Excellence in Research and Innovation for Humanity

International Science Index

Commenced in January 1999 Frequency: Monthly Edition: International Paper Count: 1574

Mathematical and Computational Sciences

1574
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):
1573
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):
1572
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):
1571
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):
1570
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):
1569
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):
1568
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):
1567
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):
1566
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):
1565
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):
1564
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):
1563
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):
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):
1558
10007401
Basket Option Pricing under Jump Diffusion Models
Abstract:
Pricing financial contracts on several underlying assets received more and more interest as a demand for complex derivatives. The option pricing under asset price involving jump diffusion processes leads to the partial integral differential equation (PIDEs), which is an extension of the Black-Scholes PDE with a new integral term. The aim of this paper is to show how basket option prices in the jump diffusion models, mainly on the Merton model, can be computed using RBF based approximation methods. For a test problem, the RBF-PU method is applied for numerical solution of partial integral differential equation arising from the two-asset European vanilla put options. The numerical result shows the accuracy and efficiency of the presented method.
Digital Article Identifier (DAI):
1557
10007869
Fuzzy Subalgebras and Fuzzy Ideals of BCI-Algebras with Operators
Abstract:
The aim of this paper is to introduce the concepts of fuzzy subalgebras, fuzzy ideals and fuzzy quotient algebras of BCI-algebras with operators, and to investigate their basic properties.
Digital Article Identifier (DAI):
1556
10007224
Effect of Manganese Doping on Ferrroelectric Properties of (K0.485Na0.5Li0.015)(Nb0.98V0.02)O3 Lead-Free Piezoceramic
Abstract:

Alkaline niobate (Na0.5K0.5)NbO3 ceramic system has attracted major attention in view of its potential for replacing the highly toxic but superior lead zirconate titanate (PZT) system for piezoelectric applications. Recently, a more detailed study of this system reveals that the ferroelectric and piezoelectric properties are optimized in the Li- and V-modified system having the composition (K0.485Na0.5Li0.015)(Nb0.98V0.02)O3. In the present work, we further study the pyroelectric behaviour of this composition along with another doped with Mn4+. So, (K0.485Na0.5Li0.015)(Nb0.98V0.02)O3 + x MnO2 (x = 0, and 0.01 wt. %) ceramic compositions were synthesized by conventional ceramic processing route. X-ray diffraction study reveals that both the undoped and Mn4+-doped ceramic samples prepared crystallize into a perovskite structure having orthorhombic symmetry. Dielectric study indicates that Mn4+ doping has little effect on both the Curie temperature (Tc) and tetragonal-orthorhombic phase transition temperature (Tot). The bulk density, room-temperature dielectric constant (εRT), and room-c The room-temperature coercive field (Ec) is observed to be lower in Mn4+ doped sample. The detailed analysis of the P-E hysteresis loops over the range of temperature from about room temperature to Tot points out that enhanced ferroelectric properties exist in this temperature range with better thermal stability for the Mn4+ doped ceramic. The study reveals that small traces of Mn4+ can modify (K0.485Na0.5Li0.015)(Nb0.98V0.02)O3 system so as to improve its ferroelectric properties with good thermal stability over a wide range of temperature.

Digital Article Identifier (DAI):
1555
10007567
Skew Cyclic Codes over Fq+uFq+…+uk-1Fq
Abstract:

This paper studies a special class of linear codes, called skew cyclic codes, over the ring R= Fq+uFq+…+uk-1Fq, where q is a prime power. A Gray map ɸ from R to Fq and a Gray map ɸ' from Rn to Fnq are defined, as well as an automorphism Θ over R. It is proved that the images of skew cyclic codes over R under map ɸ' and Θ are cyclic codes over Fq, and they still keep the dual relation.

Digital Article Identifier (DAI):
1554
10007035
Efficiency of Robust Heuristic Gradient Based Enumerative and Tunneling Algorithms for Constrained Integer Programming Problems
Abstract:

This paper presents performance of two robust gradient-based heuristic optimization procedures based on 3n enumeration and tunneling approach to seek global optimum of constrained integer problems. Both these procedures consist of two distinct phases for locating the global optimum of integer problems with a linear or non-linear objective function subject to linear or non-linear constraints. In both procedures, in the first phase, a local minimum of the function is found using the gradient approach coupled with hemstitching moves when a constraint is violated in order to return the search to the feasible region. In the second phase, in one optimization procedure, the second sub-procedure examines 3n integer combinations on the boundary and within hypercube volume encompassing the result neighboring the result from the first phase and in the second optimization procedure a tunneling function is constructed at the local minimum of the first phase so as to find another point on the other side of the barrier where the function value is approximately the same. In the next cycle, the search for the global optimum commences in both optimization procedures again using this new-found point as the starting vector. The search continues and repeated for various step sizes along the function gradient as well as that along the vector normal to the violated constraints until no improvement in optimum value is found. The results from both these proposed optimization methods are presented and compared with one provided by popular MS Excel solver that is provided within MS Office suite and other published results.

Digital Article Identifier (DAI):
1553
10008305
Solutions of Fuzzy Transportation Problem Using Best Candidates Method and Different Ranking Techniques
Abstract:

Transportation Problem (TP) is based on supply and demand of commodities transported from one source to the different destinations. Usual methods for finding solution of TPs are North-West Corner Rule, Least Cost Method Vogel’s Approximation Method etc. The transportation costs tend to vary at each time. We can use fuzzy numbers which would give solution according to this situation. In this study the Best Candidate Method (BCM) is applied. For ranking Centroid Ranking Technique (CRT) and Robust Ranking Technique have been adopted to transform the fuzzy TP and the above methods are applied to EDWARDS Vacuum Company, Crawley, in West Sussex in the United Kingdom. A Comparative study is also given. We see that the transportation cost can be minimized by the application of CRT under BCM.

Digital Article Identifier (DAI):
1552
10007127
Conjugate Mixed Convection Heat Transfer and Entropy Generation of Cu-Water Nanofluid in an Enclosure with Thick Wavy Bottom Wall
Abstract:
Mixed convection of Cu-water nanofluid in an enclosure with thick wavy bottom wall has been investigated numerically. A co-ordinate transformation method is used to transform the computational domain into an orthogonal co-ordinate system. The governing equations in the computational domain are solved through a pressure correction based iterative algorithm. The fluid flow and heat transfer characteristics are analyzed for a wide range of Richardson number (0.1 ≤ Ri ≤ 5), nanoparticle volume concentration (0.0 ≤ ϕ ≤ 0.2), amplitude (0.0 ≤ α ≤ 0.1) of the wavy thick- bottom wall and the wave number (ω) at a fixed Reynolds number. Obtained results showed that heat transfer rate increases remarkably by adding the nanoparticles. Heat transfer rate is dependent on the wavy wall amplitude and wave number and decreases with increasing Richardson number for fixed amplitude and wave number. The Bejan number and the entropy generation are determined to analyze the thermodynamic optimization of the mixed convection.
Digital Article Identifier (DAI):
1551
10006985
On CR-Structure and F-Structure Satisfying Polynomial Equation
Abstract:
The purpose of this paper is to show a relation between CR structure and F-structure satisfying polynomial equation. In this paper, we have checked the significance of CR structure and F-structure on Integrability conditions and Nijenhuis tensor. It was proved that all the properties of Integrability conditions and Nijenhuis tensor are satisfied by CR structures and F-structure satisfying polynomial equation.
Digital Article Identifier (DAI):
1550
10006914
Lowering Error Floors by Concatenation of Low-Density Parity-Check and Array Code
Abstract:
Low-density parity-check (LDPC) codes have been shown to deliver capacity approaching performance; however, problematic graphical structures (e.g. trapping sets) in the Tanner graph of some LDPC codes can cause high error floors in bit-error-ratio (BER) performance under conventional sum-product algorithm (SPA). This paper presents a serial concatenation scheme to avoid the trapping sets and to lower the error floors of LDPC code. The outer code in the proposed concatenation is the LDPC, and the inner code is a high rate array code. This approach applies an interactive hybrid process between the BCJR decoding for the array code and the SPA for the LDPC code together with bit-pinning and bit-flipping techniques. Margulis code of size (2640, 1320) has been used for the simulation and it has been shown that the proposed concatenation and decoding scheme can considerably improve the error floor performance with minimal rate loss.
Digital Article Identifier (DAI):
1549
10006879
Entropy Measures on Neutrosophic Soft Sets and Its Application in Multi Attribute Decision Making
Abstract:
The focus of the paper is to furnish the entropy measure for a neutrosophic set and neutrosophic soft set which is a measure of uncertainty and it permeates discourse and system. Various characterization of entropy measures are derived. Further we exemplify this concept by applying entropy in various real time decision making problems.
Digital Article Identifier (DAI):
1548
10006825
A Fuzzy Mathematical Model for Order Acceptance and Scheduling Problem
Authors:
Abstract:

The problem of Order Acceptance and Scheduling (OAS) is defined as a joint decision of which orders to accept for processing and how to schedule them. Any linear programming model representing real-world situation involves the parameters defined by the decision maker in an uncertain way or by means of language statement. Fuzzy data can be used to incorporate vagueness in the real-life situation. In this study, a fuzzy mathematical model is proposed for a single machine OAS problem, where the orders are defined by their fuzzy due dates, fuzzy processing times, and fuzzy sequence dependent setup times. The signed distance method, one of the fuzzy ranking methods, is used to handle the fuzzy constraints in the model.

Digital Article Identifier (DAI):
1547
10006659
Sensitivity Analysis during the Optimization Process Using Genetic Algorithms
Abstract:
Genetic algorithms (GA) are applied to the solution of high-dimensional optimization problems. Additionally, sensitivity analysis (SA) is usually carried out to determine the effect on optimal solutions of changes in parameter values of the objective function. These two analyses (i.e., optimization and sensitivity analysis) are computationally intensive when applied to high-dimensional functions. The approach presented in this paper consists in performing the SA during the GA execution, by statistically analyzing the data obtained of running the GA. The advantage is that in this case SA does not involve making additional evaluations of the objective function and, consequently, this proposed approach requires less computational effort than conducting optimization and SA in two consecutive steps.
Digital Article Identifier (DAI):
1546
10008418
Invariant Characters of Tolerance Class and Reduction under Homomorphism in IIS
Abstract:

Some invariant properties of incomplete information systems homomorphism are studied in this paper. Demand conditions of tolerance class, attribute reduction, indispensable attribute and dispensable attribute being invariant under homomorphism in incomplete information system are revealed and discussed. The existing condition of endohomomorphism on an incomplete information system is also explored. It establishes some theoretical foundations for further investigations on incomplete information systems in rough set theory, like in information systems.

Digital Article Identifier (DAI):
1545
10006683
An Analytical Method for Solving General Riccati Equation
Abstract:

In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.

Digital Article Identifier (DAI):
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