bluuebunny/crossref_metadata_2025 huggingface dataset:
Regular boundary integral solution with dual and complementary variational formulations applied to two‐dimensional Laplace problems
Authors: Sun Y. , Kagawa Y.
Published: August 2005

Regular boundary integral elements are employed for the dual and complementary variational formulations of Laplace problems. The problems are defined only on the boundary as usual, but as in the manner of charge simulation method (CSM), the source terms are arranged outside the domain so that the singular integral can be avoided. The Laplace problems are analysed and the usefulness of the formulation is discussed in comparison with direct BEM. The scalar potential and electric displacement vector potential functions are used in the dual and complementary formulations, with which the upper and lower bounds of the system energy or the capacitance can also accurately be evaluated.
A frequency‐independent circuit model of a conductor under surge conditions
Authors: Davies A. E. , Tong Y. K. , Lewin P. L. , German D. M.
Published: August 2005

This paper presents a circuit‐based model of a current carrying conductor that can provide instantaneous ohmic losses under surge conditions. The model is frequency independent and can be used to calculate transient current characteristics of surges on overhead transmission lines. The theoretical current distribution under lightning surge conditions is used to demonstrate the validity of the model and the results are compared with values obtained using a finite element analysis package. There is a good correlation between the two methods with the circuit‐based model having the advantages of being less cumbersome, requiring shorter computation time and being simple to implement in transient analysis packages.
An introduction to PEPSE (‘parallel electromagnetics problem solving environment’): And considerations for parallelization of a finite difference time domain solver
Authors: Perala Rod , Whittle Steve , Hargreaves Martin , Kerton Peter
Published: August 2005

This document describes the background and motivation behind the PEPSE project. It describes separately the components which make up PEPSE, the parallel design philosophy and aspects of parallel implementation.
The approximation of two‐fluid plasma flow with explicit upwind scemes
Authors: Schneider R. , Munz C.‐D.
Published: August 2005

A non‐stationary longitudinal model of a thermal two‐component plasma is investigated with numerical methods based on so‐called high‐resolution schemes. The inhomogeneous model system is solved numerically applying a splitting method, where the homogeneous conservation laws for the electrons and ions are approximated by explicit Godunov‐type schemes. Coupling of both plasma components is achieved by the electric field, which is also calculated in an explicit manner after reformulating Coulomb's law. A new numerical method is proposed for the expansion of the plasma into the vacuum. This tracking method is based on the solution of the vacuum Riemann problem and avoids the difficulties of numerical approximation introduced by the vacuum where the longitudinal plasma model is not valid. This new approach of tracking resolves sharply the plasma vacuum interface and captures this boundary very well during the temporal evolution of the model system. Two test problems show the interplay, the quality and properties of the approximation methods applied.
Efficient modelling of curved surfaces by planar patches and wire grids for electromagnetic scattering
Authors: Heras Fernando Las , Jambrina J. L. Fernández
Published: August 2005

The scattering of conducting regular polyhedrons of resonant size is studied by means of the electrical field integral equation (EFIE) and the method of moments (MoM). Two models are generated for each polyhedron, a wire grid model and a triangular patch model. Two numerical codes associated with those modelling techniques are used to obtain the radar cross section (RCS) of the polyhedrons. The calculated results are compared with the analytical results of the scattering of a perfectly conducting sphere. Practical criteria relating geometric properties of the sphere and the polyhedrons are investigated for the modelling of curved surfaces by facets in electromagnetic simulations.
The climate of Scotland over the last 5000 years inferred from multiproxy peatland records: inter‐site correlations and regional variability
Authors: Langdon Peter G. , Barber Keith E.
Published: August 2005

The mid to late‐Holocene climates of most of Scotland have been reconstructed from seven peat bogs located across north–south and east–west geographical and climatological gradients. The main techniques used for palaeoclimatic reconstruction were plant macrofossil, colorimetric humification, and testate amoebae analyses, which were supported by a radiocarbon‐based chronology, aided by markers such as tephra isochrons and recent rises in pine pollen and in spheroidal carbonaceous particles (SCPs). Field stratigraphy was undertaken at each site in order to show that the changes detected within the peat profiles were replicable. Proxy climate records were reconstructed using detrended correspondence analysis (DCA) of the plant macrofossil data and a mean water table depth transfer function on the testate amoebae data. These reconstructions, coupled with the humification data, were standardised for each site and used to produce a composite record of bog surface wetness (BSW) from each site. The results show coherent wet and dry phases over the last 5000 years and suggest regional differences in climate across Scotland, specifically between northern and southern Scotland. Distinct climatic cycles are identified, all of which record a millennial‐scale periodicity which can be correlated with previously identified marine and ice core Holocene cycles. The key role of the macrofossil remains of Sphagnum imbricatum, a taxon now extinct on many sites, is discussed in relation to the identified climatic shifts. Copyright © 2005 John Wiley & Sons, Ltd.
Sea surface temperature record off central Japan since the Last Glacial Maximum using planktonic foraminiferal Mg/Ca thermometry
Authors: Sagawa Takuya , Toyoda Kazuhiro , Oba Tadamichi
Published: August 2005

We conducted paired measurements of the Mg/Ca ratio and δ18O of planktonic foraminifera, Globigerina bulloides, from a sediment core (MD01‐2420) off central Japan in the northwest Pacific, to reconstruct current movements since the Last Glacial Maximum (LGM). These methods make it possible to determine the magnitude and timing of the sea surface temperature (SST) changes and to reconstruct the variations of the past seawater δ18O (δ18Ow) off central Japan. The amplitude of Mg/Ca‐based SST changes between the Holocene and the LGM was about 10°C. The strong resemblance of the SSTs estimated from both methods, Mg/Ca‐based and δ18O‐based, suggests that the SST changes were caused primarily by latitudinal displacement of the Kuroshio–Oyashio currents and no distinct change in the carbonate dissolution of the core. The southward migration of the water mass was 5–6° in latitude at the LGM. The values for regional δ18Ow changes, which were obtained by subtracting the ice volume contribution from the calculated δ18Ow, describe the millennial‐scale water mass migration over the last 30 kyr. Copyright © 2005 John Wiley & Sons, Ltd.
Control of Helical Sense and Tightness of Amino Acid‐Based Poly(N‐propargylamide) by Temperature and Solvents
Authors: Zhao Haichao , Sanda Fumio , Masuda Toshio
Published: August 2005

Summary: Poly(N‐(α‐tert‐butoxycarbonyl)‐L‐aspartic acid β‐cyclohexyl ester N′‐propargylamide) [poly(1)] was synthesized by the polymerization of the corresponding monomer 1 catalyzed by (nbd)Rh+[η6‐C6H5B−(C6H5)3] in CH2Cl2 at 30 °C for 2 h. Poly(1) was soluble in CH2Cl2, CHCl3, THF, and partly soluble in DMF. The specific rotation, CD, and UV‐vis spectroscopic data revealed that poly(1) exists in a helical structure in CH2Cl2, CHCl3, CHCl3/DMF, and CHCl3/MeOH. Poly(1) underwent thermo‐ and solvent‐driven switch of helical sense, accompanying the change of tightness.

Schematic representation of the synthesis of the here discussed L‐aspartic acid‐based novel polyacetylene.

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Schematic representation of the synthesis of the here discussed L‐aspartic acid‐based novel polyacetylene.
Reactive Extrusion of Starch‐Polyacrylamide Graft Copolymers: Effects of Monomer/Starch Ratio and Moisture Content
Authors: Finkenstadt Victoria L. , Willett Julious L.
Published: August 2005

Summary: The effects of monomer/starch feed ratios and moisture content during reactive extrusion of starch‐polyacrylamide graft copolymers were investigated. Acrylamide/starch ratios ranged from 0.20 to 1.87 at 50% moisture content, while moisture content was increased from 45 to 75% with an acrylamide/starch ratio of 0.33. Average conversion was 86.6% (±3.5%), independent of monomer content, at acrylamide/starch ratios of 0.77 and less. Conversion increased to approximately 95% when the acrylamide/starch ratio exceeded unity. Molecular weight of grafted polyacrylamide increased as the acrylamide/starch ratio increased. Graft efficiency was constant at approximately 75% for monomer/starch ratios of 0.77 or less, and decreased to 52.3% as the monomer/starch ratio increased to 1.87. Higher acrylamide/starch ratios gave more frequent grafts of higher molecular weight. As moisture content decreased from 75 to 45%, conversion and graft content increased from 78 and 14% to 97 and 23%, respectively. Lower moisture content gave fewer grafts of higher molecular weight. Ungrafted polyacrylamide homopolymer increased with monomer/starch ratio and moisture content. These results indicate that graft copolymer properties can be controlled through the monomer/starch ratio and moisture content during reactive extrusion.

Molecular weight distributions of grafted polyacrylamide at different moisture contents during extrusion: A) 75%; B) 65%; C) 55%; D) 45%.

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Molecular weight distributions of grafted polyacrylamide at different moisture contents during extrusion: A) 75%; B) 65%; C) 55%; D) 45%.
Psychogenic tremor disorders identified using tree‐based statistical algorithms and quantitative tremor analysis
Authors: Piboolnurak Panida , Rothey Natalia , Ahmed Anwar , Ford Blair , Yu Qiping , Xu Dong , Pullman Seth L.
Published: August 2005

Detecting psychogenic tremors (PsychT) is often challenging. As there are no laboratory investigations or imaging techniques that can confirm the diagnosis, PsychT is identified on a clinical basis. We present a tree‐based statistical algorithm derived from quantitative computerized tremor recordings as a novel method to help in the recognition of PsychT. The goal of this study was to show that objective data from computerized tremor recordings, when processed through a tree‐based statistical algorithm, can be used to determine whether a patient can be classified as having PsychT. © 2005 Movement Disorder Society
Relationship between eye symptoms and blepharospasm: A multicenter case–control study
Authors: Martino Davide , Defazio Giovanni , Alessio Giovanni , Abbruzzese Giovanni , Girlanda Paolo , Tinazzi Michele , Fabbrini Giovanni , Marinelli Lucio , Majorana Giovanni , Buccafusca Maria , Vacca Laura , Livrea Paolo , Berardelli Alfredo
Published: August 2005

Although patients with primary blepharospasm (BSP) commonly report experiencing ocular symptoms before the onset of orbicular spasms, the precise frequency and pathogenic role of this subjective ocular discomfort are poorly understood. We conducted a multicenter case–control study to investigate symptoms related to disorders of the anterior segment of the eye, administering a questionnaire to 165 patients with BSP and 180 age‐ and gender‐matched control patients with hemifacial spasm. On a validation sample, our questionnaire yielded high accuracy in detecting eye diseases (predominantly, dry eye syndrome) using detailed ophthalmological examination as the criterion. Logistic regression analysis indicated a significant association between ocular symptoms at disease onset and BSP. Ocular symptoms starting in the year preceding disease onset (short‐latency symptoms) showed a stronger association with BSP than ocular symptoms occurring earlier in time (long‐latency symptoms). The association was stronger when short‐latency symptoms developed from 40 to 59 years of age, whereas this was not observed for long‐latency symptoms. Our findings support the view that eye symptoms associated with BSP result from eye diseases and may be involved in the pathogenesis of BSP. The differential risk of developing BSP, based on age at onset of ocular symptoms, suggests that age and eye diseases may interact in giving rise to BSP. © 2005 Movement Disorder Society
Dopaminergic influence on disturbed spatial discrimination in Parkinson's disease
Authors: Shin Hae‐Won , Kang Suk Y. , Sohn Young H.
Published: August 2005

Various sensory symptoms and disturbed sensory perception are often observed in patients with idiopathic Parkinson's disease (PD). The basis of sensory disturbance in PD is unknown but possibly reflects a role for the basal ganglia in sensory processing. To investigate the relationship between the sensory dysfunction and dopaminergic deficiency in PD, we measured spatial discrimination using the Grating Orientation Task in 21 drug‐naive patients with PD, before and after long‐term antiparkinson therapy, and 25 age‐matched healthy controls. The grating orientation threshold was significantly higher in patients (3.03 ± 0.84) than controls (2.03 ± 0.79). After 3 to 10 months of antiparkinson therapy, the grating orientation threshold was significantly lowered (2.66 ± 0.84), although it was still higher than that in controls. Improvement in the patients' sensory function was significantly correlated with motor improvement (r = 0.44). These results suggest that sensory dysfunction in Parkinson's disease is related at least in part to the dopaminergic deficit. © 2005 Movement Disorder Society
On the construction of global weak solutions in the Kynch theory of sedimentation
Authors: Bustos María Cristina , Concha Fernando
Published: August 2005

We construct global weak solutions to the different modes of sedimentation appearing in the theory of Kynch and show that, with constant initial concentration, only five modes of sedimentation exist. We also generalize the method of construction to the case of a monotonically decreasing initial concentration.
The Sommerfeld half‐plane problem revisited, IV: Variations on a theme of Carlson and Heins
Authors: Heins A. E. , Pond J. M.
Published: August 2005

A plane wave is incident upon an infinite set of equally spaced, semi‐infinite parallel and staggered plates. The boundary conditions on the plates alternate between the Dirichlet and Neumann ones. This problem is formulated as a pair of coupled Wiener‐Hopf integral equations and solved by a method proposed by A. E. Heins in 1950. For the case of specular reflection, that is, a single reflected plane wave, the magnitudes of the reflection coefficient and the transmission coefficients are determined.
Sturm‐Liouville eigenvalue problems on networks
Authors: von Below Joachim
Published: August 2005

The description of heat conduction on ramified wires, for instance, leads to a Sturm‐Liouville eigenvalue problem on a network. It is shown that these problems are special canonical eigenvalue problems in the sense of Hölder, and therefore they can be investigated within the theory of S‐Hermitian eigenvalue problems. In particular, Wielandt's expansion theorem can be applied in order to obtain eigenfunction expansions.
An evolution equation with non‐local non‐linearities: Existence, uniqueness and asymptotic behaviour
Authors: Miletta Peter D.
Published: August 2005

An evolution equation with non‐linearities of non‐local type is investigated. Under various hypotheses on the non‐linearities global existence and uniqueness of solutions to initial value problems is shown. Moreover the asymptotic behaviour of the solutions is determined by topological dynamics methods.
A stability result for distributed parameter identification in bilinear systems
Authors: Hsiao G. C. , Sprekels J.
Published: August 2005

In this paper we give a stability result for the problem of identifying distributed parameters (for instance, a conductivity matrix) in partial differential equations. The result is used to establish an error estimate for an algorithm to identify the parameter.
Explicity resolvable equations with functional non‐linearities
Authors: Bazley Norman W. , Weyer Jürgen
Published: August 2005

We consider the non‐linear evolution equation μdu/dt+Bu+n(u)L(u)=h, where n(u) is a functional, and introduce assumptions which allow its explicit solution. Several concrete applications of our procedure are given.
On the radius continuity of the models of polytropic gas spheres which correspond to the positive solutions of the generalized Emden‐Fowler equation
Authors: Batt J. , Pfaffelmoser K.
Published: August 2005

We completely answer the question which positive solutions of the Emden‐Fowler equation
equation image
, n > ½, m > − 1, m+n > 0 induce models of polytropic gas spheres of finite radius or finite mass. We continue and complete the investigation of the radius continuity of these models initiated by van den Broek and Verhulst8 in connection with a numerical analysis by Hénon7.
Unique continuation for Schrödinger operators and for higher powers of the Laplacian
Authors: Łaba Izabella
Published: August 2005

In this paper we consider the unique continuation property for Schrödinger operators and its application for proving the non‐existence of positive eigenvalues (embedded in the continuous spectrum). We also use the estimate given by Jerison and Kenig9 to prove unique continuation for higher powers of the Laplace operator.
On spline approximation for a class of integral equations. I: Galerkin and collocation methods with piecewise polynomials
Authors: Elschner Johannes
Published: August 2005

We consider the numerical solution of a class of one‐dimensional non‐compact integral equations by Galerkin and collocation methods and their iterated variants, using piecewise polynomials as basis functions. In particular, we obtain new results for the stability of the approximation methods, without any restriction on the norm of the integral operators. Furthermore, we extend results of Chandler and Graham4,6 concerning error estimates and superconvergence to a more general class of operators.
On a weakly formulated exterior problem from linear hydrodynamics
Authors: Doppel K. , Schomburg B.
Published: August 2005

In this paper we investigate a certain exterior boundary value problem for the inhomogeneous Helmholtz equation. We give sufficient conditions for the unique solvability of a weak formulation of this problem and show an interior regularity result for all weak solutions. As a special case the incompresible, irrotational and stationary fluid flow around a totally immersed obstacle (submarine problem) is included.
Some remarks on Newton–Sabatier methods
Authors: Carroll Robert , Delic George , Gilbert R. P.
Published: August 2005

It is shown how Newton–Sabatier methods (arising in inverse scattering at fixed energy) can be related to spectral measures and typically when they correspond to regular potentials. A number of spectral formulae for various transmutation kernels are also given in terms of general Kontorovič–Lebedev theory and connections to generating functions, generalized orthogonal polynomials, etc. are indicated.
Almost global existence of solutions of quasi‐linear hyperbolic equations
Authors: Milani Albert J. , Brosowski B.
Published: August 2005

We consider the quasi‐linear hyperbolic initial value problem (1) of the Introduction, and prove that for any T>0 there is a bound such that if the norm of the initial data is smaller than that bound then the solution of (1) exists on all of [0, T].
On the continuation for variational inequalities depending on an eigenvalue parameter
Authors: Miersemann Erich , Mittelmann Hans D. , Törnig W.
Published: August 2005

In this paper we generalize recent theoretical results on the local continuation of parameter‐dependent non‐linear variational inequalities. The variational inequalities are rather general and describe, for example, the buckling of beams, plates or shells subject to obstacles. Under a technical hypothesis that is satisfied by the simply supported beam, we obtain the existence of a continuation of both the solution and the eigenvalue with respect to a local parameter. A numerical continuation method is presented that easily overcomes turning points. Numerical results are presented for the non‐linear beam.
Multiple scales expansions for eddy current computation in layered media
Authors: Chiampi M. , Negro A. , Serra E. , Eckhaus W.
Published: August 2005

An asymptotic expansion is derived by the multiple scales method for the electromagnetic potential in a one‐dimensional model problem for eddy current computations in periodic non‐homogeneous layered media in presence of an integral constraint for each period.

Error estimates for approximations with partial sums of any order are established. Numerical computations of correctors up to the fourth order are performed and the results are compared with the exact solution in some significant cases.
A global existence theorem for the general coagulation–fragmentation equation with unbounded kernels
Authors: Stewart I. W. , Meister E.
Published: August 2005

In this article an existence theorem is proved for the coagulation–fragmentation equation with unbounded kernel rates. Solutions are shown to be in the space X+ = {c∈L1: ∫ (1 + x)∣c(x)∣dx < ∞} whenever the kernels satisfy certain growth properties and the non‐negative initial data belong to X+. The proof is based on weak L1 compactness methods applied to suitably chosen approximating equations.
Resonance phenomena for a class of partial differential equations of higher order in cylindrical waveguides
Authors: Lesky P. , Werner P.
Published: August 2005

We consider a domain Ω in ℝn of the form Ω = ℝl × Ω′ with bounded Ω′ ⊂ ℝn−l. In Ω we study the Dirichlet initial and boundary value problem for the equation ∂ u + [(− ∂ −… − ∂)m + (− ∂ −… − ∂)m]u = fe−iωt. We show that resonances can occur if 2m ≥ l. In particular, the amplitude of u may increase like tα (α rational, 0<α<1) or like in t as t∞∞. Furthermore, we prove that the limiting amplitude principle holds in the remaining cases.
Pseudo‐transparent boundary conditions for the diffusion equation. Part I
Authors: Joly P. , Nedelec J. C.
Published: August 2005

In this article, we introduce and study a family of artificial boundary conditions for the diffusion equation. These conditions are local in time and non‐local in space. We describe the principle of the approximation, show that the corresponding approximate problems are mathematically well‐posed and give convergence results, as well as error estimates, of the approximate solution to the exact one.
Free‐boundary values in an elastic‐plastic torsion problem
Authors: Ting Tsuan Wu , Hsiao C. G.
Published: August 2005

Consider a cylindrical pipe twisted by terminal couples. For a large twist θ, the elastic‐plastic stress function, Ψ (·,θ), is shown to be the positive in the interior of the pipe, an increasing function of θ and converging to the completely plastic stress function, \documentclass{article}\pagestyle{empty}\begin{document}$ \bar \Psi \left(\cdot \right) $\end{document} (·), as θ→∞. A geometric procedure for constructing Ψ(·) has been developed to provide qualitative information. The main result states that \documentclass{article}\pagestyle{empty}\begin{document}$ \psi \left({\cdot,\theta} \right) = \bar \Psi \left(\cdot \right) $\end{document} on the cross‐sectional boundary of the pipe, if θ is greater than or equal to a certain critical value, In addition, an example has been constructed to give additional insights.
A free boundary problem and stability for the rectangular plate
Authors: Miersemann Erich , Mittelmann Hans D.
Published: August 2005

In the recent paper [13] we have answered the question of stability for the linear circular plate which is being axially compressed by a force greater than the critical value and contacts a plane obstacle. In this case there are radially symmetric solutions and the contact region is a disk of a smaller radius. This simplified the determination of the critical parameter values for which the plane jumps to another state. For the rectangular plate continuation has to be applied to the variational inequality in order to determine the contact region and evalute the stability criterion. A numerical method is developed for a discretization of the problem and is used to compute the critical load both in the simply supported and the clamped case.
Linear stability condition for explicit Runge–Kutta methods to solve the compressible Navier‐Stokes equations
Authors: Müller Bernhard
Published: August 2005

A linear stability condition is dervied for explicit Runge–Kutta methods to solve the compressible Navier–Stokes equations by central second‐order finite‐difference and finite‐volume methods. The equations in non‐conservative form are simplified to quasilinear form, and the eigenvalues of the resulting coefficient matrices are determined for general co‐ordinates. Assuming a well‐posed Cauchy problem with constant coefficients, the von Neumann stability analysis yields sufficient stability conditions for viscous–inviscid operator‐splitting schemes. They have been applied in computational aerodynamics to solve the compressible Navier–Stokes equations by an unsplit explicit Runge–Kutta finite‐volume method.
Global solutions of Yang–Mills–Higgs systems on four‐dimensional Minkowski space: I. Existence
Authors: Łada A.
Published: August 2005

The existence of global solutions to the Cauchy problem for Yang–Mills–Higgs systems in the temporal gauge is examined. The results apply to the self‐coupling of the Higgs field. Results from other works are strengthened.
Singular integral equations applied to free surface seepage from non‐linear channels
Authors: Oestreich Dieter
Published: August 2005

The problem of two‐dimensional seepage from a non‐linear channel through a homogeneous medium underlain at a finite depth by a drain will be considered. A new approach is given, transforming the seepage problem to a non‐linear singular integral equation for which the unique existence of the solution is proved. The free boundaries of the seepage region can be described explicitly.
Solution of a class of partial differential equations. Some diffusion equations
Authors: Abdel‐Gawad H. I.
Published: August 2005

In this article we present the solution of linear partial differential equations of the form ∂tf = L̂f, for initial value problems. Also the solution of some diffusion equations will be discussed.
An adapted Galerkin method for the resolution of Dirichlet and Neumann problems in a polygonal domain
Authors: Bourlard Maryse , Nicaise Serge , Paquet Luc
Published: August 2005

The Neumann problem for Laplace's equation in a polygonal domain is associated with the exterior Dirichlet problem obtained by requiring the continuity of the potential through the boundary. Then the solution is the simple layer potential of the charge q on the boundary. q is the solution of a Fredholm integral equation of the second kind that we solve by the Galerkin method. The charge q has a singular part due to the corners, so the optimal order of convergence is not reached with a uniform mesh. We restore this optimal order by grading the mesh adequately near the corners. The interior Dirichlet problem is solved analogously, by expressing the solution as a double layer potential.
A uniqueness condition for the polyharmonic equation in free space
Authors: Lesky P.
Published: August 2005

Consider the polyharmonic wave equation ∂u + (− Δ)mu = f in ℝn × (0, ∞) with time‐independent right‐hand side. We study the asymptotic behaviour of u (x, t) as t → ∞ and show that u(x, t) either converges or increases with order tα or In t as t → ∞. In the first case we study the limit \documentclass{article}\pagestyle{empty}\begin{document}$ u_0 \left({\bf x} \right) \colone \mathop {\lim }\limits_{t \to \infty } \,u\left({{\bf x},t} \right) $\end{document} and give a uniqueness condition that characterizes u0 among the solutions of the polyharmonic equation ( − Δ)mu = f in ℝn. Furthermore we prove in the case 2m ⩾ n that the polyharmonic equation has a solution satisfying the uniqueness condition if and only if f is orthogonal to certain solutions of the homogeneous polyharmonic equation.
Junction between a 3‐D Stokes flow and a 2‐D thin film with pressure boundary conditions
Authors: Bayada G. , Chambat M.
Published: August 2005

A 3‐D Stokes equation modelling the flow in the inlet region of a lubricated device is studied. Boundary conditions on both the pressure and the velocity are considered. The geometry induces that the flow region is divided into two parts: the first one is a thin gap with height ϵh, where a change of scale is performed, and the second one is a cavity whose dimensions are large with respect to ϵ. Two equivalent variational formulations are proposed and lead to accurate a priori estimates. The resulting asymptotic equation for the pressure in the thin gap is the currently used Reynolds equation, whose boundary conditions are obtained via the junction with the 3‐D cavity. Both hydrostatic and hydrodynamic cases are considered.
The three‐dimensional wigner‐poisson problem: Existence, uniqueness and approximation
Authors: Brezzi Franco , Markowich Peter A.
Published: August 2005

We prove the existence of a unique, global classical solution of the quantum Vlasov–Poisson problem posed on the phase space ℝ × ℝ. The proof is based on a reformulation of the quantum Vlasov–Poisson problem as a system of countably many Schrödinger equations coupled to a Poisson equation for the potential. The Schrödinger‐Poisson problem is first analysed on a bounded domain in ℝ and the solution of the whole‐space problem is then obtained by a limiting procedure in which the domains ‘tend’ to ℝ.
Dynamical shape control and the stabilization of non‐linear thin rods
Authors: Sokolowski J. , Sprekels J.
Published: August 2005

In this paper we consider the problem of stabilizing the motion of the tip of a thin rod by controlling the shape of the rod, that is its length, dynamically. Well‐posedness of the associated state equations, valid on a moving domain, is proved, and the necessary conditions of optimality for the control problem are derived. The theory applies to materials where the stress–strain relation is both non‐linear and non monotone, so that hysteresis effects arising from solid–solid phase transitions in the rod are included.
On the mildly degenerate Kirchhoff string
Authors: Arosio A. , Garavaldi S.
Published: August 2005

Let us consider the Cauchy problem for the abstract evolution equation, which describes the Kirchhoff sring
u″ + m(〈Au, u〉) Au = 0, (t > 0),
Where ( )′ = d/dt, A is any symmetric isomorphism of a Hilbert space V into its (anti) dual V′ and m is a function of one real variable. Following physical considerations, we allow m(·) to be any non‐decreasing, non‐negative continuous function (a degenerate Kirchhoff string).

We assume that the initial value u0 satisfies: m(〈Au0, u0〉)>0 (a mildly degenerate Kirchhoff string), that m is locally Lipschitz continuous in the open region where it does not vanish, and that m has a finite order of vanishing (e.g., m(ρ) = ργ, γ > 0).

We establish the local well‐posedness of the Cauchy problem in the class D(Aα/2) × D(A(α−1)/2), For each α ⩾ 3/2. This improves the results of Medeiros and Miranda [15], Ebihara et al.[9] and a result of Yamada [27].

We are not able to prove the global existence of the solution; however, we provide a lower estimate for the life span of the solution, which yields the almost global existence (AGE) in the case when m(ρ) = ργ (γ>0).
A uniqueness theorem in the dynamical theory of piezoelectricity
Authors: Morro A. , Straughan B.
Published: August 2005

The solution to the linearized equations of dynamical linear piezoelectricity is shown to be unique without requiring definiteness conditions in the elastic coefficients. Only continuity of the normal component of the electric displacement field across the boundary between the elastic body and free space is required. The proof employs a logarithmic convexity argument.
Diffraction by an acoustically transmissive or an electromagnetically dielectric half‐plane
Authors: Rawlins A. D. , Meister E. , Speck F. ‐O.
Published: August 2005

This work gives a mathematical model for an acoustically penetrable or electromagnetically dielectric half‐plane. An approximate boundary condition is used that depends on the thickness of, and the material constants for, the half‐plane. A solution is obtained, by using the approximate boundary condition, for the problem of a line source field diffracted by a penetrable/dielectric half‐plane. The asymmetry of the approximate boundary condition results in a matrix Wiener–Hopf problem, which is solved explicitly.
Global smooth solution for a coupled non‐linear wave equations
Authors: Boling Guo , Shaobin Tan
Published: August 2005

In this paper, the global existence and uniqueness of smooth solution to the initial‐value problem for coupled non‐linear wave equations are studied using the method of a priori estimates.
Physical model, theoretical aspects and applications of the flight of a ball in the atmosphere. Part I: Modelling of forces and torque, and theoretical prospects
Authors: Fuchs P. M.
Published: August 2005

A model of the forces and the torque operating on a ball that is flying with rotation in the atmosphere of the Earth, and the resulting system of ordinary differential equations, are derived from mechanics and aerodynamics.

The system of equations allows the theoretical aspects of the flight of a ball, such as the boundedness of its kinetic energy, the curvature of the orbit or the velocity function, to be investigated using certain transformations of the variables.

The solutions of the corresponding ordinary or boundary value problems, computed numerically, are used to treat certain tasks in international ball games, for example, the maximum and minimum velocities of a volleyball service.
Physical model, theoretical aspects and applications of the flight of a ball in the atmosphere. Part II: Theoretical aspects in the case of vertical angular frequency and applications
Authors: Fuchs P. M.
Published: August 2005

If a ball is viewed as a rigid body, its flight in the atmosphere can be described by a system of six ordinary differential equations, which has been derived in the first part of this paper.

In this following second part, the theoretical aspects such as the curvature of the orbit and certain velocity functions will be investigated in the case of the vertical angular frequency of the rotating ball, in which the differential equations reduce to a planar dynamical system. This system turns out to be not explicity solvable.

The solutions of the corresponding ordinary or boundary value problems. computed numerically, are used to treat certain problems in international ball games. for example, the maximum and minimum velocities of a volleyball service.
A trace theorem for solutions of linear partial differential equations
Authors: Bao Gang , Symes William W.
Published: August 2005

In this paper, we prove a trace regularity theorem for the solutions of general linear partial differential equations with smooth coefficients. Our result shows that by imposing additional microlocal smoothness along certain directions, the trace of the solution on a codimension‐one hypersuface will be just as regular as the solution itself. The proof is based on the Hörmander–Nirenberg pseudo‐differential cut‐off technique and a ‘fattening’ lemma, together with standard energy estimates.
The two‐dimensional Wigner–Poisson problem for an electron gas in the charge neutral case
Authors: Arnold Anton , Nier Francis
Published: August 2005

We prove the global existence of a unique classical solution of the two‐dimensional Wigner–Poisson problem by a reformulation as a system of countably many Schrödinger equations coupled to a Poisson equation. The charge neutrality of the system implies the boundedness of the electrostatic potential in two dimensions, which is an important ingredient for the proof.
Solutions of the equation \documentclass{article}\pagestyle{empty}\begin{document}$$ \partial _t^n f(x,t) = \hat L(x,t)f(x,t) + S(x,t) $$\end{document}. Exact solutions of some partial differential equations in mechanics and physics
Authors: Abdel‐Gawad H. I.
Published: August 2005

The solutions of the equation \documentclass{article}\pagestyle{empty}\begin{document}$ \partial _t^n f(x,t) = \hat L(x,t)f(x,t) + S(x,t) $\end{document}, for L̂ a linear operator are derived. Different forms for L̂ whether it is time independent or time dependent and self‐commutative (or not) at different times are considered separately. By using the results obtained, exact solutions of some partial differential equations are found for the first time.
Vacuum decay of non‐Abelian vortices
Authors: Yang Yisong
Published: August 2005

This note is a case study of a general SU(2) gauge vortex model where the two Higgs multiplets are in the adjoint representation of the gauge group and the Higgs potential energy density contains cross interaction terms The vacuum decay of finite‐energy solutions is proved and the existence of a non‐trivial solution is established. Moreover, for a special choice of the parameter region, the occurrence of a non‐linear desingularization phenomenon is observed.
The domain decomposition method for parabolic transmission problems
Authors: Pankov Alexander , (Korovkina) Tatyana Pankova
Published: August 2005

An estimate of the rate of convergence is given for the domain decomposition method for the second‐order parabolic transmission problem. A brief discussion of the method and some of its applications are presented.
On the moving Preisach model
Authors: Brokate Martin
Published: August 2005

It is shown that the moving model, which is a variant of the Preisach model for hysteresis, possesses the wiping out property and is continuous in C[0, T] under natural assumptions.
Inversion of the Radon transform with incomplete data
Authors: Ramm A. G.
Published: August 2005

The Radon transform R(p, θ), θ∈Sn−1, p∈ℝ1, of a compactly supported function f(x) with support in a ball Ba of radius a centred at the origin is given for all \documentclass{article}\pagestyle{empty}\begin{document}$ \theta \in \mathop {S^{n - 1} }\limits^\tilde $\end{document}, where \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {S^{n - 1} }\limits^\tilde $\end{document} is an open set on Sn−1, and all p∈(− ∞, ∞), n≥2. An approximate formula is given to calculate f(x) from the given data.
Existence of solutions to some non‐linear thermoelastic systems with viscosity
Authors: Hoffmann K.‐H. , Zochowski A.
Published: August 2005

In this paper a non‐linear system of equations
magnified image
in a one‐dimensional domain is considered, where both the viscosity, v, and R are positive. The existence of solutions in the case of Neumann boundary conditions for θ and a polynomial form of p(θ, ϵ) is proved. When θ satisfies the Dirichlet boundary condition, the existence of solutions is obtained under additional assumptions limiting the growth of p(θ, ϵ) with respect to θ. In both cases the uniqueness of the solutions is also established.
Phase transition in binary systems and the binary alloy problem
Authors: Xie Weiqing
Published: August 2005

In this paper we consider a phase transition in binary systems describing the solidification of a dilute alloy in one space dimension, in which the equations of heat and mass transfer are coupled through the conditions at the free boundary. A kinetic condition is introduced to suggest a regularization of the model, which admits a unique solution, and to obtain the generalized solution of the dilute‐alloy problem under an additional assumption.
Pseudodifferential operators with real analytic symbols and approximation methods for pseudodifferential equations
Authors: Van Tran Duc , Hào Dinh Nho
Published: August 2005

This paper introduces some methods (including an approximation method) for investigating pseudodifferential equations and related problems (Cauchy problems, boundary value problems,…) based on the technique of pseudodifferential operators with real analytic symbols.
Wave equations with time‐dependent spatial operators of higher order
Authors: Lesky Peter
Published: August 2005

We study the initial‐boundary value problem for ∂t2u(t,x)+A(t)u(t,x)+B(t)∂tu(t,x)=f(t,x) on [0,T]×Ω(Ω⊂ℝn) with a homogeneous Dirichlet boundary condition; here A(t) denotes a family of uniformly strongly elliptic operators of order 2m, B(t) denotes a family of spatial differential operators of order less than or equal to m, and u is a scalar function. We prove the existence of a unique strong solution u. Furthermore, an energy estimate for u is given.
On degenerate diffusion with very strong absorption
Authors: Kawohl Bernhard , Kersner Robert
Published: August 2005

We prove the existence of weak global solutions to the degenerate diffusion equation (1) with singular absorption term. Moreover we investigate the regularity up to the quenching time and we show by means of explicit solutions that our regularity results are optimal.
On a free‐boundary problem arising in the study of flame propagation
Authors: Ton Bui An
Published: August 2005

The existence of a weak solution of a two‐dimensional non‐stationary free‐boundary problem related to flame propagation is established. The main feature of the problem is that the nonlinear coupling of the two parabolic equations occur on the free boundary and has exponential growth.
On the determination of the worst sampling error in a communication system for pulse‐amplitude‐modulated signals. I: The general model
Authors: Kerber Dirk
Published: August 2005

We present a mathematical model of a communication system perturbed by statistical sampling errors (timing jitter). The aim is to find an ‘optimal’ impulse response for the system, the optimization problem actually being a minimax problem. that is we put the model into a game‐theoretical framework. The basic game turns out to be a statistical game similar to those arising from estimation problems in statistics.

Earlier results concerning least‐favourable sampling error distributions published by Krabs and Vogel are supplemented by estimations of the number of support points of the least‐favourable distribution.

Furthermore, we state the existence of the saddle points of our game, which formerly has only been proved for some special cases. In the first part we treat the general situation, where one strategy set for the game—the set of all feasible impulse responses—forms a vector space with infinite dimension. In the second part we discuss the problem in the case that the impulse responses are restricted to a finite‐dimensional subspace of the whole infinite‐dimensional subspace.
Characterization of functions as radiation patterns in linear elasticity
Authors: Charalambopoulos Antonios , Kiriaki Kiriakie
Published: August 2005

In this paper a necessary and sufficient condition for a pair of vector functions to be radiation patterns is presented. More precisely, it is proved that two vector functions, the first in the radial direction and the second in the tangential one, are radiation patterns if and only if there are two entire harmonic vector functions whose radial and tangential projections, respectively, are identical with the previous functions on the unit sphere and whose L2‐norm over a sphere of radius R is a function of exponential type in the variable R.
A stability analysis for semilinear Neumann problems with concave non‐linearities
Authors: Bandle C. , Brauner C. M. , Schmidt‐Lainé C.
Published: August 2005

This paper is concerned with non‐linear parabolic problems. This particular type of probiem arose from the study of the instability of transverse detonation waves in channels. A fairly complete account of the equilibrium states is given. A global approach is adopted for the upper and lower solutions and the energy estimates. Finally, the invariant manifolds that describe the asymptotic behaviour of the solutions near the equilibrium states are discussed.
A contribution to matrix equations arising in system theory
Authors: Szczepaniak Piotr S.
Published: August 2005

A useful relationship between solutions is derived for a class of matrix equations arising in the system theory, particularly in the context of the orthogonal approximation of linear dynamic systems. The computational aspects of the result are discussed and illustrated on an example of practical importance.
High‐frequency asymptotics in inverse scattering by ellipsoids
Authors: Arnaoudov Yani , Dassios George , Georgiev Vladimir
Published: August 2005

A triaxial ellipsoid of unknown position, size and orientation is located somewhere in space. High‐frequency asymptotics for the scattering amplitude and the sojourn time for the travelling of a high‐frequency acoustic plane wave are utilized to determine the position of a supporting plane for the ellipsoid. We describe a method that identifies the coordinates of the centre, the three semiaxes, and the three angles of the ellipsoid from the knowledge of nine sojourn times corresponding to nine directions of excitation. The method is independent of boundary conditions, it is applicable to any restricted non‐zero‐measure angle of observation, and leads to numerics that avoid elliptic integrals. A priori information about the location of the ellipsoid reduces the number of measurements to six, while the corresponding algorithm demands the solution of a linear system and the inversion of a dyadic.
Behaviour of mushy regions under the action of a volumetric heat source
Authors: Andreucci Daniele
Published: August 2005

In this paper we consider solutions to Stefan problems in spatial dimensions N ⩾ 1. We find the necessary conditions on the heat source for the appearance of a ‘mushy region’ (i.e. a region where the temperature coincides identically with the temperature of the change of phase) inside a purely liquid (or solid) phase. For sources depending on energy such conditions are connected only with the local behaviour of the source near the energy level corresponding to the beginning of the change or phase. Both weak and smooth solutions are considered; in the latter case the behaviour of the solution at the free boundary is investigated in detail.
Initial‐boundary value problems for non‐linear equations of generalized thermoelasticity and elasticity
Authors: Chrzęszczyk Andrzej
Published: August 2005

We formulate a local existence theorem for the initial‐boundary value problems of generalized thermoelasticity and classical elasticity. We present a unified approach to such boundary conditions as, for example, the boundary condition of traction, pressure or place combined with the boundary condition of heat flux or temperature.