bluuebunny/crossref_metadata_2025 huggingface dataset:
Expression pattern of stop lacZ reporter gene in adult and developing mouse brain
Authors: Couégnas Alice , Schweitzer Annie , Andrieux Annie , Ghandour M. Said , Boehm Nelly
Published: March 2007

Stable tubulin‐only polypeptide (STOP) proteins are microtubule‐associated proteins responsible for microtubule stabilization in neurons. STOP null mice show apparently normal cerebral anatomy but display synaptic defects associated with neuroleptic‐sensitive behavioral disorders. STOP null mice have therefore been proposed as an animal model for the study of schizophrenia. In the present study, the expression pattern of STOP gene in developing and adult brain has been examined by using lacZ gene inserted in the STOP locus, as a reporter gene. β‐Galactosidase (β‐gal) immunostaining was confined to neuronal cells and projections. Strong labeling was observed in the whole olfactory system, cortical layer VII, hippocampus, hypothalamus, cerebellum, habenula, fasciculus retroflexus, and interpeduncular nucleus in adults. Additionally, ventral thalamic nucleus, clusters of positive cells in striatum, and Cajal‐Retzius cells of cortical layer I were labeled in young mice. The strong expression of STOP lacZ reporter gene observed in brain is confined to areas that may be involved in the schizophrenia‐related symptoms observed in STOP‐deficient mice. © 2007 Wiley‐Liss, Inc.
Ergosterol and mycotoxins in grain dusts from fourteen Belgian cereal storages: A preliminary screening survey
Authors: Tangni Emmanuel K , Pussemier Luc
Published: March 2007

Grain dusts from farms and storage companies are generally used in animal feeding. They can give rise to airborne dust in the environment of workers or accidentally contaminate the following stored grains. Because dusts are potential mycotoxin‐rich materials, this preliminary screening survey was undertaken on citreoviridin, citrinin, cyclopiazonic acid, deoxynivalenol, gliotoxin, helvolic acid, mycophenolic acid, nivalenol, ochratoxin A, patulin, penicillic acid, secalonic acid D, sterigmatocystin, zearalenol and zearalenone. Furthermore, ergosterol was determined as a fungal growth marker. Fourteen grain dusts collected from farms and storage companies in Belgium were assayed and toxins co‐occurred at uneven distributions with wide ranges of concentrations. Median concentrations exceeded 1 µg g−1 for penicillic acid, gliotoxin, deoxynivalenol, helvolic acid, mycophenolic acid, patulin, sterigmatocystin and zearalenol. Using the median values, an assessment of worker exposure indicated that mycotoxin uptake through dust inhalation may simultaneously contribute to 0.5, 0.5, 0.7 and 0.1% of the respective tolerable daily intake of ochratoxin A, patulin, deoxynivalenol and zearalenone. In spite of these low values, the question of multi‐contamination of grain dusts and, consequently, exposure to several mycotoxins should not be underestimated. Moreover, inhalation of contaminated airborne aerosols can represent an additional route of exposure which has not been exhaustively investigated so far. Copyright © 2007 Society of Chemical Industry
Chemical composition and antimicrobial activity of Anzer tea essential oil
Authors: Şekeroǧlu Nazım , Deveci Metin , Buruk C Kurtuluş , Gürbüz Bilal , İpek Arif
Published: March 2007

Anzer tea (Thymus praecox, subsp. caucasicus var. caucasicus) naturally grows in the eastern Black Sea region of Turkey. Anzer tea, a creeping plant with crimson‐pink flowers, is important for honey production in the region. In the present study, content, composition and antimicrobial properties of Anzer tea's essential oil were investigated. Essential oil content of dried aerial plant parts varied between 1.53% and 2.05%. Essential oil composition was studied by means of gas chromatography–mass spectrometry, and 26 components were identified. The major components were thymol (47.45%), γ‐terpinene (8.73%), p‐cymene (8.30%), terpinyl acetate (4.88%) and carvacrol (4.66%). Essential oil was also screened for its antibacterial activity. In a screen for antibacterial activity, Anzer tea essential oil had significant activity against Staphylococcus aureus, Bacillus subtilis, Escherichia coli and Candida albicans. Copyright © 2007 Society of Chemical Industry
Das asymptotische verhalten der greenschen funktion N‐irregulaärer eigenwertprobleme mit zerfallenden randbedingungen
Authors: Wolter M. , Neunzert H.
Published: March 2007

We prove asymptotic estimates for the Green's function of N‐irregular eigenvalue problems My = λNγ with splitting boundary conditions.

In contrast to the N‐regular case the Green's function G(x,ζ,λ) grows exponentially for |λ| → ∞ if x > ζ.

These estimates are fundamental for the expansion of functions into a series of eigenfunctions of N‐irregular eigenvalue problems. In a subsequent paper it will be shown that this irregular behavior of G(x,ζ,λ) implies that only a very small class of functions can be expanded into a series of eigenfunctions of such problems.
On turning points
Authors: Stork W. , Robinowitz P.
Published: March 2007

For a family {T + Nλ: λ ϵ [a, b]} of semilinear operators T + Nλ in L2(Ω) the solution set {(λ, uλ) ϵ J × D(T): Tuλ + Nλuλ = h} is investigated with respect to turning points. By Ljapunov‐Schmidt‐reduction and calculation of the derivatives of the bifurcation equation a class of turning points is characterized by properties of these derivatives.
Stabilität bei Systemen mit quasizyklischen Koordinaten
Authors: Otterbein S. , Hagedorn P.
Published: March 2007

Quasicyclic or quasiignorable coordinates occur in mechanical systems with equations of motion of the Lagrangian type and can be interpreted as a generalisation of the well known cyclic or ignorable coordinates. In this paper parts of the theory of cyclic coordinates are extended to quasicyclic coordinates. Especially we present sufficient conditions for the existence of the reduced system and generalize the Routh‐Salvadori theorem about the stability of stationary motions.
Évolution quasi‐statique des milieux visco‐plastiques de maxwell‐norton
Authors: Djaoua M. , Suquet P. , Nedelec J. C.
Published: March 2007

In this paper, we deal with the existence and unicity of a solution of the Maxwell‐Norton quasi‐static problem. Some fundamental results concerning the functional spaces are first recalled. Then, by an implicit scheme, we obtain a discretized problem which is well‐posed. By monotonicity techniques, we finally prove the convergence of the discrete solutions to the solution of the initial problem.
Weak solutions of the initial value problem for the unmodified non‐linear vlasov equation
Authors: Horst E. , Hunze R. , Neunzert H.
Published: March 2007

The existence of weak LL‐solutions of the initial value problem for Vlasov's equation is proved under rather general assumptions. In the three‐dimensional case the solutions exist on the entire time axis.
A generalized jacobi theta function
Authors: Lehnigk S. H. , Roach G. F.
Published: March 2007

The delta function initial condition solution v*(x,t;y) at x = y ≥ 0 of the generalized Feller equation is used to define a generalized Jacobi Theta function for a sufficiently rapidly increasing and unbounded positive sequence {yy}. It is shown that Θ(x,t) is analytic in each variable in certain regions of the complex x and t planes and that it is a solution of the generalized Feller equation. For those parameters for which this equation reduces to the heat equation, Θ(x,t) reduces to the third Jacobi Theta function.
Forward speed motions of a submerged body. The cauchy problem
Authors: Hamdache K. , Nedelec J. C.
Published: March 2007

We consider the linearized problem for the ideal fluid flow induced by the horizontal motion of a fully immersed body. The system of equations is made up of an elliptic problem (P) and an initialvalue problem (R) which are coupled by a pseudo‐differential operator T.

We define a regularized Cauchy problem (Rϵ) using the Yosida approximation of T; we give energy and wave resistance estimates and finally we obtain existence uniqueness and regularity of the weak solution of (R) by taking the limit when ϵ goes to zero.
Two classes of explicit solutions of the carleman model
Authors: Wick J. , Neunzert H.
Published: March 2007

For the Carleman model we show two classes of global explicit solutions.
Numerical Computation of Waves at High Frequencies by an Iterated WKB‐Method
Authors: Alber H. D. , Leis R.
Published: March 2007

An integral operator is defined, which allows to solve the equation

equation image

by Neumann series for sufficiently large k > 0. The kernel is constructed by a modification of the WKB‐method. This kernel is so simple that the operator can be used effectively for numerical calculations. Numerical results are discussed.
On the Vlasov‐Fokker‐Planck equation
Authors: Neunzert H. , Pulvirenti M. , Triolo L.
Published: March 2007

We study a modification of the Vlasov‐Poisson equation, obtained by adding a diffusion term with respect to velocity. It describes, from a physical point of view, a plasma in thermal equilibrium, in a mean field limit situation. We find that the already known results concerning existence and uniqueness of the solutions for the ordinary Vlasov equation (constructive results and counterexamples) translate to our case.
On the statistical solutions of the two‐dimensional, periodic Euler equation
Authors: Caprino S. , De Gregorio S. , Neunzert H.
Published: March 2007

We investigate the problem to define statistical solutions for the two‐dimensional, periodic Euler Equation and prove a theorem of global existence and uniqueness for a regularized version. Moreover, we deduce the existence of the Euler flow in a weak form.
On spline collocation methods for boundary integral equations in the plane
Authors: Schmidt G. , Wendland W.
Published: March 2007

Nowadays boundary elemen; methods belong to the most popular numerical methods for solving elliptic boundary value problems. They consist in the reduction of the problem to equivalent integral equations (or certain generalizations) on the boundary Γ of the given domain and the approximate solution of these boundary equations. For the numerical treatment the boundary surface is decomposed into a finite number of segments and the unknown functions are approximated by corresponding finite elements and usually determined by collocation and Galerkin procedures. One finds the least difficulties in the theoretical foundation of the convergence of Galerkin methods for certain classes of equations, whereas the convergence of collocation methods, which are mostly used in numerical computations, has yet been proved only for special equations and methods.

In the present paper we analyse spline collocation methods on uniform meshes with variable collocation points for one‐dimensional pseudodifferential equations on a closed curve with convolutional principal parts, which encompass many classes of boundary integral equations in the plane. We give necessary and sufficient conditions for convergence and prove asymptotic error estimates. In particular we generalize some results on nodal and midpoint collocation obtained in [2], [7] and [8].

The paper is organized as follows. In Section 1 we formulate the problems and the results, Section 2 deals with spline interpolation in periodic Sobolev spaces, and in Section 3 we prove the convergence theorems for the considered collocation methods.
Radial sums of ridge functions: A characterization
Authors: Madych W. R. , Nelson S. A. , Payne L. E.
Published: March 2007

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

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

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

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

We study the differential‐delay equation x′(t) = −αf(x(t–1)), where α is a positive parameter and f is an odd function which decays like x−r at infinity. In particular, we consider the case r ⩽ 2, and prove the existence of periodic solutions with special symmetries which are different from previously known periodic solutions of minimal period 4. For r = 2 we prove sharp asymptotic estimates for the minimal periods of these solutions.

Our results disprove a conjecture of R. D. Nussbaum.
An integral equation of elasticity
Authors: Kolakowski H. , Piskorek A.
Published: March 2007

In this work a certain mixed problem in R for the Lamé equations in the theory of elasticity is reduced to the integral equation

magnified image

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

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

We consider (in two‐dimensional Euclidean space) the scattering of a plane, time‐harmonic acoustic wave by an inhomogeneous medium Ω with compact support and a bounded obstacle D lying completely outside of the inhomogeneous medium. We show that one may determine the shape of D and the local speed of sound in Ω from a knowledge of the asymptotic behavior of the scattered wave (i.e. the far field). This is done by considering a constrained optimization problem and employing integral equation and conformal mapping techniques.

By assuming a priori that the functions which determine the shape of D and the local speed of sound in Ω lie in given compact sets, we show that the problem is stable, in the sense that the solution of the inverse scattering problem depends continuously on the far field data.
Taylor series for the dirac function on perturbed surfaces with applications to mechanics
Authors: Codaccioni R. Caboz J.‐P. , Constantinescu F. , Meister E.
Published: March 2007

Let H0 be the Hamiltonian of an unperturbed oscillating system and let V be a small perturbation which is analytic in a neighborhood of the surface H0 = E, E > 0.

If H0 = H + λ V is the total Hamiltonian, we prove that there is a Taylor expansion of the Dirac function δ for small |λ|

magnified image

When applied to test functions which are analytic near H0 = E.

The connection of this result with the classical Lagrange‐Bürmann theorem and some applications to the mechanics of non‐linear systems are discussed.
A class of explicitly resolvable evolution equations
Authors: Bazley N. W. , Weinacht R. J. , de Jager E.
Published: March 2007

We consider a class of evolution equations with “scalar nonlinearities” and the associated steady equations. An explicit representation of solutions is obtained in terms of the solution of a scalar nonlinear functional differential equation. Convergence to an equilibrium solution is discussed.
On the absolutely continuous spectrum of MHD plasma confined in the flat torus
Authors: Kako T. , Fujita H.
Published: March 2007

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

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

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

The paper concerns the investigation of two classes of nonlinear singular integral equations with Cauchy kernel important in the applications. There are given uniqueness and existence theorems, the last by a novel application of Schauder's fixed point theorem to this type of equations.
A remark on N. Korevaar's concavity maximum principle and on the asymptotic uniqueness of solutions to the plasma problem
Authors: Kawohl B. , Payne L.
Published: March 2007

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

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

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

A scheme for the simulation of solutions of the Boltzmann equation derived by Nanbu is investigated. Rigorous results concerning questions of justification, the computation effort and the energy fluctuations are presented.
Polarized light transfer above a reflecting surface
Authors: van der Mee C. V. M. , Neunzert H.
Published: March 2007

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

Recently, the control engineers interest turns upon material with structural damping, such as hysteretic effects in elastoplastic systems [27] and flexible space structures [30] and in particular with damping due to the viscoelastic nature of the material, in the sense of Kelvin, [7], [12]. The reason for this renewed interest is the possibility of constructing finite rank compensators with small spillover in the observation [1], [5], [11], [25].

However, a control theory for the infinite system does not seem to exist in the literature. It is shown that the trajectories, initially in a certain subspace, can be steered to rest in any time T > 0 using distributed load controls

The reesults are partially contained in [19].

. Furthermore, and perhaps more interesting, the L2 (0, T, H)‐norm of the control decreases as T increases. This gives rise to the problem of time‐optimal‐controllability and the correlation to the problem of minimum norm controllability.

It is shown that the time‐optimal control is characterized by a weak “bang‐bang” principle.
Distribution of resistive body‐force in curved free‐surface flow
Authors: Sivakumaran N. S. , Dressler R. F. , Brosowski B.
Published: March 2007

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

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

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

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

We study stationary solutions of the Vlasov‐Fokker‐Planck Equation, a modification of the Vlasov‐Poisson Equation, obtained by adding a diffusion term with respect to velocity. From a physical point of view it describes a plasma in thermal equilibrium.

We prove existence of stationary solutions; for the mollified equation even an existence‐ and uniqueness theorem holds for sufficiently high temperature.
Zu einigen mathematischen problemen in der theorie der transonischen strömung
Authors: Kozel K. , Polášek J. , Meister E.
Published: March 2007

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

We show the convergence in the L∞ norm of the approximation by finite element of the Hamilton‐Jacobi‐Bellman equation.
equation image

The proof uses the subsolution's method and the notion of discret regularity. Since the submission, the optimal result has been obtained.
On an initial boundary‐value problem for a model system of equations of a granulated medium
Authors: Łukaszewicz G. , Piskorek A.
Published: March 2007

In this paper we consider an initial boundary‐value problem for the system of equations describing the motion of a granulated medium with constant density.

We introduce the notion of a weak solution of the problem and prove the existence of such a solution.
A free boundary problem and stability for the circular plate
Authors: Miersemann E. , Mittelmann H. D. , Törnig W.
Published: March 2007

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

A general optimal control model for running and swimming is developed, whose principal parameters are the energy reserves, the breathing rate and the force. This model is then applied to the world records in these disciplines. It describes the data very well and the parameters employed have values, which agree closely with those obtained by other means.
On the low wave number asymtotics for the two‐dimensional exterior dirichlet problem for the reduced wave equation
Authors: Kress R. , Brosowski B.
Published: March 2007

A new proof is given for the low wave number asymptotics for the solutions to the exterior Dirichlet problem for the reduced wave equation in two dimensions.
Time optimal boundary controllability of a simple linear viscoelastic liquid
Authors: Leugering G. , Hagedorn P.
Published: March 2007

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

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

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

This paper is dedicated to the identification of constitutive parameters of the Mohr–Coulomb constitutive model from in situ geotechnical measurements. A pressuremeter curve and the horizontal displacements of a sheet pile wall retaining an excavation are successively used as measurements. Two kinds of optimization algorithms are used to minimize the error function, the first one based on a gradient method and the second one based on a genetic algorithm. The efficiency of each algorithm related to the error function topology is discussed. Finally, it is shown that the use of a genetic algorithm to identify the soil parameters seems particularly suitable when the topology of the error function is
complex. Copyright © 2007 John Wiley & Sons, Ltd.
A critical review of the pharmacology of the plant extract of Pygeum africanum in the treatment of LUTS
Authors: Edgar Alan D. , Levin Robert , Constantinou Christos E. , Denis Louis
Published: March 2007

Despite an unremitting increase in the number of patients presenting symptoms of benign prostate hyperplasia (BPH), the viable treatment options remain relatively limited when compared to other disorders of aging. This has spurred an interest in so‐called alternative medicines, many of which continue to be used in spite of the more recent emergence of rationally targeted therapies. Nonetheless, in the case of plant extracts, the vast majority of these have not been subjected to the same rigorous pre‐clinical pharmacological testing and large‐scale clinical trials now required by health authorities. Furthermore, demonstration of their clinical efficacy in BPH has been hindered by trials of limited duration with a high placebo response. Beginning with a preliminary demonstration of in vitro inhibition of growth factor‐mediated fibroblast proliferation with Pygeum africanum extract, a detailed series of in vitro and in vivo studies on prostate growth and bladder function were undertaken. These studies, reviewed herein, have permitted the identification of putative molecular targets of Pygeum africanum extract affecting both growth factor‐mediated prostate growth as well as specific parameters of bladder function. These results, corroborated in part by short‐term clinical efficacy, set the stage for a large‐scale clinical trial to investigate the efficacy of Pygeum africanum extract in the treatment of lower urinary tract symptoms. Neurourol. Urodynam. 26:458–463, 2007. © 2007 Wiley‐Liss, Inc.
Alternating direction finite volume element methods for 2D parabolic partial differential equations
Authors: Wang Tongke
Published: March 2007

On the basis of rectangular partition and bilinear interpolation, this article presents alternating direction finite volume element methods for two dimensional parabolic partial differential equations and gives three computational schemes, one is analogous to Douglas finite difference scheme with second order splitting error, the second has third order splitting error, and the third is an extended locally one dimensional scheme. Optimal L2 norm or H1 semi‐norm error estimates are obtained for these schemes. Finally, two numerical examples illustrate the effectiveness of the schemes. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007
Analysis and finite element simulations of a second‐order fluid model in a bounded domain
Authors: Arada Nadir , Correia Paulo , Sequeira Adélia
Published: March 2007

This article is concerned with the equations governing the steady motion of a viscoelastic incompressible second‐order fluid in a bounded domain. A new proof of existence and uniqueness of strong solutions is given. In addition, using appropriate finite element methods to approximate a coupled equivalent problem, sharp error estimates are obtained using a fixed point argument. The method is applied to the two‐dimensional lid‐driven cavity problem, at low Reynolds number and in a certain range of values of the viscoelastic parameters, to analyze the combined effects of inertia and viscoelasticity on the flow. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007
Industrial applications of the surface activity of polydimethylsiloxanes
Authors: Owen Michael J. , Evans John I.
Published: March 2007

The surface properties of silicones are responsible for many of their varied applications. An explanation in basic terms is given in this paper for this surface activity together with some insight into several of the applications that result from this surface activity.
Pyrolysis study of bromo‐ and chloroethyl benzenes in micropulse and flow reactors
Authors: Daren Stephen , Levy Moshe , Vofsi David
Published: March 2007

The pyrolytic and catalytic dehydrobromination of 2‐bromoethyl bromobenzene was studied as a step in the production of bromostyrene. The studies were carried out in a micropulse reactor attached to a gas chromatograph and in a number of ordinary flow reactors. Most of the work was carried out on 2‐Cl and 2‐Br ethyl benzene as model compounds. Catalytic effects of metals, oxides and molten salts were found. The pyrolytic reaction in the micropulse and flow reactors proved to be much faster than expected from the literature data on the monomolecular elimination studied in static systems. The addition of peroxides accelerates the reaction further and results in high conversions and high purity monomers at relatively low temperatures.
Inorganic oxide glasses as ionic polymers
Authors: Ray Neil H.
Published: March 2007

Oxide glasses can be regarded as network polymers consisting of oxygen atoms linked through multivalent atoms such as boron, silicon and phosphorus, and many of their properties can be related to two simple parameters of the network; the crosslink density and the packing density of oxygen atoms. The effects of changes in composition on the transformation temperatures of phosphate, borate, and borophosphate glasses can be rationalised in terms of these two network parameters.
Shish kebab formation on polyethylene monofilaments
Authors: Smith Paul , Pennings Albert J.
Published: March 2007

A study has been made on skin formation of melt spun polyethylene monfilaments, which were solidified in air or in cold solvents and non‐solvents. Application of air or non‐solvents, such as water and acetone, as cooling media induced spherulitic crystallisation of the polymer, as was revealed in the scanning electron microscope. When the flowing polyethylene melt was quenched in good solvents, a 0.5 mm thick layer of lamellar or shish kebab structures developed on the polymeric fibres. It was established that shish kebabs were formed when the solvents, in which the polymer filament was quenched, were boiling during this solidification process.
Synthesis and characterisation of fluorine‐containing poly α‐esters. II. Thermal and hydroxyl‐initiated polymerisation of pentafluorophenyl‐substituted anhydrosulphites and anhydrocarboxylates of α‐hydroxycarboxylic acids
Authors: Smith Ian J. , Tighe Brian J.
Published: March 2007

The use of anhydrosulphite and anhydrocarboxylate derivatives of α‐pentafluorophenyl‐α‐hydroxypropanoic acid as precursors in the formation of fluorine‐containing poly α‐esters is described. Kinetic studies have enabled the nature of the competing mechanisms to be determined and compared with those occurring in the hydrocarbon analogues. The pentafluorophenyl group markedly enhances the susceptibility of both ring systems to hydroxyl‐initiated polymerisation and in the case of the anhydrocarboxylate this is the only viable polymerisation mechanism under the conditions described here. Although polymerisation of the anhydrosulphites is possible, purification of both the phenyl, and especially the pentafluorophenyl substituted monomer, is more difficult than in the case of either alkyl substituted anhydrosulphites or phenyl and pentafluorophenyl substituted anhydrocarboxylates. For this reason anhydrocarboxylate polymerisation represents the preferred route to pentafluorophenyl substituted poly α‐esters. The characterisation of the polymers produced is discussed.
Influence of non‐ionic surfactant on the stability of styrene—acrylonitrile copolymer latices
Authors: Ono Hiroshi , Jidai Eiki
Published: March 2007

Styrene–acrylonitrile copolymer latices were prepared by emulsion polymerisation using sodium lauryl sulphate as emulsifier and potassium persulphate as initiator. The effect of polyoxyethylene nonyl phenyl ether on the stability of these copolymer latices has been investigated using magnesium chloride as a flocculating agent by measuring the rates of flocculation in the presence of various concentrations of surfactant. The values of the critical coagulation concentration (c.c.c.) were found to increase with increasing surfactant concentration for all latices. The rates of increase in c.c.c. with increasing surfactant concentrations were found to increase uniformly with increase in the content of acrylonitrile. The electrophoretic behaviour of these latices in the presence of surfactant has also been investigated. The values of mobilities at c.c.c. were found to decrease with increasein concentration of surfactant.
Thermal degradation of some perfluoroalkylene‐linked polymers
Authors: Cotter John L. , Knight Graham J. , Wright Walter W.
Published: March 2007

Poly (1,3‐phenylenehexafluorotrimethylene) and perfluoroalkylene‐linked polyanhydride, polycarbonate and polyester have been studied by thermogravimetry, pyrolysis–gas chromatography–mass spectrometery and fluoride ion analysis. The thermal stability is governed by the ease of formation of specific cyclic degradation products.
Application of gel permeation chromatography to the study of shear degradation of polymeric viscosity index improvers used in automotive engine oils
Authors: Hillman Donald E. , Lindley Helen M. , Paul John I. , Pickles Donald
Published: March 2007

Gel permeation chromatography (g.p.c.) was used to monitor the degradation of polymeric viscosity index improvers in multigrade oils when subjected to mechanical shear using a Kurt Orbahn diesel injector rig. These tests are normally evaluated by measurement of viscosity of the oils before and after shear. For model systems of a base oil containing each of ten viscosity index improvers there is good correlation between viscosity and chromatography results. Tests on a multigrade oil subjected to sonic shear showed that g.p.c. can be used to follow qualitatively the degradation of one polymeric additive in the presence of another.
The thermal decomposition of some polyurethane foams
Authors: Chambers John , Reese Colin B.
Published: March 2007

Polyurethanes exposed to fire conditions might generate decomposition products which would be responsible for a significant part of the toxicity of the fire gases.

Polyurethanes have been prepared from a commercial mixture of tolylene‐2, 4‐ and 2,6‐di‐isocyanates, pure tolylene‐2,4‐di‐isocyanate, pure tolylene‐2,6‐di‐isocyanate and pure m‐phenylene di‐isocyanate. All polymers except that prepared from tolylene‐2,6‐di‐isocyanate were obtained as flexible foams. When each polyurethane was heated at 300°C in a stream of nitrogen, a sublimate was obtained. The sublimates were all apparently polymers derived from the di‐isocyanate rather than from the diol constituents of the polyurethanes. Pyrolysis of these materials at high temperatures (800–1000°C) led to similar mixtures of volatile products: at 1000°C the most abundant nitrogenous product, in each case, was hydrogen cyanide.
A proton magnetic resonance study of the self‐condensation of formaldehyde
Authors: Jones R. G. , Kodama Y.
Published: March 2007

The self‐condensation of formaldehyde in heavy water (D2O) has been studied against the more general background of the urea—formaldehyde system. Proton magnetic resonance data are reported for monomethylol urea (MMU), dimethylol urea, methylolbisurea (MBU) and solutions of formaldehyde in D2O at various concentrations over a limited temperature range. The results for formaldehyde lead to disagreement with the statistical interpretation of previous workers. The more accurate n.m.r. data presented here fit the random difunctional polycondensation model with a single parameter, within experimental, error, in contrast to the two needed by other authors.