Scholarly

Migration of a Drop in Simple Shear Flow at Finite Reynolds Numbers: Size and Viscosity Ratio Effects

Year: 2010 Volume: 4 Issue: 1 198 - 204 Pages

Abstract: The migration of a deformable drop in simple shear flow at finite Reynolds numbers is investigated numerically by solving the full Navier-Stokes equations using a finite difference/front tracking method. The objectives of this study are to examine the effectiveness of the present approach to predict the migration of a drop in a shear flow and to investigate the behavior of the drop migration with different drop sizes and non-unity viscosity ratios. It is shown that the drop deformation depends strongly on the capillary number, so that; the proper non-dimensional number for the interfacial tension is the capillary number. The rate of migration increased with increasing the drop radius. In other words, the required time for drop migration to the centreline decreases. As the viscosity ratio increases, the drop rotates more slowly and the lubrication force becomes stronger. The increased lubrication force makes it easier for the drop to migrate to the centre of the channel. The migration velocity of the drop vanishes as the drop reaches the centreline under viscosity ratio of one and non-unity viscosity ratios. To validate the present calculations, some typical results are compared with available experimental and theoretical data.

Numerical Investigation of Two-dimensional Boundary Layer Flow Over a Moving Surface

Year: 2010 Volume: 4 Issue: 1 195 - 197 Pages

Abstract: In this chapter, we have studied Variation of velocity in incompressible fluid over a moving surface. The boundary layer equations are on a fixed or continuously moving flat plate in the same or opposite direction to the free stream with suction and injection. The boundary layer equations are transferred from partial differential equations to ordinary differential equations. Numerical solutions are obtained by using Runge-Kutta and Shooting methods. We have found numerical solution to velocity and skin friction coefficient.

Bifurcation Analysis in a Two-neuron System with Different Time Delays

Year: 2010 Volume: 4 Issue: 1 187 - 194 Pages

Authors:
Changjin Xu

Abstract: In this paper, we consider a two-neuron system with time-delayed connections between neurons. By analyzing the associated characteristic transcendental equation, its linear stability is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulation results are given to support the theoretical predictions. Finally, main conclusions are given.

Global Exponential Stability of Impulsive BAM Fuzzy Cellular Neural Networks with Time Delays in the Leakage Terms

Year: 2010 Volume: 4 Issue: 1 179 - 186 Pages

Abstract: In this paper, a class of impulsive BAM fuzzy cellular neural networks with time delays in the leakage terms is formulated and investigated. By establishing a delay differential inequality and M-matrix theory, some sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive BAM fuzzy cellular neural networks with time delays in the leakage terms are obtained. In particular, a precise estimate of the exponential convergence rate is also provided, which depends on system parameters and impulsive perturbation intention. It is believed that these results are significant and useful for the design and applications of BAM fuzzy cellular neural networks. An example is given to show the effectiveness of the results obtained here.

Forecasting Malaria Cases in Bujumbura

Year: 2010 Volume: 4 Issue: 1 173 - 178 Pages

Abstract: The focus in this work is to assess which method allows a better forecasting of malaria cases in Bujumbura ( Burundi) when taking into account association between climatic factors and the disease. For the period 1996-2007, real monthly data on both malaria epidemiology and climate in Bujumbura are described and analyzed. We propose a hierarchical approach to achieve our objective. We first fit a Generalized Additive Model to malaria cases to obtain an accurate predictor, which is then used to predict future observations. Various well-known forecasting methods are compared leading to different results. Based on in-sample mean average percentage error (MAPE), the multiplicative exponential smoothing state space model with multiplicative error and seasonality performed better.

Existence and Stability of Anti-periodic Solutions for an Impulsive Cohen-Grossberg SICNNs on Time Scales

Year: 2010 Volume: 4 Issue: 1 166 - 172 Pages

Authors:
Meng Hu
Lili Wang

Abstract: By using the method of coincidence degree and constructing suitable Lyapunov functional, some sufficient conditions are established for the existence and global exponential stability of antiperiodic solutions for a kind of impulsive Cohen-Grossberg shunting inhibitory cellular neural networks (CGSICNNs) on time scales. An example is given to illustrate our results.

New Application of EHTA for the Generalized(2+1)-Dimensional Nonlinear Evolution Equations

Year: 2010 Volume: 4 Issue: 1 159 - 165 Pages

Abstract: In this paper, the generalized (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff (shortly CBS) equations are investigated. We employ the Hirota-s bilinear method to obtain the bilinear form of CBS equations. Then by the idea of extended homoclinic test approach (shortly EHTA), some exact soliton solutions including breather type solutions are presented.

Laser Excited Nuclear γ -Source of High Spectral Brightness

Year: 2010 Volume: 4 Issue: 1 152 - 158 Pages

Abstract: This paper considers various channels of gammaquantum generation via an ultra-short high-power laser pulse interaction with different targets.We analyse the possibilities to create a pulsed gamma-radiation source using laser triggering of some nuclear reactions and isomer targets. It is shown that sub-MeV monochromatic short pulse of gamma-radiation can be obtained with pulse energy of sub-mJ level from isomer target irradiated by intense laser pulse. For nuclear reaction channel in light- atom materials, it is shown that sub-PW laser pulse gives rise to formation about million gamma-photons of multi-MeV energy.

Existence and Globally Exponential Stability of Equilibrium for BAM Neural Networks with Mixed Delays and Impulses

Year: 2010 Volume: 4 Issue: 1 146 - 151 Pages

Abstract: In this paper, a class of generalized bi-directional associative memory (BAM) neural networks with mixed delays is investigated. On the basis of Lyapunov stability theory and contraction mapping theorem, some new sufficient conditions are established for the existence and uniqueness and globally exponential stability of equilibrium, which generalize and improve the previously known results. One example is given to show the feasibility and effectiveness of our results.

Structure of Covering-based Rough Sets

Year: 2010 Volume: 4 Issue: 1 142 - 145 Pages

Abstract: Rough set theory is a very effective tool to deal with granularity and vagueness in information systems. Covering-based rough set theory is an extension of classical rough set theory. In this paper, firstly we present the characteristics of the reducible element and the minimal description covering-based rough sets through downsets. Then we establish lattices and topological spaces in coveringbased rough sets through down-sets and up-sets. In this way, one can investigate covering-based rough sets from algebraic and topological points of view.

On the Prediction of Transmembrane Helical Segments in Membrane Proteins

Year: 2010 Volume: 4 Issue: 1 138 - 141 Pages

Authors:
Yu Bin
Zhang Yan

Abstract: The prediction of transmembrane helical segments (TMHs) in membrane proteins is an important field in the bioinformatics research. In this paper, a method based on discrete wavelet transform (DWT) has been developed to predict the number and location of TMHs in membrane proteins. PDB coded as 1F88 was chosen as an example to describe the prediction of the number and location of TMHs in membrane proteins by using this method. One group of test data sets that contain total 19 protein sequences was utilized to access the effect of this method. Compared with the prediction results of DAS, PRED-TMR2, SOSUI, HMMTOP2.0 and TMHMM2.0, the obtained results indicate that the presented method has higher prediction accuracy.

Improved Asymptotic Stability Analysis for Lure Systems with Neutral Type and Time-varying Delays

Year: 2010 Volume: 4 Issue: 1 131 - 137 Pages

Abstract: This paper investigates the problem of absolute stability and robust stability of a class of Lur-e systems with neutral type and time-varying delays. By using Lyapunov direct method and linear matrix inequality technique, new delay-dependent stability criteria are obtained and formulated in terms of linear matrix inequalities (LMIs) which are easy to check the stability of the considered systems. To obtain less conservative stability conditions, an operator is defined to construct the Lyapunov functional. Also, the free weighting matrices approach combining a matrix inequality technique is used to reduce the entailed conservativeness. Numerical examples are given to indicate significant improvements over some existing results.

Multiple Positive Periodic Solutions of a Competitor-Competitor-Mutualist Lotka-Volterra System with Harvesting Terms

Year: 2010 Volume: 4 Issue: 1 125 - 130 Pages

Abstract: In this paper, by using Mawhin-s continuation theorem of coincidence degree theory, we establish the existence of multiple positive periodic solutions of a competitor-competitor-mutualist Lotka-Volterra system with harvesting terms. Finally, an example is given to illustrate our results.

On the Prediction of Transmembrane Helical Segments in Membrane Proteins Based on Wavelet Transform

Year: 2010 Volume: 4 Issue: 1 119 - 124 Pages

Authors:
Yu Bin
Zhang Yan

Abstract: The prediction of transmembrane helical segments (TMHs) in membrane proteins is an important field in the bioinformatics research. In this paper, a new method based on discrete wavelet transform (DWT) has been developed to predict the number and location of TMHs in membrane proteins. PDB coded as 1KQG was chosen as an example to describe the prediction of the number and location of TMHs in membrane proteins by using this method. To access the effect of the method, 80 proteins with known 3D-structure from Mptopo database are chosen at random as the test objects (including 325 TMHs), 308 of which can be predicted accurately, the average predicted accuracy is 96.3%. In addition, the above 80 membrane proteins are divided into 13 groups according to their function and type. In particular, the results of the prediction of TMHs of the 13 groups are satisfying.

A New Direct Updating Method for Undamped Structural Systems

Year: 2010 Volume: 4 Issue: 1 113 - 118 Pages

Abstract: A new numerical method for simultaneously updating mass and stiffness matrices based on incomplete modal measured data is presented. By using the Kronecker product, all the variables that are to be modified can be found out and then can be updated directly. The optimal approximation mass matrix and stiffness matrix which satisfy the required eigenvalue equation and orthogonality condition are found under the Frobenius norm sense. The physical configuration of the analytical model is preserved and the updated model will exactly reproduce the modal measured data. The numerical example seems to indicate that the method is quite accurate and efficient.

Minimal Critical Sets of Inertias for Irreducible Zero-nonzero Patterns of Order 3

Year: 2010 Volume: 4 Issue: 1 110 - 112 Pages

Abstract: If there exists a nonempty, proper subset S of the set of all (n + 1)(n + 2)/2 inertias such that S Ôèå i(A) is sufficient for any n × n zero-nonzero pattern A to be inertially arbitrary, then S is called a critical set of inertias for zero-nonzero patterns of order n. If no proper subset of S is a critical set, then S is called a minimal critical set of inertias. In [3], Kim, Olesky and Driessche identified all minimal critical sets of inertias for 2 × 2 zero-nonzero patterns. Identifying all minimal critical sets of inertias for n × n zero-nonzero patterns with n ≥ 3 is posed as an open question in [3]. In this paper, all minimal critical sets of inertias for 3 × 3 zero-nonzero patterns are identified. It is shown that the sets {(0, 0, 3), (3, 0, 0)}, {(0, 0, 3), (0, 3, 0)}, {(0, 0, 3), (0, 1, 2)}, {(0, 0, 3), (1, 0, 2)}, {(0, 0, 3), (2, 0, 1)} and {(0, 0, 3), (0, 2, 1)} are the only minimal critical sets of inertias for 3 × 3 irreducible zerononzero patterns.

A Note on the Minimum Cardinality of Critical Sets of Inertias for Irreducible Zero-nonzero Patterns of Order 4

Year: 2010 Volume: 4 Issue: 1 107 - 109 Pages

Abstract: If there exists a nonempty, proper subset S of the set of all (n+1)(n+2)/2 inertias such that S Ôèå i(A) is sufficient for any n×n zero-nonzero pattern A to be inertially arbitrary, then S is called a critical set of inertias for zero-nonzero patterns of order n. If no proper subset of S is a critical set, then S is called a minimal critical set of inertias. In [Kim, Olesky and Driessche, Critical sets of inertias for matrix patterns, Linear and Multilinear Algebra, 57 (3) (2009) 293-306], identifying all minimal critical sets of inertias for n×n zero-nonzero patterns with n ≥ 3 and the minimum cardinality of such a set are posed as two open questions by Kim, Olesky and Driessche. In this note, the minimum cardinality of all critical sets of inertias for 4 × 4 irreducible zero-nonzero patterns is identified.

Oscillation Criteria for Nonlinear Second-order Damped Delay Dynamic Equations on Time Scales

Year: 2010 Volume: 4 Issue: 1 99 - 106 Pages

Abstract: In this paper, we establish several oscillation criteria for the nonlinear second-order damped delay dynamic equation r(t)|xΔ(t)|β-1xΔ(t)Δ + p(t)|xΔσ(t)|β-1xΔσ(t) + q(t)f(x(τ (t))) = 0 on an arbitrary time scale T, where β > 0 is a constant. Our results generalize and improve some known results in which β > 0 is a quotient of odd positive integers. Some examples are given to illustrate our main results.

Remarks on Some Properties of Decision Rules

Year: 2010 Volume: 4 Issue: 1 95 - 98 Pages

Abstract: This paper shows that some properties of the decision rules in the literature do not hold by presenting a counterexample. We give sufficient and necessary conditions under which these properties are valid. These results will be helpful when one tries to choose the right decision rules in the research of rough set theory.

The RK1GL2X3 Method for Initial Value Problems in Ordinary Differential Equations

Year: 2010 Volume: 4 Issue: 1 92 - 94 Pages

Authors:
J.S.C. Prentice

Abstract: The RK1GL2X3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on the RK1GL2 method which, in turn, is a particular case of the general RKrGLm method. The RK1GL2X3 method is a fourth-order method, even though its underlying Runge-Kutta method RK1 is the first-order Euler method, and hence, RK1GL2X3 is considerably more efficient than RK1. This enhancement is achieved through an implementation involving triple-nested two-point Gauss- Legendre quadrature.

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