|
Basis (other)
Basis may refer to: Finance and accounting *Adjusted basis, the net cost of an asset after adjusting for various tax-related items *Basis point, 0.01%, often used in the context of interest rates *Basis trading, a trading strategy consisting of the purchase of a security and the sale of a similar security **Basis of futures, the value differential between a future and the spot price **Basis (options), the value differential between a call option and a put option **Basis swap, an interest rate swap *Cost basis, in income tax law, the original cost of property adjusted for factors such as depreciation *Tax basis, cost of an asset and technology *Basis function *Basis (linear algebra) **Dual basis **Orthonormal basis **Schauder basis *Basis (universal algebra) *Basis of a matroid *Generating set of an ideal (ring theory), ideal: **Gröbner basis **Hilbert's basis theorem *Generating set of a group *Base (topology) *Change of basis *Greedoid *Normal basis *Polynomial basis *Radial ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adjusted Basis
In tax accounting, adjusted basis is the net cost of an asset after adjusting for various tax-related items. Adjusted Basis or Adjusted Tax Basis refers to the original cost or other basis of property, reduced by depreciation deductions and increased by capital expenditures. Example: Brad buys a lot for $100,000. He then erects a retail facility for $600,000, then depreciates the improvements for tax purposes at the rate of $15,000 per year. After three years his adjusted tax basis is $655,000 100,000 + $600,000 - (3 x $15,000) Adjusted basis is one of two variables in the formula used to compute gains and losses when determining gross income for tax purposes. The Amount Realized – Adjusted Basis tells the amount of Realized Gain (if positive) or Realized Loss (if negative). Statutory definition Section 1012 of the Internal Revenue Code defines “basis” as a taxpayer’s cost in acquiring property, except as provided in Sections 1001-1092. Section 1016 then lists 27 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dry Basis
Dry basis is an expression of the calculation in chemistry, chemical engineering and related subjects, in which the presence of water (and/or other solvents) is neglected for the purposes of the calculation. Water (and/or other solvents) is neglected because addition and removal of water (and/or other solvents) are common processing steps, and also happen naturally through evaporation and condensation; it is frequently useful to express compositions on a dry basis to remove these effects. Example An aqueous solution containing 2 g of glucose and 2 g of fructose per 100 g of solution contains 2/100=2% glucose on a wet basis Dry basis is an expression of the calculation in chemistry, chemical engineering and related subjects, in which the presence of water (and/or other solvents) is neglected for the purposes of the calculation. Water (and/or other solvents) is neglec ..., but 2/4=50% glucose on a dry basis. If the solution had contained 2 g of glucose and 3&nbs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Basis Set (chemistry)
In theoretical and computational chemistry, a basis set is a set of functions (called basis functions) that is used to represent the electronic wave function in the Hartree–Fock method or density-functional theory in order to turn the partial differential equations of the model into algebraic equations suitable for efficient implementation on a computer. The use of basis sets is equivalent to the use of an approximate resolution of the identity: the orbitals , \psi_i\rangle are expanded within the basis set as a linear combination of the basis functions , \psi_i\rangle \approx \sum_\mu c_ , \mu\rangle, where the expansion coefficients c_ are given by c_ = \sum_\nu \langle \mu, \nu \rangle^ \langle \nu , \psi_i \rangle. The basis set can either be composed of atomic orbitals (yielding the linear combination of atomic orbitals approach), which is the usual choice within the quantum chemistry community; plane waves which are typically used within the solid state community, or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Basis (crystal Structure)
In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric patterns that repeat along the principal directions of three-dimensional space in matter. The smallest group of particles in the material that constitutes this repeating pattern is the unit cell of the structure. The unit cell completely reflects the symmetry and structure of the entire crystal, which is built up by repetitive translation of the unit cell along its principal axes. The translation vectors define the nodes of the Bravais lattice. The lengths of the principal axes, or edges, of the unit cell and the angles between them are the lattice constants, also called ''lattice parameters'' or ''cell parameters''. The symmetry properties of the crystal are described by the concept of space groups. All possible symmetric arrangements of particles ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Basis Database
Basis database or OpenText Collections Server is an Extended Relational Database Management System (RDBMS) produced by OpenText. BASIS was originally developed by the Battelle Institute, and was spun off into Information Dimensions, a private company based out of Columbus Ohio. The strength of BASIS was its Full Text Indexing. The original version of BASIS was eventually merged with an RDBMS system called DM, and the resulting product was called BASISplus. Information Dimensions was bought and sold a number of times before being acquired by OpenText Corporation in summer 1998. Although the product is an extremely powerful and robust Full Text Database that incorporates a number of interesting features such as an integrated Thesaurus, early SGML The Standard Generalized Markup Language (SGML; ISO 8879:1986) is a standard for defining generalized markup languages for documents. ISO 8879 Annex A.1 states that generalized markup is "based on two postulates": * Declarative: Mar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transcendence Basis
In abstract algebra, the transcendence degree of a field extension ''L'' / ''K'' is a certain rather coarse measure of the "size" of the extension. Specifically, it is defined as the largest cardinality of an algebraically independent subset of ''L'' over ''K''. A subset ''S'' of ''L'' is a transcendence basis of ''L'' / ''K'' if it is algebraically independent over ''K'' and if furthermore ''L'' is an algebraic extension of the field ''K''(''S'') (the field obtained by adjoining the elements of ''S'' to ''K''). One can show that every field extension has a transcendence basis, and that all transcendence bases have the same cardinality; this cardinality is equal to the transcendence degree of the extension and is denoted trdeg''K'' ''L'' or trdeg(''L'' / ''K''). If no field ''K'' is specified, the transcendence degree of a field ''L'' is its degree relative to the prime field of the same characteristic, i.e., the rational numbers field Q if ''L'' is of characteristic 0 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard Basis
In mathematics, the standard basis (also called natural basis or canonical basis) of a coordinate vector space (such as \mathbb^n or \mathbb^n) is the set of vectors whose components are all zero, except one that equals 1. For example, in the case of the Euclidean plane \mathbb^2 formed by the pairs of real numbers, the standard basis is formed by the vectors :\mathbf_x = (1,0),\quad \mathbf_y = (0,1). Similarly, the standard basis for the three-dimensional space \mathbb^3 is formed by vectors :\mathbf_x = (1,0,0),\quad \mathbf_y = (0,1,0),\quad \mathbf_z=(0,0,1). Here the vector e''x'' points in the ''x'' direction, the vector e''y'' points in the ''y'' direction, and the vector e''z'' points in the ''z'' direction. There are several common notations for standard-basis vectors, including , , , and . These vectors are sometimes written with a hat to emphasize their status as unit vectors (standard unit vectors). These vectors are a basis in the sense that any other vector can ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radial Basis Function
A radial basis function (RBF) is a real-valued function \varphi whose value depends only on the distance between the input and some fixed point, either the origin, so that \varphi(\mathbf) = \hat\varphi(\left\, \mathbf\right\, ), or some other fixed point \mathbf, called a ''center'', so that \varphi(\mathbf) = \hat\varphi(\left\, \mathbf-\mathbf\right\, ). Any function \varphi that satisfies the property \varphi(\mathbf) = \hat\varphi(\left\, \mathbf\right\, ) is a radial function. The distance is usually Euclidean distance, although other metrics are sometimes used. They are often used as a collection \_k which forms a basis for some function space of interest, hence the name. Sums of radial basis functions are typically used to approximate given functions. This approximation process can also be interpreted as a simple kind of neural network; this was the context in which they were originally applied to machine learning, in work by David Broomhead and David Lowe in 1988, which st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polynomial Basis
In mathematics the monomial basis of a polynomial ring is its basis (as a vector space or free module over the field or ring of coefficients) that consists of all monomials. The monomials form a basis because every polynomial may be uniquely written as a finite linear combination of monomials (this is an immediate consequence of the definition of a polynomial). One indeterminate The polynomial ring of univariate polynomials over a field is a -vector space, which has 1, x, x^2, x^3, \ldots as an (infinite) basis. More generally, if is a ring then is a free module which has the same basis. The polynomials of degree at most form also a vector space (or a free module in the case of a ring of coefficients), which has 1, x, x^2, \ldots as a basis. The canonical form of a polynomial is its expression on this basis: a_0 + a_1 x + a_2 x^2 + \dots + a_d x^d, or, using the shorter sigma notation: \sum_^d a_ix^i. The monomial basis is naturally totally ordered, either by increasing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal Basis
In mathematics, specifically the algebraic theory of fields, a normal basis is a special kind of basis for Galois extensions of finite degree, characterised as forming a single orbit for the Galois group. The normal basis theorem states that any finite Galois extension of fields has a normal basis. In algebraic number theory, the study of the more refined question of the existence of a normal integral basis is part of Galois module theory. Normal basis theorem Let F\subset K be a Galois extension with Galois group G. The classical normal basis theorem states that there is an element \beta\in K such that \ forms a basis of ''K'', considered as a vector space over ''F''. That is, any element \alpha \in K can be written uniquely as \alpha = \sum_ a_g\, g(\beta) for some elements a_g\in F. A normal basis contrasts with a primitive element basis of the form \, where \beta\in K is an element whose minimal polynomial has degree n= :F/math>. Group representation point of view A field e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greedoid
In combinatorics, a greedoid is a type of set system. It arises from the notion of the matroid, which was originally introduced by Whitney in 1935 to study planar graphs and was later used by Edmonds to characterize a class of optimization problems that can be solved by greedy algorithms. Around 1980, Korte and Lovász introduced the greedoid to further generalize this characterization of greedy algorithms; hence the name greedoid. Besides mathematical optimization, greedoids have also been connected to graph theory, language theory, order theory, and other areas of mathematics. Definitions A set system (''F'', E) is a collection ''F'' of subsets of a ground set E (i.e. ''F'' is a subset of the power set of E). When considering a greedoid, a member of ''F'' is called a feasible set. When considering a matroid, a feasible set is also known as an ''independent set''. An accessible set system (''F'', E) is a set system in which every nonempty feasible set X contains an element ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
