Sigma-additive set functionIn mathematics, an additive set function is a function mapping sets to numbers, with the property that its value on a union of two disjoint sets equals the sum of its values on these sets, namely, If this additivity property holds for any two sets, then it also holds for any finite number of sets, namely, the function value on the union of k disjoint sets (where k is a finite number) equals the sum of its values on the sets. Therefore, an additive set function is also called a finitely additive set function (the terms are equivalent).
Harmonic analysisHarmonic analysis is a branch of mathematics concerned with investigating the connections between a function and its representation in frequency. The frequency representation is found by using the Fourier transform for functions on the real line, or by Fourier series for periodic functions. Generalizing these transforms to other domains is generally called Fourier analysis, although the term is sometimes used interchangeably with harmonic analysis.
Lebesgue differentiation theoremIn mathematics, the Lebesgue differentiation theorem is a theorem of real analysis, which states that for almost every point, the value of an integrable function is the limit of infinitesimal averages taken about the point. The theorem is named for Henri Lebesgue. For a Lebesgue integrable real or complex-valued function f on Rn, the indefinite integral is a set function which maps a measurable set A to the Lebesgue integral of , where denotes the characteristic function of the set A.
Square-integrable functionIn mathematics, a square-integrable function, also called a quadratically integrable function or function or square-summable function, is a real- or complex-valued measurable function for which the integral of the square of the absolute value is finite. Thus, square-integrability on the real line is defined as follows. One may also speak of quadratic integrability over bounded intervals such as for . An equivalent definition is to say that the square of the function itself (rather than of its absolute value) is Lebesgue integrable.
ShillongShillong (pronʃɪˈlɒŋ) is a hill station and the capital of Meghalaya, a state in northeastern India. It is the headquarters of the East Khasi Hills district. Shillong is the 330th most populous city in India with a population of 143,229 according to the 2011 census. It is said that the rolling hills around the town reminded the British of Scotland. Hence, they would also refer to it as the "Scotland of the East". Shillong has steadily grown in size since it was made the civil station of the Khasi and Jaintia Hills in 1864 by the British.
Khasi peopleThe Khasi people are an ethnic group of Meghalaya in north-eastern India with a significant population in the bordering state of Assam, and in certain parts of Bangladesh. Khasi people form the majority of the population of the eastern part of Meghalaya, that is Khasi Hills, constituting 78.3% of the region's population, and is the state's largest community, with around 48% of the population of Meghalaya. They are among the few Austroasiatic-speaking peoples in South Asia.
MeghalayaMeghalaya (ˌmeɪgəˈleɪə, or meɪˈgɑːləjə, meaning "abode of clouds"; from Sanskrit megha, "cloud" + ā-laya, "abode") is a state in northeast India. Meghalaya was formed on 21 January 1972 by carving out two districts from the state of Assam: (a) the United Khasi Hills and Jaintia Hills and (b) the Garo Hills. The population of Meghalaya as of 2014 is estimated to be 3,211,474. Meghalaya covers an area of approximately 22,429 square kilometres, with a length-to-breadth ratio of about 3:1.
Integration by partsIn calculus, and more generally in mathematical analysis, integration by parts or partial integration is a process that finds the integral of a product of functions in terms of the integral of the product of their derivative and antiderivative. It is frequently used to transform the antiderivative of a product of functions into an antiderivative for which a solution can be more easily found. The rule can be thought of as an integral version of the product rule of differentiation.
Khasi languageKhasi (Ka Ktien Khasi) is an Austroasiatic language with just over a million speakers in north-east India, primarily the Khasi people in the state of Meghalaya. It has associate official status in some districts of this state. The closest relatives of Khasi are the other languages in the Khasic group of the Shillong Plateau; these include Pnar, Lyngngam and War. Khasi is written using the Latin and Bengali-Assamese scripts. Khasi is natively spoken by people in India (as of 2011).
Bayesian information criterionIn statistics, the Bayesian information criterion (BIC) or Schwarz information criterion (also SIC, SBC, SBIC) is a criterion for model selection among a finite set of models; models with lower BIC are generally preferred. It is based, in part, on the likelihood function and it is closely related to the Akaike information criterion (AIC). When fitting models, it is possible to increase the maximum likelihood by adding parameters, but doing so may result in overfitting.
FinA fin is a thin component or appendage attached to a larger body or structure. Fins typically function as foils that produce lift or thrust, or provide the ability to steer or stabilize motion while traveling in water, air, or other fluids. Fins are also used to increase surface areas for heat transfer purposes, or simply as ornamentation. Fins first evolved on fish as a means of locomotion. Fish fins are used to generate thrust and control the subsequent motion.
Akaike information criterionThe Akaike information criterion (AIC) is an estimator of prediction error and thereby relative quality of statistical models for a given set of data. Given a collection of models for the data, AIC estimates the quality of each model, relative to each of the other models. Thus, AIC provides a means for model selection. AIC is founded on information theory. When a statistical model is used to represent the process that generated the data, the representation will almost never be exact; so some information will be lost by using the model to represent the process.
