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The product of a family {X_i}_(i in I) of objects of a category is an object P=product_(i in I)X_i, together with a family of morphisms {p_i:P->X_i}_(i in I) such that for ...

A leg of a right triangle (i.e., a side adjacent the right angle) is also known as a cathetus (plural: catheti). While this usage is rather rare in English, the terms ...

This theorem states that, for a partial differential equation involving a time derivative of order n, the solution is uniquely determined if time derivatives up to order n-1 ...

Let {a_n} be a series of positive terms with a_(n+1)<=a_n. Then sum_(n=1)^(infty)a_n converges iff sum_(k=0)^infty2^ka_(2^k) converges.

Cauchy conditions are initial conditions (time conditions) rather than boundary conditions (space conditions). An initial-value problem is often termed a Cauchy problem. ...

The Cauchy remainder is a different form of the remainder term than the Lagrange remainder. The Cauchy remainder after n terms of the Taylor series for a function f(x) ...

The curve which is the envelope of reflected (catacaustic) or refracted (diacaustic) rays of a given curve for a light source at a given point (known as the radiant point).

If, in two solids of equal altitude, the sections made by planes parallel to and at the same distance from their respective bases are always equal, then the volumes of the ...

Given A = |a_(11)-x a_(12) ... a_(1m); a_(21) a_(22)-x ... a_(2m); | | ... |; a_(m1) a_(m2) ... a_(mm)-x| (1) = x^m+c_(m-1)x^(m-1)+...+c_0, (2) then ...

The parameters alpha, beta, gamma, and delta which, like the three Euler angles, provide a way to uniquely characterize the orientation of a solid body. These parameters ...