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https://en.wikipedia.org/wiki/NUTS%20statistical%20regions%20of%20Latvia
The three NUTS (Nomenclature of Territorial Units for Statistics) levels for Latvia (LV) are: NUTS codes LV0 Latvia LV00 Latvia LV003 Kurzeme LV005 Latgale LV006 Rīga LV007 Pierīga LV008 Vidzeme LV009 Zemgale Local administrative units NUTS 3 level is subdivided into LAU 1 units. LAU 1 units are subdivided into LAU 2 units. LAU (Local Administrative Units) in Latvia according to NUTS regulation (up to 31.12.2011): History of changes of LAU 2 codes till 1 July 2009 can be viewed here. LAU in Latvia according to NUTS regulation (starting 01.01.2012): * Due to Administrative Territorial Reform (1 July 2009) administrative districts no longer exist as administrative units in Latvia. Municipalities and parishes amalgamated and formed new LAU 2 units – municipalities. LAU 2 codes from 1 July 2009 updated version. Changes of LAU 2 codes on 1 July 2009 can be viewed here See also Subdivisions of Latvia ISO 3166-2 codes of Latvia FIPS region codes of Latvia Sources Hierarchical list of the Nomenclature of territorial units for statistics - NUTS and the Statistical regions of Europe Correspondence between the NUTS levels and the local administrative units of each EU country List of current NUTS codes Download current NUTS codes (ODS format) Municipalities of Latvia, Statoids.com Latvia Nuts Reform in Latvia
https://en.wikipedia.org/wiki/NUTS%20statistical%20regions%20of%20Malta
In the NUTS (Nomenclature of Territorial Units for Statistics) codes of Malta (MT), the three levels are: NUTS codes MT0 Malta MT00 Malta MT001 Malta (island) MT002 Gozo and Comino Local administrative units Below the NUTS levels, the two LAU (Local Administrative Units) levels are: The LAU codes of Malta can be downloaded here: See also Regions of Malta Subdivisions of Malta ISO 3166-2 codes of Malta Sources Hierarchical list of the Nomenclature of territorial units for statistics - NUTS and the Statistical regions of Europe Overview map of EU Countries - NUTS level 1 MALTA - NUTS level 2 MALTA - NUTS level 2 Correspondence between the NUTS levels and the national administrative units List of current NUTS codes Download current NUTS codes (ODS format) Regions of Malta, Statoids.com Malta Nuts
https://en.wikipedia.org/wiki/Harmonic%20progression%20%28mathematics%29
In mathematics, a harmonic progression (or harmonic sequence) is a progression formed by taking the reciprocals of an arithmetic progression. Equivalently, a sequence is a harmonic progression when each term is the harmonic mean of the neighboring terms. As a third equivalent characterization, it is an infinite sequence of the form where a is not zero and −a/d is not a natural number, or a finite sequence of the form where a is not zero, k is a natural number and −a/d is not a natural number or is greater than k. Examples In the following is a natural number, in sequence: is called the harmonic sequence 12, 6, 4, 3, 30, −30, −10, −6, 10, 30, −30, −10, −6, Sums of harmonic progressions Infinite harmonic progressions are not summable (sum to infinity). It is not possible for a harmonic progression of distinct unit fractions (other than the trivial case where a = 1 and k = 0) to sum to an integer. The reason is that, necessarily, at least one denominator of the progression will be divisible by a prime number that does not divide any other denominator. Use in geometry If collinear points A, B, C, and D are such that D is the harmonic conjugate of C with respect to A and B, then the distances from any one of these points to the three remaining points form harmonic progression. Specifically, each of the sequences AC, AB, AD; BC, BA, BD; CA, CD, CB; and DA, DC, DB are harmonic progressions, where each of the distances is signed according to a fixed orientation of the line. In a triangle, if the altitudes are in arithmetic progression, then the sides are in harmonic progression. Leaning Tower of Lire An excellent example of Harmonic Progression is the Leaning Tower of Lire. In it, uniform blocks are stacked on top of each other to achieve the maximum sideways or lateral distance covered. The blocks are stacked 1/2, 1/4, 1/6, 1/8, 1/10, … distance sideways below the original block. This ensures that the center of gravity is just at the center of the structure so that it does not collapse. A slight increase in weight on the structure causes it to become unstable and fall. See also Geometric progression Harmonic series List of sums of reciprocals Harmonics (in music) References Mastering Technical Mathematics by Stan Gibilisco, Norman H. Crowhurst, (2007) p. 221 Standard mathematical tables by Chemical Rubber Company (1974) p. 102 Essentials of algebra for secondary schools by Webster Wells (1897) p. 307 Mathematical series Sequences and series
https://en.wikipedia.org/wiki/Wim%20Volkers
Willem Frederik Volkers (3 October 1899 – 4 January 1990) was a Dutch football player and coach. Career statistics International goals References External links VoetbalStats.nl AFC Ajax official profile 1899 births 1990 deaths Dutch men's footballers Netherlands men's international footballers Dutch football managers AFC Ajax players AFC Ajax managers AFC Ajax chairmen and investors Footballers from Amsterdam Men's association football forwards
https://en.wikipedia.org/wiki/Mirko%20Kramari%C4%87
Mirko Kramarić (; born 27 January 1989) is a Croatian professional footballer who plays for Luxembourg National Division club FC Etzella Ettelbruck. Career statistics References External links All appearances in 2HNL season 08-09 All appearances in Croatia U17 national team All appearances in Alisontia Steinsel All appearances in Norway List of national team appearances at official website of Croatian Football Federation Mirko Kramarić at Fupa.net Mirko Kramarić photo at UEFA.com Squad number history at Sport.de 1989 births Living people Footballers from Zagreb Men's association football fullbacks Croatian men's footballers Croatia men's youth international footballers NK Lokomotiva Zagreb players NK Inter Zaprešić players NK Istra 1961 players FK Haugesund players FK Željezničar Sarajevo players NK Radomlje players NK Brežice 1919 players FC Etzella Ettelbruck players Croatian Football League players First Football League (Croatia) players Eliteserien players Premier League of Bosnia and Herzegovina players Slovenian PrvaLiga players Slovenian Second League players Luxembourg Division of Honour players Luxembourg National Division players Croatian expatriate men's footballers Expatriate men's footballers in Norway Croatian expatriate sportspeople in Norway Expatriate men's footballers in Bosnia and Herzegovina Croatian expatriate sportspeople in Bosnia and Herzegovina Expatriate men's footballers in Slovenia Croatian expatriate sportspeople in Slovenia Expatriate men's footballers in Luxembourg Croatian expatriate sportspeople in Luxembourg
https://en.wikipedia.org/wiki/Vladimir%20Rokhlin%20Jr.
Vladimir Rokhlin Jr. (born August 4, 1952) is a mathematician and professor of computer science and mathematics at Yale University. He is the co-inventor with Leslie Greengard of the fast multipole method (FMM) in 1985, recognised as one of the top-ten algorithms of the 20th century. In 2008, Rokhlin was elected as a member into the National Academy of Engineering for the development of fast multipole algorithms and their application to electromagnetic and acoustic scattering. Short biography Vladimir Rokhlin Jr. was born on August 4, 1952, in Voronezh, USSR (now Russia). In 1973 he received a M.S. in mathematics from the University of Vilnius in Lithuania, and in 1983 a Ph.D. in applied mathematics from Rice University located in Houston, Texas, United States. In 1985 Rokhlin started working at Yale University located in New Haven, Connecticut, United States, where he is now professor of computer science and mathematics. He is the son of Soviet mathematician Vladimir Abramovich Rokhlin. Awards and honors Rokhlin has received several awards and honors, including: the Leroy P. Steele Prize for Seminal Contribution to Research from the American Mathematical Society in 2001 (together with Leslie F. Greengard), for their paper describing a new algorithm: the fast multipole method (FMM) the "Rice University Distinguished Alumni Award" in 2001 elected a member of both the U.S. National Academy of Engineering (2008) and the U.S. National Academy of Sciences (1999) the IEEE Honorary Membership in 2006. elected to fellow of the Society for Industrial and Applied Mathematics in 2009 the ICIAM Maxwell Prize from the International Council for Industrial and Applied Mathematics in 2011 The William Benter Prize in Applied Mathematics from the Liu Bie Ju Centre for Mathematical Sciences in 2014 Fellow of the American Academy of Arts and Sciences, 2016 References External links Russian mathematicians Russian inventors Soviet emigrants to the United States American people of Russian-Jewish descent Fellows of the Society for Industrial and Applied Mathematics Rice University alumni Vilnius University alumni Yale University faculty 20th-century American mathematicians 21st-century American mathematicians Living people 1952 births Members of the United States National Academy of Sciences Members of the United States National Academy of Engineering Fellows of the American Academy of Arts and Sciences
https://en.wikipedia.org/wiki/Li%20Ling%20Fung
Li Ling Fung (, born 3 January 1986) is a former Hong Kong professional footballer who played as a striker or an attacking midfielder. Career statistics Club As of 11 August 2009. References External links Player information on HKFA site Player Information on tswpegasus.com (in Chinese) 1986 births Living people Hong Kong men's footballers Hong Kong First Division League players South China AA players Hong Kong Pegasus FC players Men's association football forwards
https://en.wikipedia.org/wiki/Li%20Jian%20%28footballer%2C%20born%20September%201985%29
Li Jian (, born 19 September 1985 in China) is a former Chinese-born Hong Kong professional footballer who played as a goalkeeper. Career statistics Club career As of 11 September 2009 External links Li Jian at HKFA Player Information on tswpegasus.com 1985 births Living people Chinese men's footballers Footballers from Guangdong Hong Kong men's footballers Men's association football goalkeepers Hong Kong First Division League players Expatriate men's footballers in Hong Kong Hong Kong Rangers FC players Kitchee SC players Hong Kong Pegasus FC players Chinese expatriate sportspeople in Hong Kong
https://en.wikipedia.org/wiki/Mn%C3%ABv%27s%20universality%20theorem
In algebraic geometry, Mnëv's universality theorem is a result which can be used to represent algebraic (or semi algebraic) varieties as realizations of oriented matroids, a notion of combinatorics. Oriented matroids For the purposes of Mnëv's universality, an oriented matroid of a finite subset is a list of all partitions of points in induced by hyperplanes in . In particular, the structure of oriented matroid contains full information on the incidence relations in , inducing on a matroid structure. The realization space of an oriented matroid is the space of all configurations of points inducing the same oriented matroid structure on . Stable equivalence of semialgebraic sets For the purposes of universality, the stable equivalence of semialgebraic sets is defined as follows. Let and be semialgebraic sets, obtained as a disconnected union of connected semialgebraic sets We say that and are rationally equivalent if there exist homeomorphisms defined by rational maps. Let be semialgebraic sets, with mapping to under the natural projection deleting the last coordinates. We say that is a stable projection if there exist integer polynomial maps such that The stable equivalence is an equivalence relation on semialgebraic subsets generated by stable projections and rational equivalence. Mnëv's universality theorem Theorem (Mnëv's universality theorem): Let be a semialgebraic subset in defined over integers. Then is stably equivalent to a realization space of a certain oriented matroid. History Mnëv's universality theorem was discovered by Nikolai Mnëv in his 1986 Ph.D. thesis. It has numerous applications in algebraic geometry, due to Laurent Lafforgue, Ravi Vakil and others, allowing one to construct moduli spaces with arbitrarily bad behaviour. This theorem together with Kempe's universality theorem have been used also by Kapovich and Millson in the study of the moduli spaces of linkages and arrangements. See also Convex Polytopes a book that includes material on the theorem and its relation to the realizability of polytopes from their combinatorial structures. References Further reading Real algebraic geometry Oriented matroids Theorems in algebraic geometry Theorems in combinatorics
https://en.wikipedia.org/wiki/FC%20Kremin%20Kremenchuk%20statistics
FC Kremin Kremenchuk is a Ukrainian sports club. This article contains historical and current statistics and records pertaining to the club. Recent seasons Statistics in Ukrainian Premier League Seasons in Premier League: 6 Best position in Premier League: 9 (2 times) Worst position in Premier League: 15 (2 times) Longest consecutive wins in Premier League: 14 (2005–06) Longest unbeaten run in League matches: () Longest unbeaten run at home in league matches: matches () Longest winning run in the League (home): matches () Longest scoring run in the League: matches () Longest scoring run in the League (home): matches () Most goals scored in a season: 46 (1995–96) Most goals scored in a match: Kremin 6 - Karpaty 1 (1949–50) Most goals conceded in a match: Bukovyna 6 - Kremin 0 (11 October 1992) Most wins in a league season: 14 (1995–96) Most draws in a league season: 11 (1992–93) Most defeats in a league season: 20 (1996–97) Fewest wins in a league season: 4 (1992) Fewest draws in a league season: 3 (1996–97) Fewest defeats in a league season: 6 (1992) Most Point Before Winter Break: points () Historical classification of Premier League: 19 Players Internationals First international for Ukraine: Ihor Zhabchenko against Belarus (28 October 1992) Other international players for Turkmenistan: Ýuriý Magdiýew and Muslim Agaýew Most international caps as a Kremin player: 1 - Ihor Zhabchenko - Ukraine References Statistics
https://en.wikipedia.org/wiki/Johansen%20test
In statistics, the Johansen test, named after Søren Johansen, is a procedure for testing cointegration of several, say k, I(1) time series. This test permits more than one cointegrating relationship so is more generally applicable than the Engle–Granger test which is based on the Dickey–Fuller (or the augmented) test for unit roots in the residuals from a single (estimated) cointegrating relationship. There are two types of Johansen test, either with trace or with eigenvalue, and the inferences might be a little bit different. The null hypothesis for the trace test is that the number of cointegration vectors is r = r* < k, vs. the alternative that r = k. Testing proceeds sequentially for r* = 1,2, etc. and the first non-rejection of the null is taken as an estimate of r. The null hypothesis for the "maximum eigenvalue" test is as for the trace test but the alternative is r = r* + 1 and, again, testing proceeds sequentially for r* = 1,2,etc., with the first non-rejection used as an estimator for r. Just like a unit root test, there can be a constant term, a trend term, both, or neither in the model. For a general VAR(p) model: There are two possible specifications for error correction: that is, two vector error correction models (VECM): 1. The longrun VECM: where 2. The transitory VECM: where Be aware that the two are the same. In both VECM, Inferences are drawn on Π, and they will be the same, so is the explanatory power. References Further reading Mathematical finance Time series statistical tests
https://en.wikipedia.org/wiki/L-moment
In statistics, L-moments are a sequence of statistics used to summarize the shape of a probability distribution. They are linear combinations of order statistics (L-statistics) analogous to conventional moments, and can be used to calculate quantities analogous to standard deviation, skewness and kurtosis, termed the L-scale, L-skewness and L-kurtosis respectively (the L-mean is identical to the conventional mean). Standardised L-moments are called L-moment ratios and are analogous to standardized moments. Just as for conventional moments, a theoretical distribution has a set of population L-moments. Sample L-moments can be defined for a sample from the population, and can be used as estimators of the population L-moments. Population L-moments For a random variable , the th population L-moment is where denotes the th order statistic (th smallest value) in an independent sample of size from the distribution of and denotes expected value operator. In particular, the first four population L-moments are Note that the coefficients of the th L-moment are the same as in the th term of the binomial transform, as used in the -order finite difference (finite analog to the derivative). The first two of these L-moments have conventional names: is the "mean", "L-mean", or "L-location", is the "L-scale". The L-scale is equal to half the Mean absolute difference. Sample L-moments The sample L-moments can be computed as the population L-moments of the sample, summing over r-element subsets of the sample hence averaging by dividing by the binomial coefficient: Grouping these by order statistic counts the number of ways an element of an  element sample can be the th element of an  element subset, and yields formulas of the form below. Direct estimators for the first four L-moments in a finite sample of  observations are: where is the th order statistic and is a binomial coefficient. Sample L-moments can also be defined indirectly in terms of probability weighted moments, which leads to a more efficient algorithm for their computation. L-moment ratios A set of L-moment ratios, or scaled L-moments, is defined by The most useful of these are called the L-skewness, and the L-kurtosis. L-moment ratios lie within the interval Tighter bounds can be found for some specific L-moment ratios; in particular, the L-kurtosis lies in and A quantity analogous to the coefficient of variation, but based on L-moments, can also be defined: which is called the "coefficient of L-variation", or "L-CV". For a non-negative random variable, this lies in the interval and is identical to the Gini coefficient. Related quantities L-moments are statistical quantities that are derived from probability weighted moments (PWM) which were defined earlier (1979). PWM are used to efficiently estimate the parameters of distributions expressable in inverse form such as the Gumbel, the Tukey, and the Wakeby distributions. Usage There are two common ways that L-moments are
https://en.wikipedia.org/wiki/List%20of%20the%20busiest%20airports%20in%20the%20Baltic%20states
This is a list of the busiest airports in the Baltic states in terms of total number of Passengers, Aircraft movements and Freight and Mail Tonnes per year. The statistics includes major airports in the Baltic States with commercial regular traffic. Aircraft movements and Freight and Mail Tonnes only include statistics for the 5 busiest airports in 2012 since reliable data is not available for all airports. Included are also a list of the Busiest Air Routes to/from and between the Baltic States for 2011 and 2012, data for 2019 will be added as soon as the data becomes available. Passengers Graph Summary Table 2022 statistics Estonia also has four small airports with scheduled flights to some islands: Kärdla Airport, Kuressaare Airport, Pärnu Airport and Ruhnu Airfield. 2021 statistics 2020 statistics 2019 statistics 2018 statistics 2017 statistics 2013 statistics 2012 statistics Aircraft movements 2019 statistics 2012 statistics Freight and Mail Tonnes 2021 statistics 2012 statistics Busiest Air Routes Busiest nonstop air routes within and to/from the Baltic States based on total annually carried passengers on each route. Inter-Baltic routes are Bolded. 2022 statistics 21 unique destinations and two Inter-Baltic connections appear within the Top 45.Locations with multiple connections were: (5) London, (3) Antalya, Dublin, Frankfurt, Helsinki, Milan, Stockholm, Warsaw, (2) Copenhagen, Istanbul, Oslo, and Paris. Source 2010s 2019 statistics Source 2011 statistics The routes ranked no 1, 2, 5, 10, 11, 12, 14, 17 and 22 includes the following airports: No 1: London Stansted Airport and Gatwick Airport No 2: London Stansted Airport, London Luton Airport and Gatwick Airport No 5: Stockholm Arlanda Airport and Stockholm Skavsta Airport No 10: Gatwick Airport, London Stansted Airport and London Luton Airport No 11: Milan Malpensa Airport and Orio al Serio Airport No 12: Brussels Airport and Brussels South Charleroi Airport No 14: Stockholm Arlanda Airport and Stockholm Skavsta Airport No 17: London Luton Airport and London Stansted Airport No 22: Oslo Airport, Gardermoen and Moss Airport, Rygge Gallery See also List of airports in Estonia List of airports in Latvia List of airports in Lithuania List of the busiest airports in the Nordic countries List of the busiest airports in the former Soviet Union List of the busiest airports in Europe Notes References State Joint Stock Company (SJSC) Riga International Airport of the Republic of Latvia Tallinn Airport Ltd State Enterprise Vilnius International Airport State Enterprise Kaunas International Airport State Enterprise Palanga International Airport Baltic states Baltic states-related lists Busiest Busiest Busiest Baltic States Estonia transport-related lists Latvia transport-related lists Lithuania transport-related lists
https://en.wikipedia.org/wiki/Benalto
Benalto is a hamlet in central Alberta, Canada within Red Deer County. It is located approximately west of the Town of Sylvan Lake. Benalto is also recognized by Statistics Canada as a designated place. Kountry Meadows, a manufactured home community and designated place recognized by Statistics Canada, is immediately adjacent to the Hamlet of Benalto. Although it forms part of the community, the hamlet's boundaries do not include the manufactured home park at this time. Demographics In the 2021 Census of Population conducted by Statistics Canada, Benalto had a population of 198 living in 65 of its 66 total private dwellings, a change of from its 2016 population of 177. With a land area of , it had a population density of in 2021. As a designated place in the 2016 Census of Population conducted by Statistics Canada, Benalto had a population of 177 living in 63 of its 66 total private dwellings, a change of from its 2011 population of 175. With a land area of , it had a population density of in 2016. See also List of communities in Alberta List of designated places in Alberta List of hamlets in Alberta References Hamlets in Alberta Designated places in Alberta Red Deer County
https://en.wikipedia.org/wiki/Principles%20of%20Geometry
Principles of Geometry is an electronic music band from Lille, France, which consists of Guillaume Grosso and Jeremy Duval. Discography Albums Principles Of Geometry (2005, Tigersushi) Lazare (2007, Tigersushi) Burn the Land and Boil the Oceans (2012, Tigersushi) Meanstream (2014, Tigersushi) ABCDEFGHIJKLMNOPQRSTUVWXYZ (2022, Tigersushi) Singles, 12" and 7" A Mountain For President EP (2007, Tigersushi) Interstate Highway System (2008, Tigersushi) The Effect Of Adding Another Zero (Principles Of Geometry's Distributive & Associative Part One) (2009, Tigersushi/Pandamaki Records) P.O.G vs. THE EDITS EP (edits by KRIKOR, PILOOSKI & JOAKIM) (2011, Tigersushi Records) Remixes External links Label Tigersushi, Principles of Geometry publishing company Official Myspace Official Facebook Page Official Facebook group References http://www.forcedexposure.com/artists/principles.of.geometry.html French electronic music groups Musical groups from Hauts-de-France
https://en.wikipedia.org/wiki/Perfect%20digit-to-digit%20invariant
In number theory, a perfect digit-to-digit invariant (PDDI; also known as a Munchausen number) is a natural number in a given number base that is equal to the sum of its digits each raised to the power of itself. An example in base 10 is 3435, because . The term "Munchausen number" was coined by Dutch mathematician and software engineer Daan van Berkel in 2009, as this evokes the story of Baron Munchausen raising himself up by his own ponytail because each digit is raised to the power of itself. Definition Let be a natural number which can be written in base as the k-digit number where each digit is between and inclusive, and . We define the function as . (As 00 is usually undefined, there are typically two conventions used, one where it is taken to be equal to one, and another where it is taken to be equal to zero.) A natural number is defined to be a perfect digit-to-digit invariant in base b if . For example, the number 3435 is a perfect digit-to-digit invariant in base 10 because . for all , and thus 1 is a trivial perfect digit-to-digit invariant in all bases, and all other perfect digit-to-digit invariants are nontrivial. For the second convention where , both and are trivial perfect digit-to-digit invariants. A natural number is a sociable digit-to-digit invariant if it is a periodic point for , where for a positive integer , and forms a cycle of period . A perfect digit-to-digit invariant is a sociable digit-to-digit invariant with . An amicable digit-to-digit invariant is a sociable digit-to-digit invariant with . All natural numbers are preperiodic points for , regardless of the base. This is because all natural numbers of base with digits satisfy . However, when , then , so any will satisfy until . There are a finite number of natural numbers less than , so the number is guaranteed to reach a periodic point or a fixed point less than , making it a preperiodic point. This means also that there are a finite number of perfect digit-to-digit invariant and cycles for any given base . The number of iterations needed for to reach a fixed point is the -factorion function's persistence of , and undefined if it never reaches a fixed point. Perfect digit-to-digit invariants and cycles of Fb for specific b All numbers are represented in base . Convention 00 = 1 Convention 00 = 0 Programming examples The following program in Python determines whether an integer number is a Munchausen Number / Perfect Digit to Digit Invariant or not, following the convention . num = int(input("Enter number:")) temp = num s = 0.0 while num > 0: digit = num % 10 num //= 10 s+= pow(digit, digit) if s == temp: print("Munchausen Number") else: print("Not Munchausen Number") The examples below implements the perfect digit-to-digit invariant function described in the definition above to search for perfect digit-to-digit invariants and cycles in Python for the two conventions. Convention 00 = 1 def pddif(x: in
https://en.wikipedia.org/wiki/Stephen%20LaBerge
Stephen LaBerge (born 1947) is an American psychophysiologist specializing in the scientific study of lucid dreaming. In 1967 he received his bachelor's degree in mathematics. He began researching lucid dreaming for his Ph.D. in psychophysiology at Stanford University, which he received in 1980. He developed techniques to enable himself and other researchers to enter a lucid dream state at will, most notably the MILD technique (mnemonic induction of lucid dreams), which was used in many forms of dream experimentation. In 1987, he founded The Lucidity Institute, an organization that promotes research into lucid dreaming, as well as running courses for the general public on how to achieve a lucid dream. In the early 1980s, news of LaBerge's research using the technique of signalling to a collaborator monitoring his EEG with agreed-upon eye movements during REM helped to popularise lucid dreaming in the American media. Research results Results from LaBerge's lab and others include: comparison of subjective sense of time in dreams versus the waking state using eye signals comparison of electrical activity in the brain when singing while awake, and while in a dream various studies comparing physiological sexual arousal and in-dream sex and orgasm Lucid dreaming education and facilitation LaBerge developed a series of devices to help users enter a lucid state while dreaming. The original device was called a DreamLight, which was discontinued in favor of the NovaDreamer, designed by experienced lucid dreamer Craig Webb for the Lucidity Institute while he worked there and participated in lucid dreaming research at Stanford. As of 2013 it was not possible to purchase these devices from the Lucidity Institute website. An improved version, the NovaDreamer II, is a mask with flashing lights that measures eye movement. All of the devices consist of a mask worn over the eyes with LEDs positioned over the eyelids. The LEDs flash whenever the mask detects that the wearer has entered REM sleep. The stimulus is incorporated into the wearer's dreams and can be recognised as a sign that they are dreaming. LaBerge currently lectures at universities and other professional institutions, and hosts lucid dreaming sessions at various locations. Bibliography LaBerge has produced several books and tapes about lucid dreaming. References External links The Lucidity Institute LaBerge, S. (1980). Lucid dreaming: An exploratory study of consciousness during sleep. (Ph.D. thesis, Stanford University, 1980), (University Microfilms No. 80-24, 691) 21st-century American psychologists American psychology writers American male non-fiction writers American self-help writers Lucid dreams Sleep researchers Stanford University alumni 1947 births Living people Oneirologists 20th-century American psychologists
https://en.wikipedia.org/wiki/List%20of%20Major%20League%20Baseball%20career%20WHIP%20leaders
In baseball statistics, walks plus hits per inning pitched (WHIP) is a sabermetric measurement of the number of baserunners a pitcher has allowed per inning pitched. WHIP reflects a pitcher's propensity for allowing batters to reach base, therefore a lower WHIP indicates better performance. WHIP is calculated by adding the number of walks and hits allowed and dividing this sum by the number of innings pitched. Below is the list of the top 100 Major League Baseball pitchers in Walks plus hits per inning pitched (WHIP) with at least 1,000 innings pitched. Addie Joss is the all-time leader with a career WHIP of 0.9678. Jacob deGrom (0.9947) and Ed Walsh (0.9996) are the only other players with a career WHIP under 1.0000. Key List Stats updated as of September 30, 2023. Notes References External links Major League Baseball statistics WHIP
https://en.wikipedia.org/wiki/Sa%C5%A1a%20Zimonji%C4%87
Saša Zimonjić (Serbian Cyrillic: Саша Зимоњић; born 9 April 1978) is a Serbian former professional footballer. Statistics External links Saša Zimonjić at LevskiSofia.info Men's association football midfielders Expatriate men's footballers in Bosnia and Herzegovina Expatriate men's footballers in Bulgaria Expatriate men's footballers in Greece Expatriate men's footballers in Sweden FK Borac Čačak players FK Obilić players FK Slavija Sarajevo players FK Železnik players Mjällby AIF players Panionios F.C. players Footballers from Čačak PFC Levski Sofia players Serbia and Montenegro men's under-21 international footballers Serbia and Montenegro men's footballers Serbian expatriate men's footballers Serbian men's footballers 1978 births Living people
https://en.wikipedia.org/wiki/Separable%20permutation
In combinatorial mathematics, a separable permutation is a permutation that can be obtained from the trivial permutation 1 by direct sums and skew sums. Separable permutations may be characterized by the forbidden permutation patterns 2413 and 3142; they are also the permutations whose permutation graphs are cographs and the permutations that realize the series-parallel partial orders. It is possible to test in polynomial time whether a given separable permutation is a pattern in a larger permutation, or to find the longest common subpattern of two separable permutations. Definition and characterization define a separable permutation to be a permutation that has a separating tree: a rooted binary tree in which the elements of the permutation appear (in permutation order) at the leaves of the tree, and in which the descendants of each tree node form a contiguous subset of these elements. Each interior node of the tree is either a positive node in which all descendants of the left child are smaller than all descendants of the right node, or a negative node in which all descendants of the left node are greater than all descendants of the right node. There may be more than one tree for a given permutation: if two nodes that are adjacent in the same tree have the same sign, then they may be replaced by a different pair of nodes using a tree rotation operation. Each subtree of a separating tree may be interpreted as itself representing a smaller separable permutation, whose element values are determined by the shape and sign pattern of the subtree. A one-node tree represents the trivial permutation, a tree whose root node is positive represents the direct sum of permutations given by its two child subtrees, and a tree whose root node is negative represents the skew sum of the permutations given by its two child subtrees. In this way, a separating tree is equivalent to a construction of the permutation by direct and skew sums, starting from the trivial permutation. As prove, separable permutations may also be characterized in terms of permutation patterns: a permutation is separable if and only if it contains neither 2413 nor 3142 as a pattern. The separable permutations also have a characterization from algebraic geometry: if a collection of distinct real polynomials all have equal values at some number , then the permutation that describes how the numerical ordering of the polynomials changes at is separable, and every separable permutation can be realized in this way. Combinatorial enumeration The separable permutations are enumerated by the Schröder numbers. That is, there is one separable permutation of length one, two of length two, and in general the number of separable permutations of a given length (starting with length one) is 1, 2, 6, 22, 90, 394, 1806, 8558, .... This result was proven for a class of permutation matrices equivalent to the separable permutations by , by using a canonical form of the separating tree in which the righ
https://en.wikipedia.org/wiki/Permutation%20pattern
In combinatorial mathematics and theoretical computer science, a permutation pattern is a sub-permutation of a longer permutation. Any permutation may be written in one-line notation as a sequence of digits representing the result of applying the permutation to the digit sequence 123...; for instance the digit sequence 213 represents the permutation on three elements that swaps elements 1 and 2. If π and σ are two permutations represented in this way (these variable names are standard for permutations and are unrelated to the number pi), then π is said to contain σ as a pattern if some subsequence of the digits of π has the same relative order as all of the digits of σ. For instance, permutation π contains the pattern 213 whenever π has three digits x, y, and z that appear within π in the order x...y...z but whose values are ordered as y < x < z, the same as the ordering of the values in the permutation 213. The permutation 32415 on five elements contains 213 as a pattern in several different ways: 3··15, ··415, 32··5, 324··, and ·2·15 all form triples of digits with the same ordering as 213. Each of the subsequences 315, 415, 325, 324, and 215 is called a copy, instance, or occurrence of the pattern. The fact that π contains σ is written more concisely as σ ≤ π. If a permutation π does not contain a pattern σ, then π is said to avoid σ. The permutation 51342 avoids 213; it has 10 subsequences of three digits, but none of these 10 subsequences has the same ordering as 213. Early results A case can be made that was the first to prove a result in the field with his study of "lattice permutations". In particular MacMahon shows that the permutations which can be divided into two decreasing subsequences (i.e., the 123-avoiding permutations) are counted by the Catalan numbers. Another early landmark result in the field is the Erdős–Szekeres theorem; in permutation pattern language, the theorem states that for any positive integers a and b every permutation of length at least must contain either the pattern or the pattern . Computer science origins The study of permutation patterns began in earnest with Donald Knuth's consideration of stack-sorting in 1968. Knuth showed that the permutation π can be sorted by a stack if and only if π avoids 231, and that the stack-sortable permutations are enumerated by the Catalan numbers. Knuth also raised questions about sorting with deques. In particular, Knuth's question asking how many permutation of n elements are obtainable with the use of a deque remains open. Shortly thereafter, investigated sorting by networks of stacks, while showed that the permutation π can be sorted by a deque if and only if for all k, π avoids 5,2,7,4,...,4k+1,4k−2,3,4k,1, and 5,2,7,4,...,4k+3,4k,1,4k+2,3, and every permutation that can be obtained from either of these by interchanging the last two elements or the 1 and the 2. Because this collection of permutations is infinite (in fact, it is the first published examp
https://en.wikipedia.org/wiki/Jinchao%20Xu
Jinchao Xu (许进超, born 1961) is an American-Chinese mathematician. He is currently the Verne M. Willaman Professor in the Department of Mathematics at the Pennsylvania State University, University Park. He is known for his work on multigrid methods, domain decomposition methods, finite element methods, and more recently deep neural networks. Academic Biography Xu received his bachelor's degree from the Xiangtan University in 1982, his master's degree from the Peking University in 1984, and his doctoral degree from the Cornell University in 1989. He joined the Pennsylvania State University (Penn State) in 1989 as assistant professor of mathematics, was promoted to associate professor in 1991, and to professor in 1995. He was named a Distinguished Professor of Mathematics in 2007, the Francis R. and Helen M. Pentz Professor of Science in 2010, and the Verne M. Willaman Professor of Mathematics in 2015. He is currently the director of the Center for Computational Mathematics and Applications at Penn State. Xu serves on the editorial boards of many major journals in computational mathematics and co-edits many conference proceedings and research monographs. He also serves on various college and departmental committees and organizes numerous colloquiums and seminars. He has organized or served as a scientific committee member for more than 65 international conferences, workshops, and summer schools. Research Interests and Contributions Xu is an advocate of the idea that practical applications and theoretical completeness and beauty can go together. He studies numerical methods for partial differential equations and big data, especially finite element methods, multigrid methods, and deep neural networks, for their theoretical analysis, algorithmic development, and practical applications. He is well known for many groundbreaking studies in developing, designing, and analyzing fast methods for finite element discretization and for the solution of large-scale systems of equations, including several basic theories and algorithms that bear his name: the Bramble-Pasciak-Xu (BPX) preconditioner, the Hiptmair-Xu (HX) preconditioner, the Xu-Zikatanov (XZ) identity, and the Morley-Wang-Xu (MWX) element. The BPX-preconditioner is one of the two fundamental multigrid algorithms for solving large-scale discretized partial differential equations; the HX-preconditioner, which was featured in 2008 by the U.S. Department of Energy as one of the top 10 breakthroughs in computational science in recent years, is one of the most efficient solvers for the numerical simulation of electro-magnetic problems; the XZ-identity is a basic technical tool that can be used for the design and analysis of iterative methods such as the multigrid method and the method of alternating projections; the MWX-element is the only known class of finite elements universally constructed for elliptic partial differential equations of any order in any spatial dimension. Xu has published nearly 200
https://en.wikipedia.org/wiki/Yevgeni%20Klimov
Yevgeni Yuryevich Klimov (; born 21 January 1985) is a Kazakhstani former professional footballer. He also holds Russian citizenship. Career statistics International Statistics accurate as of match played 29 February 2012 References External links 1985 births Living people Kazakhstani men's footballers Men's association football defenders Kazakhstan men's international footballers PFC CSKA Moscow players PFC Dynamo Stavropol players FC Vostok players FC Bayterek players Place of birth missing (living people) Expatriate men's footballers in Russia
https://en.wikipedia.org/wiki/2009%20Cambodian%20League
Statistics of Cambodian League for the 2009 season. League table Playoffs Semi-finals Third place Final Top scorers References C-League seasons Cambodia Cambodia 1
https://en.wikipedia.org/wiki/Great%20dirhombicosidodecacron
In geometry, the great dirhombicosidodecacron is a nonconvex isohedral polyhedron. It is the dual of the great dirhombicosidodecahedron. In Magnus Wenninger's Dual Models, it is represented with intersecting infinite prisms passing through the model center, cut off at a certain point that is convenient for the maker. Wenninger suggested these figures are members of a new class of stellation polyhedra, called stellation to infinity. However, he also acknowledged that strictly speaking they are not polyhedra because their construction does not conform to the usual definitions. References p. 139 External links Dual uniform polyhedra
https://en.wikipedia.org/wiki/Great%20pentagrammic%20hexecontahedron
In geometry, the great pentagrammic hexecontahedron (or great dentoid ditriacontahedron) is a nonconvex isohedral polyhedron. It is the dual of the great retrosnub icosidodecahedron. Its 60 faces are irregular pentagrams. Proportions Denote the golden ratio by . Let be the largest positive zero of the polynomial . Then each pentagrammic face has four equal angles of and one angle of . Each face has three long and two short edges. The ratio between the lengths of the long and the short edges is given by . The dihedral angle equals . Part of each face lies inside the solid, hence is invisible in solid models. The other two zeroes of the polynomial play a similar role in the description of the great pentagonal hexecontahedron and the great inverted pentagonal hexecontahedron. References External links Dual uniform polyhedra
https://en.wikipedia.org/wiki/Great%20rhombidodecacron
In geometry, the great rhombidodecacron (or Great dipteral ditriacontahedron) is a nonconvex isohedral polyhedron. It is the dual of the great rhombidodecahedron. It is visually identical to the great deltoidal hexecontahedron. Its faces are antiparallelograms. Proportions Each antiparallelogram has two angles of and two angles of . The diagonals of each antiparallelogram intersect at an angle of . The dihedral angle equals . The ratio between the lengths of the long edges and the short ones equals , which is the golden ratio. Part of each face lies inside the solid, hence is invisible in solid models. References p. 88 External links Dual uniform polyhedra
https://en.wikipedia.org/wiki/Small%20hexagrammic%20hexecontahedron
In geometry, the small hexagrammic hexecontahedron is a nonconvex isohedral polyhedron. It is the dual of the small retrosnub icosicosidodecahedron. It is partially degenerate, having coincident vertices, as its dual has coplanar triangular faces. Geometry Its faces are hexagonal stars with two short and four long edges. Denoting the golden ratio by and putting , the stars have five equal angles of and one of . Each face has four long and two short edges. The ratio between the edge lengths is . The dihedral angle equals . Part of each face is inside the solid, hence is not visible in solid models. References External links Dual uniform polyhedra
https://en.wikipedia.org/wiki/Great%20hexagonal%20hexecontahedron
In geometry, the great hexagonal hexecontahedron (or great astroid ditriacontahedron) is a nonconvex isohedral polyhedron. It is the dual of the uniform great snub dodecicosidodecahedron. It is partially degenerate, having coincident vertices, as its dual has coplanar pentagrammic faces. Proportions The faces are nonconvex hexagons. Denoting the golden ratio by , the hexagons have one angle of , one of , and four angles of . They have two long edges, two of medium length and two short ones. If the long edges have length , the medium ones have length and the short ones . The dihedral angle equals . References External links Dual uniform polyhedra
https://en.wikipedia.org/wiki/Great%20triakis%20icosahedron
In geometry, the great triakis icosahedron is a nonconvex isohedral polyhedron. It is the dual of the uniform great stellated truncated dodecahedron. Its faces are isosceles triangles. Part of each triangle lies within the solid, hence is invisible in solid models. Proportions The triangles have one angle of and two of . The dihedral angle equals . See also Triakis icosahedron References External links Dual uniform polyhedra
https://en.wikipedia.org/wiki/Great%20disdyakis%20dodecahedron
In geometry, the great disdyakis dodecahedron is a nonconvex isohedral polyhedron. It is the dual of the uniform great truncated cuboctahedron. It has 48 triangular faces. Proportions The triangles have one angle of , one of and one of . The dihedral angle equals . Part of each triangle lies within the solid, hence is invisible in solid models. Related polyhedra The great disdyakis dodecahedron is topologically identical to the convex Catalan solid, disdyakis dodecahedron, which is dual to the truncated cuboctahedron. References External links Dual uniform polyhedra
https://en.wikipedia.org/wiki/Small%20icosacronic%20hexecontahedron
In geometry, the small icosacronic hexecontahedron (or small lanceal trisicosahedron) is a nonconvex isohedral polyhedron. It is the dual of the uniform small icosicosidodecahedron. Its faces are kites. Part of each kite lies inside the solid, hence is invisible in solid models. Proportions The kites have two angles of , one of and one of . The dihedral angle equals . The ratio between the lengths of the long and short edges is . References External links Dual uniform polyhedra
https://en.wikipedia.org/wiki/Small%20hexagonal%20hexecontahedron
In geometry, the small hexagonal hexecontahedron is a nonconvex isohedral polyhedron. It is the dual of the uniform small snub icosicosidodecahedron. It is partially degenerate, having coincident vertices, as its dual has coplanar triangular faces. Geometry Treating it as a simple non-convex solid (without intersecting surfaces), it has 180 faces (all triangles), 270 edges, and 92 vertices (twelve with degree 10, twenty with degree 12, and sixty with degree 3), giving an Euler characteristic of 92 − 270 + 180 = +2. Faces The faces are irregular hexagons with two short and four long edges. Denoting the golden ratio by and putting , the hexagons have five equal angles of and one of . Each face has four long and two short edges. The ratio between the edge lengths is . The dihedral angle equals . Construction Disregarding self-intersecting surfaces, the small hexagonal hexecontahedron can be constructed as a Kleetope of a pentakis dodecahedron. It is therefore a second order Kleetope of the regular dodecahedron. In other words, by adding a shallow pentagonal pyramid to each face of a regular dodecahedron, we get a pentakis dodecahedron. By adding an even shallower triangular pyramid to each face of the pentakis dodecahedron, we get a small hexagonal hexecontahedron. The 60 vertices of degree 3 correspond to the apex vertex of each triangular pyramid of the Kleetope, or to each face of the pentakis dodecahedron. The 20 vertices of degree 12 and 12 vertices of degree 10 correspond to the vertices of the pentakis dodecahedron, and also respectively to the 20 hexagons and 12 pentagons of the truncated icosahedron, the dual solid to the pentakis dodecahedron. References External links Dual uniform polyhedra
https://en.wikipedia.org/wiki/Great%20ditrigonal%20dodecacronic%20hexecontahedron
In geometry, the great ditrigonal dodecacronic hexecontahedron (or great lanceal trisicosahedron) is a nonconvex isohedral polyhedron. It is the dual of the uniform great ditrigonal dodecicosidodecahedron. Its faces are kites. Part of each kite lies inside the solid, hence is invisible in solid models. Proportions Kite faces have two angles of , one of and one of . Its dihedral angles equal . The ratio between the lengths of the long edges and the short ones equals . References p. 62 External links Dual uniform polyhedra
https://en.wikipedia.org/wiki/Small%20ditrigonal%20dodecacronic%20hexecontahedron
In geometry, the small ditrigonal dodecacronic hexecontahedron (or fat star) is a nonconvex isohedral polyhedron. It is the dual of the uniform small ditrigonal dodecicosidodecahedron. It is visually identical to the small dodecicosacron. Its faces are darts. A part of each dart lies inside the solid, hence is invisible in solid models. Proportions Faces have two angles of , one of and one of . Its dihedral angles equal . The ratio between the lengths of the long and short edges is . References External links Dual uniform polyhedra
https://en.wikipedia.org/wiki/Medial%20icosacronic%20hexecontahedron
In geometry, the medial icosacronic hexecontahedron (or midly sagittal ditriacontahedron) is a nonconvex isohedral polyhedron. It is the dual of the uniform icosidodecadodecahedron. Its faces are darts. Part of each dart lies inside the solid, hence is invisible in solid models. Proportions Faces have two angles of , one of and one of . Its dihedral angles equal . The ratio between the lengths of the long and short edges is . References External links Dual uniform polyhedra
https://en.wikipedia.org/wiki/Medial%20hexagonal%20hexecontahedron
In geometry, the medial hexagonal hexecontahedron (or midly dentoid ditriacontahedron) is a nonconvex isohedral polyhedron. It is the dual of the uniform snub icosidodecadodecahedron. Proportions The faces of the medial hexagonal hexecontahedron are irregular nonconvex hexagons. Denote the golden ratio by , and let be the real zero of the polynomial . The number can be written as , where is the plastic number. Then each face has four equal angles of , one of and one of . Each face has two long edges, two of medium length and two short ones. If the medium edges have length , the long ones have length and the short ones . The dihedral angle equals . References External links Dual uniform polyhedra
https://en.wikipedia.org/wiki/Great%20pentakis%20dodecahedron
In geometry, the great pentakis dodecahedron is a nonconvex isohedral polyhedron. It is the dual of the uniform small stellated truncated dodecahedron. The pentagonal faces pass close to the center in the uniform polyhedron, causing this dual to be very spikey. It has 60 intersecting isosceles triangle faces. Part of each triangle lies within the solid, hence is invisible in solid models. Proportions The triangles have one very acute angle of and two of . The dihedral angle equals . References External links Dual uniform polyhedra
https://en.wikipedia.org/wiki/Medial%20disdyakis%20triacontahedron
In geometry, the medial disdyakis triacontahedron is a nonconvex isohedral polyhedron. It is the dual of the uniform truncated dodecadodecahedron. It has 120 triangular faces. Proportions The triangles have one angle of , one of and one of . The dihedral angle equals . Part of each triangle lies within the solid, hence is invisible in solid models. References External links Dual uniform polyhedra
https://en.wikipedia.org/wiki/Great%20dodecacronic%20hexecontahedron
In geometry, the great dodecacronic hexecontahedron (or great lanceal ditriacontahedron) is a nonconvex isohedral polyhedron. It is the dual of the uniform great dodecicosidodecahedron. Its 60 intersecting quadrilateral faces are kites. Part of each kite lies inside the solid, hence is invisible in solid models. Proportions Each kite has two angles of , one of and one of . The dihedral angle equals . The ratio between the lengths of the long and short edges is . References External links Dual uniform polyhedra
https://en.wikipedia.org/wiki/Salil%20Vadhan
Salil Vadhan is an American computer scientist. He is Vicky Joseph Professor of Computer Science and Applied Mathematics at Harvard University. After completing his undergraduate degree in Mathematics and Computer Science at Harvard in 1995, he obtained his PhD in Applied Mathematics from Massachusetts Institute of Technology in 1999, where his advisor was Shafi Goldwasser. His research centers around the interface between computational complexity theory and cryptography. He focuses on the topics of pseudorandomness and zero-knowledge proofs. His work on the zig-zag product, with Omer Reingold and Avi Wigderson, was awarded the 2009 Gödel Prize. Contributions Zig-zag graph product for constructing expander graphs One of the main contributions of his work is a new type of graph product, called the zig-zag product. Taking a product of a large graph with a small graph, the resulting graph inherits (roughly) its size from the large one, its degree from the small one, and its expansion properties from both. Iteration yields simple explicit constructions of constant-degree expanders of every size, starting from one constant-size expander. Crucial to the intuition and simple analysis of the properties of the zig-zag product is the view of expanders as functions that act as "entropy wave" propagators—they transform probability distributions in which entropy is concentrated in one area to distributions where that concentration is dissipated. In these terms, the graph product affords the constructive interference of two such waves. A variant of this product can be applied to extractors, giving the first explicit extractors whose seed length depends on only the entropy deficiency of the source (rather than its length) and that extract almost all the entropy of high min-entropy sources. These high min-entropy extractors have several interesting applications, including the first constant-degree explicit expanders that beat the "eigenvalue bound." Vadhan also came up with another simplified approach to the undirected ST-connectivity problem following Reingold's breakthrough result. Also the zig-zag product was useful in Omer Reingold's proof that SL=L. Zero-knowledge proofs His work in this area is to use complexity-theoretic methods to understand the power and limitations of zero-knowledge proofs. In a series of papers with Oded Goldreich and Amit Sahai, they gained thorough understanding of the class SZK of problems possessing statistical zero-knowledge proofs, characterized the class SZK and proved that SZK is closed under various operations. Recently his work was trying to work on the zero-knowledge proof beyond the confines of SZK class. Randomness extractors With Lu, Omer Reingold, and Avi Wigderson, he gave the first construction of randomness extractors that are "optimal up to constant factors," reaching a milestone in a decade of work on the subject. With Trevisan, Zuckerman, Kamp, and Rao, he developed a theory of randomness extraction
https://en.wikipedia.org/wiki/Hungarian%20Central%20Statistical%20Office
The Hungarian Central Statistical Office (HSCO; , ) is a quango responsible for collecting, processing and publishing statistics about Hungary, its economy, and its inhabitants. The office provides details for parliamentary and administrative offices, local councils and academia, financial institutions, the public at large and the media. Functions To devise and conduct surveys To demand collection of statistical data for the central state statistical system To process and analyse information from the collection of statistical data based on compulsory and voluntary data supply To supply data and analysis for state organizations To satisfy requests from non-governmental organisations, parties, local government, academic researchers and the general public To prepare and make the census and to process and publish the data from it. Regulation Legal reference: KSH - Rules on Statistics Organization of National Statistics Act No. XXV of 1874 Hungarian Royal Central Statistical Office Act No XXXV of 1897 Official Statistical Service Act No XIX of 1929 State Statistics Act No VI. of 1952 Statistics Act No. V. of 1973 Statistics Act No. XLVI of 1993 The organisation is also covered by European Union regulation. Organization structure There are around 1,050 people employed at the central office, with a further 450 at regional offices. The head of the Office is called the President, and leads a number of organizational units each headed by a Deputy President and having several departments: Departments reporting directly to the president Internal Audit Section Administration and International Departments reporting to the Deputy President responsible for statistical issues Price Statistics Living Standards and Labour Statistics Foreign Trade Statistics Agriculture and Environment Statistics National Accounts Population Statistics Statistical Research and Methodology Department Sector Accounts Services Statistics Social Services Statistics Business Statistics Departments reporting to the Deputy President responsible for economic affairs Financial Management Technical and System Monitoring Information Technology Dissemination Planning Directorates Debrecen Győr Miskolc Pécs Szeged Veszprém See also Demographics of Hungary References National statistical services Demographics of Hungary
https://en.wikipedia.org/wiki/Modern%20social%20statistics%20of%20Native%20Americans
Modern social statistics of Native Americans serve as defining characteristics of Native American life, and can be compared to the average United States citizens’ social statistics. Areas from their demographics and economy to health standards, drug and alcohol use, and land use and ownership all lead to a better understanding of Native American life. Health standards for Native Americans have notable disparities from that of all United States racial and ethnic groups. They have higher rates of disease, higher death rates, and a lack of medical coverage. These health issues are matched by illegal drug abuse; abuse levels are higher than any other demographic group in the United States. Methamphetamine abuse on reservations is a particular area of concern for tribal and federal governments. General demographics Native American population demographics are studied by the federal government in conjunction with the Native Alaskan population. According to 2008 US Census projections, those who are Native American and Alaska Natives alone number 3.08 million of the total US population of 304 million, or 1.01 percent of the nation's entire population. Those who are Native American alone or in combination with other races measure as 4.86 million individuals, or 1.60 percent of the nation's entire population. The Native population continues to grow yearly. The Census Bureau projects that American Indian and Alaska Natives will reach 5 million individuals by 2065. At the present time there are 574 federally recognized tribes. The population of Native Americans however extends beyond those with this federal recognition. Certain tribes have much larger population bases than others. The United States Census has documented 1.93 million individuals that are American Indian or Alaskan Native alone (not in combination with other races) with specified tribes. The tribe with the largest population base, for 2008, was the tribe of Navajo people with 307,555 individuals. The Cherokee tribe had the second largest population, with 262,224 individuals. Follow in third and fourth are the Sioux tribe and Chippewa tribe with 114,047 individuals and 107,322 individuals, respectively. The remainder of the Native American tribes have populations below one hundred thousand. This does not account for those who do not have specified tribes or are of multiple races. The distribution of age of Native Americans and Alaskan Natives differs from the general population of the United States, according to 2008 Census data. Of those who are strictly Native American or Alaskan Native, 28.3% are below the age of 18. 64.3% are between 18 and 64 years of age, while the remaining 7.4% are 65 years of age and older. This is a notably younger population than the overall population. The median age of Native Americans and Alaskan Native is 31.2, while the male median age is 30.0 and female median age is 32.8. Native Americans and Alaskan Natives also differ in their household composition. Of t
https://en.wikipedia.org/wiki/Chain%20rule%20%28disambiguation%29
Chain rule may refer to: Chain rule in calculus: Cyclic chain rule, or triple product rule: Chain rule (probability): Chain rule for Kolmogorov complexity: Chain rule for information entropy:
https://en.wikipedia.org/wiki/Chain%20rule%20%28probability%29
In probability theory, the chain rule (also called the general product rule) describes how to calculate the probability of the intersection of, not necessarily independent, events or the joint distribution of random variables respectively, using conditional probabilities. The rule is notably used in the context of discrete stochastic processes and in applications, e.g. the study of Bayesian networks, which describe a probability distribution in terms of conditional probabilities. Chain rule for events Two events For two events and , the chain rule states that , where denotes the conditional probability of given . Example An Urn A has 1 black ball and 2 white balls and another Urn B has 1 black ball and 3 white balls. Suppose we pick an urn at random and then select a ball from that urn. Let event be choosing the first urn, i.e. , where is the complementary event of . Let event be the chance we choose a white ball. The chance of choosing a white ball, given that we have chosen the first urn, is The intersection then describes choosing the first urn and a white ball from it. The probability can be calculated by the chain rule as follows: Finitely many events For events whose intersection has not probability zero, the chain rule states Example 1 For , i.e. four events, the chain rule reads . Example 2 We randomly draw 4 cards without replacement from deck with 52 cards. What is the probability that we have picked 4 aces? First, we set . Obviously, we get the following probabilities . Applying the chain rule, . Statement of the theorem and proof Let be a probability space. Recall that the conditional probability of an given is defined as Then we have the following theorem. Chain rule for discrete random variables Two random variables For two discrete random variables , we use the eventsand in the definition above, and find the joint distribution as or where is the probability distribution of and conditional probability distribution of given . Finitely many random variables Let be random variables and . By the definition of the conditional probability, and using the chain rule, where we set , we can find the joint distribution as Example For , i.e. considering three random variables. Then, the chain rule reads Bibliography , p. 496. References Bayesian inference Bayesian statistics Mathematical identities Probability theory
https://en.wikipedia.org/wiki/PARI/GP
PARI/GP is a computer algebra system with the main aim of facilitating number theory computations. Versions 2.1.0 and higher are distributed under the GNU General Public License. It runs on most common operating systems. System overview The PARI/GP system is a package that is capable of doing formal computations on recursive types at high speed; it is primarily aimed at number theorists. Its three main strengths are its speed, the possibility of directly using data types that are familiar to mathematicians, and its extensive algebraic number theory module. The PARI/GP system consists of the following standard components: PARI is a C library, allowing for fast computations, and which can be called from a high-level language application (for instance, written in C, C++, Pascal, Fortran, Perl, or Python). gp is an easy-to-use interactive command line interface giving access to the PARI functions. It functions as a sophisticated programmable calculator which contains most of the control instructions of a standard language like C. GP is the name of gp's scripting language which can be used to program gp. Also available is gp2c, the GP-to-C compiler, which compiles GP scripts into the C language and transparently loads the resulting functions into gp. The advantage of this is that gp2c-compiled scripts will typically run three to four times faster. gp2c understands almost all of GP. PARI/GP performs arbitrary precision calculations (e.g., the significand can be millions of digits long—and billions of digits on 64-bit machines). It can compute factorizations, perform elliptic curve computations and perform algebraic number theory calculations. It also allows computations with matrices, polynomials, power series, algebraic numbers and implements many special functions. PARI/GP comes with its own built-in graphical plotting capability. PARI/GP has some symbolic manipulation capability, e.g., multivariate polynomial and rational function handling. It also has some formal integration and differentiation capabilities. PARI/GP can be compiled with GMP (GNU Multiple Precision Arithmetic Library) providing faster computations than PARI/GP's native arbitrary-precision kernel. History PARI/GP's progenitor was a program named Isabelle, an interpreter for higher arithmetic, written in 1979 by Henri Cohen and François Dress at the Université Bordeaux 1. PARI/GP was originally developed in 1985 by a team led by Henri Cohen at Laboratoire A2X and is now maintained by Karim Belabas at the Université Bordeaux 1 with the help of many volunteer contributors. Etymology The name PARI is a pun about the project's early stages when the authors started to implement a library for "Pascal ARIthmetic" in the Pascal programming language (although they quickly switched to C), and after "pari de Pascal" (Pascal's Wager). The first version of the gp calculator was originally called GPC, for Great Programmable Calculator. The trailing C was eventually dropped. Usage
https://en.wikipedia.org/wiki/George%20B.%20Purdy
George Barry Purdy (20 February 1944 – 30 December 2017) was a mathematician and computer scientist who specialized in cryptography, combinatorial geometry and number theory. Purdy received his Ph.D. from the University of Illinois at Urbana–Champaign in 1972, officially under the supervision of Paul T. Bateman, but his de facto adviser was Paul Erdős. He was on the faculty in the mathematics department at Texas A&M University for 11 years, and was appointed the Geier Professor of computer science at the University of Cincinnati in 1986. Purdy had Erdős number one and coauthored many papers with Paul Erdős, who regarded him as his own student. He is the "P" in G.W. Peck, a pseudonym for the group of mathematicians that also included Ronald Graham, Douglas West, Paul Erdős, Fan Chung, and Daniel Kleitman. Purdy polynomial In 1971, Purdy was asked by Larry Roberts, the director of the DARPA Information Processing Techniques Office, to develop a secure hash function to protect passwords on ARPANET. Purdy developed the so-called Purdy polynomial, which was a polynomial of degree 224 + 17 computed modulo the 64-bit prime p = 264 - 59. The terms of the polynomial could be computed using modular exponentiation. DARPA was satisfied with the hash function, and also allowed Purdy to publish it in Communications of the ACM. It was well received around the world, and DEC eventually used it in their OpenVMS operating system. A DEC report said they chose it because it was very secure and because the existing standard DES could not be exported, which meant that an alternative was needed. OpenVMS uses a 64-bit version, based on a 64-bit prime, the same size as the one in the paper. Purdy's conjecture While at Texas A&M, Purdy made an empirical observation about distances between points on two lines. Suppose that n points are to be chosen on line L and another n points on line M. If L and M are perpendicular or parallel, then the points can be chosen so that the number of distinct distances determined is bounded by a constant multiple of n, but otherwise the number is much larger. Erdős was very struck by this conjecture and told it to many others, and it was published in a book of unsolved problems by William Moser in 1981. It came to the attention of György Elekes, who eventually proved the conjecture as the first application of new tools from algebraic geometry that he was developing. After Elekes's untimely death, Micha Sharir collected Elekes's notes and published an organized presentation of these algebraic methods, including work of his own. This, in turn, enabled Katz and Guth to solve the Erdős distinct distances problem, a 1946 problem of Erdős. Work continues on improvements in Purdy's conjecture. Awards In 2015, Purdy was awarded the IEEE Joseph Desch Award for Innovation for his work on the Arpa Network and the Purdy Polynomial. Selected publications References 20th-century American mathematicians 21st-century American mathematicians Ame
https://en.wikipedia.org/wiki/2006%20Uzbek%20League
The 2006 Uzbek League season was the 15th edition of top level football in Uzbekistan since independence from the Soviet Union in 1992. League table Season statistics Top goalscorers Last updated: 12 November 2006 References Uzbekistan - List of final tables (RSSSF) Uzbekistan Super League seasons 1 Uzbek Uzbek
https://en.wikipedia.org/wiki/Basque%20Center%20for%20Applied%20Mathematics
The Basque Center of Applied Mathematics (BCAM) is a research center on applied mathematics, created with the support of the Basque Government and the University of the Basque Country. The BCAM headquarters are in Alda. Mazarredo, 14 in Bilbao, the capital of the province of Biscay in the Basque Country of northern Spain. Background In January 2007, the Department of Education, Universities and Research of the Basque Government set up Ikerbasque, the Basque Foundation for Science, which was charged with three objectives: the attraction and recovery of front-rank, consolidated researchers; the creation of new research centers with standards of excellence, and social outreach for science. The creation and current activity of BCAM – the Basque Center for Applied Mathematics - fall within the framework of the second of these objectives. In early 2008, Ikerbasque commissioned Enrique Zuazua to carry out a prospective study on the viability of setting up a center for mathematical research in the Basque Country. In March, 2008, the Ikerbasque Board of Trustees decided to go ahead with the creation of such a center as part of the BERC program (Basque Excellent Research Centres), later to become known as BCAM – Basque Center for Applied Mathematics. At the same time, the first international call for submissions for posts of director, managers and scientists was made. The center is located in the province of Biscay, given the extensive industrial fabric that the region has had traditionally as well as its current development of R+D+i activities. BCAM was officially created as a non-profit Association on September 1, 2008, and backed by the following three institutions: Ikerbasque, the University of the Basque Country (UPV-EHU), Innobasque, the Basque Foundation for Innovation and The Biscay Government. Scientific Directors of BCAM till today Jose Antonio Lozano - In charge since January 10, 2019 Luis Vega González - from May 8, 2013 till January 9, 2019. Tomás Chacón, from October 1, 2012 till March 10, 2013. Enrique Zuazua, from September 1, 2008 till July 31, 2012. Research lines The scientific program is structured in 5 research areas. These areas are intended to be the catalyst between basic research and technology transfer: Computational Mathematics (CM) Mathematical Modelling With Multidisciplinary Applications (M3A) Mathematical Physics (MP) Partial Differential Equations, Control And Numerics (DCN) Data Science and Artificial Intelligence (DS) See also Basque Government Ikerbasque Innobasque University of the Basque Country References External links http://www.bcamath.org Applied mathematics Mathematical institutes Research institutes in the Basque Country (autonomous community)
https://en.wikipedia.org/wiki/Amath%20Diedhiou
Amath André Diedhiou (born 19 November 1989, Dakar) is a Senegalese footballer who last played for UE Engordany. Career Diedhiou joined Sheriff Tiraspol in January 2009. Career statistics Honours Sheriff Tiraspol Moldovan National Division (2): 2008–09, 2009–10 Moldovan Cup (2): 2008–09, 2009–10 References External links 1989 births Living people Senegalese men's footballers Senegalese expatriate men's footballers Expatriate men's footballers in Moldova Expatriate men's footballers in France Moldovan Super Liga players Championnat National players Championnat National 2 players FC Sheriff Tiraspol players US Quevilly-Rouen Métropole players Men's association football forwards Senegalese expatriate sportspeople in Moldova Senegalese expatriate sportspeople in France
https://en.wikipedia.org/wiki/Edna%20Manning
Edna McDuffie Manning (born 1942) was the first president of the Oklahoma School of Science and Mathematics. She also owns a ranch on which she raises limousin cattle. In 2007 she was inducted into the Oklahoma Educators Hall of Fame. Education and career In February 1986, Manning became superintendent of the school district in Shawnee, Oklahoma. Facing a $1.2 million deficit, she reorganized the district's elementary schools, converting the small neighborhood schools into grade centers, each housing a single grade. This reorganization aroused strong feelings among some of the parents in the district, and resulted in several threats. In 1988 Manning was appointed president of the Oklahoma School of Science and Mathematics, opened to students in 1990. Manning aided in the building and development of the institution, supervising the selection of faculty and the development of the curriculum. In 2006, the OSSM board of trustees voted to rename the OSSM classroom building, previously called the Lincoln School, the Manning Academic Center. In September 2007, Manning was inducted into the Oklahoma Educators Hall of Fame. Manning retired from her position as president of OSSM in June 2012, and was succeeded by Dr. Frank Y.H. Wang. References http://newsok.com/oklahoma-school-of-science-and-mathematics-has-new-president/article/3727350 http://okcfriday.com/presidency-fulfills-wangs-dream-p7492-92.htm External links Oklahoma School of Science and Mathematics Oklahoma Educators Hall of Fame 21st-century American women American cattlewomen American educators Living people Women academic administrators Women presidents of organizations 1942 births
https://en.wikipedia.org/wiki/Adaptive%20estimator
In statistics, an adaptive estimator is an estimator in a parametric or semiparametric model with nuisance parameters such that the presence of these nuisance parameters does not affect efficiency of estimation. Definition Formally, let parameter θ in a parametric model consists of two parts: the parameter of interest , and the nuisance parameter . Thus . Then we will say that is an adaptive estimator of ν in the presence of η if this estimator is regular, and efficient for each of the submodels Adaptive estimator estimates the parameter of interest equally well regardless whether the value of the nuisance parameter is known or not. The necessary condition for a regular parametric model to have an adaptive estimator is that where zν and zη are components of the score function corresponding to parameters ν and η respectively, and thus Iνη is the top-right k×m block of the Fisher information matrix I(θ). Example Suppose is the normal location-scale family: Then the usual estimator is adaptive: we can estimate the mean equally well whether we know the variance or not. Notes Basic references Other useful references I. V. Blagouchine and E. Moreau: "Unbiased Adaptive Estimations of the Fourth-Order Cumulant for Real Random Zero-Mean Signal", IEEE Transactions on Signal Processing, vol. 57, no. 9, pp. 3330–3346, September 2009. Estimator
https://en.wikipedia.org/wiki/Jim%20Geelen
Jim Geelen is a professor at the Department of Combinatorics and Optimization in the faculty of mathematics at the University of Waterloo, where he holds the Canada Research Chair in Combinatorial optimization. He is known for his work on Matroid theory and the extension of the Graph Minors Project to representable matroids. In 2003, he won the Fulkerson Prize with his co-authors A. M. H. Gerards, and A. Kapoor for their research on Rota's excluded minors conjecture. In 2006, he won the Coxeter–James Prize presented by the Canadian Mathematical Society. He received a Bachelor of Science degree in 1992 from Curtin University in Australia, and obtained his Ph.D. in 1996 at the University of Waterloo under the supervision of William Cunningham. After brief postdoctoral fellowships in the Netherlands, Germany, and Japan, he returned to the University of Waterloo in 1997. References Living people Academic staff of the University of Waterloo University of Waterloo alumni Combinatorialists Canada Research Chairs Year of birth missing (living people)
https://en.wikipedia.org/wiki/Stanley%E2%80%93Reisner%20ring
In mathematics, a Stanley–Reisner ring, or face ring, is a quotient of a polynomial algebra over a field by a square-free monomial ideal. Such ideals are described more geometrically in terms of finite simplicial complexes. The Stanley–Reisner ring construction is a basic tool within algebraic combinatorics and combinatorial commutative algebra. Its properties were investigated by Richard Stanley, Melvin Hochster, and Gerald Reisner in the early 1970s. Definition and properties Given an abstract simplicial complex Δ on the vertex set {x1,...,xn} and a field k, the corresponding Stanley–Reisner ring, or face ring, denoted k[Δ], is obtained from the polynomial ring k[x1,...,xn] by quotienting out the ideal IΔ generated by the square-free monomials corresponding to the non-faces of Δ: The ideal IΔ is called the Stanley–Reisner ideal or the face ideal of Δ. Properties The Stanley–Reisner ring k[Δ] is multigraded by Zn, where the degree of the variable xi is the ith standard basis vector ei of Zn. As a vector space over k, the Stanley–Reisner ring of Δ admits a direct sum decomposition whose summands k[Δ]σ have a basis of the monomials (not necessarily square-free) supported on the faces σ of Δ. The Krull dimension of k[Δ] is one larger than the dimension of the simplicial complex Δ. The multigraded, or fine, Hilbert series of k[Δ] is given by the formula The ordinary, or coarse, Hilbert series of k[Δ] is obtained from its multigraded Hilbert series by setting the degree of every variable xi equal to 1: where d = dim(Δ) + 1 is the Krull dimension of k[Δ] and fi is the number of i-faces of Δ. If it is written in the form then the coefficients (h0, ..., hd) of the numerator form the h-vector of the simplicial complex Δ. Examples It is common to assume that every vertex {xi} is a simplex in Δ. Thus none of the variables belongs to the Stanley–Reisner ideal IΔ. Δ is a simplex {x1,...,xn}. Then IΔ is the zero ideal and is the polynomial algebra in n variables over k. The simplicial complex Δ consists of n isolated vertices {x1}, ..., {xn}. Then and the Stanley–Reisner ring is the following truncation of the polynomial ring in n variables over k: Generalizing the previous two examples, let Δ be the d-skeleton of the simplex {x1,...,xn}, thus it consists of all (d + 1)-element subsets of {x1,...,xn}. Then the Stanley–Reisner ring is following truncation of the polynomial ring in n variables over k: Suppose that the abstract simplicial complex Δ is a simplicial join of abstract simplicial complexes Δ′ on x1,...,xm and Δ′′ on xm+1,...,xn. Then the Stanley–Reisner ring of Δ is the tensor product over k of the Stanley–Reisner rings of Δ′ and Δ′′: Cohen–Macaulay condition and the upper bound conjecture The face ring k[Δ] is a multigraded algebra over k all of whose components with respect to the fine grading have dimension at most 1. Consequently, its homology can be studied by combinatorial and g
https://en.wikipedia.org/wiki/Anders%20%C3%98stli
Anders Østli (born 8 January 1983) is a Norwegian footballer currently under contract for Norwegian side Kråkerøy, where he is a playing assistant coach. Career statistics References External links Anders Østli at Soccerway Anders Østli at Fotball.no 1983 births Living people Norwegian men's footballers Men's association football defenders Fredrikstad FK players Moss FK players Sønderjyske Fodbold players Boldklubben Skjold players Lillestrøm SK players Sarpsborg 08 FF players Eliteserien players Norwegian First Division players Danish Superliga players Norwegian expatriate men's footballers Expatriate men's footballers in Denmark Norwegian expatriate sportspeople in Denmark Footballers from Fredrikstad
https://en.wikipedia.org/wiki/Chris%20Godsil
Christopher David Godsil is a professor and the former Chair at the Department of Combinatorics and Optimization in the faculty of mathematics at the University of Waterloo. He wrote the popular textbook on algebraic graph theory, entitled Algebraic Graph Theory, with Gordon Royle, His earlier textbook on algebraic combinatorics discussed distance-regular graphs and association schemes. Background He started the Journal of Algebraic Combinatorics, and was the Editor-in-Chief of the Electronic Journal of Combinatorics from 2004 to 2008. He is also on the editorial board of the Journal of Combinatorial Theory Series B and Combinatorica. He obtained his Ph.D. in 1979 at the University of Melbourne under the supervision of Derek Alan Holton. He wrote a paper with Paul Erdős, so making his Erdős number equal to 1. Notes References Living people Academic staff of the University of Waterloo University of Melbourne alumni Graph theorists Year of birth missing (living people)
https://en.wikipedia.org/wiki/Sultan%20Bargash
Sultan Saleh Bargash Jaralla Al Menhali (born 18 January 1989) is an Emirati footballer who plays as a midfielder for the UAE Under-20. Career statistics Club 1Continental competitions include the AFC Champions League 2Other tournaments include the UAE President Cup and Etisalat Emirates Cup National team As of 27 September 2009 1Continental competitions include the AFC U-19 Championship 2Other tournaments include the FIFA U-20 World Cup International goals References External links Al Jazira Club Official site Jazrawi Al3ankaboot Sultan Bargash Profile 1989 births Living people Emirati men's footballers Al Jazira Club players Hatta Club players Baynounah SC players UAE Pro League players UAE First Division League players UAE Second Division League players Footballers at the 2014 Asian Games Men's association football midfielders Asian Games competitors for the United Arab Emirates
https://en.wikipedia.org/wiki/2008%E2%80%9309%20in%20Swiss%20football
Statistics of the Swiss Super League for the 2008–09 football season. Statistics of the Swiss Challenge League for the 2008–09 football season. Statistics of the Swiss 1. Liga for the 2008–09 football season. Statistics of the 2. Liga Interregional for the 2008–09 football season. Super League Challenge League 1. Liga Group 1 Group 2 Group 3 Play-off to Challenge League 1st round Final round 2. Liga Interregional Gruppo 1 Gruppo 2 Gruppo 3 Gruppo 4 Gruppo 5 2. Liga Promotion to 2. Liga interregional: Aargauischer Fussballverband (AFV): FC Muri Fussballverband Bern / Jura (FVBJ): FC Lerchenfeld & FC Köniz Innerschweizerischer Fussballverband (IFV):FC Aegeri Fussballverband Nordwestschweiz (FVNWS): FC Black Stars Ostschweizer Fussballverband (OFV): FC Widnau & FC Amriswil Solothurner Kantonal-Fussballverband (SKFV): FC Härkingen Fussballverband Region Zürich (FVRZ): FC Zürich-Affoltern & FC Kosova Federazione ticinese di calcio (FTC): AC Sementina Freiburger Fussballverband (FFV): FC Kerzers Association cantonale genevoise de football (ACGF): FC Geneva Association neuchâteloise de football (ANF): Le Locle Sports Association valaisanne de football (AVF): FC Sierre Association cantonale vaudoise de football (ACVF): Lausanne-Sport U-21 References Swiss Football Federation
https://en.wikipedia.org/wiki/Cape%20Three%20Points
{ "type": "FeatureCollection", "features": [ { "type": "Feature", "properties": {}, "geometry": { "type": "Point", "coordinates": [ -2.089, 4.744 ] } } ] } Cape Three Points is a small peninsula in the Western Region of Ghana on the Atlantic Ocean. It forms the southernmost tip of Ghana. Location Cape Three Points is located between the coastal village of Dixcove and town of Princes Town, Ghana. Cape Three Points is known as the "land nearest nowhere" because it is the land nearest to a location in the sea known as Null Island, which is at 0 latitude and 0 longitude (the distance is about 570 km). Lighthouse Cape Three Points is best known for its lighthouses, the first of which was constructed in 1875 by the British as a navigational aid for trading vessels sailing through the Gulf of Guinea. The original structure has since become a ruin; however a larger and improved lighthouse was completed in 1925, and is still functioning today. References Landforms of Ghana Headlands of Africa Western Region (Ghana) Peninsulas of Africa
https://en.wikipedia.org/wiki/NUTS%20statistical%20regions%20of%20Poland
In the NUTS (Nomenclature of Territorial Units for Statistics) codes of Poland (PL), the three levels are: NUTS codes The regional coding below was last verified on October 20, 2019. The current coding as well as the history can be found under http://ec.europa.eu/eurostat/web/nuts/history Current NUTS codes In the 2018 version, the codes are as follows: Former coding 2015 NUTS codes In the 2015 version, the codes were as follows: 2008 NUTS codes In the 2008 version, the codes were as follows: PL1 REGION CENTRALNY PL11 Łódzkie PL113 Miasto Łódź PL114 Łódzki PL115 Piotrkowski PL116 Sieradzki PL117 Skierniewicki PL12 Mazowieckie PL121 Ciechanowsko-płocki PL122 Ostrołęcko-siedlecki PL127 Miasto Warszawa PL128 Radomski PL129 Warszawski-wschodni PL12A Warszawski-zachodni PL2 REGION POŁUDNIOWY PL21 Małopolskie PL213 Miasto Kraków PL214 Krakowski PL215 Nowosądecki PL216 Oświęcimski PL217 Tarnowski PL22 Śląskie PL224 Częstochowski PL225 Bielski PL227 Rybnicki PL228 Bytomski PL229 Gliwicki PL22A Katowicki PL22B Sosnowiecki PL22C Tyski PL3 REGION WSCHODNI PL31 Lubelskie PL311 Bialski PL312 Chełmsko-zamojski PL314 Lubelski PL315 Puławski PL32 Podkarpackie PL323 Krośnieński PL324 Przemyski PL325 Rzeszowski PL326 Tarnobrzeski PL33 Świętokrzyskie PL331 Kielecki PL332 Sandomiersko-jędrzejowski PL34 Podlaskie PL343 Białostocki PL344 Łomżyński PL345 Suwalski PL4 REGION PÓŁNOCNO-ZACHODNI PL41 Wielkopolskie PL411 Pilski PL414 Koniński PL415 Miasto Poznań PL416 Kaliski PL417 Leszczyński PL418 Poznański PL42 Zachodniopomorskie PL422 Koszaliński PL423 Stargardzki PL424 Miasto Szczecin PL425 Szczeciński PL43 Lubuskie PL431 Gorzowski PL432 Zielonogórski PL5 REGION POŁUDNIOWO-ZACHODNI PL51 Dolnośląskie PL514 Miasto Wrocław PL515 Jeleniogórski PL516 Legnicko-Głogowski PL517 Wałbrzyski PL518 Wrocławski PL52 Opolskie PL521 Nyski PL522 Opolski PL6 REGION PÓŁNOCNY PL61 Kujawsko-Pomorskie PL613 Bydgosko-Toruński PL614 Grudziądzki PL615 Włocławski PL62 Warmińsko-Mazurskie PL621 Elbląski PL622 Olsztyński PL623 Ełcki PL63 Pomorskie PL631 Słupski PL633 Trójmiejski PL634 Gdański PL635 Starogardzki 2003 NUTS codes In the 2003 version, the codes were as follows: PL1 CENTRALNY PL11 Lodzkie PL111 Lodzki PL112 Piotrkowsko-skierniewicki PL113 Miasto Lodz PL12 Mazowieckie PL121 Ciechanowsko-plocki PL122 Ostrolecko-siedlecki PL124 Radomski PL126 Warszawski PL127 Miasto Warszawa PL2 POLUDNIOWY PL21 Malopolskie PL211 Krakowsko-tarnowski PL212 Nowosadecki PL213 Miasto Krakow PL22 Slaskie PL224 Czestochowski PL225 Bielsko-bialski PL226 Centralny slaski PL227 Rybnicko-jastrzebski PL3 WSCHODNI PL31 Lubelskie PL311 Bialskopodlaski PL312 Chelmsko-zamojski PL313 Lubelski PL32 Podkarpackie PL321 Rzeszowsko-tarnobrzeski PL322 Krosniensko-przemyski PL33 Swietokrzyskie PL330 Swietokrzyski PL34 Podlaskie PL341 Bialostocko-suwalski PL342 Lomzynski PL4 POLNOCNO-ZACHODNI PL41 Wielkopolskie PL411 Pilski PL412 Poznanski PL413 Kaliski PL414 Koninski PL415 Miasto Poznan PL42 Zachodniopomorskie PL421 Szcz
https://en.wikipedia.org/wiki/Laplace%E2%80%93Carson%20transform
In mathematics, the Laplace–Carson transform, named after Pierre Simon Laplace and John Renshaw Carson, is an integral transform with significant applications in the field of physics and engineering, particularly in the field of railway engineering. Definition Let be a function and a complex variable. The Laplace–Carson transform is defined as: The inverse Laplace–Carson transform is: where is a real-valued constant, refers to the imaginary axis, which indicates the integral is carried out along a straight line parallel to the imaginary axis lying to the right of all the singularities of the following expression: See also Laplace transform References Integral transforms Differential equations Fourier analysis Transforms
https://en.wikipedia.org/wiki/Jewish%20population%20by%20city
This is a list of Jewish populations in different cities and towns around the world. It includes statistics for populations of metropolitan areas, as well as statistics about the number of Jews as a percentage of the total city or town population. Jewish population by Metropolitan Area Judaism is the second-largest religion practiced in New York City, with approximately 1.6 million adherents as of 2022, representing the largest Jewish community of any city in the world, greater than the combined totals of Tel Aviv and Jerusalem. Nearly half of New York City's Jews live in Brooklyn. The ethno-religious population makes up 18.4% of the city and its religious demographic makes up 8%. Census enumerations in many countries do not record religious or ethnic background, leading to a lack of certainty regarding the exact numbers of Jewish adherents. Therefore, the following list of cities ranked by Jewish population may not be complete. Many of the U.S. cities have their data sourced from the Jewish Data Bank, which records population statistics for service areas that encompass many counties in a metropolitan area. Jewish population by towns and villages as a percentage of total population List does not include cities in Israel. See also Jewish population by country References External links Israelbooks.com The Jewish People Policy Planning Institute Annual Assessment 2004–2005: Between Thriving and Decline. Gefen Publishing House. Publications on Jewish population at the Berman Jewish Policy Archive @ NYU Wagner Jewish Population and Migration, by YIVO Encyclopedia City City
https://en.wikipedia.org/wiki/Theodore%20von%20K%C3%A1rm%C3%A1n%20Prize
The Theodore von Kármán Prize in applied mathematics is awarded every fifth year to an individual in recognition of his or her notable application of mathematics to mechanics and/or the engineering sciences. This award was established and endowed in 1968 in honor of Theodore von Kármán by the Society for Industrial and Applied Mathematics (SIAM). List of recipients 1972 Geoffrey Ingram Taylor 1979 George F. Carrier and Joseph B. Keller 1984 Julian D. Cole 1989 Paul R. Garabedian 1994 Herbert B. Keller 1999 Stuart S. Antman, John M. Ball and Simone Zuccher 2004 Roland Glowinski 2009 Mary F. Wheeler 2014 Weinan E and Richard D. James 2020 Kaushik Bhattacharya See also List of mathematics awards References Awards established in 1968 Awards of the Society for Industrial and Applied Mathematics 1968 establishments in the United States
https://en.wikipedia.org/wiki/List%20of%20AFL%20debuts%20in%202005
This is a listing of Australian rules footballers who made their senior debut for an Australian Football League (AFL) club in 2005. The statistics refer only to a player's career with the club mentioned. Debuts References Australian rules football records and statistics Australian rules football-related lists 2005 in Australian rules football
https://en.wikipedia.org/wiki/General%20Household%20Survey
The General Household Survey (GHS) was a survey conducted of private households in Great Britain by the Office for National Statistics (ONS). The aim of this survey was to provide government departments and organisations with information on a range of topics concerning private households for monitoring and policy purposes. The Survey was last run in 2007. Thereafter, its questions were taken over by the General Lifestyle Survey, which was in turn ended in January 2012. History The GHS has been carried out continuously between 1971 and 2007 except for two breaks in 1997-1998 and in 1999-2000 when the survey was reviewed and redeveloped. From 2000 onwards, the design has been changed and, at the time of its termination, the survey had two different elements: The continuous survey, which remained unchanged over a five-year period, and extra modules called "trailers". This structure allowed different trailers to be included each year, depending on what information the sponsoring government departments require. In 2005, further changes were introduced and the time period in which the survey is conducted was changed from the financial year (April to March) to the calendar year (January to December). Additionally, the design was changed to a longitudinal survey in 2005-2006 because the European Union (EU) required all member states to collect extra data from a Survey on Income and Living Conditions (EU-SILC). The topics included in the questionnaire covered general information such as demographic information about household members, housing tenure, consumer durables including vehicle ownership and migration. The individual questionnaires, completed by all adults over 16 years of age resident in a household, also included issues such as employment, pensions, education, health, smoking and drinking, family information and income. Methodology and scope The GHS was a repeated cross-sectional study, conducted annually, which uses a sample of 9,731 households in the 2006 survey. The data were primarily collected by face-to-face interviews as well as telephone interviews. References External links Archived content for the General Household Survey ONS, GHS 2007 Overview Report (latest edition, 1 January 2009) Economic and Social Data Service (ESDS) website Demographics of the United Kingdom Office for National Statistics Publications established in 1971 Household surveys
https://en.wikipedia.org/wiki/1933%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya for the 1933 season. Overview It was contested by 10 teams, and Nacional won the championship. League standings Playoff: Nacional-Peñarol 0-0, 0-0 and 3-2 References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons Uru 1933 in Uruguayan football
https://en.wikipedia.org/wiki/1934%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya for the 1934 season. Overview It was contested by 10 teams, and Nacional won the championship. League standings References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons Uru 1934 in Uruguayan football
https://en.wikipedia.org/wiki/1935%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya for the 1935 season. Overview It was contested by 10 teams, and Peñarol won the championship. League standings References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons 1935 in Uruguayan football Uru
https://en.wikipedia.org/wiki/1936%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya for the 1936 season. Overview It was contested by 10 teams, and Peñarol won the championship. League standings References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons Uru 1936 in Uruguayan football
https://en.wikipedia.org/wiki/1937%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya for the 1937 season. Overview It was contested by 10 teams, and Peñarol won the championship. League standings References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons 1937 in Uruguayan football Uru
https://en.wikipedia.org/wiki/1938%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya for the 1938 season. Overview It was contested by 11 teams, and Peñarol won the championship. League standings References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons 1938 in Uruguayan football Uru
https://en.wikipedia.org/wiki/1939%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya for the 1939 season. Overview It was contested by 11 teams, and Nacional won the championship. League standings Playoff: Nacional-Peñarol 3-2 References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons Uru 1939 in Uruguayan football
https://en.wikipedia.org/wiki/1940%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya for the 1940 season. Overview It was contested by 11 teams, and Nacional won the championship. League standings References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons 1940 in Uruguayan football Uru
https://en.wikipedia.org/wiki/1941%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya for the 1941 season. Overview It was contested by 11 teams, and Nacional won the championship. Nacional are still the only team to have scored a 100% record during a Primera Division season. League standings References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons Uru 1941 in Uruguayan football
https://en.wikipedia.org/wiki/1942%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya for the 1942 season. Overview It was contested by 10 teams, and Nacional won the championship. League standings References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons Uru 1942 in Uruguayan football
https://en.wikipedia.org/wiki/1943%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya for the 1943 season. Overview It was contested by 10 teams, and Nacional won the championship. League standings References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons 1943 in Uruguayan football Uru
https://en.wikipedia.org/wiki/1944%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya for the 1944 season. Overview It was contested by 10 teams, and Peñarol won the championship. League standings References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons 1944 in Uruguayan football Uru
https://en.wikipedia.org/wiki/1945%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya for the 1945 season. Overview It was contested by 10 teams, and Peñarol won the championship. League standings References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons 1945 in Uruguayan football Uru
https://en.wikipedia.org/wiki/1946%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya for the 1946 season. Overview It was contested by 10 teams, and Nacional won the championship. League standings References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons 1946 in Uruguayan football Uru
https://en.wikipedia.org/wiki/1947%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya for the 1947 season. Overview It was contested by 10 teams, and Nacional won the championship. League standings References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons 1947 in Uruguayan football Uru
https://en.wikipedia.org/wiki/1948%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya for the 1948 season. Overview It was contested by 10 teams, and it was not finished due to a player strike. League standings References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons Uru 1948 in Uruguayan football
https://en.wikipedia.org/wiki/1949%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya for the 1949 season. Overview It was contested by 10 teams, and Peñarol won the championship. League standings References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons 1949 in Uruguayan football Uru
https://en.wikipedia.org/wiki/1950%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya for the 1950 season. Overview It was contested by 10 teams, and Nacional won the championship. League standings References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons 1950 in Uruguayan football Uru
https://en.wikipedia.org/wiki/1951%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya for the 1951 season. Overview It was contested by 10 teams, and Peñarol won the championship. League standings References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons 1951 in Uruguayan football Uru
https://en.wikipedia.org/wiki/1952%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya for the 1952 season. Overview It was contested by 10 teams, and Nacional won the championship. League standings References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons 1952 in Uruguayan football Uru
https://en.wikipedia.org/wiki/1953%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya for the 1953 season. Overview It was contested by 10 teams, and Peñarol won the championship. League standings References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons Uru 1953 in Uruguayan football
https://en.wikipedia.org/wiki/1955%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya for the 1955 season. Overview It was contested by 10 teams, and Nacional won the championship. League standings References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons Uru 1955 in Uruguayan football
https://en.wikipedia.org/wiki/1956%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya for the 1956 season. Overview It was contested by 10 teams, and Nacional won the championship. League standings References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons Uru 1956 in Uruguayan football
https://en.wikipedia.org/wiki/1957%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya in the 1957 season. Overview It was contested by 10 teams, and Nacional won the championship. League standings References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons 1957 in Uruguayan football Uru
https://en.wikipedia.org/wiki/1958%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya for the 1958 season. Overview It was contested by 10 teams, and Peñarol won the championship. League standings References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons 1958 in Uruguayan football Uru
https://en.wikipedia.org/wiki/1959%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya for the 1959 season. Overview It was contested by 10 teams, and Peñarol won the championship. League standings References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons 1959 in Uruguayan football Uru
https://en.wikipedia.org/wiki/1960%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya for the 1960 season. Overview It was contested by 10 teams, and Peñarol won the championship. League standings References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons Uru 1
https://en.wikipedia.org/wiki/1961%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya for the 1961 season. Overview It was contested by 10 teams, and Peñarol won the championship. League standings References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons Uru 1
https://en.wikipedia.org/wiki/1962%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya for the 1962 season. Overview The division was contested by 10 teams, and Peñarol won the championship. League standings References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons Uru 1
https://en.wikipedia.org/wiki/1963%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya for the 1963 season. Overview It was contested by 10 teams, and Nacional won the championship. League standings References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons Uru 1
https://en.wikipedia.org/wiki/1964%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya for the 1964 season. Overview It was contested by 10 teams, and Peñarol won the championship. League standings References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons Uru 1
https://en.wikipedia.org/wiki/1965%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya for the 1965 season. Overview It was contested by 10 teams, and Peñarol won the championship. League standings References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons 1 Uru
https://en.wikipedia.org/wiki/1966%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya for the 1966 season. Overview It was contested by 10 teams, and Nacional won the championship. League standings References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons Uru 1
https://en.wikipedia.org/wiki/1967%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya for the 1967 season. Overview It was contested by 10 teams, and Peñarol won the championship. League standings References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons Uru 1
https://en.wikipedia.org/wiki/1968%20Uruguayan%20Primera%20Divisi%C3%B3n
Statistics of Primera División Uruguaya for the 1968 season. Overview It was contested by 10 teams, and Peñarol won the championship. League standings References Uruguay - List of final tables (RSSSF) Uruguayan Primera División seasons Uru 1