bluuebunny/crossref_metadata_2025 huggingface dataset:
Low power microwave‐assisted enzymatic esterification of starch
Authors: Lukasiewicz Marcin , Kowalski Stanislaw
Published: November 2011

A series of starch esters was obtained using microwave‐assisted enzymatic transformation of starch. For the reaction hog pancreas lipase was used as a biocatalyst as well as followed acyl donors: acetic, lauric, and stearic acid. DMF and DMSO were applied as a reaction media. Experiments focused on low level microwave irradiation were compared with conventional heating of the reaction mixture. The structure of obtained starch esters was investigated by means of FTIR, analysis of substitution degree, changes in molecular parameters (MWs and MWs distributions), and microscopic studies (SEM). The spectroscopic analysis confirmed the ester bond formation. The microwave‐assisted reaction in DMF and lauric acid as an acyl donor, gave the highest degree of substitution (0.513) what followed the lowest polysaccharide degradation and maintaining the granular structure of starch. According to all the results the significant shortening in the reaction time (about 2.5 times) for microwave‐assisted reactions were observed. The influence of microwaves on esterification of starch was discussed focusing on reaction media and acyl donor type. The investigated reaction systems were demonstrated as new protocols for obtaining starch ester with higher efficiency in comparison to those known as conventional. Replacement of sophisticated derivatives including vinyl esters or acyl chlorides by simple acyl donors were shown as an additional benefit of proposed starch esterification method.
Computational toxicology: a tool for all industries
Authors: Marchant Carol A.
Published: November 2011

Statistical, expert system, and machine learning methods among others have been used to developin silicotools for the prediction of toxicological hazard from chemical structure. The models are being applied to the mammalian and environmental toxicological assessment of chemicals across a range of industries including cosmetics, foods, industrial chemicals, and pharmaceuticals. Their use within a regulatory environment has also been encouraged by recent legislation. Generally, the models address the potential toxicity of low to medium molecular weight organic chemicals but models for other chemical types such as proteins and nanoparticles have also received some attention. © 2011 John Wiley & Sons, Ltd.

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Computer and Information Science > Chemoinformatics
Carry-over effect of host nutritional quality on performance of spruce budworm progeny
Authors: Fuentealba A. , Bauce É.
Published: November 2011

The effect of host nutritional quality on spruce budworm (Choristoneura fumiferana(Clemens)) parental and offspring performance was studied using field and laboratory rearing experiments, and foliar chemical analyses. Foliage of balsam fir (Abies balsamea(L.) Mill.), white spruce (Picea glauca(Moench) Voss) and black spruce (P. mariana(Mill.) BSP) was used to rear the parental generation in the field, whereas an artificial diet was used to rear the progeny under laboratory conditions. Important differences in the food quality were provided by the three hosts. Black spruce foliage had higher concentrations of certain monoterpene deterrents and total phenolics, together with stronger seasonal declines in nutrients such as N, P and Mg, compared with the other hosts. We hypothesise that this trend may be related to poor performance and survival of the progeny. Laboratory rearing showed that progeny of parents that fed on black spruce exhibited longer developmental times and greater mortality, and had lower pupal mass than progeny of parents fed on the other hosts. Further, artificial food-fed progeny of insects reared on black spruce reached sixth-instar later, with lower mass, and exhibited higher relative growth rate (RGR) than progeny of parents fed on the other hosts. These results suggest nutritionally-based parental effects. These results also confirmed that the quality of food consumed by the parents can influence the fitness of the next generation.
On the Economic Consequences of the Peace: Trade and Borders After Versailles
Authors: WOLF NIKOLAUS , SCHULZE MAX-STEPHAN , HEINEMEYER HANS-CHRISTIAN
Published: November 2011

The First World War radically altered the political landscape of Central Europe. The new borders after 1918 are typically viewed as detrimental to the region's economic integration and development. We argue that this view lacks historical perspective. It fails to take into account that the new borders followed a pattern of economic fragmentation that had emerged during the late nineteenth century. We estimate the effects of the new borders on trade and find that the “treatment effects” of these borders were quite limited. There is strong evidence that border changes occurred systematically along barriers which existed already before 1914.
Catching-Up and Falling Behind: Knowledge Spillover from American to German Machine Toolmakers
Authors: RICHTER RALF , STREB JOCHEN
Published: November 2011

Today, German machine toolmakers accuse their Chinese competitors of violating patent rights and imitating German technology. A century ago, German machine toolmakers used the same methods to imitate American technology. To understand the dynamics of this catching-up process, we use patent statistics to analyze firms’ activities between 1877 and 1932. We show that German firms deployed imitating strategies in the late nineteenth century and the 1920s to catch-up to their American competitors. The German administration supported this strategy by stipulating a patent law that discriminated against foreign patent holders and by delaying the granting of patents to foreign applicants.
Perturbational analysis of dual trigonometric series associated with boundary conditions of first and third kind
Authors: Kelman Robert B.
Published: November 2011

Synopsis

Existence and uniqueness theorems are established for dual trigonometric equations having right-hand sides that are given functions of bounded variation. The first equation in each pair has coefficients, say {Jn(n + h)} or (jn(n + h – ½)}, and the second equation coefficients {jn)}, where h is a nonnegative constant. A potential problem involving mixed boundary conditions of first and third kind is associated with each dual series. The potential problem is analysed using a stepwise perturbation procedure involving solutions in powers of h. The analysis demonstrates that the present dual series problem can be resolved if the dual series problem associated with the case h = 0 is solvable, the latter being a result obtained earlier.
Electrostatics in a gravitational field
Authors: Copson E. T.
Published: November 2011

Synopsis

In this paper, the electrostatic potential of a point charge in a Reisser-Nordström gravitational field is found in closed form by using the theory of Hadamard's elementary solution of a partial differential equation of elliptic type.
The asymptotic behaviour of semigroups of nonlinear contractions having large sets of fixed points
Authors: Pazy A.
Published: November 2011

Synopsis

The asymptotic behaviour of semigroups of nonlinear contractions which have a set of fixed points containing a ball of finite codimension is studied. It is shown that the ω-limit sets of such semigroups are finite dimensional tori, and that an analogue of the classical Kronecker-Weil theorem holds for such semigroups.
A boundary-value problem for an ordinary differential equation whose coefficients are in a B*-algebra
Authors: Moodie James
Published: November 2011

Synopsis

We give some results on a boundary-value problem for an ordinary differential equation whose coefficients are in the B*-algebra C(K), where K is a compact metric space. We deduce the existence of a countable number of eigenvalues and corresponding eigenfunctions, the latter being complete in a certain sense. There follows an expansion result and some remarks on a self-adjoint realisation of the associated differential operator.
Non-linear Sturm-Liouville problems with no secondary bifurcation
Authors: McLeod J. B. , Stuart C. A.
Published: November 2011

Synopsis

The paper is concerned with giving sufficient conditions that in the non-linear boundary-value problem

there should be no secondary bifurcation, i.e. that, given a branch of solutions (u, λ) bifurcating from the trivial solution, there should be no further bifurcation on that branch. Sufficient conditions on G are given which include, for example, Kolodner's problem of the motion of a heavy rotating string.
The interlacing of eigenvalues for periodic multi-parameter problems
Authors: Browne Patrick J.
Published: November 2011

Synopsis

This paper studies a linked system of second order ordinary differential equations

where xx ∈ [ar, br] and the coefficients qrars are continuous, real valued and periodic of period (br − ar), 1 ≤ r,s ≤ k. We assume the definiteness condition det{ars(xr)} > 0 and 2k possible multiparameter eigenvalue problems are then formulated according as periodic or semi-periodic boundary conditions are imposed on each of the equations of (*). The main result describes the interlacing of the 2k possible sets of eigentuples thus extending to the multiparameter case the well known theorem concerning 1-parameter periodic equation.
Periodic solutions of special differential equations: an example in non-linear functional analysis
Authors: Nussbaum Roger D.
Published: November 2011

Synopsis

We consider differential-delay equations which can be written in the form

The functions fi and gk are all assumed odd. The equation

is a special case of such equations with q = N + 1 (assuming f is an odd function). We obtain an essentially best possible theorem which ensures the existence of a non-constant periodic solution x(t) with the properties (1) x(t)≧0 for 0≦t≦q, (2) x(–t) = –x(t) for all t and (3) x(t + q) = –x(t) for all t. We also derive uniqueness and constructibility results for such special periodic solutions. Our theorems answer a conjecture raised in [8].
Generic bifurcation and symmetry with an application to the Von Kármán equations
Authors: Vanderbauwhede André L.
Published: November 2011

Synopsis

A generic bifurcation theory is developed which is somewhat different from the approach in [4]. We put special emphasis on equations satisfying additional symmetry properties and on the non-generic bifurcation sets arising in this context. We apply our results on the von Kármán equations for the buckling of a rectangular plate under a compressive thrust and a normal load.
On properties related to A-compactness, an example
Authors: Voigt Jürgen
Published: November 2011

Synopsis

We present an example (section 3) which serves two purposes: it is a counterexample to a conjecture of Weidmann (see section 1) and it clarifies the relations between different properties related to A-compactness (see section 2).
Fundamental solutions for the anisotropic neutron transport equation
Authors: Conlon Joseph G.
Published: November 2011

Synopsis

We construct a fundamental solution for the n dimensional time independent anisotropic neutron transport equation. This is an operator valued distribution G(x) with a singularity at the origin. By estimating G(x) we are able to construct smooth solutions to the transport equation. We are also able to derive in a straightforward fashion results of Birkhoff and Abu-Shumays on the existence of harmonic solutions to the isotropic transport equation. When n = 1, G(x) is a function which is continuous except at x = 0. We show that the classical formula for the jump of G(x) at the origin is equivalent to the completeness of Case's full range eigenfunction expansion.
Norm inequalities involving derivatives
Authors: Evans W. D. , Zettl A.
Published: November 2011

Synopisis

A new method for studying inequalities of the type ‖y(r)‖2<ε‖Sk−ry(k)‖2 + K(ε)‖S−ry‖2 and ‖y′‖2≦ Kp(S)‖Sy″‖ ‖S−1y‖ is presented here. With this new approach we obtain new and far reaching extensions of previously known inequalities of this sort as well as simpler proofs of the known cases. In addition we obtain an inequality of type ‖Sy′‖<ε‖(Sy′)′‖ + K(ε)‖y‖ for a general class of functions S. Also we give an elementary operator-theoretic proof of Everitt's characterization of the best constant as well as all cases of equality for
Oscillation theorems for semilinear elliptic differential operators
Authors: Naito Manabu , Yoshida Norio
Published: November 2011

Synopsis

The semilinear elliptic differential operator L[u] = Δu + c(x, u) is studied and sufficient conditions are derived for all solutions of uL[u] ≦ 0 with suitable boundary conditions to be oscillatory in unbounded domains of Rn. Here, unbounded domains to be considered are cones, strips and cylinders in Rn. The results are based on the conditions for the non-existence of positive solutions of ordinary differential inequalities.
Semigroups of translations associated with functional and functional differential equations
Authors: Dyson Janet , Villella-Bressan Rosanna
Published: November 2011

Functional and functional differential equations in a Banach space X are related to systems of operators A(t) in C = C(−r, 0; X), given by

Conditions are sought on F such that A(t) generates an evolution system U(t, s)φThis system gives the segments of solution for φ in a certain domain which is determined.
Nonlinear parabolic problems in unbounded domains
Authors: Mahler Guy
Published: November 2011

We show the existence of weak solutions of nonlinear parabolic partial differential equations in unbounded domains, provided that a variant of the Leray-Lions conditions is satisfied.
Jacobi fields and geodesic spheres
Authors: Vanhecke L. , Willmore T. J.
Published: November 2011

Synopsis

This is a contribution to the general problem of determining the extent to which the geometry of a riemannian manifold is determined by properties of its geodesic spheres. In particular we show that total umbilicity of geodesic spheres determines riemannian manifolds of constant sectional curvature; quasi-umbilicity of geodesic spheres determines Kähler and nearly-Kähler manifolds of constant holomorphic sectional curvature; and the condition that geodesic spheres have only two different principal curvatures, one having multiplicity 3, determines manifolds locally isometric to the quaternionic projective spaces. The use of Jacobi vector fields leads to a unified treatment of these different cases.
Strongly irregular boundary value problems
Authors: Schultze Bernd
Published: November 2011

Synopsis

A new class of irregular boundary value problems—non-regular in the sense of Birkhoff—is studied. This class of strongly irregular problems includes the class of boundary value problems with irregular decomposing boundary conditions. For each strongly irregular problem we can find a problem with irregular decomposing boundary conditions so that we have equiconvergence with respect to Riesz typical means of the eigenfunction expansions arising from these two problems of an arbitrary summable function.
On the hypertranscendence of meromorphic solutions of certain functional equations
Authors: Bank Steven B.
Published: November 2011

Synopsis

This paper deals mainly with showing that meromorphic solutions of Poincaré functional equations cannot satisfy algebraic differential equations. Results of this type for entire solutions have previously been obtained by H. Wittich.
An asymptotic method for non-linear magnetosonic waves in an isothermal plasma with a finite conductivity
Authors: Fusco Domenico
Published: November 2011

Synopsis

The paper is concerned with a Three-dimensional theory of non-linear magnetosonic waves in a turbulent plasma. A perturbation method is used that allows us to obtain a transport equation, like Burgers equation, but with a variable coefficient.
On regularized distance and related functions
Authors: Fraenkel L. E.
Published: November 2011

Synopsis

LetFbe any closed subset of ℝN. Stein's regularized distance is a smooth (C∞) function, defined on the complementcF, that approximates the distance fromFof any pointx ∈cFin the manner shown by the inequalities (*) in the Introduction below. In this paper we use a method different from Stein's to construct a one-parameter family of smooth approximations to any positive Lipschitz continuous function, with the effect that the constants in (*) can be made arbitrarily close to 1. It is shown that partial derivatives of order two or more, while necessarily unbounded, are best possible in order of magnitude.
Positive solutions of a non-linear eigenvalue problem with discontinuous non-linearity
Authors: Nistri Paolo
Published: November 2011

Synopsis

We seek non-trivial solutions (u,λ)∈C1([0,1])×[0,∞ with u(x)≧0 for all x ∈[0,1], of the nonlinear eigenvalue problem –u″(x)=λf(u(x)) for x ∈ (0,1) and u(0)=u(1)=0,where f:[0,∞)→[0,∞) is such that f(p) = 0, for p ∈ [0,1), and f(p) = K(p), for p ∈ (1,∞), and K: [1, ∞)→(0, ∞) is assumed to be twice continuously differentiable. (The value ƒ(1) is only required to be positive.)

Existence and multiplicity theorems are given in the cases where ƒ is asymptotically sub-linear and ƒ is asymptotically super-linear. Moreover if strengthened assumptions are made on the growth of the non-linear term ƒ we obtain the precise number of non-trivial solutions for given values of λ ∈ [0, ∞).
On certain fourth-order integral inequalities
Authors: Russell A.
Published: November 2011

Synopsis

The integral inequalities with which this paper is concerned are

and

whereK(μ) andK1(μ) are positive numbers which depend on μ.

It is shown that each of these inequalities is valid only when μ = 0. Results relating to the corresponding inequalities on the extended interval (−∞, ∞) are also given.
A representation theorem for a complete Boolean algebra of projections
Authors: Dowson H. R. , Gillespie T. A.
Published: November 2011

Synopsis

Let B be a complete Boolean algebra of projections on a complex Banach space X and let (B) denote the closed algebra of operators generated by B in the norm topology. It is shown that there is a complex Hilbert space H, a complete Boolean algebra B0 of self-adjoint projections on H, and an algebraic isomorphism of B onto B. This isomorphism is bicontinuous when B and B are endowed with the norm topologies, the weak operator topologies or the ultraweak operator topologies. It is also bicontinuous on bounded sets with respect to the strong operator topologies on B and B. As an application, it is shown that the weak and ultraweak operator topologies in fact coincide on B.
Oscillation criteria for second order hyperbolic initial value problems
Authors: Pagan Gordon , Stocks David
Published: November 2011

Synopsis

It is established that under certain restrictions the solution u of the equation uxy − gu = 0 satisfying u(x, 0) = p(x) and u(0,y) = q(y) in ([0, = ∞) × [0, ∞), changes sign in where (X, Y) is any point in the relevant region.
Higher order Wirtinger inequalities
Authors: Kreith Kurt , Swanson Charles A.
Published: November 2011

Synopsis

Wirtinger-type inequalities of order n are inequalities between quadratic forms involving derivatives of order k ≦ n of admissible functions in an interval (a, b). Several methods for establishing these inequalities are investigated, leading to improvements of classical results as well as systematic generation of new ones. A Wirtinger inequality for Hamiltonian systems is obtained in which standard regularity hypotheses are weakened and singular intervals are permitted, and this is employed to generalize standard inequalities for linear differential operators of even order. In particular second order inequalities of Beesack's type are developed, in which the admissible functions satisfy only the null boundary conditions at the endpoints of [a, b] and b does not exceed the first systems conjugate point (a) of a. Another approach is presented involving the standard minimization theory of quadratic forms and the theory of “natural boundary conditions”. Finally, inequalities of order n + k are described in terms of (n, n)-disconjugacy of associated 2nth order differential operators.
An extension of the method of the hypercircle to linear operator problems with unilateral constraints
Authors: Collins W. D.
Published: November 2011

Synopsis

By using a Hilbert space decomposition theorem for two polar cones it is shown that the method of the hypercircle can be extended to determine solutions to best approximation problems involving unilateral constraints. The method is applied to abstract boundary value problems for linear operators involving such constraints.
On the local stability of wave fronts defined by eikonal equations
Authors: Rand David
Published: November 2011

SYNOPSIS

Associated with a Cauchy problem for an eikonal equation is a structure of caustics and wave fronts. The geometrical properties of these structures are of considerable interest and one would like to classify them. The first step in such a programme is to identify those solutions whose structures have certain (structural) stability properties or robustness. These are structures which survive small perturbations of the initial conditions. (It turns out that they also survive small perturbations of the equation.) This problem for caustics has been tackled with considerable success by a number of authors, in particular by Arnold. Here we develop the analogous, but different, theory for wave fronts and give an algebraic characterization of those local solutions of eikonal equations which have stable wave front structures. From this result it is easy to deduce the qualitative form of those stable wave front structures which occur when the propagation occurs in a space of dimension not greater than five. They correspond to Thorn's elementary catastrophes, as demonstrated by Zakalyukin.
Limit-point criteria for systems of differential equations
Authors: Frentzen Hilbert
Published: November 2011

SYNOPSIS

For a certain class of first order systems of differential equations several theorems are derived which give sufficient conditions for an appropriate sesquilinear form to be identically zero on suitable spaces of solutions of the system. As a consequence for second order systems limit-point criteria are obtained which include rather general criteria in the case of second order equations. The method used involves sequences of auxiliary functions and is most expedient for the proof of interval limit-point criteria. The theory is also applicable to second order equations with complex coefficients yielding sufficient conditions for the existence of solutions which are not of integrable square.
Finite direct products of finite cyclic semigroups and their characterization
Authors: Trueman D. C.
Published: November 2011

Synopsis

We prove that a finite semigroup which is decomposable into a direct product of cyclic semigroups which are not groups is uniquely so decomposable, and show how the non-group cyclic direct factors of a finite semigroup, if they exist, can be found.
The direct and inverse scattering problems for an arbitrary cylinder: Dirichlet boundary conditions
Authors: Colton David , Kleinman Ralph
Published: November 2011

Synopsis

The exterior Dirichlet problem for the Helmholtz equation in two dimensions is reduced to a boundary integral equation which is soluble by iteration. A standard application of Green's theorem leads to boundary integral equations which are not uniquely soluble because the operator has an eigenvalue. The present approach modifies the operator in such a way that the former eigenvalue is in the resolvent spectrum for low frequencies. The results are applied to the inverse scattering problem wherein the far field is known for a limited frequency range and one seeks the curve on which a plane wave is incident and a Dirichlet boundary condition is assumed. The first iterate in the solution of the boundary integral equation is used to obtain a sequence of moment problems relating the Fourier coefficients of the far field to the coefficients of the Laurent expansion of the conformai transformation which maps the exterior of a circle onto the exterior of the unknown curve. These moment problems are soluble in terms of the mapping radius which in turn may be determined from scattered far field data for an incident plane wave from a second direction.
A comparison theorem for the first nodal line of the solutions of quasilinear hyperbolic equations with non-increasing initial values
Authors: Hsiang Wu-Teh , Kwong Man Kam
Published: November 2011

Synopsis

The oscillatory behaviour of quasilinear hyperbolic equations of the form

is studied using a Sturmian-type comparison theorem. We assume that for some function ψ′(x)≦0 and ψ′(x≦0.) The existence of the first nodal line of u is then inferred from the existence of that of the solution ν of

with .Some results of Pagan are improved using this approach and a problem posed by him is also studied.
On the essential spectrum of self-adjoint operators
Authors: Harris B. J.
Published: November 2011

Synopsis

We provide estimates of the form

for the length of gap centre μ in the essential spectrum of a self-adjoint operator generated by a matrix differential expression.
On Jenkins-Strebel differentials for open Riemann surfaces
Authors: Gardiner Frederick P.
Published: November 2011

Synopsis

Dual extremum problems associated with an infinite family of admissible loops on a Riemann surface are shown to be solvable by Jenkins-Strebel differentials. Then the inequalities associated with these problems are used to calculate the first derivatives of extremal length functionals on Teichmüller space and to estimate the difference quotients for the second derivatives of these functions.
Another positivity result for determinantal operators
Authors: Binding Paul
Published: November 2011

Synopsis

Let Vrs, s = 1 … k, be Hermitian operators on separable Hilbert spaces Hr, r = 1 … k. For x⊗ = x1⊗ … ⊗ xk ∈ H = H1⊗…Δx⊗ by the formal determinantal expansion ⊗ det [Vrsxr Δ is then extended by linearity and continuity to H. It is shown that a positive definiteness condition on Δ need be checked only for decomposable tensors like x⊗. Applications are given to several conditions in the multiparameter eigenvalue literature.
Application to magnetohydrodynamic duct flows of a singular elliptic problem associated with a rectangle
Authors: Nye V. A.
Published: November 2011

Synopsis

The analysis developed by the author in a previous paper is used to discuss two magnetohydrodynamic duct flows for which the boundary conditions are not of Dirichlet type. To the accuracy stated, the results obtained confirm those obtained by previous authors who used different approaches to the problems. A feature of the present analysis is that it yields the magnitude of the error entailed by the use of approximate forms for flow quantities. This has been lacking in previous analyses.
On nonlinear mixed boundary value problems for second order elliptic differential equations on domains with corners
Authors: Kawohl Bernhard
Published: November 2011

Synopsis

We investigate the existence, uniqueness and regularity of solutions to the linear differential equationLu=funder nonlinear mixed boundary conditions on domains with singular boundary points.
On oscillations in a compressible laminar boundary layer
Authors: Gribben R. J.
Published: November 2011

Synopsis

The behaviour of heat transfer and skin friction is analysed in a compressible laminar boundary layer with external velocity Ue(x)(l + α sin ωt The Mach number M is assumed small but finite so that high frequency flows (s ≫1) in which c =αγM2s/2 = O(1) are considered. Solutions, obtained by matching in the Stokes and Prandtl layers, involve summation of Fourier-like series to give the dominant terms in the heat transfer and skin friction. Results, for c =½, verify that a previous approximate method gives a reasonable description of unsteady heat transfer and skin friction; forc =1 there is a substantial increase in amplitude of heat transfer but little change of phase.
Existence conditions for two-parameter eigenvalue problems
Authors: Binding Paul , Browne Patrick J. , Turyn Lawrence
Published: November 2011

Synopsis

We discuss necessary and sufficient conditions for the existence of eigentuples λ=(λl,λ2) and eigenvectors x1≠0, x2≠0 for the problem Wr(λ)xr = 0, Wr(λ)≧0, (*), where Wr(λ)= Tr + λ1Vr2, r=1,2. Here Tr and Vrs are self-adjoint operators on separable Hilbert spaces Hr. We assume the Vrs to be bounded and the Tr bounded below with compact resolvent. Most of our conditions involve the cones

We obtain results under various conditions on the Tr, but the following is typical:

THEOREM. If (*) has a solution for all choices ofT1, T2then (a)0∉ V1UV2,(b)V1∩(—V2) =∅ and (c) V1⊂V2∪{0}, V2⊈V1∪{0}. Conversely, if (a) and (b) hold andV1⊈V2∪∩{0}, V2⊈ then (*) has a solution for all choices ofT1, T2.
Hele—Shaw flow model of the injection by a point source
Authors: Čížek Pavel , Janovský Vladimír
Published: November 2011

Synopsis

A variational formulation of the Hele—Shaw flow model of the point injection of fluid into a laminar cell is introduced. The analysis concerning the existence, uniqueness and regularity of a solution to the variational problem is presented.
Integral representation of functionals defined on curves ofW1,p
Authors: Amar Micol , Bellettini Giovanni , Venturini Sergio
Published: November 2011

LetI⊂ ℝ be a bounded open interval,(I) be the family of all open subintervals ofIand letp> 1. The aim of this paper is to give an integral representation result for abstract functionalsF:W1,p(I;ℝn) ×(I) → [0, + ∞) which are lower semicontinuous and satisfy suitable properties. In particular, we prove an integral representation theorem for the Г-limit of a sequence {Fh}h, of functionals of the form

where eachfhis a Borel function satisfying proper growth conditions.
Stability of a front for a nonlocal conservation law
Authors: Asselah Amine
Published: November 2011

We study the stability of a front for the law 2wt − (wx − γ(1 − w2)(K * w)x)x = 0. It was proved by Del Passo and De Mottoni that an increasing stationary solution, u, exists. We show that it is stable in the following sense: there is ε > 0 such that if w(0) = u + v with |v|2 < ε, then there is α(t) differentiable such that w(x, t) = u(α(t) + x) + v(x, t) and supℝ |v(x, t)| converges to 0 as t goes to infinity. Also, if v is initially odd, α(t) ≡ 0.
Periodic structures in a van der Waals fluid
Authors: Fife Paul C. , Wang Xiao-Ping
Published: November 2011

A system of partial differential equations modelling a van der Waals fluid or an elastic medium with nonmonotone pressure-density relation is studied. As the system changes type, regularisations are considered. The existence of one-dimensional periodic travelling waves, with prescribed average density in a certain range, average velocity and wavelength, is proved. They exhibit layer structure when the regularisation parameter is small. Similarities with the Cahn–Hilliard equation are explored.
Semigroups with zero whose idempotents form a subsemigroup
Authors: Gomes Gracinda M. S. , Howie John M.
Published: November 2011

The structure of a categorical,E*-dense,E*-unitaryE-semigroupSis elucidated in terms of a ‘B-quiver’, whereBis a primitive inverse semigroup. In the case whereSis strongly categorical,Bis a Brandt semigroup. A covering theorem is also proved, to the effect that every categoricalE*-denseE-semigroup has a cover which is a categorical,E*-dense,E*-unitaryE-semigroup.
Generic affine differential geometry of space curves
Authors: Izumiya Shyuichi , Sano Takasi
Published: November 2011

We study affine invariants of space curves from the viewpoint of singularity theory of smooth functions. With the aid of singularity theory, we define a new equi-affine frame for space curves. We also introduce two surfaces associated with this equi-affine frame and give a generic classification of the singularities of those surfaces.
Long-time behaviour for porous medium equations with convection
Authors: Laurençot Ph. , Simondon F.
Published: November 2011

Long-time behaviour of solutions to porous medium equations with convection is investigated when the initial datum is a non-negative and integrable function on the real line. The long-time profile of the solutions is determined, and depends on whether the convective or the diffusive effect dominates for large times. Sharp temporal decay estimates are also provided.
Construction of an infinitely generated group that is not a free product of surface groups and abelian groups, but which acts freely on an ℝ-tree
Authors: Zastrow Andeas
Published: November 2011

The existence of a group H as described in the title shows that the statement of Rips's Theorem for finitely generated groups cannot be extended without further complications to infinitely generated groups. The construction as given in this paper uses a careful combinatorial description of the fundamental group of the Hawaiian Earrings and a length function that can be put on a special subgroup. Then the existence of H follows using a theorem of Chiswell, Alperin and Moss.
A description of E-unitary inverse semigroups
Authors: Wilkinson Ross
Published: November 2011

Synopsis

An E-unitary inverse semigroup, S, has the property that, if x=S, and e2 = e=S, then (xe)2 = xe implies that x2 = x. As a consequence of this, we can see that S is an extension of its semilattice of idempotents, E, by its maximal group morphic image, G. Thus, following McAlister (1974), we attempt to describe S in terms of E and G. If we extend the semilattice E to a larger semilattice F, we are able to describe S in terms of a semi-direct product of F and G, giving a new interpretation to the approach of Schein (1975).
Bounds for the best constant in Landau/s inequality on the line
Authors: Franco Z. M. , Kaper Hans G. , Kwong Man Kam , Zettl A.
Published: November 2011

Synopsis

Explicit formulae and numerical values for upper and lower bounds for the best constant in Landau/s inequality on the real line are given. For p > 3, the value of the upper bound is less than the value of the best constant conjectured by Gindler and Goldstein (J. Analyse Math. 28 (1975), 213–238).
The Euler–Maclaurin formula generated by a summation operator
Authors: Miller John Boris
Published: November 2011

Synopsis

A closed summation operator, whose spectrum lies within a certain region, generates a derivation and antiderivation, and an Euler–Maclaurin sum formula among these three operators.
Asymptotics of the Titchmarsh—Weyl m-coefficient for non-integrable potentials
Authors: Atkinson F. V. , Fulton C. T.
Published: November 2011

Asymptotic formulae for the Titchmarsh—Weyl m-coefficient on rays in the complex λ-plane for the equation − y ″ + qy = λy whenthe potential is limit circle and non-oscillatory at x = 0 are obtained under assumptions slightly more general than xq(x) ∈ L1(0,c). The behaviour of q at the right end-point is arbitrary and may fall in either the limit-point or limit-circle case. A method of regularization of the equation is given that can be made to depend either on a solution of the equation for λ = 0 or more directly on an approximation to the solution in terms of q. This enables equivalent definitions of the m-coefficient to be given for the singular Sturm—Liouville problem associated with a singular limit-circle boundary condition, and its associatedregular Sturm—Liouville problem. As a consequence, it becomes possible to apply asymptotic results obtained by Atkinson for the regular problem in order to give asymptoticresults for the singular problem. Potentials of the form q(x) = C/xj, 1 ≤ j < 2, are included. In the case j = 1, an independent calculation of the limit-point m-coefficient over the range (0,∞), relying on Whittaker functions, verifies the main result.
Commutators and analytic families of operators
Authors: Carro María J.
Published: November 2011

This work connects the theory of commutators with analytic families of operators in abstract interpolation theory. Our main result asserts that if {Lξ}0≤Reξ≤1 is an analytic family of operators satisfying some conditions, then [Lθ,Ω] +(Lξ)′(θ): Āθ→ Bθ is bounded. From this, we can deduce the boundedness of the commutator .
Generic space curves and secants
Authors: Bruce J. W.
Published: November 2011

Synopsis

In this paper, we study the local structure of the secant mapping of a pair of disjoint curves. We show that for generic curves, the secant map and unit secant maps are locally stable. If we allow our curves to coincide, we can define anew unit secant map to be the natural unit tangent map near the diagonal. This is, for a generic curve, a locally stablemap away from the diagonal. Along the diagonal, it is locally stable as a ℤ2 symmetric germ (the ℤ2 symmetry originating with reflection in the diagonal).
A Titchmarsh-Weyl matrix function for symmetric differential equations of order 2n with an indefinite weight function
Authors: Daho Karim
Published: November 2011

Synopsis

A Titchmarsh-Weyl matrix function W(λ) is defined for the differential equation of order 2n

with po>0, pk≧0, k = 1, 2, …, n on 005B;0, b), λєℂ and an indefinite weight function r. It is shown that this function W(λ) belongs to some class and that some operators associated with the above equation are definitizable in the Krein space . In the particular case n = 1, these results are contained in an earlier paper by the present author and H. Langer.
The reciprocal variational approach to the Signorini problem with friction. Approximation results
Authors: Haslinger J. , Panagiotopoulos P. D.
Published: November 2011

Synopsis

In this paper, a new variational formulation of the Signorini problem with friction is given in terms of the contact stresses. The method corresponds to the direct integral equation approach in classical elastostatic problems. First the displacement and mixed problems are briefly described together with some numerical results. Next the displacements are eliminated by the use of Green's function, and a constrained minimum problem with respect to the normal and tangential tractions on the contact boundary is derived. Then the resulting approximation procedure is studied and certain convergence results are proved. Finally, some remarks on the Signorini problem with Coulomb friction are presented. Numerical results illustrate the theory.
Gradient estimates for semilinear elliptic equations
Authors: Lieberman Gary M.
Published: November 2011

Synopsis

Estimates on the gradient of solutions to the Dirichlet problem for a semilinear elliptic equation are given when the nonlinearity in the equation is quadratic with respect to the gradient of the solution. These estimates extend results of F. Tomi to less smooth boundary data and results of the author to the full quadratic growth.
Energy decay for the wave equation with a degenerate dissipative term
Authors: Nakao Mitsuhiro
Published: November 2011

Synopsis

Decay estimates for the energy are derived for the initial boundary value problem of the wave equation with a degenerate dissipative term:

where Ω is a bounded domain in Rn, a(×) is a nonnegative function such that a1 ∊Lp(Ω) for some p > 0 and f is a function tending to 0 rapidly as t → ∞
Inverse multi-parameter eigenvalue problems for matrices
Authors: Browne Patrick J. , Sleeman B. D.
Published: November 2011

Synopsis

We study the possibility of perturbing a matrix A by a diagonal matrix so that an eigenvalue problem with leading matrix A has specifiedeigenvalues when A is replaced by A+D. The particular cases presented are the one-parameter generalized eigenvalue problem (A× = λB μ×, a two-parameter eigenvalue problem (A + λB + μC)× = 0, a linked system ofsuch two-parameter problems and a quadratic eigenvalue problem (A + λB + λ2C)× = 0. The work extends results of Hadeler for the classical problem A× = λ×.
A classification of the solutions of a differential equation according to their behaviour at infinity, II
Authors: Elias Uri
Published: November 2011

Synopsis

The solutions of the differential equation Lny + p(×)y = 0, where Ln is a disconjugate operator, are classified according to their behaviour as × →∞. The solution space is decomposed into disjoint sets. We study the dominance properties of the solutions which belong to different sets.
Best constants in norm inequalities for derivatives on a half-line
Authors: Franco Z. M. , Kaper Hans G. , Kwong Man Kam , Zettl A.
Published: November 2011

Synopsis

Let K be the class of all operators T in a Banach space × which have the property that, for any pair of integers (n, k) with n ≧2 and l≦ k ≦ n – l, there exists a constant Cnk such that

for all fϵdom Tn. If T ϵ K, then the best possible constant for the norm inequality (*) is the smallest non-negative value of the constant Cnk in (*). Any operator T which is the adjoint of a maximal symmetric operator in a Hilbert space belongs to the class K, as was shown by Ljubič [Izv. Akad. Nauk SSSR, Ser. Mat. 24 (1960), 825–864].

This article is concerned with the computation of the best possible constant for the differentiation operator Tf=if′ on the maximal domain in L2(0, ∞). Three algorithms, proposed by Ljubič [ibid.] and Kupcov [Trudy Mat. Inst. Steklov. 138 (1975)], are discussed and related to one another, asymptotic expressions (valid for large n) and numerical values of the best possible constant are presented, and the extremals (i.e. the elements / ∈ dom Tn for which equality holds in (*) with the best possible constant) are given.
Products of idempotent linear transformations
Authors: Reynolds M. A. , Sullivan R. P.
Published: November 2011

Synopsis

In 1966, J. M. Howie characterised the transformations of an arbitrary set that can be written as a product (under composition) of idempotent transformations of the same set. In 1967, J. A. Erdos considered the analogous problem for linear transformations of a finite-dimensional vector space and in 1983, R. J. Dawlings investigated the corresponding idea for bounded operators on a separable Hilbert space. In this paper we study the case of arbitrary vector spaces.
Non-linear mixed boundary value problems for parabolic partial differential equations
Authors: Bailet-Intissar Joelle
Published: November 2011

Synopsis

A sufficient condition on the angles of a bounded open subset Ω of ℝn is given for the best possible regularity of a solution to a class of parabolic problems with non-linear mixed boundary conditions.
Generalizations of Hardy's Integral Inequality
Authors: Love E. R.
Published: November 2011

Synopsis

Extensions of the integral version of Hardy's Inequality were given by Kadlec and Kufner (1967) and by Copson (1976). This paper provides several levels of further generalization of their results, obtained mostly by specializing four main inequalities. Most of the inequalities have the form ∥Kf∥ ≤C∥f∥, whereKis an integral transform and ∥.∥ is a generalizedLp-norm; some have the inequality sign reversed. Best possible constantsCare obtained in several cases, under mild extra hypotheses.
The asymptotic form of the spectral functions associated with a class of Sturm–Liouville equations
Authors: Harris B. J.
Published: November 2011

Synopsis

We use a modified form of the Stieltjes inversion formula due to Atkinson together with some recent results on the asymptotic form of Titchmarch–Weyl m-functions to obtain an asymptotic expression for the spectral functions τ(t) associated with the differential equation
Minimax methods for open-loop equilibria in N-person differential games. Part I: Linear quadratic games and constrained games
Authors: Chen Goong , Zheng Quan , Zhou Jian-Xin
Published: November 2011

Synopsis

In [13], Nikaido and Isoda generalised von Neumann's symmetrisation method for matrix games. They showed that N-person noncooperative games can be treated by a minimax method.

We apply this method to N-person differential games. Lukes and Russell [11] first studied N-person nonzero sum linear quadratic games in 1971. Here we have reproduced and strengthened their results. The existence and uniqueness of equilibria are completely determined by the invertibility of the decision operator, and the nonuniqueness of equilibrium strategies is only up to a finite dimensional subspace of the space of all admissible strategies.

In the constrained case, we have established an existence result for games with a much weaker convexity assumption subject to compact convex constraints. We have also derived certain results for games with noncompact constraints. Several examples of quadratic and non-quadratic games are given to illustrate the theorem.

Numerical computations are also possible and are given in the sequel [3].
On the stability of the limit-point property of “Kauffman expressions” under relatively bounded perturbations
Authors: Mergler Bernhard , Schultze Bernd
Published: November 2011

Synopsis

In this paper we show that for the whole class of differential expressions in the limit-point case considered by Kauffman in [2], the perturbation theory yields a limit-point criterion for a much wider class of ordinary differential expressions. More general coefficients are admitted which may be eventually negative provided they are “dominated” by some other positive coefficients. This generalises results in [4], [5] and [6].
Kinetic conditions for the existence of wave fronts in reaction-diffusion systems
Authors: Fraile José M. , Sabina José
Published: November 2011

Synopsis

This paper deals with the existence of bounded plane wave fronts of reaction-diffusion systems. The main result ensures the partial invariance of a certain region, under kinetic conditions commonly used in the literature. This allows us to construct bounded plane wave fronts taking their values in that domain. We also give an estimate of the minimum permissible value of the propagation velocity of those plane wave fronts. Some examples are given.
Remarks on complemented subspaces of von Neumann algebras
Authors: Pisier G.
Published: November 2011

Synopsis

In this note we include two remarks about bounded (not necessarily contractive) linear projections on a von Neumann algebra. We show that if M is a von Neumann subalgebra of B(H) which is complemented in B(H) and isomorphic to M⊗M, then M is injective (or equivalently M is contractively complemented). We do not know how to get rid of the second assumption on M. In the second part, we show that any complemented reflexive subspace of a C*-algebra is necessarily linearly isomorphic to a Hilbert space.
Stochastic reinforcement problems and ergodic theory
Authors: Balzano M. , Paderni G.
Published: November 2011

Synopsis

We study the asymptotic behaviour of Dirichlet problems in domains of R2 bounded by thin layers whose thickness is given by means of an assigned ergodic random function. Using a capacitary method together with ergodic theorems for additive and superadditive processes, we are able to characterise the limit problem precisely.
Exponential length and exponential rank in C*-algebras
Authors: Ringrose J. R.
Published: November 2011

Synopsis

In an operator algebra, the general element of the connected component of the unitary group can beexpressed as a finite product of exponential unitary elements. The recently introduced concept of exponential rank is defined in terms of the number of exponentials required for this purpose. The present paper is concerned with a concept of exponential length, determined not by the number of exponentials but by the sum of the norms of their self-adjoint logarithms. Knowledge of the exponential length of an algebra provides an upper bound for its exponential rank (but not conversely). This is used to estimate the exponential rank of certain algebras of operator-valued continuous functions.
Fundamental semigroups
Authors: Edwards P. M.
Published: November 2011

Synopsis

An idempotent-separating congruence μ is studied further in this paper. It is shown to satisfy special properties with respect to regular elements and to group-bound elements. It is shown that for any semigroup S, μ is the identity congruence on S/μ. From this, it can be shown that S/μ is fundamental for any semigroup S. Some alternative characterizations of μ are given and applied to yield sufficient conditions for a subsemigroup T of S to satisfy μ (T) = μ (S) ∩ (T × T), whence T is fundamental if S is fundamental.