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Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Articles in this Issue were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence. Articles are hosted by MDPI on mdpi.com as a courtesy and upon agreement with the previous journal publisher.

Table of Contents

Math. Comput. Appl., Volume 9, Issue 2 (August 2004) , Pages 125-332

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Open AccessArticle
An Infinite Plate with a Curvilinear Hole and Flowing Heat
Math. Comput. Appl. 2004, 9(2), 321-332; https://doi.org/10.3390/mca9020321
Published: 1 August 2004
Viewed by 473 | PDF Full-text (623 KB)
Abstract
In the present paper, we apply the complex variable method (Cauchy method) to derive exact expressions for the Goursat's functions for the boundary value problem of infinite plate weakened by a curvilinear hole. The hole is conformally mapped on the domain outside a [...] Read more.
In the present paper, we apply the complex variable method (Cauchy method) to derive exact expressions for the Goursat's functions for the boundary value problem of infinite plate weakened by a curvilinear hole. The hole is conformally mapped on the domain outside a unit circle by means of a general rational mapping function. Also the stress components, when an initial heat is uniformly flowing in the perpendicular direction of the hole, are obtained, Some applications are investigated. The interesting cases, when the shape of the hole takes different famous formulas are included as special cases, The work of many previous authors can be considered as special cases of this work. Full article
Open AccessArticle
On Sister Celine’s Polynomials of Several Variables
Math. Comput. Appl. 2004, 9(2), 309-320; https://doi.org/10.3390/mca9020309
Published: 1 August 2004
Viewed by 455 | PDF Full-text (620 KB)
Abstract
The aim of the present paper is to define Sister Celine's polynomials of two and more variables. We reduce the two variables Sister Celine's polynomials into many classical orthogonal polynomials and their product also such as – Jacobi, Gegenbauer, Legendre, Laguerre, Bessel and [...] Read more.
The aim of the present paper is to define Sister Celine's polynomials of two and more variables. We reduce the two variables Sister Celine's polynomials into many classical orthogonal polynomials and their product also such as – Jacobi, Gegenbauer, Legendre, Laguerre, Bessel and some discrete polynomials Bateman, Pasternak, Hahn, Krawtchouk, Meixner, Poisson-Charlier & others. Many integral representations and generating function relations are also established. Full article
Open AccessArticle
A Note on the Norms of the GCD Matrix
Math. Comput. Appl. 2004, 9(2), 303-308; https://doi.org/10.3390/mca9020303
Published: 1 August 2004
Viewed by 541 | PDF Full-text (1856 KB)
Abstract
Let \(S=\{1,2,..., n\}\) be a set of positive integers. The \(n\times n\) matrix \([S]=(i,j)\), where \(s_{ij}=(x_{i},x_{j})\) the greatest common divisor of \(x_{i}\) and \(x_{j}\), is called the greatest common divisor GCD matrix on \(S\). In this study, we have obtained some bounds of [...] Read more.
Let \(S=\{1,2,..., n\}\) be a set of positive integers. The \(n\times n\) matrix \([S]=(i,j)\), where \(s_{ij}=(x_{i},x_{j})\) the greatest common divisor of \(x_{i}\) and \(x_{j}\), is called the greatest common divisor GCD matrix on \(S\). In this study, we have obtained some bounds of norms of this matrix. In addition, we have obtained upper bounds of norms of the almost Hilbert-Smith GCD matrix is defined \((S)=\left[ \frac{(i,j)}{ij} \right]^{n}_{i,j=1}\) Full article
Open AccessArticle
Estimation of Efficiency and Infinitesimals in Data Envelopment Analysis
Math. Comput. Appl. 2004, 9(2), 299-302; https://doi.org/10.3390/mca9020299
Published: 1 August 2004
Viewed by 516 | PDF Full-text (500 KB)
Abstract
The role of the non-Archimedean construct ε in the DEA models is clarified. It is established that the multiplier (envelopment) forms of DEA models can be infeasible (unbounded). Sufficient conditions are established for feasibility (bounded ness) of multiplier (envelopment) forms of DEA models [...] Read more.
The role of the non-Archimedean construct ε in the DEA models is clarified. It is established that the multiplier (envelopment) forms of DEA models can be infeasible (unbounded). Sufficient conditions are established for feasibility (bounded ness) of multiplier (envelopment) forms of DEA models and a method of securing a global assurance interval for ε is provided. Full article
Open AccessArticle
General Fermion Triangle Amplitude in the Coupling of Spin-1 Particles and Ward Identities
Math. Comput. Appl. 2004, 9(2), 285-298; https://doi.org/10.3390/mca9020285
Published: 1 August 2004
Viewed by 490 | PDF Full-text (671 KB)
Abstract
The general off mass-shell one-loop amplitude ta the termion triangle diagrams is calculated, in theories with γ5 couplings for spin-1 particles. Properties of the Bose symmetry and Ward identities for the couplings of neutral particles are investigated . The VVA and AAA [...] Read more.
The general off mass-shell one-loop amplitude ta the termion triangle diagrams is calculated, in theories with γ5 couplings for spin-1 particles. Properties of the Bose symmetry and Ward identities for the couplings of neutral particles are investigated . The VVA and AAA triangle diagrams are obtained from our general form. All resulting amplitudes are consistent with Ward identities. The amplitude for the coupling of three identical spin-1 particles is given. This amplitude obeys Bose symmetry and Ward identities for anomaly free theory. Full article
Open AccessArticle
Effects of Periodic Magnetic Field to the Dynamics of Vibrating Beam
Math. Comput. Appl. 2004, 9(2), 275-284; https://doi.org/10.3390/mca9020275
Published: 1 August 2004
Cited by 2 | Viewed by 499 | PDF Full-text (625 KB)
Abstract
Dynamics of a magnetoelastic beam in a periodic magnetic field is investigated. For this aim, a new measurement tool for the observation of vibrations of the beam is introduced in place of Using common strain-gauge technique. Several analyses including power spectra, maximal Lyapunov [...] Read more.
Dynamics of a magnetoelastic beam in a periodic magnetic field is investigated. For this aim, a new measurement tool for the observation of vibrations of the beam is introduced in place of Using common strain-gauge technique. Several analyses including power spectra, maximal Lyapunov exponent, correlation dimension and time series clustering are carried out to determine vibrational aspects of the system. As a result of these analyses, it is found that the system extremely depends on the frequency of external field, even, the nonlinear character of the motion exhibits more complexity for the odd excitation frequencies. Full article
Open AccessArticle
On the Unsteady Flows Generated by Impulsive Motion of a Boundary
Math. Comput. Appl. 2004, 9(2), 265-274; https://doi.org/10.3390/mca9020265
Published: 1 August 2004
Viewed by 512 | PDF Full-text (629 KB)
Abstract
Some properties of unsteady unidirectional flows of viscous fluids are examined for flows impulsively started from rest by the motion of a boundary or two boundaries. Three illustrative examples are given. The first example is the unsteady Couette flow, the second is the [...] Read more.
Some properties of unsteady unidirectional flows of viscous fluids are examined for flows impulsively started from rest by the motion of a boundary or two boundaries. Three illustrative examples are given. The first example is the unsteady Couette flow, the second is the unsteady flow between two parallel plates suddenly set in motion with the same speed and the third is the unsteady flow in a circular cylinder moving parallel to its length. It is shown that if the conditions for which the values of the quantities such as velocity, flux and skin friction obtained for large times are nearly the same with those obtained for small times are established, the expressions of the quantities obtained for one of large times or small times can also be used for the Other. Full article
Open AccessArticle
Free Vibration Analysis of Elastic Beams Using Harmonic Differential Quadraure (HDQ)
Math. Comput. Appl. 2004, 9(2), 257-264; https://doi.org/10.3390/mca9020257
Published: 1 August 2004
Cited by 2 | Viewed by 578 | PDF Full-text (577 KB)
Abstract
Harmonic differential quadrature method is developed for the free vibration analysis of linear elastic beams. In the method of differential quadrature, partial space derivatives of a function appearing in a differential equation are approximated by means of a polynomial expressed as the weighted [...] Read more.
Harmonic differential quadrature method is developed for the free vibration analysis of linear elastic beams. In the method of differential quadrature, partial space derivatives of a function appearing in a differential equation are approximated by means of a polynomial expressed as the weighted linear sum of the function values at a preselected grid of discrete points. The weighting coefficients are treated as the unknowns. Applying this concept to the governing differential equation of beam gives a set of linear simultaneous equations, which are solved for the unknown weighting coefftcients by accounting for the boundary conditions. Beams of different support combinations such as clamped, simply supported, guided, and free are selected to demonstrate the accuracy of the method. Flexural vibration case is taken into consideration. First two frequencies are obtained in the applications. Numerical results are presented to illustrate the method and demonstrate its efficiency. Full article
Open AccessArticle
Determination of Hardness of Pre-Aged AA 6063 Aluminum Alloy by Means of Artificial Neural Networks Method
Math. Comput. Appl. 2004, 9(2), 249-256; https://doi.org/10.3390/mca9020249
Published: 1 August 2004
Cited by 1 | Viewed by 613 | PDF Full-text (544 KB)
Abstract
A lot of experiments must be conducted in order to find an appropriate technology for the calculation of strength of the materials, which wastes both man power and money. For this reason artificial neural networks (ANNs) have been used to search the optimum [...] Read more.
A lot of experiments must be conducted in order to find an appropriate technology for the calculation of strength of the materials, which wastes both man power and money. For this reason artificial neural networks (ANNs) have been used to search the optimum technology proper for pre-aged AA 6063 aluminum alloy. In this study, ANNs were used to compare experimental results and test data were used for teaching of the ANNs. This paper examines the changes in the hardness of AA 6063 alloys when heat treated at different pre-aging treatments. The alloy was solution treated for 1 hour at 525±3 °C and quenched in water. After quenching, samples were subjected to five different pre aging times, 2 hours, I day, 3 days, 7 days. On the other hand, some specimens were not pre-aged. Artificial age temperatures were selected as 160 °C and 180 °C. The hardness values of these under-aged alloys were measured. When the pre-aging time was 7 days, the hardness values of the specimens increased. An excellent correlation was found between experimental hardness results and ANNs hardness results. Full article
Open AccessArticle
Thermoelastic Problem for an Infinite Plate with a Curvilinear Hole Having Finite Poles
Math. Comput. Appl. 2004, 9(2), 237-248; https://doi.org/10.3390/mca9020237
Published: 1 August 2004
Viewed by 517 | PDF Full-text (612 KB)
Abstract
In the present paper, Muskhelishvili's complex variable method of solving two-dimensional elasticity problems has been applied to derive exact expressions for Goursat's functions for the boundary value problems of the infinite plate weakened by a hole having many poles and arbitrary shape which [...] Read more.
In the present paper, Muskhelishvili's complex variable method of solving two-dimensional elasticity problems has been applied to derive exact expressions for Goursat's functions for the boundary value problems of the infinite plate weakened by a hole having many poles and arbitrary shape which is conformally mapped n the dorhain outside a unit circle by means of general rational mapping function. Also the components of stress are obtained, when a stationary heat is flowing uniformly in the perpendicular direction of the hole. Some applications are considered. The interesting cases when the shape of the hole takes different shapes are included as special cases. Full article
Open AccessArticle
On a Class of Nonlinear Singular Integral Equations with Carleman Shift in Generalized Holder Spaces
Math. Comput. Appl. 2004, 9(2), 225-236; https://doi.org/10.3390/mca9020225
Published: 1 August 2004
Viewed by 491 | PDF Full-text (624 KB)
Abstract
The paper concerns with the investigation of a class of nonlinear singular integral equations with Carlernan shift. Existence results are given by application of Schauder's fixed-point theorem to this type of equations in generalized Holder space. Full article
Open AccessArticle
Green’s Function for Parallel Planes and an Open Rectangular Channel-Flow
Math. Comput. Appl. 2004, 9(2), 215-224; https://doi.org/10.3390/mca9020215
Published: 1 August 2004
Viewed by 455 | PDF Full-text (555 KB)
Abstract
Here we use a more convenient technique to generate a faster convergent Green's function needed for solving Laplace's equation in two cases: the first domain is bounded by two parallel planes; and the second is an infinite open rectangular prism. Green's function usually [...] Read more.
Here we use a more convenient technique to generate a faster convergent Green's function needed for solving Laplace's equation in two cases: the first domain is bounded by two parallel planes; and the second is an infinite open rectangular prism. Green's function usually is expressed as a series of images which is slowly convergent, and that is why we transform it into an integral representation which is rapidly convergent and stable. Many examples are herein given and discussed for the numerical applications of the above two cases; and then we make a comparison between our calculations and some others. Full article
Open AccessArticle
Extrapolation Method for Improving the Solution of Fuzzy Initial Value Problems
Math. Comput. Appl. 2004, 9(2), 205-214; https://doi.org/10.3390/mca9020205
Published: 1 August 2004
Cited by 1 | Viewed by 502 | PDF Full-text (502 KB)
Abstract
In this paper we apply extrapolation to increase the accuracy of approximations to the solution of the fuzzy initial value problems, based on the standard Euler method and Midpoint method, [11]. The method in detail is discussed and is illustrated by solving sme [...] Read more.
In this paper we apply extrapolation to increase the accuracy of approximations to the solution of the fuzzy initial value problems, based on the standard Euler method and Midpoint method, [11]. The method in detail is discussed and is illustrated by solving sme linear and nonlinear fuzzy Cauchy problems. Full article
Open AccessArticle
An Existence Theorem for General Mixed Multivalued Mildly Nonlinear Variational Inequalities without Convexity
Math. Comput. Appl. 2004, 9(2), 201-203; https://doi.org/10.3390/mca9020201
Published: 1 August 2004
Viewed by 436 | PDF Full-text (201 KB)
Abstract
A general mixed multivalued mildly nonlinear variational inequality is considered. We establish an existence result for (GMMMNVIP) in H-spaces by using the new result of Chang et al [21]. Full article
Open AccessArticle
Presentations for Regular Unbranched Cp-Coverings of a Klein Bottle
Math. Comput. Appl. 2004, 9(2), 191-199; https://doi.org/10.3390/mca9020191
Published: 1 August 2004
Viewed by 448 | PDF Full-text (395 KB)
Abstract
In this paper, we obtain presentations for the non-equivalent regular unbranched Cp-coverings of a Klein Bottle by using the Reidemeister-Schreier method, where Cp =< a | ap =1 > is a cyclic group of order p (p is a prime). Full article
Open AccessArticle
A Formulation of Peaceman and Rachford ADI Method for the Three-Dimensional Heat Diffusion Equation
Math. Comput. Appl. 2004, 9(2), 183-189; https://doi.org/10.3390/mca9020183
Published: 1 August 2004
Viewed by 641 | PDF Full-text (370 KB)
Abstract
A formulation of an alternating direction implicit (ADI) method is given by extending peaceman and Rachford Scheme to three dimensions. The scheme becomes conditionally stable. The von Neumann stability analysis is performed. Numerical results for solving heat diffusion equation have been obtained for [...] Read more.
A formulation of an alternating direction implicit (ADI) method is given by extending peaceman and Rachford Scheme to three dimensions. The scheme becomes conditionally stable. The von Neumann stability analysis is performed. Numerical results for solving heat diffusion equation have been obtained for different specified boundary value problems to obtain a simple explicit stability. Full article
Open AccessArticle
Crossed Modules of Algebras
Math. Comput. Appl. 2004, 9(2), 173-182; https://doi.org/10.3390/mca9020173
Published: 1 August 2004
Viewed by 441 | PDF Full-text (536 KB)
Abstract
In this paper we will give some algebraic results of crossed modules of algebras. Full article
Open AccessArticle
Proximal Methods for Generalized Nonlinear Quasi-Variational Inclusions
Math. Comput. Appl. 2004, 9(2), 165-171; https://doi.org/10.3390/mca9020165
Published: 1 August 2004
Viewed by 453 | PDF Full-text (395 KB)
Abstract
We consider the solvability, based on iterative algorithms, of the generalized nonlinear quasi-variational inclusion problems involving the relaxed Lipschitz and relaxed monotone mappings. Full article
Open AccessArticle
A Designed ADI Software for Solving Poisson’s Equation
Math. Comput. Appl. 2004, 9(2), 157-164; https://doi.org/10.3390/mca9020157
Published: 1 August 2004
Viewed by 562 | PDF Full-text (498 KB)
Abstract
In This paper, a software has been designed to perform the alternating direction implicit, ADI, method for the case of two dimensional flow represented by Poisson's equation. A square mesh with varying mesh size has been adopted. The results came out very much [...] Read more.
In This paper, a software has been designed to perform the alternating direction implicit, ADI, method for the case of two dimensional flow represented by Poisson's equation. A square mesh with varying mesh size has been adopted. The results came out very much complying with the analytical solutions asserting the rigour of the software. Full article
Open AccessArticle
A Method for Solving 0-1 Multiple Objective Programming Problem Using Data Envelopment Analysis Technique
Math. Comput. Appl. 2004, 9(2), 147-156; https://doi.org/10.3390/mca9020147
Published: 1 August 2004
Viewed by 495 | PDF Full-text (553 KB)
Abstract
In this paper a method for finding efficient solutions of a 0-1 Multiple Objective Linear (Nonlinear) programming Problem using Data Envelopment Analysis (DEA) technique is proposed. In this method, for each feasible solution of 04 Multiple Objective Programming (0-1 MOP) problem, a Decision [...] Read more.
In this paper a method for finding efficient solutions of a 0-1 Multiple Objective Linear (Nonlinear) programming Problem using Data Envelopment Analysis (DEA) technique is proposed. In this method, for each feasible solution of 04 Multiple Objective Programming (0-1 MOP) problem, a Decision Making Unit (DMU) is introduced. Using the additive model, the relative efficiency of these DMUs is evaluated. Each feasible solution corresponding to an efficient DMU is the efficient solution of 0-1 MOP problem. Full article
Open AccessArticle
Effect of Forward Speed on Ship Rolling and Stability
Math. Comput. Appl. 2004, 9(2), 133-145; https://doi.org/10.3390/mca9020133
Published: 1 August 2004
Cited by 3 | Viewed by 519 | PDF Full-text (865 KB)
Abstract
Ship stability is evaluated at zero speed most of the time. Majority of the stability criteria is also based on the behavior of ships at standstill. However unlike fixed offshore platfoims, ships are on the move due to their nature of operation. Therefore [...] Read more.
Ship stability is evaluated at zero speed most of the time. Majority of the stability criteria is also based on the behavior of ships at standstill. However unlike fixed offshore platfoims, ships are on the move due to their nature of operation. Therefore a ship's hydrostatic and hydrodynamic characteristics undergo changes because of the varying underwater volume, centers of buoyancy and gravity and pressure distribution. This work deals with the effects of forward speed on ship stability and motions, particularly on rolling motion in synchronous beam waves. An equation of nonlinear roll motion is chosen to calculate roll responses of a test vessel in beam seas. The speed of advance is incremented and roll responses are determined at each speed interval. Various characteristics of GZ curve for the selected test vessel are altered systematically to observe their effects on roll responses along with the forward speed. Several computer programs are also employed to handle colossal mathematical manipulations. Full article
Open AccessArticle
Projection Methods for Quasi-Variational Inequalities
Math. Comput. Appl. 2004, 9(2), 125-131; https://doi.org/10.3390/mca9020125
Published: 1 August 2004
Cited by 2 | Viewed by 508 | PDF Full-text (442 KB)
Abstract
In this paper, we consider a new class of variational inequalities which is called the general mixed multivalued nonlinear quasi-variational inequality. We define an iterative algorithm and prove the existence solution for our general mixed multivalued nonlinear quasi-variational inequality by using the updating [...] Read more.
In this paper, we consider a new class of variational inequalities which is called the general mixed multivalued nonlinear quasi-variational inequality. We define an iterative algorithm and prove the existence solution for our general mixed multivalued nonlinear quasi-variational inequality by using the updating projection method and convergence criteria for iterative sequences generated by algorithm are also discussed. Full article
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