bluuebunny/crossref_metadata_2025_split huggingface dataset:
Stiff systems of ordinary differential equations
Authors: Mahony J. J. , Shepherd J. J. 
Published: February 2009

AbstractSolutions of the stiff system of linear differential equationsare obtained in a form yielding tight estimates of their properties, and conditions are obtained under which the operator norm of the map from r to the solution x does not become exponentially large for small values of ε. When these conditions are satisfied, the solutions are shown to be close to those of Ax + r = 0, save at any singular points of A, and in boundary layers. The behaviour of solutions near admissible singular points is also obtained.The results are used to characterize those boundary-value problems for the above system in which the solution defines maps from the data that are of “moderate” operator norm. This leads to a constructive existence theory for a limited class of boundary-value problems for the nonlinear systemIt is suggested that the treatment of more general classes of boundary-value problems may be simplified using these results. By the use of simple examples, the problems involving large operator norms are shown to be related to the stability properties of the possible branches of the outer solutions close to those of
Extended optima and equilibria for continuous games
Authors: Gates D. J. , Westcott M. 
Published: February 2009

AbstractFor the class of continuous games where σi and fi {σi, φ(σ1, …, σN)} are the strategy of and payoff to player i for i = 1, …, N, it is proved that the set of weak type I optima defined in Paper I conicide with the set of solution of a matrix condition. The latter condition restricts the equilibrium solutions of an adjustment process. Numerical results for N = 2 and N = 3 indicate that the set of all equilibrium solutions coincides with the above sets. The optima of types I to IV from Paper I are described fairly completely for the given class of games.
Linearized planing-surface theory with surface tension. Part II: Detachment with discontinuous slope
Authors: Tuck E. O. 
Published: February 2009

AbstractIn Part I of this series, surface tension was included in the classical two-dimensional planing-surface problem, and the usual smooth-detachment trailing-edge condition enforced. However, the results exhibited a paradox, in that the classical results were not approached in the limit as the surface tension approached zero. This paradox is resolved here by abandoning the smooth-detachment condition, that is, by allowing a jump discontinuity in slope between the planing surface and the free surface at the trailing edge. A unique solution is obtainable for any input planing surface at fixed wetted length if one allows such jumps at both leading and trailing edges. If, as is the case in practice, the wetted length is allowed to vary, uniqueness may be restored by requiring either, but not both, of these slope discontinuities to vanish. The results of Part I correspond to the seemingly more-natural choice of making the trailing-edge detachment continuous, but it appears that the correct choice is to require the leading-edge attachment to be continuous.
The commutation relation i[Y, Z] = 2Y and the absolutely continuous spectrum of Y
Authors: Corbett J. V. 
Published: February 2009

AbstractA relation between positive commutators and absolutely continuous spectrum is obtained. If i[Y, Z] = 2Y holds on a core for Z and if Y is positive then we have a system of imprimitivity for the group on , from which it follows that Y has no singular continuous spectrum.
Selective withdrawal from stratified streams
Authors: Yih Chia-Shun , Zhu Songping 
Published: February 2009

AbstractSelective withdrawal from a stratified stream is considered. The average density of the withdrawn fluid and the flow pattern are found, within the limitations on the densimetric Froude number and the withdrawal rate specified in this paper, to depend on the strength and location of the sink, and very little on any slight variation in the velocity distribution far upstream and the densimetric Froude number. The upstream density distribution is assumed linear, but many other density distributions can be similarly treated.
Nonlinear free-surface flows emerging from vessels and flows under a sluice gate
Authors: Asavanant J. , Vanden-Broeck J.-M. 
Published: February 2009

AbstractSteady two-dimensional flows in a domain bounded below by an infinite horizontal wall and above by a semi-infinite horizontal wall, a vertical wall and a free surface are considered. The fluid is assumed to be inviscid and incompressible, and gravity is taken into account. The problem is solved numerically by series truncation. It is shown that for a given length of the vertical wall, there are two families of solutions. One family is characterized by a continuous slope at the separation point and a limiting configuration with a stagnation point and a 120° angle corner at the separation point. The other family is characterized by a stagnation point and a 90° angle corner at the separation point. Flows under a sluice gate with and without a rigid lid approximation upstream are also considered.
The sputtering temperature of a cooling cylindrical rod without and with an insulated core in a two-fluid medium
Authors: Bera R. K. , Chakrabarti A. 
Published: February 2009

AbstractUtilising Jones' method associated with the Wiener-Hopf technique, explicit solutions are obtained for the temperature distributions on the surface of a cylindrical rod without an insulated core as well as that inside a cylindrical rod with an insulated inner core when the rod, in either of the two cases, is allowed to enter, with a uniform speed, into two different layers of fluid with different cooling abilities. Simple expressions are derived for the values of the sputtering temperatures of the rod at the points of entry into the respective layers, assuming the upper layer of the fluid to be of finite depth and the lower of infinite extent. Both the problems are solved through a three-part Wiener-Hopf problem of special type and the numerical results under certain special circumstances are obtained and presented in tabular forms.
Variance Minimization – Relationship between Completion-Time Variance and Waiting-Time Variance
Authors: Zhou S. , Cai X. 
Published: February 2009

AbstractThe completion-time variance (CTV) and the waiting-time variance (WTV) are two performance measures which are commonly used in optimization of single-machine scheduling systems. This paper shows that when the number of jobs is large the two measures are nearly equivalent in a probabilistic environment.
On generalised convex multi-objective nonsmooth programming
Authors: Mishra S. K. , Mukherjee R. N. 
Published: February 2009

AbstractWe extend the concept of V-pseudo-invexity and V-quasi-invexity of multi-objective programming to the case of nonsmooth multi-objective programming problems. The generalised subgradient Kuhn-Tucker conditions are shown to be sufficient for a weak minimum of a multi-objective programming problem under certain assumptions. Duality results are also obtained.
Oscillatory and asymptotic behavior of solutions of nonlinear neutral-type difference equations
Authors: Graef John R. , Miciano Agnes , Spikes Paul W. , Sundaram P. , Thandapani E. 
Published: February 2009

AbstractThe authors consider the higher-order nonlinear neutral delay difference equationand obtain results on the asymptotic behavior of solutions when (pn) is allowed to oscillate about the bifurcation value –1. We also consider the case where the sequence {pn} has arbitrarily large zeros. Examples illustrating the results are included, and suggestions for further research are indicated.
A two-sided shooting method in computation of travelling combustion waves of a solid material
Authors: Andonowati  
Published: February 2009

AbstractNumerical solutions for travelling combustion waves of a solid material are sought. The algorithm of computation is based on a two-sided shooting method. It is found that there is a lower bound of the wave speed c, say c*, such that for c < c* no numerical solution can be constructed. This c* is a function of the activation energy of the medium.
Subharmonic orbits in an anharmonic oscillator
Authors: Christie J. R. , Gopalsamy K. , Panizza M. P. 
Published: February 2009

AbstractIn a recent paper, Christie and Gopalsamy [2] used Melnikov's method to establish a sufficient condition for the existence of chaotic behaviour, in the sense of Smale, in a particular time-periodically perturbed planar autonomous system of ordinary differential equations. They then concluded with an application to the dynamics of a one-dimensional anharmonic oscillator. In this paper, the same system is considered and a condition for the existence of subharmonic orbits in the perturbed system is deduced, using the subharmonic Melnikov theory. Finally, an application is given to the dynamical behaviour of the one-dimensional anharmonic oscillator system.
A C0-Collocation-like method for elliptic equations on rectangular regions
Authors: Leyk Zbigniew 
Published: February 2009

AbstractWe describe a C0-collocation-like method for solving two-dimensional elliptic Dirichlet problems on rectangular regions, using tensor products of continuous piecewise polynomials. Nodes of the Lobatto quadrature formula are taken as the points of collocation. We show that the method is stable and convergent with order hr(r ≥ 1) in the H1–norm and hr+1(r ≥ 2) in the L2–norm, if the collocation solution js a piecewise polynomial of degree not greater than r with respect to each variable. The method has an advantage over the Galerkin procedure for the same space in that no integrals need be evaluated or approximated.
Combustion waves
Authors: Weber R. O. , Watt S. D. 
Published: February 2009

AbstractFinding critical phenomena in two-dimensional combustion is normally done numerically. By using a centre-manifold reduction, we can find a reduced equation in one dimension. Once we have found the reduced equation, it is simpler to find critical phenomena. We consider two different problems. One is spontaneous ignition. We compare our results with known critical parameters to give some validity to our reduction technique. We also look at a combustion model with three equilibrium states. For this model, the possible transitions can occur as travelling waves between the unstable to either of the stable equilibrium or from one stable to the other stable state. For the latter transition, the direction of the transition tells us whether we have an extinction or ignition wave. We find the critical parameters when the direction of the wave changes.
Numerical study of a problem in the combustion of a porous medium
Authors: Tam K. K. , Andonowati  
Published: February 2009

AbstractA spectral method is used to consider the porous medium combustion in an infinite slab. The infinite system of ordinary differential equations for the amplitude functions is truncated and comparisons are made for different numbers of modes included in the numerical computation. It is shown that the qualitative behaviour of the solution is captured by the first eigenmode. Dependence of the solution on initial data and a parameter is also considered.
Existence of solutions of plane traction problems for inextensible transversely isotropic elastic solids
Authors: Morland L. W. 
Published: February 2009

AbstractA plane strain or plane stress configuration of an inextensible transversely isotropic linear elastic solid with the axis of symmetry in the plane, leads to a harmonic lateral displacement field in stretched coordinates. Various displacement and mixed displacement-traction boundary conditions yield standard boundary-value problems of potential theory for which uniqueness and existence of solutions are well established. However, the important case of prescribed tractions at each boundary point gives a non-standard potential problem involving linking of boundary values at opposite ends of chords parallel to the axis of material symmetry. Uniqueness and existence of solutions, within arbitrary rigid motions, are now established for the traction problem for general domains.
The measurement of blood pressure
Authors: Patterson J. C. , Fitz-Gerald J. M. 
Published: February 2009

AbstractIn this paper, the procedure of the clinical measurement of blood pressure is modelled by the application of a uniform pressure band to a long, homogeneous, isotropic cylinder. The deformations are assumed to be infinitesimal, and transform methods are used to analyse the resulting equations. The inversion of the resulting transforms is carried out numerically. It is shown that, in spite of the fairly crude assumptions of the model, the actual load on the artery may be markedly different from that applied to the surface, leading to inaccuracies in the measured blood pressure. The parameter of importance is shown to be the ratio of pressure band width to arm diameter.
Swimming of slender fish in a non-uniform velocity field
Authors: Newman J. N. 
Published: February 2009

AbstractThe hydrodynamic pressure forces acting upon a slender fish are derived for the case of a fish swimming in a non-uniform velocity field. Possible applications are the effects on fish propulsion of swimming in waves, in turbulent eddies, and in the presence of other fish or a moving ship. The fish is assumed to be a slender body, with no vorticity shed into the fluid except at a single abrupt trailing edge located at the posterior end of the fish, and to be performing small lateral swimming undulations of its body. The non-uniform field through which the fish swims is assumed to be irrotational, and this field as well as the body undulations must be slowly-varying on the length-scale of the lateral fish dimensions. Expressions are derived for the local force and the time-averaged total thrust force. These are applied to the study of steady-state bow-riding and wave-riding of porpoises.
Thermodynamic limit for a system with dipole-dipole interactions
Authors: Smith E. R. , Perram J. W. 
Published: February 2009

AbstractIt is shown that for the three dimensional Ising model with dipole-dipole interactions, the thermodynamic limit of the free energy with simple boundary conditions is not the same as the thermodynamic limit of the free energy with periodic boundary conditions. A variational principle is developed to connect the two free energies.
The effect of viscous dissipation on non-linear convection at high Rayleigh number
Authors: Van der Borght R. 
Published: February 2009

AbstractWhen studying deep convection in a compressible medium the effects of viscous dissipation can become important and must be taken into account in any realistic model. But even in shallow convection, for which the Boussinesq approximation is valid, the viscous dissipation effects will become important at high Rayleigh numbers. These effects are estimated with the help of asymptotic methods and the results are compared with those obtained by numerical integration.
A formula for summing divergent series
Authors: Drummond J. E. 
Published: February 2009

AbstractA formula is given for assigning sums to divergent series where the ratio of adjacent terms varies slowly along the series. This formula consistş of a weighted average of partial sums and is shown to be a general formula which can be easily calculated using a simple recurrence relation. It appears to be more powerful than a repeated Aitken or Shankse1process as long as the transformed series remains divergent and it is also compared with the Padé approximants. It is demonstrated on a factorial series, on a nearly geometric divergent series and for the extrapolation of a velocity formula for small amplitudes of motion.
A generalisation of the study of sum and square law signal processors with multiple clipped inputs
Authors: Keats R. G. , Yu V. K-K. 
Published: February 2009

AbstractThe recent work of Cheng and Stokes on the processing of clipped signals from two or three receivers is extended and generalised by removing a number of restrictions. In particular, there is no restriction on the number of receivers and the restrictions on the statistical properties of the signal and noise processes have been considerably relaxed.Mathematically—Plackett's result is used to expand the orthant proabilities involved in increasing powers of the input signal to noise ratio.
On the variational derivation of Einstein's strong field equations
Authors: Gregory L. J. , Klotz A. H. 
Published: February 2009

AbstractIt is shown that the necessary and sufficient condition for the transposition invariance of the field equations derivable from an Einstein-Kaufman variational action principle is the vanishing of xythe vector Γλ. When this condition is satisfied, the field equations become the so-called strong field equations of Einstein. In this sense, the latter can be claimed to follow from the same action principle.
A Boltzmann-type equation in the kinetic theory of vehicular traffic
Authors: Pao C. V. 
Published: February 2009

AbstractIn the theory of vehicular traffic flow on a highway the traffic interaction process is often considered as a collision similar to the particles' interaction in the kinetic theory of gases. This concept leads to a Boltzmann-type nonlinear intergro-differential equation which governs the traffic density function. The purpose of this paper is to present a constructive method for the determintation of a solution for this type of equation under certain boundary and initial conditions. Our method is by successive approximation which yields existence of both global and local solutions of the problem.
Sufficient Fritz John optimality conditions for nondifferentiable convex programming
Authors: Craven B. D. , Mond B. 
Published: February 2009

AbstractThe Fritz John necessary conditions for optimality of a differentiable nonlinear programming problem have been shown, given additional convexity hypotheses, to be also sufficient (by Gulati, Craven, and others). This sufficiency theorem is now extended to minimization (suitably defined) of a function taking values in a partially ordered space, and to (convex) objective and constraint functions which are not always differentiable. The results are expressed in terms of subgradients.
A dam with general release rule
Authors: Yeo Geoffrey 
Published: February 2009

AbstractA dam is considered with independently and identically distributed inputs occurring in a renewal process, and in particular a Poisson process, with a general release rate r(·) depending on the content. This is related to a GI/G/1 queue with service times dependent on the waiting time. Some results are obtained for the limiting content distribution when it exists; these are more complete for some special release rates, such as r(x) = μxα and r(x) = a + μx, and particular input size distributions.
Homogeneous Newtonian cosmologies and their perturbations
Authors: Szekeres Peter , Rankin John R. 
Published: February 2009

AbstractA review of Heckmann and Schücking's formulation of Newtonian cosmology is presented, which permits the discussion of models more general than those possessing both homogeneity and isotropy. In particular it is shown that all homogeneous cosmologies may be uniquely specified by the rate of shear tensor as an arbitrary function of time and specifying arbitrary initial values for expansion, rotation and density. Perturbations of these models are now discussed, with a view to their possible implications for galaxy formation. The Jeans criterion is shown to hold in all these models, even in the presence of viscosity; this generalizes a result of Bonnor which only applied to the isotropic case. Furthermore, Bonnor's analysis is considerably simplified in the present paper. Finally, a WKB-type of approximation procedure is described which appears to be successful in estimating the growth rate of unstable fluctuations.
An elementary derivation of Pontrayagin's maximum principle of optimal control theory
Authors: Blatt J. M. , Gray J. D. 
Published: February 2009

AbstractPontryagin's maximum principle is derived by elementary mathematical techniques. The conditions on the functions which enter are generally somewhat more stringent than in Pontryagin's derivation, but one (practically very awkward) condition of Pontryagin can be relaxed: continuity in the time variable can be replaced by a much weaker condition.
A note on continuation methods for the solution of nonlinear equations
Authors: Abbott James P. , Brent Richard P. 
Published: February 2009

AbstractIn this note we present a variable order continuation method for the solution of nonlinear equations when only a poor estimate of a solution is known. The method changes continuously from one which improves the global convergence characteristics to one which attains rapid convergence to a solution and proves to be more efficient than methods previously presented in [2].
Green's function of the clamped punctured disk
Authors: Nakai Mitsuru , Sario Leo 
Published: February 2009

If a thin elastic circular plate B: ∣z∣ < 1 is clamped (simply supported, respectively) along its edge ∣z∣ = 1, its deflection at z ∈ B under a point load at ζ ∈ B, measured positively in the direction of the gravitational pull, is the biharmonic Green's function β(z, ζ) of the clamped plate (γ(z, ζ) of the simply supported plate, respectively). We ask: how do β(z, ζ) and γ(z, ζ) compare with the corresponding deflections β0(z, ζ) and γ0(z, ζ) of the punctured circular plate B0: 0 < ∣ z ∣ < 1 that is “clamped” or “simply supported”, respectively, also at the origin? We shall show that γ(z, ζ) is not affected by the puncturing, that is, γ(·, ζ) = γ0(·, ζ), whereas β(·, ζ) is:on B0 × B0. Moreover, while β((·, ζ) is of constant sign, β0(·, ζ) is not. This gives a simple counterexmple to the conjecture of Hadamard [6] that the deflection of a clampled thin elastic plate be always of constant sign:The biharmonic Gree's function of a clampled concentric circular annulus is not of constant sign if the radius of the inner boundary circle is sufficiently small.Earlier counterexamples to Hadamard's conjecture were given by Duffin [2], Garabedian [4], Loewner [7], and Szegö [9]. Interest in the problem was recently revived by the invited address of Duffin [3] before the Annual Meeting of the American Mathematical Society in 1974. The drawback of the counterexample we will present is that, whereas the classical examples are all simply connected, ours is not. In the simplicity of the proof, however, there is no comparison.
Are wave functions uniquely determined by their position and momentum distributions?
Authors: Corbett J. V. , Hurst C. A. 
Published: February 2009

AbstractThe problem of determining a square integrable function from both its modulus and the modulus of its Fourier transform is studied. It is shown that for a large class of real functions the function is uniquely determined from this data. We also construct fundamental subsets of functions that are not uniquely determined. In quantum mechanical language, bound states are uniquely determined by their position and momentum distributions but, in general, scattering states are not.
A class of axially symmetric stationary exact solutions of Einstein's vacuum field equations
Authors: Patel M. D. 
Published: February 2009

AbstractEinstein's vacuum field equations of an axially symmetric stationary rotating source are studied. Using the oblate spheroidal coordinate system, a class of asymptotically fiat solutions representing the exterior gravitational field of a stationary rotating oblate spheroidal source is obtained. Also it is proved that an analytic axisymmetric and stationary distribution of dust cannot be the source for the gravitational field described by the axisymmetric stationary metric.