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I. Guidine
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 chemical ele ... [...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] |
Unit Interval
In mathematics, the unit interval is the closed interval , that is, the set of all real numbers that are greater than or equal to 0 and less than or equal to 1. It is often denoted ' (capital letter ). In addition to its role in real analysis, the unit interval is used to study homotopy theory in the field of topology. In the literature, the term "unit interval" is sometimes applied to the other shapes that an interval from 0 to 1 could take: , , and . However, the notation ' is most commonly reserved for the closed interval . Properties The unit interval is a complete metric space, homeomorphic to the extended real number line. As a topological space, it is compact, contractible, path connected and locally path connected. The Hilbert cube is obtained by taking a topological product of countably many copies of the unit interval. In mathematical analysis, the unit interval is a one-dimensional analytical manifold whose boundary consists of the two points 0 and 1. Its ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Identity Matrix
In linear algebra, the identity matrix of size n is the n\times n square matrix with ones on the main diagonal and zeros elsewhere. Terminology and notation The identity matrix is often denoted by I_n, or simply by I if the size is immaterial or can be trivially determined by the context. I_1 = \begin 1 \end ,\ I_2 = \begin 1 & 0 \\ 0 & 1 \end ,\ I_3 = \begin 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end ,\ \dots ,\ I_n = \begin 1 & 0 & 0 & \cdots & 0 \\ 0 & 1 & 0 & \cdots & 0 \\ 0 & 0 & 1 & \cdots & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & 0 & \cdots & 1 \end. The term unit matrix has also been widely used, but the term ''identity matrix'' is now standard. The term ''unit matrix'' is ambiguous, because it is also used for a matrix of ones and for any unit of the ring of all n\times n matrices. In some fields, such as group theory or quantum mechanics, the identity matrix is sometimes denoted by a boldface one, \mathbf, or called "id" (short for identity). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Imaginary Unit
The imaginary unit or unit imaginary number () is a solution to the quadratic equation x^2+1=0. Although there is no real number with this property, can be used to extend the real numbers to what are called complex numbers, using addition and multiplication. A simple example of the use of in a complex number is 2+3i. Imaginary numbers are an important mathematical concept; they extend the real number system \mathbb to the complex number system \mathbb, in which at least one root for every nonconstant polynomial exists (see Algebraic closure and Fundamental theorem of algebra). Here, the term "imaginary" is used because there is no real number having a negative square. There are two complex square roots of −1: and -i, just as there are two complex square roots of every real number other than zero (which has one double square root). In contexts in which use of the letter is ambiguous or problematic, the letter or the Greek \iota is sometimes used instead. For example, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roman Numeral
Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, each letter with a fixed integer value, modern style uses only these seven: The use of Roman numerals continued long after the decline of the Roman Empire. From the 14th century on, Roman numerals began to be replaced by Arabic numerals; however, this process was gradual, and the use of Roman numerals persists in some applications to this day. One place they are often seen is on clock faces. For instance, on the clock of Big Ben (designed in 1852), the hours from 1 to 12 are written as: The notations and can be read as "one less than five" (4) and "one less than ten" (9), although there is a tradition favouring representation of "4" as "" on Roman numeral clocks. Other common uses include year numbers on monuments and buildings and c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Internet-related Prefixes
Internet-related prefixes such as '' e-'', '' i-'', ''cyber-'', ''info-'', ''techno-'' and ''net-'' are added to a wide range of existing words to describe new, Internet- or computer-related flavors of existing concepts, often electronic products and services that already have a non-electronic counterpart. The adjective '' virtual'' is often used in a similar manner. Cyber-, e-, i, and virtual "Cyber-" ''Cyber-'' is derived from "cybernetic", from the Greek κυβερνητικός 'skilled in steering or governing'. Examples: ''cyberspace'', ''cyberlaw'', ''cyberbullying'', ''cybercrime'', ''cyberwarfare'', ''cyberterrorism'', ''cybersex'', and ''cyberdelic''. It is commonly used for policies and politics regarding computer systems and networks (as in the above cases), but also for information technology products and services. "E-" ''E-'', standing for ''electronic'', is used in the terms ''e-mail'', ''e-commerce'', ''e-business'', ''e-banking'', ''e-sports'', ''e-paper'', ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apple Inc
Apple Inc. is an American multinational technology company headquartered in Cupertino, California, United States. Apple is the largest technology company by revenue (totaling in 2021) and, as of June 2022, is the world's biggest company by market capitalization, the fourth-largest personal computer vendor by unit sales and second-largest mobile phone manufacturer. It is one of the Big Five American information technology companies, alongside Alphabet, Amazon, Meta, and Microsoft. Apple was founded as Apple Computer Company on April 1, 1976, by Steve Wozniak, Steve Jobs and Ronald Wayne to develop and sell Wozniak's Apple I personal computer. It was incorporated by Jobs and Wozniak as Apple Computer, Inc. in 1977 and the company's next computer, the Apple II, became a best seller and one of the first mass-produced microcomputers. Apple went public in 1980 to instant financial success. The company developed computers featuring innovative graphical user inter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
