Volume 2 (2010), Number 1
One Derivative of One Component Regularity Criterion for the Navier-Stokes Equations
Author(s): YUAN-SHAN ZHAO AND YUE HU
Abstract: We study the incompressible Navier-Stokes equations in the entire three-dimensional space and we prove that if there exists one derivative of one component of the velocity then the solution is regular. This extends one result of Patrick Penel, Toulon, Milan Pokorý, Praha [Appl.Math.,49,483-493(2004)]
DownloadOn Some Multiplier Difference Sequence Spaces Defined over a 2-normed Linear Space
Author(s): B.SURENDER REDDY AND HEMEN DUTTA
Abstract: In this paper, we introduce a new class of generalized difference sequences with base space, a real linear 2-normed space and by means of a fixed multiplier. We study the spaces of thus constructed classes of sequences for relevant linear topological structures. Further we investigate the spaces for solidity, monotonicity, symmetricity etc. We also obtain some relations between these spaces as well as prove some inclusion results.
DownloadOn Some Inequalities of Simpson-type Via Quasi-Convex Functions and Applications
Author(s): MOHAMMAD ALOMARI AND MASLINA DARUS
Abstract: Some inequalities of Simpson's type for quasi-convex functions are introduced. In the literature the error estimates for the midpoint rule is , in this paper we restrict the conditions on f to get better error estimates than the original.
DownloadSolving Cauchy Problem for a Class of Sixth-order Hyperbolic Equations with Triple Characteristics
Author(s): LAZHAR BOUGOFFA AND HIND K. AL-JEAID
Abstract: In this paper, the Cauchy problem for a class of the homogeneous hyperbolic equations for sixth-order with triple characteristics is considered and can be solved analytically by direct integration techniques. Also, an efficient modification of Adomian decomposition method is proposed for solving this type of problems. We then conduct a comparative study between the ADM and direct method with the help of several illustrative examples.
DownloadNew Explicit and Implicit Solutions to Elliptic Equations with Two Space Variables
Author(s): MOHAMMED A. AL-KADHI
Abstract: We present a direct method for finding a new explicit and implicit solutions of elliptic equations with hyperbolic, trigonometric and exponential nonlinearities.
DownloadBAICA-CARDU Paratrigonometry, a Generalization of the Classical and Some New Non-classical Trigonometries and Its Application in Mechanics and Wave Theory
Author(s): M. BAICA AND M.CARDU
Abstract: In their previous papers the authors introduced some new Trigonometries as: 1. Quadratic Trigonometry (QT), 2. Polygonal Trigonometry (PT), 3. Trans Trigonometry (TT), 4. Infra Trigonometry (IT), 5. Ultra-Trigonometry (UT), 6. Extra Trigonometry (ET), 7. Para-Trigonometry (PRT). This time in this paper we perform a synthesis of all these Trigonometries and state some of their applications.
DownloadOscillation of a Class of Two-variables Functional Equations with Variable Coefficients
Author(s): WENGUI YANG
Abstract: In this paper we will establish some sufficient conditions of oscillation of a class of two-variables functional equations with variable coefficients. Our results extend Zhang and Zhou's results (B.G. Zhang and Y. Zhou, Comput. Math. Appl. 42 (3-5) (2001) 369-378).
DownloadOn Algebraic Properties of the Generalized Chebyshev Polynomials
Author(s): AHMET İPEK
Abstract: Chebyshev polynomials are of great importance in many areas of mathematics, particularly approximation theory. Numerous articles and books have been written about this topic. Analytical properties of Chebyshev polynomials are well understood, but algebraic properties less so. In this paper, new generalized Chebyshev polynomials of the first and second kinds have been introduced and studied. Many of the properties of these polynomials are proved.
DownloadA Note on Bounds for the Spectral Norms of Circulant-Cauchy-Toeplitz Matrices
Author(s): AHMET İPEK
Abstract: In this paper, we established lower and upper bounds for the spectral norms of some Circulant-Cauchy-Toeplitz matrices.
DownloadA Nonlinear Mixed Type Volterra-Fredholm Functional Integral Equation Via Perov's Theorem
Author(s): MARCEL-ADRIAN ȘERBAN
Abstract: In this paper we study the following mixed type Volterra-Fredholm functional integral equation . Using the Perov's Theorem and the Picard operator technique we establish existence, uniqueness, data dependence and Gronwall results for the solutions.
DownloadThe Solution of a System of Nonlinear Integral Equations from Physics
Author(s): MARIA DOBRIŢOIU
Abstract: Using the Perov's Theorem and the General data dependence Theorem, in this paper, we obtain some conditions concerning the existence and uniqueness of the solution in the Banach space and the continuous data dependence of the solution of the following system of nonlinear integral equations from physics: . An example is also given here.
DownloadDouble Inequalities of Boole's Quadrature Rule
Author(s): MARIUS HELJIU
Abstract: In this paper double inequalities of Boole's type quadrature rule are given. These inequalities are sharp.
DownloadThe Green's Matrix and the Green's Type Integral Formula for an Elastic Strip
Author(s): TATIANA SPEIANU
Abstract: An efficient unified method to derive Green's matrices, called the incompressible influence elements method (IIEM), had been elaborated and published earlier by V. D. Șeremet [Handbook of Green's Functions and Matrices, WIT press, Southampton, Boston, 2003]. The main point of this method is general integral representations for Green's matrices in terms of Green's functions for Poisson's equation. This paper uses above mentioned representations to derive the Green's matrix and the Green's type integral formula for a boundary value problem (BVP) for an elastic strip. All results are obtained exactly and in elementary functions. To obtain these results some Green's functions for Posson's equation for a strip are derived. An exact solution for a particular BVP for an elastic strip also is included.
Download