International Journal of Engineering, Mathematical and Physical Sciences

Computational Methods in Official Statistics with an Example on Calculating and Predicting Diabetes Mellitus [DM] Prevalence in Different Age Groups within Australia in Future Years, in Light of the Aging Population

Year: 2014 Volume: 8 Issue: 10 1315 - 1319 Pages

Authors:
D. Hilton

Abstract: An analysis of the Australian Diabetes Screening Study estimated undiagnosed diabetes mellitus [DM] prevalence in a high risk general practice based cohort. DM prevalence varied from 9.4% to 18.1% depending upon the diagnostic criteria utilised with age being a highly significant risk factor. Utilising the gold standard oral glucose tolerance test, the prevalence of DM was 22-23% in those aged >= 70 years and

Transformations between Bivariate Polynomial Bases

Year: 2014 Volume: 8 Issue: 10 1311 - 1314 Pages

Abstract: It is well known, that any interpolating polynomial p (x, y) on the vector space Pn,m of two-variable polynomials with degree less than n in terms of x and less than m in terms of y, has various representations that depends on the basis of Pn,m that we select i.e. monomial, Newton and Lagrange basis e.t.c.. The aim of this short note is twofold : a) to present transformations between the coordinates of the polynomial p (x, y) in the aforementioned basis and b) to present transformations between these bases.

Cubic Trigonometric B-spline Approach to Numerical Solution of Wave Equation

Year: 2014 Volume: 8 Issue: 10 1306 - 1310 Pages

Abstract: The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature.

A New Tool for Global Optimization Problems- Cuttlefish Algorithm

Year: 2014 Volume: 8 Issue: 9 1239 - 1243 Pages

Abstract: This paper presents a new meta-heuristic bio-inspired optimization algorithm which is called Cuttlefish Algorithm (CFA). The algorithm mimics the mechanism of color changing behavior of the cuttlefish to solve numerical global optimization problems. The colors and patterns of the cuttlefish are produced by reflected light from three different layers of cells. The proposed algorithm considers mainly two processes: reflection and visibility. Reflection process simulates light reflection mechanism used by these layers, while visibility process simulates visibility of matching patterns of the cuttlefish. To show the effectiveness of the algorithm, it is tested with some other popular bio-inspired optimization algorithms such as Genetic Algorithms (GA), Particle Swarm Optimization (PSO) and Bees Algorithm (BA) that have been previously proposed in the literature. Simulations and obtained results indicate that the proposed CFA is superior when compared with these algorithms.

Stability Criteria for Neural Networks with Two Additive Time-varying Delay Components

Year: 2014 Volume: 8 Issue: 5 877 - 881 Pages

Abstract: This paper is concerned with the stability problem with two additive time-varying delay components. By choosing one augmented Lyapunov-Krasovskii functional, using some new zero equalities, and combining linear matrix inequalities (LMI) techniques, two new sufficient criteria ensuring the global stability asymptotic stability of DNNs is obtained. These stability criteria are present in terms of linear matrix inequalities and can be easily checked. Finally, some examples are showed to demonstrate the effectiveness and less conservatism of the proposed method.

Airport Investment Risk Assessment under Uncertainty

Year: 2014 Volume: 8 Issue: 9 1234 - 1238 Pages

Abstract: The construction of a new airport or the extension of an existing one requires massive investments and many times public private partnerships were considered in order to make feasible such projects. One characteristic of these projects is uncertainty with respect to financial and environmental impacts on the medium to long term. Another one is the multistage nature of these types of projects. While many airport development projects have been a success, some others have turned into a nightmare for their promoters. This communication puts forward a new approach for airport investment risk assessment. The approach takes explicitly into account the degree of uncertainty in activity levels prediction and proposes milestones for the different stages of the project for minimizing risk. Uncertainty is represented through fuzzy dual theory and risk management is performed using dynamic programming. An illustration of the proposed approach is provided.

On Algebraic Structure of Improved Gauss-Seidel Iteration

Year: 2014 Volume: 8 Issue: 10 1300 - 1305 Pages

Abstract: Analysis of real life problems often results in linear systems of equations for which solutions are sought. The method to employ depends, to some extent, on the properties of the coefficient matrix. It is not always feasible to solve linear systems of equations by direct methods, as such the need to use an iterative method becomes imperative. Before an iterative method can be employed to solve a linear system of equations there must be a guaranty that the process of solution will converge. This guaranty, which must be determined apriori, involve the use of some criterion expressible in terms of the entries of the coefficient matrix. It is, therefore, logical that the convergence criterion should depend implicitly on the algebraic structure of such a method. However, in deference to this view is the practice of conducting convergence analysis for Gauss- Seidel iteration on a criterion formulated based on the algebraic structure of Jacobi iteration. To remedy this anomaly, the Gauss- Seidel iteration was studied for its algebraic structure and contrary to the usual assumption, it was discovered that some property of the iteration matrix of Gauss-Seidel method is only diagonally dominant in its first row while the other rows do not satisfy diagonal dominance. With the aid of this structure we herein fashion out an improved version of Gauss-Seidel iteration with the prospect of enhancing convergence and robustness of the method. A numerical section is included to demonstrate the validity of the theoretical results obtained for the improved Gauss-Seidel method.

Spectral Broadening in an InGaAsP Optical Waveguide with χ(3) Nonlinearity Including Two Photon Absorption

Year: 2014 Volume: 8 Issue: 10 1296 - 1299 Pages

Abstract: We have studied a method to widen the spectrum of optical pulses that pass through an InGaAsP waveguide for application to broadband optical communication. In particular, we have investigated the competitive effect between spectral broadening arising from nonlinear refraction (optical Kerr effect) and shrinking due to two photon absorption in the InGaAsP waveguide with χ(3) nonlinearity. The shrunk spectrum recovers broadening by the enhancement effect of the nonlinear refractive index near the bandgap of InGaAsP with a bandgap wavelength of 1490 nm. The broadened spectral width at around 1525 nm (196.7 THz) becomes 10.7 times wider than that at around 1560 nm (192.3 THz) without the enhancement effect, where amplified optical pulses with a pulse width of ∼ 2 ps and a peak power of 10 W propagate through a 1-cm-long InGaAsP waveguide with a cross-section of 4 (μm)2.

Defuzzification of Periodic Membership Function on Circular Coordinates

Year: 2014 Volume: 8 Issue: 10 1292 - 1295 Pages

Abstract: This paper presents circular polar coordinates transformation of periodic fuzzy membership function. The purpose is identification of domain of periodic membership functions in consequent part of IF-THEN rules. Proposed methods in this paper remove complicatedness concerning domain of periodic membership function from defuzzification in fuzzy approximate reasoning. Defuzzification on circular polar coordinates is also proposed.

Multi-Wavelength Q-Switched Erbium-Doped Fiber Laser with Photonic Crystal Fiber and Multi-Walled Carbon Nanotubes

Year: 2014 Volume: 8 Issue: 10 1288 - 1291 Pages

Abstract: A simple multi-wavelength passively Q-switched Erbium-doped fiber laser (EDFL) is demonstrated using low cost multi-walled carbon nanotubes (MWCNTs) based saturable absorber (SA), which is prepared using polyvinyl alcohol (PVA) as a host polymer. The multi-wavelength operation is achieved based on nonlinear polarization rotation (NPR) effect by incorporating 50 m long photonic crystal fiber (PCF) in the ring cavity. The EDFL produces a stable multi-wavelength comb spectrum for more than 14 lines with a fixed spacing of 0.48 nm. The laser also demonstrates a stable pulse train with the repetition rate increases from 14.9 kHz to 25.4 kHz as the pump power increases from the threshold power of 69.0 mW to the maximum pump power of 133.8 mW. The minimum pulse width of 4.4 μs was obtained at the maximum pump power of 133.8 mW while the highest energy of 0.74 nJ was obtained at pump power of 69.0 mW.

Image Segmentation by Mathematical Morphology: An Approach through Linear, Bilinear and Conformal Transformation

Year: 2014 Volume: 8 Issue: 8 1149 - 1152 Pages

Abstract: Image segmentation process based on mathematical morphology has been studied in the paper. It has been established from the first principles of the morphological process, the entire segmentation is although a nonlinear signal processing task, the constituent wise, the intermediate steps are linear, bilinear and conformal transformation and they give rise to a non linear affect in a cumulative manner.

Dual Solutions in Mixed Convection Boundary Layer Flow: A Stability Analysis

Year: 2014 Volume: 8 Issue: 9 1230 - 1233 Pages

Authors:
Anuar Ishak

Abstract: The mixed convection stagnation point flow toward a vertical plate is investigated. The external flow impinges normal to the heated plate and the surface temperature is assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the mixed convection parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

Implementation of Intuitionistic Fuzzy Approach in Maximizing Net Present Value

Year: 2014 Volume: 8 Issue: 7 1069 - 1073 Pages

Abstract: The applicability of Net Present Value (NPV) in an investment project is becoming more and more popular in the field of engineering economics. The classical NPV methodology involves only the precise and accurate data of the investment project. In the present communication, we give a new mathematical model for NPV which uses the concept of intuitionistic fuzzy set theory. The proposed model is based on triangular intuitionistic fuzzy number, which may be known as Intuitionistic Fuzzy Net Present Value (IFNPV). The model has been applied to an example and the results are presented.

Exp-Function Method for Finding Some Exact Solutions of Rosenau Kawahara and Rosenau Korteweg-de Vries Equations

Year: 2014 Volume: 8 Issue: 6 990 - 996 Pages

Authors:
Ehsan Mahdavi

Abstract: In this paper, we apply the Exp-function method to Rosenau-Kawahara and Rosenau-KdV equations. Rosenau-Kawahara equation is the combination of the Rosenau and standard Kawahara equations and Rosenau-KdV equation is the combination of the Rosenau and standard KdV equations. These equations are nonlinear partial differential equations (NPDE) which play an important role in mathematical physics. Exp-function method is easy, succinct and powerful to implement to nonlinear partial differential equations arising in mathematical physics. We mainly try to present an application of Exp-function method and offer solutions for common errors wich occur during some of the recent works.

The Application of the Queuing Theory in the Traffic Flow of Intersection

Year: 2014 Volume: 8 Issue: 6 986 - 989 Pages

Abstract: It is practically significant to research the traffic flow of intersection because the capacity of intersection affects the efficiency of highway network directly. This paper analyzes the traffic conditions of an intersection in certain urban by the methods of queuing theory and statistical experiment, sets up a corresponding mathematical model and compares it with the actual values. The result shows that queuing theory is applied in the study of intersection traffic flow and it can provide references for the other similar designs.

Fuzzy Multi-Component DEA with Shared and Undesirable Fuzzy Resources

Year: 2014 Volume: 8 Issue: 9 1221 - 1229 Pages

Abstract: Multi-component data envelopment analysis (MC-DEA) is a popular technique for measuring aggregate performance of the decision making units (DMUs) along with their components. However, the conventional MC-DEA is limited to crisp input and output data which may not always be available in exact form. In real life problems, data may be imprecise or fuzzy. Therefore, in this paper, we propose (i) a fuzzy MC-DEA (FMC-DEA) model in which shared and undesirable fuzzy resources are incorporated, (ii) the proposed FMC-DEA model is transformed into a pair of crisp models using α cut approach, (iii) fuzzy aggregate performance of a DMU and fuzzy efficiencies of components are defined to be fuzzy numbers, and (iv) a numerical example is illustrated to validate the proposed approach.

Evaluation of the exIWO Algorithm Based On the Traveling Salesman Problem

Year: 2014 Volume: 8 Issue: 9 1217 - 1220 Pages

Abstract: The expanded Invasive Weed Optimization algorithm (exIWO) is an optimization metaheuristic modelled on the original IWO version created by the researchers from the University of Tehran. The authors of the present paper have extended the exIWO algorithm introducing a set of both deterministic and non-deterministic strategies of individuals’ selection. The goal of the project was to evaluate the exIWO by testing its usefulness for solving some test instances of the traveling salesman problem (TSP) taken from the TSPLIB collection which allows comparing the experimental results with optimal values.

Transverse Vibration of Non-Homogeneous Rectangular Plates of Variable Thickness Using GDQ

Year: 2014 Volume: 8 Issue: 9 1211 - 1216 Pages

Authors:
R. Saini
R. Lal

Abstract: The effect of non-homogeneity on the free transverse vibration of thin rectangular plates of bilinearly varying thickness has been analyzed using generalized differential quadrature (GDQ) method. The non-homogeneity of the plate material is assumed to arise due to linear variations in Young’s modulus and density of the plate material with the in-plane coordinates x and y. Numerical results have been computed for fully clamped and fully simply supported boundary conditions. The solution procedure by means of GDQ method has been implemented in a MATLAB code. The effect of various plate parameters has been investigated for the first three modes of vibration. A comparison of results with those available in literature has been presented.

Keywords:
Bilinear thickness
generalized differential quadrature (GDQ)
non-homogeneous
Rectangular.

Exponential State Estimation for Neural Networks with Leakage, Discrete and Distributed Delays

Year: 2014 Volume: 8 Issue: 5 866 - 876 Pages

Abstract: In this paper, the design problem of state estimator for neural networks with the mixed time-varying delays are investigated by constructing appropriate Lyapunov-Krasovskii functionals and using some effective mathematical techniques. In order to derive several conditions to guarantee the estimation error systems to be globally exponential stable, we transform the considered systems into the neural-type time-delay systems. Then with a set of linear inequalities(LMIs), we can obtain the stable criteria. Finally, three numerical examples are given to show the effectiveness and less conservatism of the proposed criterion.

The Bent and Hyper-Bent Properties of a Class of Boolean Functions

Year: 2014 Volume: 8 Issue: 5 859 - 865 Pages

Abstract: This paper considers the bent and hyper-bent properties of a class of Boolean functions. For one case, we present a detailed description for them to be hyper-bent functions, and give a necessary condition for them to be bent functions for another case.