bluuebunny/crossref_metadata_2025_split huggingface dataset:
The Taylor series for bandlimited signals
Authors: Veron M. A. Hernandez 
Published: February 2009

AbstractWe study a special type of infinite product, called an infinite product of Cardano type, and we obtain its Taylor series. We prove that Hadamard's factorization of bandlimited signals is given by an infinite product of Cardano type, and apply our results to obtain the Taylor series for bandlimited signals.
Controllability of nonlinear neutral Volterra integrodifferential systems
Authors: Balachandran K. , Balasubramaniam P. 
Published: February 2009

AbstractSufficient conditions for the controllability of nonlinear neutral Volterra integrodifferential systems with implicit derivative are established. The results are a generalisation of the previous results, through the notions of condensing map and measure of noncompactness of a set.
On an optimization problem with cost of rapid variation of control
Authors: Idczak D. , Kibalczyc K. , Walczak S. 
Published: February 2009

AbstractIn the paper we give sufficient conditions for the existence of a solution for a Darboux-Goursat optimization problem with a cost functional depending on the number of switchings of a control and the rapidity of its changes. An application is given to a gas absorption problem.
A gradient technique for an optimal control problem governed by a system of nonlinear first order partial differential equations
Authors: Kazemi Mohammad A. 
Published: February 2009

AbstractIn this paper a class of optimal control problems with distributed parameters is considered. The governing equations are nonlinear first order partial differential equations that arise in the study of heterogeneous reactors and control of chemical processes. The main focus of the present paper is the mathematical theory underlying the algorithm. A conditional gradient method is used to devise an algorithm for solving such optimal control problems. A formula for the Fréchet derivative of the objective function is obtained, and its properties are studied. A necessary condition for optimality in terms of the Fréchet derivative is presented, and then it is shown that any accumulation point of the sequence of admissible controls generated by the algorithm satisfies this necessary condition for optimality.
Smoothing approximations to nonsmooth optimization problems
Authors: Yang X.Q. 
Published: February 2009

AbstractWe study certain types of composite nonsmooth minimization problems by introducing a general smooth approximation method. Under various conditions we derive bounds on error estimates of the functional values of original objective function at an approximate optimal solution and at the optimal solution. Finally, we obtain second-order necessary optimality conditions for the smooth approximation prob lems using a recently introduced generalized second-order directional derivative.
Travelling waves in phase field models of solidification
Authors: Barber Michael N. , Singleton David 
Published: February 2009

AbstractThe existence and selection of steady-state travelling planar fronts in a set of typical phase field equations for solidification are investigated by a combination of numerical and analytical methods. Such solutions are conjectured to exist only for a unique velocity of propagation and to be unique except for translation. This behaviour is in marked contrast to the situation in conventional Stefan models in which travelling fronts exist for all velocities. The value of the steady-state velocity depends upon the various material parameters which enter the phase field equations. Numerical and, in certain tractable limits, analytical results for the velocity are presented for a number of physical situations.
Scattering of water waves by a submerged nearly circular cylinder
Authors: Mandal B. N. , Banerjea Sudeshna 
Published: February 2009

AbstractThe problem of scattering of surface water waves by a horizontal circular cylinder totally submerged in deep water is well studied in the literature within the framework of linearised theory with the remarkable conclusion that a normally incident wave train experiences no reflection. However, if the cross-section of the cylinder is not circular then it experiences reflection in general. The present paper studies the case when the cylinder is not quite circular and derives expressions for reflection and transmission coefficients correct to order ∈, where ∈ is a measure of small departure of the cylinder cross-section from circularity. A simplified perturbation analysis is employed to derive two independent boundary value problems (BVP) up to first order in ∈. The first BVP corresponds to the problem of water wave scattering by a submerged circular cylinder. The reflection coefficient up to first order and the first order correction to the transmission coefficient arise in the second BVP in a natural way and are obtained by a suitable use of Green' integral theorem without solving the second BVP. Assuming a Fourier expansion of the shape function, these are evaluated approximately. It is noticed that for some particular shapes of the cylinder, these vanish. Also, the numerical results for the transmission coefficients up to first order for a nearly circular cylinder for which the reflection coefficients up to first order vanish, are given in tabular form. It is observed that for many other smooth cylinders, the result for a circular cylinder that the reflection coefficient vanishes, is also approximately valid.
Splash formation at the nose of a smoothly curved body in a stream
Authors: Tuck E. O. , Simakov S. T. 
Published: February 2009

AbstractIn two-dimensional flow past a body close to a free surface, the upwardly diverted portion may separate to form a splash. We model the nose of such a body by a semi-infinite obstacle of finite draft with a smoothly curved front face. This problem leads to a nonlinear integral equation with a side condition, a separation condition and an integral constraint requiring the far-upstream free surface to be asymptotically plane. The integral equation, called Villat's equation, connects a natural parametrisation of the curved front face with the parametrisation by the velocity potential near the body. The side condition fixes the position of the separation point, whereas the separation condition, known as the Brillouin-Villat condition, imposes a continuity relation to be satisfied at separation. For the described flow we derive the Brillouin-Villat condition in integral form and give a numerical solution to the problem using a polygonal approximation to the front face.
Wavelet multipliers and signals
Authors: He Z. , Wong M.W. 
Published: February 2009

AbstractThe Schatten-von Neumann property of a pseudo-differential operator is established by showing that the pseudo-differential operator is a multiplier defined by means of an admissible wavelet associated to a unitary representation of the additive group Rnon theC*-algebra of all bounded linear operators fromL2(Rn) intoL2(Rn). A bounded linear operator onL2(R) arising in the Landau, Pollak and Slepian model in signal analysis is shown to be a wavelet multiplier studied in this paper.
Fully nonlinear flow over successive obstacles: hydraulic fall and supercritical flows
Authors: Belward Shaun R. 
Published: February 2009

AbstractIn this paper we consider the flow of an incompressible, inviscid and homogeneous fluid over two obstacles in succession. The flow is assumed irrotational and solutions are sought in which a hydraulic fall occurs over the first obstacle with supercritical flow over the second. The method used to solve the problem is capable of calculating flows over topography of any shape.
On the square-root method for continuous-time algebraic Riccati equations
Authors: Lu Linzhang , Pearce C. E. M. 
Published: February 2009

AbstractWe give a simple and transparent proof for the square-root method of solving the continuous-time algebraic Riccati equation. We examine some benefits of combining the square-root method with other solution methods. The iterative square-root method is also discussed. Finally, paradigm numerical examples are given to compare the square-root method with the Schur method.
Observability-enhanced proportional navigation guidance with bearings-only measurements
Authors: Li Mingyan , Lim Cheng-Chew 
Published: February 2009

AbstractWe analyse the performance of the additive observable proportional navigation guidance system, which is well-suited for low-cost homing missiles with bearings-only measurements. Closed-form solutions are derived for both manoeuvring and non-manoeuvring targets. Guidelines on how to select the navigation constants of the control law are presented. We show that the additive observable proportional navigation guidance system can cover a larger capture area than can a conventional proportional navigation system.
Second-order time discretization with finite-element method for partial integro-differential equations with a weakly singular kernel
Authors: Kim Chang Ho , Choi U Jin 
Published: February 2009

AbstractWe propose the second-order time discretization scheme with the finite-element approximation for the partial integro-differential equations with a weakly singular kernel. The space discretization is based on the finite element method and the time discretization is based on the Crank-Nicolson scheme with a graded mesh. We show the stability of the scheme and obtain the second-order convergence result for the fully discretized scheme.
Synthesis of layered shells from a finite set of viscoelastic materials
Authors: Bondarev E. A. , Budugaeva V. A. , Gusev E. L. 
Published: February 2009

AbstractThe method suggested earlier for solving the problems of optimal design from a limited set of elastic materials is generalized to a viscoelasticity case. The computational experiment for the problem of free oscillations of a spherical shell shows that characteristics of a viscoelastic layered structure may be improved due to peculiarities of wave propagation through the boundaries of layers made of different materials.
A nonmonotonic trust region method for constrained optimization problems
Authors: Zhang Jianzhong , Zhu Detong 
Published: February 2009

AbstractIn this paper we propose an easy-to-implement algorithm for solving general nonlinear optimization problems with nonlinear equality constraints. A nonmonotonic trust region strategy is suggested which does not require the merit function to reduce its value in every iteration. In order to deal with large problems, a reduced Hessian is used to replace a full Hessian matrix. To avoid solving quadratic trust region subproblems exactly which usually takes substantial computation, we only require an approximate solution which requires less computation. The calculation of correction steps, necessary from a theoretical view point to overcome the Maratos effect but which often brings in negative results in practice, is avoided in most cases by setting a criterion to judge its necessity. Global convergence and a local superlinear rate are then proved. This algorithm has a good performance.
A numerical method for friction problems with multiple contacts
Authors: Stewart David E. 
Published: February 2009

AbstractFriction problems involving “dry” or “static” friction can be difficult to solve numerically due to the existence of discontinuities in the differential equations appearing in the right-hand side. Conventional methods only give first-order accuracy at best; some methods based on stiff solvers can obtain high order accuracy. The previous method of the author [16] is extended to deal with friction problems involving multiple contact surfaces.
Reaction waves and non-constant diffusivities
Authors: Watt S. D. , Weber R. O. 
Published: February 2009

AbstractA reaction-diffusion equation with non-constant diffusivity,ut = (D(x, t)ux)x + F(u),is studied for D(x, t) a continuous function. The conditions under which the equation can be reduced to an equivalent constant diffusion equation are derived. Some exact forms for D(x, t) are given. For D(x, t) a stochastic function, an explicit finite difference method is used to numerically determine the effect of randomness in D(x, t) upon the speed of the reaction wave solution to Fisher's equation. The extension to two spatial dimensions is considered.
Continuous-time quadratic cost flow problems with applications to water distribution networks
Authors: Ernst A. T. 
Published: February 2009

AbstractThis paper deals with a class of network optimization problems in which the flow is a function of time rather than static as in the classical network flow problem, and storage is permitted at the nodes. A solution method involving discretization will be presented as an application of the ASG algorithm. We furnish a proof that the discretized solution converges to the exact continuous solution. We also apply the method to a water distribution network where we minimize the cost of pumping water to meet supply and demand, subject to both linear and nonlinear constraints.
The control parameterization enhancing transform for constrained optimal control problems
Authors: Teo K. L. , Jennings L. S. , Lee H. W. J. , Rehbock V. 
Published: February 2009

AbstractConsider a general class of constrained optimal control problems in canonical form. Using the classical control parameterization technique, the time (planning) horizon is partitioned into several subintervals. The control functions are approximated by piecewise constant or piecewise linear functions with pre-fixed switching times. However, if the optimal control functions to be obtained are piecewise continuous, the accuracy of this approximation process greatly depends on how fine the partition is. On the other hand, the performance of any optimization algorithm used is limited by the number of decision variables of the problem. Thus, the time horizon cannot be partitioned into arbitrarily many subintervals to reach the desired accuracy. To overcome this difficulty, the switching points should also be taken as decision variables. This is the main motivation of the paper. A novel transform, to be referred to as the control parameterization enhancing transform, is introduced to convert approximate optimal control problems with variable switching times into equivalent standard optimal control problems involving piecewise constant or piecewise linear control functions with pre-fixed switching times. The transformed problems are essentially optimal parameter selection problems and hence are solvable by various existing algorithms. For illustration, two non-trivial numerical examples are solved using the proposed method.
Strict lower subdifferentiability and applications
Authors: Xu H. , Rubinov A. M. , Glover B. M. 
Published: February 2009

AbstractWe investigate the strict lower subdifferentiability of a real-valued function on a closed convex subset of Rn. Relations between the strict lower subdifferential, lower subdifferential, and the usual convex subdifferential are established. Furthermore, we present necessary and sufficient optimality conditions for a class of quasiconvex minimization problems in terms of lower and strict lower subdifferentials. Finally, a descent direction method is proposed and global convergence results of the consequent algorithm are obtained.
Necessary optimality conditions for bicriterion discrete optimal control problems
Authors: Yang X. Q. , Teo K. L. 
Published: February 2009

AbstractIn management science and system engineering, problems with two incommensurate objectives are often detected. Bicriterion optimization finds an optimal solution for the problems. In this paper it is shown that bicriterion discrete optimal control problems can be solved by using a parametric optimization technique with relaxed convexity assumptions. Some necessary optimality conditions for discrete optimal control problems subject to a linear state difference equation are derived. It is shown that in this case no adjoint equation is required.
A bridging method for global optimization
Authors: Liu Y. , Teo K. L. 
Published: February 2009

AbstractIn this paper a bridging method is introduced for numerical solutions of one-dimensional global optimization problems where a continuously differentiable function is to be minimized over a finite interval which can be given either explicitly or by constraints involving continuously differentiable functions. The concept of a bridged function is introduced. Some properties of the bridged function are given. On this basis, several bridging algorithm are developed for the computation of global optimal solutions. The algorithms are demonstrated by solving several numerical examples.
Control of continuous-time systems with discrete jumps
Authors: Shi Peng 
Published: February 2009

AbstractIn this paper, the design of output feedback controllers for linear systems under sampled measurements is investigated. The performance we use is the worst-case gain from disturbances to the controlled output, which comprises both a continuous-time and a discretetime signal to be controlled. Control problems in both the finite and infinite horizonare addressed. Necessary and sufficient conditions for the existence of a suitable sampled-data output feedback controller are given in terms of two Riccati differential equations with finite discrete jumps. A numerical example is given to show the potential of the proposed technique.
A generalized Hankel transform and its use for solving certain partial differential equations
Authors: Ali I. , Kalla S. 
Published: February 2009

AbstractWe introduce a generalized form of the Hankel transform, and study some of its properties. A partial differential equation associated with the problem of transport of a heavy pollutant (dust) from the ground level sources within the framework of the diffusion theory is treated by this integral transform. The pollutant concentration is expressed in terms of a given flux of dust from the ground surface to the atmosphere. Some special cases are derived.
Knots and gravity
Authors: Toh Tze-Chuen , Anderson Malcolm R. 
Published: February 2009

AbstractIn the loop representation theory of non-perturbative quantum gravity, gravitational states are described by functionals on the loop space of a 3-manifold. In the order to gain a deeper insight into the physical interpretation of loop states, a natural question arises: to wit, how are gravitations related to loops? Some light will be shed on this question by establishing a definite relationship between loops and 3-geometries of the 3-manifold.
Foliations in supergravity
Authors: Chan Wai Kin , Castillo Reynaldo , Lai King Fai 
Published: February 2009

AbstractFollowing upon a previous paper [1] on the existence of chiral transformations in a foliated version of the Cremmer, Julia and Scherk model, we deduce a couple of interesting properties of the model. These are:(i) TM4 is isomorphic to a quotient Lie pseudoalgebra on the algebra of basic functions in M11;(ii) There is a locally trivial fibration which exhibits M11 as M7 × U, U ⊂ W and W is the basic manifold of the foliation [5](iii) The chiral group of the model is identified as Clx (L, gL) × Clx (Q, gQ), the factors are respectively the multiplication groups of units in the Clifford algebras Clx (L, gL) and Clx (Q, gQ) and matching of this group with phenomenology is briefly discussed.
What is a shell-crossing singularity?
Authors: Szekeres Peter , Lun Anthony 
Published: February 2009

AbstractA detailed discussion of Newtonian and general relativistic spherically symmetric dust solutions leads to the following suggested criteria for a singularity to be classified as a shell-cross: (1) All Jacobi fields have finite limits (in an orthonormal parallel propagated frame) as they approach the singularity. (2) The boundary region forms an essential C2 singularity which is C1 regular, that is it can be transformed away by a C1 coordinate transformation.
Near-field expansion of the metric due to a cosmic string
Authors: Anderson Malcolm 
Published: February 2009

AbstractBy erecting a co-ordinate system tailored to the geometry of a cosmic string and examining the properties of the near gravitational field, it is possible to distinguish two types of gravitational waves supported by a general string metric. The first type, travelling waves, are completely decoupled from the curvature of the world sheet, whereas the second type, which I choose to call curvature waves, are generated in response to any non-trivial geometric structure on the string.
Forced cubic Schrödinger equation with Robin boundary data: continuous dependency result
Authors: Bu Charles 
Published: February 2009

AbstractFor the cubic Schrödinger equation iut = uxx + k|u|2u, 0 ≤ x, t < ∞, initial data u(x, 0) = u0(x) ∈ H2[0, ∞), and Robin boundary data ux(0, t) + αu(0, t) = R(t) ∈ C2[0, ∞) (where α is real), we show that the solution u depends continuously on u0 and R.
An analysis of two and three dimensional unsteady withdrawal flows, using shallow water theory
Authors: Koerber A. J. , Forbes L. K. 
Published: February 2009

AbstractThis paper examines the predictions of shallow water theory for steady and unsteady withdrawal flows through an extended sink from fluid of finite depth. Two-dimensional plane flows and three-dimensional axi-symmetric flow through a circular drain are examined. Shallow water theory indicates the presence of limiting configurations, where the surface of the fluid collapses directly into the sink. In addition, this theory suggests that some previously computed steady solutions may be unstable.
The generalized Shannon system in wavelet space
Authors: Kim Hong Oh , Park Jong Ha 
Published: February 2009

AbstractThe Shannon system is generalized and the expansion of a function in the generalized Shannon system is considered. No study of a wavelet expansion exists without the assumption of ‘fast’ decay of wavelets. The wavelet ψ which is associated with the generalized Shannon system has a ‘slow’ decay. The expansion of a function in the system is shown to converge at a point which satisfies the Lipschitz condition of order α > 0. On the other hand, there is a continuous function whose wavelet expansion in the generalized Shannon system diverges. An observation of Gibbs' phenomenon is also given.
An analysis of a fractal Michaelis-Menten curve
Authors: Heidel Jack , Maloney John 
Published: February 2009

AbstractSimple chemical reactions can be described by the Michaelis-Menten response curve relating the velocity V of the reaction and the concentration [S] of the substrate S. To handle more complicated reactions without introducing general polynomial response curves, the rate constants can be considered to be scale dependent. This leads to a new response curve with characteristic sigmoidal shape. But not all sigmoidal curves can be accurately fit with three parameters. In order to get an accurate fit, the lower part of the ∫ shaped curve cannot be too shallow and the upper part can't be too steep. This paper determines an exact mathematical expression for the steepness and shallowness allowed.
An open-channel flow meeting a barrier and forming one or two jets
Authors: Wiryanto L. H. , Tuck E. O. 
Published: February 2009

AbstractA steady two-dimensional free-surface flow in a channel of finite depth is considered. The channel ends abruptly with a barrier in the form of a vertical wall of finite height. Hence the stream, which is uniform far upstream, is forced to go upward and then falls under the effect of gravity. A configuration is examined where the rising stream splits into two jets, one falling backward and the other forward over the wall, in a fountain-like manner. The backward-going jet is assumed to be removed without disturbing the incident stream. This problem is solved numerically by an integral-equation method. Solutions are obtained for various values of a parameter measuring the fraction of the total incoming flux that goes into the forward jet. The limit where this fraction is one is also examined, the water then all passing over the wall, with a 120° corner stagnation point on the upper free surface.