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I. D. Brown
I is the ninth letter of the Latin alphabet. I or i may also refer to: Language * I (pronoun), the first-person singular subject pronoun in English * I (Cyrillic), a letter used in almost all ancient and modern Cyrillic alphabets * ı, dotless I, letter used in Turkish and Azerbaijani * i, close front unrounded vowel, in the International Phonetic Alphabet * ɨ, close central unrounded vowel, in the International Phonetic Alphabet * ɪ, near-close near-front unrounded vowel, in the International Phonetic Alphabet * I (kana), one of the Japanese kana that each represent one mora * I, male prefix to some Balinese names Science, technology, and mathematics Biology * Troponin I, one of the three troponins * Haplogroup I (mtDNA), a human mitochondrial DNA (mtDNA) haplogroup * Haplogroup I (Y-DNA), a Y-chromosomal DNA (Y-DNA) haplogroup * Olfactory nerve, the 1st cranial nerve in human anatomy * the Lợn Ỉ or Vietnamese Pot-bellied pig Chemistry * Iodine, symbol I, a chemica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
I (pronoun)
In Modern English, ''I'' is the singular, first-person pronoun. Morphology In Standard Modern English, ''I'' has five distinct word forms: * ''I'': the nominative (subjective) form **''I'' is the only pronoun form that is always capitalized in English. This practice became established in the late 15th century, though lowercase ''i'' was sometimes found as late as the 17th century. * ''me'': the accusative (objective) forms (The accusative case is also called the 'oblique'.) * ''my:'' the dependent genitive (possessive) form * ''mine'': the independent genitive * ''myself'': the reflexive form History Old English had a first person pronoun that inflected for four cases and three numbers. ''I'' originates from Old English (OE) ''ic'', which had in turn originated from the continuation of Proto-Germanic *''ik'', and ''ek''; The asterisk denotes an unattested form, but ''ek'' was attested in the Elder Futhark inscriptions (in some cases notably showing the variant ''eka''; see ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Van 't Hoff Factor
The van 't Hoff factor (named after Dutch chemist Jacobus Henricus van 't Hoff) is a measure of the effect of a solute on colligative properties such as osmotic pressure, relative lowering in vapor pressure, boiling-point elevation and freezing-point depression. The van 't Hoff factor is the ratio between the actual concentration of particles produced when the substance is dissolved and the concentration of a substance as calculated from its mass. For most non-electrolytes dissolved in water, the van 't Hoff factor is essentially 1. For most ionic compounds dissolved in water, the van 't Hoff factor is equal to the number of discrete ions in a formula unit of the substance. This is true for ideal solutions only, as occasionally ion pairing occurs in solution. At a given instant a small percentage of the ions are paired and count as a single particle. Ion pairing occurs to some extent in all electrolyte solutions. This causes the measured van 't Hoff factor to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unit Vector
In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or "hat", as in \hat (pronounced "v-hat"). The term ''direction vector'', commonly denoted as d, is used to describe a unit vector being used to represent spatial direction and relative direction. 2D spatial directions are numerically equivalent to points on the unit circle and spatial directions in 3D are equivalent to a point on the unit sphere. The normalized vector û of a non-zero vector u is the unit vector in the direction of u, i.e., :\mathbf = \frac where , u, is the norm (or length) of u. The term ''normalized vector'' is sometimes used as a synonym for ''unit vector''. Unit vectors are often chosen to form the basis of a vector space, and every vector in the space may be written as a linear combination of unit vectors. Orthogonal coordinates Cartesian coordinates Unit vectors may be us ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regularized Incomplete Beta Function
In mathematics, the beta function, also called the Euler integral of the first kind, is a special function that is closely related to the gamma function and to binomial coefficients. It is defined by the integral : \Beta(z_1,z_2) = \int_0^1 t^(1-t)^\,dt for complex number inputs z_1, z_2 such that \Re(z_1), \Re(z_2)>0. The beta function was studied by Leonhard Euler and Adrien-Marie Legendre and was given its name by Jacques Binet; its symbol is a Greek capital beta. Properties The beta function is symmetric, meaning that \Beta(z_1,z_2) = \Beta(z_2,z_1) for all inputs z_1 and z_2.Davis (1972) 6.2.2 p.258 A key property of the beta function is its close relationship to the gamma function: : \Beta(z_1,z_2)=\frac. A proof is given below in . The beta function is also closely related to binomial coefficients. When (or , by symmetry) is a positive integer, it follows from the definition of the gamma function thatDavis (1972) 6.2.1 p.258 : \Beta(m,n) =\dfrac = \frac \B ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Summation
In mathematics, summation is the addition of a sequence of any kind of numbers, called ''addends'' or ''summands''; the result is their ''sum'' or ''total''. Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined. Summations of infinite sequences are called series. They involve the concept of limit, and are not considered in this article. The summation of an explicit sequence is denoted as a succession of additions. For example, summation of is denoted , and results in 9, that is, . Because addition is associative and commutative, there is no need of parentheses, and the result is the same irrespective of the order of the summands. Summation of a sequence of only one element results in this element itself. Summation of an empty sequence (a sequence with no elements), by convention, results in 0. Very often, the elements ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix (mathematics)
In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, \begin1 & 9 & -13 \\20 & 5 & -6 \end is a matrix with two rows and three columns. This is often referred to as a "two by three matrix", a "-matrix", or a matrix of dimension . Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra. Therefore, the study of matrices is a large part of linear algebra, and most properties and operations of abstract linear algebra can be expressed in terms of matrices. For example, matrix multiplication represents composition of linear maps. Not all matrices are related to linear algebra. This is, in particular, the case in graph theory, of incidence matrices, and adjacency matrices. ''This article focuses on matrices related to linear algebra, and, unle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
