International Journal of Engineering, Mathematical and Physical Sciences

Positive Solutions for Semipositone Discrete Eigenvalue Problems via Three Critical Points Theorem

Year: 2010 Volume: 4 Issue: 9 1319 - 1322 Pages

Authors:
Benshi Zhu

Abstract: In this paper, multiple positive solutions for semipositone discrete eigenvalue problems are obtained by using a three critical points theorem for nondifferentiable functional.

Reflection of Plane Waves at Free Surface of an Initially Stressed Dissipative Medium

Year: 2008 Volume: 2 Issue: 4 294 - 301 Pages

Authors:
M. M. Selim

Abstract: The paper discuses the effect of initial stresses on the reflection coefficients of plane waves in a dissipative medium. Basic governing equations are formulated in context of Biot's incremental deformation theory. These governing equations are solved analytically to obtain the dimensional phase velocities of plane waves propagating in plane of symmetry. Closed-form expressions for the reflection coefficients of P and SV waves- incident at the free surface of an initially stressed dissipative medium are obtained. Numerical computations, using these expressions, are carried out for a particular model. Computations made with the results predicted in presence and absence of the initial stresses and the results have been shown graphically. The study shows that the presence of compressive initial stresses increases the velocity of longitudinal wave (P-wave) but diminishes that of transverse wave (SV-wave). Also the numerical results presented indicate that initial stresses and dissipation might affect the reflection coefficients significantly.

Experimental Study on Temperature Dependence of Absorption and Emission Properties of Yb:YAG Crystal as a Disk Laser Medium

Year: 2012 Volume: 6 Issue: 3 342 - 345 Pages

Abstract: In this paper, the absorption and fluorescence emission spectra of Yb:Y3Al5O12 (YAG)(25 at%) crystal as a disk laser medium are measured at high temperature (300-450K). The absorption and emission cross sections of Yb:YAG crystal are determined using Reciprocity method. Temperature dependence of 941nm absorption cross section and 1031nm emission cross section is extracted in the range of 300-450K. According to our experimental results, an exponential temperature dependence between 300K and 450K is acquired for the 1031nm peak emission cross section and also for 941nm peak absorption cross section of Yb:YAG crystal. These results could be used for simulation and design of high power highly doped Yb:YAG thin disk lasers.

Completion Latin Square for Wavelength Routing

Year: 2010 Volume: 4 Issue: 2 313 - 316 Pages

Abstract: Optical network uses a tool for routing called Latin router. These routers use particular algorithms for routing. For example, we can refer to LDF algorithm that uses backtracking (one of CSP methods) for problem solving. In this paper, we proposed new approached for completion routing table (DRA&CRA algorithm) and compare with pervious proposed ways and showed numbers of backtracking, blocking and run time for DRA algorithm less than LDF and CRA algorithm.

How are Equalities Defined, Strong or Weak on a Multiple Algebra?

Year: 2010 Volume: 4 Issue: 9 1315 - 1318 Pages

Authors:
Mona Taheri

Abstract: For the purpose of finding the quotient structure of multiple algebras such as groups, Abelian groups and rings, we will state concepts of ( strong or weak ) equalities on multiple algebras, which will lead us to research on how ( strong or weak) are equalities defined on a multiple algebra over the quotients obtained from it. In order to find a quotient structure of multiple algebras such as groups, Abelian groups and loops, a part of this article has been allocated to the concepts of equalities (strong and weak) of the defined multiple functions on multiple algebras. This leads us to do research on how defined equalities (strong and weak) are made in the multiple algebra on its resulted quotient.

Elliptic Divisibility Sequences over Finite Fields

Year: 2010 Volume: 4 Issue: 7 1029 - 1036 Pages

Abstract: In this work, we study elliptic divisibility sequences over finite fields. Morgan Ward in [14], [15] gave arithmetic theory of elliptic divisibility sequences and formulas for elliptic divisibility sequences with rank two over finite field Fp. We study elliptic divisibility sequences with rank three, four and five over a finite field Fp, where p > 3 is a prime and give general terms of these sequences and then we determine elliptic and singular curves associated with these sequences.

A Completed Adaptive De-mixing Algorithm on Stiefel Manifold for ICA

Year: 2009 Volume: 3 Issue: 9 739 - 741 Pages

Authors:
Jianwei Wu

Abstract: Based on the one-bit-matching principle and by turning the de-mixing matrix into an orthogonal matrix via certain normalization, Ma et al proposed a one-bit-matching learning algorithm on the Stiefel manifold for independent component analysis [8]. But this algorithm is not adaptive. In this paper, an algorithm which can extract kurtosis and its sign of each independent source component directly from observation data is firstly introduced.With the algorithm , the one-bit-matching learning algorithm is revised, so that it can make the blind separation on the Stiefel manifold implemented completely in the adaptive mode in the framework of natural gradient.

Cubic Trigonometric B-Spline Applied to Linear Two-Point Boundary Value Problems of Order Two

Year: 2010 Volume: 4 Issue: 10 1376 - 1381 Pages

Abstract: Linear two-point boundary value problems of order two are solved using cubic trigonometric B-spline interpolation method (CTBIM). Cubic trigonometric B-spline is a piecewise function consisting of trigonometric equations. This method is tested on some problems and the results are compared with cubic B-spline interpolation method (CBIM) from the literature. CTBIM is found to approximate the solution slightly more accurately than CBIM if the problems are trigonometric.

Transient Currents in a Double Conductor Line above a Conducting Half-Space

Year: 2012 Volume: 6 Issue: 4 482 - 486 Pages

Abstract: Transient eddy current problem is solved in the present paper by the method of the Laplace transform for the case of a double conductor line located parallel to a conducting half-space. The Fourier sine and cosine integral transforms are used in order to find the Laplace transform of the solution. The inverse Laplace transform of the solution is found in closed form. The integrated electromotive force per unit length of the double conductor line is calculated in the form of an improper integral.

A Method of Planar-Template- Based Camera Self-Calibration for Single-View

Year: 2011 Volume: 5 Issue: 12 2105 - 2111 Pages

Authors:
Yue Zhao
Chao Li

Abstract: Camera calibration is an important step in 3D reconstruction. Camera calibration may be classified into two major types: traditional calibration and self-calibration. However, a calibration method in using a checkerboard is intermediate between traditional calibration and self-calibration. A self is proposed based on a square in this paper. Only a square in the planar template, the camera self-calibration can be completed through the single view. The proposed algorithm is that the virtual circle and straight line are established by a square on planar template, and circular points, vanishing points in straight lines and the relation between them are be used, in order to obtain the image of the absolute conic (IAC) and establish the camera intrinsic parameters. To make the calibration template is simpler, as compared with the Zhang Zhengyou-s method. Through real experiments and experiments, the experimental results show that this algorithm is feasible and available, and has a certain precision and robustness.

Graphs with Metric Dimension Two-A Characterization

Year: 2009 Volume: 3 Issue: 12 1132 - 1137 Pages

Abstract: In this paper, we define distance partition of vertex set of a graph G with reference to a vertex in it and with the help of the same, a graph with metric dimension two (i.e. β (G) = 2 ) is characterized. In the process, we develop a polynomial time algorithm that verifies if the metric dimension of a given graph G is two. The same algorithm explores all metric bases of graph G whenever β (G) = 2 . We also find a bound for cardinality of any distance partite set with reference to a given vertex, when ever β (G) = 2 . Also, in a graph G with β (G) = 2 , a bound for cardinality of any distance partite set as well as a bound for number of vertices in any sub graph H of G is obtained in terms of diam H .

The Buffer Gas Influence Rate on Absolute Cu Atoms Density with regard to Deposition

Year: 2011 Volume: 5 Issue: 2 190 - 192 Pages

Abstract: The absolute Cu atoms density in Cu(2S1/2ÔåÉ2P1/2) ground state has been measured by Resonance Optical Absorption (ROA) technique in a DC magnetron sputtering deposition with argon. We measured these densities under variety of operation conditions: pressure from 0.6 μbar to 14 μbar, input power from 10W to 200W and N2 mixture from 0% to 100%. For measuring the gas temperature, we used the simulation of N2 rotational spectra with a special computer code. The absolute number density of Cu atoms decreases with increasing the N2 percentage of buffer gas at any conditions of this work. But the deposition rate, is not decreased with the same manner. The deposition rate variation is very small and in the limit of quartz balance measuring equipment accuracy. So we conclude that decrease in the absolute number density of Cu atoms in magnetron plasma has not a big effect on deposition rate, because the diffusion of Cu atoms to the chamber volume and deviation of Cu atoms from direct path (towards the substrate) decreases with increasing of N2 percentage of buffer gas. This is because of the lower mass of N2 atoms compared to the argon ones.

Very-high-Precision Normalized Eigenfunctions for a Class of Schrödinger Type Equations

Year: 2011 Volume: 5 Issue: 4 682 - 687 Pages

Abstract: We demonstrate that it is possible to compute wave function normalization constants for a class of Schr¨odinger type equations by an algorithm which scales linearly (in the number of eigenfunction evaluations) with the desired precision P in decimals.

Bifurcation Analysis of a Delayed Predator-prey Fishery Model with Prey Reserve in Frequency Domain

Year: 2011 Volume: 5 Issue: 8 1410 - 1416 Pages

Authors:
Changjin Xu

Abstract: In this paper, applying frequency domain approach, a delayed predator-prey ﬁshery model with prey reserve is investigated. By choosing the delay τ as a bifurcation parameter, It is found that Hopf bifurcation occurs as the bifurcation parameter τ passes a sequence of critical values. That is, a family of periodic solutions bifurcate from the equilibrium when the bifurcation parameter exceeds a critical value. The length of delay which preserves the stability of the positive equilibrium is calculated. Some numerical simulations are included to justify the theoretical analysis results. Finally, main conclusions are given.

Traveling Wave Solutions for Shallow Water Wave Equation by (G'/G)-Expansion Method

Year: 2013 Volume: 7 Issue: 5 865 - 869 Pages

Abstract: This paper presents a new function expansion method for finding traveling wave solution of a non-linear equation and calls it the (G'/G)-expansion method. The shallow water wave equation is reduced to a non linear ordinary differential equation by using a simple transformation. As a result the traveling wave solutions of shallow water wave equation are expressed in three forms: hyperbolic solutions, trigonometric solutions and rational solutions.

Some Investigations on Higher Mathematics Scores for Chinese University Student

Year: 2009 Volume: 3 Issue: 7 535 - 538 Pages

Authors:
Xun Ge
Jingju Qian

Abstract: To investigate some relations between higher mathe¬matics scores in Chinese graduate student entrance examination and calculus (resp. linear algebra, probability statistics) scores in subject's completion examination of Chinese university, we select 20 students as a sample, take higher mathematics score as a decision attribute and take calculus score, linear algebra score, probability statistics score as condition attributes. In this paper, we are based on rough-set theory (Rough-set theory is a logic-mathematical method proposed by Z. Pawlak. In recent years, this theory has been widely implemented in the many fields of natural science and societal science.) to investigate importance of condition attributes with respective to decision attribute and strength of condition attributes supporting decision attribute. Results of this investigation will be helpful for university students to raise higher mathematics scores in Chinese graduate student entrance examination.

Fourth Order Accurate Free Convective Heat Transfer Solutions from a Circular Cylinder

Year: 2012 Volume: 6 Issue: 8 1184 - 1188 Pages

Abstract: Laminar natural-convective heat transfer from a horizontal cylinder is studied by solving the Navier-Stokes and energy equations using higher order compact scheme in cylindrical polar coordinates. Results are obtained for Rayleigh numbers of 1, 10, 100 and 1000 for a Prandtl number of 0.7. The local Nusselt number and mean Nusselt number are calculated and compared with available experimental and theoretical results. Streamlines, vorticity - lines and isotherms are plotted.

Existence of Solution of Nonlinear Second Order Neutral Stochastic Differential Inclusions with Infinite Delay

Year: 2014 Volume: 8 Issue: 8 1119 - 1125 Pages

Authors:
Yong Li

Abstract: The paper is concerned with the existence of solution of nonlinear second order neutral stochastic differential inclusions with infinite delay in a Hilbert Space. Sufficient conditions for the existence are obtained by using a fixed point theorem for condensing maps.

Keywords:
Mild solution
Convex multivalued map
Neutral stochastic differential inclusions.

Approximations to the Distribution of the Sample Correlation Coefficient

Year: 2011 Volume: 5 Issue: 4 676 - 681 Pages

Abstract: Given a bivariate normal sample of correlated variables, (Xi, Yi), i = 1, . . . , n, an alternative estimator of Pearson’s correlation coefficient is obtained in terms of the ranges, |Xi − Yi|. An approximate confidence interval for ρX,Y is then derived, and a simulation study reveals that the resulting coverage probabilities are in close agreement with the set confidence levels. As well, a new approximant is provided for the density function of R, the sample correlation coefficient. A mixture involving the proposed approximate density of R, denoted by hR(r), and a density function determined from a known approximation due to R. A. Fisher is shown to accurately approximate the distribution of R. Finally, nearly exact density approximants are obtained on adjusting hR(r) by a 7th degree polynomial.

Fuzzy Cost Support Vector Regression

Year: 2008 Volume: 2 Issue: 8 602 - 607 Pages

Abstract: In this paper, a new version of support vector regression (SVR) is presented namely Fuzzy Cost SVR (FCSVR). Individual property of the FCSVR is operation over fuzzy data whereas fuzzy cost (fuzzy margin and fuzzy penalty) are maximized. This idea admits to have uncertainty in the penalty and margin terms jointly. Robustness against noise is shown in the experimental results as a property of the proposed method and superiority relative conventional SVR.