bluuebunny/crossref_metadata_2025_split huggingface dataset:
Mood stability during acute stimulator challenge in Parkinson's disease patients under long‐term treatment with subthalamic deep brain stimulation
Authors: Berney Alexandre , Panisset Michel , Sadikot Abbas F. , Ptito Alain , Dagher Alain , Fraraccio Maria , Savard Ghislaine , Pell Marc , Benkelfat Chawki 
Published: March 2007

AbstractAcute and chronic behavioral effects of subthalamic stimulation (STN‐DBS) for Parkinson's disease (PD) are reported in the literature. As the technique is relatively new, few systematic studies on the behavioral effects in long‐term treated patients are available. To further study the putative effects of STN‐DBS on mood and emotional processing, 15 consecutive PD patients under STN‐DBS for at least 1 year, were tested ON and OFF stimulation while on or off medication, with instruments sensitive to short‐term changes in mood and in emotional discrimination. After acute changes in experimental conditions, mood core dimensions (depression, elation, anxiety) and emotion discrimination processing remained remarkably stable, in the face of significant motor changes. Acute stimulator challenge in long‐term STN‐DBS–treated PD patients does not appear to provoke clinically relevant mood effects. © 2007 Movement Disorder Society
Lösung von Randwertproblemen der Schwingungsgleichung für ein Modell eines Triebwerkeinlaufs
Authors: Friedrich N. , Meister E 
Published: March 2007

AbstractWe consider a simple model of a jet engine inlet consisting of two coaxial cylinders. The inner cylinder extends in both directions to infinity and represents the hub of a jet engine. The outer cylinder is assumed to be semiinfinite representing the engine's jacket. This arrangement is approached by a compressible and invisced gas moving at a velocity U less than the speed of sound. Two problems are formulated. In problem A a normal speed distribution is given in the compressor‐inlet plane, in problem B we are given a pressure distribution. We look for the induced pressure and velocity fields. Using the acoustical approximation of the fundamental equations the Wiener‐Hopf‐method is applied then leading, after a multiplicative and additive decomposition procedure, to an infinite system of linear equations. These involve the expansion coefficients of the solution with respect to the eigenfunctions of the concentric cylindrical duct. Applying arguements from perturbation theory it is possible to extract the essential information from this system of equations. Apart from the possible exception of a denumerable set of values of the distance L of the blade‐row from the inlet the problem has a unique solution.
Asymptotic expansions for central limit theorems for general linear stochastic processes. I: General theorems on rates of convergence
Authors: Butzer P. L. , Gather U. , Törnig W. 
Published: March 2007

AbstractThis paper deals with so‐called general linear stochastic processes (GLSP), defined by T. Kawata in 1972 in generalization of work of R. Lugannani and J. B. Thomas of 1967/71. These second order processes (which are not necessarily stationary nor have independent increments) are described by rather weak requirements, so that several processes such as some random noise and pulse train processes are specific models of these GLSP. Part I is concerned with two general theorems giving asymptotic expansions (including those for the density function) in the central limit theorem for such GLSP, together with error rates. The assumptions for the corresponding θ– ando–error estimates seem rather natural: in the former, apart from assumptions on the inherent structure of such GLSP, the existence of certain moments of higher order as well as a Cramer‐type condition are assumed, in the latter in addition a Lindeberg‐type condition of higher order. Fourier analytic machinery is used for the proofs.
Conform and mixed finite element schemes for the Dirichlet problem for the Bilaplacian in plane domains with corners
Authors: Stephan E. , Meister E. 
Published: March 2007

AbstractIn plane domains with corners for the Bilaplacian a uniquely solvable conform variational principle is studied on weighted Sobolev spaces which is equivalent to the standard Dirichlet problem in the weak form. Clamped plates under point forces near corners are handled by this approach. With weighted Hsieh‐Clough‐Tocher elements on regular triangulations as conform C1‐finite elements a new error analysis is performed without higher regularity assumptions on the exact solution than given by the data and the boundary. The rate of convergence of the error depends on the eigenvalue with smallest imaginary part of a clamped infinite wedge since this eigenvalue describes the singularity of the exact solution in a sector with same angle. Using different spaces of trial and test functions in the standard Galerkin procedure it is shown that the error in the weighted energy norm does not pollute. For convex corners asymptotic error estimates, are proved yielding convergence for a mixed method in hydrodynamics where the solution of a system of 2nd order and its Laplacian are approximated simultaneously by C0‐finite elements being piecewise polynomials.
Über eine Verallgemeinerung des Begriffs „Charakteristik”︁ bei partiellen Differentialgleichungen erster Ordnung
Authors: Wick J. , Neunzert H. 
Published: March 2007

AbstractAs, in general, the projections of characteristics into the x‐space intersect for finite values of t, the global solution of a conservation law

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cannot be determined from the characteristic system of the equation,

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is considered. Only in the linear case, this equation coincides with the equation of the projections of characteristics. For convex h and all x0 this equation has a solution almost everywhere, and the properties of this solution permit to construct a global solution of the conservation law using strips, in the same way as this is done for linear problems by the method of characteristics.
Exotische Lösungen des Bénardschen Problems
Authors: Kirchgässner K. 
Published: March 2007

AbstractA bifurcation analysis is given for the generalized Bénard problem near the critical value of the Grashoff number. In contrast to earlier investigations where symmetry arguments were used to reduce the boundary‐value‐problem to a simple‐eigenvalue‐bifurcation, we only require double periodicity and treat high multiplicity bifurcation. It is shown that solutions of a yet unknown type exist.
Separation of variables and commuting operators
Authors: Hainzl J. , Kirchgässner K. 
Published: March 2007

AbstractFor any differential operator L, separable in some coordinate system, we construct a set of commuting operators Si such that 1) each Si maps solutions of Lu = 0 into solutions, and 2) the separated solutions of Lu = 0 are simultaneous eigenfunctions of Si. Moreover, a certain description of the separable coordinate system by Si is possible. The paper generalizes results obtained by W. Miller and others on many equations of mathematical physics.
On the time‐dependent Nernst‐Planck equations
Authors: Lange H. , Kirchgässner K. 
Published: March 2007

AbstractFor the one‐dimensional Nernst‐Planck equations of the theory of ion‐transport in thin layers or membranes which mathematically represent a nonlinear coupled parabolic integro‐differential system some global existence and uniqueness theorems for inner and outer problems are given using a priori estimates of the maximum principle type.
An existence theorem for the unmodified Vlasov Equation
Authors: Illner R. , Neunzert H. 
Published: March 2007

AbstractThe initial value problem for the modified Vlasov equation with a mollification parameter δ > 0, as introduced by Batt, has a unique global solution in the weak sense whenever f0 ε L1 and f0 ≧ 0 λ‐a.e. Assuming boundedness of f0 and boundedness of the kinetic energy, it is shown that, as δ → 0, there are subsequences δn → 0 such that the corresponding solutions converge weakly in the measure‐theoretical sense. The limits are shown to be global weak solutions of the initial value problem for Vlasov's equation, and these solutions are seen to be weakly continuous with respect to t. For the plasma physical case, boundedness of the kinetic energy is a consequence of energy conservation.
Solutions for systems of nonlinear elliptic equations with nonlinear boundary conditions
Authors: Rothe F. , Hadeler K. P. 
Published: March 2007

AbstractWe look for solutions of systems of nonlinear elliptic equations with nonlinear boundary conditions and values in some compact convex set M. If the nonlinear terms satisfy a sign condition on the boundary of M and the inhomogeneous terms assume their values in this set existence of solutions is proved.The proof is based on the homotopy invariance of the Leray‐Schauder degree and Weinberger's strong maximum principle.
On the bifurcation diagram of discrete analogues for ordinary bifurcation problems
Authors: Bohl E. , Kirchgässner K. 
Published: March 2007

AbstractOrdinary bifurcation problems of the form (1) typically have at most one nontrivial, nonnegative solution for λ > 0. The paper shows that this is in general not true for discrete analogues to (1) no matter how small the step width h > 0 is chosen.
Asymptotic study of the macroscopic behaviour of a solid‐fluid mixture
Authors: Sanchez‐Hubert J. , Eckhaus W. 
Published: March 2007

AbstractIn the framework of homogenization theory we study a mixture of an elastic solid and a viscous compressible fluid with periodic structure and its limit behaviour as the period tends to zero Existence, uniqueness and convergence theorems are given. The limit behaviour is viscoelastic.
Existence and uniqueness of solutions of quasilinear transmission problems of both elliptic and pseudoparabolic type simulating oxygen transport in capillary and tissue
Authors: Großmann U. , Brosowski B. 
Published: March 2007

AbstractQuasilinear transmission problems of both the elliptic and pseudoparabolic type with differential operators in divergence form simulating oxygen transport in capillary and tissue are investigated. Using recent methods of the theory of pseudomonotone operators and singular perturbations (elliptic regularization) the existence of weak solutions for both problems has been proven. Moreover, the weak solution of the elliptic problem proves to be a solution in the classical sense. Finally, at most one classical solution of a slightly modified pseudoparabolic problem exists.
Scattering by moving bodies: The quasi stationary approximation
Authors: Cooper J. , Wilcox C. H. 
Published: March 2007

AbstractThe scattered field produced by a rotating or vibrating object in the presence of a time harmonic plane wave is usually approximated by a time dependent sequence of stationary fields, called a quasi stationary field. Recently the mathematical theory of scattering of scalar fields of Lax and Phillips has been extended to cover moving bodies. Within this framework the quasi stationary approximation is shown to be valid in each sphere of finite radius which contains the body. Far fields for the exact field and the quasi stationary field are defined and the difference is estimated in terms of a small parameter.
A finite element method for the double‐layer potential solutions of the Neumann exterior problem
Authors: Duong Tuong Ha , Nedelec J. C. 
Published: March 2007

AbstractA variational formulation for the integral equation used for the double layer potential solution of the Neumann exterior problem in the Laplace equation was proposed in [4]. This formulation allows the use of a finite element method which we describe and experiment here.
Convergence of semigroups with an application to the carleman equation
Authors: Kaper H. G. , Leaf G. K. , Reich S. , Gilbert R. T. 
Published: March 2007

AbstractWe present a simple proof of a convergence result for nonlinear semigroups which can be applied to obtain the fluid dynamical limit of Carleman's equation. In addition, we explicitly identify a closed exponential generator of the limit semigroup. Our results are closely related to those of T. G. Kurtz and H. P. McKean.
Die Lösung der Prae‐Maxwellschen Gleichungen mit Hilfe vollständiger Lösungssysteme
Authors: Hermann P. , Kersten H. , Leis R. 
Published: March 2007

AbstractThis paper deals with the Neumann problem of the pre‐Maxwell partial differential equations

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for a vector field v defined in a region G ⊂ R3. We approximate its uniquely determined solution (integrability conditions assumed) uniformly on G by explicitly computable particular integrals and linear combinations of vector fields with a “fundamental” sequence of points .
Zur numerischen Lösung gewöhnlicher Differential‐gleichungen mit Splines in einem Sonderfall
Authors: Mülthei H. N. , Leis R. 
Published: March 2007

AbstractIn an earlier paper [1] a general procedure has been presented to obtain polynomial spline approximations for the solution of the initial value problem for ordinary differential equations. In this paper the general procedure is described by an equivalent one step method. Furthermore two convergence theorems are proved for a special case which is not included in the general convergence or divergence theory given in [1].
Eine abstrakte Theorie der Kegel‐ und Segmentbedingungen
Authors: König H. , Loch H. , Leis R. 
Published: March 2007

AbstractWe develop an abstract theory of geometric regularity conditions for subsets of normed linear spaces, of the type which occurs in the theory of Sobolev spaces (cone conditions, …). The theory is to systematize the diversity of existing conditions, to replace complicated conditions by simpler ones, and to clarify the interplay between different conditions. Our main result is a very general decomposition theorem.
On the boundary value problem of the biharmonic operator on domains with angular corners
Authors: Blum H. , Rannacher R. , Leis R. 
Published: March 2007

AbstractThe paper is concerned with boundary singularities of weak solutions of boundary value problems governed by the biharmonic operator. The presence of angular corner points or points at which the type of boundary condition changes in general causes local singularities in the solution. For that case the general theory of V. A. Kondrat'ev provides a priori estimates in weighted Sobolev norms and asymptotic singular representations for the solution which essentially depend on the zeros of certain transcendental functions. The distribution of these zeros will be analysed in detail for the biharmonic operator under several boundary conditions. This leads to sharp a priori estimates in weighted Sobolev norms where the weight function is characterized by the inner angle of the boundary corner. Such estimates for “negative” Sobolev norms are used to analyse also weakly nonlinear perturbations of the biharmonic operator as, for instance, the von Kármán model in plate bending theory and the stream function formulation of the steady state Navier‐Stokes problem. It turns out that here the structure of the corner singularities is essentially the same as in the corresponding linear problem.
On the construction of minimizing sequences for convex functionals with upper and lower bounding functionals
Authors: Smith P. , Roach G. F. 
Published: March 2007

AbstractA method is described for constructing upper and lower bounds for the stationary values of a general class of convex functionals. The method relies of the existence of approximating convex functionals whose Gâteaux derivatives are presumed to have simpler structure than the original. The method is iterative in that convergent sequences of bounds can be constructed. Some applications to the Laplacian operator are included.
On the existence of small‐amplitude optimum hydrofoil propulsion
Authors: Sparenberg J. A. , Thomas E. G. F. , van de Vooren A. I. 
Published: March 2007

AbstractThe trust production by means of a periodic heaving motion of a rigid profile is discussed. It is proved by using Bauer's maximum principle, that when a constraint is put on the magnitude of the amplitude, optimum motions do exist.
An integral equation approximation of the mixed problem for the laplacian in R3
Authors: Baldino R. R. , Nedelec J. C. 
Published: March 2007

AbstractAn integral representation for the solutions of the interior and exterior homogeneous mixed problems on a regular bounded open set in R3 is given in terms of a potential of simple layer on the Dirichlet data and of double layer on the Neumann data. A coercive non‐symmetric bilinear form is provided. Singular finite elements containing the first terms of the assymptotic expansion of the singularity are built and error estimates for the surface distributions are given.
Stability and instability of the energy dependent diffusion system in reactor dynamics
Authors: Pao C. V. , Meister E. 
Published: March 2007

AbstractThe purpose of this paper is to give a systematic analysis for the linear energy dependent diffusion system in reactor dynamics, taking into consideration of delayed neutrons. This analysis includes the existence of a unique positive solution for the time dependent system, the asymptotic behaviour of the solution as t → ∞, the stability and instability of steady‐state solutions, and the existence and uniqueness of a steady‐state solution for the time‐independent system. Using the notion of upper and lower solution, we establish some threshold conditions for insuring the asymptotic behaviour of the solution and the stability and the instability of any given unperturbed solution, including steady‐state solution. In fact, these conditions characterize the stability and the instability property of the solution, and yield a bifurcation result in terms of either the size of the diffusion domain or the physical parameters of the diffusion medium. We also discuss the case without the effect of delayed neutrons.
On the classical solutions of the initial value problem for the unmodified non‐linear vlasov equation II special cases
Authors: Horst E. , Neunzert H. 
Published: March 2007

AbstractThe theory of part I is applied to prove several existence and non‐existence results for special cases. If N = 3, a global classical solution of P° exists, if φ ⩾ 0 has rotational symmetry. If N ⩾ 4, global classical solutions of P° do not always exist.
On complete recovery of geophysical data
Authors: Carroll Robert , Santosa Fadil , Payne L. 
Published: March 2007

AbstractOne considers an elastic halfspace with depth (x1) dependent density Q and Lamé moduli (λ,m̈). Impulsive stresses τli = δ(x2, x3)δ(t) for x1 = 0 are applied with displacement responses ui = gi(t, x2, x3) at x1 = 0 (i = 1, 2, 3). Let vi(t, x1) = ∫∫uidx2dx3 (i = 1, 2 is enough) and set w(t, x1) = ∫∫x2u1dx2dx3. One obtains a system of 3 differential equations for v1, v2, and w to which the spectral techniques of inverse scattering theory are applied as in [25]. The inverse problems for the uncoupled vi can then be solved to produce 2 functions A1 and A2 involving (Q, λ, μ) as functions of “bound” variables y1 and y2 containing (Q, λ, μ), between which a relation then is determined. Analysis of the coupled equation for w then leads to a Fredholm integral equation whose solution provides an additional relation between (Q, λ, μ) from which (Q, λ, μ) can be determined as functions of x1. The integral equation is reduced to a Volterra type equation by results and techniques of transmutation and then solved by a modification of standard techniques. A number of features and results of independent mathematical interest arise from the transmutation theory.
Crank‐nicolsen‐Galerkin approximation for Maxwell's equations
Authors: Hoppe Ronald H. W. , Brosowski B. 
Published: March 2007

AbstractThe Maxwell equations are formulated as an evolution equation in a suitable chosen Hilbert space involving a densely defined closed skew‐Hermitian operator which generates a unitary group. A Crank‐Nicolsen‐Galerkin approximation is then established and convergence is shown by arguments from the theory of approximation of groups of operators.
On the transition from supercritical to subcritical Hopf bifurcations
Authors: Chow Shui.‐Ne E. , White Robert G. , Hadeler K. P. 
Published: March 2007

AbstractBy using the method of averaging, we give a complete Hopf bifurcation diagram when the differential equation has more than one parameter. The method is applied to a system of parabolic equations with nonlinear coupling on the boundary. This set of equations is a mathematical model which describes the normalized concentrations of substances in a solution produced by two enzymes.
Ein gemischtes randwertproblem der kreiszylinderschale mit beliebigen ausschnitten
Authors: Hein J. C. , Meister E. 
Published: March 2007

AbstractThe problem of stress determination in the area of cut‐outs in circular cylindrical shells at given loads is of great interest in industrial practice. This work deals with a mixed boundary value problem of a differential equation derived according to the theory of shallow shells. On partCt1of the boundary, the displacements are given, whereas the stresses are specified on the remaining partCt2. Starting from the Betti‐Maxwell principle and with the aid of the fundamental solutions for unit loads and unit displacements, integral representations can be derived for the displacement functions as well as the stress functions.The problem is then transformed into an equivalent system of Fredholm integral equations of the first kind with logarithmic kernels as the main part. As the integral equations together with the auxiliary conditions form a strongly elliptical system of pseudo‐differential operators, the Galerkin method converges. Assuming that curvesCt1andCt1do not have points of intersection and that the data are sufficiently regular, the required functions are approximated by cubic splines and, for simplicity's sake, the integral equation system is solved by approximation with a collocation method. In view of the complicated terms of the kernel functions, the kernels are split into a regular and a singular part, the regular part being in turn replaced by cubic splines. The remaining integrations are done numerically by means of Gaussian quadrature formulae. The applicability of the method is demonstrated with the example of a cylinder under internal pressure.
Approximation von extremalflächenstücken (hyperbolischen typs) durch charakteristische räumliche vierecke
Authors: Hölder Ernst , Wendland W. 
Published: March 2007

AbstractWe consider solutions z of the Cauchy‐problem for hyperbolic Euler‐Lagrange equations derived from a general Lagrangian f(x, y, z; zx, zy) in two independent variables x, y. z is supposed to be an extremal of the corresponding variational problem. Visualizing z as a surface in R3 we give a geometric interpretation of Lewy's well‐known characteristic approximation scheme for the numerical solution of second order hyperbolic equations by approximating z via a polyhedral construction built up from subunits which consist of two characteristic triangles having one side in common but lying on different planes in R3. Utilizing ideas from Cartan‐geometry one can (in an appropriate sense) introduce the “mean curvature” of these subunits and it is seen that this curvature vanishes (up to terms of higher order). That is a highly plausible result for the polyhedral approximation of “minimal surfaces”.
Ein nichtlineares Glättungsverfahren zur rekonstruktion von flugbahnen aus radardaten
Authors: Mieth H.‐J. , Wendland W. 
Published: March 2007

AbstractData processing is an important tool in airspace surveillance and air traffic control today. In this paper the problem is treated how to reconstruct a flown trajectory from its correlated radar plots subject to a certain knowledge of the aircraft manoeuverability and the radar measurement statistics. A variational approach leads to a generalized smoothing spline method. Simulation results are presented.