bluuebunny/crossref_metadata_2025_split huggingface dataset:
Radial sums of ridge functions: A characterization
Authors: Madych W. R. , Nelson S. A. , Payne L. E. 
Published: March 2007

AbstractWe extend and sharpen the characterization of radial sums of ridge functions of two variables given in an earlier paper. More precisely, a bound on the degree of certain polynomials is given which depends on the angles between the ridges; not only is this bound best possible but also a converse result holds. Furthermore, variants of this characterization which hold for higher dimensional analogues are also given. These results are then applied to certain parallel am models in computed tomography to obtain more precise and otherwise improved characterizations of algorithms which commute with rigid motions.
A method of iterative data refinement and its applications
Authors: Censor Y. , Elfving T. , Herman G. T. , Brosowski B. 
Published: March 2007

AbstractIterative data refinement (IDR) is a general procedure for producing a sequence of estimates of the data that would be collected by a measuring device which is idealized to a certain extent, starting from the data that are collected by an actual measuring device. Following a discussion of the fundamentals of IDR, we present a number of previously published procedures which are special cases of it. We concentrate on examples from medical imaging. In particular, we discuss beam hardening correction in x‐ray computerized tomography, attenuation correction in emission computerized tomography, and compensation for missing data in reconstruction from projections. We also show that a standard method of numerical mathematics (the parallel chord method) as well as a whole family of constrained iterative restoration algorithms are special cases of IDR. Thus IDR provides a common framework within which a number of originally different looking procedures are presented and discussed. We also present a result of theoretical nature concerning the initial behavior of IDR.
On the existence of optimum large amplitude hydrofoil propulsion
Authors: Urbach H. P. , van de Vooren A. I. 
Published: March 2007

AbstractThe possibility of optimum thrust‐production by means of periodic motions of a flexible wing is discussed. The disturbance velocities are assumed to be small so that a linearized theory is valid. It is proved that when adequate constraints are put upon the amplitude of the path of the wing and on the amplitude of its slopes and curvature, an optimum path exists.
Zur Asymptotik der wellengleichung und der wärmeleitungsgleichung in zweidimensionalen außenräumen
Authors: Werner P. 
Published: March 2007

AbstractWe study initial and boundary value problems for the wave equation and the heat equation with a time‐independent right‐hand term f in two space dimensions in the exterior of a closed curve C. In the case of Neumann's boundary condition ∂u/∂n = 0 on C, the solutions increase with a logarithmic rate as t → ∞ if ∫ fdx ≠ 0. In contrast to this, the solutions of the corresponding Dirichlet problems converge to the solution of the related static problem as t → ∞. In the case of the wave equation, these results have already been obtained by L: A. Muravei under the additional assumption that the curvature of C is positive, by using high frequency estimates for the reduced wave equation Δ U + ϰ2 U = 0. The analysis presented here is based on different methods, which can be applied to arbitrary smooth curves.
Asymptotic analysis of differential‐delay equations and nonuniqueness of periodic solutions
Authors: Chapin S. , Payne L. E. 
Published: March 2007

AbstractWe study the differential‐delay equation x′(t) = −αf(x(t–1)), where α is a positive parameter and f is an odd function which decays like x−r at infinity. In particular, we consider the case r ⩽ 2, and prove the existence of periodic solutions with special symmetries which are different from previously known periodic solutions of minimal period 4. For r = 2 we prove sharp asymptotic estimates for the minimal periods of these solutions.Our results disprove a conjecture of R. D. Nussbaum.
An integral equation of elasticity
Authors: Kolakowski H. , Piskorek A. 
Published: March 2007

AbstractIn this work a certain mixed problem in R for the Lamé equations in the theory of elasticity is reduced to the integral equationmagnified imageAn explicit formula for the solutions is given for either Ω = {x:x2 > 0} or Ω = {x:∥x∥<r}. The question of smoothness of the solutions is also discused. Another formulae on Ω = {x:∥x∥<r} are found in [5], [4]. It seems that the techniques used below allows a deeper investigation of properties of the solutions to problem (*).
Feynman‐diagramme als vektorsysteme invariantentheoretisch behandelt (compton‐streuung, elektron‐positron‐vernichtung
Authors: Hölder E. , Dirac P. M. , Werner P. 
Published: March 2007

AbstractEmploying a special contact transformation devised by S. Lie, which takes spheres into lines, we interpret the Feynman diagrams of photon electron scattering in terms of vector systems. This gives a nice kinematic model of Compton scattering. We further compute in detail the transition probabilities of the Compton scattering process by making use of the calculus of chains of complexes from classical invariant theory rather than applying the usual Dirac‐matrix technique. In the final paragraph of this paper an application of our calculations to the treatment of myon decay is indicated.
Stable methods for an inverse problem in acoustic scattering by an obstacle and an inhomogeneous medium
Authors: Smith R. T. , Hsiao G. C. 
Published: March 2007

AbstractWe consider (in two‐dimensional Euclidean space) the scattering of a plane, time‐harmonic acoustic wave by an inhomogeneous medium Ω with compact support and a bounded obstacle D lying completely outside of the inhomogeneous medium. We show that one may determine the shape of D and the local speed of sound in Ω from a knowledge of the asymptotic behavior of the scattered wave (i.e. the far field). This is done by considering a constrained optimization problem and employing integral equation and conformal mapping techniques.By assuming a priori that the functions which determine the shape of D and the local speed of sound in Ω lie in given compact sets, we show that the problem is stable, in the sense that the solution of the inverse scattering problem depends continuously on the far field data.
Taylor series for the dirac function on perturbed surfaces with applications to mechanics
Authors: Codaccioni R. Caboz J.‐P. , Constantinescu F. , Meister E. 
Published: March 2007

AbstractLet H0 be the Hamiltonian of an unperturbed oscillating system and let V be a small perturbation which is analytic in a neighborhood of the surface H0 = E, E > 0.If H0 = H + λ V is the total Hamiltonian, we prove that there is a Taylor expansion of the Dirac function δ for small |λ|magnified imageWhen applied to test functions which are analytic near H0 = E.The connection of this result with the classical Lagrange‐Bürmann theorem and some applications to the mechanics of non‐linear systems are discussed.
On the absolutely continuous spectrum of MHD plasma confined in the flat torus
Authors: Kako T. , Fujita H. 
Published: March 2007

AbstractThe spectral properties of the linearized MHD operator are investigated applying the theory of trace class perturbation. Especially, it is shown that the essential spectrum in the positive (stable) part of the spectrum contains the absolutely continuous one and the corresponding part of the spectrum is unitarily equivalent to some multiplication operator.
Exact and approximate pulsed beam solutions of Maxwell's equations
Authors: Cooper J. , Wilcox C. H. 
Published: March 2007

AbstractAn exact solution of Maxwell's equations is constructed which represents a pulse of finite energy propagating along a given axis. To simplify the computation of such a pulse, an approximate solution is constructed as a superposition of solutions of the paraxial equation. This approximation is vectorial in nature and satisfies the divergence‐free condition. The difference between the exact and approximate solutions is estimated relative to the total energy transfer of the exact solution.
The exterior dirichlet problem for the Laplace equation
Authors: Ahner J. F. , Hsiao G. C. 
Published: March 2007

AbstractUsing a standard application of Green's theorem, the exterior Dirichlet problem for the Laplace equation in three dimensions is reduced to a pair of integral equations. One integral equation is of the second kind and the other is of the first kind. It is known that the integral equation of the second kind is not uniquely solvable, however, it has been demonstrated that the pair of integral equations has a unique solution. The present approach is based on the observation that the known function appearing in the integral equation of the second kind lies in a certain Banach space E which is a proper subspace of the Banach space of continuous complex‐valued functions equipped with the maximum norm. Furthermore, it can be shown that the related integral operator when restricted to E has spectral radius less than unity. Consequently, a particular solution to the integral equation of the second kind can be obtained by the method of successive approximations and the unique solution to the problem is then obtained by using the integral equation of the first kind. Comparisons are made between the present algorithm and other known constructive methods. Finally, an example is supplied to illustrate the method of this paper.
A remark on N. Korevaar's concavity maximum principle and on the asymptotic uniqueness of solutions to the plasma problem
Authors: Kawohl B. , Payne L. 
Published: March 2007

AbstractRecently N. Korevaar developed a method of proving that solutions to elliptic and parabolic boundary value problems on convex domains ω ⊂ Rn are convex functions. He introduced a concavity functionmagnified imageand used the classical maximum principle to prove that C ⩾ 0 on ω × ω, i.e. that u is convex. Both he and independently L. Caffarelli and J. Spruck applied this method successfully to various boundary value problems. In this note we weaken the assumptions of their theorems and obtain some interesting new applications which are not covered by their previous results [CS, Ko].
Low frequency asymptotics for the reduced wave equation in two‐dimensional exterior spaces
Authors: Werner P. 
Published: March 2007

AbstractWe consider the Dirichlet problem for the reduced wave equation ΔUx + x2Ux = 0 in a two‐dimensional exterior domain with boundary C, where C consists of a finite number of smooth closed curves C1,…,Cm. The question of interest is the behavior of Ux as ϰ → 0. We show that U converges to the solution of the corresponding exterior Dirichlet problem of potential theory if the boundary data converge to a limit uniformly on C. This generalizes a well‐known result of R. C. MacCamy for the case m = 1.
Integral equations for the Fourier‐transformed boundary values for the transmission problems for right‐angled wedges and octants
Authors: Meister E. 
Published: March 2007

AbstractA 4×4‐system of integral equations for the Fourier transformed boundary values of the normal derivatives of the wave functions defined in the four quadrants of R2‐space is derived. This system results from the scalar transmission problem with continuous passage of the boundary values of the total wave‐fields and of the weighted normal derivatives corresponding to the case of magnetically polarized fields. Several equivalent systems of integral equations are deduced then which show that Banach's fixed point principle may be applied at least for slightly differing media in the four quadrants. The method, which is equivalent to a compatibility condition for holomorphic functions, may be generalized to the case of the scalar transmission problem for octants in R3‐space. There a 12 × 12‐system of integral equations for the Fourier transformed normal derivatives on the quarter‐plane faces is established.
Polarized light transfer above a reflecting surface
Authors: van der Mee C. V. M. , Neunzert H. 
Published: March 2007

AbstractThe existence and uniqueness are established for the solution of the equation of transfer of polarized light in a homogeneous atmosphere of finite optical thickness, assuming reflection by the planetary surface. A general Lp‐space formulation is adopted. The boundary value problem is first written as a vector‐valued integral equation. Using monotonicity properties of the spectral radii of the integral operators involved as well as recent half‐range completeness results for kinetic equations with reflective boundary conditions, the present results follow as a corollary.
Optimal controllability in viscoelasticity of rate type
Authors: Leugering G. , Meister E. 
Published: March 2007

AbstractRecently, the control engineers interest turns upon material with structural damping, such as hysteretic effects in elastoplastic systems [27] and flexible space structures [30] and in particular with damping due to the viscoelastic nature of the material, in the sense of Kelvin, [7], [12]. The reason for this renewed interest is the possibility of constructing finite rank compensators with small spillover in the observation [1], [5], [11], [25].However, a control theory for the infinite system does not seem to exist in the literature. It is shown that the trajectories, initially in a certain subspace, can be steered to rest in any time T > 0 using distributed load controlsThe reesults are partially contained in [19].
. Furthermore, and perhaps more interesting, the L2 (0, T, H)‐norm of the control decreases as T increases. This gives rise to the problem of time‐optimal‐controllability and the correlation to the problem of minimum norm controllability.It is shown that the time‐optimal control is characterized by a weak “bang‐bang” principle.
Distribution of resistive body‐force in curved free‐surface flow
Authors: Sivakumaran N. S. , Dressler R. F. , Brosowski B. 
Published: March 2007

AbstractThe customary procedure for including resistive effects in turbulent hydraulic and stratified atmospheric flows is to integrate the empirically‐known boundary shears over the entire wetted boundary of a thin fluid slab. A resistive body‐force is then assumed to exist everywhere in each slab to replace the boundary shearing force. For the classical Saint‐Venant model, this body‐force can be shown to have a constant distribution in the vertical direction, and therefore can be evaluated for use in the momentum differential equation. In the newer Dressler theory, however, for unsteady flow over curved beds, it is proved here that a constant body‐force distribution is not possible. We determine its variable distribution and its magnitude for use in the curved‐flow equations. This vasriable distribution acts to produce an equal resultant in every thin layer of fluid parallel to the bed in an angular wedge over the curved channel bed. The new curved‐flow equations are therefore extended to include resistive effects.
Local existence of solutions of the vlasov‐maxwell equations and convergence to the vlasov‐poisson equations for infinite light velocity
Authors: Degond P. , Neunzert H. 
Published: March 2007

AbstractWe prove the local existence of smooth solutions for the Vlasov‐Maxwell equations in three space variables. The existence time for such solutions is independent of the light velocity c. Then we derive regularity results for both the Vlasov‐Poisson and the Vlasov‐Maxwell equations. The last part of the paper is devoted to a proof of weak and strong convergence of the Vlasov‐Maxwell equations towards the Vlasov‐Poisson equations, when the light velocity c goes to infinity.
Stationary, oscillatory and solitary wave type solution of singular nonlinear schrödinger equations
Authors: Brüll L. , Lange H. , de Jager E. 
Published: March 2007

AbstractIt is proven that for a certain class of singular nonlinear Schrödinger equations there exist stationary ground state and oscillatory solutions. Furthermore the existence of those solitary wave type solutions is considered which do not necessarely vanish at infinity. The results are applied to problems from plasma physics; to superfluid films, and to the Heisenberg ferromagnet spin chain.
On an iterative method for a class of integral equations of the first kind
Authors: Mülthei H. N. , Schorr B. , Törnig W. 
Published: March 2007

AbstractIn this paper, we investigate an iterative method which has been proposed [1] for the numerical solution of a special class of integral equations of the first kind, where one of the essential assumptions is the positivity of the kernel and the given right‐hand side. Integral equations of this special type occur in experimental physics, astronomy, medical tomography and other fields where density functions cannot be measured directly, but are related to observable functions via integral equations. In order to take into account the non‐negativity of density functions, the proposed iterative scheme was defined in such a way that only non‐negative solutions can be approximated. The first part of the paper presents a motivation for the iterative method and discusses its convergence. In particular, it is shown that there is a connection between the iterative scheme and a certain concave functional associated with integral equations of this type. This functional can be interpreted as a generalization of the log‐likelihood function of a model from emission tomography. The second part of the paper investigates the convergence properties of the discrete analogue of the iterative method associated with the discretized equation. Sufficient conditions for local convergence are given; and it is shown that, in general, convergence is very slow. Two numerical examples are presented.
Stationary solutions of the vlasov‐fokker‐planck equation
Authors: Dressler K. , Neunzert H. 
Published: March 2007

AbstractWe study stationary solutions of the Vlasov‐Fokker‐Planck Equation, a modification of the Vlasov‐Poisson Equation, obtained by adding a diffusion term with respect to velocity. From a physical point of view it describes a plasma in thermal equilibrium.We prove existence of stationary solutions; for the mollified equation even an existence‐ and uniqueness theorem holds for sufficiently high temperature.
Zu einigen mathematischen problemen in der theorie der transonischen strömung
Authors: Kozel K. , Polášek J. , Meister E. 
Published: March 2007

AbstractThe work deals with a definition of a weak solution of steady plane transonic flows past a thin profile, with the properties of the solution across a shock wave, and with a derivation of a conservative difference scheme suitable for numerical solution of the above mentioned problem by a finite difference method. The work presents several examples of numerical solution of transonic flows past a profile, through a plane cascade and some three‐dimensional results. The numerical results presented are compared with experimental results or with numerical results by other authors.
Sur l'Analyse Numérique des Equations de Hamilton‐Jacobi‐Bellman
Authors: Cortey‐Dumont Ph. , Nedelec J. C. 
Published: March 2007

AbstractWe show the convergence in the L∞ norm of the approximation by finite element of the Hamilton‐Jacobi‐Bellman equation.
equation image
The proof uses the subsolution's method and the notion of discret regularity. Since the submission, the optimal result has been obtained.
A free boundary problem and stability for the circular plate
Authors: Miersemann E. , Mittelmann H. D. , Törnig W. 
Published: March 2007

AbstractIn the recent paper [6] we have answered the question of stability for the nonlinear beam which is being axially compressed by a force greater than the critical value and contacts a plane obstacle. The basic idea that was first used in a numerical solution and subsequently in the mathematical analysis was to consider the free boundary problem in the interval in which the beam is not in contact with the obstacle. In this work we consider the analogous problem for the linear circular plate. Numerical computations are crucial here to establish conditions essential for the problem of stability and they also yield the critical parameter values, i.e., the secondary bifurcation points.
Optimization models for the force and energy in competitive sports
Authors: Behncke Horst , Brosowski B. 
Published: March 2007

AbstractA general optimal control model for running and swimming is developed, whose principal parameters are the energy reserves, the breathing rate and the force. This model is then applied to the world records in these disciplines. It describes the data very well and the parameters employed have values, which agree closely with those obtained by other means.
Time optimal boundary controllability of a simple linear viscoelastic liquid
Authors: Leugering G. , Hagedorn P. 
Published: March 2007

AbstractA viscoelastic liquid confined between two parallel plates is considered under the action of L2 (O, T)‐boundary controls. Applying Laplace‐Transform‐techniques it is shown that L2 (O, l)‐states are exactly controllable in finite time, depending on the speed of propagation of singularities. Finally the existence of time‐optimal controls respecting a given norm bound is shown.
Diffraction d'une Onde Acoustique par une Paroi Absorbante: Nouvelles Equations Intégrales
Authors: Bamberger A. , Ha Duong T. , Nedelec J. C. 
Published: March 2007

AbstractWe present here a new formulation of the exterior Robin problem of the reduced wave equation, using boundary integrals with the jumps of the function and its normal derivative as variables. Our system of integral equations present an important advantage for any numerical purpose: it can be transformed in a variational problem where the sesqui‐linear form is coercive and is exempt of hyper singular integrals.
Über das homogene Dirichlet‐Problem bei nichtlinearen partiellen Differentialgleichungen vom Typ der Boussinesq‐Gleichung
Authors: Warnecke G. , Hsiao G. C. 
Published: March 2007

AbstractSemilinear equations of Boussinesq type, e.g. utt + uxx − uxxxx + (u2)xx = 0, utt + uxx − uxxxx + uxuxx = 0, or certain equations containing the squared wave operator, e.g. uxxtt − uk = 0, k ϵ N k ≥ 2, are studied. A generalized boundary value problem on bounded domains can be treated using Hilbert space methods. The linear parts of these equations are not elliptic, the latter not even hypoelliptic. A mountain pass lemma is used to prove the existence of nontrivial weak solutions. These solutions are obtained in anisotropic Sobolev spaces.
Soil parameter identification using a genetic algorithm
Authors: Levasseur S. , Malécot Y. , Boulon M. , Flavigny E. 
Published: March 2007

AbstractThis paper is dedicated to the identification of constitutive parameters of the Mohr–Coulomb constitutive model from in situ geotechnical measurements. A pressuremeter curve and the horizontal displacements of a sheet pile wall retaining an excavation are successively used as measurements. Two kinds of optimization algorithms are used to minimize the error function, the first one based on a gradient method and the second one based on a genetic algorithm. The efficiency of each algorithm related to the error function topology is discussed. Finally, it is shown that the use of a genetic algorithm to identify the soil parameters seems particularly suitable when the topology of the error function is
complex. Copyright © 2007 John Wiley & Sons, Ltd.