The triangular array of binomial coefficients 012301111212131331… is said to have undergone a j-shift if the r-th row of the triangle is shifted rj units to the right (r=0,1,2,…). Mann and Shanks have proved that in a 2-shifted array a column number c>1 is prime if and only if every entry in the c-th column is divisible by its row number. Extensions of this result to j-shifted...

The aim of the paper is to give an oscillation theorem for inhomogeneous Stieltjes integro-differential equation of the form p(t)x′

We prove that if f(z) is a continuous real-valued function on ℝ with the properties f(0)=f(1)=0 and that ‖f‖ z =infx,t|f(x

The aim of this paper is to determine both the Zariski constructible set of characteristically nilpotent filiform Lie algebras g of dimension 8 and that of the set of nilpotent filiform Lie algebras whose group of automorphisms consists of unipotent automorphisms, in the variety of filiform Lie algebras of dimension 8 over C.

We use Stein's method to find a bound for Cauchy approximation. The random variables which are considered need to be independent.

Given a Lie groupoid Ω, we construct a groupoid J1Ω equipped with a universal connection from which all the connections of Ω are obtained by certain pullbacks. We show that this general construction leads to universal connections on principal bundles (considered by García (1972)) and universal linear connections on vector bundles (ultimately related with those of Cordero et al...

We give an algorithm to compute the series expansion for the inverse of a given function. The algorithm is extremely easy to implement and gives the first N terms of the series. We show several examples of its application in calculating the inverses of some special functions.

We investigate the structure of the singular part of the second bounded cohomology group of amalgamated products of groups by constructing an analog of the initial segment of the Mayer-Vietoris exact cohomology sequence for the spaces of pseudocharacters.

We present a rather simple proof of the existence of resonant frequencies for the direct scattering problem associated to a system of elastic wave equations with Dirichlet boundary condition. Our approach follows techniques similar to those in Cortés-Vega (2003). The proposed technique relies on a stationary approach of resonant frequencies, that is, the poles of the analytic...

In the last few years various infinite dimensional extensions to Krasnoselski's Theorem on starshaped sets [14] have been made. These began with a paper by Edelstein and Keener [8] and have culminated in the papers by Borwein, Edelstein and O'Brien [3] [4] by Edelstein, Keener and O'Brien [9] and finally by O'Brien [16].

A Bloch function is exhibited which has radial limits of modulus one almost everywhere but fails to belong to Hp for each 0<p≤∞.

We consider the second coefficient of a class of functions, univalent and normalized, and with all derivatives univalent in the unit disk D, and improve on a known result. It is also shown that this bound is in a sense best possible.

We consider Harmonic Functions, H of several variables. We obtain necessary and sufficient conditions on its Fourier coefficients so that H is an entire harmonic (that is, has no finite singularities) function; the radius of harmonicity in terms of its Fourier coefficients in case H is not entire. Further, we obtain, in terms of its Fourier coefficients, the Order and Type growth...

A (commutative) ring R (with identity) is called m-linear (for an integer m≥2) if (a

It is proved that if R is a semiprime ELT-ring and every simple right R-module is flat then R is regular. Is R regular if R is a semiprime ELT-ring and every simple right R-module is flat? In this note, we give a positive answer to the question.

In an earlier paper concerning a solvable Inodel in statistical mechanics, Miwa and Jimbo state a theta-function identity which they have checked to the 200th power, but of which they do not have a proof. The main objective of this note is to provide such a proof.

A new notion of weighted hyperbolic polynomials is introduced and their properties are discussed in this paper.

This paper gives relationships between continuous maps, closed maps, perfect maps, and maps with closed graph in certain classes of topological spaces.

Functional representation of a topological algebra (A,T) has been studied in many papers under various assumptions for the topology T on A. Usually the image Aˆ of the Gelfand map has been equipped with the compact-open topology. This leads, in several cases, to such kind of difficulties as, for instance, that the Gelfand map is not necessarily continuous or that the compact-open...

We find all complex potentials Q such that the general Schrödinger operator on ℝn, given by L=−Δ

Inspired by the two envelopes exchange paradox, a finitely additive probability measure m on the natural numbers is introduced. The measure is uniform in the sense that m({i})=m({j}) for all i,j∈ℕ. The measure is shown to be translation invariant and has such desirable properties as m({i∈ℕ|i≡0(mod2)})=1/2. For any r∈[0,1], a set A is constructed such that m(A)=r; however, m is...

By introducing three parameters r, s, and λ, we give a generalization of Mulholland's inequality with a best constant factor involving the β function. As its applications, we also consider its equivalent form and some particular results.

A numerical algorithm, based on a decomposition technique, is presented for solving a class of nonlinear integral equations. The scheme is shown to be highly accurate, and only few terms are required to obtain accurate computable solutions.

In this paper, a new type of non-self-mapping, called Berinde MT-cyclic contractions, is introduced and studied. Best proximity point theorems for this type of mappings in a metric space are presented. Some examples illustrating our main results are also given. Our results generalize and improve some known results in the literature.

Let G denote the dyadic group, which has as its dual group the Walsh(-Paley) functions. In this paper we formulate a condition for functions in L1(G) which implies that their Walsh-Fourier series converges in L1(G)-norm. As a corollary we obtain a Dini-Lipschitz-type theorem for L1(G) convergence and we prove that the assumption on the L1(G) modulus of continuity in this theorem...