Excellence in Research and Innovation for Humanity

International Science Index

Commenced in January 1999 Frequency: Monthly Edition: International Paper Count: 1588

Mathematical and Computational Sciences

1588
10009087
Improving the Analytical Power of Dynamic DEA Models, by the Consideration of the Shape of the Distribution of Inputs/Outputs Data: A Linear Piecewise Decomposition Approach
Abstract:

In Dynamic Data Envelopment Analysis (DDEA), which is a subfield of Data Envelopment Analysis (DEA), the productivity of Decision Making Units (DMUs) is considered in relation to time. In this case, as it is accepted by the most of the researchers, there are outputs, which are produced by a DMU to be used as inputs in a future time. Those outputs are known as intermediates. The common models, in DDEA, do not take into account the shape of the distribution of those inputs, outputs or intermediates data, assuming that the distribution of the virtual value of them does not deviate from linearity. This weakness causes the limitation of the accuracy of the analytical power of the traditional DDEA models. In this paper, the authors, using the concept of piecewise linear inputs and outputs, propose an extended DDEA model. The proposed model increases the flexibility of the traditional DDEA models and improves the measurement of the dynamic performance of DMUs.

Digital Article Identifier (DAI):
1587
10009051
Applying p-Balanced Energy Technique to Solve Liouville-Type Problems in Calculus
Abstract:

We are interested in solving Liouville-type problems to explore constancy properties for maps or differential forms on Riemannian manifolds. Geometric structures on manifolds, the existence of constancy properties for maps or differential forms, and energy growth for maps or differential forms are intertwined. In this article, we concentrate on discovery of solutions to Liouville-type problems where manifolds are Euclidean spaces (i.e. flat Riemannian manifolds) and maps become real-valued functions. Liouville-type results of vanishing properties for functions are obtained. The original work in our research findings is to extend the q-energy for a function from finite in Lq space to infinite in non-Lq space by applying p-balanced technique where q = p = 2. Calculation skills such as Hölder's Inequality and Tests for Series have been used to evaluate limits and integrations for function energy. Calculation ideas and computational techniques for solving Liouville-type problems shown in this article, which are utilized in Euclidean spaces, can be universalized as a successful algorithm, which works for both maps and differential forms on Riemannian manifolds. This innovative algorithm has a far-reaching impact on research work of solving Liouville-type problems in the general settings involved with infinite energy. The p-balanced technique in this algorithm provides a clue to success on the road of q-energy extension from finite to infinite.

Digital Article Identifier (DAI):
1586
10009046
A Mixed Integer Linear Programming Model for Flexible Job Shop Scheduling Problem
Authors:
Abstract:
In this paper, a mixed integer linear programming (MILP) model is presented to solve the flexible job shop scheduling problem (FJSP). This problem is one of the hardest combinatorial problems. The objective considered is the minimization of the makespan. The computational results of the proposed MILP model were compared with those of the best known mathematical model in the literature in terms of the computational time. The results show that our model has better performance with respect to all the considered performance measures including relative percentage deviation (RPD) value, number of constraints, and total number of variables. By this improved mathematical model, larger FJS problems can be optimally solved in reasonable time, and therefore, the model would be a better tool for the performance evaluation of the approximation algorithms developed for the problem.
Digital Article Identifier (DAI):
1585
10009086
Mean-Variance Optimization of Portfolios with Return of Premium Clauses in a DC Pension Plan with Multiple Contributors under Constant Elasticity of Variance Model
Abstract:

In this paper, mean-variance optimization of portfolios with the return of premium clauses in a defined contribution (DC) pension plan with multiple contributors under constant elasticity of variance (CEV) model is studied. The return clauses which permit death members to claim their accumulated wealth are considered, the remaining wealth is not equally distributed by the remaining members as in literature. We assume that before investment, the surplus which includes funds of members who died after retirement adds to the total wealth. Next, we consider investments in a risk-free asset and a risky asset to meet up the expected returns of the remaining members and obtain an optimized problem with the help of extended Hamilton Jacobi Bellman equation. We obtained the optimal investment strategies for the two assets and the efficient frontier of the members by using a stochastic optimal control technique. Furthermore, we studied the effect of the various parameters of the optimal investment strategies and the effect of the risk-averse level on the efficient frontier. We observed that the optimal investment strategy is the same as in literature, secondly, we observed that the surplus decreases the proportion of the wealth invested in the risky asset.

Digital Article Identifier (DAI):
1584
10008947
Total Chromatic Number of Δ-Claw-Free 3-Degenerated Graphs
Abstract:
The total chromatic number χ"(G) of a graph G is the minimum number of colors needed to color the elements (vertices and edges) of G such that no incident or adjacent pair of elements receive the same color Let G be a graph with maximum degree Δ(G). Considering a total coloring of G and focusing on a vertex with maximum degree. A vertex with maximum degree needs a color and all Δ(G) edges incident to this vertex need more Δ(G) + 1 distinct colors. To color all vertices and all edges of G, it requires at least Δ(G) + 1 colors. That is, χ"(G) is at least Δ(G) + 1. However, no one can find a graph G with the total chromatic number which is greater than Δ(G) + 2. The Total Coloring Conjecture states that for every graph G, χ"(G) is at most Δ(G) + 2. In this paper, we prove that the Total Coloring Conjectur for a Δ-claw-free 3-degenerated graph. That is, we prove that the total chromatic number of every Δ-claw-free 3-degenerated graph is at most Δ(G) + 2.
Digital Article Identifier (DAI):
1583
10008748
On the Bootstrap P-Value Method in Identifying out of Control Signals in Multivariate Control Chart
Authors:
Abstract:

In any production process, every product is aimed to attain a certain standard, but the presence of assignable cause of variability affects our process, thereby leading to low quality of product. The ability to identify and remove this type of variability reduces its overall effect, thereby improving the quality of the product. In case of a univariate control chart signal, it is easy to detect the problem and give a solution since it is related to a single quality characteristic. However, the problems involved in the use of multivariate control chart are the violation of multivariate normal assumption and the difficulty in identifying the quality characteristic(s) that resulted in the out of control signals. The purpose of this paper is to examine the use of non-parametric control chart (the bootstrap approach) for obtaining control limit to overcome the problem of multivariate distributional assumption and the p-value method for detecting out of control signals. Results from a performance study show that the proposed bootstrap method enables the setting of control limit that can enhance the detection of out of control signals when compared, while the p-value method also enhanced in identifying out of control variables.

Digital Article Identifier (DAI):
1582
10008697
Similarity Based Membership of Elements to Uncertain Concept in Information System
Abstract:

The process of determining the degree of membership for an element to an uncertain concept has been found in many ways, using equivalence and symmetry relations in information systems. In the case of similarity, these methods did not take into account the degree of symmetry between elements. In this paper, we use a new definition for finding the membership based on the degree of symmetry. We provide an example to clarify the suggested methods and compare it with previous methods. This method opens the door to more accurate decisions in information systems.

Digital Article Identifier (DAI):
1581
10008777
Numerical Solution of Steady Magnetohydrodynamic Boundary Layer Flow Due to Gyrotactic Microorganism for Williamson Nanofluid over Stretched Surface in the Presence of Exponential Internal Heat Generation
Abstract:

This paper focuses on the study of two dimensional magnetohydrodynamic (MHD) steady incompressible viscous Williamson nanofluid with exponential internal heat generation containing gyrotactic microorganism over a stretching sheet. The governing equations and auxiliary conditions are reduced to a set of non-linear coupled differential equations with the appropriate boundary conditions using similarity transformation. The transformed equations are solved numerically through spectral relaxation method. The influences of various parameters such as Williamson parameter γ, power constant λ, Prandtl number Pr, magnetic field parameter M, Peclet number Pe, Lewis number Le, Bioconvection Lewis number Lb, Brownian motion parameter Nb, thermophoresis parameter Nt, and bioconvection constant σ are studied to obtain the momentum, heat, mass and microorganism distributions. Moment, heat, mass and gyrotactic microorganism profiles are explored through graphs and tables. We computed the heat transfer rate, mass flux rate and the density number of the motile microorganism near the surface. Our numerical results are in better agreement in comparison with existing calculations. The Residual error of our obtained solutions is determined in order to see the convergence rate against iteration. Faster convergence is achieved when internal heat generation is absent. The effect of magnetic parameter M decreases the momentum boundary layer thickness but increases the thermal boundary layer thickness. It is apparent that bioconvection Lewis number and bioconvection parameter has a pronounced effect on microorganism boundary. Increasing brownian motion parameter and Lewis number decreases the thermal boundary layer. Furthermore, magnetic field parameter and thermophoresis parameter has an induced effect on concentration profiles.

Digital Article Identifier (DAI):
1580
10008601
A Note on MHD Flow and Heat Transfer over a Curved Stretching Sheet by Considering Variable Thermal Conductivity
Abstract:

The mixed convective flow of MHD incompressible, steady boundary layer in heat transfer over a curved stretching sheet due to temperature dependent thermal conductivity is studied. We use curvilinear coordinate system in order to describe the governing flow equations. Finite difference solutions with central differencing have been used to solve the transform governing equations. Numerical results for the flow velocity and temperature profiles are presented as a function of the non-dimensional curvature radius. Skin friction coefficient and local Nusselt number at the surface of the curved sheet are discussed as well.

Digital Article Identifier (DAI):
1579
10008565
Fuzzy Logic and Control Strategies on a Sump
Abstract:

Sump can be defined as a reservoir which contains slurry; a mixture of solid and liquid or water, in it. Sump system is an unsteady process owing to the level response. Sump level shall be monitored carefully by using a good controller to avoid overflow. The current conventional controllers would not be able to solve problems with large time delay and nonlinearities, Fuzzy Logic controller is tested to prove its ability in solving the listed problems of slurry sump. Therefore, in order to justify the effectiveness and reliability of these controllers, simulation of the sump system was created by using MATLAB and the results were compared. According to the result obtained, instead of Proportional-Integral (PI) and Proportional-Integral and Derivative (PID), Fuzzy Logic controller showed the best result by offering quick response of 0.32 s for step input and 5 s for pulse generator, by producing small Integral Absolute Error (IAE) values that are 0.66 and 0.36 respectively.

Digital Article Identifier (DAI):
1578
10008516
Similarity Solutions of Nonlinear Stretched Biomagnetic Flow and Heat Transfer with Signum Function and Temperature Power Law Geometries
Abstract:

Biomagnetic fluid dynamics is an interdisciplinary field comprising engineering, medicine, and biology. Bio fluid dynamics is directed towards finding and developing the solutions to some of the human body related diseases and disorders. This article describes the flow and heat transfer of two dimensional, steady, laminar, viscous and incompressible biomagnetic fluid over a non-linear stretching sheet in the presence of magnetic dipole. Our model is consistent with blood fluid namely biomagnetic fluid dynamics (BFD). This model based on the principles of ferrohydrodynamic (FHD). The temperature at the stretching surface is assumed to follow a power law variation, and stretching velocity is assumed to have a nonlinear form with signum function or sign function. The governing boundary layer equations with boundary conditions are simplified to couple higher order equations using usual transformations. Numerical solutions for the governing momentum and energy equations are obtained by efficient numerical techniques based on the common finite difference method with central differencing, on a tridiagonal matrix manipulation and on an iterative procedure. Computations are performed for a wide range of the governing parameters such as magnetic field parameter, power law exponent temperature parameter, and other involved parameters and the effect of these parameters on the velocity and temperature field is presented. It is observed that for different values of the magnetic parameter, the velocity distribution decreases while temperature distribution increases. Besides, the finite difference solutions results for skin-friction coefficient and rate of heat transfer are discussed. This study will have an important bearing on a high targeting efficiency, a high magnetic field is required in the targeted body compartment.

Digital Article Identifier (DAI):
1577
10008892
Optimal Portfolio Selection in a DC Pension with Multiple Contributors and the Impact of Stochastic Additional Voluntary Contribution on the Optimal Investment Strategy
Abstract:

In this paper, we studied the optimal portfolio selection in a defined contribution (DC) pension scheme with multiple contributors under constant elasticity of variance (CEV) model and the impact of stochastic additional voluntary contribution on the investment strategies. We assume that the voluntary contributions are stochastic and also consider investments in a risk free asset and a risky asset to increase the expected returns of the contributing members. We derived a stochastic differential equation which consists of the members’ monthly contributions and the invested fund and obtained an optimized problem with the help of Hamilton Jacobi Bellman equation. Furthermore, we find an explicit solution for the optimal investment strategy with stochastic voluntary contribution using power transformation and change of variables method and the corresponding optimal fund size was obtained. We discussed the impact of the voluntary contribution on the optimal investment strategy with numerical simulations and observed that the voluntary contribution reduces the optimal investment strategy of the risky asset.

Digital Article Identifier (DAI):
1576
10008424
Stochastic Repair and Replacement with a Single Repair Channel
Abstract:
This paper examines the behavior of a system, which upon failure is either replaced with certain probability p or imperfectly repaired with probability q. The system is analyzed using Kolmogorov's forward equations method; the analytical expression for the steady state availability is derived as an indicator of the system’s performance. It is found that the analysis becomes more complex as the number of imperfect repairs increases. It is also observed that the availability increases as the number of states and replacement probability increases. Using such an approach in more complex configurations and in dynamic systems is cumbersome; therefore, it is advisable to resort to simulation or heuristics. In this paper, an example is provided for demonstration.
Digital Article Identifier (DAI):
1575
10008295
Mathematical Modeling and Analysis of Forced Vibrations in Micro-Scale Microstretch Thermoelastic Simply Supported Beam
Abstract:
The present paper deals with the flexural vibrations of homogeneous, isotropic, generalized micropolar microstretch thermoelastic thin Euler-Bernoulli beam resonators, due to Exponential time varying load. Both the axial ends of the beam are assumed to be at simply supported conditions. The governing equations have been solved analytically by using Laplace transforms technique twice with respect to time and space variables respectively. The inversion of Laplace transform in time domain has been performed by using the calculus of residues to obtain deflection.The analytical results have been numerically analyzed with the help of MATLAB software for magnesium like material. The graphical representations and interpretations have been discussed for Deflection of beam under Simply Supported boundary condition and for distinct considered values of time and space as well. The obtained results are easy to implement for engineering analysis and designs of resonators (sensors), modulators, actuators.
Digital Article Identifier (DAI):
1574
10008987
Investigating the Dynamics of Knowledge Acquisition in Learning Using Differential Equations
Abstract:
A mathematical model for knowledge acquisition in teaching and learning is proposed. In this study we adopt the mathematical model that is normally used for disease modelling into teaching and learning. We derive mathematical conditions which facilitate knowledge acquisition. This study compares the effects of dropping out of the course at early stages with later stages of learning. The study also investigates effect of individual interaction and learning from other sources to facilitate learning. The study fits actual data to a general mathematical model using Matlab ODE45 and lsqnonlin to obtain a unique mathematical model that can be used to predict knowledge acquisition. The data used in this study was obtained from the tutorial test results for mathematics 2 students from the Central University of Technology, Free State, South Africa in the department of Mathematical and Physical Sciences. The study confirms already known results that increasing dropout rates and forgetting taught concepts reduce the population of knowledgeable students. Increasing teaching contacts and access to other learning materials facilitate knowledge acquisition. The effect of increasing dropout rates is more enhanced in the later stages of learning than earlier stages. The study opens up a new direction in further investigations in teaching and learning using differential equations.
Digital Article Identifier (DAI):
1573
10008281
All-or-None Principle and Weakness of Hodgkin-Huxley Mathematical Model
Abstract:

Mathematical and computational modellings are the necessary tools for reviewing, analysing, and predicting processes and events in the wide spectrum range of scientific fields. Therefore, in a field as rapidly developing as neuroscience, the combination of these two modellings can have a significant role in helping to guide the direction the field takes. The paper combined mathematical and computational modelling to prove a weakness in a very precious model in neuroscience. This paper is intended to analyse all-or-none principle in Hodgkin-Huxley mathematical model. By implementation the computational model of Hodgkin-Huxley model and applying the concept of all-or-none principle, an investigation on this mathematical model has been performed. The results clearly showed that the mathematical model of Hodgkin-Huxley does not observe this fundamental law in neurophysiology to generating action potentials. This study shows that further mathematical studies on the Hodgkin-Huxley model are needed in order to create a model without this weakness.

Digital Article Identifier (DAI):
1572
10008379
Generalized Fuzzy Subalgebras and Fuzzy Ideals of BCI-Algebras with Operators
Abstract:
The aim of this paper is to introduce the concepts of generalized fuzzy subalgebras, generalized fuzzy ideals and generalized fuzzy quotient algebras of BCI-algebras with operators, and to investigate their basic properties.
Digital Article Identifier (DAI):
1571
10008113
Subclasses of Bi-Univalent Functions Associated with Hohlov Operator
Abstract:

The coefficients estimate problem for Taylor-Maclaurin series is still an open problem especially for a function in the subclass of bi-univalent functions. A function f ϵ A is said to be bi-univalent in the open unit disk D if both f and f-1 are univalent in D. The symbol A denotes the class of all analytic functions f in D and it is normalized by the conditions f(0) = f’(0) – 1=0. The class of bi-univalent is denoted by  The subordination concept is used in determining second and third Taylor-Maclaurin coefficients. The upper bound for second and third coefficients is estimated for functions in the subclasses of bi-univalent functions which are subordinated to the function φ. An analytic function f is subordinate to an analytic function g if there is an analytic function w defined on D with w(0) = 0 and |w(z)| < 1 satisfying f(z) = g[w(z)]. In this paper, two subclasses of bi-univalent functions associated with Hohlov operator are introduced. The bound for second and third coefficients of functions in these subclasses is determined using subordination. The findings would generalize the previous related works of several earlier authors.

Digital Article Identifier (DAI):
1570
10007982
Analytical Formulae for the Approach Velocity Head Coefficient
Abstract:

Critical depth meters, such as abroad crested weir, Venture Flume and combined control flume are standard devices for measuring flow in open channels. The discharge relation for these devices cannot be solved directly, but it needs iteration process to account for the approach velocity head. In this paper, analytical solution was developed to calculate the discharge in a combined critical depth-meter namely, a hump combined with lateral contraction in rectangular channel with subcritical approach flow including energy losses. Also analytical formulae were derived for approach velocity head coefficient for different types of critical depth meters. The solution was derived by solving a standard cubic equation considering energy loss on the base of trigonometric identity. The advantage of this technique is to avoid iteration process adopted in measuring flow by these devices. Numerical examples are chosen for demonstration of the proposed solution.

Digital Article Identifier (DAI):
1569
10007933
Forecasting the Volatility of Geophysical Time Series with Stochastic Volatility Models
Abstract:
This work is devoted to the study of modeling geophysical time series. A stochastic technique with time-varying parameters is used to forecast the volatility of data arising in geophysics. In this study, the volatility is defined as a logarithmic first-order autoregressive process. We observe that the inclusion of log-volatility into the time-varying parameter estimation significantly improves forecasting which is facilitated via maximum likelihood estimation. This allows us to conclude that the estimation algorithm for the corresponding one-step-ahead suggested volatility (with ±2 standard prediction errors) is very feasible since it possesses good convergence properties.
Digital Article Identifier (DAI):
1568
10008378
(∈,∈∨q)-Fuzzy Subalgebras and Fuzzy Ideals of BCI-Algebras with Operators
Abstract:
The aim of this paper is to introduce the concepts of (∈, ∈∨q)-fuzzy subalgebras, (∈,∈∨q)-fuzzy ideals and (∈,∈∨q)-fuzzy quotient algebras of BCI-algebras with operators, and to investigate their basic properties.
Digital Article Identifier (DAI):
1567
10008011
Generalized π-Armendariz Authentication Cryptosystem
Abstract:

Algebra is one of the important fields of mathematics. It concerns with the study and manipulation of mathematical symbols. It also concerns with the study of abstractions such as groups, rings, and fields. Due to the development of these abstractions, it is extended to consider other structures, such as vectors, matrices, and polynomials, which are non-numerical objects. Computer algebra is the implementation of algebraic methods as algorithms and computer programs. Recently, many algebraic cryptosystem protocols are based on non-commutative algebraic structures, such as authentication, key exchange, and encryption-decryption processes are adopted. Cryptography is the science that aimed at sending the information through public channels in such a way that only an authorized recipient can read it. Ring theory is the most attractive category of algebra in the area of cryptography. In this paper, we employ the algebraic structure called skew -Armendariz rings to design a neoteric algorithm for zero knowledge proof. The proposed protocol is established and illustrated through numerical example, and its soundness and completeness are proved.

Digital Article Identifier (DAI):
1566
10007960
Generalized Rough Sets Applied to Graphs Related to Urban Problems
Abstract:
Branch of modern mathematics, graphs represent instruments for optimization and solving practical applications in various fields such as economic networks, engineering, network optimization, the geometry of social action, generally, complex systems including contemporary urban problems (path or transport efficiencies, biourbanism, & c.). In this paper is studied the interconnection of some urban network, which can lead to a simulation problem of a digraph through another digraph. The simulation is made univoc or more general multivoc. The concepts of fragment and atom are very useful in the study of connectivity in the digraph that is simulation - including an alternative evaluation of k- connectivity. Rough set approach in (bi)digraph which is proposed in premier in this paper contribute to improved significantly the evaluation of k-connectivity. This rough set approach is based on generalized rough sets - basic facts are presented in this paper.
Digital Article Identifier (DAI):
1565
10007741
Fourier Galerkin Approach to Wave Equation with Absorbing Boundary Conditions
Abstract:
Numerical computation of wave propagation in a large domain usually requires significant computational effort. Hence, the considered domain must be truncated to a smaller domain of interest. In addition, special boundary conditions, which absorb the outward travelling waves, need to be implemented in order to describe the system domains correctly. In this work, the linear one dimensional wave equation is approximated by utilizing the Fourier Galerkin approach. Furthermore, the artificial boundaries are realized with absorbing boundary conditions. Within this work, a systematic work flow for setting up the wave problem, including the absorbing boundary conditions, is proposed. As a result, a convenient modal system description with an effective absorbing boundary formulation is established. Moreover, the truncated model shows high accuracy compared to the global domain.
Digital Article Identifier (DAI):
1564
10007698
Zero Divisor Graph of a Poset with Respect to Primal Ideals
Abstract:
In this paper, we extend the concepts of primal and weakly primal ideals for posets. Further, the diameter of the zero divisor graph of a poset with respect to a non-primal ideal is determined. The relation between primary and primal ideals in posets is also studied.
Digital Article Identifier (DAI):
1563
10008907
Model-Driven and Data-Driven Approaches for Crop Yield Prediction: Analysis and Comparison
Abstract:
Crop yield prediction is a paramount issue in agriculture. The main idea of this paper is to find out efficient way to predict the yield of corn based meteorological records. The prediction models used in this paper can be classified into model-driven approaches and data-driven approaches, according to the different modeling methodologies. The model-driven approaches are based on crop mechanistic modeling. They describe crop growth in interaction with their environment as dynamical systems. But the calibration process of the dynamic system comes up with much difficulty, because it turns out to be a multidimensional non-convex optimization problem. An original contribution of this paper is to propose a statistical methodology, Multi-Scenarios Parameters Estimation (MSPE), for the parametrization of potentially complex mechanistic models from a new type of datasets (climatic data, final yield in many situations). It is tested with CORNFLO, a crop model for maize growth. On the other hand, the data-driven approach for yield prediction is free of the complex biophysical process. But it has some strict requirements about the dataset. A second contribution of the paper is the comparison of these model-driven methods with classical data-driven methods. For this purpose, we consider two classes of regression methods, methods derived from linear regression (Ridge and Lasso Regression, Principal Components Regression or Partial Least Squares Regression) and machine learning methods (Random Forest, k-Nearest Neighbor, Artificial Neural Network and SVM regression). The dataset consists of 720 records of corn yield at county scale provided by the United States Department of Agriculture (USDA) and the associated climatic data. A 5-folds cross-validation process and two accuracy metrics: root mean square error of prediction(RMSEP), mean absolute error of prediction(MAEP) were used to evaluate the crop prediction capacity. The results show that among the data-driven approaches, Random Forest is the most robust and generally achieves the best prediction error (MAEP 4.27%). It also outperforms our model-driven approach (MAEP 6.11%). However, the method to calibrate the mechanistic model from dataset easy to access offers several side-perspectives. The mechanistic model can potentially help to underline the stresses suffered by the crop or to identify the biological parameters of interest for breeding purposes. For this reason, an interesting perspective is to combine these two types of approaches.
Digital Article Identifier (DAI):
1562
10008144
A Study of Hamilton-Jacobi-Bellman Equation Systems Arising in Differential Game Models of Changing Society
Abstract:
This paper is concerned with a system of Hamilton-Jacobi-Bellman equations coupled with an autonomous dynamical system. The mathematical system arises in the differential game formulation of political economy models as an infinite-horizon continuous-time differential game with discounted instantaneous payoff rates and continuously and discretely varying state variables. The existence of a weak solution of the PDE system is proven and a computational scheme of approximate solution is developed for a class of such systems. A model of democratization is mathematically analyzed as an illustration of application.
Digital Article Identifier (DAI):
1561
10008068
Turing Pattern in the Oregonator Revisited
Abstract:
In this paper, we reconsider the analysis of the Oregonator model. We highlight an error in this analysis which leads to an incorrect depiction of the parameter region in which diffusion driven instability is possible. We believe that the cause of the oversight is the complexity of stability analyses based on eigenvalues and the dependence on parameters of matrix minors appearing in stability calculations. We regenerate the parameter space where Turing patterns can be seen, and we use the common Lyapunov function (CLF) approach, which is numerically reliable, to further confirm the dependence of the results on diffusion coefficients intensities.
Digital Article Identifier (DAI):
1560
10007927
Multisymplectic Geometry and Noether Symmetries for the Field Theories and the Relativistic Mechanics
Abstract:

The problem of symmetries in field theory has been analyzed using geometric frameworks, such as the multisymplectic models by using in particular the multivector field formalism. In this paper, we expand the vector fields associated to infinitesimal symmetries which give rise to invariant quantities as Noether currents for classical field theories and relativistic mechanic using the multisymplectic geometry where the Poincaré-Cartan form has thus been greatly simplified using the Second Order Partial Differential Equation (SOPDE) for multi-vector fields verifying Euler equations. These symmetries have been classified naturally according to the construction of the fiber bundle used.  In this work, unlike other works using the analytical method, our geometric model has allowed us firstly to distinguish the angular moments of the gauge field obtained during different transformations while these moments are gathered in a single expression and are obtained during a rotation in the Minkowsky space. Secondly, no conditions are imposed on the Lagrangian of the mechanics with respect to its dependence in time and in qi, the currents obtained naturally from the transformations are respectively the energy and the momentum of the system.

Digital Article Identifier (DAI):
1559
10007822
Secure E-Pay System Using Steganography and Visual Cryptography
Abstract:

Today’s internet world is highly prone to various online attacks, of which the most harmful attack is phishing. The attackers host the fake websites which are very similar and look alike. We propose an image based authentication using steganography and visual cryptography to prevent phishing. This paper presents a secure steganographic technique for true color (RGB) images and uses Discrete Cosine Transform to compress the images. The proposed method hides the secret data inside the cover image. The use of visual cryptography is to preserve the privacy of an image by decomposing the original image into two shares. Original image can be identified only when both qualified shares are simultaneously available. Individual share does not reveal the identity of the original image. Thus, the existence of the secret message is hard to be detected by the RS steganalysis.

Digital Article Identifier (DAI):
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