Showing papers in "Applied and Computational Mathematics in 2017"

Close Form Solutions of the Fractional Generalized Reaction Duffing Model and the Density Dependent Fractional Diffusion Reaction Equation

Abstract: The two variable (G'⁄G, 1⁄G)-expansion method is significant for finding the exact traveling wave solution to nonlinear evolution equations (NLEEs) in mathematical physics, applied mathematics and engineering. In this article, we exert the two variable (G'⁄G, 1⁄G)-expansion method for investigating the fractional generalized reaction Duffing model and density dependent fractional diffusion reaction equation and obtain exact solutions containing parameters. When the parameters are taken particular values, traveling wave solutions are transferred into the solitary wave solutions. The two variable (G'⁄G, 1⁄G)-expansion method is the generalization of the original (G'⁄G)-expansion method established by Wang et al [21].

Gesture Control Robotic Arm Using Flex Sensor

Abstract: The design and implementation of a gesture control robotic arm using flex sensor is proposed. The robotic arm is designed in such a way that it consists of four movable fingers, each with three linkages, an opposing thumb, a rotating wrist and an elbow. The robotic arm is made to imitate the human hand movements using a hand glove. The hand glove consists 5 flex sensor for controlling the finger movements and an Accelerometer for the wrist and elbow movements. The actuators used for the robotic arm are servo motors. The finger movements are controlled using cables that act like the tendons of human arm. The robotic arm is controlled from a distant location using a wireless module. A prototype of the robotic arm was constructed and tested for various hand movements.

A Holistic Review of Soft Computing Techniques

Abstract: Due to notable technological convergence that brought about exponential growth in computer world, Soft Computing (SC) has played a vital role with automation capability features to new levels of complex applications. In this research paper, the authors reviewed journals related to the subject matter with the aim of striking a convincing balance between a system that is capable of tolerance to uncertainty, imprecision, approximate reasoning and partial truth to achieve tractability, robustness, economy of communication, high machine intelligence quotient (MIQ), low cost solution and better rapport with reality to conventional techniques. This paper gives an insight on four major consortiums of SC that sprang from the concept of cybernetics, explores and reviews the different techniques, methodologies; application areas and algorithms are formulated to give an idea on how these computing techniques are applied to create intelligent agents to solve a variety of problems. The mechanisms highlighted can serve as an inspiration platform and awareness to new and old researchers that are not or fully grounded in this unique area of research and to create avenue in order to fully embrace the techniques in research communities.

Factors Affecting Cloud Computing Adoption in Higher Education in Bangladesh: A Case of University of Dhaka

Abstract: In the arena of education, Cloud computing is more apparent technology to ensure availability and sharing of resources through virtualization To acquire benefit from this technology boon, it is important for an educational institution to identify the important factors that contribute on cloud computing adoption So, this study has been conducted to identify the factors that will affect cloud computing adoption in educational sector University of Dhaka is chosen as a case for this paper Both primary and secondary sources are used for data collection Seventeen potential factors are taken into consideration, on which survey has been conducted focusing primary sources After performing multiple regression, variance inflation factor and factor analysis on data of primary source, six factors are identified as core factors to cloud computing adoption, these are- service availability, cloud control ability, resource need, usefulness in education, lack of proper infrastructure, lack of training of staff These findings can be used as a theoretical base and future development of technological adoption in higher education

MHD Boundary Layer Flow of Nanofluid over a Continuously Moving Stretching Surface

Abstract: The present investigation provides an insight in the steady, incompressible and electrically conducting boundary layer flow of viscoelastic nanofluid flowing due to a moving, linearly stretched surface. The governing system of nonlinear partial differential equations is simplified by considering Boussinesq and boundary layer approximations. An analytical solution of the resulting nonlinear ordinary differential equations for momentum, energy and concentration profiles is obtained using the homotopy analysis method (HAM).

A Comparative Study on Fourth Order and Butcher’s Fifth Order Runge-Kutta Methods with Third Order Initial Value Problem (IVP)

Abstract: In this paper, Butcher’s fifth order Runge-Kutta (RK5) and fourth order Runge-Kutta (RK4) methods have been employed to solve the Initial Value Problems (IVP) involving third order Ordinary Differential Equations (ODE). These two proposed methods are quite proficient and practically well suited for solving engineering problems based on such problems. To obtain the accuracy of the numerical outcome for this study, we have compared the approximate results with the exact results and found a good agreement between the exact and approximate solutions. In addition, to achieve more accuracy in the solution, the step size needs to be very small. Moreover, the error terms have been analyzed for these two methods and also compared by an appropriate example.

Analysis of Computer Virus Propagation Based on Compartmental Model

Abstract: Computer viruses pose a considerable problem for users of personal computers. In order to effectively defend against a virus, this paper proposes a compartmental model SAEIQRS (Susceptible – Antidotal – Exposed - Infected – Quarantine - Recovered - Susceptible) of virus transmission in a computer network. The differential transformation method (DTM) is applied to obtain an improved solution of each compartment. We have achieved an accuracy of order O(h6) and validated the results of DTM with fourth-order Runge-Kutta (RK4) method. Based on the basic reproduction number, we analyzed the local stability of the model for virus free and endemic equilibria. Using a Lyapunov function, we demonstrated the global stability of virus free equilibria. Numerically the eigenvalues are computed using two different sets of parameter values and the corresponding dominant eigenvalues are determined by means of power method. Finally, we simulate the system in MATLAB. Based on the analysis, aspects of different compartments are investigated.

Double-Diffusion MHD Free Convective Flow along a Sphere in the Presence of a Homogeneous Chemical Reaction and Soret and Dufour Effects

Abstract: A numerical solution is presented for the effects of chemical reaction, thermal radiation, Soret number, Dufour number and magnetic field on double-diffusion free convection flow along a sphere. The governing boundary-layer equations of the problem are formulated and transformed into non-similar form. The obtained equations are solved numerically by an efficient, iterative, tri-diagonal, implicit finite-difference method. The Roseland approximation is used to describe the radiative heat flux in the energy equation. Representative results for the fluid velocity, temperature and solute concentration profiles as well as the local heat and mass transfer rates for various values of the physical parameters are displayed in both graphical and tabular forms.

Bifurcation Behaviour and Stability Analysis of a Nano-Beam Subjected to Electrostatic Pressure

Abstract: This paper deals with the study of bifurcation behavior of a capacitive nano-beam considering electrostatic, Casimir and van der Waals forces. A modified mass-spring model has been implemented for analysis of the nano-beam behavior. The model has been adjusted and corrected with Euler-Bernoulli beam model, because of its less accuracy compared to distributed models. Fixed or equilibrium points of the nano-beam have been obtained, and has been shown that with variation of the applied voltage and the length of the nano-beam as control parameters the number of equilibrium points is changed. The stability of the fixed points has been investigated drawing motion trajectories in phase portraits and basins of attractions and repulsion have been illustrated. Critical values of the applied voltage and the length of the nano-beam leading to qualitative changes in the nano-beam behavior have been obtained.

Lacunary Statistical Convergence in Fuzzy Normed Linear Spaces

Abstract: In this paper, it is introduced the concept of lacunary statistical convergence with respect to a fuzzy norm by using lacunary statistical convergence of a sequence and statistical convergent of a sequence with respect to fuzzy norm. It also has studied the relation between these concepts.

Convergence Analysis of Piecewise Polynomial Collocation Methods for System of Weakly Singular Volterra Integral Equations of The First Kind

Abstract: We study regularity of solutions of weakly singular Volterra integral equations of the first kind. We then study the numerical analysis of discontinuous piecewise polynomial collocation methods for solving such systems. The main purpose of this paper is the derivation of global convergent and super-convergent properties of introduced methods on the graded meshes. We apply relevant methods to a system of fractional differential equations and analyze them. The numerical experiments confirm the theoretical results.

New Orbital Free Simulation Method Based on the Density Functional Theory

Abstract: A practical way to simulate multi-atomic systems without using of wave functions (orbitals) is proposed. Kinetic functionals for each type of atoms are constructed and then are used for complex systems. On examples of clusters containing Al, Si, C, and O it is shown that this method can describe structures and energies of multi-atomic systems not worse than the Kohn-Sham method but faster. Besides, it is demonstrated that the orbital-free version of the density functional theory may be used for finding equilibrium configurations of multi-atomic systems with covalent bonding. The equilibrium interatomic distances, interbonding angles and binding energies for Si3 and C3 clusters are found in good accordance with known data.

A New Entropic Riemann Solver of Conservation Law of Mixed Type Including Ziti’s δ-Method with some Experimental Tests

Abstract: Many problems in fluid mechanics and material sciences deal with liquid-vapour flows. In these flows, the ideal gas assumption is not accurate and the van der Waals equation of state is usually used. This equation of state is non-convex and causes the solution domain to have two hyperbolic regions separated by an elliptic region. Therefore, the governing equations of these flows have a mixed elliptic-hyperbolic nature. Numerical oscillations usually appear with standard finite-difference space discretization schemes, and they persist when the order of accuracy of the semi-discrete scheme is increased. In this study, we propose to use a new method called δ-ziti’s method for solving the governing equations. This method gives a new class of semi discrete, high-order scheme which are entropy conservative if the viscosity term is neglected. We implement a high resolution scheme for our mixed type problems that select the same viscosity solution as the Lax Friederich scheme with higher resolution. Several tests have been carried out to compare our results with those of [6] [9] [16], in the same situations, we obtained the same results but faster thanks to the CFL condition which reaches 0.8 and the simplicity of the method. We consider three types of pressure in these tests: Cubic, Van der Waals and linear in pieces. The comparison proved that the δ-ziti's method respects the generalized Liu entropy conditions, e.g. the existence of a viscous profile.

Solving a Nonlinear Equation Using a New Two-Step Derivative Free Iterative Methods

Abstract: In this paper, suggest anew two step iterative method for solving a nonlinear equation, which is derivative free by approximating a derivative in the iterative method by central difference with one parameter θ. The anew derivative free iterative method has a convergence of order four and computational cost the family requires three evaluations of functions per iteration. Numerical experiments show that the proposed a method is comparable to the existing method in terms of the number of iterations.

The N-Point Definite Integral Approximation Formula (N-POINT DIAF)

Abstract: Various authors have discovered formulae for numerical integration approximation. However these formulae always result to some amount of error which may differ in size depending on the formula. It’s therefore important that a formula with highest precision has been discovered and should be implemented for use in numerical integration approximations problems, especially for the definite integrals which cannot be evaluated by applying the analytical techniques. The present paper therefore explores the derivation of the N-point Definite Integral Approximation Formula (N-point DIAF) which amounts to the discovery of the 2-Point DIAF. This formula will assist in almost accurate evaluation of all definite integrals numerically. The proof of the formula is given, a specific test problem is then solved using the discovered 2-Point DIAF to obtain the solution numerically, which has the highest precision compared to other numerical methods of integration. Further the error terms are obtained and compared with the existing methods. Finally, the effectiveness of the proposed formula is illustrated by means of a numerical example.

Mathematical Analysis of Diffusion and Kinetics of Immobilized Enzyme Systems that Follow the Michaelis – Menten Mechanism

Abstract: In this paper, mathematical models of immobilized enzyme system that follow the Michaelis-Menten mechanism for both reversible and irreversible reactions are discussed. This model is based on the diffusion equations containing the non-linear term related to Michaelis-Menten kinetics. An approximate analytical technique employing the modified Adomian decomposition method is used to solve the non-linear reaction diffusion equation in immobilized enzyme system. The concentration profile of the substrate is derived in terms of all parameters. A simple expression of the substrate concentration is obtained as a function of the Thiele modulus and the Michaelis constant. The numerical solutions are compared with our analytical solutions for slab, cylinder and spherical pellet shapes. Satisfactory agreement for all values of the Thiele modulus and the Michaelis constant is noted. Graphical results and tabulated data are presented and discussed quantitatively to illustrate the solution.

A Convergence Analysis of Discontinuous Collocation Method for IAEs of Index 1 Using the Concept “Strongly Equivalent”

Abstract: We introduce the concept “strongly equivalent” for integral algebraic equations (IAEs). This definition and its corresponding theorems construct powerful tools for the classifying and analyzing of IAEs (especially numerical analysis). The related theorems with short proofs provide powerful techniques for the complete convergence analysis of discretised collocation methods on discontinuous piecewise polynomial spaces.

Using Structure Holes for Determining Key Factors: An Illustration of Reporting Eradication of Amoebiasis

Abstract: Background: Many researches aim to determine key factors affecting their concerns of interest using traditional statistical techniques, such as logistical or linear regressions. Social network analysis (SNA) is a newly novel way determining key roles through the use of network and graph theories recently. An example of commonly visualized through SNA is the disease transmission path of Middle East respiratory syndrome (MERS). Purpose: To determine key roles using structure holes of SNA for further improvement, and to show the SNA advantage over traditional classic test theory. Methods: Data were records regarding 443 adult mentally retarded residents who were infected with amoebiasis and distributed in 10 houses in past 10 years. A series of intensive mass screenings and treatment interventions were conducted. Structure holes were applied to verify the efficacy of determining key roles and strong associations for the domains of interest in a network and compared with the result obtained from the traditional Chi-square statistics. Results: The classification of key roles in a network (e.g., with which year the residency room with amoebiasis cases has strongly association) can be effectively discriminated through the structure holes of SNA. Though the result is similar to the traditional Chi-square statistics, the structure holes can release much more useful and valuable information for further investigation. Conclusions: Because of advances in computer technology, the number of healthcare studies for the group classification and association assertion continues to increase and benefit comparisons of data if structure holes of SNA are applied.

Global Optimization with Descending Region Algorithm

Abstract: Global optimization is necessary in some cases when we want to achieve the best solution or we require a new solution which is better the old one. However global optimization is a hazard problem. Gradient descent method is a well-known technique to find out local optimizer whereas approximation solution approach aims to simplify how to solve the global optimization problem. In order to find out the global optimizer in the most practical way, I propose a so-called descending region (DR) algorithm which is combination of gradient descent method and approximation solution approach. The ideology of DR algorithm is that given a known local minimizer, the better minimizer is searched only in a so-called descending region under such local minimizer. Descending region is begun by a so-called descending point which is the main subject of DR algorithm. Descending point, in turn, is solution of intersection equation (A). Finally, I prove and provide a simpler linear equation system (B) which is derived from (A). So (B) is the most important result of this research because (A) is solved by solving (B) many enough times. In other words, DR algorithm is refined many times so as to produce such (B) for searching for the global optimizer. I propose a so-called simulated Newton – Raphson (SNR) algorithm which is a simulation of Newton – Raphson method to solve (B). The starting point is very important for SNR algorithm to converge. Therefore, I also propose a so-called RTP algorithm, which is refined and probabilistic process, in order to partition solution space and generate random testing points, which aims to estimate the starting point of SNR algorithm. In general, I combine three algorithms such as DR, SNR, and RTP to solve the hazard problem of global optimization. Although the approach is division and conquest methodology in which global optimization is split into local optimization, solving equation, and partitioning, the solution is synthesis in which DR is backbone to connect itself with SNR and RTP.

The Global Exponential Stability Analysis of Nonlinear Dynamic System and Application

Abstract: This paper studies the global exponential stability for a class of nonlinear dynamical systems. A new state feedback controller is designed, which can effectively stabilize this kind of nonlinear system to the equilibrium point at exponential rate. The feasibility of the method is proved theoretically, and an algorithm is systematically proposed to configure the related parameters of the controller. Then simulation results show the effectiveness of the proposed control method.

Schultz and Modified Schultz Polynomials of Cog-Complete Bipartite Graphs

Abstract: Let G be a simple connected graph, the vertex- set and edge- set of G are denoted by V(G) and E(G) , respectively. The molecular graph G, the vertices represent atoms and the edges represent bonds. In graph theory, we have many invariant polynomials and many invariant indices of a connected graph G. Topological indices based on the distance between the vertices of a connected graph are widely used in theoretical chemistry to establish relation between the structure and the properties of molecules. The coefficients of polynomials are also important in the knowledge some properties in application chemistry. The Schultz and modified Schultz polynomials, Schultz and modified Schultz indices and average distance of Schultz and modified Schultz of Cog-complete bipartite graphs are obtained in this paper.

Credibility Evaluation Algorithm Based on Deep Learning

Abstract: The credibility of a recommendation system is a hot focus nowadays in the field of personalized recommendation research. However, it is difficult to carry out effective credibility evaluation for the users in the presence of a false recommendation system, say nothing of eliminating suspicious users and further more improve the security and reliability of the system. This paper proposed a new method of reliability assessment based on deep learning. According to the users’ rating database, community of users with average scores is constructed and traditional credibility algorithm is used to calculate the initial credibility of the users. With the average users' reliability value as a criterion, the second assessment to the credibility based on deep learning algorithm is applied to other users, the results of which are arranged in ascending order. Then suspicious users ranking top-L will be removed and a trustfully adjacent group for the target users will be created. Experiments show that the improved algorithm can optimize the recommendation system with better security, accuracy and reliability as well.

New Approach of Homotopy Perturbation Method for Solving the Equations in Enzyme Biochemical Systems

Abstract: In this paper, new homotopy perturbation method (iteration scheme) will be employed to solve the nonlinear dynamical problems that arise in thin membrane kinetics. More precisely, the method will be used to mathematically model and solve the kinetics of the thin membrane. A main property that makes the proposed method superior to other iterative methods is the way it handles boundary value problems, where both mixed Dirichlet and Neumann boundary conditions are taken into consideration, while other iterative methods only make account of the initial point and as a result, the approximate solution may deteriorate for values that are far away from the initial point and closer to the other endpoint. Our analytical results are compared with numerical solution. The method is found to be easily implemented, fast, and computationally economical and attractive.

Nonrelativistic Studies of Diatomic Molecules of Schrödinger Particles with Yukawa Plus Ring-Shaped Potential Model

Abstract: In this paper, we have solved the Schrodinger wave equation with Yukawa plus ring-shaped potential model using powerful Nikiforov-Uvarov method and obtained the energy eigenvalues and corresponding wave functions in terms of Jacobi and Laguerre polynomials for the angular and radial part respectively. We have also presented the effect of angle dependent solution on radial solutions and also applied our results to obtain numerical values for some selected diatomic molecules which suggest usefulness to other physical systems. We also studied the behavior of our potential graphically for H2 diatomic molecule.

Derivation of Adams Method for the Numerical Solution of Ordinary Differential Equations Via Computer Algebra

Abstract: In this paper, a well-known computer algebra system (CAS) was considered for the derivation of Numerical method for the solution of initial value problems. This was achieved by the use of maple software. Numerical methods were derived through Lagrange interpolation method. Both the implicit and explicit method was derived with the help of the Computer algebra system. In particular, a review of Maple’s functional role in the derivation of numerical methods was also presented. The main challenge was that the efficient handling and simplifying of very long expressions, which was met by the power of Maple’s build-in functionality. The use of the maple procedure had significantly reduced the errors and hence improved efficiency in derivation of higher order Adams Methods.

Possible Similarity Cases for Internal Heat Generation, Thermal Radiation and Free Convection of Unsteady Boundary Layer Flow Over a Vertical Plate

Abstract: In this paper we analyze the effects of free convection for internal heat generation and thermal radiation of an unsteady boundary layer flow over a vertical plate. We have applied free parameter method to obtain possible similarity cases. One of these cases have been investigated analytically and numerically. In this case, the governing non-linear partial differential equations are transformed into a system of coupled non-linear ordinary differential equations using similarity transformations and then solved numerically using the Runge–Kutta method with shooting technique for better accuracy. The effects of the governing parameters on the flow and thermal fields are investigated numerically and displayed graphically. The skin-friction coefficient, heat transfer coefficient have also been obtained and presented in tabular form.

The Research of Refugee Quota Plan on the Basis of Grey Model and Muti-Objective Analysis

Abstract: In recent years, it brings lots of challenges for European governments with the influx of refugees Hence, we build relative models to solve this situation In this paper, we get relative data from UNHCR statistical yearbook and make a short-term prediction of refugee number via grey GM (1, 1) model at first Then we select five limited indexes for the multi-objective analysis, in order to build the optimal quota model and get optimal quota plan Finally, we put forward some feasible suggestions to EU about refugee quota plan on the basis of former analyses

A Combined Analytic and Numerical Procedure for Stagnation-Point Flow

Abstract: The two dimensional vector form of the Navier-Stokes equation is reduced to a fourth–order equation for the streamfunction. Boundary conditions arise from considerations of the no-slip constraint at the surface as well the interaction of viscous flow with potential-flow at the edge of the boundary layer. By employing a separation of variables technique and introducing certain dimensionless variables, the stream function equation is converted into its dimensionless analog with appropriate boundary conditions. The resulting quasi-linear third-order ordinary differential equation facilitates the numerical computation of the velocity and the pressure terms. This is achieved by solving the nonlinear two-point boundary-value problem with a time-marching method involving a Crank-Nicolson and Newton-linearization schemes until steady-state solution is obtained. The velocity, stream-function and pressure profiles are discussed with reference to various computation parameters and are found to be in good agreement with the physics of the problem. It was also found that there is no penalty in accuracy for a broad range of CFL numbers. However as the CFL number exceeds a certain threshold, the approach to convergence becomes erratic as indicated by the spurious results produced by the solution residuals.

A Robust Preconditioned Iterative Method for the Navier-Stokes Equations with High Reynolds Numbers

Abstract: In this paper, we proposed a new solver for the Navier-Stokes equations coming from the channel flow with high Reynolds number. We use the preconditioned Krylov subspace iterative methods such as Generalized Minimum Residual Methods (GMRES). We consider the variation of the Hermitian and Skew-Hermitian splitting to construct the preconditioner. Convergence of the preconditioned iteration is analyzed. We can show that the proposed preconditioner has a robust behavior for the Navier-Stokes problems in variety of models. Numerical experiments show the robustness and efficiency of the preconditioned GMRES for the Navier-Stokes problems with Reynolds numbers up to ten thousands.

Mobile Online Computer-Adaptive Tests (CAT) for Gathering Patient Feedback in Pediatric Consultations

Abstract: Background: Few studies have used online patient feedback from smartphones for computer adaptive testing (CAT). Objective: We developed a mobile online CAT survey procedure and evaluated whether it was more precise and efficient than traditional non-adaptive testing (NAT) when gathering patient feedback about their perceptions of interaction with a physician after a consultation. Method: Two hundred proxy participants (parents or guardians) were recruited to respond to twenty 5-point questions (the P4C_20 scale) about perceptions of doctor-patient and doctor-family interaction in clinical pediatric consultations. Through the parameters calibrated using a Rasch partial credit model (PCM) and a Rasch rating scale model (RSM), two paired comparisons of empirical and simulation data were administered to calculate and compare the efficiency and precision of CAT and NAT in terms of shorter item length and fewer counts of difference number ratio (< 5%) using independent t tests. An online CAT was designed using two modes of PCM and RSM for use in clinical settings. Results: The graphical online CAT for smartphones used by the parents or guardians of pediatric hospital patients was more efficient and no less precise than NAT. Conclusions: CAT-based administration of the P4C_20 substantially reduced respondent burden without compromising measurement precision.