bluuebunny/crossref_metadata_2025_split huggingface dataset:
Approximate Hessian matrices and second-order optimality conditions for nonlinear programming problems with C1-data
Authors: Jeyakumar V. , Wang X. 
Published: February 2009

AbstractIn this paper, we present generalizations of the Jacobian matrix and the Hessian matrix to continuous maps and continuously differentiable functions respectively. We then establish second-order optimality conditions for mathematical programming problems with continuously differentiable functions. The results also sharpen the corresponding results for problems involving C1.1-functions.
Reductions and exact solutions of some nonlinear partial differential equations under four types of generalized conditional symmetries
Authors: Qu Changzheng 
Published: February 2009

AbstractThe generalized conditional symmetry method is applied to study the reduction to finite-dimensional dynamical systems and construction of exact solutions for certain types of nonlinear partial differential equations which have many physically significant applications in physics and related sciences. The exact solutions of the resulting equations are derived via the compatibility of the generalized conditional symmetries and the considered equations, which reduces to solving some systems of ordinary differential equations. For some unsolvable systems of ordinary differential equations, the dynamical behavior and qualitative properties are also considered. To illustrate that the approach has wide application, the exact solutions of a number of nonlinear partial differential equations are also given. The method used in this paper also provides a symmetry group interpretation to some known results in the literature which cannot be obtained by the nonclassical symmetry method due to Bluman and Cole.
When can sigmoidal data be fit to a Hill curve?
Authors: Heidel Jack , Maloney John 
Published: February 2009

AbstractThe Hill equation is a fundamental expression in chemical i kinetics relating velocity of response to concentration. It is known that the Hill equation is parameter identifiable in the sense that perfect data yield a unique set of defining parameters. However not all sigmoidal curves can be well fit by Hill curves. In particular the lower part of the curve can't be too shallow and the upper part can't be too steep. In this paper an exact mathematical criterion is derived to describe the degree of shallowness allowed.
Existence of solutions of a class of stochastic Volterra integral equations with applications to chemotherapy
Authors: Subramaniam R. , Balachandran K. 
Published: February 2009

AbstractIn this paper we establish the existence of solutions of a more general class of stochastic integral equation of Volterra type. The main tools used here are the measure of noncompactness and the fixed point theorem of Darbo. The results generalize the results of Tsokos and Padgett [9] and Szynal and Wedrychowicz [7]. An application to a stochastic model arising in chemotherapy is discussed.
Extending the utility of perturbation series in problems of laminar flow in a porous pipe and a diverging channel
Authors: Makinde O. D. 
Published: February 2009

AbstractIn this paper, we exploit a new series summation and convergence improvement technique (that is, Drazin and Tourigny [5]), in order to study the steady flow of a viscous incompressible fluid both in a porous pipe with moving walls and an exponentially diverging asymmetrical channel. The solutions are expanded into Taylor series with respect to the corresponding Reynolds number. Using the D-T method, the bifurcation and the internal flow separation studies are performed.
A numerical solution to the flow between eccentric rotating cylinders with a slotted sleeve
Authors: Hird L. D. , Siew P. F. , Wang S. 
Published: February 2009

AbstractThe flow between two eccentric rotating cylinders with a slotted sleeve placed around the inner cylinder is determined numerically using an exponentially fitted finite-volume method. The flow field is determined for various Reynolds numbers, eccentricities and rotational speeds for the cases when the cylinders rotate in the same sense and rotate in opposite senses. The flow field developed when both cylinders rotate in the same sense is characterised, for sufficiently large eccentricity and rotational rate, by two counter-rotating eddies. Only one eddy is observed when the cylinders rotate in opposite senses. The presence of these eddies restricts the flow through the slotted sleeve in the former case but encourages through flow in the latter. For both cases, the eccentricity affects the location of the eddies, while changing the relative rotational rate only affects the eddy location for the case when the cylinders rotate in opposite directions. The change in Reynolds number has little effect on the flow field for the problems considered here. The vorticity generated by the slotted sleeve is convected into the main body of the flow field. No inviscid core within the main body of the flow field is observed for the range of Reynolds number considered.
Apparent horizons in vacuum Robinson-Trautman spacetimes
Authors: Chow E. W. M. , Lun A. W.-C. 
Published: February 2009

AbstractVacuum asymptotically flat Robinson-Trautman spacetimes are a well known class of spacetimes exhibiting outgoing gravitational radiation. In this paper we describe a method of locating the past apparent horizon in these spacetimes and discuss the properties of the horizon. We show that the past apparent horizon is non-timelike and that its surface area is a decreasing function of the retarded time. A numerical simulation of the apparent horizon is also discussed.
Numerical integration of the axisymmetric Robinson-Trautman equation by a spectral method
Authors: Prager D. A. , Lun A. W.-C. 
Published: February 2009

AbstractWe have adapted the Spectral Transform Method, a technique commonly used in non-linear meteorological problems, to the numerical integration of the Robinson-Trautman equation. This approach eliminates difficulties due to the S2 × R+ topology of the equation. The method is highly accurate for smooth data and is numerically robust. Under spectral decomposition the long-time equilibrium state takes a particularly simple form: all nonlinear (l ≥ 2) modes tend to zero. We discuss the interaction and eventual decay of these higher order modes, as well as the evolution of the Bondi mass and other derived quantities. A qualitative comparison between the Spectral Transform Method and two finite difference schemes is given.
Instantaneous point source solutions in nonlinear diffusion with nonlinear loss or gain
Authors: Philip J. R. 
Published: February 2009

AbstractExact solutions are developed for instantaneous point sources subject to nonlinear diffusion and loss or gain proportional to nth power of concentration, with n > 1. The solutions for the loss give, at large times, power-law decrease to zero of slug central concentration and logarithmic increase of slug semi-width. Those for gain give concentration decreasing initially, going through a minimum, and then increasing, with blow-up to infinite concentration in finite time. Slug semi-width increases with time to a finite maximum in finite time at a blow-up. Taken in conjunction with previous studies, these new results provide an overall schema for instantaneous nonlinear diffusion point sources with nonlinear loss or gain for the total range n ≥ 0. Six distinct regimes of behaviour of slug semi-width and concentration are identified, depending on the range of n, 0 ≤ n < 1, n = 1, or n > 1. Three of them are for loss, and three for gain. The classical Barenblatt-Pattle nonlinear instantaneous point-source solutions with material concentration occupy a central place in the total schema.
Final iterations in interior point methods – preconditioned conjugate gradients and modified search directions
Authors: Wang Weichung 
Published: February 2009

AbstractIn this article we consider modified search directions in the endgame of interior point methods for linear programming. In this stage, the normal equations determining the search directions become ill-conditioned. The modified search directions are computed by solving perturbed systems in which the systems may be solved efficiently by the preconditioned conjugate gradient solver. A variation of Cholesky factorization is presented for computing a better preconditioner when the normal equations are ill-conditioned. These ideas have been implemented successfully and the numerical results show that the algorithms enhance the performance of the preconditioned conjugate gradients-based interior point methods.
Averaging of the Hamilton-Jacobi equation in infinite dimensions and an application
Authors: Wang Shihong , Zhou Zuoyi 
Published: February 2009

AbstractWe study the averaging of the Hamilton-Jacobi equation with fast variables in the viscosity solution sense in infinite dimensions. We prove that the viscosity solution of the original equation converges to the viscosity solution of the averaged equation and apply this result to the limit problem of the value function for an optimal control problem with fast variables.
Quasistationarity of continuous-time Markov chains with positive drift
Authors: Coolen-Schrijner Pauline , Hart Andrew , Pollett Phil 
Published: February 2009

AbstractWe shall study continuous-time Markov chains on the nonnegative integers which are both irreducible and transient, and which exhibit discernible stationarity before drift to infinity “sets in”. We will show how this ‘quasi’ stationary behaviour can be modelled using a limiting conditional distribution: specifically, the limiting state probabilities conditional on not having left 0 for the last time. By way of adualchain, obtained by killing the original process on last exit from 0, we invoke the theory of quasistationarity forabsorbingMarkov chains. We prove that the conditioned state probabilities of the original chain are equal to the state probabilities of its dual conditioned on non-absorption, thus allowing to establish the simultaneous existence and then equivalence, of their limiting conditional distributions. Although a limiting conditional distribution for the dual chain is always quasistationary distribution in the usual sense, a similar statement is not possible for the original chain.
Analysis and optimisation of looped water distribution networks
Authors: Young Brian 
Published: February 2009

AbstractA three stage procedure for the analysis and least-cost design of looped water distribution networks is considered in this paper. The first stage detects spanning trees and identifies the true global optimum for the system. The second stage determines hydraulically feasible pipe flows for the network by the numerical solution of a set of non-linear simultaneous equations and shows that these solutions are contained within closed convex polygonal regions in the solution space bounded by singularities resulting from zero flows in individual pipes. Ideal pipe diameters, consistent with the pipe flows and the constant velocity constraint adopted to prevent the system degenerating into a branched network, are selected and costed. It is found that the most favourable optimum is in the vicinity of a vertex in the solution space corresponding to the minimum spanning tree. In the third stage, commercial pipes are specified and the design finalised. Upper bound formulae for the number of spanning trees and hydraulically feasible solutions in a network have also been proposed. The treatment of large networks by a heuristic procedure is described which is shown to result in significant economies compared with designs obtained by non-linear programming.
Analytical and numerical results for flow and shock formation in two-layer gravity currents
Authors: Montgomery P. J. , Moodie T. B. 
Published: February 2009

AbstractMany gravity driven flows can be modelled as homogeneous layers of inviscid fluid with a hydrostatic pressure distribution. There are examples throughout oceanography, meteorology, and many engineering applications, yet there are areas which require further investigation. Analytical and numerical results for two-layer shallow-water formulations of time dependent gravity currents travelling in one spatial dimension are presented. Model equations for three physical limits are developed from the hydraulic equations, and numerical solutions are produced using a relaxation scheme for conservation laws developed recently by S. Jin and X. Zin [6]. Hyperbolicity of the model equations is examined in conjunction with the stability Froude number, and shock formation at the interface of the two layers is investigated using the theory of weakly nonlinear hyperbolic waves.
Jensen's inequality for distributions possessing higher moments, with application to sharp bounds for Laplace-Stieltjes transforms
Authors: Guljaš B. , Pearce C. E. M. , Pečarić J. 
Published: February 2009

AbstractA new version of Jensen's inequality is established for probability distributions on the non-negative real numbers which are characterized by moments higher than the first. We deduce some new sharp bounds for Laplace-Stieltjes transforms of such distribution functions.
An analysis of local energy and phase congruency models in visual feature detection
Authors: Aw Y. K. , Owens Robyn , Ross John 
Published: February 2009

AbstractA variety of approaches have been developed for the detection of features such as edges, lines, and corners in images. Many techniques presuppose the feature type, such as a step edge, and use the differential properties of the luminance function to detect the location of such features. The local energy model provides an alternative approach, detecting a variety of feature types in a single pass by analysing order in the phase components of the Fourier transform of the image. The local energy model is usually implemented by calculating the envelope of the analytic signal associated with the image function. Here we analyse the accuracy of such an implementation, and show that in certain cases the feature location is only approximately given by the local energy model. Orientation selectivity is another aspect of the local energy model, and we show that a feature is only correctly located at a peak of the local energy function when local energy has a zero gradient in two orthogonal directions at the peak point.
Strongly nonlinear vortices in magnetized ferrofluids
Authors: Russell Craig L. , Blennerhassett P.J. , Stiles P.J. 
Published: February 2009

AbstractNonlinear convective roll cells that develop in thin layers of magnetized ferrofluids heated from above are examined in the limit as the wavenumber of the cells becomes large. Weakly nonlinear solutions of the governing equations are extended to solutions that are valid at larger distances above the curves of marginal stability. In this region, a vortex flow develops where the fundamental vortex terms and the correction to the mean are determined simultaneously rather than sequentially. The solution is further extended into the nonlinear region of parameter space where the flow has a core-boundary layer structure characterized by a simple solution in the core and a boundary layer containing all the harmonics of the vortex motion. Numerical solutions of the boundary layer equations are presented and it is shown that the heat transfer across the layer is significantly greater than in the conduction state.
The effect of randomness on the stability of deep water surface gravity waves in the presence of a thin thermocline
Authors: Bhattacharyya Sudebi , Das K. P. 
Published: February 2009

AbstractThe effect of randomness on the stability of deep water surface gravity waves in the presence of a thin thermocline is studied. A previously derived fourth order nonlinear evolution equation is used to find a spectral transport equation for a narrow band of surface gravity wave trains. This equation is used to study the stability of an initially homogeneous Lorentz shape of spectrum to small long wave-length perturbations for a range of spectral widths. The growth rate of the instability is found to decrease with the increase of spectral widths. It is found that the fourth order term in the evolution equation produces a decrease in the growth rate of the instability. There is stability if the spectral width exceeds a certain critical value. For a vanishing bandwidth the deterministic growth rate of the instability is recovered. Graphs have been plotted showing the variations of the growth rate of the instability against the wavenumber of the perturbation for some different values of spectral width, thermocline depth, angle of perturbation and wave steepness.
On the Mellin transform of a product of hypergeometric functions
Authors: Miller Allen R. , Srivastava H. M. 
Published: February 2009

AbstractWe obtain representations for the Mellin transform of the product of generalized hypergeometric functions0F1[−a2x2]1F2[−b2x2]fora, b > 0. The later transform is a generalization of the discontinuous integral of Weber and Schafheitlin; in addition to reducing to other known integrals (for example, integrals involving products of powers, Bessel and Lommel functions), it contains numerous integrals of interest that are not readily available in the mathematical literature. As a by-product of the present investigation, we deduce the second fundamental relation for3F2[1]. Furthermore, we give the sine and cosine transforms of1F2[−b2x2].
Large deviations and quasi-stationarity for density-dependent birth-death processes
Authors: Chan Terence 
Published: February 2009

AbstractConsider a density-dependent birth-death process XN on a finite state space of size N. Let PN be the law (on D([0, T]) where T > 0 is arbitrary) of the density process XN/N and let πN be the unique stationary distribution (on[0,1]) of XN/N, if it exists. Typically, these distributions converge weakly to a degenerate distribution as N → ∞ so the probability of sets not containing the degenerate point will tend to 0; large deviations is concerned with obtaining the exponential decay rate of these probabilities. Friedlin-Wentzel theory is used to establish the large deviations behaviour (as N → ∞) of PN. In the one-dimensional case, a large deviations principle for the stationary distribution πN is obtained by elementary explicit computations. However, when the birth-death process has an absorbing state at 0 (so πN no longer exists), the same elementary computations are still applicable to the quasi-stationary distribution, and we show that the quasi-stationary distributions obey the same large deviations principle as in the recurrent case. In addition, we address some questions related to the estimated time to absorption and obtain a large deviations principle for the invariant distribution in higher dimensions by studying a quasi-potential.
Fractional convolution
Authors: Mustard David 
Published: February 2009

AbstractA continuous one-parameter set of binary operators on L2(R) called fractional convolution operators and which includes those of multiplication and convolution as particular cases is constructed by means of the Condon-Bargmann fractional Fourier transform. A fractional convolution theorem generalizes the standard Fourier convolution theorems and a fractional unit distribution generalizes the unit and delta distributions. Some explicit double-integral formulas for the fractional convolution between two functions are given and the induced operation between their corresponding Wigner distributions is found.
Computing optimal control With a hyperbolic partial differential equation
Authors: Rehbock V. , Wang S. , Teo K.L. 
Published: February 2009

AbstractWe present a method for solving a class of optimal control problems involving hyperbolic partial differential equations. A numerical integration method for the solution of a general linear second-order hyperbolic partial differential equation representing the type of dynamics under consideration is given. The method, based on the piecewise bilinear finite element approximation on a rectangular mesh, is explicit. The optimal control problem is thus discretized and reduced to an ordinary optimization problem. Fast automatic differentiation is applied to calculate the exact gradient of the discretized problem so that existing optimization algorithms may be applied. Various types of constraints may be imposed on the problem. A practical application arising from the process of gas absorption is solved using the proposed method.
Effect of a community-based intervention on nutritional behaviour in a developing country setting: the Isfahan Healthy Heart Programme
Authors: Mohammadifard Noushin , Kelishadi Roya , Safavi Morteza , Sarrafzadegan Nizal , Sajadi Firoozeh , Sadri Gholam Hosein , Maghroon Maryam , Alikhasi Hasan , Heydari Said , Sarmadi Fereshteh 
Published: February 2009

AbstractObjectiveThe present study was conducted to determine the impact of a community-based intervention on the nutritional behaviour of a representative sample of Iranian adults.DesignThe Isfahan Healthy Heart Programme (IHHP), a six-year, action-oriented, integrated community-based study aimed at health promotion through the reduction of CVD risk factors, targeted the whole population living in two intervention cities, and compared outcomes with the population of a non-intervention city considered as reference. Dietary interventions were performed as educational, environmental and/or legislative strategies. A global dietary index (GDI) was calculated representing the general dietary behaviour. In addition, two consumption indices were calculated for specific food groups, i.e. meat products and major sources of fat. Univariate AVOVA was conducted to evaluate the impact of the intervention on dietary behaviours.SettingIsfahan and Najaf-Abad (intervention cities) and Arak (reference city), central Iran.SubjectsThe baseline survey was conducted among 12514 randomly selected adults aged ≥19 years in both intervention and reference areas. The survey was repeated annually among about 5000 persons (2002–2005) in the intervention and reference communities.ResultsAccording to significant year × group interactions in mean fat consumption index (FCI) and meat consumption index (MCI) in the total population, a significant improvement in FCI and MCI was found in the intervention areasv. the reference area (P< 0·001). In addition, the GDI improved significantly in the intervention areasv. the reference area (P< 0·001).ConclusionsThe IHHP interventions were effective in improving dietary behaviours at the population level. The highest effectiveness was documented in the change in the type of fat consumed. Such simple and integrated interventions can be adopted in other developing countries with limited financial resources.
The Pinochet Cases in the United Kingdom
Authors: Warbrick Colin , Salgado Elena Martin , Goodwin Nicholas 
Published: February 2009

The activities of the regime of General, then President, Pinochet after his military coup in Chile in September 1973 are politically, legally and, one might almost say, popularly, one of the landmarks in the development of the international regime of human rights. Pinochet, then Commander of the Armed Forces, led a coup against President Allende, which resulted in a Military Junta seizing power on 11 September 1973. Pinochet became President of Chile in 1974 and remained in that position until 11 March 1990, when democracy was restored. He continued on as Commander of the Armed Forces until March 1998, when he was made Senator for Life.The legal significance of the reaction to events following the coup lies in the response of the United Nations to the excesses of the Pinochet government. The condemnation of Chile by the General Assembly for its policy of gross violations of human rights was the first occasion on which the Assembly had taken this step without invoking either a threat to the peace or a consideration of self-determination.