On Some Infinite Series Introduced by Tschuprow

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

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...

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.

Error Introduced by the Infinite - Sites Model 1

In a recent paper, Henry Harpending and I (Rogers and Harpending 1992) interpret variation in human mitochondrial DNA by using a model by Li ( 1977 ) . The model is unrealistic in several respects, one of which is its use of the “infinite sites” model (Kimura 1969 ) of molecular evolution. This model assumes that no nucleotide (or restriction) site mutates more than once, an assumption that is ...