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In a complete metric space, a countable union of nowhere dense sets is said to be meager; the complement of such a set is a residual set.

sum_(k=0)^dr_k^B(d-k)!x^k=sum_(k=0)^d(-1)^kr_k^(B^_)(d-k)!x^k(x+1)^(d-k).

If the matrices A, X, B, and C satisfy AX-XB=C, then [I X; 0 I][A C; 0 B][I -X; 0 I]=[A 0; 0 B], where I is the identity matrix.

Deciding whether a given Boolean formula in conjunctive normal form has an assignment that makes the formula "true." In 1971, Cook showed that the problem is NP-complete.

A diagonal matrix whose diagonal elements all contain the same scalar lambda. A scalar matrix is therefore equivalent to lambdaI, where I is the identity matrix.

If J is a simple closed curve in R^2, the closure of one of the components of R^2-J is homeomorphic with the unit 2-ball. This theorem may be proved using the Riemann mapping ...

Let a general theta function be defined as T(x,q)=sum_(n=-infty)^inftyx^nq^(n^2), then

An Auslander algebra which connects the representation theories of the symmetric group of permutations and the general linear group GL(n,C). Schur algebras are ...

The Seiberg-Witten equations are D_Apsi = 0 (1) F_A^+ = -tau(psi,psi), (2) where tau is the sesquilinear map tau:W^+×W^+->Lambda^+ tensor C.

X subset= R^n is semianalytic if, for all x in R^n, there is an open neighborhood U of x such that X intersection U is a finite Boolean combination of sets {x^_ in ...