$Open Mathematics$

Open Access Published by De Gruyter Open Access

Volume 2 Issue 4

August 2004

Issue of Open Mathematics

Submit manuscript

Contents
Journal Overview

Open Access August 1, 2004

On the riemann zeta-function and the divisor problem

Aleksandar Ivić

Page range: 494-508

More Download PDF

Abstract

Let Δ(x) denote the error term in the Dirichlet divisor problem, and E(T) the error term in the asymptotic formula for the mean square of $$\left| {\varsigma \left( {\tfrac{1}{2} + it} \right)} \right|$$ . If $$E^* \left( t \right) = E\left( t \right) - 2\pi \Delta ^* \left( {t / 2\pi } \right)$$ with $$\Delta ^* \left( x \right) = - \Delta \left( x \right) + 2\Delta \left( {2x} \right) - \tfrac{1}{2}\Delta \left( {4x} \right)$$ , then we obtain $$\int_0^T {\left( {E^* \left( t \right)} \right)^4 dt \ll _e T^{16/9 + \varepsilon } } $$ . We also show how our method of proof yields the bound $$\sum\limits_{r = 1}^R {\left( {\int_{tr - G}^{tr + G} {\left| {\varsigma \left( {\tfrac{1}{2} + it} \right)} \right|^2 dt} } \right)^4 \ll _e T^{2 + e} G^{ - 2} + RG^4 T^\varepsilon } $$ , where T 1/5+ε≤G≪T, T<t 1<...<t R≤2T, t r +1−t r≥5G (r=1, ..., R−1).

Open Access August 1, 2004

On the apostol-bernoulli polynomials

Qiu-Ming Luo

Page range: 509-515

More Download PDF

Abstract

In the present paper, we obtain two new formulas of the Apostol-Bernoulli polynomials (see On the Lerch Zeta function. Pacific J. Math., 1 (1951), 161–167.), using the Gaussian hypergeometric functions and Hurwitz Zeta functions respectively, and give certain special cases and applications.

Open Access August 1, 2004

Distinguished geodesics and jacobi fields on first order jet spaces

Vladimir Balan, Nicoleta Voicu

Page range: 516-526

More Download PDF

Abstract

In the framework of jet spaces endowed with a non-linear connection, the special curves of these spaces (h-paths, v-paths, stationary curves and geodesics) which extend the corresponding notions from Riemannian geometry are characterized. The main geometric objects and the paths are described and, in the case when the vertical metric is independent of fiber coordinates, the first two variations of energy and the extended Jacobi field equations are derived.

Open Access August 1, 2004

A compound of the generalized negative binomial distribution with the generalized beta distribution

Tadeusz Gerstenkorn

Page range: 527-537

More Download PDF

Abstract

This paper presents a compound of the generalized negative binomial distribution with the generalized beta distribution. In the introductory part of the paper, we provide a chronological overview of recent developments in the compounding of distributions, including the Polish results. Then, in addition to presenting the probability function of the compound generalized negative binomial-generalized beta distribution, we present special cases as well as factorial and crude moments of some compound distributions.

Open Access August 1, 2004

Zero-dimensional subschemes of ruled varieties

Edoardo Ballico, Cristiano Bocci, Claudio Fontanari

Page range: 538-560

More Download PDF

Abstract

Here we study zero-dimensional subschemes of ruled varieties, mainly Hirzebruch surfaces and rational normal scrolls, by applying the Horace method and the Terracini method

Open Access August 1, 2004

Local properties of the solution set of the operator equation in Banach spaces in a neighbourhood of a bifurcation point

Joanna Janczewska

Page range: 561-572

More Download PDF

Abstract

In this work we study the problem of the existence of bifurcation in the solution set of the equation F(x, λ)=0, where F: X×R k →Y is a C 2-smooth operator, X and Y are Banach spaces such that X⊂Y. Moreover, there is given a scalar product 〈·,·〉: Y×Y→R 1 that is continuous with respect to the norms in X and Y. We show that under some conditions there is bifurcation at a point (0, λ0)∈X×R k and we describe the solution set of the studied equation in a small neighbourhood of this point.

Open Access August 1, 2004

On the existence of solutions for nonlinear impulsive periodic viable problems

Tiziana Cardinali, Raffaella Servadei

Page range: 573-583

More Download PDF

Abstract

In this paper we prove the existence of periodic solutions for nonlinear impulsive viable problems monitored by differential inclusions of the type x′(t)∈F(t,x(t))+G(t,x(t)). Our existence theorems extend, in a broad sense, some propositions proved in [10] and improve a result due to Hristova-Bainov in [13].

Open Access August 1, 2004

Folding theory applied to BL-algebras

Young Jun, Jung Ko

Page range: 584-592

More Download PDF

Abstract

The notion of n-fold grisly deductive systems is introduced. Some conditions for a deductive system to be an n-fold grisly deductive system are provided. Extension property for n-fold grisly deductive system is established.

Open Access August 1, 2004

Generalization of weierstrass canonical integrals

Olga Veselovska

Page range: 593-604

More Download PDF

Abstract

In this paper we prove that a subharmonic function in ℝm of finite λ-type can be represented (within some subharmonic function) as the sum of a generalized Weierstrass canonical integral and a function of finite λ-type which tends to zero uniformly on compacts of ℝm. The known Brelot-Hadamard representation of subharmonic functions in ℝm of finite order can be obtained as a corollary from this result. Moreover, some properties of R-remainders of λ-admissible mass distributions are investigated.

Open Access August 1, 2004

Approximation properties of wavelets and relations among scaling moments II

Václav Finěk

Page range: 605-613

More Download PDF

Abstract

A new orthonormality condition for scaling functions is derived. This condition shows a close connection between orthonormality and relations among discrete scaling moments. This new condition in connection with certain approximation properties of scaling functions enables to prove new relations among discrete scaling moments and consequently the same relations for continuous scaling moments.

Open Access August 1, 2004

Addendum to “Hochschild cohomology of skew group rings and invariants”

E. Marcos, R. Martínez-Villa, Ma. Martins

Page range: 614-614

Download PDF

About this journal

Open Mathematics is a fully peer-reviewed open access journal that publishes original and relevant works on topics across the full span of mathematics. The journal's primary goal is to maintain the high quality of its published content and to provide free, instant, and continued access to all content worldwide.

AIMS AND SCOPE
Open Mathematics aims to promote knowledge directly relevant to all fields of mathematics. Subject areas suitable for publication include, but are not limited to, the following:

Algebra, Algebraic Geometry, Category Theory, Complex Analysis, Control Theory and Optimization, Differential Equations, Differential Geometry, Discrete Mathematics, Dynamical Systems and Ergodic Theory, Functional Analysis, Geometry, Mathematical Logic and Foundations, Mathematical Physics, Number Theory, Numerical Analysis, Operator Theory, Probability Theory and Statistics, Real Analysis, and Topology.

The journal accepts submissions of research articles, reviews, and communications. Submission of a manuscript implies that the work described is not copyrighted, published or submitted elsewhere, except in abstract form. The corresponding author should ensure that all authors approve the manuscript before its submission.