Showing papers in "Applied Mathematics-a Journal of Chinese Universities Series B in 2012"
TL;DR: In this paper, a recent implementation of genetic algorithms is used to study a range of standard benchmark functions for global optimization, and it turns out that some of them are not very useful as challenging test functions, since they neither allow for a discrimination between different variants of genetic operators nor exhibit a dimensionality scaling resembling that of real-world problems, for example that of global structure optimization of atomic and molecular clusters.
Abstract: We have employed a recent implementation of genetic algorithms to study a range of standard benchmark functions for global optimization. It turns out that some of them are not very useful as challenging test functions, since they neither allow for a discrimination between different variants of genetic operators nor exhibit a dimensionality scaling resembling that of real-world problems, for example that of global structure optimization of atomic and molecular clusters. The latter properties seem to be simulated better by two other types of benchmark functions. One type is designed to be deceptive, exemplified here by Lunacek’s function. The other type offers additional advantages of markedly increased complexity and of broad tunability in search space characteristics. For the latter type, we use an implementation based on randomly distributed Gaussians. We advocate the use of the latter types of test functions for algorithm development and benchmarking.
80 citations
TL;DR: In this article, the boundary layer flow of viscous incompressible fluid over a stretching cylinder has been considered to study flow field and temperature field and the dependence of velocity profile and temperature profile on the dimensionless parameter of practical interest has been analyzed in detail by graphs.
Abstract: The boundary layer flow of viscous incompressible fluid over a stretching cylinder has been considered to study flow field and temperature field. Due to non-linearity, a numerical approach called Keller-box technique has been used to compute the values of velocity function f and temperature field at different points of dynamic region. The expressions for skin friction and Nusselt number have also been obtained. The dependence of velocity profile and temperature profile on the dimensionless parameter of practical interest has been analyzed in detail by graphs. The dependence of Skin friction and Nusselt number has been seen through tables.
79 citations
TL;DR: Cho et al. as mentioned in this paper proved a common fixed point theorem for a pair of weakly compatible mappings in fuzzy metric space using the joint common limit in the range property of mappings called (JCLR) property.
Abstract: In this paper, we prove a common fixed point theorem for a pair of weakly compatible mappings in fuzzy metric space using the joint common limit in the range property of mappings called (JCLR) property. An example is also furnished which demonstrates the validity of main result. We also extend our main result to two finite families of self mappings. Our results improve and generalize results of Cho et al. [Y. J. Cho, S. Sedghi and N. Shobe, “Generalized fixed point theorems for compatible mappings with some types in fuzzy metric spaces,” Chaos, Solitons & Fractals, Vol. 39, No. 5, 2009, pp. 2233-2244.] and several known results existing in the literature.
58 citations
TL;DR: In this article, some refinements and generalizations of some well known inequalities concerning polynomials and their derivatives are obtained, and certain refinements of well-known inequalities are obtained.
Abstract: Certain refinements and generalizations of some well known inequalities concerning the polynomials and their derivatives are obtained.
56 citations
TL;DR: In this article, simple formulas for the semi-axes and the center of the ellipse are given, involving only the semiaxes of an ellipsoid, the componentes of the unit normal vector of the plane and the distance of a plane from the center-of-coordinates.
Abstract: It is well known that the line of intersection of an ellipsoid and a plane is an ellipse. In this note simple formulas for the semi-axes and the center of the ellipse are given, involving only the semi-axes of the ellipsoid, the componentes of the unit normal vector of the plane and the distance of the plane from the center of coordinates. This topic is relatively common to study, but, as indicated in [1], a closed form solution to the general problem is actually very difficult to derive. This is attemped here. As applications problems are treated, which were posed in the internet [1,2], pertaining to satellite orbits in space and to planning radio-therapy treatment of eyes.
50 citations
TL;DR: In this article, the authors deal with the Copenhagen problem where the two big bodies of equal masses are also magnetic dipoles and study some aspects of the dynamics of a charged particle which moves in the electromagnetic field produced by the primaries.
Abstract: We deal with the Copenhagen problem where the two big bodies of equal masses are also magnetic dipoles and we study some aspects of the dynamics of a charged particle which moves in the electromagnetic field produced by the primaries. We investigate the equilibrium positions of the particle and their parametric variations, as well as the basins of attraction for various numerical methods and various values of the parameter λ.
45 citations
TL;DR: In this article, the flow of blood through a multistenosed artery under the influence of external applied magnetic field is modeled as a circular tube and the effect of non-Newtonian nature of blood in small blood vessels has been taken into account by modeling blood as a Casson fluid.
Abstract: The flow of blood through a multistenosed artery under the influence of external applied magnetic field is studied The artery is modeled as a circular tube The effect of non-Newtonian nature of blood in small blood vessels has been taken into account by modeling blood as a Casson fluid The effect of magnetic field, height of stenosis, parameter determin- ing the shape of the stenosis on velocity field, volumetric flow rate in stenotic region and wall shear stress at surface of stenosis are obtained and shown graphically Some important observations regarding the flow of blood in multi stenosed artery are obtained leading to medical interest
44 citations
TL;DR: In this article, a comparison between numerical and analytic methods has been introduced and some of the examples are illustrated, where numerical solutions of Lane-Emden differential equations of order fractional have been considered by collocation method.
Abstract: Lane-Emden differential equations of order fractional has been studied.Numerical solution of this type is considered by collocation method. Some of examples are illustrated. The comparison between numerical and analytic methods has been introduced.
42 citations
TL;DR: An interactive procedure which will involve the decision-maker in the optimization process helping to choose a single solution at the end and is compared with the excising novel method of Interactive Multiobjective Optimization and Decision-Making, using Evolutionary method.
Abstract: During the last few years we have witnessed impressive developments in the area of stochastic local search techniques for intelligent optimization and Reactive Search Optimization. In order to handle the complexity, in the framework of stochastic local search optimization, learning and optimization has been deeply interconnected through interaction with the decision maker via the visualization approach of the online graphs. Consequently a number of complex optimization problems, in particular multiobjective optimization problems, arising in widely different contexts have been effectively treated within the general framework of RSO. In solving real-life multiobjective optimization problems often most emphasis are spent on finding the complete Pareto-optimal set and less on decision-making. However the com-plete task of multiobjective optimization is considered as a combined task of optimization and decision-making. In this paper, we suggest an interactive procedure which will involve the decision-maker in the optimization process helping to choose a single solution at the end. Our proposed method works on the basis of Reactive Search Optimization (RSO) algorithms and available software architecture packages. The procedure is further compared with the excising novel method of Interactive Multiobjective Optimization and Decision-Making, using Evolutionary method (I-MODE). In order to evaluate the effectiveness of both methods the well-known study case of welded beam design problem is reconsidered.
41 citations
TL;DR: In this paper, the generalized expressions for the eccentric connectivity index and polynomial of the thorn graphs are presented, and then some particular cases are considered, such as the case where the eccentricity of the vertices of a graph is a function of its degree and eccentricity.
Abstract: The eccentric connectivity index based on degree and eccentricity of the vertices of a graph is a widely used graph invariant in mathematics. In this paper we present the explicit generalized expressions for the eccentric connectivity index and polynomial of the thorn graphs, and then consider some particular cases.
36 citations
TL;DR: A computational method for solving eigenvalue problems of fourth-order ordinary differential equations which based on the use of Chebychev method is presented.
Abstract: In this work, we present a computational method for solving eigenvalue problems of fourth-order ordinary differential equations which based on the use of Chebychev method. The efficiency of the method is demonstrated by three numerical examples. Comparison results with others will be presented.
TL;DR: Two new efficient and reliable computational algorithms are given that are suited for implementation using computer algebra systems such as Mathematica, Macsyma and Maple.
Abstract: The current paper is mainly devoted to construct a generalized symbolic Thomas algorithm that will never fail. Two new efficient and reliable computational algorithms are given. The algorithms are suited for implementation using computer algebra systems (CAS) such as Mathematica, Macsyma and Maple. Some illustrative examples are given.
TL;DR: In this paper, the authors established new Hermite-Hadamard type inequalities for functions whose 3rd derivatives are P-convex, where P is the dimension of the function.
Abstract: In the paper, the authors establish some new Hermite-Hadamard type inequalities for functions whose 3rd derivatives are P-convex.
TL;DR: The experimental results indicate that GA-SVR can achieve better forecasting accuracy and performance than traditional SVR and artificial neural network (ANN) prediction models in sales volume forecasting.
Abstract: Budgeting planning plays an important role in coordinating activities in organizations. An accurate sales volume forecasting is the key to the entire budgeting process. All of the other parts of the master budget are dependent on the sales volume forecasting in some way. If the sales volume forecasting is sloppily done, then the rest of the budgeting process is largely a waste of time. Therefore, the sales volume forecasting process is a critical one for most businesses, and also a difficult area of management. Most of researches and companies use the statistical methods, regression analysis, or sophisticated computer simulations to analyze the sales volume forecasting. Recently, various prediction Artificial Intelligent (AI) techniques have been proposed in forecasting. Support Vector Regression (SVR) has been applied successfully to solve problems in numerous fields and proved to be a better prediction model. However, the select of appropriate SVR parameters is difficult. Therefore, to improve the accuracy of SVR, a hybrid intelligent support system based on evolutionary computation to solve the difficulties involved with the parameters selection is presented in this research. Genetic Algorithms (GAs) are used to optimize free parameters of SVR. The experimental results indicate that GA-SVR can achieve better forecasting accuracy and performance than traditional SVR and artificial neural network (ANN) prediction models in sales volume forecasting.
TL;DR: In this paper, the authors determined the best combination of extrusion process variables for the production of a high antioxidant extruded amaranth flour (EAF) suitable to elaborate a nutraceutical beverage.
Abstract: The objective of this research was to determine the best combination of extrusion process variables for the production of a high antioxidant extruded amaranth flour (EAF) suitable to elaborate a nutraceutical beverage. Extrusion operation conditions were obtained from a factorial combination of process variables: Extrusion temperature (ET, 70℃ - 130?℃) and screw speed (SS, 100 - 220 rpm). Response surface methodology was employed as optimization technique; both the numeric and graphical methods were applied to obtain maximum values for response variables [Antioxidant capacity (AoxC) and water solubility index (WSI)]. The best combination of extrusion process variables was: Extrusion tem- perature (ET) = 130℃/Screw speed (SS) = 124 rpm. The raw amaranth flour (RAF) and optimized extruded amaranth flour (EAF) had an antioxidant activity of 3475 and 3903 μmol Trolox equivalents/100 g sample (dw), respectively. A 200 mL portion of the beverage prepared with 22 g of optimized EAF contained 3.16 g proteins, 1.09 g lipids, 17.39 g carbohydrates and 92 kcal. This portion covers 25.3% and 16.9% of the daily protein requirements for children 1-3 and 4 - 8 years old, respectively. A 200 mL portion of the beverage from optimized EAF contributes with 15.5% - 25.5% of the recommended daily intake for antioxidants, respectively. The nutraceutical beverage was evaluated with an average acceptability of 8.4 (level of satisfaction between “I like it” and “I like it extremely”) and could be used for health promotion and disease prevention as an alternative to beverages with low nutritional/nutraceutical value.
TL;DR: In this paper, the Soret and Dufour effects on MHD mixed convection flow past an infinite radiative vertical porous plate embedded in a porous medium in the presence of chemical reaction have been studied.
Abstract: The Soret and Dufour effects on unsteady MHD mixed convection flow past an infinite radiative vertical porous plate embedded in a porous medium in the presence of chemical reaction have been studied. A uniform magnetic field acts perpendicular to the porous surface. The Rosseland approximation has been used to describe the radiative heat flux in energy equation. The governing equations are solved numerically by applying explicit finite difference Method. The effects of various parameters on the velocity, temperature and concentration fields have been examined with the help of graphs.
TL;DR: The paper describes a symmetric encryption algorithm based on bit permutations and using an iterative process combined with a chaotic function that is applied on the image encryption where the plain-image is viewed as binary sequence.
Abstract: The paper describes a symmetric encryption algorithm based on bit permutations and using an iterative process combined with a chaotic function. The main advantages of such a cryptosystem is its ability to encrypt securely bit sequences and assuring confusion, diffusion and indistinguishability properties in the cipher. The algorithm is applied on the image encryption where the plain-image is viewed as binary sequence. The results of statistical analysis about randomness, sensitivity and correlation on the cipher-images show the relevance of the proposed cryptosystem.
TL;DR: In this article, the authors investigated the blow-up time of nonlinear parabolic systems with time dependent coefficients and derived lower and upper bounds for the blowup time when blowup occurs.
Abstract: Blow-up phenomena for solutions of some nonlinear parabolic systems with time dependent coefficients are investigated. Both lower and upper bounds for the blow-up time are derived when blow-up occurs.
TL;DR: In this article, the authors have obtained exact traveling wave solutions of the nonlinear partial differential equation, namely, the fourth order Boussinesq equation involving parameters via the (G'/G)-expansion method.
Abstract: The (G'/G)-expansion method is simple and powerful mathematical tool for constructing traveling wave solutions of nonlinear evolution equations which arise in engineering sciences, mathematical physics and real time application fields. In this article, we have obtained exact traveling wave solutions of the nonlinear partial differential equation, namely, the fourth order Boussinesq equation involving parameters via the (G'/G)-expansion method. In this method, the general solution of the second order linear ordinary differential equation with constant coefficients is implemented. Further, the solitons and periodic solutions are described through three different families. In addition, some of obtained solutions are described in the figures with the aid of commercial software Maple.
TL;DR: In this article, the sinc-collocation method was used for solving linear and nonlinear systems of second order differential equation and a comparison with B-spline method was made.
Abstract: Sinc methods are now recognized as an efficient numerical method for problems whose solutions may have singularities, or infinite domains, or boundary layers This work deals with the sinc-collocation method for solving linear and nonlinear system of second order differential equation The method is then tested on linear and nonlinear examples and a comparison with B-spline method is made It is shown that the sinc-collocation method yields better results
TL;DR: In this article, the sharp upper and lower bounds on the atom-bond connectivity index of chemical bicyclic graphs have been obtained for linear and branched alkanes as well as cycloalkanes.
Abstract: The atom-bond connectivity (ABC) index provides a good model for the stability of linear and branched alkanes as well as the strain energy of cycloalkanes, which is defined as ABC(G )= uv∈E(G) du + dv � 2 dudv ,w heredu denotes the degree of a vertex u in G.A chemical graph is a graph in which no vertex has degree greater than 4. In this paper, we obtain the sharp upper and lower bounds on ABC index of chemical bicyclic graphs.
TL;DR: In this paper, the problem of magneto-hydrodynamic flow and heat transfer of an electrically conducting non-Newtonian power-law fluid past a non-linearly stretching surface in the presence of a transverse magnetic field is considered.
Abstract: The problem of magneto-hydrodynamic flow and heat transfer of an electrically conducting non-Newtonian power-law fluid past a non-linearly stretching surface in the presence of a transverse magnetic field is considered. The stretching velocity, the temperature and the transverse magnetic field are assumed to vary in a power-law with the distance from the origin. The flow is induced due to an infinite elastic sheet which is stretched in its own plane. The governing equations are reduced to non-linear ordinary differential equations by means of similarity transformations. These equations are then solved numerically by an implicit finite-difference scheme known as Keller-Box method. The numerical solution is found to be dependent on several governing parameters, including the magnetic field parameter, power-law index, velocity exponent parameter, temperature exponent parameter, Modified Prandtl number and heat source/sink parameter. A systematic study is carried out to illustrate the effects of these parameters on the fluid velocity and the temperature distribution in the boundary layer. The results for the local skin-friction coefficient and the local Nusselt number are tabulated and discussed. The results obtained reveal many interesting behaviors that warrant further study on the equations related to non-Newtonian fluid phenomena.
TL;DR: In this paper, the authors show that the stationary distributions of the n × n north-west corner augmentations of Q converge in total variation to the stationary distribution of the process under exponential ergodicity and stochastic monotonicity.
Abstract: Let Q be the Q-matrix of an irreducible, positive recurrent Markov process on a countable state space. We show that, under a number of conditions, the stationary distributions of the n × n north-west corner augmentations of Q converge in total variation to the stationary distribution of the process. Two conditions guaranteeing such convergence include exponential ergodicity and stochastic monotonicity of the process. The same also holds for processes dominated by a stochastically monotone Markov process. In addition, we shall show that finite perturbations of stochastically monotone processes may be viewed as being dominated by a stochastically monotone process, thus extending the scope of these results to a larger class of processes. Consequently, the augmentation method provides an attractive, intuitive method for approximating the stationary distributions of a large class of Markov processes on countably infinite state spaces from a finite amount of known information.
TL;DR: In this article, the dynamic behaviors of a discrete predator-prey system with Beddington-DeAngelis function response were discussed and it was shown that under some suitable assumption, the system is permanent.
Abstract: This paper discusses the dynamic behaviors of a discrete predator-prey system with Beddington-DeAngelis function response. We first show that under some suitable assumption, the system is permanent. Furthermore, by constructing a suitable Lyapunov function, a sufficient condition which guarantee the global attractivity of positive solutions of the system is established
TL;DR: This paper presents an efficient genetic algorithm for solving multiobjective transportation problem, assignment, and transshipment Problems that integrates the merits of both genetic algorithm (GA) and local search (LS) scheme.
Abstract: This paper presents an efficient genetic algorithm for solving multiobjective transportation problem, assignment, and transshipment Problems. The proposed approach integrates the merits of both genetic algorithm (GA) and local search (LS) scheme. The algorithm maintains a finite-sized archive of non-dominated solutions which gets iteratively updated in the presence of new solutions based on clustering algorithm. The use clustering algorithm makes the algorithms practical by allowing a decision maker to control the resolution of the Pareto set approximation. To increase GAs’ problem solution power, local search technique is implemented as neighborhood search engine where it intends to explore the less-crowded area in the current archive to possibly obtain more nondominated solutions. The inclusion of local search and clustering algorithm speeds-up the search process and also helps in obtaining a fine-grained value for the objective functions. Finally, we report numerical results in order to establish the actual computational burden of the proposed algorithm and to assess its performances with respect to classical approaches for solving MOTP.
TL;DR: In this article, it was shown that regression analysis can not be justified without Bayes' theorem, which may imply that even the conventional classification of (Fisher's) statistics and Bayesian statistics should be reconsidered.
Abstract: It is a matter of course that Kolmogorov’s probability theory is a very useful mathematical tool for the analysis of statistics. However, this fact never means that statistics is based on Kolmogorov’s probability theory, since it is not guaranteed that mathematics and our world are connected. In order that mathematics asserts some statements concerning our world, a certain theory (so called “world view”) mediates between mathematics and our world. Recently we propose measurement theory (i.e., the theory of the quantum mechanical world view), which is characterized as the linguistic turn of quantum mechanics. In this paper, we assert that statistics is based on measurement theory. And, for example, we show, from the pure theoretical point of view (i.e., from the measurement theoretical point of view), that regression analysis can not be justified without Bayes’ theorem. This may imply that even the conventional classification of (Fisher’s) statistics and Bayesian statistics should be reconsidered.
TL;DR: In this article, a model of viral infection of monocytes population by dengue virus is formulated in a system of four ordinary differenttial equations, which takes into account the immune response and the incidence rate of susceptible and free virus particle as Beddington-DeAngelis functional response.
Abstract: A model of viral infection of monocytes population by dengue virus is formulated in a system of four ordinary differenttial equations. The model takes into account the immune response and the incidence rate of susceptible and free virus particle as Beddington-DeAngelis functional response. By constructing a block, the global stability of the unin-fected steady state is investigated. This steady state always exists. If this is the only steady state, then it is globally asymptotically stable. If any infected steady state exists, then uninfected steady state is unstable and one of the infected steady states is locally asymptotically stable. These different cases depend on the values of the basic reproduction ratio and the other parameters.
TL;DR: In this article, a nonlinear one-dimensional heat transfer model based on temperature-dependent blood perfusion was used to predict temperature distribution in dermis and subcutaneous tissues subjected to point heating sources.
Abstract: We have used a nonlinear one-dimensional heat transfer model based on temperature-dependent blood perfusion to predict temperature distribution in dermis and subcutaneous tissues subjected to point heating sources. By using Jacobi elliptic functions, we have first found the analytic solution corresponding to the steady-state temperature distribution in the tissue. With the obtained analytic steady-state temperature, the effects of the thermal conductivity, the blood perfusion, the metabolic heat generation, and the coefficient of heat transfer on the temperature distribution in living tissues are numerically analyzed. Our results show that the derived analytic steady-state temperature is useful to easily and accurately study the thermal behavior of the biological system, and can be extended to such applications as parameter measurement, temperature field reconstruction and clinical treatment.
TL;DR: In this paper, the amplitude ratios of reflection and refraction waves in pyroelectric and piezo-electric media under initial stresses and two relaxation times influence by apply suitable conditions.
Abstract: The present paper concentrates on the study of reflection and refraction phenomena of waves in pyroelectric and piezo-electric media under initial stresses and two relaxation times influence by apply suitable conditions. The generalized theories of linear piezo-thermoelasticity have been employed to investigate the problem. In two-dimensional model of transversely isotropic piezothermoelastic medium, there are four types of plane waves quasi-longitudinal (qP), quasi-transverse (qSV), thermal wave (T-mode), and potential electric waves (φ-mode) The amplitude ratios of reflection and refraction waves have been obtained. Finally, the results in each case are presented graphically.
TL;DR: It is argued that the self-identity and self-management processes of a DIME network inject the elements of cognition into Turing machine based computing as is demonstrated by two prototypes eliminating the complexity introduced by hypervisors, virtual machines and other layers of ad-hoc management software in today’s distributed computing environments.
Abstract: Cognition is the ability to process information, apply knowledge, and change the circumstance. Cognition is associated with intent and its accomplishment through various processes that monitor and control a system and its environment. Cognition is associated with a sense of “self” (the observer) and the systems with which it interacts (the environment or the “observed”). Cognition extensively uses time and history in executing and regulating tasks that constitute a cognitive process. Whether cognition is computation in the strict sense of adhering to Turing-Church thesis or needs additional constructs is a very relevant question for addressing the design of self-managing (autonomous) distributed computing systems. In this paper we argue that cognition requires more than mere book-keeping provided by the Turing machines and certain aspects of cognition such as self-identity, self-description, self-monitoring and self-management can be implemented using parallel extensions to current serial von-Neumann stored program control (SPC) Turing machine implementations. We argue that the new DIME (Distributed Intelligent Computing Element) computing model, recently introduced as the building block of the DIME network architecture, is an analogue of Turing’s O-machine and extends it to implement a recursive managed distributed computing network, which can be viewed as an interconnected group of such specialized Oracle machines, referred to as a DIME network. The DIME network architecture provides the architectural resiliency, which is often associated with cellular organisms, through auto-failover; auto-scaling; live-migration; and end-to-end transaction security assurance in a distributed system. We argue that the self-identity and self-management processes of a DIME network inject the elements of cognition into Turing machine based computing as is demonstrated by two prototypes eliminating the complexity introduced by hypervisors, virtual machines and other layers of ad-hoc management software in today’s distributed computing environments.