On some infinite series of (r,1)-designs

Some Remarks on Infinite Series

In the present paper we investigate the following problems. Suppose an >O for n_-I and Z a,=-. n=1 N° 1. Does there exist a sequence of natural numbers No =O, Ni l-, such that it decomposes the series monotone decreasingly : In order to state the second problem we define the index nk (c) as the minimum m such that (2) Now the second problem is as follows. are equiconvergent. m kc a j. j=1 N° 2....

The Integrity of Some Infinite Series

Characterization on Some Absolute Summability Factors of Infinite Series

A general theorem concerning some absolute summability factors of infinite series is proved. This theorem characterizes as well as generalizes our previous result [4]. Other results are also deduced.

Some Infinite Families of Large Sets of t-Designs

A set of necessary conditions for existence of a large set of a t-design, LS ( (v−t k−t ) /n; t, k, v ) , is n| (v−i k−i ) for i = 0, 1, · · · , t. We show that these conditions are sufficient for n = 3, t = 2, 3, or 4, and k ≤ 8.

On Some Infinite Series Related to the Twin Primes

It is shown that all positive integers can be divided into numbers that can lead to a pair of twin primes by a simple algebraic operation and numbers that cannot. The paper devises a formula for finding the numbers in each category, and shows that the numbers in the second category can be arranged in infinite groups and super-groups with an inner symmetry, a precise interval length and a well-d...