A necessary and sufficient condition that a summability method be stronger than convergence

A Simple Sufficient Condition That a Method of Summability Be Stronger than Convergence

and a method A of summability by means of which a given sequence Su S2, • • • is summable to <r as w—»oo. If a sequence sn is summable A, we say that A {sn} exists and that sn belongs to the summability field of A. If sn is summable A to <r, we say that A {sn} = <r. The method A is regular if A {sn} = lim sn whene...

Necessary and sufficient conditions for matrix summability methods to be stronger than multisummability

A Necessary and Sufficient Condition for Partition Testing to be Better Than Random Testing

A necessary a n d sufficient condition is given for par t i t ion testing to be better t h a n random testing. I . INTRODUCTION Partition testing is an approach to program testing in which the input domain of the program is divided into partitions and test cases are selected from these partitions. A number of papers have attempted to clarify the relation between the performance of these two tes...

A Sufficient Condition That a C-Characteristic Be Geometric.

These inequalities express the fact that no curve of order k and defined at the p points can meet the net in more than yok points. Coble' has conjectured that the conditions (1) and (2) are sufficient as well as necessary. In this paper we will show that the conditions (2) are actually sufficient. Indeed, the less stringent set of inequalities given in (5) will suffice. The notation and point o...

A Necessary and Sufficient Condition for Transcendency

As has been known for many years (see, e.g., K. Mahler, /. Reine Angew. Math., v. 166, 1932, pp. 118-150), a real or complex number f is transcendental if and only if the following condition is satisfied. To every positive number co there exists a positive integer n and an infinite sequence of distinct polynomials {p,(z)} = {pr + pr z + • • • + p z } at most of 0 1 n degree n with integral coef...