bluuebunny/crossref_metadata_2025 huggingface dataset:
Asymptotic profiles for the Kirchhoff equation
Authors: MATSUYAMA TOKIO
Published: December 2009

The first aim of this paper is to find asymptotic profiles for Kirchhoff equation. More precisely, it will be shown that there exists a small amplitude solution which is not asymptotically free. The second aim is to prove the existence of scattering states for the small amplitude solutions with data belonging to

H^{\sigma(p),p}\times H^{\sigma(p)-1,p}

, where

\sigma(p)= n(\frac{2}{p}-1)+1

,

p\in [1,\frac{2(n-1)}{n+1})

and

n \ge 4

.
Existence of periodic solutions for some second order quasi-linear Hamiltonian systems
Authors: Girardi Mario , Matzeu Michele
Published: December 2009

A class of second order nonautonomous quasilinear Hamiltonian systems

(S)

is considered. One states that, for any

T<T_0

, depending on the growth coefficients of the Hamiltonian function

H

, there exists a

T

-periodic and

T/2

-antiperiodic solution of

(S)

, in case that two symmetry conditions hold for

H

.
A mathematical model of frying processes
Authors: Mancini Alberto , Primicerio Mario , Yang Yiqing
Published: December 2009

We present a mathematical model for the process of frying a rather thick sample of an indeformable porous material saturated with water (e.g. a potato slice). The model is based on thermodynamical arguments and results in an initial-boundary value problem for a system of equations satisfied by the temperature and vapour content, with a free boundary separating the region saturated with water and the vapour region.

We provide some results of numerical simulations.
The balance between diffusion and absorption in semilinear parabolic equations
Authors: Shishkov Andrey , Véron Laurent
Published: December 2009

Let

h:[0,\infty)\mapsto [0,\infty)

be continuous and nondecreasing,

h(t)>0

if

t>0

, and

m,q

be positive real numbers. We investigate the behavior when

k\to\infty

of the fundamental solutions

u=u_{k}

of

\partial_{t} u-\Delta u^m+h(t)u^q=0

in

\Omega\times (0,T)

satisfying

u_{k}(x,0)=k\delta_0

. The main question is wether the limit is still a solution of the above equation with an isolated singularity at

(0,0)

, or a solution of the associated ordinary differential equation

u'+h(t)u^q=0

which blows up at

t=0

.
Modified log-Sobolev inequalities and isoperimetry
Authors: Kolesnikov Alexander V.
Published: December 2009

We find sufficient conditions for a probability measure

\mu

to satisfy an inequality of the type

\int_{\R^d} f^2 F\Bigl( \frac{f^2}{\int_{\R^d} f^2 \,d \mu} \Bigr) \,d \mu \le C \int_{\R^d} f^2 c^{*}\Bigl( \frac{|\nabla f|}{|f|} \Bigr) \,d \mu + B \int_{\R^d} f^2 \,d \mu,

where

F

is concave and

c

(a cost function) is convex. We show that under broad assumptions on

c

and

F

the above inequality holds if for some

\delta>0

and

\varepsilon>0

one has

\int_{0}^{\varepsilon} \Phi\Bigl(\delta c\Bigl[\frac{t F(\frac{1}{t})}{{\mathcal I}_{\mu}(t)} \Bigr] \Bigr) \,dt < \infty,

where

{\mathcal I}_{\mu}

is the isoperimetric function of

\mu

and

\Phi = (y F(y) -y)^{*}

. In a partial case

{\mathcal I}_{\mu}(t) \ge k t \varphi ^{1-\frac{1}{\alpha}} (1/t),

where

\varphi

is a concave function growing not faster than

\log

,

k>0

,

1 < \alpha \le 2

and

t \le 1/2

, we establish a family of tight inequalities interpolating between the

F

-Sobolev and modified inequalities of log-Sobolev type. A basic example is given by convex measures satisfying certain integrability assumptions.
Gaussian estimates for hypoelliptic operators via optimal control
Authors: Boscain Ugo , Polidoro Sergio
Published: December 2009

We obtain Gaussian lower bounds for the fundamental solution of a class of hypoelliptic equations, by using repeatedly an invariant Harnack inequality. Our main result is given in terms of the value function of a suitable optimal control problem.
Vanishing and conservativeness of harmonic forms of a non-compact CR manifold
Authors: Masamune Jun
Published: December 2009

The self-adjointness of a sublaplacian and Kohn-Rossi laplacians on a non-compact strictly pseudoconvex CR manifold is proved. As applications to geometry, the vanishing and the conservativeness of harmonic forms are obtained.
Positive solutions of nonlinear Schrödinger–Poisson systems with radial potentials vanishing at infinity
Authors: Mercuri Carlo
Published: December 2009

We deal with a weighted nonlinear Schrödinger–Poisson system, allowing the potentials to vanish at infinity.
Boundary regularity of minima
Authors: Kristensen Jan , Mingione Giuseppe
Published: December 2009

Let

u: Ω → ℝ^N

be any given solution to the Dirichlet variational problem

\min\limits{w} ∫_Ω F(x,w,Dw) dx,\quad   w ≡ u_0 \quad\text{on } ∂Ω,

where the integrand

F(x,w,Dw)

is strongly convex in the gradient variable

Dw

, and suitably Hölder continuous with respect to

(x,w)

. We prove that almost every boundary point, in the sense of the usual surface measure of

∂Ω

, is a regular point for

u

. This means that

Du

is Hölder continuous in a relative neighborhood of the point. The existence of even one of such regular boundary points was an open problem for the general functionals considered here, and known only under certain very special structure assumptions.
A spectral Schwarz lemma
Authors: Vesentini Edoardo
Published: December 2009

The classical Schwarz lemma for any scalar-valued holomorphic function

h

mapping the open unit disc

\Delta \subset \mathbb{C}

into itself is generalized, replacing

h

by a holomorphic map

f

of

\Delta

into a unital associative Banach algebra

{\cal A}

, and

| h(z) |

by the spectral radius of

f(z)

(

z \in \Delta

). If

{\cal A} = {\cal L}({\cal H})

and

{\cal H}

is a complex Hilbert space, the behaviour of the numerical radius of

f(z)

is also investigated.
On a conjecture of J. Serrin
Authors: Brezis Haïm
Published: December 2009

In 1964 J. Serrin proposed the following conjecture. Let

u \in W_{\mathrm{loc}}^{1,1}(Ω)

be a weak solution of the second order elliptic equation (1) below, in divergence form, with Hölder continuous coefficients

a_{ij}(x)

; then

u

is a “classical” solution. We announce a solution of this conjecture assuming only

u \in BV_{\mathrm{loc}}(Ω)

and Dini continuous coefficients.
Multipartite entanglement in qubit systems
Authors: Facchi Paolo
Published: December 2009

We introduce a potential of multipartite entanglement for a system of n qubits, as the average over all balanced bipartitions of a bipartite entanglement measure, the purity. We study in detail its expression and look for its minimizers, the maximally multipartite entangled states. They have a bipartite entanglement that does not depend on the bipartition and is maximal for all possible bipartitions. We investigate their structure and consider several examples for small n.
Alternative Forms of the Harnack Inequality for Non-Negative Solutions to Certain Degenerate and Singular Parabolic Equations
Authors: DiBenedetto Emmanuele , Gianazza Ugo , Vespri Vincenzo
Published: December 2009

Non-negative solutions to quasi-linear, degenerate or singular parabolic partial differential equations, of
p
-Laplacian type for
p
> 2_N_/(
N
+1), satisfy Harnack-type estimates in some intrinsic geometry ([2, 3]). Some equivalent alternative forms of these Harnack estimates are established, where the supremum and the inﬁmum of the solutions play symmetric roles, within a properly redeﬁned intrinsic geometry. Such equivalent forms hold for the non-degenerate case
p
= 2 following the classical work of Moser ([5, 6]), and are shown to hold in the intrinsic geometry of these degenerate and/or parabolic p.d.e.’s. Some new forms of such an estimate are also established for 1 <
p
< 2.
Invariant Measures in Quasi-Metric Spaces
Authors: Marchi Maria Vittoria
Published: December 2009

We prove that in separable, complete, quasi-metric spaces there exists exactly one probability measure with bounded support, invariant with respect to given families of contractions and weights. The invariant measure has compact support and is an attractor in the space of probability measures with bounded support equipped with a metric defined in term of Hölder continuous functions.
Integrable Singularities and Weakly Sequentially Continuous Maps
Authors: Agarwal Ravi P. , O'Regan Donal
Published: December 2009

New existence results for singular second order boundary value problems, where the singularity is integrable, are presented using fixed point theory for weakly sequentially continuous maps.
Necessary Conditions for Local and Global Solvability of Non-Diagonal Degenerate Systems
Authors: El Hamidi Abdallah
Published: December 2009

Cross-diffusion has been widely considered either in the mechanical description of diffusion or in the stochastic point process description of interacting populations, in the mathematical modelling of spatially structured epidemic or ecological systems and for the geographical diffusion of innovation. In this paper, specific attention is devoted to blowing-up solutions of some systems which may reflect either failures in the modelling or genuine phenomena like aggregation of populations. Furthemore, necessary conditions for local and global existence of solutions to the considered systems are presented.
Harnack Inequality for a Class of Degenerate Elliptic Operators
Authors: Fernandes Jose D. , Groisman Jorge , Melo Severino T.
Published: December 2009

We prove a Harnack inequality for a class of two-weight degenerate elliptic operators. The metric distance is induced by continuous Grushin-type vector fields. It is not know whether there exist cutoffs fitting the metric balls. This obstacle is bypassed by means of a covering argument that allows the use of rectangles in the Moser iteration.
On Closed Form Expressions for Trigonometric Series and Series Involving Bessel or Struve Functions
Authors: Tričković Slobodan B. , Stanković Miomir S. , Aleksis Violeta N.
Published: December 2009

We first consider a summation procedure for some trigonometric series in terms of the Riemann zeta and related functions. In some cases these series can be brought in closed form, which means that the infinite series are represented by finite sums. Afterwards, we show some applications of our results to the summation of series involving Bessel or Struve functions. Further, relying on results from the previous sections, we obtain sums of series involving a Bessel or Struve integral. These series are also represented as series in terms of the Riemann zeta and related functions of reciprocal powers and can be brought in closed form in certain cases as well. By replacing the function appearing in a Bessel and Struve integral with particular functions, we find sums of new series.
On Harmonic Potential Fields and the Structure of Monogenic Functions
Authors: Brackx Fred , Delanghe R.
Published: December 2009

In specific open domains of Euclidean space, a correspondence is established between a monogenic function and a sequence of harmonic potential fields, leading to the construction of a unique vector-valued conjugate harmonic homogeneous polynomial to a given real-valued solid harmonic.
A Note on μ-Stable Surfaces with Prescribed Constant Mean Curvature
Authors: Fröhlich Steffen
Published: December 2009

Using a generalized stability condition we give an upper bound of the principle curvatures of certain constant mean curvature surfaces. This implies a theorem of Bernstein type.
Fixed-Point Properties of Roughly Contractive Mappings
Authors: Phú Hoàng Xuân
Published: December 2009

For given

k \in (0,1)

and

r > 0

, a self-mapping

T: \, M \to M

is said to be

r

-roughly

k

-contractive provided

\|Tx - Ty\| \le k\,\|x - y\| + r \quad (x,y \in M).

To state fixed-point properties of such a mapping, the self-Jung constant

J_s(X)

is used, which is defined as the supremum of the ratio

2\,r_{\mathrm{conv} S}(S)/\mathrm{diam} S

over all non-empty, non-singleton and bounded subsets

S

of some normed linear space

X

, where

r_{\mathrm{conv} S}(S) = \inf_{x\in\mathrm{conv} S} \sup_{y\in S} \|x - y\|

is the self-radius of

S

and

\mathrm{diam} S

is its diameter. If

M

is a closed and convex subset of some finite-dimensional normed space

X

and if

T: \, M \to M

is

r

-roughly

k

-contractive, then for all

\varepsilon > 0

there exists

x^* \in M

such that

\|x^* - Tx^*\| < \frac12\,J_s(X)\, r + \varepsilon.

If

\mathrm{dim} X = 1

, or

X

is some two-dimensional strictly convex normed space, or

X

is some Euclidean space, then there is

x^* \in M

satisfying

\|x^* - Tx^*\| \le {1 \over 2}\,J_s(X)\,r

.
Maximum Local Lyapunov Dimension Bounds the Box Dimension. Direct Proof for Invariant Sets on Riemannian Manifolds
Authors: Gelfert Karin
Published: December 2009

For a C^1 map φ on a Riemannian manifold and for a compact invariant set K it is proven that the maximal local Lyapunov dimension of φ on K bounds the box dimension of K from above. A version for Hilbert spaces is also presented. The introduction of an adapted Riemannian metric provides in a certain sense an optimal upper bound for the box dimension of the Lorenz attractor.
About the Sign of Oriented Fredholm Operators between Banach Spaces
Authors: Benevieri Pierluigi , Furi Massimo , Pera Maria Patrizia , Spadini Marco
Published: December 2009

We give conditions for an oriented family of bounded Fredholm operators of index zero between Banach spaces to have a sign jump. In particular, we discuss criteria for detecting the sign jump in some special situations. For instance, when a sort of Crandall-Rabinowitz condition for bifurcation is assumed or in the case of a family of Leray-Schauder type. Finally, some examples of ordinary differential operators are presented to illustrate the meaning of the abstract results.
A Note on the Poincaré Inequality for Convex Domains
Authors: Bebendorf Mario
Published: December 2009

A proof for the Poincaré inequality with explicit constant for convex domains is given. This proof is a modification of the original proof of L. F. Payne and H. F. Weinberger [Arch. Rat. Mech. Anal. 5 (1960) 286–292], which is valid only for the two-dimensional case.
A System of Multi-Valued Generalized Order Complementarity Problems in Ordered Metric Spaces
Authors: Fang Ya-ping , Huang Nan-jing , Kim Jong Kyu
Published: December 2009

Some existence results for a system of multi-valued generalized order complementarity problems are established in terms of fixed point theorems for multi-valued increasing-type mappings and decreasing mappings in ordered metric spaces.
Fixed Point Theorems for Decomposable Multi-Valued Maps and Applications
Authors: Precup Radu
Published: December 2009

We present fixed point theorems for weakly sequentially upper semicontinuous decomposable non-convex-valued maps. They are based on an extension of the Arino–Gautier–Penot Fixed Point Theorem for weakly sequentially upper semicontinuous maps with convex values. Applications are given to abstract operator inclusions in

L^p

spaces. An example is included to illustrate the theory.
Non-Oscillatory Solutions of Higher Order Nonlinear Neutral Delay Difference Equation
Authors: Zhou Yong
Published: December 2009

Consider the forced higher order nonlinear neutral delay difference equation

L_m( x(n) + cx(n - τ) ) + F ( n, x(σ(n) ) ) = g(n)\quad (n ≥ n_0).

We obtain a global result (with respect to

c

), which consists of some sufficient conditions for the existence of a non-oscillatory solution of the above equation. Our results improve and extend a number of existing results.
A Simple Proof of the Mountain Circle Theorem
Authors: Comparato Susanna
Published: December 2009

We give an alternative proof of Fournier-Willem's Mountain Circle Theorem. Our proof, which is simpler than the original one proposed by these authors, is based on a Lusternik-Schnirelman-type theory and some results of elementary Brouwer degree theory.
Energy Form on a Closed Fractal Curve
Authors: Freiberg Uta R. , Lancia Maria Rosaria
Published: December 2009

The energy form on a closed fractal curve F is constructed. As F is neither self-similar nor nested, it is regarded as a "fractal manifold". The energy is obtained by integrating the Lagrangian on F.s.
On the Basin of Attraction of Limit Cycles in Periodic Differential Equations
Authors: Giesl Peter
Published: December 2009

We consider a general system of ordinary differential equations

\dot{x}=f(t,x)

where

x\in\mathbb R^n

, and

f(t+T,x)=f(t,x)

for all

(t,x)\in\mathbb R\times \mathbb R^n

is a periodic function. We give a sufficient and necessary condition for the existence and uniqueness of an exponentially asymptotically stable periodic orbit. Moreover, this condition is sufficient and necessary to prove that a subset belongs to the basin of attraction of the periodic orbit. The condition uses a Riemannian metric, and we present methods to construct such a metric explicitly.
On Some Local Geometric Properties in Musielak-Orlicz Function Spaces
Authors: Hudzik Henryk , Kowalewski Wojciech
Published: December 2009

Criteria for compactly locally uniformly rotund points in Musielak-Orlicz spaces equipped with the Luxemburg and the Orlicz-Amemiya norms are given. Next, criteria for compact local uniform rotundity and local uniform rotundity of the spaces for both norms are deduced. These properties are important because, for any Banach space X, both of them imply the Kadec-Klee property and this property, together with reflexivity, is equivalent to approximative compactness of X. Approximative compactness of X gives that any nonempty convex and closed set in X is proximinal in X and the projection PA( . ) from X to A is a continuous operator [see I. Singer: The Theory of Best Approximation and Functional Analysis. Springer-Verlag 1970].
Weighted Integrals of Holomorphic Functions on the Polydisc II
Authors: Stevic Stevo
Published: December 2009

Let

{\mathcal L}^p_{\alpha}(U^n)

denote the class of all measurable functions defined on the unit polydisc

U^n=\{z\in {\bf C}^n\, \big| \;|z_i|<1,\ i=1,...,n\}

such that

\|f\|^p_{{\mathcal L}_{\alpha}(U^n)}=\int_{U^n}|f(z)|^p\prod_{j=1}^n (1-|z_j|^2)^{\alpha_j}dm(z_j)<\infty,

where

\alpha_j>-1

,

j=1,...,n

, and

dm(z_j)

is the normalized area measure on the unit disk

U

,

H(U^n)

the class of all holomorphic functions on

U^n

, and let

{\mathcal A}^p_{\alpha}(U^n)={\mathcal L}^p_{\alpha}(U^n) \cap H(U^n)

(the weighted Bergman space). In this paper we prove that for

p\in (0,\infty),

f\in {\mathcal A}^p_{\alpha}(U^n)

if and only if the functions

\prod_{j\in S}(1-|z_j|^2)\frac{\partial ^{|S|} f} {\prod_{j\in S}\partial z_j}\big(\chi_S(1)z_1, \chi_S(2)z_2,..., \chi_S(n)z_n\big)

belong to the space

{\cal L}^p_{\alpha}(U^n)

for every

S\subseteq \{1,2,...,n\},

where

\chi_S(\cdot)

is the characteristic function of

S,

|S|

is the cardinal number of

S,

and

\prod_{j\in S}\partial z_j=\partial z_{j_1}\cdots\partial z_{j_{|S|}},

where

j_k\in S, \, k=1,...,|S|.

This result extends Theorem 22 of Kehe Zhu in Trans. Amer. Math. Soc. 309 (1988) (1), 253–268, when

p\in (0,1).

Also in the case

p\in [1,\infty)

, we present a new proof.
Decay Bounds for Solutions of Second Order Parabolic Problems and their Derivatives III
Authors: Payne L. E. , Philippin G. A.
Published: December 2009

Further extending investigations carried out in previous papers, the authors deal in this paper with another non-linear initial-boundary value problem whose solution, without appropriate data restrictions, might blow up at some finite time. The purpose of this paper is to determine conditions on the geometry and data sufficient to insure that the solution remains bounded and with those conditions to derive exponential decay bounds for the solution and its gradient.
Quadratic Spline Collocation for Volterra Integral Equation
Authors: Oja Peeter , Saveljeva Darja
Published: December 2009

In the traditional step-by-step collocation method with quadratic splines for Volterra integral equations an initial condition is replaced by a not-a-knot boundary condition at the other end of the interval. Such a nonlocal method gives the uniform boundedness of collocation projections for all parameters c in (0,1) characterizing the position of collocation points between spline knots. For c = 1 the projection norms have linear growth and, therefore, for any choice of c some general convergence theorems may be applied to establish the convergence with two-sided error estimates. The numerical tests supporting the theoretical results are also presented.
Function Spaces as Dirichlet Spaces (About a Paper by Maz'ya and Nagel)
Authors: Jacob Niels , Schilling René L.
Published: December 2009

V. G. Maz'ya and J. Nagel [Beitr. Anal. 12 (1978) 7–17] found for certain classes of weighted Sobolev norms (defined using the Fourier transform) equivalent Slobodeckij-type difference representations. We extend these considerations to a wider class of anisotropic norms which arise in the theory of Markov processes. In particular we show that these Sobolev norms are equivalent to Dirichlet norms.
On a Class of Physically Admissible Variational Solutions to the Navier-Stokes-Fourier System
Authors: Feireisl Eduard , Novotný Antonín , Petzeltová Hana
Published: December 2009

The main objective of the present paper is to introduce a class of admissible variational solutions to the Navier-Stokes-Fourier system of equations based on the second law of thermodynamics. We also show that the solutions exist globally in time regardless the size of the initial data. Finally, the question of the long-time behaviour of these solutions is being addressed.
Regularity of the Adjoint State for the Instationary Navier-Stokes Equations
Authors: Rösch Arnd , Wachsmuth Daniel
Published: December 2009

We are considering imbeddings of abstract functions in spaces of functions being continuous in time. A family of functions depending on certain parameters is discussed in detail. In particular, this example shows that such functions do not belong to the space C([0, T], H). In the second part, we investigate an optimal control problem for the instationary Navier-Stokes equation. We will answer the question, in what sense the initial value problem for the adjoint equation can be solved.
Asymptotic Behavior of Discontinuous Solutions to Thermoelastic Systems with Second Sound
Authors: Racke Reinhard , Wang Ya-Guang
Published: December 2009

We consider the Cauchy problem for linear and semilinear thermoelastic systems with second sound in one space dimension with discontinuous initial data. Due to Cattaneo's law, replacing Fourier's law for heat conduction, the system is strictly hyperbolic. We investigate the behavior of discontinuous solutions as the relaxation parameter tends to zero, which corresponds to a formal convergence of the system to the hyperbolic-parabolic type of classical thermoelasticity. We obtain that the jump of the temperature goes to zero while the jumps of the gradient of the displacement and the spatial derivative of the temperature are propagated along the characteristic curves of the elastic fields when the relaxation parameter vanishes. Moreover, when certain growth conditions are imposed on the nonlinear functions, we deduce that these jumps decay exponentially when the time goes to infinity, more rapidly for small heat conduction coefficient.
Minimal Quasidifferential of a Piecewise Linear Function in R^3
Authors: Grzybowski Jerzy
Published: December 2009

A quasidifferential of a piecewise linear function in R3 can be a pair of polytopes (A, B). We prove that a minimal pair (C, D) of compact convex sets which is equivalent to (A, B) is a pair of polytopes for n = 3.
Mackey Topologies on Vector-Valued Function Spaces
Authors: Nowak Marian
Published: December 2009

Let

\,E\,

be an ideal of

\,L^{0}\,

over a

\,\sigma

-finite measure space

\,(\Omega,\Sigma,\mu)

, and let

\,(X,\|\cdot\|_X)\,

be a real Banach space. Let

\,E(X)\,

be a subspace of the space

\,L^{0}(X)\,

of

\,\mu

-equivalence classes of all strongly

\,\Sigma

-measurable functions

\,f: \Omega\to X\,

and consisting of all those

\,f\in L^{0}(X)\,

for which the scalar function

\,\|f(\cdot)\|_X\,

belongs to

\,E

. Let

\,E(X)_n^{\sim}\,

stand for the order continuous dual of

\,E(X)

. We examine the Mackey topology

\,\tau(E(X),E(X)_n^{\sim})

in case when it is locally solid. It is shown that

\,\tau(E(X),E(X)_n^{\sim})\,

is the finest Hausdorff locally convex-solid topology on

\,E(X)\,

with the Lebesgue property. We obtain that the space

\,(E(X),\tau(E(X), E(X)_n^{\sim}))\,

is complete and sequentially barreled whenever

\,E\,

is perfect. As an application, we obtain the Hahn-Vitali-Saks type theorem for sequences in

\,E(X)_n^{\sim}

. In particular, we consider the Mackey topology

\,\tau(L^{\Phi}(X), L^{\Phi}(X)_n^{\sim})\,

on Orlicz-Bochner spaces

\,L^{\Phi}(X)

. We show that the space

\,(L^{\Phi}(X), \tau(L^{\Phi}(X), L^{\Phi}(X)_n^{\sim}))\,

is complete iff

\,L^{\Phi}\,

is perfect. Moreover, it is shown that the Mackey topology

\,\tau(L^{\infty}(X), L^{\infty}(X)_n^{\sim})\,

is a mixed topology.
Long Time Behavior of Solutions to the Caginalp System with Singular Potential
Authors: Grasselli Maurizio , Petzeltová Hana , Schimperna Giulio
Published: December 2009

We consider a nonlinear parabolic system which governs the evolution of the (relative) temperature

\vartheta

and of an order parameter

\chi

. This system describes phase transition phenomena like, e.g., melting-solidification processes. The equation ruling

\chi

is characterized by a singular potential

W

which forces

\chi

to take values in the interval

[-1,1]

. We provide reasonable conditions on

W

which ensure that, from a certain time on,

\chi

stays uniformly away from the pure phases

1

and

-1

. Combining this separation property with the Łojasiewicz–Simon inequality, we show that any smooth and bounded trajectory uniformly converges to a stationary state and we give an estimate of the decay rate.
A Parabolic Integro-Differential Identification Problem in a Barrelled Smooth Domain
Authors: Janno Jaan , Lorenzi Alfredo
Published: December 2009

We consider the problem of recovering a space- and time-dependent kernel in a parabolic integro-differential equation. The related domain is assumed to be smooth and provided with two bases. Global existence and uniqueness results are proved.
On a Boundary-Value Problem for Pseudo-Differential Operators and its Relation to Jump Processes
Authors: Knopova V.
Published: December 2009

We show the solvability of Dirichlet and Neumann boundary-value problems in

L_p(\mathbb{R}^n_+)

for an operator

A

of some special type. In case

p=2

it is possible to give another description of the trace of the domain of

A

on

\mathbb{R}^{n-1}

.
Asymptotics of Determinants and Traces of Toeplitz Matrices with Symbols in Weighted Wiener Algebras
Authors: Karlovich Alexei Yu.
Published: December 2009

We prove asymptotic formulas for determinants and traces of finite block Toeplitz matrices with symbols belonging to Wiener algebras with weights satisfying natural submultiplicativity, monotonicity, and regularity conditions. The remainders in these formulas depend on the weights and go rapidly to zero for very smooth symbols. These formulas refine or extend some previous results by Szegö, Widom, Böttcher, and Silbermann.
The New Maximal Measures for Stochastic Processes
Authors: König Heinz
Published: December 2009

In recent work the author proposed a reformed notion of stochastic processes, which in particular removes notorious problems with uncountable time domains. In case of a Polish state space the new stochastic processes are in one-to-one correspondence with the traditional ones. This implies for a stochastic process that the traditional
canonical
measure on the path space receives a certain distinguished
maximal
measure extension which has an immense domain. In the present paper we prove, under a certain local compactness condition on the Polish state space and for the time domain

[0,\infty [

, that the maximal domain in question has, for
all
stochastic processes, three distinguished members: the set of all continuous paths, the set of all paths with one-sided limits, and its subset of those paths which at each time are either left or right continuous. In all these cases the maximal measure of the set is equal to its outer canonical measure. However, the situation will be seen to be different for the set of the càdlàg paths, for example in the Poisson process.
Quasi-Periodic Solutions in Nonlinear Asymmetric Oscillations
Authors: Yang Xiaojing , LO KUEIMING
Published: December 2009

The existence of Aubry–Mather sets and infinitely many subharmonic solutions to the following

p

-Laplacian like nonlinear equation

(p-1)^{-1}(\phi_p(x'))'+[\alpha\phi_p(x^+)-\beta\phi_p(x^-)]+g(x) = h(t)

is discussed, where

\phi_p(u)=|u|^{p-2}u, \,p>1

,

\alpha, \beta

are positive constants satisfying

\alpha^{-\frac{1}{p}}+\beta^{-\frac{1}{p}}=\frac2n

with

n\in \mathbb N

,

h

is piece-wise two times differentiable and

2\pi_p

-periodic,

g\in C^1(R)

is bounded,

x^{\pm}=\max \{\pm x, 0\}

,

\pi_p=\frac{2\pi}{p\sin(\pi/p)}.
On Summands Properties and Minkowski Subtraction
Authors: Borowska D. , Przybycien H. , Urbanski R.
Published: December 2009

In this paper we generalise the Sallee theorem from [J. Geom. 29 (1987)(1), 1–11, Theorem 4.3] into non-symmetric sets and give its proof in the terms of Minkowski subtraction.
Homogenization of Scalar Problem for a Combined Structure with Singular or Thin Reinforcement
Authors: Cardone Giuseppe , Corbo Esposito A. , Pastukhova S.E.
Published: December 2009

The homogenization of quadratic integral functionals for combined structures with singular or asymptotically singular reinforcement is studied in a model case in dimension

N=2.

Generalizations to more general cases in dimension

N=2

or to some model cases in dimension

N>2

are discussed.

Such results are obtained in the frame of homogenization of problems depending on two parameters developed by V. V. Zhikov in [
Funct. Anal. Appl.
33 (1999)(1)], [
Sb. Math.
191 (2000)(7-8)], and [
Izv. Math.
66 (2002)(2)]. In particular, an essential tool is the notion of two-scale convergence of sequences of functions belonging to Sobolev spaces with respect to variable measures.
Existence Results for Strongly Nonlinear Elliptic Equations of Infinite Order
Authors: Benkirane A. , Chrif Moussa , El Manouni Said
Published: December 2009

In this work, generalized Sobolev spaces and Sobolev spaces of infinite order are considered. Existence of solutions for strongly nonlinear equation of infinite order of the form

Au+g(x,u)=f

is established. Here

A

is an elliptic operator from a functional space of Sobolev type to its dual and

g(x,s)

is a lower order term satisfying a sign condition on

s.
A Note on Compactness of Commutators for Fractional Integrals Associated with Nondoubling Measures
Authors: Betancor Jorge J. , Farina J.C.
Published: December 2009

In this note we study the compactness of the commutator of fractional integrals associated with nondoubling measures.
Interpolation and Transmutation
Authors: Boumenir Amin
Published: December 2009

We show that the existence of a transmutation between two self-adjoint operators

L_{1}

and

L_{2}

is equivalent to the existence of an interpolation operator in the spectral variable. This equivalence helps construct a transmutation operator between abstract self-adjoint operators.
Asymptotic Self-Similarity for Solutions of Partial Integro-Differential Equations
Authors: Engler Hans
Published: December 2009

The question is studied whether weak solutions of linear partial integro-differential equations approach a constant spatial profile after rescaling, as time goes to infinity. The possible limits and corresponding scaling functions are identified and are shown to actually occur. The limiting equations are fractional diffusion equations which are known to have self-similar fundamental solutions. For an important special case, is is shown that the asymptotic profile is Gaussian and convergence holds in

L^2

, that is, solutions behave like fundamental solutions of the heat equation to leading order. Systems of integro-differential equations occurring in viscoelasticity are also discussed, and their solutions are shown to behave like fundamental solutions of a related Stokes system. The main assumption is that the integral kernel in the equation is regularly varying in the sense of Karamata.
On Ren-Kähler's Paper “Hardy-Littlewood Inequalities and $Q_p$-Spaces” Z. Anal. Anwendungen 24 (2005), 375 – 388
Authors: Stevic Stevo
Published: December 2009

In this note we prove that a harmonic function

u

on the unit ball

B\subset\mathbb R^n

belongs to the harmonic mixed norm space

{\cal A}^{p,q}_s(B)

, when

p,q\in (0,\infty]

and

s>0

, if and only if all weighted tangential derivatives of order

k

(with positive orders of derivatives) belong to the related weighted Lebesgue mixed norm space

{\cal L}^{p,q}_s(B).

Our proof of the result for the case

q\in (0,1)

and

k

is odd, corrects the corresponding one in the paper: G. Ren and U. Kähler, Hardy–Littlewood inequalities and

Q_p

-spaces,
Z. Anal. Anwendungen
24 (2005), 375–388.
Decay Estimates of Solutions to the Cauchy Problem for a Wave Equation with a Bounded Nonlinear Dissipation
Authors: Benaissa Abbes , Mokeddem Soufiane
Published: December 2009

In this paper we prove the global existence and study decay properties of the solutions to the Cauchy problem for a wave equation with a bounded nonlinear dissipative term.
Approximate Approximations with Data on a Perturbed Uniform Grid
Authors: Lanzara Flavia , Maz'ya Vladimir G. , Schmidt Gunther
Published: December 2009

The aim of this paper is to extend the approximate quasi-interpolation on a uniform grid by dilated shifts of a smooth and rapidly decaying function to the case that the data are given on a perturbed uniform grid. It is shown that high order approximation of smooth functions up to some prescribed accuracy is possible.
Transition to Instability of Planar Viscous Shock Fronts: the Refined Stability Condition
Authors: Benzoni-Gavage Sylvie , Serre Denis , Zumbrun Kevin
Published: December 2009

Classical inviscid stability analysis determines stability of shock waves only up to a region of neutral stability occupying an open set of physical parameters. To locate a precise transition point within this region, it has been variously suggested that nonlinear and or viscous effects should be taken into account. Recently, Zumbrun and Serre showed that transition under localized (

L^1\cap H^s

) perturbations is in fact entirely decided by viscous effects, and gave an abstract criterion for transition in terms of an effective viscosity coefficient

\beta

determined by second derivatives of the Evans function associated with the linearized operator about the wave. Here, generalizing earlier results of Kapitula, Bertozzi et al, and Benzoni-Gavage et al., we develop a simplified perturbation formula for

\beta

, applicable to general shock waves, that is convenient for numerical and analytical investigation.
Existence of Solutions for some Quasiaffine PDEs
Authors: Giannetti Flavia , Pisante Giovanni
Published: December 2009

We prove the existence of solutions of problems of the type

\left\{ \begin{aligned} \Phi(Du(x)) &= f(x) &\quad &\text{\rm in } \, \Omega\\ u(x) &=\xi_0 x &\quad &\text{\rm on } \, \partial \Omega \end{aligned} \right.

with

\Phi:\mathbb{R}^{n\times n} \to \mathbb{R}

quasiaffine function and

\xi_0\in \mathbb{R}^{n\times n}

fixed.
Generalized Rademacher–Stepanov Type Theorem and Applications
Authors: Ranjbar-Motlagh Alireza
Published: December 2009

The main purpose of this article is to generalize a theorem of Stepanov which provides a necessary and sufficient condition for almost everywhere differentiability of functions over Euclidean spaces. We state and prove an

L^p

-type generalization of the Stepanov theorem and then we extend it to the context of Orlicz spaces. Then, this generalized Rademacher–Stepanov type theorem is applied to the Sobolev and bounded variation maps with values into a metric space. It is shown that several generalized differentiability type theorems are valid for the Sobolev maps from a Lipschitz manifold into a metric space. As a byproduct, it is shown that the Sobolev spaces of Korevaar–Schoen and Reshetnyak are equivalent.
Delay Diﬀerential Equations on Manifolds and Applications to Motion Problems for Forced Constrained Systems
Authors: Benevieri Pierluigi , Calamai Alessandro , Furi Massimo , Pera Maria Patrizia
Published: December 2009

We prove a global bifurcation result for

T

-periodic solutions of the delay

T

-periodic diﬀerential equation

x'(t) = λf(t,x(t), x(t − 1))

on a smooth manifold (

λ

is a nonnegative parameter). The approach is based on the asymptotic ﬁxed point index theory for

C^1

maps due to Eells–Fournier and Nussbaum. As an application, we prove the existence of forced oscillations of motion problems on topologically nontrivial compact constraints. The result is obtained under the assumption that the frictional coeﬃcient is nonzero, and we conjecture that it is still true in the frictionless case.
Imidazolium Ion‐Tagged Proline Organocatalyst for α‐Aminoxylation of Aldehydes and Ketones in Ionic Liquids
Authors: Ding Xiong , Tang Wenming , Zhu Chengjian , Cheng Yixiang
Published: December 2009

A novel imidazolium ion‐tagged L‐proline catalyst has been developed. The asymmetric α‐aminoxylation of aldehydes and ketones with excellent enantioselectivities, up to 99% ee, and high yields in ionic liquids has been achieved. The system can be easily recycled and reused for at least six times without significant loss of yields and enantioselectivity.
A backoff strategy for model‐based experiment design under parametric uncertainty
Authors: Galvanin Federico , Barolo Massimiliano , Bezzo Fabrizio , Macchietto Sandro
Published: December 2009

Model‐based experiment design techniques are an effective tool for the rapid development and assessment of dynamic deterministic models, yielding the most informative process data to be used for the estimation of the process model parameters. A particular advantage of the model‐based approach is that it permits the definition of a set of constraints on the experiment design variables and on the predicted responses. However, uncertainty in the model parameters can lead the constrained design procedure to predict experiments that turn out to be, in practice, suboptimal, thus decreasing the effectiveness of the experiment design session. Additionally, in the presence of parametric mismatch, the feasibility constraints may well turn out to be violated when that optimally designed experiment is performed, leading in the best case to less informative data sets or, in the worst case, to an infeasible or unsafe experiment. In this article, a general methodology is proposed to formulate and solve the experiment design problem by explicitly taking into account the presence of parametric uncertainty, so as to ensure both feasibility and optimality of the planned experiment. A prediction of the system responses for the given parameter distribution is used to evaluate and update suitable backoffs from the nominal constraints, which are used in the design session to keep the system within a feasible region with specified probability. This approach is particularly useful when designing optimal experiments starting from limited preliminary knowledge of the parameter set, with great improvement in terms of design efficiency and flexibility of the overall iterative model development scheme. The effectiveness of the proposed methodology is demonstrated and discussed by simulation through two illustrative case studies concerning the parameter identification of physiological models related to diabetes and cancer care. © 2009 American Institute of Chemical Engineers AIChE J, 2010
Diagnostic utility of daytime salivary melatonin levels in Smith–Magenis syndrome
Authors: Chik Constance L. , Rollag Mark D. , Duncan Wallace C. , Smith Ann C.M.
Published: December 2009

An inverted circadian rhythm of melatonin (MT) likely contributes to the sleep disturbance in patients with Smith–Magenis syndrome (SMS). Plasma MT levels have documented this altered rhythm, but daytime levels of salivary MT has not been determined. Daytime measures of salivary MT might have utility in home/outpatient settings for assessing MT levels in undiagnosed patients with clinical features of SMS. The objective of this study was to determine the utility of daytime salivary MT as a diagnostic test in SMS. Thirty individuals with confirmed SMS [28 with del 17p11.2 and 2 with the retinoic acid induced 1 (RAI1) gene mutation] and five controls were studied. Single or serial daytime salivary MT levels were measured. The mean midday salivary MT level was 79.0 pg/ml in SMS patients, compared with 16.3 pg/ml in controls, with nine patients having values similar to controls. The median MT level in SMS patients was 49.0 pg/ml (first and third quartile values = 15.5 and 106.8 pg/ml). Twenty‐six (90%) of 29 patients had at least one MT value >15.5 pg/ml, including 70 (78%) of 90 samples from patients with del 17p11.2 and one (20%) of five samples from the two patients with the RAI1 mutation. Neither the pattern of medication use nor age had an effect on daytime salivary MT levels. Although most SMS patients had elevated daytime salivary MT levels, multiple sampling appears necessary to distinguish patients with SMS from other conditions. © 2009 Wiley‐Liss, Inc.
An unusual severe vascular case of pseudoxanthoma elasticum presenting as generalized arterial calcification of infancy
Authors: Le Boulanger G. , Labrèze C. , Croué A. , Schurgers L.J. , Chassaing N. , Wittkampf T. , Rutsch F. , Martin L.
Published: December 2009

Pseudoxanthoma elasticum (PXE) is an autosomal recessive disease affecting tissues rich in elastic fibers such as the skin, retina, and cardiovascular system. Mutations in the ABCC6 gene are known to be causative in most patients. Generalized arterial calcification of infancy (GACI) is characterized by extensive hydroxyapatite deposits in the internal elastic laminae in large and medium‐sized arteries, leading to arterial stenoses and early and severe myocardial ischemia. GACI has been found to be primarily caused by mutations in the ENPP1 gene. We report two brothers born to unrelated parents. The elder developed uncomplicated PXE in adolescence and harbored mutations in the ABCC6 gene. The younger child died of a condition strikingly reminiscent of GACI at 15 months of age. This case of GACI was independent of mutations in the ENPP1 gene but was probably related to ABCC6 mutations. We demonstrate that matrix Gla protein and fetuin‐A, involved in PXE, are also expressed in this case of GACI. These proteins could act as local and systemic inhibitors to limit the extension of mineralization. This report emphasizes concurrently that ABCC6 may be a relevant candidate gene in some cases of GACI with no mutations in the ENPP1 gene, and that GACI may be an atypical and severe end of the vascular phenotype spectrum of PXE. © 2009 Wiley‐Liss, Inc.
Speech characteristics in neurofibromatosis type 1
Authors: Alivuotila Lotta , Hakokari Jussi , Visnapuu Vivian , Korpijaakko‐Huuhka Anna‐Maija , Aaltonen Olli , Happonen Risto‐Pekka , Peltonen Sirkku , Peltonen Juha
Published: December 2009

Neurofibromatosis 1 (NF1) is a neurocutaneous‐skeletal disorder often accompanied with varying degrees of cognitive and motor problems that potentially affect speech and language. While previous studies have shown that NF1 may be associated with a variety of deviations in the patients' speech, they have not investigated the characteristics in phonetic detail. Our clinical observation that many patients share a distinct voice and manner of speaking led to the primary aim of this study, which was to present a comprehensive description of speech in NF1. A total of 62 patients with NF1 (age range 7–66 years), and a control group of 24 speakers (age range 7–62 years) were evaluated for their speech. The test sessions were recorded and the data were analyzed both by ear and by acoustic measurements. The data were analyzed separately by two trained phoneticians, and a summary was produced after comparing the two independent analyses. Various speech problems were observed among patients with NF1. Individual variation was remarkable, but the deviations were more common and severe in children than in adult patients. In addition, men with NF1 had more speech deviations than women with NF1. Findings include deviations in voice quality, problems in regulating pitch, deviant nasality, misarticulation, and disfluency. We suggest that difficulties in speech, particularly in regulating pitch, may have negative social implications. Our results highlight which components of speech require particular attention in speech therapy for patients with NF1. © 2009 Wiley‐Liss, Inc.
Enthesopathies as occupational stress markers: Evidence from the upper limb
Authors: Villotte Sébastien , Castex Dominique , Couallier Vincent , Dutour Olivier , Knüsel Christopher J. , Henry‐Gambier Dominique
Published: December 2009

Enthesopathies—that is, “musculo‐skeletal stress markers”—are frequently used to reconstruct past lifestyles and activity patterns. Relatively little attention has been paid in physical anthropology to methodological gaps implicit in this approach: almost all methods previously employed neglect current medical insights into enthesopathies and the distinction between healthy and pathological aspects has been arbitrary. This study presents a new visual method of studying fibrocartilaginous enthesopathies of the upper limb (modified from Villotte: Bull Mém Soc Anthropol Paris n.s. 18 (2006) 65–85), and application of this method to 367 males who died between the 18th and 20th centuries, from four European identified skeletal collections: the Christ Church Spitalfields Collection, the identified skeletal collection of the anthropological museum of the University of Coimbra, and the Sassari and Bologna collections of the museum of Anthropology, University of Bologna. The analysis, using generalized estimating equations to model repeated binary outcome variables, has established a strong link between enthesopathies and physical activity: men with occupations involving heavy manual tasks have significantly (P‐value < 0.001) more lesions of the upper limbs than nonmanual and light manual workers. Probability of the presence of an enthesopathy also increases with age and is higher for the right side compared with the left. Our study failed to distinguish significant differences between the collections when adjusted for the other effects. It appears that enthesopathies can be used to reconstruct past lifestyles of populations if physical anthropologists: 1) pay attention to the choice of entheses in their studies and 2) use appropriate methods. Am J Phys Anthropol, 2010. © 2009 Wiley‐Liss, Inc.