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He’s Homotopy Perturbation Method for solving Linear and Non-Linear Fredholm Integro-Differential Equations
Bijan Krishna Saha,
A. M. Mohiuddin,
Sushanta Parua
Issue:
Volume 3, Issue 6, December 2017
Pages:
174-181
Received:
29 April 2017
Accepted:
8 October 2017
Published:
10 November 2017
Abstract: In this paper, linear and non-linear Fredholm Integro-Differential Equations with initial conditions are presented. Aiming to find out an analytic and approximate solutions to linear and non-linear Fredholm Integro-Differential Equations, this paper presents a comparative study of He’s Homotopy perturbation method with other traditional methods namely the Variational iteration method (VIM), the Adomian decomposition method (ADM), the Series solution method (SSM) and the Direct computation method (DCM). Comparison of the applied methods of analytic solutions reveals that He’s Homotopy perturbation method is tremendously powerful and effective mathematical tool.
Abstract: In this paper, linear and non-linear Fredholm Integro-Differential Equations with initial conditions are presented. Aiming to find out an analytic and approximate solutions to linear and non-linear Fredholm Integro-Differential Equations, this paper presents a comparative study of He’s Homotopy perturbation method with other traditional methods nam...
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New Fixed Point Theorems for Mixed Monotone Operators with Perturbation and Applications
Issue:
Volume 3, Issue 6, December 2017
Pages:
182-190
Received:
29 September 2017
Accepted:
23 October 2017
Published:
15 November 2017
Abstract: By using the properties of cone and the fixed point theorem for mixed monotone operators in ordered Banach spaces, we investigate the mixed monotone operators of a new type with perturbation. We establish some sufficient conditions for such operators to have a new existence and uniqueness fixed point and provide monotone iterative techniques which give sequences convergent to the fixed point. Finally, as applications, we apple the results obtained in this paper to study the existence and uniqueness of positive solutions for nonlinear fractional differential equation boundary value problems.
Abstract: By using the properties of cone and the fixed point theorem for mixed monotone operators in ordered Banach spaces, we investigate the mixed monotone operators of a new type with perturbation. We establish some sufficient conditions for such operators to have a new existence and uniqueness fixed point and provide monotone iterative techniques which ...
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Damping Properties of Vibrations of Three-Layer VIscoelastic Plate
Safarov Ismail Ibrahimovich,
Teshayev Muhsin Khudoyberdiyevich,
Boltayev Zafar Ixtiyorovich,
Akhmedov Maqsud Sharipovich
Issue:
Volume 3, Issue 6, December 2017
Pages:
191-198
Received:
28 September 2017
Accepted:
3 November 2017
Published:
30 November 2017
Abstract: The work is devoted to the study of harmonic waves in a hereditarily elastic plate with two viscoelastic coatings, the properties of the material, which are described by the equations of state in integral form. The fractional exponential function of Rabotnov and Koltunov-Rzhanitsyn was chosen as the kernel of the integral operator. Two cases are considered: the case of a stress-strain state symmetric and antisymmetric in the normal coordinate (VAT). In the study of natural oscillations, the properties of those modes that are time-dependent by harmonic law are investigated. For both cases, dispersion equations are derived, which are solved numerically. Asymptotics of the roots of dispersion equations for small and large frequencies are also obtained. The analysis of the obtained solutions made it possible to draw conclusions about the influence of hereditary factors on the behavior of dispersion curves. A comparative analysis of numerical solutions and their asymptotics is carried out.
Abstract: The work is devoted to the study of harmonic waves in a hereditarily elastic plate with two viscoelastic coatings, the properties of the material, which are described by the equations of state in integral form. The fractional exponential function of Rabotnov and Koltunov-Rzhanitsyn was chosen as the kernel of the integral operator. Two cases are co...
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New Pragmatic Algorithms to Improve Factoring of Large Numbers
Mohamed Zaki Abd El-Mageed,
Hassan Hussein
Issue:
Volume 3, Issue 6, December 2017
Pages:
199-202
Received:
28 September 2017
Accepted:
13 November 2017
Published:
5 December 2017
Abstract: Rivest, Shamir, Adleman, RSA algorithm is a popular public key cryptosystem and is known to be secure, however, this fact relies on the difficulty of factoring large numbers. No algorithm has been published that can factor all integers in polynomial time. This paper proposes a new function that can be used to improve the process of factoring integer numbers. It gets the factor faster than known methods. By making use of such proposed function, corresponding two algorithms are proposed and pseudocoded. The utilization of these algorithms along with the basics of the theory of numbers led to three other new factoring algorithms. The five algorithms are implemented and verified using Python Language. The tabulated results that represent the time of factorization versus the number of digits of the large number have indicated the applicability of the last three algorithms.
Abstract: Rivest, Shamir, Adleman, RSA algorithm is a popular public key cryptosystem and is known to be secure, however, this fact relies on the difficulty of factoring large numbers. No algorithm has been published that can factor all integers in polynomial time. This paper proposes a new function that can be used to improve the process of factoring intege...
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On the Equilibrium Without Loss in the Discrete Time Models of Economic Dynamics
Issue:
Volume 3, Issue 6, December 2017
Pages:
203-209
Received:
8 August 2017
Accepted:
9 November 2017
Published:
13 December 2017
Abstract: The model of economic dynamics with a fixed budget is considered. The conditions are derived under which the model with a fixed budget has an equilibrium state with the equilibrium prices. The necessary and sufficient conditions for the existence of equilibrium prices are found.
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A Differential Evolution Heuristic for Integrated Production-Distribution Scheduling in Supply Chain Management
Setareh Abedinzadeh,
Hamid Reza Erfanian,
Mojtaba Arabmomeni,
Roya Soltani
Issue:
Volume 3, Issue 6, December 2017
Pages:
210-218
Received:
27 September 2016
Accepted:
5 January 2017
Published:
18 December 2017
Abstract: A supply chain may be considered as an integrated process in which a group of several organizations, work together. The two core optimization problems in a supply chain are production and distribution planning. In this research, we develop an integrated production-distribution (P-D) model. The problem is formulated as a mixed integer programming (MIP) model, which could then be solved using GAMS optimization software. A differential evolution (DE) algorithm is applied to solve large-sized MIP models. To the best of our knowledge, it is the first paper which applied DE algorithm to solve the integrated (P-D) planning models in supply chain management (SCM). The solutions obtained by GAMS are compared with those obtained from DE and the results show that DE is efficient in terms of computational time and the quality of solutions obtained.
Abstract: A supply chain may be considered as an integrated process in which a group of several organizations, work together. The two core optimization problems in a supply chain are production and distribution planning. In this research, we develop an integrated production-distribution (P-D) model. The problem is formulated as a mixed integer programming (M...
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The Proof of the Riemann Hypothesis on a Relativistic Turing Machine
Issue:
Volume 3, Issue 6, December 2017
Pages:
219-224
Received:
2 October 2017
Accepted:
13 November 2017
Published:
2 January 2018
Abstract: In this article, the proof of the Riemann hypothesis is considered using the calculation of the Riemann ζ-function on a relativistic computer. The work lies at the junction of the direction known as "Beyond Turing", considering the application of the so-called "relativistic supercomputers" for solving non-computable problems and a direction devoted to the study of non-trivial zeros of the Riemann ζ-function. Considerations are given in favor of the validity of the Riemann hypothesis with respect to the distribution of non-trivial zeros of the ζ-function.
Abstract: In this article, the proof of the Riemann hypothesis is considered using the calculation of the Riemann ζ-function on a relativistic computer. The work lies at the junction of the direction known as "Beyond Turing", considering the application of the so-called "relativistic supercomputers" for solving non-computable problems and a direction devoted...
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Differential Geometry: An Introduction to the Theory of Curves
Kande Dickson Kinyua,
Kuria Joseph Gikonyo
Issue:
Volume 3, Issue 6, December 2017
Pages:
225-228
Received:
4 December 2016
Accepted:
18 January 2017
Published:
10 January 2018
Abstract: Differential geometry is a discipline of mathematics that uses the techniques of calculus and linear algebra to study problems in geometry. The theory of plane, curves and surfaces in the Euclidean space formed the basis for development of differential geometry during the 18th and the 19th century. The core idea of both differential geometry and modern geometrical dynamics lies under the concept of manifold. A manifold is an abstract mathematical space, which locally resembles the spaces described by Euclidean geometry, but which globally may have a more complicated structure. The purpose of this paper is to give an elaborate introduction to the theory of curves, and those are, in general, curved. Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and in the Euclidean space by applying the concept of differential and integral calculus. The curves are represented in parametrized form and then their geometric properties and various quantities associated with them, such as curvature and arc length expressed via derivatives and integrals using the idea of vector calculus.
Abstract: Differential geometry is a discipline of mathematics that uses the techniques of calculus and linear algebra to study problems in geometry. The theory of plane, curves and surfaces in the Euclidean space formed the basis for development of differential geometry during the 18th and the 19th century. The core idea of both differential geometry and mo...
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A Hybrid Genetic Algorithm-Simulated Annealing for Integrated Production-Distribution Scheduling in Supply Chain Management
Setareh Abedinzadeh,
Hamid Reza Erfanian,
Mojtaba Arabmomeni
Issue:
Volume 3, Issue 6, December 2017
Pages:
229-238
Received:
27 September 2016
Accepted:
10 January 2017
Published:
14 January 2018
Abstract: In this paper, we present an integrated production-distribution (P-D) model which considers rail transportation to move deteriorating items. The problem is formulated as a mixed integer programming (MIP) model, which could then be solved using GAMS optimization software. A hybrid genetic algorithm-simulated annealing (GA-SA) is developed to solve the real-size problems in a reasonable time period. The solutions obtained by GAMS are compared with those obtained from the hybrid GA-SA and the results show that the hybrid GA-SA is efficient in terms of computational time and the quality of the solution obtained.
Abstract: In this paper, we present an integrated production-distribution (P-D) model which considers rail transportation to move deteriorating items. The problem is formulated as a mixed integer programming (MIP) model, which could then be solved using GAMS optimization software. A hybrid genetic algorithm-simulated annealing (GA-SA) is developed to solve t...
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Structural Controllability and Observability in Industrial N 2 State Charts Applied to a Supervisory Servo Controller
Issue:
Volume 3, Issue 6, December 2017
Pages:
239-243
Received:
7 June 2017
Accepted:
24 July 2017
Published:
14 January 2018
Abstract: This paper presents that the structural controllability and observability can be used for a class of discrete event systems modeled by industry-standard N-squared diagrams. The main results of this paper provide analytical assessment of large scale industrial system properties before the software simulation and hardware demonstration; therefore it offers immense savings in verification time and cost. The dynamics of N-squared diagrams are represented by linear time-invariant systems over the Boolean algebra. Structural controllability and structural observability of discrete event systems are transformed to “standard” controllability and observability problems in traditional linear systems over real numbers. The rank of the controllability and observability matrices determine not only the structural controllability and observability, but also which discrete nodes cannot be reached by the initial states and which discrete states have no outgoing paths to the output nodes, respectively. This rank condition is extremely easy to be verified through computer software, such as MATLAB, it can be used in large scale industrial systems or communication networks.
Abstract: This paper presents that the structural controllability and observability can be used for a class of discrete event systems modeled by industry-standard N-squared diagrams. The main results of this paper provide analytical assessment of large scale industrial system properties before the software simulation and hardware demonstration; therefore it ...
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