Negative values of cosine sums

Some Special Values of Cosine

Strong Laws for Weighted Sums of Negative Dependent Random Variables

In this paper, we discuss strong laws for weighted sums of pairwise negatively dependent random variables. The results on i.i.d case of Soo Hak Sung [9] are generalized and extended.

A Note on Cosine Power Sums

where ⌊x⌋ denotes the largest integer not greater than x. Under certain conditions, these cosine power sums can be determined exactly, without approximations [5]. If f(x) = a0 + a1x+ a2x 2 + · · ·+ anx + · · · is a finite or convergent infinite series, then for 0 ≤ r < n the sum arx r + ar+nx r+n + ar+2nx r+2n + · · · is given by the multisection formula (see [1, Ch. 16], [4, Ch. 4, S. 4.3] and...

Cosine Products, Fourier Transforms, and Random Sums

one gets the first actual formula for 7r that mankind ever discovered, dating from 1593 and due to Frangois Viete (1540-1603), whose Latinized name is Vieta. (Was any notice taken of the formula's 400th anniversary, perhaps by the issue of a postage stamp?) From the samples of a function t(x) at equally spaced points x", n E z, one can reconstruct the complete function with the aid of sin x/x, ...

How to Compare the Absolute Values of Operator Sums and the Sums of Absolute Values?

We address the problem of comparing |A+B| and |A|+ |B| , for A,B ∈Mn(C) . Some results are obtained by using a technique of positive linear maps and several open questions are proposed. Mathematics subject classification (2010): Primary 15A60, 47A30, 47A60.