International Journal of Engineering Mathematics
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Open Access journal
ISSN (Print) 2314-6109
Published by Hindawi [333 journals]
- Modelling of the Deformation Diffusion Areas on a Para-Aramid Fabric with
Abstract: The geometrical modelling of the planar energy diffusion behaviors of the deformations on a para-aramid fabric has been performed. In the application process of the study, in the experimental period, drop test with bullets of different weights has been applied. The B-spline curve-generating technique has been used in the study. This is an efficient method for geometrical modelling of the deformation diffusion areas formed after the drop test. Proper control points have been chosen to be able to draw the borders of the diffusion areas on the fabric which is deformed, and then the De Casteljau and De Boor algorithms have been used. The Holditch area calculation according to the beams taken at certain fixed lengths has been performed for the B-spline border curve obtained as a closed form. After the calculations, it has been determined that the diffusion area where the bullet with pointed end was dropped on a para-aramid fabric is bigger and the diffusion area where the bullet with rounded end was dropped is smaller when compared with the areas where other bullets with different ends were dropped.
PubDate: Mon, 20 Feb 2017 00:00:00 +000
- Transient Free Convective MHD Flow Past an Exponentially Accelerated
Vertical Porous Plate with Variable Temperature through a Porous Medium
Abstract: This paper is concerned with analytical solution of one-dimensional unsteady laminar boundary layer MHD flow of a viscous incompressible fluid past an exponentially accelerated infinite vertical plate in presence of transverse magnetic field. The vertical plate and the medium of flow are considered to be porous. The fluid is assumed to be optically thin and the magnetic Reynolds number is considered small enough to neglect the induced hydromagnetic effects. The governing boundary layer equations are first converted to dimensionless form and then solved by Laplace transform technique. Numerical values of transient velocity, temperature, skin friction, and Nusselt number are illustrated and are presented in graphs for various sets of physical parametric values, namely, Grashof number, accelerating parameter, suction parameter, permeability parameter, radiation parameter, magnetic parameter, and time. It is found that the velocity decreases with increases of the suction parameter for both cases of cooling and heating of the porous plate whereas skin friction increases with increase of suction parameter.
PubDate: Tue, 17 Jan 2017 00:00:00 +000
- A New Iterative Numerical Continuation Technique for Approximating the
Solutions of Scalar Nonlinear Equations
Abstract: The present study concerns the development of a new iterative method applied to a numerical continuation procedure for parameterized scalar nonlinear equations. Combining both a modified Newton’s technique and a stationary-type numerical procedure, the proposed method is able to provide suitable approximate solutions associated with scalar nonlinear equations. A numerical analysis of predictive capabilities of this new iterative algorithm is addressed, assessed, and discussed on some specific examples.
PubDate: Mon, 16 Jan 2017 09:10:23 +000
- Unsteady Natural Convection Flow past an Infinite Cylinder with Thermal
and Mass Stratification
Abstract: This paper presents an analytical solution of unsteady one-dimensional free convection flow past an infinite vertical circular cylinder in a stratified fluid medium. The dimensionless coupled linear governing partial differential equations are solved by Laplace transform technique for unit Prandtl number and Schmidt number. Effects of various physical parameters are presented with graphs. Numerical values of boundary layer thickness for different parameters are presented in table. Due to the effects of thermal and mass stratifications, the velocity, temperature, and skin friction, Nusselt number shows oscillatory behaviour at smaller times and then reaches steady state at larger times.
PubDate: Wed, 11 Jan 2017 12:39:54 +000
- On the Extension of Sarrus’ Rule to Matrices: Development of New Method
for the Computation of the Determinant of Matrix
Abstract: The determinant of a matrix is very powerful tool that helps in establishing properties of matrices. Indisputably, its importance in various engineering and applied science problems has made it a mathematical area of increasing significance. From developed and existing methods of finding determinant of a matrix, basketweave method/Sarrus’ rule has been shown to be the simplest, easiest, very fast, accurate, and straightforward method for the computation of the determinant of 3 × 3 matrices. However, its gross limitation is that this method/rule does not work for matrices larger than 3 × 3 and this fact is well established in literatures. Therefore, the state-of-the-art methods for finding the determinants of 4 × 4 matrix and larger matrices are predominantly founded on non-basketweave method/non-Sarrus’ rule. In this work, extension of the simple, easy, accurate, and straightforward approach to the determinant of larger matrices is presented. The paper presents the developments of new method with different schemes based on the basketweave method/Sarrus’ rule for the computation of the determinant of 4 × 4. The potency of the new method is revealed in generalization of the basketweave method/non-Sarrus’ rule for the computation of the determinant of () matrices. The new method is very efficient, very consistence for handy calculations, highly accurate, and fastest compared to other existing methods.
PubDate: Mon, 05 Dec 2016 12:21:03 +000
- Various Fixed Point Theorems in Complex Valued -Metric Spaces
Abstract: We prove some common fixed point results for a pair of mappings which satisfy generalized contractive conditions with rational expressions having point-dependent control functions as coefficients in complex valued -metric spaces. The results of this paper generalize and extend the several known results in complex valued -metric spaces. Finally, examples are provided to verify the effectiveness and to usability of our main results.
PubDate: Thu, 03 Nov 2016 11:37:38 +000
- Reflection of Plane Waves in Generalized Thermoelastic Half Space under
the Action of Uniform Magnetic Field
Abstract: Reflection of longitudinal displacement waves in a generalized thermoelastic half space under the action of uniform magnetic field has been investigated. The magnetic field is applied in such a direction that the problem can be considered as a two-dimensional one. The discussion is based on the three theories of generalized thermoelasticity: Lord-Shulman (L-S), Green-Lindsay (G-L), and Green-Naghdi (G-N) with energy dissipation. We compute the possible wave velocities for different models. Amplitude ratios have been presented. The effects of magnetic field on various subjects of interest are discussed and shown graphically.
PubDate: Wed, 02 Nov 2016 13:09:41 +000
- An Efficient and Straightforward Numerical Technique Coupled to Classical
Newton’s Method for Enhancing the Accuracy of Approximate Solutions
Associated with Scalar Nonlinear Equations
Abstract: This study concerns the development of a straightforward numerical technique associated with Classical Newton’s Method for providing a more accurate approximate solution of scalar nonlinear equations. The proposed procedure is based on some practical geometric rules and requires the knowledge of the local slope of the curve representing the considered nonlinear function. Therefore, this new technique uses, only as input data, the first-order derivative of the nonlinear equation in question. The relevance of this numerical procedure is tested, evaluated, and discussed through some examples.
PubDate: Wed, 02 Nov 2016 13:00:47 +000
- Perturbation Solutions for Hagen-Poiseuille Flow and Heat Transfer of
Third-Grade Fluid with Temperature-Dependent Viscosities and Internal Heat
Abstract: Regular perturbation technique is applied to analyze the fluid flow and heat transfer in a pipe containing third-grade fluid with temperature-dependent viscosities and heat generation under slip and no slip conditions. The obtained approximate solutions were used to investigate the effects of slip on the heat transfer characteristics of the laminar flow in a pipe under Reynolds’s and Vogel’s temperature-dependent viscosities. Also, the effects of parameters such as variable viscosity, non-Newtonian parameter, viscous dissipation, and pressure gradient at various values were established. The results of this work were compared with the numerical results found in literature and good agreements were established. The results can be used to advance the analysis and study of the behavior of third-grade fluid flow and steady state heat transfer processes such as those found in coal slurries, polymer solutions, textiles, ceramics, catalytic reactors, and oil recovery applications.
PubDate: Mon, 10 Oct 2016 10:22:34 +000
- Qualitative Analysis of a Leslie-Gower Predator-Prey System with Nonlinear
Harvesting in Predator
Abstract: This paper deals with the study of the stability and the bifurcation analysis of a Leslie-Gower predator-prey model with Michaelis-Menten type predator harvesting. It is shown that the proposed model exhibits the bistability for certain parametric conditions. Dulac’s criterion has been adopted to obtain the sufficient conditions for the global stability of the model. Moreover, the model exhibits different kinds of bifurcations (e.g., the saddle-node bifurcation, the subcritical and supercritical Hopf bifurcations, Bogdanov-Takens bifurcation, and the homoclinic bifurcation) whenever the values of parameters of the model vary. The analytical findings and numerical simulations reveal far richer and complex dynamics in comparison to the models with no harvesting and with constant-yield predator harvesting.
PubDate: Mon, 03 Oct 2016 09:27:13 +000
- Sensitivity Studies and Parameters Identification for Noisy 3D Moving AWJM
Abstract: This work focuses on the identification of optimal model parameters related to Abrasive Waterjet Milling (AWJM) process. The evenly movement as well as variations of the jet feed speed was taken into account and studied in terms of 3D time dependent AWJM model. This gives us the opportunity to predict the shape of the milled trench surfaces. The required trench profile could be obtained with high precision in lack of knowledge about the model parameters and based only on the experimental measurements. We use the adjoint approach to identify the AWJM model parameters. The complexity of inverse problem paired with significant amount of unknowns makes it reasonable to use automatic differentiation software to obtain the adjoint statement. The interest in investigating this problem is caused by needs of industrial milling applications to predict the behavior of the process. This study proposes the possibility of identifying the AWJM model parameters with sufficiently high accuracy and predicting the shapes formation relying on self-generated data or on experimental measurements for both evenly jets movement and arbitrary changes of feed speed. We provide the results acceptable in the production and estimate the suitable parameters taking into account different types of model and measurement errors.
PubDate: Tue, 06 Sep 2016 14:05:58 +000
- A New Accurate and Efficient Iterative Numerical Method for Solving the
Scalar and Vector Nonlinear Equations: Approach Based on Geometric
Abstract: This paper deals with a new numerical iterative method for finding the approximate solutions associated with both scalar and vector nonlinear equations. The iterative method proposed here is an extended version of the numerical procedure originally developed in previous works. The present study proposes to show that this new root-finding algorithm combined with a stationary-type iterative method (e.g., Gauss-Seidel or Jacobi) is able to provide a longer accurate solution than classical Newton-Raphson method. A numerical analysis of the developed iterative method is addressed and discussed on some specific equations and systems.
PubDate: Sun, 07 Aug 2016 08:10:36 +000
- On Stability of Vector Nonlinear Integrodifferential Equations
Abstract: Let be a bounded domain in a real Euclidean space. We consider the equation , where and are matrix-valued functions and is a nonlinear mapping. Conditions for the exponential stability of the steady state are established. Our approach is based on a norm estimate for operator commutators.
PubDate: Wed, 25 May 2016 13:58:22 +000
- Numerical Solution of the Blasius Viscous Flow Problem by Quartic B-Spline
Abstract: A numerical method is proposed to study the laminar boundary layer about a flat plate in a uniform stream of fluid. The presented method is based on the quartic B-spline approximations with minimizing the error -norm. Theoretical considerations are discussed. The computed results are compared with some numerical results to show the efficiency of the proposed approach.
PubDate: Mon, 11 Apr 2016 11:27:38 +000
- New Improvement of the Expansion Methods for Solving the Generalized
Fitzhugh-Nagumo Equation with Time-Dependent Coefficients
Abstract: An improvement of the expansion methods, namely, the improved -expansion method, for solvingnonlinear second-order partial differential equation, is proposed. The implementation of the new approach is demonstrated by solvingthe generalized Fitzhugh-Nagumo equation with time-dependentcoefficients. As a result, many new and more general exacttravelling wave solutions are obtained including periodic functionsolutions, soliton-like solutions, and trigonometric functionsolutions. The exact particular solutions contain four types:hyperbolic function solution, trigonometric function solution,exponential solution, and rational solution. We obtained further solutions comparing this method with other methods. Theresults demonstrate that the new -expansion method is more efficient than the Ansatz method andTanh method applied by Triki and Wazwaz (2013). Recently, this methodis developed for searching exact travelling wave solutions ofnonlinear partial differential equations. Abundant exacttravelling wave solutions including solitons, kink, and periodic andrational solutions have been found. These solutions might play animportant role in engineering fields. It is shown that thismethod, with the help of symbolic computation, provides astraightforward and powerful mathematical tool for solving thenonlinear physics.
PubDate: Wed, 16 Dec 2015 14:24:10 +000
- Effects of Temperature and Stirring on Mass Transfer to Maximize Biodiesel
Production from Jatropha curcas Oil: A Mathematical Study
Abstract: Biodiesel, the most promising renewable and alternative energy, is produced through transesterification of vegetable oils. One of the most cost effective sources of biodiesel is Jatropha curcas oil. Transesterification of Jatropha oil depends significantly on reaction parameters such as reaction time, temperature, molar ratio, catalyst amount, and stirrer speed. Among these parameters temperature and stirring have noteworthy effect on mass transfer. In this research article, we have shown the simultaneous effect of temperature and stirring on mass transfer by considering a mathematical model. The optimal profiles of temperature and stirring are determined as a combined parameter, for which maximum biodiesel can be obtained. Further, we have shown that this pair exists and is unique for the optimality of the system.
PubDate: Tue, 27 Oct 2015 14:02:39 +000
- Successive Complementary Expansion Method for Solving Troesch’s Problem
as a Singular Perturbation Problem
Abstract: A simple and efficient method that is called Successive Complementary Expansion Method (SCEM) is applied forapproximation to an unstable two-point boundary value problem which is knownas Troesch’s problem. In this approach, Troesch’s problem is considered as asingular perturbation problem. We convert the hyperbolic-type nonlinearityinto a polynomial-type nonlinearity using an appropriate transformation, andthen we use a basic zoom transformation for the boundary layer and finallyobtain a nonlinear ordinary differential equation that contains SCEMcomplementary approximation. We see that SCEM gives highly accurateapproximations to the solution of Troesch’s problem for various parametervalues. Moreover, the results are compared with Adomian Decomposition Method (ADM)and Homotopy Perturbation Method (HPM) by using tables.
PubDate: Tue, 27 Oct 2015 06:32:42 +000
- An Efficient Method to Find Solutions for Transcendental Equations with
Abstract: This paper presents a method for obtaining a solution for all the roots of a transcendental equation within a bounded region by finding a polynomial equation with the same roots as the transcendental equation. The proposed method is developed using Cauchy’s integral theorem for complex variables and transforms the problem of finding the roots of a transcendental equation into an equivalent problem of finding roots of a polynomial equation with exactly the same roots. The interesting result is that the coefficients of the polynomial form a vector which lies in the null space of a Hankel matrix made up of the Fourier series coefficients of the inverse of the original transcendental equation. Then the explicit solution can be readily obtained using the complex fast Fourier transform. To conclude, the authors present an example by solving for the first three eigenvalues of the 1D transient heat conduction problem.
PubDate: Thu, 15 Oct 2015 13:06:26 +000
- Mixed Convection Flow of Magnetic Viscoelastic Polymer from a
Nonisothermal Wedge with Biot Number Effects
Abstract: Magnetic polymers are finding increasing applications in diverse fields of chemical and mechanical engineering. In this paper, we investigate the nonlinear steady boundary layer flow and heat transfer of such fluids from a nonisothermal wedge. The incompressible Eyring-Powell non-Newtonian fluid model is employed and a magnetohydrodynamic body force is included in the simulation. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite difference Keller Box technique. The numerical code is validated with previous studies. The influence of a number of emerging nondimensional parameters, namely, the Eyring-Powell rheological fluid parameter (), local non-Newtonian parameter based on length scale (), Prandtl number (Pr), Biot number (), pressure gradient parameter (), magnetic parameter (), mixed convection parameter (), and dimensionless tangential coordinate (), on velocity and temperature evolution in the boundary layer regime is examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate and local skin friction are also investigated.
PubDate: Mon, 12 Oct 2015 12:55:18 +000
- Robust Adaptive Exponential Synchronization of Two Different Stochastic
Perturbed Chaotic Systems with Structural Perturbations
Abstract: The robust adaptive exponential synchronization problem of stochastic chaotic systems with structural perturbations is investigated in mean square. The stochastic disturbances are assumed to be Brownian motions that act on the slave system and the norm-bounded uncertainties exist in all parameters after decoupling. The stochastic disturbances could reflect more realistic dynamical behaviors of the coupled chaotic system presented within a noisy environment. By using a combination of the Lyapunov functional method, the robust analysis tool, the stochastic analysis techniques, and adaptive control laws, we derive several sufficient conditions that ensure the coupled chaotic systems to be robustly exponentially synchronized in the mean square for all admissible parameter uncertainties. This approach cannot only make the outputs of both master and slave systems reach synchronization with the passage of time between both systems but also attenuate the effects of the perturbation on the overall error system to a prescribed level. The main results are shown to be general enough to cover many existing ones reported in the literature.
PubDate: Tue, 29 Sep 2015 07:49:15 +000
- Block Backward Differentiation Formulas for Fractional Differential
Abstract: This paper concerns the numerical approximation of Fractional Initial Value Problems (FIVPs). This is achieved by constructing -step continuous BDFs. These continuous schemes are developed via the interpolation and collocation approach and are used to obtain the discrete -step BDF and () additional methods which are applied as numerical integrators in a block-by-block mode for the integration of FIVP. The properties of the methods are established and regions of absolute stability of the methods are plotted in the complex plane. Numerical tests including large systems arising form the semidiscretization of one-dimensional fractional Burger’s equation show that the methods are highly accurate and efficient.
PubDate: Tue, 29 Sep 2015 07:39:16 +000
- Homotopy Simulation of Nonlinear Unsteady Rotating Nanofluid Flow from a
Abstract: The development of new applications of nanofluids in chemical engineering and other technologies has stimulated significant interest in computational simulations. Motivated by coating applications of nanomaterials, we investigate the transient nanofluid flow from a time-dependent spinning sphere using laminar boundary layer theory. The free stream velocity varies continuously with time. The unsteady conservations equations are normalized with appropriate similarity transformations and rendered into a ninth-order system of nonlinear coupled, multidegree ordinary differential equations. The transformed nonlinear boundary value problem is solved using the homotopy analysis method (HAM), a semicomputational procedure achieving fast convergence. Computations are verified with an Adomian decomposition method (ADM). The influence of acceleration parameter, rotational body force parameter, Brownian motion number, thermophoresis number, Lewis number, and Prandtl number on surface shear stress, heat, and mass (nanoparticle volume fraction) transfer rates is evaluated. The influence on boundary layer behavior is also investigated. HAM demonstrates excellent stability and leads to highly accurate solutions.
PubDate: Sun, 27 Sep 2015 09:04:28 +000
- Improving the Performance of Metaheuristics: An Approach Combining
Response Surface Methodology and Racing Algorithms
Abstract: The setup of heuristics and metaheuristics, that is, the fine-tuning of their parameters, exercises a great influence in both the solution process, and in the quality of results of optimization problems. The search for the best fit of these algorithms is an important task and a major research challenge in the field of metaheuristics. The fine-tuning process requires a robust statistical approach, in order to aid in the process understanding and also in the effective settings, as well as an efficient algorithm which can summarize the search process. This paper aims to present an approach combining design of experiments (DOE) techniques and racing algorithms to improve the performance of different algorithms to solve classical optimization problems. The results comparison considering the default metaheuristics and ones using the settings suggested by the fine-tuning procedure will be presented. Broadly, the statistical results suggest that the fine-tuning process improves the quality of solutions for different instances of the studied problems. Therefore, by means of this study it can be concluded that the use of DOE techniques combined with racing algorithms may be a promising and powerful tool to assist in the investigation, and in the fine-tuning of different algorithms. However, additional studies must be conducted to verify the effectiveness of the proposed methodology.
PubDate: Wed, 16 Sep 2015 09:36:25 +000
- Rational-Like Solutions of a Differential-Difference Equation Related to
Ablowitz-Ladik Spectral Problem
Abstract: By using the Casoratian technique, we construct the double Casoratian solutions whose entries satisfy matrix equation of a differential-difference equation related to the Ablowitz-Ladik spectral problem. Soliton solutions and rational-like solutions are obtained from taking special cases in general solutions.
PubDate: Thu, 03 Sep 2015 14:00:43 +000
- A Wavelet Algorithm for Fourier-Bessel Transform Arising in Optics
Abstract: The aim of the paper is to propose an efficient and stable algorithm that is quite accurate and fast for numerical evaluation of the Fourier-Bessel transform of order , using wavelets. The philosophy behind the proposed algorithm is to replace the part of the integral by its wavelet decomposition obtained by using CAS wavelets thus representing as a Fourier-Bessel series with coefficients depending strongly on the input function . The wavelet method indicates that the approach is easy to implement and thus computationally very attractive.
PubDate: Mon, 31 Aug 2015 13:00:10 +000
- Global Stability of a Delayed SIRI Epidemic Model with Nonlinear Incidence
Abstract: In this paper we propose the global dynamics of an SIRI epidemic modelwith latency and a general nonlinear incidence function. The model is basedon the susceptible-infective-recovered (SIR) compartmental structure withrelapse (SIRI). Sufficient conditions for the global stability of equilibria (thedisease-free equilibrium and the endemic equilibrium) are obtained by meansof Lyapunov-LaSalle theorem. Also some numerical simulations are given toillustrate this result.
PubDate: Sun, 07 Dec 2014 07:38:14 +000
- Influence of Variable Thermal Conductivity on MHD Boundary Layer Slip Flow
of Ethylene-Glycol Based Cu Nanofluids over a Stretching Sheet with
Convective Boundary Condition
Abstract: An analysis is carried out to investigate the influence of variable thermal conductivity and partial velocity slip on hydromagnetic two-dimensional boundary layer flow of a nanofluid with Cu nanoparticles over a stretching sheet with convective boundary condition. Using similarity transformation, the governing boundary layer equations along with the appropriate boundary conditions are transformed to a set of ordinary differential equations. Employing Runge-kutta fourth-order method along with shooting technique, the resultant system of equations is solved. The influence of various pertinent parameters such as nanofluid volume fraction parameter, the magnetic parameter, radiation parameter, thermal conductivity parameter, velocity slip parameter, Biot number, and suction or injection parameter on the velocity of the flow field and heat transfer characteristics is computed numerically and illustrated graphically. The present results are compared with the existing results for the case of regular fluid and found an excellent agreement.
PubDate: Thu, 06 Nov 2014 12:43:54 +000
- Aligned Magnetic Field, Radiation, and Rotation Effects on Unsteady
Hydromagnetic Free Convection Flow Past an Impulsively Moving Vertical
Plate in a Porous Medium
Abstract: We analyse the effects of aligned magnetic field, radiation, and rotation on unsteady hydromagnetic free convection flow of a viscous incompressible electrically conducting fluid past an impulsively moving vertical plate in a porous medium in presence of heat source. An exact solution of the governing equations in dimensionless form is obtained by Laplace transform technique in ramped temperature case. To compare the results obtained in this case with that of isothermal plate, the exact solution of the governing equations is also obtained for isothermal plate and results are discussed graphically in both ramped temperature and isothermal cases.
PubDate: Tue, 21 Oct 2014 09:06:38 +000
- Quadratic Prediction Models for the Performance Comparison of a Marine
Engine Fuelled with Biodiesels B5 and B20
Abstract: According to Thailand’s renewable energy development plan, biodiesel is one of the interesting alternative energies. In this research, biodiesels B5 and B20 are tested in a marine engine. The experimental results are then compared by using three different techniques including (1) the conventional technique, (2) average of the point-to-point comparisons, and (3) a comparison by using quadratic prediction models. This research aims to present the procedures of these techniques in-depth. The results show that the comparison by using quadratic prediction models can accurately predict ample amounts of results and make the comparison more logical. The results are compatible with those of the conventional technique, while the average of the point-to-point comparisons shows diverse results. These results are also explained on the fuel property basis, confirming that the quadratic prediction model and the conventional technique are practical, but the average of the point-to-point comparison technique presents an inaccurate result. The benefit of this research shows that the quadratic prediction model is more flexible for future science and engineering experimental design, thus reducing cost and time usage. The details of the calculation, results, and discussion are presented in the paper.
PubDate: Tue, 30 Sep 2014 08:34:28 +000
- A New Approach to Solve Intuitionistic Fuzzy Optimization Problem Using
Possibility, Necessity, and Credibility Measures
Abstract: Corresponding to chance constraints, real-life possibility, necessity, and credibility measures on intuitionistic fuzzy set are defined. For the first time the mathematical and graphical representations of different types of measures in trapezoidal intuitionistic fuzzy environment are defined in this paper. We have developed intuitionistic fuzzy chance constraints model (CCM) based on possibility and necessity measures. We have also proposed a new method for solving an intuitionistic fuzzy CCMusing chance operators. To validate the proposed method, we have discussed three different approaches to solve the intuitionistic fuzzy linear programming (IFLPP) using possibility, necessity and credibility measures. Numerical and graphical representations of optimal solutions of the given example at different possibility and necessity, levels have been discussed.
PubDate: Thu, 25 Sep 2014 13:03:03 +000