bluuebunny/crossref_metadata_2025_split huggingface dataset:
Case of symptomatic propriospinal myoclonus evolving toward acute “myoclonic status”
Authors: Manconi Mauro , Sferrazza Barbara , Iannaccone Sandro , Massimo Antonio , Zucconi Marco , Ferini‐Strambi Luigi 
Published: August 2005

AbstractPropriospinal myoclonus is a rare motor disorder consisting of involuntary spinal‐generated muscular jerks. Here, we report a severe and uncommon case of propriospinal myoclonus that appeared after a vertebral fracture of T11. In this patient, the polysomnographic investigation showed continuing focal myoclonic activity in axial muscles during stable sleep and an acute progression into a myoclonic “status” associated with respiratory failure and loss of consciousness. It is necessary to consider this severe progression and support it with prompt emergency maneuvers and adequate pharmacotherapy. © 2005 Movement Disorder Society
Frequent sequence variation at the ETM2 locus and its association with sporadic essential tremor in Korea
Authors: Kim Jeong‐Hyun , Cho Yoon‐Hee , Kim Jeong‐Kook , Park Yong‐Gou , Chang Jin Woo 
Published: August 2005

AbstractEssential tremor (ET) is the most common but a complex neurological movement disorder. ET usually affects hands, but it may also affect head, neck, face, jaw, tongue, voice, trunk and, rarely, legs and feet. Although two susceptibility loci were identified on chromosome 2p24 (ETM2) and 3q13 (ETM1 or FET1), the exact transcript(s) has not been cloned. We analyzed unrelated Korean individuals with ET for a genetic association with three reported polymorphic loci (STS‐etm1240, STS‐etm1231, and STS‐etm1234) in a candidate region on chromosome 2p24.1. We investigated sequence polymorphisms at these three loci in 30 ET patients and 30 controls using polymerase chain reaction (PCR) amplification followed by sequence analysis. Eight different sequence variants (5 at etm1234, 2 at etm1240, and 1 at etm1231) were detected from 7 patients. Of interest, sequence variants were found only in classic ET patients but not in nonclassic ET patients and healthy individuals. Additionally, we also observed that a decrease in the number of short tandem repeats within etm1234 locus is more frequent in ET patients compared to controls. Our data thus support that ET development would be linked with the ETM2 locus and will facilitate the search for the ETM2 gene transcript. © 2005 Movement Disorder Society
A Hilbert space approach to maximum entropy reconstruction
Authors: Klaus Martin , Smith Robert T. 
Published: August 2005

AbstractWe examine here the problem of reconstructing an X‐ray attenuation function from measurements of its integrals. The approach that is taken is to maximize the difference of the entropy and the residual error in meeting the measurements. The solution of this optimization problem is constrained by requiring that the solution lie in a certain weakly compact subset of L2, to be determined by physical information.We show that the constrained optimization problem is well‐posed: there exists a unique solution (even when the measured data are inconsistent) and the solution depends continuously on the measurements. In the course of proving this, we show that the entropy functional is continuous on L2. We further demonstrate that the solution of the optimization problem for a special case, must be piecewise constant.
Time‐periodic solutions of wave equations on ℝ1 and ℝ3
Authors: Smiley Michael W. 
Published: August 2005

AbstractThe classical Paiey‐Wiener theorem and Hilbert space methods are used to show the existence of time‐periodic solutions of the wave equation wtt−wrr+λw=h, 0 < r < + ∞, which are radially symmetric and have exponential decay as r → + ∞. This problem is obtained when considering a one‐dimensional or three‐dimensional problem, and should be thought of as a linearization of a semilinear problem in which the associated linear operator has point spectrum (− ∞, λ). When λ ⩽ 0 there is uniqueness, otherwise there is a non‐trivial finite‐dimensional null space. Estimates on w, wt, wr are obtained, which show that in either case there is a continuous correspondence h → w, where w is a uniquely characterized solution.
The optimal stability estimate for some ill‐posed Cauchy problems for a parabolic equation
Authors: Knabner Peter , Vessella Sergio 
Published: August 2005

AbstractIn this paper we consider the non‐characteristic Cauchy problem ut−a(x)uxx−b(x)ux−c(x)u = 0, x ∈ (0, l), t ∈ I, u(0, t) = φ(t), ux(0, t) = 0, t ∈ I, where I = ℝ or I = ℝ+ and u(x, 0) = 0, x ∈ [0, l], in the case I = ℝ+. Assuming an a priori bound for ‖u(l,.)‖, we derive the exact Hölder type dependence of on ‖u(x,.)‖ on ‖φ‖.
On the principles of limiting absorption and limit amplitude for a class of locally perturbed waveguides. Part 2: Time‐dependent theory
Authors: Morgenröther K. , Werner P. 
Published: August 2005

AbstractIn part 1Math. meth. in the Appl. Sci, 10, 125–144 (1988).
we studied the principle of limiting absorption for local perturbations Ω of the n‐dimensional domain Ω0 = ℝn−1 × (0, π). In this second part we extend our investigations to the time‐dependent theory and show that absence of admissible standing waves implies the validity of the principle of limiting amplitude for every frequency ω≥0 if n ≠ 3 and for ω ≠ 2, 3,… if n = 3, respectively. In particular, the principle of limiting amplitude holds for every ω≥0 in the case n ≠ 3 and for every ω ≠ 2, 3,… in the case n = 3 if Ω≠Ω0 and ν·x′ ⩽0 on ∂Ω, where x′ = (x1,…, xn−1, 0) and ν is the normal unit vector on ∂Ω pointing into the complement of Ω This result stands in remarkable contrast to the fact that both principles are violated in the case of the unperturbed domain Ω0 at the frequencies ω = 1, 2,… if n⩽3. The question of the asymptotic behaviour of the solution as t→∞ for n = 3 and ω = 2, 3,… will be discussed in two subsequent papers.
A free boundary problem of biological interest
Authors: Colli Pierluigi , Visintin Augusto , Hadeler K. P. 
Published: August 2005

AbstractDuring fertilization of certain echinoderms, a long actin‐filled tube is extended by the sperm towards the interior of the egg. This yields a parabolic free boundary problem, which differs from the classical one‐phase Stefan problem by the presence of a convective term in the partial differential equation, and because the equilibrium interface condition θ(s(t),t) = 0 is here replaced by a kinetic law s′(t) = vθ(s(t),t). This problem is set in variational form and the existence of a solution is proved by means of a Faedo–Galerkin approximation procedure.
Existence and stability of travelling waves in fixed‐bed reactors
Authors: Knöpp Ulrich , Eckhaus W. 
Published: August 2005

AbstractThe model equations of the catalytic fixed‐bed reactor often possess solutions in the form of travelling wave fronts similar to the well‐known case of Fisher's equation. The mathematical investigation of these waves requires searching for solutions of singular boundary value problems in the phase plane or in the three‐dimensional phase space. In this paper necesary and sufficient conditions are derived which are to be satisfied by the model parameters and the propagation velocity of the wave front if wave solutions exist. Moreover, sufficient conditions for the asymptotic stability of these solutions are proved where the perturbations are supposed to belong to a certain weighted L2‐space. Finally, the connection between the initial distribution of the state variable and the velocity of the wave is discussed.
Properties of far‐field operators in acoustic scattering
Authors: Kirsch A. , Hsiao G. C. 
Published: August 2005

AbstractThe far‐field operator for an exterior boundary value problem for the Helmholtz equation maps the boundary data onto the far‐field pattern of the solution. This paper computes the L2‐adjoint of this operator for various choices of boundary conditions. In scattering theory the boundary data are given by the traces of plane waves. We characterize the closure of the span of the images of these plane waves under the far field operator.Finally, the results are extended to more general topologies including Sobolev and Hölder norms.
Duality theorems in some overdetermined boundary value problems
Authors: Payne L. E. , Schaefer Philip W. 
Published: August 2005

AbstractWe consider several elliptic boundary value problems for which there is an overspecification of data on the boundary of the domain. After reformulating the problems in an equivalent integral form, we use the alternate integral formulation to deduce that if a solution exists, then the domain must be an N‐ball. Various Green's functions and classical boundary value problems of second, fourth and higher order are included among the problems considered here.
A constructive method for solving the displacement boundary‐value problem of elastostatics by use of global basis systems
Authors: Freeden Willi , Reuter Richard 
Published: August 2005

AbstractIn this paper we are concerned with the three‐dimensional homogeneous isotropic elastostatic boundary‐value problem. Global basis vector fields are shown to be constructive structures for approximating the solution. The theoretical tool is a regularity condition developed from the classical integral equation approach. The paper ends with some reflections on the practical computability and numerical applicability.
Continuous dependence on data for solutions of a conducting dusty gas model backwards in time
Authors: Calmelet‐Eluhu Colette , Crooke Philip 
Published: August 2005

AbstractA conducting dusty gas flow in the presence of a given applied magnetic field is modelled by an initial boundary value problem. The continuous dependence of solutions backward in time to this model is studied. The electric and induced magnetic fields are assumed to be negligible and the dust particles are non‐conducting. A uniqueness result is also derived.
Regularity of mixed boundary value problems in ℝ3and boundary element methods on graded meshes
Authors: Von Petersdorff T. , Stephan E. P. 
Published: August 2005

AbstractThe solution of the three‐dimensional mixed boundary value problem for the Laplacian in a polyhedral domain has special singular forms at corners and edges. A ‘tensor‐product’ decomposition of those singular forms along the edges is derived. We present a strongly elliptic system of boundary integral equations which is equivalent to the mixed boundary value problem. Regularity results for the solution of this system of integral equations are given which allow us to analyse the influence of graded meshes on the rate of convergence of the corresponding boundary element Galerkin solutions. We show that it suffices to refine the mesh only towards the edges of the surfaces to regain the optimal rate of convergence.
A remark on the regularity of solutions of Maxwell's equations on Lipschitz domains
Authors: Costabel Martin 
Published: August 2005

AbstractLet u be a vector field on a bounded Lipschitz domain in ℝ3, and let u together with its divergence and curl be square integrable. If either the normal or the tangential component of u is square integrable over the boundary, then u belongs to the Sobolev space H1/2 on the domain. This result gives a simple explanation for known results on the compact embedding of the space of solutions of Maxwell's equations on Lipschitz domains into L2.
Non‐linear flexings in a periodically forced floating beam
Authors: Lazer A. C. , McKenna P. J. 
Published: August 2005

AbstractThis paper considers periodic flexing in a floating beam, in the presence of a small periodic forcing term. The beam is considered as a vibrating beam with the free‐end boundary condition, in the presence of an additional restoring force due to flotation, which becomes zero as soon as the beam lifts out of the water. The equation is therefore non‐linear. A theorem is proved which shows that in the presence of small periodic forcing terms, both small‐ and large‐amplitude solutions can exist. Numerical evidence is presented, which shows that the large‐amplitude solutions are stable over a wide range of frequency and amplitude, and suggests a cusp‐like surface for the multiple solutions.
A half‐space problem for a non‐linear Boltzmann equation arising in semiconductor statistics
Authors: Poupaud F. 
Published: August 2005

AbstractIn semiconductors the distributions of electrons satisfy a non‐linear Boltzmann–Vlasov equation. We consider the half‐space problem arising in the study of boundary layers when the mean free path tends to zero. We prove the existence and the uniqueness of the solution for any prescribed entering distribution. We establish that this solution tends towards a Fermi–Dirac distribution exponentially fast.
An artificial boundary condition for an advection–diffusion equation
Authors: Lohéac Jean‐Pierre 
Published: August 2005

AbstractConsider the advection–diffusion equation: u1 + aux1 − vδu = 0 in ℝn × ℝ+ with initial data u0; the Support of u0 is contained in ℝ(x1 < 0) and a: ℝn → ℝ is positive. In order to approximate the full space solution by the solution of a problem in ℝ × ℝ+, we propose the artificial boundary condition: u1 + aux1 = 0 on ∑. We study this by means of a transmission problem: the error is an O(v2) for small values of the viscosity v.
Resonances in periodic media
Authors: Werner P. 
Published: August 2005

AbstractWe study the propagation of linear acoustic waves (a) in an infinite string with a periodic material distribution, (b) in an infinite cylinder with a meterial distribution that is periodic in the longitudinal direction and does not depend on the transverse coordinates. We assume that the wave field is generated by a time‐harmonic force distribution of frequency ω acting in a compact set. We show in both cases that resonances of order t1/2 occur for a discrete set of frequencies and that the solution is bounded as t→∞ for the remaining frequencies. In case (a) ω is a resonance frequency if and only if ω2 is a boundary point of one of the spectral bands of the corresponding spatial differential operator of Hill's type. A similar characterization of the resonance frequencies is given in case (b).
Differential stability of solutions to parametric optimization problems
Authors: Rao Murali , Sokolowski Jan 
Published: August 2005

AbstractA method for the differential stability of solutions to a class of solutions to a class of parametric optimization problem is prposed. Any solution of the parametric optimization problem is given as a fixed point of the metric projection onto the set of admissible coefficients. A new result on the differential stability of the metric projection in Sobolev space H2(Ω)onto a set of admissible parameters is obtained. The stability results with respect to perturbations of observations for the solutions to a coefficient estimation problem for a second‐order elliptic equation are derived.
Charge transport in semiconductors with degeneracy effects
Authors: Poupaud Frédéric , Schmeiser Christian 
Published: August 2005

AbstractIt has been a common procedure to derive a model for charge transport in degenerate semiconductor material by incorporating a Fermi–Dirac distribution into the classical drift–diffusion model. In this work a Boltzmann equation with a non‐linear collision term is considered. A new fluid dynamical model is derived by considering small perturbations of the thermal equilibrium. The analysis contains an existence and uniqueness proof for the Boltzmann equation, a justification of the perturbation argument and a study of initial boundary value problems for the new fluid dynamical model.
On a class of ill‐posed non‐linear integral equations arising in the interpretation of indirect measurements
Authors: Hofmann Bernd 
Published: August 2005

AbstractIn this paper we consider a class of specific Urysohn integral equations for which the solutions are only determined with the exception of rearrangements of function values and associated arguments. As an alternative to Tikhonov's regularization method approximating minimum‐norm solutions for this ill‐posed class of inverse problems, a constrained least‐squares approach is presented. This approach is aimed at finding decreasing rearrangements serving as appropriate solution representatives. It is shown that the inverses of these decresing solutions solve a Fredholm linear integral equation of the first kind.
On the linear piezoelectricity of composite materials
Authors: Turbé N. , Maugin G. A. 
Published: August 2005

AbstractFrom the equations of the linear piezoelectricity for a composite material with a periodic structure we derive the dynamical solution by means of Bloch expansion techniques. This expression techniques. This expression allows, as a limit case, a comparison with the homogenization method, and the macroscopic coefficients are also deduced.
Time decay of solutions of semilinear strongly damped generalized wave equations
Authors: Biler Piotr 
Published: August 2005

AbstractWe study the asymptotic behaviour in time of the solutions of dissipative perturbations of wave‐type equations in ℝN, utt + But + Au + G(u) = 0, with commuting positive operators A, B and a power like non‐linearity G(u). First we give some (pseudo) conformal invariants of the linear operator in the equation. This allows us to derive optimal decay rates for the solutions of the linearized problems. We then prove some decay estimates for the non‐linear problems using the tools of scattering theory and the aforementioned conformal invariants.
Generalized limiting absorption method and multidimensional inverse scattering theory
Authors: Weder Ricardo 
Published: August 2005

AbstractWe generalize the classical limiting absorption method. This generalization is applied to the study of the Faddeev–Lippmann–Schwinger equations in the Faddeev–Newton approach to multidimensional inverse scattering theory. In particular, we give a new proof, under more general conditions than were known previously, of the absence of exceptional points for small potentials and large values of the parameters, and on the existence of real exceptional points if there are complex ones, in particular for potentials that produce negative eigenvalues.
Wiener‐hopf equations for waves scattered by a system of parallel sommerfeld half‐planes
Authors: Meister E. , Rottbrand K. 
Published: August 2005

AbstractA scalar time‐harmonic wave (governed by Helmholtz's equation) impinges on N semi‐infinite half‐planes. The scattered field is sought when first, second, and third‐kind boundary conditions or even general linear transmission conditions on the plates ∑m and their complementary parts ∑ are prescribed. Making use of the Fourier transform a representation formula for H1 (Ω) solutions is presented. The boundary/transmission problem is shown to be equivalent to a (2N × 2N)‐Wiener–Hopf (WH) system for jumps of the Dirichlet–and Neumann–Cauchy data across the semi‐infinite screens ∑m. The (2N × 2N)‐Fourier symbol matrix 𝔖𝒫 contains N block matrices on the diagonal corresponding to Sommerfeld boundary/transmission problems for a single plate. These (2 × 2)‐symbol matrices are factorizable and thus the full WH system is invertible by a perturbation argument for not too small spacings of neighbouring screens ∑m.
On mathematical modelling of absorption and dispersion of seismic waves for low frequencies
Authors: Von Wolfersdorf L. , Rost L. 
Published: August 2005

AbstractThe problem of determining the dispersion and absorption of plane seismic waves by a given seismic quality factor is dealt with in the case that the quality factor tends to a positive limit as the frequency goes to zero.General formulae are derived for the phase velocity and the attenuation coefficient by solving the corresponding Riemann–Hilbert problems for analytic functions in the upper half‐plane.
Green's contact functions for heat conduction of two half‐spaces and half‐planes with application to several boundary contact problems
Authors: Jentsch Lothar 
Published: August 2005

AbstractGreen's contact functions are constructed for two half‐spaces and two half‐planes for materials with different thermal conductivities. With the aid of these contact functions some bimetal problems are reduced to boundary integral equations along the outer boundary where only the boundary conditions are to be satisfied. The boundary integral operators are investigated in the plane case. They are Fredholm operators with index zero. The asymptotics of the density of the potentials, which depends on the material parameters and on the angles between the contact line and the outer boundary, is determined by the Mellin transform technique.
Time delay and finite differences for the non‐stationary non‐linear Navier–Stokes equations
Authors: Varnhorn Werner 
Published: August 2005

AbstractIn the present paper we use a time delay ϵ > 0 for an energy conserving approximation of the non‐linear term of the non‐stationary Navier–Stokes equations. We prove that the corresponding initial‐value problem (Nϵ) in smoothly bounded domains G ⊆ ℝ3 is well‐posed. We study a semidiscretized difference scheme for (Nϵ) and prove convergence to optimal order in the Sobolev space H2(G). Passing to the limit ϵ→0 we show that the sequence of stabilized solutions has an accumulation point such that it solves the Navier–Stokes problem (No) in a weak sense (Hopf).
Global solution to the Cauchy problem in non‐linear hyperbolic thermoelasticity
Authors: Gawinecki Jerzy 
Published: August 2005

AbstractWe prove the existence of global solutions for small data to the initial value problem for the non‐linear hyperbolic system of partial differential equations describing a thermoelastic medium in a three‐dimensional space under the assumption that the coefficients in the non‐linear terms are smooth functions of their arguments and behave like 0(∣η∣) for k0 ≥ 2 near the origin. The asymptotic behaviour of the solution as t → ∞ is also described.
Regularized inner products of distorted plane waves and near‐forward inverse scattering
Authors: Kurylev Yaroslav V. 
Published: August 2005

AbstractRegularized inner products, r(s, e1, e2,) of the distorted plane waves fór the plasma wave equation uu − Δu + qu = 0 are introduced for potentials with compact support. The regularized inner product may be represented in terms of the far‐field pattern. The use of the WKB approximation shows that the behaviour of r as e2 → − e1 is closely related to the Radon transform of q. This observation indicates the possibility of finding the Radon transform of q in terms of r(s, e1, e2) and then of recovering q by means of the inverse Radon transform.
An extended equivariant branching theory
Authors: Allgower Eugene L. , Böhmer Klaus , Zhen Mei 
Published: August 2005

AbstractRecent monographs and research articles have demonstrated that the highly complicated bifurcation structure, which usually arises in the presence of high symmetries, can often be systematically reduced with group theoretic concepts. Equivariant branching theorems and bifurcation subgroups have been the principle tools in this direction of investigation. The generalizations that we give allow the discussions of new classes of problems and the weakening of the usual hypotheses of absolute irreducibility of the group representation or of the appropriate subspaces. These extensions are illustrated in the case of a class of planar semilinear elliptic partial differential equations, which are usually treated as model problems in fluid mechanics and chemical reactions.
On the fundamental solutions of the operators of S. Timoshenko and R. D. Mindlin
Authors: Ortner Norbert , Wagner Peter 
Published: August 2005

AbstractOur recent paper about some new fundamental solutions is complemented by a representation of the fundamental solution of certain evolution operators of fourth order in terms of a family of fundamental solutions of operators of second order. By applying this to the operators of vibrating beams and plates we deduce representations of their fundamental solutions as simple definite integrals over tabulated functions.