Search Results for ""

A special case of Hölder's sum inequality with p=q=2, (sum_(k=1)^na_kb_k)^2<=(sum_(k=1)^na_k^2)(sum_(k=1)^nb_k^2), (1) where equality holds for a_k=cb_k. The inequality is ...

The conjecture that, for any triangle, 8omega^3<ABC (1) where A, B, and C are the vertex angles of the triangle and omega is the Brocard angle. The Abi-Khuzam inequality ...

By the duality principle, for every polyhedron, there exists another polyhedron in which faces and polyhedron vertices occupy complementary locations. This polyhedron is ...

For positive numbers a and b with a!=b, (a+b)/2>(b-a)/(lnb-lna)>sqrt(ab).

A convex planar domain in which the minimal generalized diameter is >1 always contains a circle of radius 1/3.

If, in the Gershgorin circle theorem for a given m, |a_(jj)-a_(mm)|>Lambda_j+Lambda_m for all j!=m, then exactly one eigenvalue of A lies in the disk Gamma_m.

int_a^bf_1(x)dxint_a^bf_2(x)dx...int_a^bf_n(x)dx <=(b-a)^(n-1)int_a^bf_1(x)f_2(x)...f_n(x)dx, where f_1, f_2, ..., f_n are nonnegative integrable functions on [a,b] which are ...

Define a cell in R^1 as an open interval or a point. A cell in R^(k+1) then has one of two forms, {(x,y):x in C, and f(x)<y<g(x)} (1) or {(x,y):x in C, and y=f(x)}, (2) where ...

Let A be a matrix and x and b vectors. Then the system Ax=b, x>=0 has no solution iff the system A^(T)y>=0, b^(T)y<0 has a solution, where y is a vector (Fang and Puthenpura ...

When applied to a system possessing a length R at which solutions in a variable r change character (such as the gravitational field of a sphere as r runs from the interior to ...