bluuebunny/crossref_metadata_2025 huggingface dataset:
A comparison of two- and three-variable models for combustion in sealed containers
Authors: Trenham Claire E. , Forbes Larry K.
Published: February 2009

This paper analyses a model for combustion of a self-heating chemical (such as pool chlorine), stored in drums within a shipping container. The system is described by three coupled nonlinear differential equations for the concentration of the chemical, its temperature and the temperature within the shipping container. Self-sustained oscillations are found to occur, as a result of Hopf bifurcation. Temperature and concentration profiles are presented and compared with the predictions of a simpler two-variable approximation for the system. We study the period of oscillation and its variation with respect to the ambient temperature and the reaction parameter. Nonlinear resonances are found to exist, as the solution jumps between branches having different periods.
Robust guaranteed cost control for descriptor systems with Markov jumping parameters and state delays
Authors: Fu Yan-Ming , Wu Di , Duan Guang-Ren
Published: February 2009

This paper deals with robust guaranteed cost control for a class of linear uncertain descriptor systems with state delays and jumping parameters. The transition of the jumping parameters in the systems is governed by a finite-state Markov process. Based on stability theory for stochastic differential equations, a sufficient condition on the existence of robust guaranteed cost controllers is derived. In terms of the LMI (linear matrix inequality) approach, a linear state feedback controller is designed to stochastically stabilise the given system with a cost function constraint. A convex optimisation problem with LMI constraints is formulated to design the suboptimal guaranteed cost controller. A numerical example demonstrates the effect of the proposed design approach.
Multiple integration is intractable but not hopeless
Authors: Sloan Ian H.
Published: February 2009

Multiple integrals in ten or twenty variables are often needed by atomic, molecular and nuclear physicists, because of the large number of degrees of freedom in the quantum systems with which they must deal. In statistics too there is often a need to evaluate integrals with many degrees of freedom. It is in mathematical finance, however, that the most striking examples are seen, with claims of integrals being evaluated during recent years with many hundreds of variables.
Scoring with constraints
Authors: Osborne Michael R.
Published: February 2009

This paper considers the solution of estimation problems based on the maximum likelihood principle when a fixed number of equality constraints are imposed on the parameters of the problem. Consistency and the asymptotic distribution of the parameter estimates are discussed as n → ∞, where n is the number of independent observations, and it is shown that a suitably scaled limiting multiplier vector is known. It is also shown that when this information is available then the good properties of Fisher's method of scoring for the unconstrained case extend to a class of augmented Lagrangian methods for the constrained case. This point is illustrated by means of an example involving the estimation of a mixture density.
Solution of nonlinear equations and computation of multiple solutions of a simple reaction-diffusion equation
Authors: Swift Adrian , Balakrishnan Easwaran
Published: February 2009

The first part of this paper starts with a brief discussion of some methods for solution of nonlinear equations which have interested the first author over the last twenty years or so. In the second part we discuss a recent research involvement, the success of which relies heavily on the numerical solution of nonlinear equation systems. We briefly describe path-following methods and then present an application to a simple steady-state reaction-diffusion equation arising in combustion theory. Results for some regular geometric shapes are shown and compared with those from an approximate method.
Integral equation methods in inverse obstacle scattering
Authors: Kress Rainer
Published: February 2009

In this survey we consider a regularized Newton method for the approximate solution of the inverse problem to determine the shape of an obstacle from a knowledge of the far field pattern for the scattering of time-harmonic acoustic or electromagnetic plane waves. Our analysis is in two dimensions and the numerical scheme is based on the solution of boundary integral equations by a Nyström method. We include an example of the reconstruction of a planar domain with a corner both to illustrate the feasibility of the use of radial basis functions for the reconstruction of boundary curves with local features and to connect the presentation to some of the research work of Professor David Elliott.
The Lebesgue function for generalized Hermite-Fejér interpolation on the Chebyshev nodes
Authors: Byrne Graeme J. , Mills T. M. , Smith Simon J.
Published: February 2009

This paper presents a short survey of convergence results and properties of the Lebesgue function λm,n(x) for(0, 1, …, m)Hermite-Fejér interpolation based on the zeros of the nth Chebyshev polynomial of the first kind. The limiting behaviour as n → ∞ of the Lebesgue constant Λm,n = max{λm,n(x): −1 ≤ x ≤ 1} for even m is then studied, and new results are obtained for the asymptotic expansion of Λm,n. Finally, graphical evidence is provided of an interesting and unexpected pattern in the distribution of the local maximum values of λm,n(x) if m ≥ 2 is even.
Quadrature errors in finite element eigenvalue computations
Authors: Andrew Alan L.
Published: February 2009

Some recent results on the optimal choice of quadrature rules for the finite element solution of eigenvalue problems are discussed in the light of some results of the author and J. Paine.
Diagonal scaling of stiffness matrices in the Galerkin boundary element method
Authors: Ainsworth Mark , McLean Bill , Tran Thanh
Published: February 2009

A boundary integral equation of the first kind is discretised using Galerkin's method with piecewise-constant trial functions. We show how the condition number of the stiffness matrix depends on the number of degrees of freedom and on the global mesh ratio. We also show that diagonal scaling eliminates the latter dependence. Numerical experiments confirm the theory, and demonstrate that in practical computations involving strong local mesh refinement, diagonal scaling dramatically improves the conditioning of the Galerkin equations.
Uniform convergence of the collocation method for Prandtl's Integro-differential equation
Authors: Capobianco M. R. , Criscuolo G. , Junghanns P. , Luther U.
Published: February 2009

An integro-differential equation of Prandtl's type and a collocation method as well as a collocation-quadrature method for its approximate solution is studied in weighted spaces of continuous functions.
A brief survey of extrapolation quadrature
Authors: Lyness J. N.
Published: February 2009

This is a short précis of a presentation on some of the recent advances in the area of extrapolation quadrature; given at David Elliott's 65th birthday conference in Hobart in February 1997.
Accelerated spectral refinement Part II: Cluster of eigenvalues
Authors: Alam Rafikul , Kulkarni Rekha P. , Limaye Balmohan V.
Published: February 2009

The framework for accelerated spectral refinement for a simple eigenvalue developed in Part I of this paper is employed to treat the general case of a cluster of eigenvalues whose total algebraic multiplicity is finite. Numerical examples concerning the largest and the second largest multiple eigenvalues of an integral operator are given.
Lattice vibrations with Rayleigh dissipation
Authors: Boyd J. N. , Raychowdhury P. N.
Published: February 2009

We approximate a linear array of coupled harmonic oscillators as a symmetric circular array of identical masses and springs. The springs are taken to possess mass distributed along their lengths. We give a Lagrangian formulation of the problem of finding the natural frequencies of oscillation for the array. Damping terms are included by means of the Rayleigh dissipation function. A transformation to symmetry coordinates as determined by the group of rotations of the circle uncouples the equations of motion.
Some integral inequalities with bounds for moments of distribution II
Authors: Varošanec Sanja , Pečarić Josip
Published: February 2009

Several generalizations are given of the Gauss-Winckler inequality for the moments of a probability distribution.
On the solution of the problem of scattering of surface water waves by a sharp discontinuity in the surface boundary conditions
Authors: Chakrabarti A.
Published: February 2009

Closed-form analytical expressions are derived for the reflection and transmission coefficients for the problem of scattering of surface water waves by a sharp discontinuity in the surface-boundary-conditions, for the case of deep water. The method involves the use of the Havelock-type expansion of the velocity potential along with an analysis to solve a Carleman-type singular integral equation over a semi-infinite range. This method of solution is an alternative to the Wiener-Hopf technique used previously.
On the solution of a class of second-order quasi-linear PDEs and the Gauss equation
Authors: Selvaratnam A. R. , Vlieg-Hulstman M. , van-Brunt B. , Halford W. D.
Published: February 2009

Gauss' Theorema Egregium produces a partial differential equation which relates the Gaussian curvature K to components of the metric tensor and its derivatives. Well-known partial differential equations (PDEs) such as the Schrödinger equation and the sine-Gordon equation can be derived from Gauss' equation for specific choices of K and coördinate systems. In this paper we consider a class of Bäcklund Transformations which corresponds to coördinate transformations on surfaces with a given Gaussian curvature. These Bäcklund Transformations lead to the construction of solutions to certain classes of non-linear second order PDEs of hyperbolic type by identifying these PDEs as the Gauss equation in some coördinate system. The possibility of solving the Cauchy Problem has also been explored for these classes of equations.
Smoothly attaching bow flows with constant vorticity
Authors: McCue S. W. , Forbes L. K.
Published: February 2009

The free surface flow of a finite depth fluid past a semi-infinite body is considered. The fluid is assumed to have constant vorticity throughout and the free surface is assumed to attach smoothly to the front face of the body. Numerical solutions are found using a boundary integral method in the physical plane and it is shown that solutions exist for all supercritical Froude numbers. The related problem of the cusp-like flow due to a submerged sink in a comer is also considered. Vorticity is included in the flow and it is shown that the behaviour of the solutions is qualitatively the same as that found in the problem described above.
Equilibrium with fixed budgets and superlinear connections
Authors: Rubinov A. M. , Glover B. M.
Published: February 2009

We study models of economic equilibrium with fixed budgets and assuming superlinear connections between consumption and production. Extremal problems and the existence of equilibria are discussed for such models along with some related differential properties. Examples to illustrate the broad nature of the model are discussed.
Early quasi-steady electro-magnetic fields about conducting surfaces
Authors: Weir Graham J.
Published: February 2009

Step changes in current through either grounded or ungrounded wires lying on the surface of a uniformly conducting half-space produce image current sources within the surface the conductor. This image current is effectively the only source term for initial changes in ∂1Bz, Ex and Ey. The general steady state electric and magnetic field components resulting from steady currents flowing through either grounded or ungrounded wires of finite length lying on the surface of a uniform half- space are derived. Then the operators mapping these steady fields into the early values of ∂tBz, Ex and Ey on or above the conducting half-plane resulting from instantaneously stopping the current flow through the wires are derived.
On monotonicity and superadditivity properties of the entropy function
Authors: Dragomir S. S. , Goh C. J.
Published: February 2009

We apply superadditivity and monotonicity properties associated with the Jensen discrete inequality to derive relationships between the entropy function of a probability vector and a renormalized arbitrary sub-vector. The results are extended to cover other entropy measures such as joint entropy, conditional entropy and mutual information.
Optimal control for quasilinear retarded parabolic systems
Authors: Pan Liping , Yong Jiongmin
Published: February 2009

We study an optimal control problem for a quasilinear parabolic equation which has delays in the highest order spatial derivative terms. The cost functional is Lagrange type and some terminal state constraints are presented. A Pontryagin-type maximum principle is derived.
Comparison and linearized oscillation theorems for a nonlinear partial difference equation
Authors: Zhang B. G. , Yu Jian-She
Published: February 2009

Connections between a linear partial difference equation with constant coefficients and a nonlinear partial difference equation are established by means of a comparison theorem and a continuous dependence of parameters theorem. A linearized oscillation theorem is also established as an application.
Determining rotational deformity in broken forearms
Authors: Stokes Y. M.
Published: February 2009

To assess rotational deformity in a broken forearm, an orthopaedic surgeon needs to determine the amount of rotation of the radius from one or more two-dimensional x-rays of the fracture. This requires only simple first-year university mathematics — rotational transformations of ellipses plus a little differential calculus — which yields a general formula giving the rotation angle from information obtained from an x-ray. Preliminary comparisons with experimental results are excellent. This is a practical problem that may be useful to motivate the teaching of conic sections.
Global attractivity of the periodic Kolmogorov system
Authors: Wen Xianzhang , Wang Zhicheng
Published: February 2009

We study a periodic Kolmogorov model with m predators and n prey. By means of the comparison theorem and a Liapunov function, a set of easily verifiable sufficient conditions that guarantee the existence, uniqueness and global attractivity of the positive periodic solution is obtained. Finally, some suitable applications are given to illustrate that the conditions of the main theorem are feasible.
A variation-of-constants formula for a linear abstract evolution equation in Hilbert space
Authors: Wu Hanzhong
Published: February 2009

A variation-of-constants formula is obtained for a linear abstract evolution equation in Hilbert space with unbounded perturbation and free term. As an application, the state of the abstract controlled system with unbounded mixed controls is explicitly given.
Examples of the nonexistence of a solution in the presence of upper and lower solutions
Authors: Habets Patrick , Pouso Rodrigo L.
Published: February 2009

Standard results for boundary value problems involving second-order ordinary differential equations ensure that the existence of a well-ordered pair of lower and upper solutions together with a Nagumo condition imply existence of a solution. In this note we introduce some examples which show that existence is not guaranteed if no Nagumo condition is satisfied.
A new trust region method for nonsmooth equations
Authors: Yang Y. F.
Published: February 2009

We propose a new trust region algorithm for solving the system of nonsmooth equations F(x) = 0 by using a smooth function satisfying the Jacobian consistency property to approximate the nonsmooth function F(x). Compared with existing trust region methods for systems of nonsmooth equations, the proposed algorithm possesses some nice convergence properties. Global convergence is established and, in particular, locally superlinear or quadratical convergence is obtained if F is semismooth or strongly semismooth at the solution.
Inequalities for the beta function of n variables
Authors: Alzer Horst
Published: February 2009

We present various inequalities for Euler's beta function of n variables. One of our theorems states that the inequalities

hold for all xi ≥ (i = 1,… n; n ≥ 3) with the best possible constants an = 0 and bn = 1 − 1/(n − 1)!. This extends a recently published result of Dragomir et al., who investigated (*) for the special case n = 2.
A flat ship theory on bow and stern flows
Authors: Zhu Songping , Zhang Yinglong
Published: February 2009

An analytical solution of a two-dimensional bow and stern flow model based on a flat ship theory is presented for the first time. The flat ship theory is a counterpart to Michell's thin ship theory and leads to a mixed initial-boundary value problem, which is usually difficult to solve analytically. Starting from the transient problem, we shall first show that a steady state is attainable at the large time limit. Then the steady problem is solved in detail by means of the Wiener-Hopf technique and closed-form far-field results are obtained for an arbitrary hull shape. Apart from providing a better understanding of the underlying physics, the newly found analytical solution has shed some light on solving a longtime outstanding problem in the engineering practice of ship building, the optimisation of hull shape.
Traces of localisation operators with two admissible wavelets
Authors: Wong M. W. , Zhang Zhaohui
Published: February 2009

The resolution of the identity formula for a localisation operator with two admissible wavelets on a separable and complex Hilbert space is given and the traces of these operators are computed.
Derivation of the probability density function for ultimate muscle pH in slaughtered animals
Authors: Pleasants A. B. , Wake G. C. , Daly C. C.
Published: February 2009

We consider the form of the probability density function for the ultimate muscle pH in slaughtered animals. Muscle pH in slaughtered animals is dependent on a biochemical process which forms lactic acid from the breakdown of glycogen stored in the muscle at slaughter. The relationship between glycogen and muscle pH after slaughter is expressed as a pair of coupled differential equations. The solution of this system for the equilibrium muscle pH as time → ∞ gives the form of the probability density for the ultimate muscle pH. When the initial density for the muscle glycogen is normal, the density for the ultimate muscle pH is shown to be approximately a mixed normal density.
Numerical algorithms for constrained maximum likelihood estimation
Authors: Li Z. F. , Osborne M. R. , Prvan T.
Published: February 2009

This paper describes a SQP-type algorithm for solving a constrained maximum likelihood estimation problem that incorporates a number of novel features. We call it MLESOL. MLESOL maintains the use of an estimate of the Fisher information matrix to the Hessian of the negative log-likelihood but also encompasses a secant approximation S to the second-order part of the augmented Lagrangian function along with tests for when to use this information. The local quadratic model used has a form something like that of Tapia's SQP augmented scale BFGS secant method but explores the additional structure of the objective function. The step choice algorithm is based on minimising a local quadratic model subject to the linearised constraints and an elliptical trust region centred at the current approximate minimiser. This is accomplished using the Byrd and Omojokun trust region approach, together with a special module for assessing the quality of the step thus computed. The numerical performance of MLESOL is studied by means of an example involving the estimation of a mixture density.
Existence of optimal controls for semilinear elliptic equations without Cesari-type conditions
Authors: Lou Hongwei
Published: February 2009

Optimal control problems governed by semilinear elliptic partial differential equations are considered. No Cesari-type conditions are assumed. By proving an existence theorem and the Pontryagin maximum principle of optimal “state-control” pairs for the corresponding relaxed problems, we establish an existence theorem of optimal pairs for the original problem.
A two-sided iterative method for computing positive definite solutions of a nonlinear matrix equation
Authors: El-Sayed Salah M.
Published: February 2009

In several recent papers, a one-sided iterative process for computing positive definite solutions of the nonlinear matrix equationX+A*X−1A=Q, whereQis positive definite, has been studied. In this paper, a two-sided iterative process for the same equation is investigated. The novel idea here is that the two sequences obtained by starting at two different values provide (a) an interval in which the solution is located, that is,Xk≤X≤Ykfor allkand (b) a better stopping criterion. Some properties of solutions are discussed. Sufficient solvability conditions on a matrixAare derived. Moreover, when the matrixAis normal and satisfies an additional condition, the matrix equation has smallest and largest positive definite solutions. Finally, some numerical examples are given to illustrate the effectiveness of the algorithm.
The solution and the stability of a nonlinear age-structured population model
Authors: Norhayati  , Wake G. C.
Published: February 2009

We consider an age-structured population model achieved by modifying the classical Sharpe-Lotka-McKendrick model, incorporating an overcrowding effect or competition for resources term. This term depends on the whole population rather than on any specific age group, in the case of overcrowding or limitation of resources. We investigate the solutions for arbitrary initial conditions. We consider the existence of a steady age distribution and its stability and are able to determine this for a simple illustrative case. If the non-trivial steady age distribution is unstable, there is a critical initial population size beyond which the population explodes. This watershed is independent of the shape of the initial age distribution.
Singular problems modelling phenomena in the theory of pseudoplastic fluids
Authors: Agarwal Ravi P. , O'Regan Donal
Published: February 2009

Existence criteria are presented for nonlinear singular initial and boundary value problems. In particular our theory includes a problem arising in the theory of pseudoplastic fluids.
On the influence of wall properties in the peristaltic motion of micropolar fluid
Authors: Muthu P. , Rathish Kumar B. V. , Chandra Peeyush
Published: February 2009

We carry out a study of the peristaltic motion of an incompressible micropolar fluid in a two-dimensional channel. The effects of viscoelastic wall properties and micropolar fluid parameters on the flow are investigated using the equations of the fluid as well as of the deformable boundaries. A perturbation technique is used to determine flow characteristics. The velocity profile is presented and discussed briefly. We find the critical values of the parameters involving wall characteristics, which cause mean flow reversal.
An analysis of a fractal kinetics curve of Savageau
Authors: Maloney John , Heidel Jack
Published: February 2009

The fractal kinetics curve derived by Savageau is analysed to show that its parameters are not uniquely determined given four appropriately situated data points. Comparison is made with an alternate fractal Michaelis-Menten equation derived by Lopez-Quintela and Casado.
A unified presentation of generalised Voigt functions
Authors: Kamarujjama M.
Published: February 2009

Voigt functions occur frequently in a wide variety of problems in several diverse fields of physics. This paper presents a unified study of generalised Voigt functions. In particular, some expansions of unified Voigt functions are given in terms of the original functions. Some deductions from these representations are obtained which give us an opportunity to underline the special rôle of the associated generating functions.
Decomposition method for solving a nonlinear business cycle model
Authors: Deeba Elias , Dibeh Ghassan , Khuri Suheil , Xie Shishen
Published: February 2009

In this paper we present a Kaleckian-type model of a business cycle based on a nonlinear delay differential equation. A numerical algorithm based on a decomposition scheme is implemented for the approximate solution of the model. The numerical results of the underlying equation show that the business cycle is stable.
Some remarks on a Neumann boundary value problem arising in fluid dynamics
Authors: Torres Pedro J.
Published: February 2009

It is proved that the Neumann boundary value problem, which Mays and Norbury have recently connected with a certain fluid dynamics equation, has a positive solution for any positive value of a particular parameter. Uniform bounds for the solutions and symmetry on a given range of the parameter are also introduced. The proofs include Krasnoselskii's classical fixed-point theorem on cones of a Banach space and basic comparison techniques.
Rumours with general initial conditions
Authors: Belen Selma , Pearce C. E. M.
Published: February 2009

An analysis is made of the Daley-Kendall and Maki-Thompson rumour models starting from general initial proportions of ignorants, spreaders and stiflers in the population. We investigate as a function of the initial conditions the composition of the final population when the rumour has run its course.
Harvesting in a two-prey one-predator fishery: a bioeconomic model
Authors: Kar T. K. , Chaudhuri K. S.
Published: February 2009

A multispecies harvesting model with interference is proposed. The model is based on Lotka-Volterra dynamics with two competing species which are affected not only by harvesting but also by the presence of a predator, the third species. In order to understand the dynamics of this complicated system, we choose to model the simplest possible predator response function in which the feeding rate of the predator increases linearly with prey density. We derive the conditions for global stability of the system using a Lyapunov function. The possibility of existence of a bioeconomic equilibrium is discussed. The optimal harvest policy is studied and the solution is derived in the equilibrium case using Pontryagin's maximal principle. Finally, some numerical examples are discussed.
A probabilistic algorithm for finding the rate matrix of a block-GI/M/1 Markov chain
Authors: Hunt Emma
Published: February 2009

An efficient probabilistic algorithm is presented for the determination of the rate matrix of a block-GI/M/1 Markov chain. Recurrence of the chain is not assumed.
Performance of various BFGS implementations with limited precision second-order information
Authors: Byatt D. , Coope I. D. , Price C. J.
Published: February 2009

The BFGS formula is arguably the most well known and widely used update method for quasi-Newton algorithms. Some authors have claimed that updating approximate Hessian information via the BFGS formula with a Cholesky factorisation offers greater numerical stability than the more straightforward approach of performing the update directly. Other authors have claimed that no such advantage exists and that any such improvement is probably due to early implementations of the DFP formula in conjunction with low accuracy line searches.

This paper supports the claim that there is no discernible advantage in choosing factorised implementations (over non-factorised implementations) of BFGS methods when approximate Hessian information is available to full machine precision. However the results presented in this paper show that a factorisation strategy has clear advantages when approximate Hessian information is available only to limited precision. These results show that a conjugate directions factorisation outperforms the other methods considered in this paper (including Cholesky factorisation).
Efficiency and generalised convexity in vector optimisation problems
Authors: Sach Pham Huu , Lee Gue Myung , Kim Do Sang
Published: February 2009

This paper gives a necessary and sufficient condition for a Kuhn-Tucker point of a non-smooth vector optimisation problem subject to inequality and equality constraints to be an efficient solution. The main tool we use is an alternative theorem which is quite different to a corresponding result by Xu.
Oscillation of first-order delay differential equations
Authors: Zhao Aimin , Tang Xianhua , Yan Jurang
Published: February 2009

This paper is concerned with the oscillation of first-order delay differential equations

wherep(t) and τ(t) are piecewise continuous and nonnegative functions and τ(t) is non-decreasing. A new oscillation criterion is obtained.
Oscillation of symplectic dynamic systems
Authors: Bohner Martin , Došlý Ondřej
Published: February 2009

We investigate oscillatory properties of a perturbed symplectic dynamic system on a time scale that is unbounded above. The unperturbed system is supposed to be nonoscillatory, and we give conditions on the perturbation matrix, which guarantee that the perturbed system becomes oscillatory. Examples illustrating the general results are given as well.
Existence of solutions of third-order functional problems with nonlinear boundary conditions
Authors: Cabada Alberto , Heikkilä Seppo
Published: February 2009

In this paper some existence results for third-order differential equations with nonlinear boundary value conditions are derived. Functional dependence in the data is allowed. In the proofs we use the method of upper and lower solutions, Schauder's fixed point theorem and results from Cabada and Heikkilä on third-order differential equations with linear and nonfunctional initial-boundary value conditions.
E. R. Love's integral equation for the circular plate condenser
Authors: Reich Edgar
Published: February 2009

In a classical paper, E. R. Love considered a certain function defined by a singular integral which is harmonic outside a circular disk. Love's objective was to derive a simple integral equation whose solution leads to a useful formula for the capacitance of the condenser consisting of two parallel circular plates. We close a gap in Love's derivation by finding a new nonsingular representation of Love's singular integral which permits one to draw the required conclusions about its boundary values and thereby establishes the correctness of Love's expression for the capacitance.
On existence, uniqueness and Lr-exponential stability for stationary solutions to the MHD equations in three-dimensional domains
Authors: Zhao Chunshan , Li Kaitai
Published: February 2009

The existence of stationary solutions to the MHD equations in three-dimensional bounded domains will be proved. At the same time if the assumption of smallness is made on external forces, uniqueness of the stationary solutions can be guaranteed and it can be shown that any Lr (r > 3) global bounded non-stationary solution to the MHD equations approaches the stationary solution under both L2 and Lr norms exponentially as time goes to infinity.
A note on the extension of a family of biorthogonal Coifman wavelet systems
Authors: Jiang Zhuhan , Guo Xiling
Published: February 2009

Wavelet systems with a maximum number of balanced vanishing moments are known to be extremely useful in a variety of applications such as image and video compression. Tian and Wells recently created a family of such wavelet systems, called the biorthogonal Coifman wavelets, which have proved valuable in both mathematics and applications. The purpose of this work is to establish along with direct proofs a very neat extension of Tian and Wells' family of biorthogonal Coifman wavelets by recovering other “missing” members of the biorthogonal Coifman wavelet systems.
Persistence and global stability in a delayed predator-prey system with Holling-type functional response
Authors: Xu Rui , Chen Lansun , Chaplain M. A. J.
Published: February 2009

A delayed predator-prey system with Holling type III functional response is investigated. It is proved that the system is uniformly persistent under some appropriate conditions. By means of suitable Lyapunov functionals, sufficient conditions are derived for the local and global asymptotic stability of a positive equilibrium of the system. Numerical simulations are presented to illustrate the feasibility of our main results.
Effects of velocity-slip and viscosity variation on journal bearings
Authors: Rao R. Raghavendra , Prasad K. R.
Published: February 2009

A generalised form of the Reynolds equation for two symmetrical surfaces is derived by considering slip at the bearing surfaces. This equation is then used to study the effects of velocity-slip for the lubrication of journal bearings using half-Sommerfeld boundary conditions. Expressions for pressure and load capacity and the coefficient of friction are obtained and numerically analysed for various parameters. It is found that the load capacity decreases with slip. This is unfavourable for lubrication. The coefficient of friction decreases with a high viscous layer and increases with slip.
A fast algorithm for constructing orthogonal multiwavelets
Authors: Shouzhi Yang
Published: February 2009

Multiwavelets possess some nice features that uniwavelets do not. A consequence of this is that multiwavelets provide interesting applications in signal processing as well as in other fields. As is well known, there are perfect construction formulas for the orthogonal uniwavelet. However, a good formula with a similar structure for multiwavelets does not exist. In particular, there are no effective methods for the construction of multiwavelets with a dilation factor a (a ≥ 2, a ∈ Z). In this paper, a procedure for constructing compactly supported orthonormal multiscaling functions is first given. Based on the constructed multiscaling functions, we then propose a method of constructing multiwavelets, which is similar to that for constructing uniwavelets. In addition, a fast numerical algorithm for computing multiwavelets is given. Compared with traditional approaches, the algorithm is not only faster, but also computationally more efficient. In particular, the function values of several points are obtained simultaneously by using our algorithm once. Finally, we give three examples illustrating how to use our method to construct multiwavelets.
Solving rank one revised linear systems by the scaled ABS method
Authors: Amini Keyvan
Published: February 2009

In mathematical programming, an important tool is the use of active set strategies to update the current solution of a linear system after a rank one change in the constraint matrix. We show how to update the general solution of a linear system obtained by use of the scaled ABS method when the matrix coefficient is subjected to a rank one change.
Rolling of a rigid ball on a horizontal deformable surface
Authors: Brearley Maurice N. , De Mestre Neville J.
Published: February 2009

The rolling of a ball on a horizontal deformable surface was investigated under the assumptions that the ball was a rigid sphere and the surface was elastic. Finite strain theory was used to develop theoretical results which were found to match observations well in cases where the ball and surface involved were such as to ensure no slipping at the region of contact, including a lawn bowl rolling on a grass rink and a billiard ball rolling on carpet. The theory did not match well the behaviour of a golf ball on a grass green because the ball was too light to enforce the no-slipping condition.
Independent non-identical five-parameter gamma-Weibull variates and their sums
Authors: Leipnik Roy B. , Pearce Charles E. M.
Published: February 2009

Gamma-Weibull variates with five parameters are defined by multiplication of gamma and Weibull densities and renormalising. Sums of independent such variates are distributed as combinations of products of gammas and confluent hypergeometric functions and are explicitly determined. Sums of independent non-identical Weibulls arise as a special case. These variates can be used to model moderately extreme scenarios between gamma and Weibull that occur in many natural applications. All results are exact.
Nonnegative solutions for a heterogeneous degenerate competition model
Authors: Suárez Antonio
Published: February 2009

This paper deals with the existence, uniqueness and qualitative properties of nonnegative and nontrivial solutions of a spatially heterogeneous Lotka-Volterra competition model with nonlinear diffusion. We give conditions in terms of the coefficients involved in the setting of the problem which assure the existence of nonnegative solutions as well as the uniqueness of a positive solution. In order to obtain these results we employ monotonicity methods, singular spectral theory and a fixed point index.
A bioeconomic model of nonselective harvesting of two competing fish species
Authors: Purohit D. , Chaudhuri K. S.
Published: February 2009

This paper deals with the combined bioeconomic harvesting of two competing fish species, each of which obeys the Gompertz law of growth. The catch-rate functions are chosen so as to reflect saturation effects with respect to stock abundance as well as harvesting effort. The stability of the dynamical system is discussed and the existence of a bionomic equilibrium is examined. The optimal harvest policy is studied with the help of Pontryagin's maimum principle. The results are illustrated with the help of a numerical example.
A note on withdrawal from a fluid of finite depth through a point sink
Authors: Hocking G. C. , Vanden-Broeck J.-M. , Forbes L. K.
Published: February 2009

The problem of withdrawal through a point sink of water from a fluid of finite depth with a free surface is considered. Assuming the flow to be axisymmetric, it is found that there is a maximum Froude number at which such flows can exist. This maximum corresponds to the formation of a secondary stagnation ring on the free surface. This result extends earlier work on this problem. Comparison is made with a small Froude number solution and past experimental results.
Newton's diagram method for nonlinear equations with several small parameters
Authors: Aizengendler Peter
Published: February 2009

In this article, we generalise Newton's diagram method for finding small solutions ξ(λ) of equations f (ξ,λ) = 0 (0,0) = 0 with f analytic (see [1, 2, 4, 6]) to the case of a multi-dimensional function f, unknown variable ζ and small parameter λ. This method was briefly described in [1]. The method has many different applications and allows one to solve some inflexible problems. In particular, the method can be used in very difficult bifurcation problems, for example, for systems with small imperfections.
Extreme stability and almost periodicity in continuous and discrete neuronal models with finite delays
Authors: Mohamad S. , Gopalsamy K.
Published: February 2009

We consider the dynamical characteristics of a continuous-time isolated Hopfield-type neuron subjected to an almost periodic external stimulus. The model neuron is assumed to be dissipative having finite time delays in the process of encoding the external input stimulus and recalling the encoded pattern associated with the external stimulus. By using non-autonomous Halanay-type inequalities we obtain sufficient conditions for the hetero-associative stable encoding of temporally non-uniform stimuli. A brief study of a discrete-time model derived from the continuous-time system is given. It is shown that the discrete-time model preserves the stability conditions of the continuous-time system.
Some results on generalised voigt functions
Authors: Gupta K. C. , Goyal S. P. , Mukherjee Rohit
Published: February 2009

Recently, Srivastava, Pathan and Kamarujjama established several results for generalised Voigt functions which play an important role in several diverse fields of physics—such as astrophysical spectroscopy and the theory of neutron reactions. In the present paper we aim to generalise some partly bilateral and partly unilateral representations and generating functions of Srivastava et al. by considering a specialised version of the Srivastava-Chen definition of the unified Voigt functions. Several special cases of our main results are mentioned briefly.
The dual reciprocity boundary element method for magnetohydrodynamic channel flows
Authors: Liu Huan-Wen , Zhu Song-Ping
Published: February 2009

In this paper, we consider the problem of the steady-state fully developed magnetohydrodynamic (MHD) flow of a conducting fluid through a channel with arbitrary wall conductivity in the presence of a transverse external magnetic field with various inclined angles. The coupled governing equations for both axial velocity and induced magnetic field are firstly transformed into decoupled Poisson-type equations with coupled boundary conditions. Then the dual reciprocity boundary element method (DRBEM) [20] is used to solve the Poisson-type equations. As testing examples, flows in channels of three different crosssections, rectangular, circular and triangular, are calculated. It is shown that solutions obtained by the DRBEM with constant elements are accurate for Hartmann number up to 8 and for large conductivity parameters comparing to exact solutions and solutions by the finite element method (FEM).
Vaskuläre Risikofaktoren beim Glaukom – Diagnostik
Authors: Gugleta
Published: February 2009

Der Hauptrisikofaktor für das Glaukom ist der erhöhte Augendruck, dessen pharmakologische und/oder chirurgische Reduktion zu einer erheblichen Verlangsamung der Krankheitsprogression führt. Allerdings wird die Krankheitsentwicklung nicht aufgehalten, eine Tatsache die auf die Beteiligung anderer Risikofaktoren hinweist. Zahlreiche Studien belegen eine Assoziation zwischen den vaskulären Riskofaktoren und dem Glaukomschaden. Zu nennen sind hier insbesondere ein erniedrigter okulärer Perfusionsdruck, vor allem nächtliche arterielle Hypotonien und eine vaskuläre Dysregulation mit vasospastischer Tendenz. Kombiniert mit dem inadäquaten Augendruck führen diese Faktoren zu schwankenden Perfusionsverhältnissen im Sehnervenkopf und zu einem durch den oxidativen Stress bedingten Reperfusionsschaden. Dieser manifestiert sich durch den Verlust der Axone und durch den Gewebeumbau der Papille (Exkavationszunahme). Die Erfassung des vaskulären Risikoprofils ist deshalb entscheidend für eine individuell angepasste Therapie.
Therapie der Colitis ulcerosa
Authors: Vavricka  , Rogler
Published: February 2009

Die Therapie der Colitis ulcerosa richtet sich nach der Krankheitsaktivität vergleichbar mit dem Morbus Crohn aber auch nach der Ausdehnung der Erkrankung. Unterschiedliche Therapiekonzepte kommen dabei zur Anwendung je nachdem ob die Colitis ulcerosa in Form einer Proktitis, einer linksseitigen Kolitis, einer Pankolitis oder einem fulminanten Schub auftritt und ob es sich um eine chronisch aktive Kolitis oder eine Remissionserhaltung handelt. Die folgende Übersicht soll die wichtigsten Konzepte kurz vorstellen.
Proactive Coping, Positive Affect, and Well-Being
Authors: Greenglass Esther R. , Fiksenbaum Lisa
Published: February 2009

Traditionally, psychological research has focused on negative states, their determinants, and consequences. Theoretical conceptions of coping focus on strategies used to diminish distress. This approach is derived from the perspective that coping is mainly reactive, a strategy used once stress has been experienced. In contrast, proactive coping involves goal setting, having efficacious beliefs, and is associated with resources for self-improvement, including social support. In the present research, a theoretical model was developed in which coping and social support were seen in a synergistic relationship and were associated with a positive state that, in turn, was expected to relate to better psychological functioning. The general theoretical model was tested in three different samples: First year university students coping with depression (n = 68), rehabilitation patients mastering independent functioning following major surgery (n = 151), and employee absenteeism (n = 313). Results of path analyses showed that proactive coping was a partial mediator of social support on positive affect and that positive affect was associated with better psychological functioning. In students only, positive affect mediated the relationship between proactive coping and depression. This research represents a contribution within the field of positive psychology by empirically demonstrating how positive constructs contribute to improved psychological functioning. Theoretical and applied implications of the results are discussed.
Transmission of Depressive Symptoms
Authors: Knoll Nina , Schwarzer Ralf , Pfüller Bettina , Kienle Rolf
Published: February 2009

Transmission of depressive symptoms among spouses is well documented. In accordance with the transactional stress model, cognitive appraisals were tested as indirect effects in transmission. In 82 couples (age range women: 23–44, men: 26–55), both partners stress appraisals and depressive symptoms were assessed at three measurement points throughout assisted-reproduction treatment. Relations among partners variables were tested using the actor-partner interdependence model. Findings indicated positive transmission effects of depressive symptoms from men to women across both measurement intervals. A positive transmission effect of stress appraisals from men to women was observed from before until after the pregnancy test. Womens stress appraisals mediated part of the transmission of depressive symptoms from men to women. Mens stress appraisals, however, were unrelated to womens earlier depressive symptoms. Mens earlier depressive symptoms might have operated as cues for womens adjustment of their own stress appraisals, which then predicted womens increased depressive symptoms. Using the transactional model as a framework for the study of emotional transmission may help to gain a better understanding of its underlying mechanisms and possible gender or role effects involved.
Who Watches Verbally Aggressive Shows?
Authors: Banerjee Smita C. , Greene Kathryn , Krcmar Marina , Bagdasarov Zhanna
Published: February 2009

A television-use questionnaire was completed by undergraduate college students (N = 773). Based on results from the television-use survey, respondents’ popular television programs (33 shows) were content-analyzed for amounts of verbal aggression. A measure called the Verbal Aggression Television Consumption Index (VATCI) was calculated for each individual by combining the results of the content analysis with participants’ reported viewing levels. We examined the effects of various personality factors on the VATCI (both overall and by genre). Additionally, the relationship between the VATCI and risk behaviors was evaluated. Both sensation seeking and viewer aggression positively predicted overall VATCI and, in particular, VATCI for animated sitcoms and political satires. Overall VATCI was positively associated with risky driving, fighting, delinquency, alcohol drinking, and drug use. Implications of findings are discussed.
Suboptimal Affective Primes in Video Messages
Authors: Kivikangas Markus J. , Ravaja Niklas
Published: February 2009

The authors examined the effects of suboptimally presented primes (facial expressions) embedded into video messages on self-reported positive activation (PA) and negative activation (NA). The results showed that joyful facial primes elicited increased PA only for positively valenced messages, whereas angry facial primes prompted increased NA (fear) only for negatively valenced messages. In addition, high-arousal facial primes prompted increased PA only for high-arousal messages. Both joyful and angry facial primes may influence affective responses when the prime and message content are affectively congruent and when affective responses are measured in terms of PA and NA. When ethical issues are appropriately taken into account, suboptimal affective priming might provide a method to increase the effectiveness of different types of media messages.