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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 | {
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"features": [
{
"type": "Feature",
"properties": {},
"geometry": {
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-2.089,
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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 |
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