bluuebunny/crossref_metadata_2025_split huggingface dataset:
The brain at work: A cerebral metabolic manifestation of central fatigue?
Authors: Dalsgaard Mads K. , Secher Niels H. 
Published: March 2007

AbstractCentral fatigue refers to circumstances in which strength appears to be limited by the ability of the central nervous system to recruit motoneurons. Central fatigue manifests when the effort to contract skeletal muscles is intense and, thus, is aggravated when exercise is performed under stress, whereas it becomes attenuated following training. Central fatigue has not been explained, but the cerebral metabolic response to intense exercise, as to other modalities of cerebral activation, is a reduction in its “metabolic ratio” (MR), i.e., the brain's uptake of oxygen relative to that of carbohydrate. At rest the MR is close to 6 but during intense whole‐body exercise it decreases to less than 3, with the uptake of lactate becoming as important as that of glucose. It remains debated what underlies this apparent inability of the brain to oxidize the carbohydrate taken up, but it may approach ∼10 mmol glucose equivalents. In the case of exercise, a concomitant uptake of ammonium for formation of amino acids may account for only ∼10% of this “extra” carbohydrate taken up. Also, accumulation of intermediates in metabolic pathways and compartmentalization of metabolism between astrocytes and neurons are avenues that have to be explored. Depletion of glycogen stores and subsequent supercompensation during periods of low neuronal activity may not only play a role but also link brain metabolism to its function. © 2007 Wiley‐Liss, Inc.
Preparation of lactose‐free milk by using salt‐fractionated almond (Amygdalus communis) β‐galactosidase
Authors: Haider Toshiba , Husain Qayyum 
Published: March 2007

Abstractβ‐galactosidase was isolated from almond (Amygdalus communis) extract by ammonium sulfate precipitation. Almond proteins precipitated by using ammonium sulfate and then dialysed exhibited 5.3‐fold purification of β‐galactosidase, and the yield of enzyme preparation was 96.5%. The partially purified β‐galactosidase exhibited pH and temperature optima at pH 5.5 and 50 °C, respectively. The enzyme was significantly stable against heat, pH, calcium and magnesium ions andD‐galactose. The almond β‐galactosidase preparation exhibited over 89% activity even after 2 months storage at 4 °C. Hydrolysis of lactose in milk and whey was performed in a stirred batch process by using this enzyme preparation. These observations indicated that the hydrolysis of lactose increased continuously with time. The enzyme could hydrolyse 94% of lactose in buffer solution and whey whereas 90% of lactose hydrolysis was achieved in milk. The main aim of the present study was to prepare lactose‐free milk, which must be free from contamination, and the process should be inexpensive. Copyright © 2007 Society of Chemical Industry
Gruppentheoretische aspekte der signalübertragung und der kardinalen interpolationssplines I
Authors: Schempp W. , Brosowski B. 
Published: March 2007

AbstractAs is well known the real Heisenberg nilpotent group A(R) constitutes the group‐theoretic embodiment of the Heisenberg canonical commutation relations (CCR) of classical quantum mechanics. In this connection, quantum mechanics stands for the quantum‐mechanical description, at a given instant of time, of a non‐relativistic microparticle moving in the one‐dimensional configuration space R and having the plane R2 as its (flat) phase space. In fact, the (nilpotent) Lie algebra n of Ã(R) reflects the Weyl equations which are global versions of the Heisenberg CCR. Unfortunately, the subject of Heisenberg nilpotent groups is outside quantum mechanics and all the more outside mathematical physics not as commonly known as it should be considering its wide range of applications in a variety of different fields. The present paper which has two parts aims to develop a central topic of nilpotent harmonic analysis, to wit, the microparticle model, the lattice model which will be realized on the Heisenberg compact nilmanifold, and the complex wave model (or Bargmann‐Fock‐Segal model) of the linear Schrödinger representation of Ã(R) in order to examine geometrically several applications which are governed by the real Heisenberg nilpotent group Ã(R). These applications are in Part I the classical Whittaker‐Shannon sampling theorem which is of basic importance in signal processing, to wit, for the transmission of digital signals as well as analog signals, and in Part II the Subbotin‐Schoenberg existence and uniqueness theorem of cardinal spline interpolation. Moreover, Part II indicates briefly some connections of the aforementioned models to the Wigner phase‐space quasiprobability density function of quantum statistical mechanics via the Schwartz kernels theory on unimodular Lie groups, an approach to the cross‐ and autoambiguity functions of radar synthesis, and to the Zak transform of solid state physics. The second part also points out some relations of harmonic analysis of the finite nilpotent group A(Z/NZ) to periodic spline interpolants admitting N equidistant knots on the one‐dimensional compact torus group T. These last examples should serve mainly as hints for some further lines of investigations in the field of applications of nilpotent harmonic analysis.
The sommerfeld half‐plane problem revisited III: Parallel plate media with mixed boundary conditions
Authors: Heins A. E. , Meister E. 
Published: March 2007

AbstractA plane wave is normally incident upon an infinite stack of equally spaced parallel plates which are semi‐infinite and not staggered. The plates satisfy the so‐called “Rawlins” boundary conditions. This problem is formulated as a pair of simultaneous integral equations of the Wiener‐Hopf type and solved by a method proposed by A. E. Heins in 1950.
Multiparameter acoustic imaging in the born approximation
Authors: Wilcox C. H. 
Published: March 2007

AbstractSamples of biological tissue are modelled as inhomogeneous fluids with density ϱ(X) and sound speed c(x) at point x. The samples are contained in the sphere |x| ⩽ δ and it is assumed that ϱ(x)  ϱ0 = 1 and c(x)  c0 = 1 for |x| ⩾ δ, and |γn(x)| ≪ 1 and |∇γϱ(x)| ≫ 1 where γϱ(x) = ϱ(x) − 1 and γn(x) = c−2(x) − 1. The samples are insonified by plane pulses s(x · θ0 – t) where x = |θ0| = 1 and the scattered pulse is shown to have the form |x|−1 es(|x| – t, θ, θ0) in the far field, where x = |x| θ. The response es(τ, θ, θ0) is measurable. The goal of the work is to construct the sample parameters γn and γϱ from es(τ, θ, θ0) for suitable choiches of s, θ and θ0.In the limiting case of constant density: γϱ(x)ϱ 0 it is shown thatmagnified imageWhere δ represents the Dirac δ and S2 is the unit sphere |θ| = 1. Analogous formulas, based on two sets of measurements, are derived for the case of variable c(x) and ϱ(x).
Interactions of fast and slow waves in hyperbolic systems with two time scales
Authors: Barker J. W. , Kreiss H.O. 
Published: March 2007

AbstractWe consider certain symmetric hyperbolic systems of nonlinear partial differential equations whose solutions vary on two time scales. The large part of the spatial operator is assumed to have constant coefficients, but a nonlinear term multiplying the time derivatives is allowed. We show that if the initial data are not prepared correctly for the suppression of the fast scale motion, but contain errors of amplitude O(ϵ), then the perturbation in the solution will also be of amplitude O(ϵ). Further, if the large part of the spatial operator is nonsingular, we show that the error introduced in the slow scale motion will be of amplitude O(ϵ2), even though fast scale waves of amplitude O(ϵ) will be present in the solution.
Local existence and uniqueness theorems for a free boundary problem
Authors: Wegmann R. , Brosowski B. 
Published: March 2007

AbstractFree boundary problems are considered, where the tangential and normal components ut and un of an otherwise unknown plane harmonic vector field are prescribed along the unknown boundary curve as a function of the coordinates x, y and the tangent angle θ. The vector field is required to exist either in the interior region G+ or in the exterior G−. In each case the free boundary is characterized by a nonlinear integral equation. A linearised version of this equation is a one‐dimensional singular integral equation. Under rather general hypotheses which are easy to check, the properties of the linear equation are described by Noether's theorems. The regularity of the solution is studied and the effect of the nonlinear terms is estimated. A variant of the Nash‐Moser implicit‐function theorem can be applied. This yields local existence and uniqueness theorems for the free boundary problem in Hölder‐classes H2+μ. The boundary curve depends continuously on the defining data. Finally some examples are given, where the linearised equation can be completely discussed.
Existence for a characteristic boundary value problem for an equation of mixed type in three‐dimensional space
Authors: Müller‐Rettkowski A. H. , Gilbert P.P. 
Published: March 2007

AbstractThe equation of mixed typemagnified imageWith k(x3) = sign x3|x3|m, m > 0, dϵC1(Ḡ), x = (x1, x2, x3), is considered in the threedimensional region G which is bounded by the surfaces: a piecewise smooth surface Γ0 lying in the half‐space x3 > 0 which intersects the plane x3 = 0 in the unit circle, and for x3 < 0 by the characteristic surfacesmagnified imageWe prove existence of a generalized solution for the characteristic boundary value problem: Lu = fin G, uΓ0∪Γ1 = 0. The result is obtained by using a variant of the energy‐integral method.
Layer potentials and boundary value problems for the helmholtz equation in the complement of a thin obstacle
Authors: Durand M. , Meister E. 
Published: March 2007

AbstractOur purpose is to show in a precise manner the mathematical approach of the problem of the acoustic diffraction by an infinitely thin screen. The classical equations of acoustics are transformed into integral equations. The sound field diffracted by the obstacle is described by a double layer potential, the density of which is equal to the step of the potential across the screen. To avoid the mathematical difficulties, the infinitely thin screen will be considered as the limit of a sequence of obstacles with finite thickness. On such obstacles, the operators can be defined, thanks to the theory of Pseudo‐differential operators and Pseudo‐Poisson kernels. Then a limiting process is used and gives existence and unicity of the desired solutions in Sobolev spaces.
An approximation method for a fokker‐planck‐vlasov equation
Authors: Hebeker F.‐K. , Neunzert H. 
Published: March 2007

AbstractA simplified Fokker‐Planck equation of statistical plasma physics is mathematically investigated. For the Cauchy problem a constructive approximation method is introduced. This procedure yields a sequence (fn) of approximate densities, uniformly converging to the problem's global classical solution with linear convergence velocity.
Bifurcation of periodic solutions for wave equations with scalar nonlinearities
Authors: Bazley N. W. , Weinacht R. J. , de Jager E. 
Published: March 2007

AbstractWe treat wave equations with “scalar nonlinearities” and demonstrate the connection between the bifurcation theory of an associated system of Hammerstein integral equations and the existence of periodic solutions of the nonlinear wave equation.
Bifurcation phenomena in a free boundary problem for a circulating flow with surface tension
Authors: Okamoto Hisashi , Fujita H. 
Published: March 2007

AbstractA free boundary problem for a flow around a circle is analyzed. We find and mathematically prove that bifurcations from the trivial flow actually take place. Golubitsky‐Schaeffer theory, together with a formula concerning variations of domains, enables us to clarify the behaviors of the branches of nontrivial solutions.
Truncated random variables with application to random surfaces
Authors: Phillips M. J. , Roach G. F. 
Published: March 2007

AbstractThere has been considerable interest in obtaining discrete results for random surfaces. Standard results have been published in journals of physics or engineering which have emphasised the applications. This paper gives a detailed background of the mathematical methods needed so that the central connection, namely truncated random variables, between these standard results can be understood. Distributions of discrete peak measures are obtained from the distributions of discrete profile measures of a random Gaussian surface by applying results for the distributions of truncated random variables. This enable the moments to be obtained from known results for the truncated distributions.
Some applications of a galerkin‐collocation method for boundary integral equations of the first kind
Authors: Hsiao G. C. , Kopp P. , Wendland W. L. 
Published: March 2007

AbstractHere we apply the boundary integral method to several plane interior and exterior boundary value problems from conformal mapping, elasticity and fluid dynamics. These are reduced to equivalent boundary integral equations on the boundary curve which are Fredholm integral equations of the first kind having kernels with logarithmic singularities and defining strongly elliptic pseudodifferential operators of order ‐ 1 which provide certain coercivity properties. The boundary integral equations are approximated by Galerkin's method usingB‐splines on the boundary curve in connection with an appropriate numerical quadrature, which yields a modified collocation scheme. We present a complete asymptotic error analysis for the fully discretized numerical equations which is based on superapproximation results for Galerkin's method, on consistency estimates and stability properties in connection with the illposedness of the first kind equations inL2. We also present computational results of several numerical experiments revealing accuracy, efficiency and an amazing asymptotical agreement of the numerical with the theoretical errors. The method is used for computations of conformal mappings, exterior Stokes flows and slow viscous flows past elliptic obstacles.
L2‐boundary integral equations for the robin problem
Authors: Angell T. S. , Kress R. , Roach G. F. 
Published: March 2007

AbstractIn this paper we study an integral equation method for the exterior Robin problem for the Helmholtz equation where the boundary condition is interpreted in the L2‐sense. In particular, we derive a composite integral equation from Green's theorem which is uniquely solvable for all wave numbers.
Applications of convex analysis and comparison functionals to extremum principles
Authors: Bailey Pat , Smith Peter , Roach G. F. 
Published: March 2007

AbstractIn many areas of applied mathematics, the govering equations can be expressed as dual equations which are elements in two vector spaces where a given functional defined on a cartesian product space has zero gradients. If this functional has a global saddle structure then the variational principle can be replaced by dual extremum principles of the Noble and Sewell type. The purpose of the present paper is to investigate how comparison functional which have convex, concave or saddle structure can be used to generate upper and lower bounding principles and critical sequences. The methods are illustrated by applications to the periodic solutions of a non‐linear differential equation and the Fredholm integral equation.
Half‐ and finite‐range completeness for the equation of transfer of polarized light
Authors: Van Mee C. V. M. Der , Neunzert H. 
Published: March 2007

AbstractOn neglecting reflection by the surface the existence and uniqueness are proved for the solution of the equation of transfer of polarized light in a homogeneous semi‐infinite or finite plane‐parallel medium. A general LL‐space formulation, where 1 ≤ p < ∞, is adopted. The analysis concerns a vector‐valued convolution equation, which is an equivalent form of the equation of radiative transfer and is solved with the help of Wiener‐Hopf factorization, Fredholm index and cone preservation methods. The results are also proved for the equations obtained from the full equation of transfer by means of Fourier expansion and symmetry relations.
Transmutation via the momentum plane
Authors: Carroll R. , Jones D. S. 
Published: March 2007

AbstractTransmutation methods are developed for equations of the form x2 φ“ + x2(k2” ‐ q̃(x)) φ = (v2 ‐ (1/4)) φ, with v as spectral variable, which correspond to problems in quantum scattering theory at fixed energy k2 (here v ˜ l + (1/2) with l complex angular momentum). Spectral formulas for transmutation kernels are constructed and the machinery of transmutation theory developed by the author for spectral variable k is shown to have a version here. General Kontrorovič‐Lebedev theorems are also proved.
Two remarks on continuation procedures for solving some nonlinear equations
Authors: Descloux J. , Nedelec J. C. 
Published: March 2007

AbstractLet F be a mapping from Rn+1 into Rn, x(t) be a parametrization for ∣t − t0 ∣ < c, of a smooth solution branch of the equation F(x) = 0, A(t) be the jacobian (n + 1) associated to a standard continuation method used for computing the solution branch. We study for a class of singularities at x(t0) the behaviour, near t = t0, of the determinant of A(t).
Die lösung der maxwellschen gleichungen durch vollständige flächenfeldsysteme
Authors: Kersten H. , Leis R. 
Published: March 2007

AbstractThe paper deals with approximation theorems for the solution of Maxwell's equations governing the mathematical description of the propagation of electromagnetic waves.The well‐known results ([10]) for the Helmholtz equation are generalized to Maxwell's equations: Systems of electric (resp. magnetic) dipoles are proved to span the space of all solutions of rot H + iωE = 0, rotE ‐ iωH = 0, with n × E prescribed on the boundary. The same result holds for the “Mie‐potentials”magnified imageWhich can be proved by a Lemma of Mie [6].Two numerical examples for the three‐dimensional boundary value problems (field of a dipole, field of reflection) are presented.
Étude asymptotique des phénomènes acoustiques dans un mélange fluide‐solide thermoélastique
Authors: Fleury F. , Nedelec J. C. 
Published: March 2007

AbstractAsymptotic study of the macroscopie behaviour of a fluid‐thermoelastic solid mixture. The homogenization theory is applied to the study of small perturbations in a mixture of a thermoelastic solid and a viscous compressible fluid. There appear memory phenomena in the bulk behaviour as well as a modification in the initial data regarding the original problem. The convergence of the formal asymptotic expansion to the solution of the homogenized equations is proved.
Qualitative properties of the boundary derivative of the capacity potential for special classes of annular domains
Authors: Acker A. , Payne L. E. 
Published: March 2007

AbstractLet U(p) denote the capacity potential in an annular domain Ω (bounded by Jordan curves). We describe the qualitative behavior of ∥Δ∥ on the line segments of ∂Ω which are arbitrary, radial, or ν‐directional (for some vector ν ≠ 0) in the respective cases where Ω is a convex, starlike, or ≠‐convex annular domain. We apply these results to some free‐boundary extremal problems in which the capacity plus weighted area functional is minimized in restricted classes of annular domains Ω.
Ein eindeutigkeitssatz für strahlungslösungen eines übergangsproblems zur schwingungsgleichung mit unbeschränkter trennfläche
Authors: Beck P. , Leis R. 
Published: March 2007

AbstractWe shall derive a Rellich‐type‐estimate for solutions in RN of a transmission problem associated with a second order uniformly elliptic differential operator of Helmholtz‐type. The transitional surface is supposed to be unbounded and a characterization of its behaviour at infinity is given. Using this estimate, we can prove a uniqueness theorem for radiation solutions of the transmission problem.
Erhaltungssätze und schwache lösungen in der gasdynamik
Authors: Bruhn G. , Wendland W. 
Published: March 2007

AbstractThe fundamental laws of Gasdynamics can be formulated very naturally as conservation laws in the form of integral relations. This formulation includes not only continuously differentiable processes but also the very important discontinuous shocks. On the other side one has the tool of weak solutions of the differential equations of Gasdynamics due to P. D. Lax and several other authors. While the conservation laws of integral type are determined by Physics in an unique way the differential equations of Gasdynamics, even if written in divergence form, are not. Hence the question arises which form of the differential equations in the weak sense is the “correct” interpretation of the physical conservation laws. This paper tries to give an answer by investigating the connections between the two formulations. At first the integral equations of Gasdynamics are written in space‐time divergence form. Thus, independently from Gasdynamics, one has Haar's lemma stating that for each weak solution of a partial differential equation (in divergence form) a corresponding integral equation of conservation law type is valid for almost every family member, the family consisting of some simple domains like spheres or squares. Moreover the converse of Haar's lemma is also true. In this paper Haar's lemma is extended to a more general class of domains. This yields that both formulations of conservation laws are essentially equivalent. Additionally a divergence definition due to C. Müller is considered. As is shown by a simple example C. Müller's divergence concept leads to a more general class of solutions, not all of them being solutions of the corresponding conservation laws.
Remarks on perfectly absorbing boundary conditions
Authors: Kołakowski H. , Piskorek A. 
Published: March 2007

AbstractA mixed problem imitating the Cauchy problem is considered. This problem is also a mixed problem with perfectly absorbing boundary conditions. A theorem about the form of the problem imitating the Cauchy problem for a scalar operator was given in [3]. Some theorems concerning perfectly absorbing boundary condition can be found in [1], [2].
A reaction‐diffusion system modelling the spread of bacterial infections
Authors: Blat J. , Brown K. J. , Hadeler K. P. 
Published: March 2007

AbstractWe investigate a system of reaction‐diffusion equations which model the spread of a bacterial infection in a human population. A decoupling technique together with global bifurcation theory is used to study the steady‐state solutions of the system. The asymptotic behaviour of solutions is discussed by using sub and subersolutions and the quasimonotonicity of the system.
On a nonlinear volterra equation
Authors: Wroclaw W. Okrasiński , Meister E. 
Published: March 2007

AbstractNonnegative solutions u of the nonlinear Volterra equation u = a * g(u) (g(0) = 0) in mathematical physics are considered. Under certain assumptions the nonhomogenuous equation u = a * g(u) + ƒ is studied. Some approximations of nonnegative solutions of the homogenuous equation are considered by the nonnegative solutions of the nonhomogenuous one.
Exterior stokes problems and decay at infinity
Authors: Specovius‐Neugebauer Maria , Wendland W. 
Published: March 2007

AbstractWe study the exterior Dirichlet and Neumann problem for the 3‐dimensional Stokes equations. By the use of the theory of hydrodynamical potentials, the decay at infinity can be completely characterized in the framework of weighted Sobolev spaces. The results are applied to the theory of weak solutions and to the Whitehead paradox.