Scholarly

Comparison Results of Two-point Fuzzy Boundary Value Problems

Year: 2011 Volume: 5 Issue: 3 318 - 324 Pages

Authors:
Hsuan-Ku Liu

Abstract: This paper investigates the solutions of two-point fuzzy boundary value problems as the form x = f(t, x(t)), x(0) = A and x(l) = B, where A and B are fuzzy numbers. There are four different solutions for the problems when the lateral type of H-derivative is employed to solve the problems. As f(t, x) is a monotone function of x, these four solutions are reduced to two different solutions. As f(t, x(t)) = λx(t) or f(t, x(t)) = -λx(t), solutions and several comparison results are presented to indicate advantages of each solution.

Three Steps of One-way Nested Grid for Energy Balance Equations by Wave Model

Year: 2011 Volume: 5 Issue: 3 310 - 317 Pages

Abstract: The three steps of the standard one-way nested grid for a regional scale of the third generation WAve Model Cycle 4 (WAMC4) is scrutinized. The model application is enabled to solve the energy balance equation on a coarse resolution grid in order to produce boundary conditions for a smaller area by the nested grid technique. In the present study, the model takes a full advantage of the fine resolution of wind fields in space and time produced by the available U.S. Navy Global Atmospheric Prediction System (NOGAPS) model with 1 degree resolution. The nested grid application of the model is developed in order to gradually increase the resolution from the open ocean towards the South China Sea (SCS) and the Gulf of Thailand (GoT) respectively. The model results were compared with buoy observations at Ko Chang, Rayong and Huahin locations which were obtained from the Seawatch project. In addition, the results were also compared with Satun based weather station which was provided from Department of Meteorology, Thailand. The data collected from this station presented the significant wave height (Hs) reached 12.85 m. The results indicated that the tendency of the Hs from the model in the spherical coordinate propagation with deep water condition in the fine grid domain agreed well with the Hs from the observations.

A Novel System of Two Coupled Equations for the Longitudinal Components of the Electromagnetic Field in a Waveguide

Year: 2011 Volume: 5 Issue: 3 306 - 309 Pages

Abstract: In this paper, a novel wave equation for electromagnetic waves in a medium having anisotropic permittivity has been derived with the help of Maxwell-s curl equations. The x and y components of the Maxwell-s equations are written with the permittivity () being a 3 × 3 symmetric matrix. These equations are solved for Ex , Ey, Hx, Hy in terms of Ez, Hz, and the partial derivatives. The Z components of the Maxwell-s curl are then used to arrive to the generalized Helmholtz equations for Ez and Hz.

Exterior Calculus: Economic Growth Dynamics

Year: 2011 Volume: 5 Issue: 3 302 - 305 Pages

Authors:
Troy L. Story

Abstract: Mathematical models of dynamics employing exterior calculus are mathematical representations of the same unifying principle; namely, the description of a dynamic system with a characteristic differential one-form on an odd-dimensional differentiable manifold leads, by analysis with exterior calculus, to a set of differential equations and a characteristic tangent vector (vortex vector) which define transformations of the system. Using this principle, a mathematical model for economic growth is constructed by proposing a characteristic differential one-form for economic growth dynamics (analogous to the action in Hamiltonian dynamics), then generating a pair of characteristic differential equations and solving these equations for the rate of economic growth as a function of labor and capital. By contracting the characteristic differential one-form with the vortex vector, the Lagrangian for economic growth dynamics is obtained.

Similarity Measures and Weighted Fuzzy C-Mean Clustering Algorithm

Year: 2011 Volume: 5 Issue: 3 298 - 301 Pages

Abstract: In this paper we study the fuzzy c-mean clustering algorithm combined with principal components method. Demonstratively analysis indicate that the new clustering method is well rather than some clustering algorithms. We also consider the validity of clustering method.

Information Measures Based on Sampling Distributions

Year: 2011 Volume: 5 Issue: 3 293 - 297 Pages

Abstract: Information theory and Statistics play an important role in Biological Sciences when we use information measures for the study of diversity and equitability. In this communication, we develop the link among the three disciplines and prove that sampling distributions can be used to develop new information measures. Our study will be an interdisciplinary and will find its applications in Biological systems.

Neighbors of Indefinite Binary Quadratic Forms

Year: 2011 Volume: 5 Issue: 3 286 - 292 Pages

Authors:
Ahmet Tekcan

Abstract: In this paper, we derive some algebraic identities on right and left neighbors R(F) and L(F) of an indefinite binary quadratic form F = F(x, y) = ax2 + bxy + cy2 of discriminant Δ = b2 -4ac. We prove that the proper cycle of F can be given by using its consecutive left neighbors. Also we construct a connection between right and left neighbors of F.

Selective Wet-Etching of Amorphous/Crystallized Sb20se80 Thin Films

Year: 2011 Volume: 5 Issue: 3 282 - 285 Pages

Abstract: The selective wet-etching of amorphous and crystalline region of Sb20Se80 thin films was carried out using organic based solution e.g. amines. We report the development of an in situ real-time method to study the wet chemical etching process of thin films. Characterization of the structure and surface of films studied by X-ray diffraction, SEM and EBSD methods has been done and potential application suggested.

Analytical Solution for the Zakharov-Kuznetsov Equations by Differential Transform Method

Year: 2011 Volume: 5 Issue: 3 276 - 281 Pages

Abstract: This paper presents the approximate analytical solution of a Zakharov-Kuznetsov ZK(m, n, k) equation with the help of the differential transform method (DTM). The DTM method is a powerful and efficient technique for finding solutions of nonlinear equations without the need of a linearization process. In this approach the solution is found in the form of a rapidly convergent series with easily computed components. The two special cases, ZK(2,2,2) and ZK(3,3,3), are chosen to illustrate the concrete scheme of the DTM method in ZK(m, n, k) equations. The results demonstrate reliability and efficiency of the proposed method.

Dispersion of a Solute in Peristaltic Motion of a Couple Stress Fluid in the Presence of Magnetic Field

Year: 2011 Volume: 5 Issue: 3 270 - 275 Pages

Abstract: An analytical solution for dispersion of a solute in the peristaltic motion of a couple stress fluid in the presence of magnetic field with both homogeneous and heterogeneous chemical reactions is presented. The average effective dispersion coefficient has been found using Taylor-s limiting condition and long wavelength approximation. The effects of various relevant parameters on the average effective coefficient of dispersion have been studied. The average effective dispersion coefficient tends to decrease with magnetic field parameter, homogeneous chemical reaction rate parameter and amplitude ratio but tends to increase with heterogeneous chemical reaction rate parameter.

Analysis of Periodic Solution of Delay Fuzzy BAM Neural Networks

Year: 2011 Volume: 5 Issue: 3 264 - 269 Pages

Abstract: In this paper, by employing a new Lyapunov functional and an elementary inequality analysis technique, some sufficient conditions are derived to ensure the existence and uniqueness of periodic oscillatory solution for fuzzy bi-directional memory (BAM) neural networks with time-varying delays, and all other solutions of the fuzzy BAM neural networks converge the uniqueness periodic solution. These criteria are presented in terms of system parameters and have important leading significance in the design and applications of neural networks. Moreover an example is given to illustrate the effectiveness and feasible of results obtained.

Fuzzy Decision Making via Multiple Attribute

Year: 2011 Volume: 5 Issue: 3 259 - 263 Pages

Abstract: In this paper, a method for decision making in fuzzy environment is presented.A new subjective and objective integrated approach is introduced that used to assign weight attributes in fuzzy multiple attribute decision making (FMADM) problems and alternatives and fmally ranked by proposed method.

Elastic-Plastic Analysis for Finite Deformation of a Rotating Disk Having Variable Thickness with Inclusion

Year: 2011 Volume: 5 Issue: 3 249 - 258 Pages

Abstract: Transition theory has been used to derive the elasticplastic and transitional stresses. Results obtained have been discussed numerically and depicted graphically. It is observed that the rotating disk made of incompressible material with inclusion require higher angular speed to yield at the internal surface as compared to disk made of compressible material. It is seen that the radial and circumferential stresses are maximum at the internal surface with and without edge load (for flat disk). With the increase in thickness parameter (k = 2, 4), the circumferential stress is maximum at the external surface while the radial stress is maximum at the internal surface. From the figures drawn the disk with exponentially varying thickness (k = 2), high angular speed is required for initial yielding at internal surface as compared to flat disk and exponentially varying thickness for k = 4 onwards. It is concluded that the disk made of isotropic compressible material is on the safer side of the design as compared to disk made of isotropic incompressible material as it requires higher percentage increase in an angular speed to become fully plastic from its initial yielding.

A Finite-Time Consensus Protocol of the Multi-Agent Systems

Year: 2011 Volume: 5 Issue: 3 246 - 248 Pages

Abstract: According to conjugate gradient algorithm, a new consensus protocol algorithm of discrete-time multi-agent systems is presented, which can achieve finite-time consensus. Finally, a numerical example is given to illustrate our theoretical result.

Parametric and Nonparametric Analysis of Breast Cancer Treatments

Year: 2011 Volume: 5 Issue: 3 242 - 245 Pages

Abstract: The objective of the present research manuscript is to perform parametric, nonparametric, and decision tree analysis to evaluate two treatments that are being used for breast cancer patients. Our study is based on utilizing real data which was initially used in “Tamoxifen with or without breast irradiation in women of 50 years of age or older with early breast cancer" [1], and the data is supplied to us by N.A. Ibrahim “Decision tree for competing risks survival probability in breast cancer study" [2]. We agree upon certain aspects of our findings with the published results. However, in this manuscript, we focus on relapse time of breast cancer patients instead of survival time and parametric analysis instead of semi-parametric decision tree analysis is applied to provide more precise recommendations of effectiveness of the two treatments with respect to reoccurrence of breast cancer.

Effect of Variable viscosity on Convective Heat Transfer along an Inclined Plate Embedded in Porous Medium with an Applied Magnetic Field

Year: 2011 Volume: 5 Issue: 3 237 - 241 Pages

Abstract: The flow and heat transfer characteristics for natural convection along an inclined plate in a saturated porous medium with an applied magnetic field have been studied. The fluid viscosity has been assumed to be an inverse function of temperature. Assuming temperature vary as a power function of distance. The transformed ordinary differential equations have solved by numerical integration using Runge-Kutta method. The velocity and temperature profile components on the plate are computed and discussed in detail for various values of the variable viscosity parameter, inclination angle, magnetic field parameter, and real constant (λ). The results have also been interpreted with the aid of tables and graphs. The numerical values of Nusselt number have been calculated for the mentioned parameters.

On the Fuzzy Difference Equation xn+1 = A +

Year: 2011 Volume: 5 Issue: 3 231 - 236 Pages

Abstract: In this paper, we study the existence, the boundedness and the asymptotic behavior of the positive solutions of a fuzzy nonlinear difference equations xn+1 = A + k i=0 Bi xn-i , n= 0, 1, · · · . where (xn) is a sequence of positive fuzzy numbers, A,Bi and the initial values x-k, x-k+1, · · · , x0 are positive fuzzy numbers. k ∈ {0, 1, 2, · · ·}.

Codes and Formulation of Appropriate Constraints via Entropy Measures

Year: 2011 Volume: 5 Issue: 3 226 - 230 Pages

Authors:
R. K. Tuli

Abstract: In present communication, we have developed the suitable constraints for the given the mean codeword length and the measures of entropy. This development has proved that Renyi-s entropy gives the minimum value of the log of the harmonic mean and the log of power mean. We have also developed an important relation between best 1:1 code and the uniquely decipherable code by using different measures of entropy.

Block Homotopy Perturbation Method for Solving Fuzzy Linear Systems

Year: 2011 Volume: 5 Issue: 3 222 - 225 Pages

Authors:
Shu-Xin Miao

Abstract: In this paper, we present an efficient numerical algorithm, namely block homotopy perturbation method, for solving fuzzy linear systems based on homotopy perturbation method. Some numerical examples are given to show the efficiency of the algorithm.

Applications of Entropy Measures in Field of Queuing Theory

Year: 2011 Volume: 5 Issue: 3 217 - 221 Pages

Authors:
R.K.Tuli

Abstract: In the present communication, we have studied different variations in the entropy measures in the different states of queueing processes. In case of steady state queuing process, it has been shown that as the arrival rate increases, the uncertainty increases whereas in the case of non-steady birth-death process, it is shown that the uncertainty varies differently. In this pattern, it first increases and attains its maximum value and then with the passage of time, it decreases and attains its minimum value.

International Journal of Engineering, Mathematical and Physical Sciences

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