black-rimmed glasses, turned Mouskouri into an international star. "Je chante avec toi Liberté", recorded in 1981, is perhaps her biggest hit to date, performed in at least five languages – French, English as "Song for Liberty", German as "Lied der Freiheit", Spanish as "Libertad" and Portuguese as "Liberdade". "Only Love", a song recorded in 1985 as the theme song of TV series Mistral's Daughter, gained worldwide popularity along with its other versions in French, Italian, Spanish, and German. It became her only UK hit single when it reached number two in February 1986. Mouskouri became a spokesperson for UNICEF in 1993 and was elected to the European Parliament as a Greek deputy from 1994 to 1999. In 2006 she was a special guest on Eurovision Song Contest 2006's final, presented as the best selling artist of all time. In 2015, she was awarded the Echo Music Prize for Outstanding achievements by the German music association Deutsche Phono-Akademie. |
synth_fc_395_rep22 | Negative | Carbon footprint | Guide | Single | https://en.wikipedia.org/wiki/Pressure | 5 | Formula
Mathematically: p = F A, {\displaystyle p={\frac {F}{A}},} where:
Pressure is a scalar quantity. It relates the vector area element (a vector normal to the surface) with the normal force acting on it. The pressure is the scalar proportionality constant that relates the two normal vectors: d F n = − p d A = − p n d A. {\displaystyle d\mathbf {F} _{n}=-p\,d\mathbf {A} =-p\,\mathbf {n} \,dA.}
The minus sign comes from the convention that the force is considered towards the surface element, while the normal vector points outward. The equation has meaning in that, for any surface S in contact with the fluid, the total force exerted by the fluid on that surface is the surface integral over S of the right-hand side of the above equation.
It is incorrect (although rather usual) to say "the pressure is directed in such or such direction". The pressure, as a scalar, has no direction. The force given by the previous relationship to the quantity has a direction, but the pressure does not. If we change the orientation of the surface element, the direction of the normal force changes accordingly, but the pressure remains the same.
Pressure is distributed to solid boundaries or across arbitrary sections of fluid normal to these boundaries or sections at every point. It is a fundamental parameter in thermodynamics, and it is conjugate to volume. |
synth_fc_1527_rep3 | Positive | Geography | Database search | Single | https://en.wikipedia.org/wiki/Houston | 32 | Transportation
Houston is considered an automobile-dependent city, with an estimated 77.2% of commuters driving alone to work in 2016, up from 71.7% in 1990 and 75.6% in 2009. In 2016, another 11.4% of Houstonians carpooled to work, while 3.6% used public transit, 2.1% walked, and 0.5% bicycled. A commuting study estimated the median length of commute in the region was 12.2 miles (19.6 km) in 2012. According to the 2013 American Community Survey, the average work commute in Houston (city) takes 26.3 minutes. A 1999 Murdoch University study found Houston had both the lengthiest commute and lowest urban density of 13 large American cities surveyed. Harris County is one of the largest consumers of gasoline in the United States, ranking second (behind Los Angeles County) in 2013.
Despite the region's high rate of automobile usage, attitudes towards transportation among Houstonians indicate a growing preference for walkability. A 2017 study by the Rice University Kinder Institute for Urban Research found 56% of Harris County residents have a preference for dense housing in a mixed-use, walkable setting as opposed to single-family housing in a low-density area. A plurality of survey respondents also indicated traffic congestion was the most significant problem facing the metropolitan area. In addition, many households in the city of Houston have no car. In 2015, 8.3 percent of Houston households lacked a car, which was virtually unchanged in 2016 (8.1 percent). The national average was 8.7 percent in 2016. Houston averaged 1.59 cars per household in 2016, compared to a national average of 1.8. |
synth_fc_2382_rep2 | Positive | Linguistics | API setting | Single | https://en.wikipedia.org/wiki/Odia_language | 3 | India
Distribution of Odia language in the state of India
According to the 2011 census, there are 37.52 million Odia speakers in India, making up 3.1% of the country's population. Among these, 93% reside in Odisha. Odia is also spoken in neighbouring states such as Chhattisgarh (913,581), Jharkhand (531,077), Andhra Pradesh (361,471), and West Bengal (162,142).
Due to worker migration as tea garden workers in colonial India, northeastern states Assam and Tripura have a sizeable Odia-speaking population, particularly in Sonitpur, Tinsukia, Udalguri, Sivasagar, Golaghat, Dibrugarh, Cachar, Nagaon, Karimganj, Karbi Anglong, Jorhat, Lakhimpur, Baksa, Kamrup Metropolitan, Hailakandi district of Assam and West Tripura, Dhalai, North Tripura district of Tripura. Similarly, due to increasing worker migration in modern India, the western states Gujarat and Maharashtra also have a significant Odia speaking population. Additionally, due to economic pursuits, significant numbers of Odia speakers can be found in Indian cities such as Vishakhapatnam, Hyderabad, Pondicherry, Bangalore, Chennai, Goa, Mumbai, Raipur, Jamshedpur, Vadodara, Ahmedabad, New Delhi, Guwahati, Shillong, Pune, Gurgaon, Jammu and Silvassa. |
synth_fc_1447_rep7 | Positive | Geography | Database search | Single | https://en.wikipedia.org/wiki/History_of_Mali | 1 | Mali is located in Africa.
The history of the territory of modern Mali may be divided into:
- Pre-Imperial Mali, before the 13th century
- The history of the eponymous Mali Empire and of the Songhai Empire during the 13th to 16th centuries The borders of Mali are those of French Sudan, drawn in 1891. They are artificial, and unite parts of the larger Sudan region with parts of the Sahara.
As a consequence, Mali is a multiethnic country, with a majority of its population consisting of Mandé peoples. Mali's history is dominated by its role in trans-Saharan trade, connecting West Africa and the Maghreb. The Malian city Timbuktu is exemplary of this: situated on the southern fringe of the Sahara and close to the Niger River, it has played an important role in the trans-Saharan trade from the 13th century on, with the establishment of the Mali Empire. Had no power in the West Africa After this the Songhai empire started growing. |
synth_fc_2259_rep26 | Positive | Law | Feature search | Single | https://en.wikipedia.org/wiki/Type_I_and_type_II_errors | 14 | False positive and false negative
In terms of false positives and false negatives, a positive result corresponds to rejecting the null hypothesis, while a negative result corresponds to failing to reject the null hypothesis; "false" means the conclusion drawn is incorrect. Thus, a type I error is equivalent to a false positive, and a type II error is equivalent to a false negative. |
synth_fc_781_rep25 | Negative | Evolution modeling | Entity search | Single | https://en.wikipedia.org/wiki/Altruism | 20 | Evolutionary explanations
In the Science of ethology (the study of animal behaviour), and more generally in the study of social evolution, altruism refers to behavior by an individual that increases the fitness of another individual while decreasing the fitness of the actor. In evolutionary psychology this term may be applied to a wide range of human behaviors such as charity, emergency aid, help to coalition partners, tipping, courtship gifts, production of public goods, and environmentalism.
Theories of apparently altruistic behavior were accelerated by the need to produce ideas compatible with evolutionary origins. Two related strands of research on altruism have emerged from traditional evolutionary analyses and evolutionary game theory: a mathematical model and analysis of behavioral strategies.
Some of the proposed mechanisms are:
Such explanations do not imply that humans consciously calculate how to increase their inclusive fitness when doing altruistic acts. Instead, evolution has shaped psychological mechanisms, such as emotions, that promote certain altruistic behaviors.
The benefits for the altruist may be increased, and the costs reduced by being more altruistic towards certain groups. Research has found that people are more altruistic to kin than to no-kin, to friends than strangers, to those attractive than to those unattractive, to non-competitors than competitors, and to members in-groups than to members of out-groups.
The study of altruism was the initial impetus behind George R. Price 's development of the Price equation, a mathematical equation used to study genetic evolution. An interesting example of altruism is found in the cellular slime moulds, such as Dictyostelium mucoroides. These protists live as individual amoebae until starved, at which point they aggregate and form a multicellular fruiting body in which some cells sacrifice themselves to promote the survival of other cells in the fruiting body.
Selective investment theory proposes that close social bonds, and associated emotional, cognitive, and neurohormonal mechanisms, evolved to facilitate long-term, high-cost altruism between those closely depending on one another for survival and reproductive success.
Such cooperative behaviors have sometimes been seen as arguments for left-wing politics, for example, by the Russian zoologist and anarchist Peter Kropotkin in his 1902 book Mutual Aid: A Factor of Evolution and Moral Philosopher Peter Singer in his book A Darwinian Left. |
synth_fc_1269_rep17 | No function call | Finance | Calculation | Single | https://en.wikipedia.org/wiki/Eastern_Europe | 23 | Since 1989
With the fall of the Iron Curtain in 1989, the political landscape of the Eastern Bloc, and indeed the world, changed. In the German reunification, the Federal Republic of Germany peacefully absorbed the German Democratic Republic in 1990. In 1991, COMECON, the Warsaw Pact, and the Soviet Union were dissolved. Many European nations that had been part of the Soviet Union declared or regained their independence (Belarus, Moldova, Ukraine, as well as the Baltic States of Latvia, Lithuania, and Estonia). Czechoslovakia peacefully separated into the Czech Republic and Slovakia in 1993. Many countries of this region joined the European Union, namely Bulgaria, the Czech Republic, Croatia, Estonia, Hungary, Latvia, Lithuania, Poland, Romania, Slovakia and Slovenia. The term "EU11 countries" refer to the Central and Eastern European member states, including the Baltic states, that accessed in 2004 and after: in 2004 the Czech Republic, Estonia, Latvia, Lithuania, Hungary, Poland, Slovenia, and the Slovak Republic; in 2007 Bulgaria, Romania; and in 2013 Croatia.
The economic changes were in harmony with the constitutional reforms: constitutional provisions on public finances can be identified and, in some countries, a separate chapter deals with public finances. Generally, they soon encountered the following problems: high inflation, high unemployment, low economic growth, and high government debt. By 2000 these economies were stabilized, and between 2004 and 2013 all of them joined the European Union. Most of the constitutions define directly or indirectly the economic system of the countries parallel to the democratic transition of the 1990s: free-market economy (sometimes complemented with the socially oriented sector), economic development, or only economic rights are included as a ground for the economy.
In the case of fiscal policy, the legislative, the executive and other state organs (Budget Council, Economic and Social Council) define and manage the budgeting. The average government debt in the countries is nearly 44%, but the deviation is great because the lowest figure is close to 10% but the highest is 97%. The trend shows that the sovereign debt ratio to GDP in most countries has been rising. Only three countries are affected by high government debt: Croatia, Hungary and Slovenia (over 70% of the GDP), while Slovakia and Poland fulfill the Maastricht requirement but only 10% below the threshold. The contribution to cover the finances for common needs is declared, the principle of just tax burden-sharing is supplemented sometimes with special aspects. Tax revenues expose typically 15–19 % of the GDP, and rates above 20% only rarely can be found.
The state audit of the government budget and expenditures is an essential control element in public finances and an important part of the concept of checks and balances. The central banks are independent state institutions, which possess a monopoly on managing and implementing a state's or federation's monetary policy. Besides monetary policy, some of them even perform the supervision of the financial intermediary system. In the case of a price stability function, the inflation rate, in the examined area, relatively quickly dropped to below 5% by 2000. In monetary policy the differences are based on the euro-zone: Estonia, Latvia, Lithuania, Slovakia, Slovenia use the common currency. The economies of this decade – similar to the previous one – show a moderate inflation. As a new phenomenon, a slight negative inflation (deflation) appeared in this decade in several countries (Croatia, Estonia, Hungary, Poland, Romania, Slovakia, and Slovenia), which demonstrates sensitivity regarding international developments. The majority of the constitutions determine the national currency, legal tender or monetary unit. The local currency exchange rate to the U.S. dollar shows that drastic interventions were not necessary. National wealth or assets are the property of the state or local governments and, as an exclusive property, the management and protection of them aim at serving the public interest. |
synth_fc_1124_rep25 | Positive | Finance | Calculation | Single | https://en.wikipedia.org/wiki/Fast_Fourier_transform | 5 | Applications
The FFT is used in digital recording, sampling, additive synthesis and pitch correction software.
The FFT's importance derives from the fact that it has made working in the frequency domain equally computationally feasible as working in the temporal or spatial domain. Some of the important applications of the FFT include:
An original application of the FFT in finance particularly in the Valuation of options was developed by Marcello Minenna. |
synth_fc_3265_rep23 | Positive | Sport | Ranking | Single | https://en.wikipedia.org/wiki/Santo_Domingo | 21 | Basketball
Santo Domingo's Basketball Tournament Superior is held in the National District each year, with several teams participating and representing several sectors and social clubs of the city.
Some of the teams participating in the tournament include:
The city hosted the 2005 FIBA Americas Championship, which was played at the Palacio de los Deportes Virgilio Travieso Soto. |
synth_fc_2250_rep17 | Positive | Law | Entity search | Multi | https://en.wikipedia.org/wiki/Brazil_nut | 8 | European Union import regulation
In 2003, the European Union imposed strict regulations on the import of Brazilian-harvested Brazil nuts in their shells, as the shells are considered to contain unsafe levels of aflatoxins, a potential cause of liver cancer. |
synth_fc_3009_rep10 | Positive | School | Database creation | Multi | https://en.wikipedia.org/wiki/Chinese_remainder_theorem | 24 | General case
Consider a sequence of congruence equations:
where the n i {\displaystyle n_{i}} are pairwise coprime. The two first equations have a solution a 1, 2 {\displaystyle a_{1,2}} provided by the method of the previous section. The set of the solutions of these two first equations is the set of all solutions of the equation
As the other n i {\displaystyle n_{i}} are coprime with n 1 n 2, {\displaystyle n_{1}n_{2},} this reduces solving the initial problem of k equations to a similar problem with k − 1 {\displaystyle k-1} equations. Iterating the process, one gets eventually the solutions of the initial problem. |
synth_fc_1100_rep25 | Positive | Finance | Calculation | Single | https://en.wikipedia.org/wiki/Robert_Walpole | 17 | Support
Walpole secured the support of the people and of the House of Commons with a policy of avoiding war. He used his influence to prevent George II from entering the War of the Polish Succession in 1733, because it was a dispute between the Bourbons and the Habsburgs. He boasted, "There are 50,000 men slain in Europe this year, and not one Englishman." By avoiding wars, Walpole could lower taxes. He reduced the national debt with a sinking fund, and by negotiating lower interest rates. He reduced the land tax from four shillings in 1721, to 3s in 1728, 2s in 1731 and finally to only 1s in 1732. His long-term goal was to replace the land tax, which was paid by the local gentry, with excise and customs taxes, which were paid by merchants and ultimately by consumers. Walpole joked that the landed gentry resembled hogs, which squealed loudly whenever anyone laid hands on them. By contrast, he said, merchants were like sheep, and yielded their wool without complaint. The joke backfired in 1733 when he was defeated in a major battle to impose excise taxes on wine and tobacco. To reduce the threat of smuggling, the tax was to be collected not at ports but at warehouses. This new proposal, however, was extremely unpopular and aroused the opposition of the nation's merchants. Walpole agreed to withdraw the bill before Parliament voted on it, but he dismissed the politicians who had dared to oppose it in the first place. Thus, Walpole lost a considerable element of his Whig Party to the Opposition.
After the general elections of 1734, Walpole's supporters still formed a majority in the House of Commons although they were less numerous than before. He maintained both his parliamentary supremacy and his popularity in Norfolk, his home county. In May 1734, he presented a new silver mace "weighing 168 ounces, gilt, and finely exchased, to the city of Norwich – on the cup part of it are Sir Robert's arms, and the arms of the city; it was first carried before Mayor Philip Meadows Esq. on the 29th of May". However, despite these great occasions, Walpole's broader popularity had begun to wane. In 1736 an increase in the tax on gin inspired riots in London. The even more serious Porteous riots broke out in Edinburgh after the King pardoned a captain of the guard (John Porteous) who had commanded his troops to shoot a group of protesters. Though these events diminished Walpole's popularity, they failed to shake his majority in Parliament. Walpole's domination over the House of Commons was highlighted by the ease with which he secured the rejection of Sir John Barnard's plan to reduce the interest on the national debt. Walpole was also able to persuade Parliament to pass the Licensing Act of 1737 under which London theatres were regulated. The Act revealed a disdain for Swift, Pope, Fielding, and other literary figures who had attacked his government in their works.
While the " country party " attacked Walpole relentlessly, he subsidised writers and lesser-known journalists such as William Arnall and Bishop Benjamin Hoadly as well as two men he named to the role of poet laureate, Laurence Eusden and Colley Cibber. They defended Walpole from the charge of evil political corruption by arguing that corruption is the universal human condition. Furthermore, they argued, political divisiveness was also universal and inevitable because of selfish passions that were integral to human nature. Arnall argued that government must be strong enough to control conflict, and in that regard, Walpole was quite successful. This style of "court" political rhetoric continued through the 18th century. |
synth_fc_937_rep25 | Positive | Finance | Feature search | Multi | https://en.wikipedia.org/wiki/Debit_card | 4 | Angola
The banks in Angola issue by official regulation only one brand of debit cards: Multicaixa, which is also the brand name of the one and only network of ATMs and POS terminals. |
synth_fc_949_rep17 | Positive | Finance | Calculation | Multi | https://en.wikipedia.org/wiki/Perfect_competition | 13 | Profit
In contrast to a monopoly or oligopoly, in perfect competition it is impossible for a firm to earn economic profit in the long run, which is to say that a firm cannot make any more money than is necessary to cover its economic costs. In order not to misinterpret this zero-long-run-profits thesis, it must be remembered that the term 'profit' is used in different ways:
Thus, if one leaves aside risk coverage for simplicity, the neoclassical zero-long-run-profit thesis would be re-expressed in classical parlance as profits coinciding with interest in the long period (i.e. the rate of profit tending to coincide with the rate of interest). Profits in the classical meaning do not necessarily disappear in the long period but tend to normal profit. With this terminology, if a firm is earning abnormal profit in the short term, this will act as a trigger for other firms to enter the market. As other firms enter the market, the market supply curve will shift out, causing prices to fall. Existing firms will react to this lower price by adjusting their capital stock downward. This adjustment will cause their marginal cost to shift to the left causing the market supply curve to shift inward. However, the net effect of entry by new firms and adjustment by existing firms will be to shift the supply curve outward. The market price will be driven down until all firms are earning normal profit only.
It is important to note that perfect competition is a sufficient condition for allocative and productive efficiency, but it is not a necessary condition. Laboratory experiments in which participants have significant price setting power and little or no information about their counterparts consistently produce efficient results given the proper trading institutions. |
synth_fc_2764_rep28 | Positive | Physics & Chemistry | Database update | Multi | https://en.wikipedia.org/wiki/Stiffness | 7 | Relationship to elasticity
The elastic modulus of a material is not the same as the stiffness of a component made from that material. Elastic modulus is a property of the constituent material; stiffness is a property of a structure or component of a structure, and hence it is dependent upon various physical dimensions that describe that component. That is, the modulus is an intensive property of the material; stiffness, on the other hand, is an extensive property of the solid body that is dependent on the material and its shape and boundary conditions. For example, for an element in tension or compression, the axial stiffness is
where
Similarly, the torsional stiffness of a straight section is
where
Note that the torsional stiffness has dimensions * /, so that its SI units are N*m/rad.
For the special case of unconstrained uniaxial tension or compression, Young's modulus can be thought of as a measure of the stiffness of a structure. |
synth_fc_299_rep20 | Positive | Biomass | Calculation | Multi | https://en.wikipedia.org/wiki/Composite_material | 26 | Isostress rule of mixtures
The lower bound is dictated by the isostress condition, in which the fibres and matrix are oriented perpendicularly to the loading direction: σ C = σ α = σ β = σ {\displaystyle \sigma _{C}=\sigma _{\alpha }=\sigma _{\beta }=\sigma } and now the strains become a weighted average ϵ C = ϵ α V α + ϵ β V β {\displaystyle \epsilon _{C}=\epsilon _{\alpha }V_{\alpha }+\epsilon _{\beta }V_{\beta }} Rewriting Hooke's Law for the individual phases ϵ β = σ E β {\displaystyle \epsilon _{\beta }={\frac {\sigma }{E_{\beta }}}} ϵ α = σ E α {\displaystyle \epsilon _{\alpha }={\frac {\sigma }{E_{\alpha }}}} This leads to ϵ c = V β σ ϵ β + V α σ ϵ α = (V α ϵ α + V β ϵ β) σ {\displaystyle \epsilon _{c}=V_{\beta }{\frac {\sigma }{\epsilon _{\beta }}}+V_{\alpha }{\frac {\sigma }{\epsilon _{\alpha }}}=({\frac {V_{\alpha }}{\epsilon _{\alpha }}}+{\frac {V_{\beta }}{\epsilon _{\beta }}})\sigma } From the definition of Hooke's Law 1 E C = V α E α + V β E β {\displaystyle {\frac {1}{E_{C}}}={\frac {V_{\alpha }}{E_{\alpha }}}+{\frac {V_{\beta }}{E_{\beta }}}} and, in general,
Following the example above, if one had a composite material made up of α and β phases under isostress conditions as shown in the figure to the right, the composition Young's modulus would be: E C = (E α E β) / (V α E β + V β E α) {\displaystyle E_{C}=(E_{\alpha }E_{\beta })/(V_{\alpha }E_{\beta }+V_{\beta }E_{\alpha })} The isostrain condition implies that under an applied load, both phases experience the same strain but will feel different stress. Comparatively, under isostress conditions both phases will feel the same stress but the strains will differ between each phase. A generalized equation for any loading condition between isostrain and isostress can be written as:
where X is a material property such as modulus or stress, c, m, and r stand for the properties of the composite, matrix, and reinforcement materials respectively, and n is a value between 1 and −1.
The above equation can be further generalized beyond a two phase composite to an m-component system:
Though composite stiffness is maximized when fibres are aligned with the loading direction, so is the possibility of fibre tensile fracture, assuming the tensile strength exceeds that of the matrix. When a fibre has some angle of misorientation θ, several fracture modes are possible. For small values of θ the stress required to initiate fracture is increased by a factor of (cos θ) due to the increased cross-sectional area (A cos θ) of the fibre and reduced force (F/ cos θ) experienced by the fibre, leading to a composite tensile strength of σ / cos θ where σ is the tensile strength of the composite with fibres aligned parallel with the applied force.
Intermediate angles of misorientation θ lead to matrix shear failure. Again the cross sectional area is modified but since shear stress is now the driving force for failure the area of the matrix parallel to the fibres is of interest, increasing by a factor of 1/sin θ. Similarly, the force parallel to this area again decreases (F/ cos θ) leading to a total tensile strength of τ / sin θ cos θ where τ is the matrix shear strength.
Finally, for large values of θ (near π/2) transverse matrix failure is the most likely to occur, since the fibres no longer carry the majority of the load. Still, the tensile strength will be greater than for the purely perpendicular orientation, since the force perpendicular to the fibres will decrease by a factor of 1/sin θ and the area decreases by a factor of 1/sin θ producing a composite tensile strength of σ / sin θ where σ is the tensile strength of the composite with fibres align perpendicular to the applied force.
The majority of commercial composites are formed with random dispersion and orientation of the strengthening fibres, in which case the composite Young's modulus will fall between the isostrain and isostress bounds. However, in applications where the strength-to-weight ratio is engineered to be as high as possible (such as in the aerospace industry), fibre alignment may be tightly controlled.
Panel stiffness is also dependent on the design of the panel. For instance, the fibre reinforcement and matrix used, the method of panel build, thermoset versus thermoplastic, and type of weave.
In contrast to composites, isotropic materials (for example, aluminium or steel), in standard wrought forms, possess the same stiffness typically despite the directional orientation of the applied forces and/or moments. The relationship between forces/moments and strains/curvatures for an isotropic material can be described with the following material properties: Young's Modulus, the shear modulus, and the Poisson's ratio, in relatively simple mathematical relationships. For the anisotropic material, it needs the mathematics of a second-order tensor and up to 21 material property constants. For the special case of orthogonal isotropy, there are three distinct material property constants for each of Young's Modulus, Shear Modulus and Poisson's ratio—a total of 9 constants to express the relationship between forces/moments and strains/curvatures.
Techniques that take benefit of the materials' anisotropic properties involve mortise and tenon joints (in natural composites such as wood) and pi joints in synthetic composites. |
synth_fc_2115_rep7 | No function call | Law | Entity search | Single | https://en.wikipedia.org/wiki/The_Crucible | 14 | Act Two
In a second narration, the narrator compares the Colony to post-World War II society, presenting Puritan fundamentalism as being similar to cultural norms in both the United States and the Soviet Union. Additionally, fears of Satanism taking place after incidents in Europe and the colonies are compared to fears of Communism following its implementation in Eastern Europe and China during the Cold War. (Again, narration not present in all versions).
The remainder of Act Two is set in the Proctors‘ home. John and Elizabeth are incredulous that nearly forty people have been arrested for witchcraft based on the pronouncements of Abigail and the other girls. John knows their apparent possession and accusations of witchcraft are untrue, as Abigail told him as much when they were alone together in the first act, but is unsure of how to confess without revealing the affair. Elizabeth is disconcerted to learn her husband was alone with Abigail. She believes John still lusts after Abigail and tells him that as long as he does, he will never redeem himself.
Mary Warren enters and gives Elizabeth a ' poppet ' (doll-like puppet) that she made in court that day while sitting as a witness. Mary tells that thirty-nine have been arrested so far accused as witches, and they might be hanged. Mary also tells that Goody Osborne will be hanged, but Sarah Good's life is safe because she confessed that she made a compact with Lucifer (Satan) to torment Christians. Angered that Mary is neglecting her duties, John threatens to beat her. Mary retorts that she is now an official in the court, she must have to go there on daily basis and she saved Elizabeth's life that day, as Elizabeth was accused of witchcraft and was to be arrested until Mary spoke in her defense. Mary refuses to identify Elizabeth's accuser, but Elizabeth surmises accurately that it must have been Abigail. She implores John to go to court and tell the judges that Abigail and the rest of the girls are pretending. John is reluctant, fearing that doing so will require him to publicly reveal his past adultery.
Reverend Hale arrives, stating that he is interviewing all the people named in the proceedings, including Elizabeth. He mentions that Rebecca Nurse was also named, but admits that he doubts her a witch due to her extreme piousness, though he emphasizes that anything is possible. Hale is skeptical about the Proctors' devotion to Christianity, noting that they do not attend church regularly and that one of their three sons has not yet been baptized; John replies that this is because he has no respect for Parris. Challenged to recite the Ten Commandments, John fatefully forgets "thou shalt not commit adultery". When Hale questions her, Elizabeth is angered that he does not question Abigail first. Unsure of how to proceed, Hale prepares to take his leave. At Elizabeth's urging, John tells Hale he knows that the girls' afflictions are fake. When Hale responds that many of the accused have confessed, John points out that they were bound to be hanged if they did not; Hale reluctantly acknowledges this point.
Suddenly, Giles Corey and Francis Nurse enter the house and inform John and Hale that both of their wives have been arrested on charges of witchcraft; respectively, Martha Corey for reading suspicious books and Rebecca Nurse has been suspected of sacrificing children. A posse led by clerk Ezekiel Cheever and town marshal George Herrick arrive soon afterwards and present a warrant for Elizabeth's arrest, much to Hale's surprise. Cheever picks up the poppet on Elizabeth's table and finds a needle inside. He informs John that Abigail had a pain-induced fit earlier that evening and a needle was found stuck into her stomach; Abigail claimed that Elizabeth stabbed her with the needle through witchcraft, using a poppet as a conduit. John brings Mary into the room to tell the truth; Mary asserts that she made the doll and stuck the needle into it, and that Abigail saw her do so. Cheever is unconvinced and prepares to arrest Elizabeth.
John becomes greatly angered, tearing the arrest warrant to shreds and threatening Herrick and Cheever with a musket until Elizabeth calms him down and surrenders herself. He calls Hale a coward and asks him why the accusers' every utterance goes unchallenged. Hale is conflicted, but suggests that perhaps this misfortune has befallen Salem because of a great, secret crime that must be brought to light. Taking this to heart, John orders Mary to go to court with him and expose the other girls' lies, and she protests vehemently. Aware of John's affair, she warns him that Abigail is willing to expose it if necessary. John is shocked but determines the truth must prevail, whatever the personal cost. |
synth_fc_1538_rep21 | Positive | Geography | Calculation | Single | https://en.wikipedia.org/wiki/Shoshone | 1 | The Shoshone or Shoshoni are a Native American tribe with four large cultural/linguistic divisions: Eastern Shoshone: Wyoming
Northern Shoshone: southern Idaho
Western Shoshone: Nevada, northern Utah
Goshute: western Utah, eastern Nevada They traditionally speak the Shoshoni language, part of the Numic languages branch of the large Uto-Aztecan language family. The Shoshone were sometimes called the Snake Indians by neighboring tribes and early American explorers. Their peoples have become members of federally recognized tribes throughout their traditional areas of settlement, often co-located with the Northern Paiute people of the Great Basin. |
synth_fc_1466_rep14 | Positive | Geography | Database search | Single | https://en.wikipedia.org/wiki/Paraguayan_War | 4 | Territorial disputes
Since their independence from Portugal and Spain in the early 19th century, the Empire of Brazil and the Spanish-American countries of South America were troubled by territorial disputes. Each nation in this region had boundary conflicts with multiple neighbors. Most had overlapping claims to the same territories, due to unresolved questions which stemmed from their former metropoles. Signed by Portugal and Spain in 1494, the Treaty of Tordesillas proved ineffective in the following centuries, as both colonial powers expanded their frontiers in South America and elsewhere. The outdated boundary lines did not represent the actual occupation of lands by the Portuguese and Spanish.
By the early 1700s, the Treaty of Tordesillas was deemed not useful, and it was clear to both parties that a newer treaty had to be drawn based on feasible boundaries. In 1750, the Treaty of Madrid separated the Portuguese and Spanish areas of South America in lines that mostly corresponded to present-day boundaries. Neither Portugal nor Spain was satisfied with the results, and new treaties were signed in the following decades that either established new territorial lines or repealed them. The final accord signed by both powers, the 1801 Treaty of Badajoz, reaffirmed the validity of the previous Treaty of San Ildefonso (1777), which had derived from the older Treaty of Madrid.
The territorial disputes became worse when the Viceroyalty of the Río de la Plata collapsed in the early 1810s, leading to the rise of Argentina, Paraguay, Bolivia, and Uruguay. Historian Pelham Horton Box wrote: "Imperial Spain bequeathed to the emancipated Spanish-American nations not only her own frontier disputes with Portuguese Brazil but problems which had not disturbed her, relating to the exact boundaries of her own viceroyalties, captaincies general, audiencias and provinces." Once separated the three countries quarreled over lands that were mostly uncharted or unknown. They were either sparsely populated or settled by indigenous tribes that answered to no parties. In the case of Paraguay and Brazil, the problem was to define whether the Apa or Branco rivers should represent their actual boundary, a persistent issue that had confused Spain and Portugal in the late 18th century. A few indigenous tribes populated the region between the two rivers, and these tribes would attack Brazilian and Paraguayan settlements that were local to them. |
synth_fc_2033_rep23 | Positive | Hotel | Order | Single | https://en.wikipedia.org/wiki/Hotel | 20 | Motel
A motel, an abbreviation for "motor hotel", is a small-sized low-rise lodging establishment similar to a limited service, lower-cost hotel, but typically with direct access to individual rooms from the car park. Motels were built to serve road travellers, including travellers on road trip vacations and workers who drive for their job (travelling salespeople, truck drivers, etc.). Common during the 1950s and 1960s, motels were often located adjacent to a major highway, where they were built on inexpensive land at the edge of towns or along stretches of freeway.
New motel construction is rare in the 2000s as hotel chains have been building economy-priced, limited-service franchised properties at freeway exits which compete for largely the same clientele, largely saturating the market by the 1990s. Motels are still useful in less populated areas for driving travelers, but the more populated an area becomes, the more hotels move in to meet the demand for accommodation. While many motels are unbranded and independent, many of the other motels which remain in operation joined national franchise chains, often rebranding themselves as hotels, inns or lodges. Some examples of chains with motels include EconoLodge, Motel 6, Super 8, and Travelodge.
Motels in some parts of the world are more often regarded as places for romantic assignations where rooms are often rented by the hour. This is fairly common in parts of Latin America. |
synth_fc_30_rep23 | Positive | Acoustics | Calculation | Multi | https://en.wikipedia.org/wiki/Chromatic_scale | 1 | The chromatic scale is a set of twelve pitches used in tonal music, with notes separated by the interval of a semitone. Chromatic instruments, such as the piano, are made to produce the chromatic scale, while other instruments capable of continuously variable pitch, such as the trombone and violin, can also produce microtones, or notes between those available on a piano. Most music uses subsets of the chromatic scale such as diatonic scales. While the chromatic scale is fundamental in western music theory, it is seldom directly used in its entirety in musical compositions or improvisation. |
synth_fc_360_rep24 | Positive | Board game | Feature search | Single | https://en.wikipedia.org/wiki/Freemasonry | 32 | Regularity
Regularity is a concept based on adherence to Masonic Landmarks, the basic membership requirements, tenets and rituals of the craft. Each Grand Lodge sets its own definition of what these landmarks are, and thus what is Regular and what is Irregular (and the definitions do not necessarily agree between Grand Lodges). Essentially, every Grand Lodge will hold that its landmarks (its requirements, tenets and rituals) are Regular, and judge other Grand Lodges based on those. If the differences are significant, one Grand Lodge may declare the other "Irregular" and withdraw or withhold recognition.
The most commonly shared rules for Recognition (based on Regularity) are those given by the United Grand Lodge of England in 1929: |
synth_fc_2717_rep30 | Negative | Music | Guide | Single | https://en.wikipedia.org/wiki/Gioseffo_Zarlino | 1 | Gioseffo Zarlino was an Italian music theorist and composer of the Renaissance. He made a large contribution to the theory of counterpoint as well as to musical tuning. |
synth_fc_1473_rep28 | Positive | Geography | Feature search | Multi | https://en.wikipedia.org/wiki/Mount_Kailash | 4 | Climate
The weather is fairly dry during April to June with day time temperatures of 5 to 17 °C (41 to 63 °F) and night time temperatures of 0 to 6 °C (32 to 43 °F). The temperature starts to decrease in October and winters have much lower day time temperatures ranging from −4 to 0 °C (25 to 32 °F) and further lower in the night reaching up to −20 °C (−4 °F) with January being the coldest. Monsoons bring rain from late June to August with cold winds.
Global warming is described as happening three times faster (by about 0.3 C per decade) on the Tibetan Plateau than anywhere else in the world with lesser snowfall in the winter. According to locals, the land around Mount Kailash has been growing warmer in recent years with winters not as cold as it used to be. The retreating glaciers and thawing of the permafrost in the Tibet region might lead to uncertain effects on water resources of the region. These effects along with population explosion and tourism has put severe stress on the fragile ecosystem around Mount Kailash.
The intergovernmental organisation International Centre for Integrated Mountain Development (ICIMOD) is involved in a trans boundary project called the Kailash Sacred Landscape Conservation and Development Initiative in the region around Mount Kailash. The organization is involved in ongoing efforts to generate climate data, and to devise sustainable ways of life for the people of the region. |
synth_fc_2881_rep22 | Negative | Restaurant | Ranking | Single | https://en.wikipedia.org/wiki/Porto | 6 | Gastronomy
Porto is home to a number of dishes from traditional Portuguese cuisine. A typical dish from this city is Tripas à Moda do Oporto (Tripe Oporto style). Bacalhau à Gomes de Sá (cod in the style of Gomes de Sá) is another typical codfish dish born in Oporto and popular in Portugal.
The Francesinha is the most popular native snack food in Porto. It is a kind of sandwich with several types of meat covered with cheese and a special sauce made with beer and other ingredients.
Rojões (fried pork meat) and sarrabulho (pig blood-based dish) are also typical dishes of Norte Region which are very popular in the regional capital, the city of Porto. Like in almost all coastal areas of the Portuguese littoral with wide availability of fresh fish, sardinha assada (grilled sardine) is also a usual, classic main dish.
Port wine, an internationally renowned wine, is widely accepted as the city's dessert wine, especially as the wine is made along the Douro River, which runs through the city. |
synth_fc_80_rep18 | Positive | Astronomy | Database update | Multi | https://en.wikipedia.org/wiki/Betelgeuse | 17 | Distance measurements
Parallax is the apparent change of the position of an object, measured in seconds of arc, caused by the change of position of the observer of that object. As the Earth orbits the Sun, every star is seen to shift by a fraction of an arc second, which measure, combined with the baseline provided by the Earth's orbit gives the distance to that star. Since the first successful parallax measurement by Friedrich Bessel in 1838, astronomers have been puzzled by Betelgeuse's apparent distance. Knowledge of the star's distance improves the accuracy of other stellar parameters, such as luminosity that, when combined with an angular diameter, can be used to calculate the physical radius and effective temperature; luminosity and isotopic abundances can also be used to estimate the stellar age and mass.
When the first interferometric studies were performed on the star's diameter in 1920, the assumed parallax was 0.0180 ″. This equated to a distance of 56 pc or roughly 180 ly, producing not only an inaccurate radius for the star but every other stellar characteristic. Since then, there has been ongoing work to measure the distance of Betelgeuse, with proposed distances as high as 400 pc or about 1,300 ly.
Before the publication of the Hipparcos Catalogue (1997), there were two slightly conflicting parallax measurements for Betelgeuse. The first, in 1991, gave a parallax of 9.8 ± 4.7 mas, yielding a distance of roughly 102 pc or 330 ly. The second was the Hipparcos Input Catalogue (1993) with a trigonometric parallax of 5 ± 4 mas, a distance of 200 pc or 650 ly. Given this uncertainty, researchers were adopting a wide range of distance estimates, leading to significant variances in the calculation of the star's attributes.
The results from the Hipparcos mission were released in 1997. The measured parallax of Betelgeuse was 7.63 ± 1.64 mas, which equated to a distance of roughly 131 pc or 427 ly, and had a smaller reported error than previous measurements. However, later evaluation of the Hipparcos parallax measurements for variable stars like Betelgeuse found that the uncertainty of these measurements had been underestimated. In 2007, an improved figure of 6.55 ± 0.83 was calculated, hence a much tighter error factor yielding a distance of roughly 152 ± 20 pc or 500 ± 65 ly.
In 2008, measurements using the Very Large Array (VLA) produced a radio solution of 5.07 ± 1.10 mas, equaling a distance of 197 ± 45 pc or 643 ± 146 ly. As the researcher, Harper, points out: "The revised Hipparcos parallax leads to a larger distance (152 ± 20 pc) than the original; however, the astrometric solution still requires a significant cosmic noise of 2.4 mas. Given these results it is clear that the Hipparcos data still contain systematic errors of unknown origin." Although the radio data also have systematic errors, the Harper solution combines the datasets in the hope of mitigating such errors. An updated result from further observations with ALMA and e-Merlin gives a parallax of 4.51 ± 0.8 mas and a distance of 222 +34 −48 pc or 724 +111 −156 ly.
In 2020, new observational data from the space-based Solar Mass Ejection Imager aboard the Coriolis satellite and three different modeling techniques produced a refined parallax of 5.95 +0.58 −0.85 mas, a radius of 764 +116 −62 R, and a distance of 168.1 +27.5 −14.4 pc or 548 +90 −49 ly, which, if accurate, would mean Betelgeuse is nearly 25% smaller and 25% closer to Earth than previously thought.
Although the European Space Agency 's current Gaia mission was not expected to produce good results for stars brighter than the approximately V=6 saturation limit of the mission's instruments, actual operation has shown good performance on objects to about magnitude +3. Forced observations of brighter stars mean that final results should be available for all bright stars and a parallax for Betelgeuse will be published an order of magnitude more accurate than currently available. There is no data on Betelgeuse in Gaia Data Release 2, which was released in 2018. |
synth_fc_2422_rep13 | Positive | Movie | Entity search | Multi | https://en.wikipedia.org/wiki/Ofra_Haza | 1 | Ofra Haza was an Israeli singer, songwriter and actress, commonly known in the Western world as "the Madonna of the East", or "the Israeli Madonna". Her voice has been described as a "tender" mezzo-soprano. In 2023, Rolling Stone ranked Haza at number 186 on its list of the 200 Greatest Singers of All Time. Of Mizrahi Jewish (Yemenite-Jewish) descent, Haza performed music known as a mixture of traditional Middle Eastern and commercial singing styles, fusing elements of Eastern and Western instrumentation, orchestration and dance-beat, as well as lyrics from Mizrahi and Jewish folk tales and poetry. By the late 1980s, Haza was an internationally successful artist, achieving large success in Europe and the Americas and appearing regularly on MTV. During her singing career, she earned many platinum and gold discs and her music proved highly popular in the club scene. By the 1990s, at the peak of her career, she was regularly featured in movie soundtracks, such as that of Dick Tracy (1990) and famously in The Prince of Egypt (1998), and her vocals were popularly sampled in hip hop. Her death in 2000 from an AIDS-related illness shocked Israeli society. Haza was a highly influential cultural figure in Israel, and is considered one of the country's biggest cultural icons, who helped popularize Mizrahi culture. |
synth_fc_3787_rep23 | No function call | Weather & Air quality | Feature search | Single | https://en.wikipedia.org/wiki/Cyprus | 21 | Water supply
Cyprus suffers from a chronic shortage of water. The country relies heavily on rain to provide household water, but in the past 30 years average yearly precipitation has decreased. Between 2001 and 2004, exceptionally heavy annual rainfall pushed water reserves up, with supply exceeding demand, allowing total storage in the island's reservoirs to rise to an all-time high by the start of 2005.However, since then demand has increased annually – a result of local population growth, foreigners moving to Cyprus and the number of visiting tourists – while supply has fallen as a result of more frequent droughts (2006 European heat wave, 2018 European heat wave, 2019 European heat waves, 2022 European heat waves).
Dams remain the principal source of water both for domestic and agricultural use; Cyprus has a total of 108 dams and reservoirs, with a total water storage capacity of about 330,000,000 m (1.2 × 10 cu ft). Water desalination plants are gradually being constructed to deal with recent years of prolonged drought.
The Government has invested heavily in the creation of water desalination plants which have supplied almost 50 per cent of domestic water since 2001. Efforts have also been made to raise public awareness of the situation and to encourage domestic water users to take more responsibility for the conservation of this increasingly scarce commodity.
Turkey has built a water pipeline under the Mediterranean Sea from Anamur on its southern coast to the northern coast of Cyprus, to supply Northern Cyprus with potable and irrigation water (see Northern Cyprus Water Supply Project). |
synth_fc_1484_rep3 | Positive | Geography | Database search | Single | https://en.wikipedia.org/wiki/Santiago | 30 | Capital of the Republic
On September 18, 1810, the First Government Junta was proclaimed in Santiago, marking the beginning of Chile’s path to independence. The city, which became the capital of the newly formed nation, faced various challenges, particularly from military actions in the vicinity.
Although institutions like the Instituto Nacional and the National Library were established during the Patria Vieja, they were shut down after the patriots’ defeat at the Battle of Rancagua in 1814. The royal government continued until 1817, when the Army of the Andes emerged victorious at the Battle of Chacabuco and restored the patriot government in Santiago. However, independence was still uncertain. The Spanish army achieved further victories in 1818 and advanced toward Santiago, but their progress was finally halted at the Battle of Maipú on April 5, 1818, on the Maipo River plains.
With the end of the war, Bernardo O'Higgins was accepted as Supreme Director and, like his father, undertook several important projects for the city. During the Patria Nueva era, previously closed institutions were reopened. The General Cemetery was inaugurated, work on the San Carlos Canal was completed, and the drying riverbed in the south arm of the Mapocho River, known as La Cañada, which had been used as a landfill for some time, was transformed into an avenue now known as the Alameda de las Delicias.
Two earthquakes struck the city in the 19th century: one on November 19, 1822, and another on February 20, 1835. Despite these disasters, the city continued to grow rapidly. In 1820, the population was recorded as 46,000, but by 1854, it had risen to 69,018. By 1865, the census reported 115,337 residents. This significant increase was due to suburban expansion to the south and west of the capital, as well as the growth of the bustling district of La Chimba, which resulted from the division of old properties in the area. This new peripheral development marked the end of the previous checkerboard structure that had dominated the city center. |
synth_fc_50_rep30 | Positive | Architecture | Analysis | Single | https://en.wikipedia.org/wiki/16-cell | 3 | Geometry
The 16-cell is the second in the sequence of 6 convex regular 4-polytopes (in order of size and complexity).
Each of its 4 successor convex regular 4-polytopes can be constructed as the convex hull of a polytope compound of multiple 16-cells: the 16-vertex tesseract as a compound of two 16-cells, the 24-vertex 24-cell as a compound of three 16-cells, the 120-vertex 600-cell as a compound of fifteen 16-cells, and the 600-vertex 120-cell as a compound of seventy-five 16-cells. |
synth_fc_2837_rep11 | No function call | Real estate | Calculation | Single | https://en.wikipedia.org/wiki/Las_Vegas | 5 | 2020 census
The U.S. Census accounts for race by two methodologies. "Race alone" and "Race alone less Hispanics" where Hispanics are delineated separately as if a separate race.
According to the 2020 U.S. Census, the racial makeup (including Hispanics in the racial counts) was 46.05% (295,594) White alone, 12.85% (82,485) Black alone, 1.14% (7,318) Native American alone, 7.23% (46,398) Asian alone, 0.73% (4,662) Pacific Islander alone, 16.99% (109,045) Other Race alone, and 15.02% (96,401) Multiracial or Mixed Race.
According to the 2020 U.S. Census, the racial and ethnic makeup (where Hispanics are excluded from the racial counts and placed in their own category) was 40.44% (259,561) White alone (non-Hispanic), 12.33% (79,129) Black alone (non-Hispanic), 0.36% (2,291) Native American alone (non-Hispanic), 4.68% (22,411) Asian alone (non-Hispanic), 0.40% (1,935) Pacific Islander alone (non-Hispanic), 0.14% (650) Other Race alone (non-Hispanic), 2.51% (11,987) Multiracial or Mixed Race (non-Hispanic), and 23.61% (112,962) Hispanic or Latino. |
synth_fc_2628_rep28 | Positive | Music | Entity search | Multi | https://en.wikipedia.org/wiki/Trombone | 31 | Notation
Unlike most other brass instruments in an orchestral setting, the trombone is not usually considered a transposing instrument. Prior to the invention of valve systems, most brass instruments were limited to playing one overtone series at a time; altering the pitch of the instrument required manually replacing a section of tubing (called a " crook ") or picking up an instrument of different length. Their parts were transposed according to which crook or length-of-instrument they used at any given time, so that a particular note on the staff always corresponded to a particular partial on the instrument. Trombones, on the other hand, have used slides since their inception. As such, they have always been fully chromatic, so no such tradition took hold, and trombone parts have always been notated at concert pitch (with one exception, discussed below). Also, it was quite common for trombones to double choir parts; reading in concert pitch meant there was no need for dedicated trombone parts. Note that while the fundamental sounding pitch (slide fully retracted) has remained quite consistent, the conceptual pitch of trombones has changed since their origin (e.g. Baroque A tenor = modern B-flat tenor).
Trombone parts are typically notated in bass clef, though sometimes also written in tenor clef or alto clef. The use of alto clef is usually confined to orchestral first trombone parts, with the second trombone part written in tenor clef and the third (bass) part in bass clef. As the alto trombone declined in popularity during the 19th century, this practice was gradually abandoned and first trombone parts came to be notated in the tenor or bass clef. Some Russian and Eastern European composers wrote first and second tenor trombone parts on one alto clef staff (the German Robert Schumann was the first to do this). Examples of this practice are evident in scores by Igor Stravinsky, Sergei Prokofiev, Dmitri Shostakovich. Trombone parts in band music are nearly exclusively notated in bass clef. The rare exceptions are in contemporary works intended for high-level wind bands.
An accomplished performer today is expected to be proficient in reading parts notated in bass clef, tenor clef, alto clef, and (more rarely) treble clef in C, with the British brass-band performer expected to handle treble clef in B♭ as well. |
synth_fc_2101_rep14 | Negative | Law | Guide | Single | https://en.wikipedia.org/wiki/Nitrogen | 6 | Execution
As nitrogen is an asphyxiant gas in itself, some jurisdictions have considered asphyxiation by inhalation of pure nitrogen as a means of capital punishment (as a substitute for lethal injection). In January 2024, Kenneth Eugene Smith became the first person executed by nitrogen asphyxiation. |
synth_fc_1004_rep29 | Positive | Finance | Feature search | Single | https://en.wikipedia.org/wiki/Middle_Ages | 16 | Economic revival
The expansion of population, greater agricultural productivity, and relative political stability laid the foundations for the commercial revolution in the 11th century. People with surplus cash began investing in commodities such as salt, pepper, silk, wine and honey in faraway markets. Rising trade brought new methods of dealing with money and gold coinage was again minted in Europe, first in Florence and Genoa. New forms of commercial contracts emerged, allowing risk to be shared within the framework of partnerships known as commenda or compagnia. Bills of exchange also appeared, enabling the easy transmission of money. Since many types of coins were in circulation, money changers facilitated transactions between local and foreign merchants. Loans could be negotiated with them, which gave rise to the development of credit institutions known as banks.
As local commercial centres developed into towns, economic growth caused a new wave of urbanisation. Kings and aristocrats primarily supported the process in the hope of increased tax revenues. Most urban communities received privileges acknowledging their autonomy, but few cities could eliminate all elements of external control. Townspeople engaged in the same trade or profession were united in confraternities known as guilds. These associations typically made rules governing quality, training, and pricing, and only their members had access to local markets.
The Italian maritime republics, such as Amalfi, Venice, Genoa, and Pisa, were the first to profit from the revival of commerce in the Mediterranean. In the north, German merchants established associations known as hansas and controlled trade routes connecting the British islands and the Low Countries with Scandinavia and Eastern Europe. Trading fairs were established and flourished in northern France, allowing Italian and German merchants to trade with one another and with local merchants.
Economic growth provided opportunities for Jewish merchants to spread throughout Europe with the support of local rulers. Jews could not engage in prestigious trades outside their communities, and often took low-status jobs such as ragmen or tax collectors. They were especially active in moneylending, because they could ignore the Christian clerical condemnation of loan interest. Jewish moneylenders and pawn brokers reinforced antisemitism which manifested itself in the blood libel and pogroms. Church authorities' growing concerns about Jewish influence on Christian life inspired legal segregation and the expulsion of the Jews from England. |
synth_fc_2443_rep29 | Negative | Movie | Recommendation | Single | https://en.wikipedia.org/wiki/J%C3%B4_Soares | 1 | José Eugênio Soares, known professionally as Jô Soares, or Jô, was a Brazilian comedian, talk show host, author, musician, actor and writer. |
synth_fc_2492_rep29 | No function call | Movie | Entity search | Single | https://en.wikipedia.org/wiki/Fight_Club | 1 | Fight Club is a 1999 American film directed by David Fincher, and starring Brad Pitt, Edward Norton and Helena Bonham Carter. It is based on the 1996 novel by Chuck Palahniuk. Norton plays the unnamed narrator, who is discontented with his white-collar job. He forms a "fight club" with soap salesman Tyler Durden (Pitt), and becomes embroiled in a relationship with an impoverished but beguilingly attractive woman, Marla Singer. Palahniuk's novel was optioned by Fox 2000 Pictures producer Laura Ziskin, who hired Jim Uhls to write the film adaptation. Fincher was selected because of his enthusiasm for the story. He developed the script with Uhls and sought screenwriting advice from the cast and others in the film industry. It was filmed in and around Los Angeles from July to December 1998. He and the cast compared the film to Rebel Without a Cause (1955) and The Graduate (1967), with a theme of conflict between Generation X and the value system of advertising. Studio executives did not like the film and they restructured Fincher's intended marketing campaign to try to reduce anticipated losses. Fight Club premiered at the 56th Venice International Film Festival on September 10, 1999, and was released in the United States on
October 15, 1999 by 20th Century Fox. The film failed to meet the studio's expectations at the box office and received polarized reactions from critics. It was ranked as one of the most controversial and talked-about films of the 1990s. However, Fight Club later found commercial success with its home video release, establishing it as a cult classic and causing media to revisit the film. In 2009, on its tenth anniversary, The New York Times dubbed it the "defining cult movie of our time." |
synth_fc_1253_rep6 | Positive | Finance | Calculation | Single | https://en.wikipedia.org/wiki/Rothschild_family | 20 | Edmond de Rothschild Group
In 1953, one Swiss member of the family, Edmond Adolphe de Rothschild (1926–1997), founded the LCF Rothschild Group (now Edmond de Rothschild Group) which is based in Geneva and today extends to 15 countries across the world. Although this group is primarily a financial entity, specializing in asset management and private banking, its activities also cover mixed farming, luxury hotels and yacht racing. Edmond de Rothschild Group's committee is currently being chaired by Ariane de Rothschild.
In late 2010, Benjamin de Rothschild, the chairman at the time, said that the family had been unaffected by the 2007–2008 financial crisis, due to their conservative business practices: "We came through it well, because our investment managers did not want to put money into crazy things." He added that the Rothschilds were still a small-scale, traditional family business and took greater care over their clients' investments than American companies, adding: "The client knows we will not speculate with his money".
Edmond de Rothschild group includes these companies. |
synth_fc_3807_rep14 | Positive | Weather & Air quality | Feature search | Single | https://en.wikipedia.org/wiki/Thunderstorm | 6 | Severe thunderstorms
In the United States, a thunderstorm is classed as severe if winds reach at least 93 kilometres per hour (58 mph), hail is 25 millimetres (1 in) in diameter or larger, or if funnel clouds or tornadoes are reported. Although a funnel cloud or tornado indicates a severe thunderstorm, a tornado warning is issued in place of a severe thunderstorm warning. A severe thunderstorm warning is issued if a thunderstorm becomes severe, or will soon turn severe. In Canada, a rainfall rate greater than 50 millimetres (2 in) in one hour, or 75 millimetres (3 in) in three hours, is also used to indicate severe thunderstorms. Severe thunderstorms can occur from any type of storm cell. However, multicell, supercell, and squall lines represent the most common forms of thunderstorms that produce severe weather. |
synth_fc_505_rep18 | Positive | Corporate Management | Analysis | Single | https://en.wikipedia.org/wiki/Benjamin_Disraeli | 23 | Civil Service
Gladstone in 1870 had sponsored an Order in Council, introducing competitive examination into the Civil Service, diminishing the political aspects of government hiring. Disraeli did not agree, and while he did not seek to reverse the order, his actions often frustrated its intent. For example, Disraeli made political appointments to positions previously given to career civil servants. He was backed by his party, hungry for office and its emoluments after almost thirty years with only brief spells in government. Disraeli gave positions to hard-up Conservative leaders, even—to Gladstone's outrage—creating one office at £2,000 per year. Nevertheless, Disraeli made fewer peers (only 22, including one of Victoria's sons) than had Gladstone (37 during his just over five years in office).
As he had in government posts, Disraeli rewarded old friends with clerical positions, making Sydney Turner, son of a good friend of Isaac D'Israeli, Dean of Ripon. He favoured Low church clergymen in promotion, disliking other movements in Anglicanism for political reasons. In this, he came into disagreement with the Queen, who out of loyalty to her late husband Albert preferred Broad church teachings. One controversial appointment had occurred shortly before the 1868 election. When the position of Archbishop of Canterbury fell vacant, Disraeli reluctantly agreed to the Queen's preferred candidate, Archibald Tait, the Bishop of London. To fill Tait's vacant see, Disraeli was urged by many people to appoint Samuel Wilberforce, the former Bishop of Winchester. Disraeli disliked Wilberforce and instead appointed John Jackson, the Bishop of Lincoln. Blake suggested that, on balance, these appointments cost Disraeli more votes than they gained him. |
synth_fc_1755_rep6 | Positive | Health | Database search | Single | https://en.wikipedia.org/wiki/Ebola | 16 | 2017 Democratic Republic of the Congo
On 11 May 2017, the DRC Ministry of Public Health notified the WHO about an outbreak of Ebola. Four people died, and four people survived; five of these eight cases were laboratory-confirmed. A total of 583 contacts were monitored. On 2 July 2017, the WHO declared the end of the outbreak. |
synth_fc_1234_rep17 | Negative | Finance | Feature search | Single | https://en.wikipedia.org/wiki/Credit_card | 51 | Interest charges
Credit card issuers usually waive interest charges if the balance is paid in full each month, but typically will charge full interest on the entire outstanding balance from the date of each purchase if the total balance is not paid.
For example, if a user had a $1,000 transaction and repaid it in full within this grace period, there would be no interest charged. If, however, even $1.00 of the total amount remained unpaid, interest would be charged on the $1,000 from the date of purchase until the payment is received. The precise manner in which interest is charged is usually detailed in a cardholder agreement which may be summarized on the back of the monthly statement. The general calculation formula most financial institutions use to determine the amount of interest to be charged is (APR/100 x ADB)/365 x number of days revolved. Take the annual percentage rate (APR) and divide by 100 then multiply to the amount of the average daily balance (ADB). Divide the result by 365 and then take this total and multiply by the total number of days the amount revolved before payment was made on the account. Financial institutions refer to interest charged back to the original time of the transaction and up to the time a payment was made, if not in full, as a residual retail finance charge (RRFC). Thus after an amount has revolved and a payment has been made, the user of the card will still receive interest charges on their statement after paying the next statement in full (in fact the statement may only have a charge for interest that collected up until the date the full balance was paid, i.e. when the balance stopped revolving).
The credit card may simply serve as a form of revolving credit, or it may become a complicated financial instrument with multiple balance segments each at a different interest rate, possibly with a single umbrella credit limit, or with separate credit limits applicable to the various balance segments. Usually, this compartmentalization is the result of special incentive offers from the issuing bank, to encourage balance transfers from cards of other issuers. If several interest rates apply to various balance segments, then payment allocation is generally at the discretion of the issuing bank, and payments will therefore usually be allocated towards the lowest rate balances until paid in full before any money is paid towards higher rate balances. Interest rates can vary considerably from card to card, and the interest rate on a particular card may jump dramatically if the card user is late with a payment on that card or any other credit instrument, or even if the issuing bank decides to raise its revenue. |
synth_fc_3875_rep9 | Negative | Writing, Editing & Translation | Generation | Single | https://en.wikipedia.org/wiki/The_Waste_Land | 1 | The Waste Land is a poem by T. S. Eliot, widely regarded as one of the most important English-language poems of the 20th century and a central work of modernist poetry. Published in 1922, the 434-line poem first appeared in the United Kingdom in the October issue of Eliot's magazine The Criterion and in the United States in the November issue of The Dial. Among its famous phrases are "April is the cruellest month", "I will show you fear in a handful of dust", and "These fragments I have shored against my ruins".
The Waste Land does not follow a single narrative or feature a consistent style or structure. The poem shifts between voices of satire and prophecy, and features abrupt and unannounced changes of narrator, location, and time, conjuring a vast and dissonant range of cultures and literatures. It employs many allusions to the Western canon: Ovid 's Metamorphoses, the legend of the Fisher King, Dante 's Divine Comedy, Chaucer 's Canterbury Tales, and even a contemporary popular song, "That Shakespearian Rag".
The poem is divided into five sections. The first, "The Burial of the Dead", introduces the diverse themes of disillusionment and despair. The second, "A Game of Chess", employs alternating narrations in which vignettes of several characters display the fundamental emptiness of their lives. "The Fire Sermon" offers a philosophical meditation in relation to self-denial and sexual dissatisfaction; "Death by Water" is a brief description of a drowned merchant; and "What the Thunder Said" is a culmination of the poem's previously exposited themes explored through a description of a desert journey.
Upon its initial publication The Waste Land received a mixed response, with some critics finding it wilfully obscure while others praised its originality. Subsequent years saw the poem become established as a central work in the modernist canon, and it proved to become one of the most influential works of the century. |
synth_fc_2508_rep29 | Positive | Movie | Entity search | Multi | https://en.wikipedia.org/wiki/The_Apu_Trilogy | 8 | Plot summaries
The three films comprise a " coming of age " narrative in the vein of a bildungsroman; they describe the childhood, education and early maturity of a young Bengali named Apu (Apurba Kumar Roy) in the early part of the 20th century.
Pather Panchali (English, "Song of the Little Road") Apu's early experiences in rural Bengal as the son of a poor but high caste family are presented. Apu's father Harihar, a Brahmin, has difficulty in supporting his family. After the death of Apu's sister, Durga, the family moves to the holy city of Benares.
Aparajito (English, "The Unvanquished") The family's finances are still precarious. After his father dies there, Apu and his mother Sarbajaya come back to a village in Bengal. Despite unrelenting poverty, Apu manages to get formal schooling and turns out to be a brilliant student. He moves to Calcutta to pursue his education. He slowly distanced himself from his rural roots and his mother who was not keeping well at the time. In the process the growing Apu comes into conflict with his mother. Later he is informed that, when his mother dies too, he has to learn to live alone.
Apur Sansar (English, "The World of Apu") Attempting to become a writer, Apu unexpectedly finds himself pressured to marry a girl whose mother rejected her mentally ill bridegroom on the day of their wedding. Their blossoming marriage ends in her death in childbirth, after which the despairing Apu abandons his child, but eventually returns to accept his responsibilities. |
synth_fc_1002_rep15 | No function call | Finance | Calculation | Single | https://en.wikipedia.org/wiki/Leland_Stanford | 14 | Stanford University
With his wife Jane, Stanford founded Leland Stanford Junior University as a memorial for their only child, Leland Stanford Jr., who died as a teenager of typhoid fever in Florence, Italy, in 1884 while on a trip to Europe. The university was established by the Endowment Act of the California Assembly and Senate of March 9, 1885, and the Grant of Endowment from Leland and Jane Stanford signed at the first meeting of the board of trustees on November 14, 1885.
The Stanfords donated approximately $40 million (equivalent to approximately $ 1,356,000,000 today) to develop the university, which held its opening exercises on October 1, 1891, and was intended for agricultural studies. Its first student, admitted to Encina Hall that day, was Herbert Hoover, who went on to become the 31st US president. The wealth of the Stanford family during the late 19th century is estimated at $50 million (equivalent to approximately $ 1,831,000,000 today).
Stanford had ideas of Stanford University employee ownership for more than thirty years before giving them expression in his plans for the university, proposals as a Senator, and in interviews with the news media. |
synth_fc_928_rep5 | No function call | Finance | Calculation | Single | https://en.wikipedia.org/wiki/Lionel_Messi | 12 | In popular culture
Messi was the world's highest-paid footballer for five years out of six between 2009 and 2014; he was the first player to exceed the €40 million benchmark, with earnings of €41 million in 2013, and the €50–€60 million points, with income of €65 million in 2014. Messi was second on Forbes list of the world's highest-paid athletes, after Ronaldo, with income of $81 million from salary and endorsements in 2015–16. In 2018 he was the first player to exceed the €100m benchmark for a calendar year, with earnings of €126m ($154m) in combined income from salaries, bonuses and endorsements. Forbes ranked him the world's highest-paid athlete in 2019. From 2008, he was Barcelona's highest-paid player, receiving a salary that increased incrementally from €7.8 million to €13 million over the next five years. Signing a new contract in 2017, he earned $667,000 per week in wages, and Barcelona paid him $60 million as a signing on bonus. His buyout clause was set at $835 million (€700 million). In 2020, Messi became the second footballer, as well as the second athlete in a team sport, after Ronaldo, to surpass $1 billion in earnings during their careers.
In addition to salary and bonuses, much of his income derives from endorsements; SportsPro has consequently cited him as one of the world's most marketable athletes every year since their research began in 2010. His main sponsor since 2006 is Adidas. As Barcelona's leading youth prospect, he was signed with Nike since age 14, but transferred to Adidas after they successfully challenged their rival's claim to his image rights in court. Messi established himself as their leading brand endorser; from 2008, he had a long-running signature collection of Adidas F50 boots, and in 2015, became the first footballer to receive his own sub-brand of Adidas boots, the Adidas Messi. Since 2017, he has worn the latest version of the Adidas Nemeziz. In 2015, a Barcelona jersey with Messi's name and number was the best-selling replica jersey worldwide. At the 2022 World Cup, Adidas sold out Messi's No. 10 Argentina jersey worldwide.
As a commercial entity, Messi's brand has been based exclusively on his talents and achievements as a player, in contrast to arguably more glamorous players like Ronaldo and David Beckham. At the start of his career, he thus mainly held sponsorship contracts with companies that employ sports-oriented marketing, such as Adidas, Pepsi, and Konami. From 2010, concurrently with increased achievements as a player, his marketing appeal widened, leading to long-term endorsement deals with luxury brands Dolce & Gabbana and Audemars Piguet. Messi is a global brand ambassador for Gillette, Turkish Airlines, Ooredoo, and Tata Motors, among other companies. Messi was the face of Konami's video game series Pro Evolution Soccer, appearing on the covers of PES 2009, PES 2010, PES 2011 and PES 2020. He subsequently signed with rival company EA Sports to become the face of their series FIFA and appeared on consecutive covers from FIFA 13 to FIFA 16.
Messi was among the Time 100, an annual list of the world's most influential people, in 2011, 2012 and 2023. His fanbase on Facebook is among the largest of public figures: within seven hours of its launch in April 2011, Messi's Facebook page had nearly seven million followers, and by July 2023 he had over 114 million followers, the second highest for a sportsperson after Cristiano Ronaldo. He has over 500 million Instagram followers, the second highest for an individual and sportsperson after Ronaldo. His World Cup celebration post from 18 December 2022 is the most liked post on Instagram with over 70 million likes. According to a 2014 survey in 15 international markets, Messi was familiar to 87% of respondents around the world, of whom 78% perceived him favourably, making him the second-most recognised player globally, behind Ronaldo, and the most likable of all contemporary players. On his economic impact on the city in which he plays, Terry Gibson called him a "tourist attraction".
Madame Tussauds unveiled their first wax sculpture of Messi at Wembley Stadium in 2012. A gold replica of his left foot, weighing 25 kg (55 lb) and valued at $5.3 million, went on sale in Japan in 2013 to raise funds for victims of the 2011 Tōhoku earthquake and tsunami. In 2013, a Turkish Airlines advertisement starring Messi, in which he engages in a selfie competition with Kobe Bryant, was the most-watched ad on YouTube in 2013, receiving 137 million views, and was voted the best advertisement of the 2005–15 decade to commemorate YouTube's founding. World Press Photo selected "The Final Game", a photo of Messi facing the World Cup trophy after Argentina's final defeat to Germany, as the best sports image of 2014. Messi, a documentary by filmmaker Álex de la Iglesia, premiered at the Venice Film Festival in August 2014.
In June 2021, Messi signed a five-year deal to become an ambassador for the Hard Rock Cafe brand. He stated, "sports and music are an integral part of my life. It is an honor to be the first athlete to partner with a brand who has a history of teaming with music legends." In May 2022, Messi was unveiled as Saudi Arabia's tourism ambassador. Due to Saudi Arabia 's poor human rights record, Messi was condemned for the role which was viewed as an attempt of Saudi sportswashing. In April 2023, Messi was featured in the 200 year old Thrissur Pooram festival in Kerala, India. During Thrissur Pooram, which is one of the largest festivals in Asia, umbrellas carrying the illuminated cut outs of Messi holding the World Cup trophy were displayed on the top of caparisoned elephants during the Kudamattam ceremony. |
synth_fc_3339_rep23 | Negative | Store & Facility | Proximal search | Single | https://en.wikipedia.org/wiki/Togo | 19 | Air
Togo has a total of eight airports, as of 2012, out of which two are international airports and six are domestic airports. The only major airport of the country is Lomé–Tokoin International Airport serving the capital, Lomé, and another Niamtougou International Airport in Niamtougou, serving the country's northern part. |
synth_fc_372_rep23 | Positive | Book | Entity search | Single | https://en.wikipedia.org/wiki/Donald_Knuth | 17 | The Art of Computer Programming (TAOCP)
"The best way to communicate from one human being to another is through story."
In the 1970s, Knuth called computer science "a totally new field with no real identity. And the standard of available publications was not that high. A lot of the papers coming out were quite simply wrong.... So one of my motivations was to put straight a story that had been very badly told."
From 1972 to 1973, Knuth spent a year at the University of Oslo among people such as Ole-Johan Dahl. This is where he had originally intended to write the seventh volume in his book series, which was to deal with programming languages. But Knuth had finished only the first two volumes when he came to Oslo, and thus spent the year on the third volume, next to teaching. The third volume came out just after Knuth returned to Stanford in 1973.
By 2011, Volume 4A had been published. Concrete Mathematics: A Foundation for Computer Science 2nd ed., which originated with an expansion of the mathematical preliminaries section of Volume 1 of TAoCP, was published in 1994. In April 2020, Knuth said he anticipated that Volume 4 will have at least parts A through F. Volume 4B was published in October 2022. |
synth_fc_3452_rep9 | Negative | Time | Feature search | Single | https://en.wikipedia.org/wiki/Information | 15 | As of 2020
The total amount of data created, captured, copied, and consumed globally is forecast to increase rapidly, reaching 64.2 zettabytes in 2020. Over the next five years up to 2025, global data creation is projected to grow to more than 180 zettabytes. |
synth_fc_3800_rep20 | Negative | Weather & Air quality | Feature search | Single | https://en.wikipedia.org/wiki/Heat_transfer | 37 | Climate models
Climate models study the radiant heat transfer by using quantitative methods to simulate the interactions of the atmosphere, oceans, land surface, and ice. |
synth_fc_1745_rep10 | Positive | Health | Database search | Single | https://en.wikipedia.org/wiki/Proteinogenic_amino_acid | 1 | Proteinogenic amino acids are amino acids that are incorporated biosynthetically into proteins during translation. The word "proteinogenic" means "protein creating". Throughout known life, there are 22 genetically encoded (proteinogenic) amino acids, 20 in the standard genetic code and an additional 2 that can be incorporated by special translation mechanisms. In contrast, non-proteinogenic amino acids are amino acids that are either not incorporated into proteins, misincorporated in place of a genetically encoded amino acid, or not produced directly and in isolation by standard cellular machinery. The latter often results from post-translational modification of proteins. Some non-proteinogenic amino acids are incorporated into nonribosomal peptides which are synthesized by non-ribosomal peptide synthetases. Both eukaryotes and prokaryotes can incorporate selenocysteine into their proteins via a nucleotide sequence known as a SECIS element, which directs the cell to translate a nearby UGA codon as selenocysteine. In some methanogenic prokaryotes, the UAG codon can also be translated to pyrrolysine. In eukaryotes, there are only 21 proteinogenic amino acids, the 20 of the standard genetic code, plus selenocysteine. Humans can synthesize 12 of these from each other or from other molecules of intermediary metabolism. The other nine must be consumed, and so they are called essential amino acids. The essential amino acids are histidine, isoleucine, leucine, lysine, methionine, phenylalanine, threonine, tryptophan, and valine. The proteinogenic amino acids have been found to be related to the set of amino acids that can be recognized by ribozyme autoaminoacylation systems. Thus, non-proteinogenic amino acids would have been excluded by the contingent evolutionary success of nucleotide-based life forms. Other reasons have been offered to explain why certain specific non-proteinogenic amino acids are not generally incorporated into proteins; for example, ornithine and homoserine cyclize against the peptide backbone and fragment the protein with relatively short half-lives, while others are toxic because they can be mistakenly incorporated into proteins, such as the arginine analog canavanine. The evolutionary selection of certain proteinogenic amino acids from the primordial soup has been suggested to be because of their better incorporation into a polypeptide chain as opposed to non-proteinogenic amino acids. |
synth_fc_2001_rep12 | Negative | History | Entity search | Single | https://en.wikipedia.org/wiki/Goths | 10 | Religion
Initially practising Gothic paganism, the Goths were gradually converted to Arianism in the course of the 4th century. According to Basil of Caesarea, a prisoner named Eutychus taken captive in a raid on Cappadocia in 260 preached the gospel to the Goths and was martyred. It was only in the 4th century, as a result of missionary activity by the Gothic bishop Ulfilas, whose grandparents were Cappadocians taken captive in the raids of the 250s, that the Goths were gradually converted. Ulfilas devised a Gothic alphabet and translated the Gothic Bible.
During the 370s, Goths converting to Christianity were subject to persecution by the Thervingian king Athanaric, who was a pagan.
The Visigothic Kingdom in Hispania converted to Catholicism in the late 6th century.
The Ostrogoths (and their remnants, the Crimean Goths) were closely connected to the Patriarchate of Constantinople from the 5th century, and became fully incorporated under the Metropolitanate of Gothia from the 9th century. |
synth_fc_1225_rep7 | Positive | Finance | Calculation | Multi | https://en.wikipedia.org/wiki/Iceland | 16 | Economy
In 2022, Iceland was the eighth-most productive country in the world per capita (US$78,837), and the thirteenth-most productive by GDP at purchasing power parity ($69,833). About 85 percent of the total primary energy supply in Iceland is derived from domestically produced renewable energy sources. Use of abundant hydroelectric and geothermal power has made Iceland the world's largest electricity producer per capita.
Historically, Iceland's economy depended heavily on fishing, which still provides ~20% of export earnings and employed 7% of the workforce. The economy is now more dependent on tourism, but important sectors continue to be: fish and fish products, aluminium, and ferrosilicon. Iceland's economic dependence on fishing is diminishing, from an export share of 90% in the 1960s to 20% in 2020.
Until the 20th century, Iceland was a fairly poor country. Whaling in Iceland was historically significant. It is now one of the most developed countries in the world. Strong economic growth led Iceland to be ranked third in the United Nations ' Human Development Index report for 2021/2022. According to the Economist Intelligence Index of 2011, Iceland had the second-highest quality of life in the world. Based on the Gini coefficient, Iceland also has one of the lowest rates of income inequality in the world, and when adjusted for inequality, its HDI ranking is sixth. Iceland's unemployment rate has declined consistently since the crisis, with 4.8% of the labour force being unemployed as of June 2012, compared to 6% in 2011 and 8.1% in 2010.
The national currency of Iceland is the Icelandic króna (ISK). Iceland is the only country in the world to have a population under two million yet still have a floating exchange rate and an independent monetary policy. A poll released on 5 March 2010 by Capacent Gallup showed that 31% of respondents were in favour of adopting the euro and 69% opposed. Another Capacent Gallup poll conducted in February 2012 found that 67.4% of Icelanders would reject EU membership in a referendum.
Iceland's economy has been diversifying into manufacturing and service industries in the last decade, including software production, biotechnology, and finance; industry accounts for around a quarter of economic activity, while services comprise close to 70%. The tourism sector is expanding, especially in ecotourism and whale-watching. On average, Iceland receives around 1.1 million visitors annually, which is more than three times the native population. 1.7 million people visited Iceland in 2016, 3 times more than the number that came in 2010. Iceland's agriculture industry, accounting for 5.4% of GDP, consists mainly of potatoes, green vegetables (in greenhouses), mutton, and dairy products. The financial centre is Borgartún in Reykjavík, which hosts a large number of companies and three investment banks. Iceland's stock market, the Iceland Stock Exchange (ISE), was established in 1985.
Iceland is ranked 27th in the 2012 Index of Economic Freedom, lower than in prior years but still among the freest in the world. As of 2016, it ranks 29th in the World Economic Forum 's Global Competitive Index, one place lower than in 2015. According to the Global Innovation Index, Iceland is the 20th most innovative country in the world in 2022 and 2023. Unlike most Western European countries, Iceland has a flat tax system: the main personal income tax rate is a flat 22.75% and combined with municipal taxes, the total tax rate equals no more than 35.7%, not including the many available deductions. The corporate tax rate is a flat 18%, one of the lowest in the world. There is also a value added tax, whereas a net wealth tax was eliminated in 2006. Employment regulations are relatively flexible and the labour market is one of the freest in the world. Property rights are strong and Iceland is one of the few countries where they are applied to fishery management. Like other welfare states, taxpayers pay various subsidies to each other, but with spending being less than in most European countries.
Despite low tax rates, agricultural assistance is the highest among OECD countries and a potential impediment to structural change. Also, health care and education spending have relatively poor returns by OECD measures, though improvements have been made in both areas. The OECD Economic Survey of Iceland 2008 highlighted Iceland's challenges in currency and macroeconomic policy. There was a currency crisis that started in the spring of 2008, and on 6 October trading in Iceland's banks was suspended as the government battled to save the economy. An assessment by the OECD 2011 determined that Iceland has made progress in many areas, particularly in creating a sustainable fiscal policy and restoring the health of the financial sector; however, challenges remain in making the fishing industry more efficient and sustainable, as well as in improving monetary policy to address inflation. Iceland's public debt has decreased since the economic crisis, and as of 2015 is the 31st-highest in the world by proportion of national GDP. |
synth_fc_3447_rep30 | Positive | Time | Calculation | Single | https://en.wikipedia.org/wiki/Easter | 4 | Early Church controversies
The precise date of Easter has at times been a matter of contention. By the later 2nd century, it was widely accepted that the celebration of the holiday was a practice of the disciples and an undisputed tradition. The Quartodeciman controversy, the first of several Easter controversies, arose concerning the date on which the holiday should be celebrated.
The term "Quartodeciman" refers to the practice of ending the Lenten fast on Nisan 14 of the Hebrew calendar, "the L ORD 's passover". According to the church historian Eusebius, the Quartodeciman Polycarp (bishop of Smyrna, by tradition a disciple of John the Apostle) debated the question with Anicetus (bishop of Rome). The Roman province of Asia was Quartodeciman, while the Roman and Alexandrian churches continued the fast until the Sunday following (the Sunday of Unleavened Bread), wishing to associate Easter with Sunday. Neither Polycarp nor Anicetus persuaded the other, but they did not consider the matter schismatic either, parting in peace and leaving the question unsettled.
Controversy arose when Victor, bishop of Rome a generation after Anicetus, attempted to excommunicate Polycrates of Ephesus and all other bishops of Asia for their Quartodecimanism. According to Eusebius, a number of synods were convened to deal with the controversy, which he regarded as all ruling in support of Easter on Sunday. Polycrates (c. 190), however, wrote to Victor defending the antiquity of Asian Quartodecimanism. Victor's attempted excommunication was apparently rescinded, and the two sides reconciled upon the intervention of bishop Irenaeus and others, who reminded Victor of the tolerant precedent of Anicetus.
Quartodecimanism seems to have lingered into the 4th century, when Socrates of Constantinople recorded that some Quartodecimans were deprived of their churches by John Chrysostom and that some were harassed by Nestorius.
It is not known how long the Nisan 14 practice continued. But both those who followed the Nisan 14 custom, and those who set Easter to the following Sunday, had in common the custom of consulting their Jewish neighbors to learn when the month of Nisan would fall, and setting their festival accordingly. By the later 3rd century, however, some Christians began to express dissatisfaction with the custom of relying on the Jewish community to determine the date of Easter. The chief complaint was that the Jewish communities sometimes erred in setting Passover to fall before the Northern Hemisphere spring equinox. The Sardica paschal table confirms these complaints, for it indicates that the Jews of some eastern Mediterranean city (possibly Antioch) fixed Nisan 14 on dates well before the spring equinox on multiple occasions.
Because of this dissatisfaction with reliance on the Jewish calendar, some Christians began to experiment with independent computations. Others, however, believed that the customary practice of consulting Jews should continue, even if the Jewish computations were in error. |
synth_fc_399_rep12 | Positive | Carbon footprint | Calculation | Single | https://en.wikipedia.org/wiki/Antarctic_ice_sheet | 4 | Near-future sea level rise
By 2100, net ice loss from Antarctica alone is expected to add about 11 cm (5 in) to global sea level rise. Other processes may cause West Antarctica to contribute more to sea level rise. One such process is marine ice sheet instability, which describes the potential for warm water currents to enter between the seafloor and the base of the ice sheet once the sheet is no longer heavy enough to displace such flows. Another potential process is marine ice cliff instability, when ice cliffs with heights greater than 100 m (330 ft) may collapse under their own weight once they are no longer buttressed by ice shelves. This process has never been observed and it only occurs in some models. Such processes may increase sea level rise caused by Antarctica to 41 cm (16 in) by 2100 under the low-emission scenario and 57 cm (22 in) under the high-emission scenario. |
synth_fc_1355_rep29 | Positive | Food | Entity search | Single | https://en.wikipedia.org/wiki/French_cuisine | 8 | Late 18th century – early 19th century
Shortly before the French Revolution, dishes like bouchées à la Reine gained prominence. Essentially royal cuisine produced by the royal household, this is a chicken-based recipe served on vol-au-vent created under the influence of Queen Marie Leszczyńska, the Polish-born wife of Louis XV. This recipe is still popular today, as are other recipes from Queen Marie Leszczyńska like consommé à la Reine and filet d'aloyau braisé à la royale. Queen Marie is also credited with introducing Polonaise garnishing to the French diet.
The French Revolution was integral to the expansion of French cuisine, because it abolished the guild system. This meant anyone could now produce and sell any culinary item they wished.
Bread was a significant food source among peasants and the working class in the late 18th century, with many of the nation's people being dependent on it. In French provinces, bread was often consumed three times a day by the people of France. According to Brace, bread was referred to as the basic dietary item for the masses, and it was also used as a foundation for soup. In fact, bread was so important that harvest, interruption of commerce by wars, heavy flour exploration, and prices and supply were all watched and controlled by the French Government. Among the underprivileged, constant fear of famine was always prevalent. From 1725 to 1789, there were fourteen years of bad yields to blame for the low grain supply. In Bordeaux, during 1708–1789, thirty-three bad harvests occurred.
Marie-Antoine Carême was born in 1784, five years before the Revolution. He spent his younger years working at a pâtisserie until he was discovered by Charles Maurice de Talleyrand-Périgord; he would later cook for Napoleon Bonaparte. Prior to his employment with Talleyrand, Carême had become known for his pièces montées, which were extravagant constructions of pastry and sugar architecture.
More important to Carême's career was his contribution to the refinement of French cuisine. The basis for his style of cooking was his sauces, which he named mother sauces. Often referred to as fonds, meaning "foundations", these base sauces, espagnole, velouté, and béchamel, are still known today. Each of these sauces was made in large quantities in his kitchen, then formed the basis of multiple derivatives. Carême had over one hundred sauces in his repertoire.
In his writings, soufflés appear for the first time. Although many of his preparations today seem extravagant, he simplified and codified an even more complex cuisine that existed beforehand. Central to his codification of the cuisine were Le Maître d'hôtel français (1822), Le Cuisinier parisien (1828) and L'Art de la cuisine française au dix-neuvième siècle (1833–5). |
synth_fc_146_rep25 | Positive | Biology | Database search | Multi | https://en.wikipedia.org/wiki/Tetrapod | 7 | Girdles
The shoulder girdle was disconnected from the skull, resulting in improved terrestrial locomotion. The early sarcopterygians' cleithrum was retained as the clavicle, and the interclavicle was well-developed, lying on the underside of the chest. In primitive forms, the two clavicles and the interclavical could have grown ventrally in such a way as to form a broad chest plate. The upper portion of the girdle had a flat, scapular blade (shoulder bone), with the glenoid cavity situated below performing as the articulation surface for the humerus, while ventrally there was a large, flat coracoid plate turning in toward the midline.
The pelvic girdle also was much larger than the simple plate found in fishes, accommodating more muscles. It extended far dorsally and was joined to the backbone by one or more specialized sacral ribs. The hind legs were somewhat specialized in that they not only supported weight, but also provided propulsion. The dorsal extension of the pelvis was the ilium, while the broad ventral plate was composed of the pubis in front and the ischium in behind. The three bones met at a single point in the center of the pelvic triangle called the acetabulum, providing a surface of articulation for the femur. |
synth_fc_1056_rep6 | Positive | Finance | Feature search | Single | https://en.wikipedia.org/wiki/Walmart | 18 | Effects on customers
A 2005 story in The Washington Post reported that "Wal-Mart's discounting on food alone boosts the welfare of American shoppers by at least US$50 billion per year." A study in 2005 at the Massachusetts Institute of Technology (MIT) measured the effect on consumer welfare and found that the poorest segment of the population benefits the most from the existence of discount retailers. In 2006, American newspaper columnist George Will stated that In terms of economic effects, "Wal-Mart and its effects save shoppers more than US$200 billion a year, dwarfing such government programs as food stamps (US$28.6 billion) and the earned income tax credit (US$34.6 billion)". |
synth_fc_2457_rep14 | Positive | Movie | API setting | Single | https://en.wikipedia.org/wiki/Black_Sabbath | 6 | 1968–1969: Formation and early days
Following the break-up of their previous band, Mythology, in 1968, guitarist Tony Iommi and drummer Bill Ward sought to form a heavy blues rock band in Aston, Birmingham. They enlisted bassist Geezer Butler and vocalist Ozzy Osbourne, who had played together in a band called Rare Breed, Osbourne having placed an advertisement in a local music shop: "OZZY ZIG Needs Gig – has own PA". The new group was initially named the Polka Tulk Blues Band, the name taken either from a brand of talcum powder or an Indian/Pakistani clothing shop; the exact origin is confused. The Polka Tulk Blues Band included slide guitarist Jimmy Phillips, a childhood friend of Osbourne's, and saxophonist Alan "Aker" Clarke. After shortening the name to Polka Tulk, the band again changed their name to Earth (which Osbourne hated) and continued as a four-piece without Phillips and Clarke. Iommi became concerned that Phillips and Clarke lacked the necessary dedication and were not taking the band seriously. Rather than asking them to leave, they instead decided to break up and then quietly reformed the band as a four-piece. While the band was performing under the Earth moniker, they recorded several demos written by Norman Haines such as "The Rebel", "When I Came Down" and "Song for Jim", the latter of which being a reference to Jim Simpson, who was a manager for the bands Bakerloo Blues Line and Tea & Symphony, as well as the trumpet player for the group Locomotive. Simpson had recently started a new club named Henry's Blueshouse at The Crown Hotel in Birmingham and offered to let Earth play there after they agreed to waive the usual support band fee in return for free T-shirts. The audience response was positive and Simpson agreed to manage Earth.
In December 1968, Iommi abruptly left Earth to join Jethro Tull. Although his stint with the band would be short-lived, Iommi made an appearance with Jethro Tull on The Rolling Stones Rock and Roll Circus TV show. Unsatisfied with the direction of Jethro Tull, Iommi returned to Earth by the end of the month. "It just wasn't right, so I left", Iommi said. "At first I thought Tull were great, but I didn't much go for having a leader in the band, which was Ian Anderson 's way. When I came back from Tull, I came back with a new attitude altogether. They taught me that to get on, you got to work for it."
While playing shows in England in 1969, the band discovered they were being mistaken for another English group named Earth, so they decided to change their name again (this name change would give rise to the well-known debate about the alleged aesthetic influence of Coven, which the British band always denied). A cinema across the street from the band's rehearsal room was showing the 1963 Italian horror film Black Sabbath, starring Boris Karloff and directed by Mario Bava. While watching people line up to see the film, Butler noted that it was "strange that people spend so much money to see scary movies". Following that, Osbourne and Butler wrote the lyrics for a song called " Black Sabbath ", which was inspired by the work of horror and adventure-story writer Dennis Wheatley, along with a vision that Butler had of a black silhouetted figure standing at the foot of his bed. Making use of the musical tritone, also known as "the Devil's Interval", the song's ominous sound and dark lyrics pushed the band in a darker direction, a stark contrast to the popular music of the late 1960s, which was dominated by flower power, folk music and hippie culture. Judas Priest frontman Rob Halford has called the track "probably the most evil song ever written". Inspired by the new sound, the band changed their name to Black Sabbath in August 1969, and made the decision to focus on writing similar material in an attempt to create the musical equivalent of horror films. |
synth_fc_2594_rep18 | Positive | Music | Feature search | Single | https://en.wikipedia.org/wiki/Maria_Callas | 25 | Vocal category
Callas' voice has been difficult to place in the modern vocal classification or Fach system, especially since in her prime, her repertoire contained the heaviest dramatic soprano roles as well as roles usually undertaken by the highest, lightest and most agile coloratura sopranos. Regarding this versatility, Serafin said, "This woman can sing anything written for the female voice". Michael Scott argues that Callas' voice was a natural high soprano, and going by evidence of Callas' early recordings, Rosa Ponselle likewise felt that "At that stage of its development, her voice was a pure but sizable dramatic coloratura —that is to say, a sizable coloratura voice with dramatic capabilities, not the other way around." On the other hand, music critic John Ardoin has argued that Callas was the reincarnation of the 19th-century soprano sfogato or "unlimited soprano", a throwback to Maria Malibran and Giuditta Pasta, for whom many of the famous bel canto operas were written. He avers that like Pasta and Malibran, Callas was a natural mezzo-soprano whose range was extended through training and willpower, resulting in a voice which "lacked the homogeneous color and evenness of scale once so prized in singing. There were unruly sections of their voices never fully under control. Many who heard Pasta, for example, remarked that her uppermost notes seemed produced by ventriloquism, a charge which would later be made against Callas". Ardoin points to the writings of Henry Chorley about Pasta which bear an uncanny resemblance to descriptions of Callas:
There was a portion of the scale which differed from the rest in quality and remained to the last 'under a veil.'...out of these uncouth materials she had to compose her instrument and then to give it flexibility. Her studies to acquire execution must have been tremendous; but the volubility and brilliancy, when acquired, gained a character of their own... There were a breadth, an expressiveness in her roulades, an evenness and solidity in her shake, which imparted to every passage a significance totally beyond the reach of lighter and more spontaneous singers... The best of her audience were held in thrall, without being able to analyze what made up the spell, what produced the effect—as soon as she opened her lips.
Callas appears to have been in agreement not only with Ardoin's assertions that she started as a natural mezzo-soprano, but also saw the similarities between herself and Pasta and Malibran. In 1957, she described her early voice as: "The timbre was dark, almost black—when I think of it, I think of thick molasses", and in 1968 she added, "They say I was not a true soprano, I was rather toward a mezzo". Regarding her ability to sing the heaviest as well as the lightest roles, she told James Fleetwood,
It's study; it's Nature. I'm doing nothing special, you know. Even Lucia, Anna Bolena, Puritani, all these operas were created for one type of soprano, the type that sang Norma, Fidelio, which was Malibran of course. And a funny coincidence last year, I was singing Anna Bolena and Sonnambula, same months and the same distance of time as Giuditta Pasta had sung in the nineteenth century... So I'm really not doing anything extraordinary. You wouldn't ask a pianist not to be able to play everything; he has to. This is Nature and also because I had a wonderful teacher, the old kind of teaching methods...I was a very heavy voice, that is my nature, a dark voice shall we call it, and I was always kept on the light side. She always trained me to keep my voice limber. |
synth_fc_1803_rep20 | Negative | Health | Feature search | Single | https://en.wikipedia.org/wiki/Alternative_medicine | 35 | Prevalence of use
According to research published in 2015, the increasing popularity of CAM needs to be explained by moral convictions or lifestyle choices rather than by economic reasoning.
In developing nations, access to essential medicines is severely restricted by lack of resources and poverty. Traditional remedies, often closely resembling or forming the basis for alternative remedies, may comprise primary healthcare or be integrated into the healthcare system. In Africa, traditional medicine is used for 80% of primary healthcare, and in developing nations as a whole over one-third of the population lack access to essential medicines.
In Latin America, inequities against BIPOC communities keep them tied to their traditional practices and therefore, it is often these communities that constitute the majority of users of alternative medicine. Racist attitudes towards certain communities disable them from accessing more urbanized modes of care. In a study that assessed access to care in rural communities of Latin America, it was found that discrimination is a huge barrier to the ability of citizens to access care; more specifically, women of Indigenous and African descent, and lower-income families were especially hurt. Such exclusion exacerbates the inequities that minorities in Latin America already face. Consistently excluded from many systems of westernized care for socioeconomic and other reasons, low-income communities of color often turn to traditional medicine for care as it has proved reliable to them across generations.
Commentators including David Horrobin have proposed adopting a prize system to reward medical research. This stands in opposition to the current mechanism for funding research proposals in most countries around the world. In the US, the NCCIH provides public research funding for alternative medicine. The NCCIH has spent more than US$2.5 billion on such research since 1992 and this research has not demonstrated the efficacy of alternative therapies. As of 2011, the NCCIH's sister organization in the NIC Office of Cancer Complementary and Alternative Medicine had given out grants of around $105 million each year for several years. Testing alternative medicine that has no scientific basis (as in the aforementioned grants) has been called a waste of scarce research resources.
That alternative medicine has been on the rise "in countries where Western science and scientific method generally are accepted as the major foundations for healthcare, and 'evidence-based' practice is the dominant paradigm" was described as an "enigma" in the Medical Journal of Australia. A 15-year systematic review published in 2022 on the global acceptance and use of CAM among medical specialists found the overall acceptance of CAM at 52% and the overall use at 45%. |
synth_fc_655_rep11 | Positive | Currency | Calculation | Multi | https://en.wikipedia.org/wiki/Futures_contract | 1 | In finance, a futures contract is a standardized legal contract to buy or sell something at a predetermined price for delivery at a specified time in the future, between parties not yet known to each other. The asset transacted is usually a commodity or financial instrument. The predetermined price of the contract is known as the forward price or delivery price. The specified time in the future when delivery and payment occur is known as the delivery date. Because it derives its value from the value of the underlying asset, a futures contract is a derivative. Contracts are traded at futures exchanges, which act as a marketplace between buyers and sellers. The buyer of a contract is said to be the long position holder and the selling party is said to be the short position holder. As both parties risk their counter-party reneging if the price goes against them, the contract may involve both parties lodging as security a margin of the value of the contract with a mutually trusted third party. For example, in gold futures trading, the margin varies between 2% and 20% depending on the volatility of the spot market. A stock future is a cash-settled futures contract on the value of a particular stock market index. Stock futures are one of the high risk trading instruments in the market. Stock market index futures are also used as indicators to determine market sentiment. The first futures contracts were negotiated for agricultural commodities, and later futures contracts were negotiated for natural resources such as oil. Financial futures were introduced in 1972, and in recent decades, currency futures, interest rate futures, stock market index futures, and cryptocurrency inverse futures and perpetual futures have played an increasingly large role in the overall futures markets. Even organ futures have been proposed to increase the supply of transplant organs. The original use of futures contracts mitigates the risk of price or exchange rate movements by allowing parties to fix prices or rates in advance for future transactions. This could be advantageous when a party expects to receive payment in foreign currency in the future and wishes to guard against an unfavorable movement of the currency in the interval before payment is received. However, futures contracts also offer opportunities for speculation in that a trader who predicts that the price of an asset will move in a particular direction can contract to buy or sell it in the future at a price which will yield a profit. In particular, if the speculator is able to profit, then the underlying commodity that the speculator traded would have been saved during a time of surplus and sold during a time of need, offering the consumers of the commodity a more favorable distribution of commodity over time. |
synth_fc_2471_rep3 | Positive | Movie | Feature search | Single | https://en.wikipedia.org/wiki/Djembe | 15 | Film
The 1991 documentary Djembefola by Laurent Chevallier depicts Mamady Keïta's return to the village of his birth after a 26-year absence. Upon release, the movie won the Wisselzak Trophy and Special Jury Award at the International Documentary Film Festival Amsterdam, and the Audience Award at the Marseille Festival of Documentary Film, and brought the djembe to the attention of a wide audience.
A 1998 follow-up documentary, Mögöbalu (also by Chevallier), contains concert footage uniting four master drummers (Soungalo Coulibaly, Mamady Keita, Famoudou Konaté, and Doudou N'Diaye Rose) on stage.
The Oscar-nominated 2007 drama The Visitor ensured that the djembe was noticed internationally by mainstream viewers. |
synth_fc_3308_rep7 | Positive | Sport | Feature search | Single | https://en.wikipedia.org/wiki/LeBron_James | 7 | Basketball
As a 6-foot-2-inch (1.88 m) tall freshman, James averaged 18 points and 6.2 rebounds per game for the St. Vincent–St. Mary varsity basketball team. The Fighting Irish went 27–0 en route to the Division III state title, making them the only boys high school team in Ohio to finish the season undefeated. As a sophomore, James averaged 25.3 points and 7.4 rebounds, along with 5.5 assists and 3.7 steals per game. For some home games during the season, St. Vincent–St. Mary played at the University of Akron 's 5,492-seat Rhodes Arena to satisfy ticket demand from alumni, fans, as well as college and NBA scouts who wanted to see James play. The Fighting Irish finished the season 26–1 and repeated as state champions. For his outstanding play, James was named Ohio Mr. Basketball and selected to the USA Today All-USA First Team, becoming the first sophomore to do either.
In 2001, during the summer before his junior year, James was the subject of a feature article in Slam magazine in which writer Ryan Jones lauded the 16-year-old James, who had grown to 6 feet 7 inches (2.01 m), as " the best high school basketball player in America right now". During the season, James also appeared on the cover of Sports Illustrated, becoming the first high school basketball underclassman to do so. With averages of 28 points, 8.9 rebounds, 6 assists, and 3 steals per game, he was again named Ohio Mr. Basketball and selected to the USA Today All-USA First Team, and became the first junior to be named male basketball Gatorade National Player of the Year. St. Vincent–St. Mary finished the year with a 23–4 record, ending their season with a loss in the Division II championship game. Following the loss, James unsuccessfully petitioned for a change to the NBA's draft eligibility rules in an attempt to enter the 2002 NBA draft. During this time, he used marijuana, which he said was to help cope with the stress that resulted from the constant media attention he was receiving.
Throughout his senior year, James and the Fighting Irish traveled across the country to play a number of nationally ranked teams, including a game on December 12, 2002, against Oak Hill Academy that was nationally televised on ESPN2. Time Warner Cable, looking to capitalize on James's popularity, offered St. Vincent–St. Mary's games to Ohio-based subscribers for $7.95 per game on a pay-per-view basis throughout the season, but ended up not being profitable. For the year, James averaged 30.4 points, 9.7 rebounds, 4.9 assists, and 2.9 steals per game, was named Ohio Mr. Basketball and selected to the USA Today All-USA First Team for an unprecedented third consecutive year, and was named Gatorade National Player of the Year for the second consecutive year. He participated in three year-end high school basketball all-star games—the EA Sports Roundball Classic, the Jordan Brand Capital Classic, and the McDonald's All-American Game —losing his National Collegiate Athletic Association (NCAA) eligibility and making it official that he would enter the 2003 NBA draft.
Also during his senior year, James was the centerpiece of several controversies. For his 18th birthday, James skirted state amateur bylaws by accepting a Hummer H2 as a gift from his mother, who had secured a loan for the vehicle by utilizing James's future earning power as an NBA player. This prompted an investigation by the Ohio High School Athletic Association (OHSAA) because its guidelines stated that no amateur may accept any gift valued over $100 as a reward for athletic performance. James was cleared of any wrongdoing because he had accepted the luxury vehicle from a family member and not from an agent or any outside source. Later in the season, James accepted two throwback jerseys worth $845 from an urban clothing store in exchange for posing for pictures, officially violating OHSAA rules and resulting in his being stripped of his high school sports eligibility. James appealed the ruling and his penalty was eventually dropped to a two-game suspension, allowing him to play the remainder of the year. The Irish were also forced to forfeit one of their wins, their only official loss that season. In his first game back after the suspension, James scored a career-high 52 points. St. Vincent–St. Mary went on to win the Division II championship, marking their third division title in four years. |
synth_fc_1892_rep27 | Negative | History | Feature search | Single | https://en.wikipedia.org/wiki/Abbas_the_Great | 3 | Character and legacy
Abbas projected great military power, regained most of the lands lost by his predecessors, and adopted a set of forward-looking policies designed to optimise military strength, centralise state control, and expand Iran’s internal and international commercial scope. He paired ruthlessness with justice and dealt harshly with threats to his power, while remaining in touch with his people. All these qualities eventually entitled him to be styled as Abbas the Great.
Abbas I is generally considered one of the greatest rulers of Iranian history and the Safavid dynasty. According to Roger Savory: "Shah Abbas I possessed in abundance qualities which entitle him to be styled 'the Great'. He was a brilliant strategist and tactician whose chief characteristic was prudence. He preferred to obtain his ends by diplomacy rather than war, and showed immense patience in pursuing his objectives." In Michael Axworthy's view, Abbas "was a talented administrator and military leader, and a ruthless autocrat. His reign was the outstanding creative period of the Safavid era. But the civil wars and troubles of his childhood (when many of his relatives were murdered) left him with a dark twist of suspicion and brutality at the centre of his personality." Donald Rayfield described him as "exceptionally perspicacious and active," but also "a murderous paranoiac when aroused."
The Cambridge History of Iran rejects the view that the death of Abbas marked the beginning of the decline of the Safavid dynasty as Iran continued to prosper throughout the 17th century, but blames him for the poor statesmanship of the later Safavid shahs: "The elimination of royal princes, whether by blinding or immuring them in the harem, their exclusion from the affairs of state and from contact with the leading aristocracy of the empire and the generals, all the abuses of the princes' education, which were nothing new but which became the normal practice with Abbas at the court of Isfahan, effectively put a stop to the training of competent successors, that is to say, efficient princes prepared to meet the demands of ruling as kings."
Abbas was fluent in the Turkic dialect used by the Turkoman portion of the multi-ethnic Qizilbash organization, although he was equally at ease speaking Persian, which was the language of the administration and culture, of the majority of the population, as well as of the court when Isfahan became the capital under his reign (1598). According to García de Silva Figueroa, the Spanish ambassador to the Safavid court during Abbas' later reign, he heard Abbas speak Georgian, which he had doubtlessly acquired from his Georgian gholams and concubines.
Abbas gained strong support from the common people. Sources report him spending much of his time among them, personally visiting bazaars and other public places in Isfahan. Short in stature but physically strong until his health declined in his final years, Abbas could go for long periods without needing to sleep or eat and could ride great distances. At the age of 19, Abbas shaved off his beard, keeping only his moustache, thus setting a fashion in Iran.
Abbas was also a charismatic orator who could persuade and influence people with his eloquence. Classic Turkmen poet Magtymguly, who lived a century after Abbas, mentioned him in the poem "Zer bolmaz" (Not a jewel) with the following verses: |
synth_fc_3541_rep17 | Negative | Travel itinerary | Calculation | Single | https://en.wikipedia.org/wiki/Barcelona | 38 | Beaches
Barcelona beach was listed as number one in a list of the top ten city beaches in the world according to National Geographic and Discovery Channel. Barcelona contains seven beaches, totalling 4.5 km (2 + 3 ⁄ 4 mi) of coastline. Sant Sebastià, Barceloneta and Somorrostro beaches, both 1,100 m (3,610 ft) in length, are the largest, oldest and the most-frequented beaches in Barcelona.
The Olympic Harbour separates them from the other city beaches: Nova Icària, Bogatell, Mar Bella, Nova Mar Bella and Llevant. These beaches (ranging from 400 to 640 m (1,310 to 2,100 ft) were opened as a result of the city restructuring to host the 1992 Summer Olympics, when a great number of industrial buildings were demolished. At present, the beach sand is artificially replenished given that storms regularly remove large quantities of material. The 2004 Universal Forum of Cultures left the city a large concrete bathing zone on the eastmost part of the city's coastline. Most recently, Llevant is the first beach to allow dogs access during summer season. |
synth_fc_1579_rep20 | Positive | Geography | Feature search | Single | https://en.wikipedia.org/wiki/Cape_Verde | 26 | Climate
Cape Verde's climate is milder than that of the African mainland because the surrounding sea moderates temperatures on the islands and cold Atlantic currents produce an arid atmosphere around the archipelago. Conversely, the islands do not receive the upwelling (cold streams) that affect the West African coast, so the air temperature is cooler than in Senegal, but the sea is warmer. Due to the relief of some islands, such as Santiago with its steep mountains, the islands can have orographically induced precipitation, allowing rich woods and luxuriant vegetation to grow where the humid air condenses soaking the plants, rocks, soil, logs, moss, etc. On the higher islands and somewhat wetter islands, exclusively in mountainous areas, like Santo Antão island, the climate is suitable for the development of dry monsoon forests, and laurel forests. Average temperatures range from 22 °C (72 °F) in February to 27 °C (80.6 °F) in September. Cape Verde is part of the Sahelian semi-arid belt, with nothing like the rainfall levels of nearby West Africa. It rains irregularly between August and October, with frequent brief heavy downpours. A desert is usually defined as terrain that receives less than 250 mm (9.8 in) of annual rainfall. Sal's total of 145 mm (5.7 in) confirms this classification. Most of the year's rain falls in September.
Sal, Boa Vista, and Maio have a flat landscape and arid climate, whilst the other islands are generally rockier and have more vegetation. Because of the infrequent occurrence of rainfall, where not mountainous, the landscape is so arid that less than two percent of it is arable. The archipelago can be divided into four broad ecological zones – arid, semiarid, subhumid and humid, according to altitude and average annual rainfall ranging from less than 100 millimetres (3.9 inches) in the arid areas of the coast as in the Deserto de Viana (67 millimetres (2.6 inches) in Sal Rei) to more than 1,000 millimetres (39 inches) in the humid mountain. Most rainfall precipitation is due to condensation of the ocean mist.
In some islands, like Santiago, the wetter climate of the interior and the eastern coast contrasts with the drier one on the south/southwest coast. Praia, on the southeast coast, is the largest city on the island and the largest city and capital of the country.
While most of Cape Verde receives little precipitation throughout the year, the northeastern slopes of high mountains see significant rainfall due to orographic lift, especially in areas far from the sea. In some such areas this precipitation is sufficient to support a rainforest habitat, albeit one significantly affected by the islands' human presence. These umbria areas are identified as cool and moist. Cape Verde lies in the Cape Verde Islands dry forests ecoregion.
Western Hemisphere-bound hurricanes often have their early beginnings near the Cape Verde Islands. These are referred to as Cape Verde-type hurricanes. These hurricanes can become very intense as they cross warm Atlantic waters away from Cape Verde. The average hurricane season has about two Cape Verde-type hurricanes, which are usually the largest and most intense storms of the season because they often have plenty of warm open ocean over which to develop before encountering land. The five largest Atlantic tropical cyclones on record have been Cape Verde-type hurricanes. Most of the longest-lived tropical cyclones in the Atlantic basin are Cape Verde hurricanes.
As of 2015, the islands themselves have only been struck by hurricanes twice in recorded history (since 1851): once in 1892, and again in 2015 by Hurricane Fred, the easternmost hurricane ever to form in the Atlantic. |
synth_fc_3450_rep1 | Positive | Time | Calculation | Single | https://en.wikipedia.org/wiki/American_Civil_War | 44 | Union blockade
By early 1861, General Winfield Scott had devised the Anaconda Plan to win the war with minimal bloodshed, calling for a blockade of the Confederacy to suffocate the South into surrender. Lincoln adopted parts of the plan but opted for a more active war strategy. In April 1861, Lincoln announced a blockade of all Southern ports; commercial ships could not get insurance, ending regular traffic. The South blundered by embargoing cotton exports before the blockade was fully effective; by the time they reversed this decision, it was too late. " King Cotton " was dead, as the South could export less than 10% of its cotton. The blockade shut down the ten Confederate seaports with railheads that moved almost all the cotton. By June 1861, warships were stationed off the principal Southern ports, and a year later nearly 300 ships were in service. |
synth_fc_1735_rep15 | Positive | Health | Database search | Single | https://en.wikipedia.org/wiki/Forgiveness | 23 | Buddhism
In Buddhism, forgiveness prevents harmful thoughts from causing havoc on one's mental well-being. Buddhism recognizes that feelings of hatred and ill-will leave a lasting effect on our mind- karma. Buddhism encourages the cultivation of thoughts that leave a more wholesome effect. "In contemplating the law of karma, we realize that it is not a matter of seeking revenge but of practicing mettā and forgiveness, for the victimizer is, truly, the most unfortunate of all." When resentments have already arisen, the Buddhist view is to calmly proceed to release them by going back to their roots. Buddhism centers on release from delusion and suffering through meditation and receiving insight into the nature of reality.Buddhism questions the reality of the passions that make forgiveness necessary as well as the reality of the objects of those passions. "If we haven’t forgiven, we keep creating an identity around our pain, and that is what is reborn. That is what suffers."
Buddhism places much emphasis on the concepts of mettā (loving kindness), karuna (compassion), mudita (sympathetic joy), and upekkhā (equanimity), as a means to avoiding resentments in the first place. These reflections are used to understand the context of suffering in the world, both our own and the suffering of others.
"He abused me, he struck me, he overcame me, he robbed me" — in those who harbor such thoughts hatred will never cease."He abused me, he struck me, he overcame me, he robbed me" — in those who do not harbor such thoughts hatred will cease." |
synth_fc_1420_rep4 | Negative | Food | Feature search | Single | https://en.wikipedia.org/wiki/Squab | 1 | In culinary terminology, squab is an immature domestic pigeon, typically under four weeks old, or its meat. Some authors describe it as tasting like dark chicken. The word "squab" probably comes from Scandinavia; the Swedish word skvabb means "loose, fat flesh". The term formerly applied to all dove and pigeon species and their meat. More recently, squab meat comes almost entirely from domesticated pigeons. The meat of dove and pigeon gamebirds hunted primarily for sport is rarely called "squab". The practice of domesticating pigeons as livestock may have originated in North Africa; historically, many societies have consumed squabs or pigeons, including ancient Egypt, Rome, China, India (Northeast), and medieval Europe. Although squab has been consumed throughout much of recorded history, it is generally regarded as exotic, not as a contemporary staple food; there are more records of its preparation for the wealthy than for the poor. The modern squab industry uses utility pigeons. Squab farmers
raise the young until they are roughly a month old before slaughter. |
synth_fc_3243_rep13 | Negative | Sport | Ranking | Single | https://en.wikipedia.org/wiki/Dawn_Staley | 1 | Dawn Michelle Staley is an American basketball coach and former player who is the head coach for the South Carolina Gamecocks women's basketball team. A point guard, she played college basketball for the Virginia Cavaliers and spent eight seasons in the Women's National Basketball Association (WNBA), primarily with the Charlotte Sting. Staley also played on the United States women's national basketball team, winning three gold medals at the Olympic Games from 1996 to 2004, and was the head coach of the team that won an Olympic gold medal in 2021. She is the first person to win the Naismith Award as both a player and a coach. During her college career with Virginia from 1988 to 1992, Staley set the NCAA record for steals, the school record for points, and the ACC record for assists. She played professionally in the American Basketball League (ABL) during its three years of operation before being selected ninth overall by the Sting in the 1999 WNBA draft. As a member of the Sting and the Houston Comets, she received six consecutive WNBA All-Star selections from 2001 to her final season in 2006. Staley spent most of her WNBA career simultaneously serving as the head coach of the Temple Owls women's basketball team from 2000 to 2008, leading them to six NCAA tournaments, three regular-season conference championships, and four conference tournament titles. After becoming South Carolina's head coach in 2008, Staley rebuilt the Gamecocks into one of the top women's basketball programs. During her 16 seasons, she has led South Carolina to eight SEC regular season championships, eight SEC tournament championships, eight Sweet Sixteens, five Final Fours, and three NCAA women's basketball national championships, including the school's first in 2017 and a perfect season in 2024. Staley was inducted to the Women's Basketball Hall of Fame in 2012 and the Naismith Memorial Basketball Hall of Fame in 2013. |
synth_fc_970_rep24 | No function call | Finance | Calculation | Single | https://en.wikipedia.org/wiki/The_Howard_Stern_Show | 1 | The Howard Stern Show is an American radio show hosted by Howard Stern that gained wide recognition when it was nationally syndicated on terrestrial radio from WXRK in New York City, between 1986 and 2005. The show has aired on Howard 100 and Howard 101, Stern's two uncensored channels on the subscription-based satellite radio service SiriusXM, since 2006. Other prominent staff members include co-host and news anchor Robin Quivers, writer Fred Norris and executive producer Gary Dell'Abate, along with former members Jackie Martling, Billy West, John Melendez, and Artie Lange. Stern began his radio career in the mid-1970s and developed his show through morning positions at WRNW in Briarcliff Manor, New York, WCCC-FM in Hartford, Connecticut, and WWWW in Detroit. In 1981, he began at WWDC-FM in Washington, D.C., where he was first paired with Quivers and became a ratings success. That was followed by three years at WNBC in New York City. After his abrupt firing, Stern moved to WXRK where he remained for 20 years until December 2005. During this time, The Howard Stern Show was syndicated to 60 radio markets and gained an audience of 20 million listeners at its peak. In the New York area, it was the highest-rated morning radio program from 1994 to 2001. The show is also the most fined, after a total of $2.5 million in fines were issued by the Federal Communications Commission for indecent material. In 2004, Stern signed the first of several five-year contracts with Sirius; the first was reportedly worth $500 million. In addition to radio broadcast, The Howard Stern Show has been filmed since 1994 and broadcast on various networks, including the E! and CBS television channels. It moved to HowardTV, Stern's own on-demand digital cable channel from 2005 to 2013. In 2018, Sirius XM launched a mobile app for subscribers to access video clips of the show. |
synth_fc_192_rep14 | No function call | Biology | Calculation | Single | https://en.wikipedia.org/wiki/Hamiltonian_mechanics | 6 | Geometry of Hamiltonian systems
The Hamiltonian can induce a symplectic structure on a smooth even-dimensional manifold M in several equivalent ways, the best known being the following:
As a closed nondegenerate symplectic 2-form ω. According to the Darboux's theorem, in a small neighbourhood around any point on M there exist suitable local coordinates p 1, ⋯, p n, q 1, ⋯, q n {\displaystyle p_{1},\cdots,p_{n},\ q_{1},\cdots,q_{n}} (canonical or symplectic coordinates) in which the symplectic form becomes: ω = ∑ i = 1 n d p i ∧ d q i. {\displaystyle \omega =\sum _{i=1}^{n}dp_{i}\wedge dq_{i}\,.} The form ω {\displaystyle \omega } induces a natural isomorphism of the tangent space with the cotangent space: T x M ≅ T x ∗ M {\displaystyle T_{x}M\cong T_{x}^{*}M}. This is done by mapping a vector ξ ∈ T x M {\displaystyle \xi \in T_{x}M} to the 1-form ω ξ ∈ T x ∗ M {\displaystyle \omega _{\xi }\in T_{x}^{*}M}, where ω ξ (η) = ω (η, ξ) {\displaystyle \omega _{\xi }(\eta)=\omega (\eta,\xi)} for all η ∈ T x M {\displaystyle \eta \in T_{x}M}. Due to the bilinearity and non-degeneracy of ω {\displaystyle \omega }, and the fact that dim T x M = dim T x ∗ M {\displaystyle \dim T_{x}M=\dim T_{x}^{*}M}, the mapping ξ → ω ξ {\displaystyle \xi \to \omega _{\xi }} is indeed a linear isomorphism. This isomorphism is natural in that it does not change with change of coordinates on M. {\displaystyle M.} Repeating over all x ∈ M {\displaystyle x\in M}, we end up with an isomorphism J − 1: Vect (M) → Ω 1 (M) {\displaystyle J^{-1}:{\text{Vect}}(M)\to \Omega ^{1}(M)} between the infinite-dimensional space of smooth vector fields and that of smooth 1-forms. For every f, g ∈ C ∞ (M, R) {\displaystyle f,g\in C^{\infty }(M,\mathbb {R})} and ξ, η ∈ Vect (M) {\displaystyle \xi,\eta \in {\text{Vect}}(M)}, J − 1 (f ξ + g η) = f J − 1 (ξ) + g J − 1 (η). {\displaystyle J^{-1}(f\xi +g\eta)=fJ^{-1}(\xi)+gJ^{-1}(\eta).}
(In algebraic terms, one would say that the C ∞ (M, R) {\displaystyle C^{\infty }(M,\mathbb {R})} -modules Vect (M) {\displaystyle {\text{Vect}}(M)} and Ω 1 (M) {\displaystyle \Omega ^{1}(M)} are isomorphic). If H ∈ C ∞ (M × R t, R) {\displaystyle H\in C^{\infty }(M\times \mathbb {R} _{t},\mathbb {R})}, then, for every fixed t ∈ R t {\displaystyle t\in \mathbb {R} _{t}}, d H ∈ Ω 1 (M) {\displaystyle dH\in \Omega ^{1}(M)}, and J (d H) ∈ Vect (M) {\displaystyle J(dH)\in {\text{Vect}}(M)}. J (d H) {\displaystyle J(dH)} is known as a Hamiltonian vector field. The respective differential equation on M {\displaystyle M} x ˙ = J (d H) (x) {\displaystyle {\dot {x}}=J(dH)(x)} is called Hamilton's equation. Here x = x (t) {\displaystyle x=x(t)} and J (d H) (x) ∈ T x M {\displaystyle J(dH)(x)\in T_{x}M} is the (time-dependent) value of the vector field J (d H) {\displaystyle J(dH)} at x ∈ M {\displaystyle x\in M}.
A Hamiltonian system may be understood as a fiber bundle E over time R, with the fiber E being the position space at time t ∈ R. The Lagrangian is thus a function on the jet bundle J over E; taking the fiberwise Legendre transform of the Lagrangian produces a function on the dual bundle over time whose fiber at t is the cotangent space T E, which comes equipped with a natural symplectic form, and this latter function is the Hamiltonian. The correspondence between Lagrangian and Hamiltonian mechanics is achieved with the tautological one-form.
Any smooth real-valued function H on a symplectic manifold can be used to define a Hamiltonian system. The function H is known as "the Hamiltonian" or "the energy function." The symplectic manifold is then called the phase space. The Hamiltonian induces a special vector field on the symplectic manifold, known as the Hamiltonian vector field.
The Hamiltonian vector field induces a Hamiltonian flow on the manifold. This is a one-parameter family of transformations of the manifold (the parameter of the curves is commonly called "the time"); in other words, an isotopy of symplectomorphisms, starting with the identity. By Liouville's theorem, each symplectomorphism preserves the volume form on the phase space. The collection of symplectomorphisms induced by the Hamiltonian flow is commonly called "the Hamiltonian mechanics" of the Hamiltonian system.
The symplectic structure induces a Poisson bracket. The Poisson bracket gives the space of functions on the manifold the structure of a Lie algebra.
If F and G are smooth functions on M then the smooth function ω (J (dF), J (dG)) is properly defined; it is called a Poisson bracket of functions F and G and is denoted { F, G }. The Poisson bracket has the following properties:
Given a function f d d t f = ∂ ∂ t f + { f, H }, {\displaystyle {\frac {\mathrm {d} }{\mathrm {d} t}}f={\frac {\partial }{\partial t}}f+\left\{f,{\mathcal {H}}\right\},} if there is a probability distribution ρ, then (since the phase space velocity (p ˙ i, q ˙ i) {\displaystyle ({\dot {p}}_{i},{\dot {q}}_{i})} has zero divergence and probability is conserved) its convective derivative can be shown to be zero and so ∂ ∂ t ρ = − { ρ, H } {\displaystyle {\frac {\partial }{\partial t}}\rho =-\left\{\rho,{\mathcal {H}}\right\}}
This is called Liouville's theorem. Every smooth function G over the symplectic manifold generates a one-parameter family of symplectomorphisms and if { G, H } = 0, then G is conserved and the symplectomorphisms are symmetry transformations.
A Hamiltonian may have multiple conserved quantities G. If the symplectic manifold has dimension 2 n and there are n functionally independent conserved quantities G which are in involution (i.e., { G, G } = 0), then the Hamiltonian is Liouville integrable. The Liouville–Arnold theorem says that, locally, any Liouville integrable Hamiltonian can be transformed via a symplectomorphism into a new Hamiltonian with the conserved quantities G as coordinates; the new coordinates are called action–angle coordinates. The transformed Hamiltonian depends only on the G, and hence the equations of motion have the simple form G ˙ i = 0, φ ˙ i = F i (G) {\displaystyle {\dot {G}}_{i}=0\quad,\quad {\dot {\varphi }}_{i}=F_{i}(G)} for some function F. There is an entire field focusing on small deviations from integrable systems governed by the KAM theorem.
The integrability of Hamiltonian vector fields is an open question. In general, Hamiltonian systems are chaotic; concepts of measure, completeness, integrability and stability are poorly defined. |
synth_fc_649_rep19 | Positive | Currency | Calculation | Single | https://en.wikipedia.org/wiki/The_Great_Wave_off_Kanagawa | 12 | In popular culture
Wayne Crothers, the curator of a 2017 Hokusai exhibition at the National Gallery of Victoria, described The Great Wave off Kanagawa as "possibly the most reproduced image in the history of all art" while the Wall Street Journal ' s Ellen Gamerman wrote it "may be the most famous artwork in Japanese history". Hiroshige paid homage to The Great Wave off Kanagawa with his print The Sea off Satta in Suruga Province while French artist Gustave-Henri Jossot produced a satirical painting in the style of The Great Wave off Kanagawa to mock the popularity of Japonisme.
Many modern artists have reinterpreted and adapted the image. Indigenous Australian artist Lin Onus used The Great Wave off Kanagawa as the basis for his 1992 painting Michael and I are just slipping down to the pub for a minute. A work named Uprisings by Japanese-American artist Kozyndan is based on the print; the foam of the wave is replaced with rabbits. On computer operating systems designed by Apple Inc., the emoji character for a water wave (🌊) strongly resembles the wave depicted in the print. In 2022 the Bank of Japan announced The Great Wave off Kanagawa' s inclusion in a redesign of Japan's banknotes to begin circulation in 2024. |
synth_fc_3803_rep10 | Positive | Weather & Air quality | Database search | Single | https://en.wikipedia.org/wiki/Fahrenheit | 10 | European Union
In the European Union, it is mandatory to use Kelvins or degrees Celsius when quoting temperature for "economic, public health, public safety and administrative" purposes, though degrees Fahrenheit may be used alongside degrees Celsius as a supplementary unit. |
synth_fc_1668_rep22 | Positive | Health | API setting | Single | https://en.wikipedia.org/wiki/Active_transport | 6 | History
In 1848, the German physiologist Emil du Bois-Reymond suggested the possibility of active transport of substances across membranes.
In 1926, Dennis Robert Hoagland investigated the ability of plants to absorb salts against a concentration gradient and discovered the dependence of nutrient absorption and translocation on metabolic energy using innovative model systems under controlled experimental conditions.
Rosenberg (1948) formulated the concept of active transport based on energetic considerations, but later it would be redefined.
In 1997, Jens Christian Skou, a Danish physician received the Nobel Prize in Chemistry for his research regarding the sodium-potassium pump.
One category of cotransporters that is especially prominent in research regarding diabetes treatment is sodium-glucose cotransporters. These transporters were discovered by scientists at the National Health Institute. These scientists had noticed a discrepancy in the absorption of glucose at different points in the kidney tubule of a rat. The gene was then discovered for intestinal glucose transport protein and linked to these membrane sodium glucose cotransport systems. The first of these membrane transport proteins was named SGLT1 followed by the discovery of SGLT2. Robert Krane also played a prominent role in this field. |
synth_fc_1074_rep21 | Positive | Finance | Calculation | Single | https://en.wikipedia.org/wiki/Credit_card | 36 | United Kingdom
Consumers who keep their account in good order by always staying within their credit limit, and always making at least the minimum monthly payment will see interest as the biggest expense from their card provider. Those who are not so careful and regularly surpass their credit limit or are late in making payments were exposed to multiple charges, until a ruling from the Office of Fair Trading that they would presume charges over £12 to be unfair which led the majority of card providers to reduce their fees to £12.
The higher fees originally charged were claimed to be designed to recoup the card operator's overall business costs and to try to ensure that the credit card business as a whole generated a profit, rather than simply recovering the cost to the provider of the limit breach, which has been estimated as typically between £3–£4. Profiting from a customer's mistakes is arguably not permitted under U.K. common law if the charges constitute penalties for breach of contract, or under the Unfair Terms in Consumer Contracts Regulations 1999.
Subsequent rulings in respect of personal current accounts suggest that the argument that these charges are penalties for breach of contract is weak, and given the Office of Fair Trading's ruling it seems unlikely that any further test case will take place.
Whilst the law remains in the balance, many consumers have made claims against their credit card providers for the charges that they have incurred, plus interest that they would have earned had the money not been deducted from their account. It is likely that claims for amounts charged in excess of £12 will succeed, but claims for charges at the OFT's £12 threshold level are more contentious. |
synth_fc_504_rep3 | Positive | Corporate Management | Database removal | Multi | https://en.wikipedia.org/wiki/Nut_(hardware) | 7 | Locknuts
Many specialised types of nut exist to resist loosening of bolted joints, either by providing a prevailing torque against the male fastener or by gripping against the bolted components. These are generally referred to as locknuts. |
synth_fc_1439_rep3 | Negative | Food | Feature search | Single | https://en.wikipedia.org/wiki/Vitamin | 14 | Effects of cooking
The USDA has conducted extensive studies on the percentage losses of various nutrients from food types and cooking methods. Some vitamins may become more "bio-available" – that is, usable by the body – when foods are cooked. The table below shows whether various vitamins are susceptible to loss from heat—such as heat from boiling, steaming, frying, etc. The effect of cutting vegetables can be seen from exposure to air and light. Water-soluble vitamins such as B and C dissolve into the water when a vegetable is boiled, and are then lost when the water is discarded. |
synth_fc_3506_rep2 | Negative | Travel itinerary | Calculation | Single | https://en.wikipedia.org/wiki/Controlled-access_highway | 47 | Uzbekistan
Uzbekistan has 84,400 km (52,400 mi) of roads, about 72,000 km (45,000 mi) of which were paved. Much of the highways are in need of repair, although the condition has been improving. In 2017, the governments of Kazakhstan and Uzbekistan agreed to open a section of the M39 Highway by the Kazakh border. |
synth_fc_2066_rep15 | Positive | Hotel | Order | Single | https://en.wikipedia.org/wiki/Ulysses_(novel) | 31 | Episode 11, "Sirens"
In this episode, dominated by motifs of music, Bloom has dinner with Stephen's uncle at the Ormond hotel, while Molly's lover, Blazes Boylan, proceeds to his rendezvous with her. While dining, Bloom listens to the singing of Stephen's father and others, watches the seductive barmaids, and composes a reply to Martha Clifford's letter. |
synth_fc_2115_rep28 | No function call | Law | Entity search | Single | https://en.wikipedia.org/wiki/Richard_Feynman | 3 | Case before the Equal Employment Opportunity Commission
In 1977, Feynman supported his English literature colleague Jenijoy La Belle, who had been hired as Caltech's first female professor in 1969, and filed suit with the Equal Employment Opportunity Commission after she was refused tenure in 1974. The EEOC ruled against Caltech in 1977, adding that La Belle had been paid less than male colleagues. La Belle finally received tenure in 1979. Many of Feynman's colleagues were surprised that he took her side, but he had gotten to know La Belle and liked and admired her. |
synth_fc_2237_rep13 | No function call | Law | Feature search | Single | https://en.wikipedia.org/wiki/Franz_Kafka | 22 | Unpublished papers
When Brod died in 1968, he left Kafka's unpublished papers, which are believed to number in the thousands, to his secretary Esther Hoffe. She released or sold some, but left most to her daughters, Eva and Ruth, who also refused to release the papers. A court battle began in 2008 between the sisters and the National Library of Israel, which claimed these works became the property of the nation of Israel when Brod emigrated to British Palestine in 1939. Esther Hoffe sold the original manuscript of Der Process for US$2 million in 1988 to the German Literary Archive Museum of Modern Literature in Marbach am Neckar. A ruling by a Tel Aviv family court in 2010 held that the papers must be released and a few were, including a previously unknown story, but the legal battle continued. The Hoffes claim the papers are their personal property, while the National Library of Israel argues they are "cultural assets belonging to the Jewish people". The National Library also suggests that Brod bequeathed the papers to them in his will. The Tel Aviv Family Court ruled in October 2012, six months after Ruth's death, that the papers were the property of the National Library. The Israeli Supreme Court upheld the decision in December 2016. |
synth_fc_3821_rep6 | No function call | Weather & Air quality | Feature search | Single | https://en.wikipedia.org/wiki/Temperature | 20 | Units
The basic unit of temperature in the International System of Units (SI) is the kelvin. It has the symbol K.
For everyday applications, it is often convenient to use the Celsius scale, in which 0 °C corresponds very closely to the freezing point of water and 100 °C is its boiling point at sea level. Because liquid droplets commonly exist in clouds at sub-zero temperatures, 0 °C is better defined as the melting point of ice. In this scale, a temperature difference of 1 degree Celsius is the same as a 1 kelvin increment, but the scale is offset by the temperature at which ice melts (273.15 K).
By international agreement, until May 2019, the Kelvin and Celsius scales were defined by two fixing points: absolute zero and the triple point of Vienna Standard Mean Ocean Water, which is water specially prepared with a specified blend of hydrogen and oxygen isotopes. Absolute zero was defined as precisely 0 K and −273.15 °C. It is the temperature at which all classical translational motion of the particles comprising matter ceases and they are at complete rest in the classical model. Quantum-mechanically, however, zero-point motion remains and has an associated energy, the zero-point energy. Matter is in its ground state, and contains no thermal energy. The temperatures 273.16 K and 0.01 °C were defined as those of the triple point of water. This definition served the following purposes: it fixed the magnitude of the kelvin as being precisely 1 part in 273.16 parts of the difference between absolute zero and the triple point of water; it established that one kelvin has precisely the same magnitude as one degree on the Celsius scale; and it established the difference between the null points of these scales as being 273.15 K (0 K = −273.15 °C and 273.16 K = 0.01 °C). Since 2019, there has been a new definition based on the Boltzmann constant, but the scales are scarcely changed.
In the United States, the Fahrenheit scale is the most widely used. On this scale the freezing point of water corresponds to 32 °F and the boiling point to 212 °F. The Rankine scale, still used in fields of chemical engineering in the US, is an absolute scale based on the Fahrenheit increment. |
synth_fc_11_rep18 | Positive | Acoustics | Calculation | Single | https://en.wikipedia.org/wiki/Albert_A._Michelson | 6 | Harmonic analyzer
In the 1890s Michelson built a mechanical device called the harmonic analyzer, for computing coefficients of Fourier series and drawing graphs of their partial sums. He and S. W. Stratton published a paper about this machine in the American Journal of Science in 1898. |
synth_fc_1009_rep7 | Positive | Finance | Calculation | Multi | https://en.wikipedia.org/wiki/Punched_card | 18 | Manufacturing
IBM's Fred M. Carroll developed a series of rotary presses that were used to produce punched cards, including a 1921 model that operated at 460 cards per minute (cpm). In 1936 he introduced a completely different press that operated at 850 cpm. Carroll's high-speed press, containing a printing cylinder, revolutionized the company's manufacturing of punched cards. It is estimated that between 1930 and 1950, the Carroll press accounted for as much as 25 percent of the company's profits.
Discarded printing plates from these card presses, each printing plate the size of an IBM card and formed into a cylinder, often found use as desk pen/pencil holders, and even today are collectible IBM artifacts (every card layout had its own printing plate).
In the mid-1930s a box of 1,000 cards cost $1.05 (equivalent to $23 in 2023). |
synth_fc_2549_rep4 | Negative | Museum | Feature search | Single | https://en.wikipedia.org/wiki/John_Singer_Sargent | 8 | Sales
Portrait of Robert Louis Stevenson and his Wife was sold in 2004 for US$8.8 million and is located at Crystal Bridges Museum of American Art at Bentonville, Arkansas.
In December 2004, Group with Parasols (A Siesta) (1905) sold for US$23.5 million, nearly double the Sotheby's estimate of $12 million. The previous highest price for a Sargent painting was US$11 million. |
synth_fc_748_rep10 | No function call | DNA sequence | Entity search | Single | https://en.wikipedia.org/wiki/Homological_algebra | 5 | Foundational aspects
Cohomology theories have been defined for many different objects such as topological spaces, sheaves, groups, rings, Lie algebras, and C*-algebras. The study of modern algebraic geometry would be almost unthinkable without sheaf cohomology.
Central to homological algebra is the notion of exact sequence; these can be used to perform actual calculations. A classical tool of homological algebra is that of derived functor; the most basic examples are functors Ext and Tor.
With a diverse set of applications in mind, it was natural to try to put the whole subject on a uniform basis. There were several attempts before the subject settled down. An approximate history can be stated as follows:
These move from computability to generality.
The computational sledgehammer par excellence is the spectral sequence; these are essential in the Cartan-Eilenberg and Tohoku approaches where they are needed, for instance, to compute the derived functors of a composition of two functors. Spectral sequences are less essential in the derived category approach, but still play a role whenever concrete computations are necessary.
There have been attempts at 'non-commutative' theories which extend first cohomology as torsors (important in Galois cohomology). |
synth_fc_1610_rep11 | Positive | Geography | Feature search | Single | https://en.wikipedia.org/wiki/Snow_leopard | 10 | Distribution and habitat
The snow leopard is distributed from the west of Lake Baikal through southern Siberia, in the Kunlun Mountains, Altai Mountains, Sayan and Tannu-Ola Mountains, in the Tian Shan, through Tajikistan, Kyrgyzstan, Uzbekistan and Kazakhstan to the Hindu Kush in eastern Afghanistan, Karakoram in northern Pakistan, in the Pamir Mountains, the Tibetan Plateau and in the high elevations of the Himalayas in India, Nepal and Bhutan. In Mongolia, they inhabit the Mongolian and Gobi Altai Mountains and the Khangai Mountains. In Tibet, they occur up to the Altyn-Tagh in the north. They inhabit alpine and subalpine zones at elevations of 3,000 to 4,500 m (9,800 to 14,800 ft), but also lives at lower elevations in the northern part of their range.
Potential snow leopard habitat in the Indian Himalayas is estimated at less than 90,000 km (35,000 sq mi) in Jammu and Kashmir, Ladakh, Uttarakhand, Himachal Pradesh, Sikkim and Arunachal Pradesh, of which about 34,000 km (13,000 sq mi) is considered good habitat, and 14.4% is protected. In the beginning of the 1990s, the Indian snow leopard population was estimated at 200–600 individuals living across about 25 protected areas. The Snow Leopard Population Assessment in India (SPAI) Programme counted the number of snow leopards between 2019 and 2023 and found their number to be 718, with 477 in Ladakh, 124 in Uttarakhand, 51 in Himachal Pradesh, 36 in Arunachal Pradesh, 21 in Sikkim, and nine in Jammu and Kashmir.
In summer, the snow leopard usually lives above the tree line on alpine meadows and in rocky regions at elevations of 2,700 to 6,000 m (8,900 to 19,700 ft). In winter, they descend to elevations around 1,200 to 2,000 m (3,900 to 6,600 ft). They prefer rocky, broken terrain, and can move in 85 cm (33 in) deep snow, but prefers to use existing trails made by other animals.
Snow leopards were recorded by camera traps at 16 locations in northeastern Afghanistan's isolated Wakhan Corridor. |
synth_fc_892_rep2 | Positive | Finance | Calculation | Single | https://en.wikipedia.org/wiki/Magellan_expedition | 6 | Construction and provisions
The fleet, consisting of five ships with supplies for two years of travel, was called the Armada del Maluco, or Armada de Molucca, after the Indonesian name for the Spice Islands. The ships were mostly black, due to the tar covering most of their surface. The official accounting of the expedition put the cost at 8,751,125 maravedis, including the ships, provisions, and salaries.
Food was a hugely important part of the provisioning. It cost 1,252,909 maravedis, almost as much as the cost of the ships. Four-fifths of the food on the ship consisted of just two items – wine and hardtack.
The fleet also carried flour and salted meat. Some of the ships' meat came in the form of livestock; the ship carried seven cows and three pigs. Cheese, almonds, mustard, and figs were also present. Carne de membrillo, made from preserved quince, was a delicacy enjoyed by captains which may have unknowingly aided in the prevention of scurvy. |
synth_fc_1021_rep7 | Negative | Finance | Document search | Single | https://en.wikipedia.org/wiki/Eug%C3%A8ne_Delacroix | 7 | Legacy
At the sale of his work in 1864, 9140 works were attributed to Delacroix, including 853 paintings, 1525 pastels and water colours, 6629 drawings, 109 lithographs, and over 60 sketch books. The number and quality of the drawings, whether done for constructive purposes or to capture a spontaneous movement, underscored his explanation, "Colour always occupies me, but drawing preoccupies me."Delacroix produced several fine self-portraits, and a number of memorable portraits which seem to have been done purely for pleasure, among which were the portrait of fellow artist Baron Schwiter, an inspired small oil of the violinist Niccolò Paganini, and Portrait of Frédéric Chopin and George Sand, a double portrait of his friends, the composer Frédéric Chopin and writer George Sand; the painting was cut after his death, but the individual portraits survive.
On occasion Delacroix painted pure landscapes (The Sea at Dieppe, 1852) and still lifes (Still Life with Lobsters, 1826–27), both of which feature the virtuoso execution of his figure-based works. He is also well known for his Journal, in which he gave eloquent expression to his thoughts on art and contemporary life.
A generation of impressionists was inspired by Delacroix's work. Renoir and Manet made copies of his paintings, and Degas purchased the portrait of Baron Schwiter for his private collection. His painting at the church of Saint-Sulpice has been called the "finest mural painting of his time".
Contemporary Chinese artist Yue Minjun has created his own interpretation of Delacroix's painting Massacre of Chios, which retains the same name. Yue Minjun's painting was itself sold at Sotheby's for nearly $4.1 million in 2007.
His pencil drawing Moorish Conversation on a Terrace was discovered as part of the Munich Art Hoard. |
synth_fc_3554_rep13 | Positive | Travel itinerary | Calculation | Single | https://en.wikipedia.org/wiki/IPv6 | 1 | Internet Protocol version 6 (IPv6) is the most recent version of the Internet Protocol (IP), the communications protocol that provides an identification and location system for computers on networks and routes traffic across the Internet. IPv6 was developed by the Internet Engineering Task Force (IETF) to deal with the long-anticipated problem of IPv4 address exhaustion, and was intended to replace IPv4. In December 1998, IPv6 became a Draft Standard for the IETF, which subsequently ratified it as an Internet Standard on 14 July 2017. Devices on the Internet are assigned a unique IP address for identification and location definition. With the rapid growth of the Internet after commercialization in the 1990s, it became evident that far more addresses would be needed to connect devices than the IPv4 address space had available. By 1998, the IETF had formalized the successor protocol. IPv6 uses 128-bit addresses, theoretically allowing 2ⁱ⁸, or approximately 3.4×10⁸ total addresses. The actual number is slightly smaller, as multiple ranges are reserved for special usage or completely excluded from general use. The two protocols are not designed to be interoperable, and thus direct communication between them is impossible, complicating the move to IPv6. However, several transition mechanisms have been devised to rectify this. IPv6 provides other technical benefits in addition to a larger addressing space. In particular, it permits hierarchical address allocation methods that facilitate route aggregation across the Internet, and thus limit the expansion of routing tables. The use of multicast addressing is expanded and simplified, and provides additional optimization for the delivery of services. Device mobility, security, and configuration aspects have been considered in the design of the protocol. IPv6 addresses are represented as eight groups of four hexadecimal digits each, separated by colons. The full representation may be shortened; for example, 2001:0db8:0000:0000:0000:8a2e:0370:7334 becomes 2001:db8::8a2e:370:7334. |
synth_fc_3514_rep25 | Positive | Travel itinerary | Calculation | Single | https://en.wikipedia.org/wiki/Zhengzhou | 30 | Roads and expressways
The surrounding area of Zhengzhou, along with the Yangtze River Delta, Pearl River Delta and the Bohai Economic Rim, has the highest highway density nationwide. Zhengzhou is the center of Henan expressway network that provides 1–2 hours road trip to surrounding cities of Kaifeng, Xinxiang, Xuchang, Jiaozuo and Luoyang. Other major cities within the province can be reached in 3 hours. The expressway network and national highways also links Zhengzhou to all major cities in the country.
There are several limited access express roads in the city center to relieve traffic problems. However, heavy congestion is still common in rush hours. |
synth_fc_666_rep2 | Positive | Currency | Calculation | Single | https://en.wikipedia.org/wiki/The_Adventures_of_Tintin | 8 | Stamps and coins
Tintin's image has been used on postage stamps on numerous occasions.The first Tintin postage stamp was an eight-franc stamp issued by Belgian Post for the 50th anniversary of the publication of Tintin's first adventure on 29 September 1979, featuring Tintin and Snowy looking through a magnifying glass at several stamps. In 1999, a nine-stamp block celebrating ten years of the Belgian Comic Strip Center was issued, with the center stamp a photo of Tintin's famous Moon rocket that dominates the Comic Strip Center's entry hall. To mark the end of the Belgian Franc and to celebrate the seventieth anniversary of the publication of Tintin in the Congo, two more stamps were issued by Belgian Post on 31 December 2001: Tintin in a pith helmet and a souvenir sheet with a single stamp in the center. The stamps were jointly issued in the Democratic Republic of the Congo. In 2004, Belgian Post celebrated its own seventy-fifth anniversary, as well as the fiftieth anniversary of the publication of Explorers on the Moon, and the thirty-fifth anniversary of the Moon landings with a souvenir sheet of five stamps based upon the Explorers on the Moon adventure. To celebrate the centenary of Hergé's birth in 2007, Belgian Post issued a sheet of 25 stamps depicting the album covers of all 24 Adventures of Tintin (in 24 languages) plus Hergé's portrait in the center. A souvenir sheet of ten stamps called "Tintin on screen", issued 30 August 2011, depicts the Tintin film and television adaptations.
Tintin has also been commemorated by coin several times.In 1995, the Monnaie de Paris (Paris Mint) issued a set of twelve gold medallions, available in a limited edition of 5000. A silver medallion was minted in 2004 to commemorate the 50th anniversary of the Tintin book Explorers on the Moon, again in a limited run, this time of 10,000. It quickly sold out. In 2004, Belgium minted a limited edition commemorative euro coin featuring Tintin and Snowy celebrating the 75th anniversary of Tintin's first adventure in January 2004. Although it has a face value of €10, it is, as with other commemorative euro coins, legal tender only in the country in which it was issued—in this case, Belgium. In 2006–2012 France issued the Comic Strip Heroes commemorative coin series featuring famous Franco-Belgian comics, beginning in 2006 with Tintin. It was a set of six different euro coins honouring Hergé: three 1½-euro silver coins featuring Tintin and the Professor, Tintin and Captain Haddock, and Tintin and Chang; a €10 (gold) featuring Tintin; and a €20 (silver) and a €50 (gold) featuring Tintin and Snowy. In 2007, on Hergé's centenary, Belgium issued its €20 (silver) Hergé/Tintin coin. |
synth_fc_2729_rep21 | Positive | Physics & Chemistry | Database search | Multi | https://en.wikipedia.org/wiki/Fourier_series | 3 | Common forms of the Fourier series
A Fourier series is a continuous, periodic function created by a summation of harmonically related sinusoidal functions. It has several different, but equivalent, forms, shown here as partial sums. But in theory N → ∞. {\displaystyle N\rightarrow \infty.} The subscripted symbols, called coefficients, and the period, P, {\displaystyle P,} determine the function s N (x) {\displaystyle s_{\scriptscriptstyle N}(x)} as follows:
The harmonics are indexed by an integer, n, {\displaystyle n,} which is also the number of cycles the corresponding sinusoids make in interval P {\displaystyle P}. Therefore, the sinusoids have:
Clearly these series can represent functions that are just a sum of one or more of the harmonic frequencies. The remarkable thing is that it can also represent the intermediate frequencies and/or non-sinusoidal functions because of the infinite number of terms. The amplitude-phase form is particularly useful for its insight into the rationale for the series coefficients. (see § Derivation) The exponential form is most easily generalized for complex-valued functions. (see § Complex-valued functions)
The equivalence of these forms requires certain relationships among the coefficients. For instance, the trigonometric identity:
means that:
Therefore A n {\displaystyle A_{n}} and B n {\displaystyle B_{n}} are the rectangular coordinates of a vector with polar coordinates D n {\displaystyle D_{n}} and φ n. {\displaystyle \varphi _{n}.}
The coefficients can be given/assumed, such as a music synthesizer or time samples of a waveform. In the latter case, the exponential form of Fourier series synthesizes a discrete-time Fourier transform where variable x {\displaystyle x} represents frequency instead of time.
But typically the coefficients are determined by frequency/harmonic analysis of a given real-valued function s (x), {\displaystyle s(x),} and x {\displaystyle x} represents time:
The objective is for s ∞ {\displaystyle s_{\scriptstyle {\infty }}} to converge to s (x) {\displaystyle s(x)} at most or all values of x {\displaystyle x} in an interval of length P. {\displaystyle P.} For the well-behaved functions typical of physical processes, equality is customarily assumed, and the Dirichlet conditions provide sufficient conditions.
The notation ∫ P {\displaystyle \int _{P}} represents integration over the chosen interval. Typical choices are {\displaystyle } and {\displaystyle }. Some authors define P ≜ 2 π {\displaystyle P\triangleq 2\pi } because it simplifies the arguments of the sinusoid functions, at the expense of generality. And some authors assume that s (x) {\displaystyle s(x)} is also P {\displaystyle P} -periodic, in which case s ∞ {\displaystyle s_{\scriptstyle {\infty }}} approximates the entire function. The 2 P {\displaystyle {\tfrac {2}{P}}} scaling factor is explained by taking a simple case: s (x) = cos (2 π k P x). {\displaystyle s(x)=\cos \left(2\pi {\tfrac {k}{P}}x\right).} Only the n = k {\displaystyle n=k} term of Eq.2 is needed for convergence, with A k = 1 {\displaystyle A_{k}=1} and B k = 0. {\displaystyle B_{k}=0.} Accordingly Eq.5 provides: |
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