bluuebunny/crossref_metadata_2025_split huggingface dataset:
Towards numerically estimating Hausdorff dimensions
Authors: Stewart David E. 
Published: February 2009

AbstractThis paper gives a numerical method for estimating the Hausdorff-Besicovitch dimension where this differs from the fractal (or capacity or box-counting) dimension. The method has been implemented, and numerical results obtained for the set {1/n | n ∈ N} and the Cantor set. Comments about the practical use of the estimation algorithms are made.
On a periodic mutualism model
Authors: Li Yongkun 
Published: February 2009

AbstractSufficient conditions are obtained for the existence of a globally attracting positive periodic solution of the mutualism modelwhere ri, Ki, αi ∈ C(R, R+) and αi > Ki, i = 1, 2, τi, σi ∈ C(R, R+), i = 1, 2, and ri, Ki, αi, τi, σi (i = 1, 2) and functions of period ω > 0.
An optimal linear filter for random signals with realisations in a separable Hilbert space
Authors: Howlett P. G. , Pearce C. E. M. , Torokhti A. P. 
Published: February 2009

AbstractLet u be a random signal with realisations in an infinite-dimensional vector space X and υ an associated observable random signal with realisations in a finite-dimensional subspace Y ⊆ X. We seek a pointwise-best estimate of u using a bounded linear filter on the observed data vector υ. When x is a finite-dimensional Euclidean space and the covariance matrix for υ is nonsingular, it is known that the best estimate û of u is given by a standard matrix expression prescribing a linear mean-square filter. For the infinite-dimensional Hilbert space problem we show that the matrix expression must be replaced by an analogous but more general expression using bounded linear operators. The extension procedure depends directly on the theory of the Bochner integral and on the construction of appropriate HilbertSchmidt operators. An extended example is given.
Seasonality and critical community size for infectious diseases
Authors: Cullen R. M. , Korobeinikov A. , Walker W. J. 
Published: February 2009

AbstractThe endemicity of infectious diseases is investigated from a deterministic viewpoint. Sustained oscillation of infectives is often due to seasonal effects which may be related to climatic changes. For example the transmission of the measles virus by droplets is enhanced in cooler, more humid seasons. In many countries the onset of cooler, more humid weather coincides with the increased aggregation of people and the seasonal effect can be exacerbated. In this paper we consider non-autonomous compartmental epidemiological models and demonstrate that the critical community size phenomenon may be associated with the seasonal variation in the disease propagation. This approach is applicable to both the prevaccination phenomenon of critical community size and the current goal of worldwide elimination of measles by vaccination.
Minimax control of an elliptic variational bilateral problem
Authors: Chen Qihong 
Published: February 2009

AbstractThis paper deals with a minimax control problem for semilinear elliptic variational inequalities associated with bilateral constraints. The control domain is not necessarily convex. The cost functional, which is to be minimised, is the sup norm of some function of the state and the control. The major novelty of such a problem lies in the simultaneous presence of the nonsmooth state equation (variational inequality) and the nonsmooth cost functional (the sup norm). In this paper, the existence conditions and the Pontryagin-type necessary conditions for optimal controls are established.
Sequential eigenfunction expansion for a problem in combustion theory
Authors: Al-Refai M. , Tam K. K. 
Published: February 2009

AbstractA method of sequential eigenfunction expansion is developed for a semi-linear parabolic equation. It allows the time-dependent coefficients of the eigenfunctions to be determined sequentially and iterated to reach convergence. At any stage, only a single ordinary differential equation needs to be considered, in contrast to the Galerkin method which requires the consideration of a system of equations. The method is applied to a central problemin combustion theory to provide a definitive answer to the question of the influence of the initial data in determining whether the solution is sub- or super-critical, in the case of multiple steady-state solutions. It is expected this method will prove useful in dealing with similar problems.
A notion of local proper efficiency in the Borwein sense in vector optimisation
Authors: Jiménez B. , Novo V. 
Published: February 2009

AbstractIn this paper we define two types of proper efficient solutions in the Borwein sense for vector optimisation problems and we compare them with the notions of local Borwein, Ishizuka-Tuan, Kuhn-Tucker and strict efficiency. A sufficient condition for a proper solution is also proved.
Natural cubic element formulation and infinite domain modelling for potential flow problems
Authors: Mohr G. A. , Power A. S. 
Published: February 2009

AbstractA simple formulation of a 9 df cubic Hermitian finite element for potential flow problems is given, using the interpolation of the BCIZ element and after Argyris, defining natural velocities parallel to the element sides. Consistent loads for body forces are also derived and it is shown that these are necessary to obtain accurate results when body forces are significant. Example problems include those of infinite domains for which simpleconditions at infinityare used.
An epidemic model for the transmission dynamics of HIV and another pathogen
Authors: Moghadas S. M. , Gumel A. B. 
Published: February 2009

AbstractA five-dimensional deterministic model is proposed for the dynamics between HIV and another pathogen within a given population. The model exhibits four equilibria: a disease-free equilibrium, an HIV-free equilibrium, a pathogen-free equilibrium and a co-existence equilibrium. The existence and stability of these equilibria are investigated. A competitive finite-difference method is constructed for the solution of the non-linear model. The model predicts the optimal therapy level needed to eradicate both diseases.
Degree reduction of Béezier curves using constrained Chebyshev polynomials of the second kind
Authors: Ahn Young Joon 
Published: February 2009

AbstractIn this paper a constrained Chebyshev polynomial of the second kind with C1-continuity is proposed as an error function for degree reduction of Bézier curves with a C1-constraint at both endpoints. A sharp upper bound of the L∞ norm for a constrained Chebyshev polynomial of the second kind with C1-continuity can be obtained explicitly along with its coefficients, while those of the constrained Chebyshev polynomial which provides the best C1-constrained degree reduction are obtained numerically. The representations in closed form for the coefficients and the error bound are very useful to the users of Computer Graphics or CAD/CAM systems. Using the error bound in the closed form, a simple subdivision scheme for C1-constrained degree reduction within a given tolerance is presented. As an illustration, our method is applied to C1-constrained degree reduction of a plane Bézier curve, and the numerical result is compared visually to that of the best degree reduction method.
The dimension of attractors of nonautonomous partial differential equations
Authors: Caraballo T. , Langa J. A. , Valero J. 
Published: February 2009

AbstractThe concept of nonautonomous (or cocycle) attractors has become a proper tool for the study of the asymptotic behaviour of general nonautonomous partial differential equations. This is a time-dependent family of compact sets, invariant for the associated process and attracting “from –∞”. In general, the concept is rather different to the classical global attractor for autonomous dynamical systems. We prove a general result on the finite fractal dimensionality of each compact set of this family. In this way, we generalise some previous results of Chepyzhov and Vishik. Our results are also applied to differential equations with a nonlinear term having polynomial growth at most.
Bifurcation phenomena for an oxidation reaction in a continuously stirred tank reactor. II Diabatic operation
Authors: Nelson M. I. , Sidhu H. S. 
Published: February 2009

AbstractWe extend an investigation into the bifurcation phenomena exhibited by an oxidation reaction in an adiabatic reactor to the case of a diabatic reactor. The primary bifurcation parameter is the fuel fraction; the inflow pressure and inflow temperature are the secondary bifurcation parameters. The inclusion of heat loss in the model does not change the static steady-state bifurcation diagram; the organising centre is a pitchfork singularity for both the adiabatic and diabatic reactors. However, unlike the adiabatic reactor, Hopf bifurcations may occur in the diabatic reactor. We construct the degenerate Hopf bifurcation curve by determining the double-Hopf locus. When the steady-state and degenerate Hopf bifurcation diagrams are combined it is found that there are 23 generic steady-state diagrams over the parameter region of interest. The implications of these structures from the perspective of flammability in the CSTR are discussed.
Conservation laws for second-order parabolic partial differential equations
Authors: Van Brunt B. , Pidgeon D. , Vlieg-Hulstman M. , Halford W. D. 
Published: February 2009

AbstractConservation laws for partial differential equations can be characterised by an operator, the characteristic and a condition involving the adjoint of the Fréchet derivatives of this operator and the operator defining the partial differential equation. This approach was developed by Anco and Bluman and we exploit it to derive conditions for second-order parabolic partial differential equations to admit conservation laws. We show that such partial differential equations admit conservation laws only if the time derivative appears in one of two ways. The adjoint condition, however, is a biconditional, and we use this to prove necessary and sufficient conditions for a certain class of partial differential equations to admit a conservation law.
An investigation into the effects of heat transfer on the motion of a spherical bubble
Authors: Harris P. J. , Al-Awadi H. , Soh W. K. 
Published: February 2009

AbstractThis paper investigates the effect of heat transfer on the motion of a spherical bubble in the vicinity of a rigid boundary. The effects of heat transfer between the bubble and the surrounding fluid, and the resulting loss of energy from the bubble, can be incorporated into the simple spherical bubble model with the addition of a single extra ordinary differential equation. The numerical results show that for a bubble close to an infiniterigid boundary there are significant differences in both the radius and Kelvin impulse of the bubble when the heat transfer effects are included.
The limiting ideal theory for shear-index cohesionless granular materials
Authors: Cox G. M. , Hill J. M. 
Published: February 2009

AbstractTo model cohesionless granular flow using continuum theory, the usual approach is to assume the cohesionless Coulomb-Mohr yield condition. However, this yield condition assumes that the angle of internal friction is constant, when according to experimental evidence for most powders the angle of internal friction is not constant along the yield locus, but decreases for decreasing normal stress component σ from a maximum value of π/2. For this reason, we consider here the more general yield function which applies for shear-index granular materials, where the angle of internal friction varies with σ. In this case, failure due to frictional slip between particles occurs when the shear and normal components of stress τ and σ satisfy the so-called Warren Spring equation (|τ|/c)n = 1 − (σ/t), where c, t and n are positive constants which are referred to as the cohesion, tensile strength and shear-index respectively, and experimental evidence indicates for many materials that the value of the shear-index n lies between 1 and 2. For many materials, the cohesion is close to zero and therefore the notion of a cohesionless shear-index granular material arises. For such materials, a continuum theory applying for shear-index cohesionless granular materials is physically plausible as a limiting ideal theory, and any analytical solutions might provide important benchmarks for numerical schemes. Here, we examine the cohesionless shearindex theory for the problem of gravity flow of granular materials through two-dimensional wedge-shaped hoppers, and we attempt to determine analytical solutions. Although some analytical solutions are found, these do not correspond to the actual hopper problem, but may serve as benchmarks for purely numerical schemes. The special analytical solutions obtained are illustrated graphically, assuming only a symmetrical stress distribution.
Maximising output from oil reservoirs without water breakthrough
Authors: Lucas S. K. 
Published: February 2009

AbstractOften in oil reservoirs a layer of water lies under the layer of oil. The suction pressure due to a distribution of oil wells will cause the oil-water interface to rise up towards the wells. Given a particular distribution of oil wells, we are interested in finding the flow rates of each well that maximise the total flow rate without the interface breaking through to the wells. A method for finding optimal flow rates is developed using the Muskat model to approximate the interface height, and a version of the Nelder-Mead simplex method for optimisation. A variety of results are presented, including the perhaps nonintuitive result that it is better to turn off some oil wells when they are sufficiently close to one another.
Memory, market stability and the nonlinear cobweb theorem
Authors: Gaffney J. M. , Pearce C. E. M. 
Published: February 2009

AbstractCarlson has shown that if the predicted price in the linear cobweb model is taken as the average of all previous actual prices, then stability results independently of parameter values provided only that the demand–curve gradient is less than that of the supply curve. This result has subsequently been generalised by Manning and by Holmes and Manning. We investigate the robustness of their results.
Non-adiabatic combustion waves for general Lewis numbers: wave speed and extinction conditions
Authors: McIntosh A. C. , Weber R. O. , Mercer G. N. 
Published: February 2009

AbstractThis paper addresses the effect of general Lewis number and heat losses on the calculation of combustion wave speeds using an asymptotic technique based on the ratio of activation energy to heat release being considered large. As heat loss is increased twin flame speeds emerge (as in the classical large activation energy analysis) with an extinction heat loss. Formulae for the non-adiabatic wave speed and extinction heat loss are found which apply over a wider range of activation energies (because of the nature of the asymptotics) and these are explored for moderate and large Lewis number cases—the latter representing the combustion wave progress in a solid. Some of the oscillatory instabilities are investigated numerically for the case of a reactive solid.
An affine scaling interior point backtracking algorithm for nonlinear constrained optimisation
Authors: Zhu Detong 
Published: February 2009

AbstractIn this paper we propose a new affine scaling interior trust region algorithm with a nonmonotonic backtracking technique for nonlinear equality constrained optimisation with nonnegative constraints on the variables. In order to deal with large problems, the general full trust region subproblem is decomposed into a pair of trust region subproblems in horizontal and vertical subspaces. The horizontal trust region subproblem in the algorithm is defined by minimising a quadratic function subject only to an ellipsoidal constraint in a null tangential subspace and the vertical trust region subproblem is defined by the least squares subproblem subject only to an ellipsoidal constraint. By adopting Fletcher's penalty function as the merit function, combining a trust region strategy and a nonmonotone line search, the mixing technique will switch to a backtracking step generated by the two trust region subproblems to obtain an acceptable step. The global convergence of the proposed algorithm is proved while maintaining a fast local superlinear convergence rate, which is established under some reasonable conditions. A nonmonotonic criterion is used to speed up the convergence progress in some highly nonlinear cases.
Singular perturbation methods for a class of initial and boundary value problems in multi-parameter classical digital control systems
Authors: Krishnarayalu M. S. 
Published: February 2009

AbstractA stable linear time-invariant classical digital control system with several widely different small coefficients multiplying the lowest functions is considered. It is formulated as a multi-parameter singularly perturbed system. Perturbation methods are developed for both initial and boundary value problems based on asymptotic expansions of the perturbation parameters. The approximate solution consists of an outer solution and a number of boundary layer correction solutions equal to the number of initial conditions lost in the process of degeneration. An example is provided for illustration.
Spectral refinement using a new projection method
Authors: Kulkarni Rekha P. , Gnaneshwar N. 
Published: February 2009

AbstractIn this paper we consider two spectral refinement schemes, elementary and double iteration, for the approximation of eigenelements of a compact operator using a new approximating operator. We show that the new method performs better than the Galerkin, projection and Sloan methods. We obtain precise orders of convergence for the approximation of eigenelements of an integral operator with a smooth kernel using either the orthogonal projection onto a spline space or the interpolatory projection at Gauss points onto a discontinuous piecewise polynomial space. We show that in the double iteration scheme the error for the eigenvalue iterates using the new method is of the order of , where h is the mesh of the partition and k = 0, 1, 2,… denotes the step of the iteration. This order of convergence is to be compared with the orders in the Galerkin and projection methods and in the Sloan method. The error in eigenvector iterates is shown to be of the order of in the new method, in the Galerkin and projection methods and in the Sloan method. Similar improvement is observed in the case of the elementary iteration. We show that these orders of convergence are preserved in the corresponding discrete methods obtained by replacing the integration by a numerical quadrature formula. We illustrate this improvement in the order of convergence by numerical examples.
Non-Newtonian conducting fluid flow and heat transfer due to a rotating disk
Authors: Attia Hazem A. , Ahmed Mohamed E. S. 
Published: February 2009

AbstractThe steady flow of an incompressible viscous non-Newtonian electrically conducting fluid and heat transfer due to the rotation of an infinite disk are studied considering the Hall effect. The effects of an externally applied uniform magnetic field, the Hall current, and the non-Newtonian fluid characteristics on the velocity and temperature distributions as well as the heat transfer are considered. Numerical solutions of the nonlinear equations which govern the magnetohydrodynamics (MHD) and energy transfer are obtained over the entire range of the physical parameters.
Exponential decay rate of the energy of a Timoshenko beam with locally distributed feedback
Authors: Shi Dong-Hua , Feng De-Xing 
Published: February 2009

AbstractThe problem of the energy exponential decay rate of a Timoshenko beam with locally distributed controls is investigated. Consider the case in which the beam is nonuniform and the two wave speeds are different. Then, using Huang's theorem and Birkhoff's asymptotic expansion method, it is shown that, under some locally distributed controls, the energy exponential decay rate is identical to the supremum of the real part of the spectrum of the closed loop system. Furthermore, explicit asymptotic locations of eigenfrequencies are derived.
Crystal structure of the conserved protein TT1542 from Thermus thermophilus HB8
Authors: Handa Noriko , Terada Takaho , Kamewari Yuki , Hamana Hiroaki , Tame Jeremy R.H. , Park Sam‐Yong , Kinoshita Kengo , Ota Motonori , Nakamura Haruki , Kuramitsu Seiki , Shirouzu Mikako , Yokoyama Shigeyuki 
Published: February 2009

AbstractThe TT1542 protein from Thermus thermophilus HB8 is annotated as a conserved hypothetical protein, and belongs to the DUF158 family in the Pfam database. A BLAST search revealed that homologs of TT1542 are present in a wide range of organisms. The TT1542 homologs in eukaryotes, PIG‐L in mammals, and GPI12 in yeast and protozoa, have N‐acetylglucosaminylphosphatidylinositol (GlcNAc‐PI) de‐N‐acetylase activity. Although most of the homologs in prokaryotes are hypothetical and have no known function, Rv1082 and Rv1170 from Mycobacterium tuberculosis are enzymes involved in the mycothiol detoxification pathway. Here we report the crystal structure of the TT1542 protein at 2.0 Å resolution, which represents the first structure for this superfamily of proteins. The structure of the TT1542 monomer consists of a twisted β‐sheet composed of six parallel β‐strands and one antiparallel β‐strand (with the strand order 3‐2‐1‐4‐5‐7‐6) sandwiched between six α‐helices. The N‐terminal five β‐strands and four α‐helices form an incomplete Rossmann fold‐like structure. The structure shares some similarity to the sugar‐processing enzymes with Rossmann fold‐like domains, especially those of the GPGTF (glycogen phosphorylase/glycosyl transferase) superfamily, and also to the NAD(P)‐binding Rossmann fold domains. TT1542 is a homohexamer in the crystal and in solution, the six monomers forming a cylindrical structure. Putative active sites are suggested by the structure and conserved amino acid residues.
Catalytic and binding poly‐reactivities shared by two unrelated proteins: The potential role of promiscuity in enzyme evolution
Authors: James Leo C. , Tawfik Dan S. 
Published: February 2009

AbstractIt is generally accepted that enzymes evolved via gene duplication of existing proteins. But duplicated genes can serve as a starting point for the evolution of a new function only if the protein they encode happens to exhibit some activity towards this new function. Although the importance of such catalytic promiscuity in enzyme evolution has been proposed, little is actually known regarding how common promiscuous catalytic activities are in proteins or their origins, magnitudes, and potential contribution to the survival of an organism. Here we describe a pattern of promiscuous activities in two completely unrelated proteins—serum albumins and a catalytic antibody (aldolase antibody 38C2). Despite considerable structural dissimilarities—in the shape of the cavities and the position of catalytic lysine residues—both active sites are able to catalyze the Kemp elimination, a model reaction for proton transfer from carbon. We also show that these different active sites can bind promiscuously an array of hydrophobic negatively charged ligands. We suggest that the basic active‐site features of an apolar pocket and a lysine residue can act as a primitive active site allowing these promiscuous activities to take place. We also describe, by modelling product formation at different substrate concentrations, how promiscuous activities of this kind— inefficient and rudimentary as they are—can provide a considerable selective advantage and a starting point for the evolution of new functions.