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A T_1-space is a topological space fulfilling the T1-separation axiom: For any two points x,y in X there exists two open sets U and V such that x in U and y not in U, and y ...

A straight line is tangent to a given curve f(x) at a point x_0 on the curve if the line passes through the point (x_0,f(x_0)) on the curve and has slope f^'(x_0), where ...

Let f:R×R->R be a one-parameter family of C^2 maps satisfying f(0,mu)=0 (1) [(partialf)/(partialx)]_(mu=0,x=0)=0 (2) [(partial^2f)/(partialxpartialmu)]_(0,0)>0 (3) ...

The interior of the triangle is the set of all points inside a triangle, i.e., the set of all points in the convex hull of the triangle's vertices. The simplest way to ...

A left Hilbert Algebra A whose involution is an antilinear isometry is called a unimodular Hilbert algebra. The involution is usually denoted xi|->xi^*.

Consider three squares erected externally on the sides of a triangle DeltaABC. Call the centers of these squares O_A, O_B, and O_C, respectively. Then the lines AO_A, BO_B, ...

A magic square is a square array of numbers consisting of the distinct positive integers 1, 2, ..., n^2 arranged such that the sum of the n numbers in any horizontal, ...

Solutions to the associated Laguerre differential equation with nu!=0 and k an integer are called associated Laguerre polynomials L_n^k(x) (Arfken 1985, p. 726) or, in older ...

Find the shape of the curve down which a bead sliding from rest and accelerated by gravity will slip (without friction) from one point to another in the least time. The term ...

The cosine function cosx is one of the basic functions encountered in trigonometry (the others being the cosecant, cotangent, secant, sine, and tangent). Let theta be an ...