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An abstract machine is a model of a computer system (considered either as hardware or software) constructed to allow a detailed and precise analysis of how the computer ...

Let A be a commutative ring and let C_r be an R-module for r=0,1,2,.... A chain complex C__ of the form C__:...|->C_n|->C_(n-1)|->C_(n-2)|->...|->C_2|->C_1|->C_0 is said to ...

Given a triangle DeltaABC, construct the contact triangle DeltaT_AT_BT_C. Now extend lines parallel to the sides of the contact triangle from the Gergonne point. These ...

The word adjoint has a number of related meanings. In linear algebra, it refers to the conjugate transpose and is most commonly denoted A^(H). The analogous concept applied ...

An affine tensor is a tensor that corresponds to certain allowable linear coordinate transformations, T:x^_^i=a^i_jx^j, where the determinant of a^i_j is nonzero. This ...

Fok (1946) and Hazewinkel (1988, p. 65) call v(z) = 1/2sqrt(pi)Ai(z) (1) w_1(z) = 2e^(ipi/6)v(omegaz) (2) w_2(z) = 2e^(-ipi/6)v(omega^(-1)z), (3) where Ai(z) is an Airy ...

The set theory symbol aleph_0 refers to a set having the same cardinal number as the "small" infinite set of integers. The symbol aleph_0 is often pronounced "aleph-null" ...

The Alexander invariant H_*(X^~) of a knot K is the homology of the infinite cyclic cover of the complement of K, considered as a module over Lambda, the ring of integral ...

Suppose that X is a vector space over the field of complex or real numbers. Then the set of all linear functionals on X forms a vector space called the algebraic conjugate ...

Let X be an alphabet (i.e., a finite and nonempty set), and call its member letters. A word on X is a finite sequence of letters a_1...a_n, where a_1,...,a_n in X. Denote the ...