bluuebunny/crossref_metadata_2025 huggingface dataset:
Bifurcation points of a degenerate elliptic boundary-value problem
Authors: Evéquoz Gilles , Stuart Charles A.
Published: December 2009

We consider the nonlinear elliptic eigenvalue problem

\begin{align*}
-\nabla\cdot\{A(x)\nabla u(x)\} & =\lambda f(u(x))\text{ for }x\in\Omega\\
u(x) & =0\text{ for }x\in\partial\Omega
\end{align*}

where

\Omega

is a bounded open subset of

\mathbb{R}^{N}

and

f\in C^{1}(\mathbb{R})

with

f(0)=0

and

f^{\prime}(0)=1

. The ellipticity is degenerate in the sense that

0\in\Omega

and

A(x)>0

for

x\neq0

but

\lim_{x\rightarrow0}\frac{A(x)}{\left\vert x\right\vert ^{2}}=1

. We show that there is vertical bifurcation at all points

\lambda

in the interval

(\frac{N^{2}}{4},\infty).

Bifurcation also occurs at any eigenvalues of the linearized problem that are below

\frac{N^{2}}{4}

. Our treatment is based on recent results concerning the bifurcation points of equations with nonlinearities that are Hadamard differentiable, but not Fréchet differentiable.
The Picard group of the moduli stack of stable hyperelliptic curves
Authors: Cornalba Maurizio
Published: December 2009

We compute the Picard group of the moduli stack of stable hyperelliptic curves of any genus, exhibiting explicit and geometrically meaningful generators and relations.
Hardy inequality and properties of the quasilinear Sturm–Liouville problem
Authors: Drábek Pavel , Kufner Alois
Published: December 2009

We present necessary and sufficient condition for discreteness of the set of all eigenvalues (having the usual Sturm–Liouville properties) of a quasilinear Sturm–Liouville-type problem with weights on an infinite interval. We point out that the same condition is necessary and sufficient for the compact embedding of certain weighted Sobolev and Lebesgue spaces. Our result completes those from the linear theory.
On the regularity of weak solutions to $H$-systems
Authors: Musina Roberta
Published: December 2009

In this paper we prove that every weak solution to the

H

-surface equation is locally bounded, provided the prescribed mean curvature

H

satisfies a suitable condition at infinity. No smoothness assumption is required on

H

. We consider also the Dirichlet problem for the

H

-surface equation on a bounded regular domain with

L^{\infty}

boundary data and the

H

-bubble problem. Under the same assumptions on

H

, we prove that every weak solution is globally bounded.
A general effective Hamiltonian method
Authors: Martinez André
Published: December 2009

We perform a general reduction scheme that can be applied in particular to the spectral study of operators of the type

P=P(x,y,hD_x,D_y)

as

h

tends to zero. This scheme permits to reduce the study of

P

to the one of a semiclassical matrix operator of the type

A=A(x,hD_x)

. Here, for any fixed

(x,\xi )\in\R^n

, the eigenvalues of the principal symbol

a(x,\xi )

of

A

are eigenvalues of the operator

P(x,y,\xi ,D_y)

.
Nonradial symmetric bound states for a system of coupled Schrödinger equations
Authors: Wei Juncheng , Weth Tobias
Published: December 2009

We consider bound state solutions of the coupled elliptic system

\Delta u - u + u^3 +\beta v^2 u=0 \ \text{in} \ \R^N,

\Delta v - v + v^3 +\beta u^2 v=0 \ \text{in} \ \R^N,

u >0, v >0, u, v \in {\mathbb H}^1 (\R^N),

where

N=2,3

. It is known ([13]) that when

\beta <0

, there are no ground states, i.e., no least energy solutions. We show that, for certain finite subgroups of

O(N)

acting on

{\mathbb H}^1 (\R^N)

, least energy solutions can be found within the associated subspaces of symmetric functions. For

\beta\le -1

these solutions are nonradial. From this we deduce, for every

\beta \le -1

, the existence of infinitely many nonradial bound states of the system.
Ostrowski type inequalities over Euclidean domains
Authors: Anastassiou George A. , Goldstein Jerome A.
Published: December 2009

The classical Ostrowski inequality for functions on intervals is extended to functions on general domains in Euclidean space. For radial functions on balls the inequality is sharp.
An explicit lower bound for the block complexity of an algebraic number
Authors: Bugeaud Yann
Published: December 2009

Let

b \ge 2

be an integer and

\xi

be an irrational real number. Among other results, we establish an explicit lower bound for the number of distinct blocks of

n

digits occurring in the

b

-ary expansion of

\xi

.
Combinatorics and topology of toric arrangements defined by root systems
Authors: Moci Luca
Published: December 2009

Given the toric (or toral) arrangement defined by a root system

\Phi

, we classify and count its components of each dimension. We show how to reduce to the case of 0-dimensional components, and in this case we give an explicit formula involving the maximal subdiagrams of the affine Dynkin diagram of

\Phi

. Then we compute the Euler characteristic and the Poincar\'{e} polynomial of the complement of the arrangement, that is the set of regular points of the torus.
Continuous dependence on the constitutive functions for a class of problems describing fluid flow in porous media
Authors: Borsi Iacopo , Farina Angiolo , Gianni Roberto , Primicerio Mario
Published: December 2009

In this paper we consider the PDE describing the fluid flow in a porous medium, focusing on the solution’s dependence upon the choice of the saturation curve and the hydraulic conductivity. Basically, we consider two different saturation curves (say

θ_1

and

θ_2

) and two different hydraulic conductivities (

\mathscr{K}_1

and

\mathscr{K}_2

) which are both “close” in the

L^∞_{\mathrm{loc}}

-norm. Then we find estimates to prove a constitutive stability for the solutions of the corresponding problems with the same boundary and initial conditions.
Efficient representation in spaces of plane curves
Authors: Leonard Kathryn
Published: December 2009

This paper evaluates the Blum medial axis representation of embeddings of

S^1

into

ℝ^2

from the perspective of efficiency, using a

C^1

-type metric. For compact classes of curves with Lipschitz tangent angle, we compute the

ε

-entropy and compare that efficiency benchmark with uniform approximation using the Blum medial axis. In the compact setting, the boundary curve is more efficient. For noncompact classes of embeddings, we establish a geometric criterion for when the medial axis will be more efficient in an adaptive approximation.
On the number of terms of a power of a polynomial
Authors: Schinzel Andrzej , Zannier Umberto
Published: December 2009

Let f(x) be a polynomial with complex coefficients. Rényi and independently Erdős in 1949 conjectured that a bound for the number of terms of f(x)2 implies a bound for the number of terms of f(x). In 1987 Schinzel found a proof of this conjecture, actually for all powers f(x)l, and he gave some explicit bounds. The aim of this paper is to improve such inequalities in a substantial way.
The limit as $p → ∞$ for the $p$-Laplacian with mixed boundary conditions and the mass transport problem through a given window
Authors: García-Azorero Jesús , Manfredi Juan J. , Peral Ireneo , Rossi Julio D.
Published: December 2009

In this paper we study the limit as

p → ∞

in a PDE problem involving the

p

-Laplacian with a right hand side,

− \mathrm{div}(|Du|^{p − 2}Du) = f

, with mixed boundary conditions,

u = 0

on

Γ

and

|Du|^{p − 2} \frac{∂u}{∂ν} = 0

on

∂Ω \backslash  Γ

. We find that this limit is related to an optimal mass transport problem, where the total mass given by

f

is transported outside the domain through a given window on the boundary

Γ

.
Uniqueness in the Cauchy problem for a class of hypoelliptic ultraparabolic operators
Authors: Cinti Chiara
Published: December 2009

We consider a class of hypoelliptic ultraparabolic operators in the form

\mathcal L=\sum_{j=1}^m X_j^2+X_0-\partial_t,

under the assumption that the vector fields

X_1,\ldots,X_m

and

X_0-\partial_t

are invariant with respect to a suitable homogeneous Lie group

\mathbb{G}

. We show that if

u,v

are two solutions of

\mathcal L u = 0

on

\mathbb R^N \times ]0,T[

and

u(\cdot,0)=\varphi

, then each of the following conditions:

|u(x,t)-v(x,t)|

can be bounded by

M \exp (c|x|_{\mathbb{G}}^2)

, or both

u

and

v

are non negative, implies

u\equiv v

. We use a technique which relies on a pointwise estimate of the fundamental solution of

\mathcal L

.
Gradient estimates in non-linear potential theory
Authors: Duzaar Frank , Mingione Giuseppe
Published: December 2009

We present pointwise gradient bounds for solutions to p-Laplacian type non-homogeneous equations employing non-linear Wolff type potentials, and then prove similar bounds, via suitable caloric potentials, for solutions to parabolic equations. A method of proof entails a family of non-local Caccioppoli inequalities, together with a DeGiorgi’s type fractional iteration.
Some (big) irreducible components of the moduli space of minimal surfaces of general type with $p_g= q = 1$ and $K^2 = 4$
Authors: Pignatelli Roberto
Published: December 2009

This paper is devoted to the irregular surfaces of general type having the smallest invariants,

p_g = q = 1

. We consider the still unexplored case

K^2 = 4

, classifying those whose Albanese morphism has general ﬁbre of genus 2 and such that the direct image of the bicanonical sheaf under the Albanese morphism is a direct sum of line bundles. We ﬁnd 8 unirational families, and we prove that all are irreducible components of the moduli space of minimal surfaces of general type. This is unexpected because the assumption on the direct image bicanonical sheaf is a priori only a closed condition. One more unexpected property is that all these components have dimension strictly bigger than the expected one.
On a Sobolev-type inequality
Authors: Alvino Angelo
Published: December 2009

A new proof of the classical Sobolev inequality in

ℝ^n

with the best constant is given. The result follows from an intermediate inequality which connects in a sharp way the

L^p

norm of the gradient of a function

u

to

L^{p^*}

and

L^{p^*}

-weak norms of

u

, where

p \in ]1; n[

and

p^* = \frac{np}{n-p}

is the Sobolev exponent.
Bernstein's 'Lethargy' Theorems in SF-Spaces
Authors: Micherda B.
Published: December 2009

We prove a version of Bernstein's 'lethargy' theorem for cones in the class of SF-spaces. Moreover, an analogue of the Bernstein theorem for linear projections onto closed subspaces of an SF-space is obtained. This extends results given by G. Lewicki.
Quaternionic Fundamental Solutions for Electromagnetic Scattering Problems and Application
Authors: Khmelnytskaya K. V. , Kravchenko Vladislav V. , Rabinovich Vladimir S.
Published: December 2009

We propose a new class of fundamental solutions for the numerical analysis of boundary value problems for the Maxwell equations. We prove completeness of systems of such fundamental solutions in appropriate Sobolev spaces on a smooth boundary and support the relevancy of our approach by numerical results.
Errata and Addendum to: Existence Result for the One-Dimensional Full Model of Phase Transitions
Authors: Luterotti F. , Stefanelli Ulisse
Published: December 2009

We state some corrections to our recent paper “Existence Result for the One-Dimensional Full Model of Phase Transitions”, Z. Anal. Anwend. 21 (2002) 335–350.
Criteria for Membership of the Mean Lipschitz Spaces
Authors: Walsh D.
Published: December 2009

Our aim is to characterize the elements in certain function spaces by means of the Cesáro means and/or partial sums of their Fourier series. Firstly, we seek to extend known results for the Besov spaces

B^s_{pq}

(1 \le p,q < \infty)

to the case where

q = \infty

. Secondly, we consider the Mean Lipschitz spaces

\Lambda(p,s)

. We confine attention to the values

1 \le p < \infty

and

0 < s \le 1

for the parameters. For

s < 1

, the spaces

B^s _{p\infty}

and

\Lambda(p,s)

coincide. For the case

p = 1

certain counter-examples are provided; some positive results are also given. We then treat the case

s = 1

and consider the spaces

B^1_{p\infty}

and

\Lambda(p,1)

separately. Analogues of some known results for the spaces

\Lambda_s

are given.
Fixed Point Theorems for a Class of Mixed Monotone Operators
Authors: Liang Zhandong , Zhang Lingling , Li Shengjia
Published: December 2009

We study a class of mixed monotone operators with convexity and concavity. In particular, we give conditions, both necessary and sufficient, for the existence and uniqueness of fixed points. Moreover, we sketch a simple application of our main theorem and generalize some previous results.
On a Quaternionic Reformulation of Maxwell's Equations for Chiral Media and its Applications
Authors: Kravchenko Vladislav V. , Oviedo H.
Published: December 2009

A quaternionic reformulation of the Maxwell equations for chiral media is proposed. Integral representations for solutions are constructed. A complete solution of the extendability problem for the electromagnetic fields in chiral media is obtained. Maxwell's equations for inhomogeneous chiral media are studied also and some classes of solutions for slowly changing media are obtained.
A Necessary and Sufficient Condition for the Existence of Positive Solutions to the Singular p-Laplacian
Authors: Agarwal Ravi P. , Lü Haishen , O'Regan Donal
Published: December 2009

This paper studies the boundary value problem

(\varphi_p(u'))' + q(t)(f(u) + g(u)) = 0 \qquad (0 < t < 1)

\ \ u(0) = u(1) = 0

in the case

p > 1

. A necessary and sufficient condition for the existence of

C^1[0,1]

positive solutions and a sufficient condition for the existence of

C[0,1]

positive solutions are presented.
Multiobjective Duality for Convex Semidefinite Programming Problems
Authors: Wanka Gert , Boţ Radu Ioan , Grad S. M.
Published: December 2009

We treat some duality assertions regarding multiobjective convex semidefinite programming problems. Having a vector minimization problem with convex entries in the objective vector function, we establish a dual for it using the so-called conjugacy approach. In order to deal with the duality assertions between these problems we need to study the duality properties and the optimality conditions of the scalarized problem associated to the initial one. Using these results we present the weak, strong and converse duality assertions regarding the primal problem and the dual we obtained for it.
Absolutely Continuous Functions of Several Variables and Quasiconformal Mappings
Authors: Hencl Stanislav
Published: December 2009

We prove that functions with bounded n-variation and n-absolutely continuous functions of n-variables in the sense introduced previously by the author [Fund. Math. 173 (2002) 175–189] are stable under quasiconformal mappings. The class of quasiconformal mappings is the best possible since every homeomorphism which induces a bounded operator between BVn spaces is a quasiconformal mapping.
On Sobolev Theorem for Riesz-Type Potentials in Lebesgue Spaces with Variable Exponent
Authors: Kokilashvili Vakhtang , Samko Stefan
Published: December 2009

The Riesz potential operator of variable order

\alpha(x)

is shown to be bounded from the Lebesgue space

L^{p(\cdot)}({\Bbb R}^n)

with variable exponent

p(x)

into the weighted space

L^{q(\cdot)}_\rho({\Bbb R}^n)

, where

\rho(x) = (1 + 'x')^{-\gamma}

with some

\gamma > 0

and

{1 \over q(x)} = {1 \over p(x)} - {\alpha(x) \over n}

when

p

is not necessarily constant at infinity. It is assumed that the exponent

p(x)

satisfies the logarithmic continuity condition both locally and at infinity and

1 < p(\infty) \le p(x) \le P < \infty

(x \in {\Bbb R}^n)

.
Solvability of Two-Point Boundary Value Problems for Fourth-Order Nonlinear Differential Equations at Resonance
Authors: Liu Yuji , Ge Weigao
Published: December 2009

Under a resonance condition involving a two-point boundary value problem for a fourth-order nonlinear differential equation, we show its solvability.
Lavrentiev Regularization for Linear Ill-Posed Problems under General Source Conditions
Authors: Nair M. Thamban , Tautenhahn Ulrich
Published: December 2009

In this paper we study the problem of identifying the solution

x^\dagger

of linear ill-posed problems

Ax = y

with non-negative and self-adjoint operators

A

on a Hilbert space

X

where instead of exact data

y

noisy data

y^δ\in X

are given satisfying

\Vert y - y^δ\Vert ≤ δ

with known noise level

δ

. Regularized approximations

x_α^δ

are obtained by the
method of Lavrentiev regularization
, that is,

x_α^δ

is the solution of the singularly perturbed operator equation

Ax + αx = y^δ

, and the regularization parameter

α

is chosen either
a priori or a posteriori
by the rule of Raus. Assuming the unknown solution belongs to some general source set

M

, we prove that the regularized approximations provide order optimal error bounds on the set

M

. Our results cover the special case of finitely smoothing operators

A

and extend recent results for infinitely smoothing operators. In addition, we generalize our results to the

method of iterated Lavrentiev regularization of order

m

and discuss a special ill-posed problem arising in inverse heat conduction.
Weighted Sharing of Three Values
Authors: Lahiri Indrajit
Published: December 2009

Using the notion of weighted sharing of values we prove some uniqueness theorems for meromorphic functions which improve some earlier results.
On the Regularity of Weak Solutions of Quasi-Linear Elliptic Transmission Problems on Polyhedral Domains
Authors: Knees Dorothee
Published: December 2009

The regularity of weak solutions of quasi-linear elliptic boundary transmission problems of p-structure on polyhedral domains Ω is considered. Ω is divided into polyhedral subdomains Ωi and it is assumed that the growth properties of the differential operator vary from subdomain to subdomain. We prove higher regularity of weak solutions up to the transmission surfaces, provided that the differential operators are distributed quasi-monotonely with respect to the subdomains Ωi. The proof relies on a difference quotient technique which is based on the ideas of C. Ebmeyer and J. Frehse.
Grand and Small Lebesgue Spaces and Their Analogs
Authors: Fiorenza Alberto , Karadzhov G. E.
Published: December 2009

We give the following, equivalent, explicit expressions for the norms of the small and grand Lebesgue spaces, which depend only on the non-decreasing rearrangement (we assume here that the underlying measure space has measure 1):

\begin{align*}
\|f\|_{L^{(p}} &\approx \int_0^1 (1-\ln t)^{-\frac{1}{p}}\left(\int_0^t [f^{\ast}(s)]^{p}ds\right)^{\frac{1}{p}} dt/t &\qquad &(1 < p < \infty) \\
\|f\|_{L^{p)}} &\approx \sup_{0 < t < 1} (1-\ln t)^{-\frac{1}{p}} \left(\int_{t}^1 [f^{\ast}(s)]^p ds\right)^{\frac{1}{p}} &\qquad &(1 < p < \infty).
\end{align*}

Similar results are proved for the generalized small and grand spaces.
Banach Frames for Conjugate Banach Spaces
Authors: Jain Pawan K. , Kaushik Shiv K. , Vashisht Lalit K.
Published: December 2009

Retro Banach frames for conjugate Banach spaces have been introduced and studied. It has been proved that a Banach space E is separable if and only if E* has a retro Banach frame. Finally, a necessary and sufficient condition for a sequence in a separable Banach space to be a retro Banach frame has been given.
On Representation, Boundedness and Convergence of Hankel-K{Mp}' Generalized Functions
Authors: Marrero Isabel
Published: December 2009

Under opportune assumptions on the defining sequence

\{M_p\}_{p=0}^{\infty}

, Hankel-

K\{M_{p}\}'

generalized functions can be represented as

f = x^{-\mu-\frac{1}{2}}(Dx^{-1})^kF(x),

where

k\in {\mathbb N}

and

F

is a continuous function on

I=(0,\infty)

such that

M^{-1}_r F\in L^q(I)

(1\le q\le \infty)

for some

r\in {\mathbb N}

. A corresponding characterization of boundedness and convergence of Hankel-

K\{M_{p}\}'

generalized functions is given.
Averaging of Perturbed One Sided Lipschitz Differential Inclusions
Authors: Donchev T. , Kamenskii Mikhail , Quincampoix Marc
Published: December 2009

We consider one sided Lipschitz differential inclusions perturbed with multimap, satisfying compactness type conditions. The state space is Banach with uniformly convex dual. Averaging result on a finite interval is proved. The averaging of functional differential inclusions is also studied.
Compression Molding II: Existence of the Solution for a Hele-Shaw Type Model
Authors: Fang Ming , Gilbert Robert P.
Published: December 2009

We discuss an idealized model for compression molding, assuming a compressible flow. Existence theorems are established for this system.
Cauchy Transform and Rectifiability in Clifford Analysis
Authors: Bory Reyes Juan , Abreu Blaya Ricardo
Published: December 2009

\def\R{\mathbb R} Let

\Gamma

be an

n

-dimensional rectifiable Ahlfors-David regular surface in

\R^{n+1}

. Let

u

be a continuous

\R_{0,n}

-valued function on

\Gamma

, where

\R_{0,n}

is the Clifford algebra associated with

\R^n

. Then we prove that the Cliffordian Cauchy transform

({\cal C}_{\Gamma}u)(x):= \int_{\Gamma}\ \frac{\overline{y-x}}{A_{n+1}|y-x|^{n+1}}n(y)u(y) \,d{\cal H}^{n}(y),\quad x\notin\Gamma,

has continuous limit values on

\Gamma

if and only if the truncated integrals

{\cal S}_{\Gamma,\,\epsilon}u(z):=\int_{\Gamma\setminus\{|y-z|\le\epsilon\}} \ \frac{\overline{y-z}}{A_{n+1}|y-z|^{n+1}}n(y)(u(y)-u(z))\,d{\cal H}^{n}(y)

converge uniformly on

\Gamma

as

\epsilon\to 0

.
On a Class of Generalized Autoconvolution Equations of the Third Kind
Authors: Berg Lothar , von Wolfersdorf Lothar
Published: December 2009

Existence, uniqueness, smoothness, and asymptotics of solutions to a class of generalized autoconvolution equations with outer and inner coefficient are investigated. Further, holomorphic and asymptotic solutions of the equations are derived, and a numerical procedure for an approximate solving of the equations is tested by an example.
Existence and Multiplicity of Positive Solutions for Singular $p$-Laplacian Equations
Authors: Lü Haishen , Xie Yi
Published: December 2009

Positive solutions are obtained for the boundary value problem

\begin{cases}
-\Delta_{p}u= \lambda (u^{\beta }+\tfrac{1}{u^{\alpha }}) &\quad \text{in} \quad \Omega \\
u> 0 &\quad \text{in} \quad\Omega \qquad (*) \\
u= 0 &\quad \text{on} \quad \partial \Omega
\end{cases}

where

\Delta _{p}u=\mathrm{div}(| \nabla u| ^{p-2}\nabla u)

,

1
0

is a real parameter. We obtain that Problem (

*

) has two positive weakly solutions if

\lambda

is small enough.
On the Extension of a Certain Class of Carleman Operators
Authors: Bahri S. M.
Published: December 2009

The integral operators of Carleman play an important role in the spectral theory of selfadjoint operators and made the object of several works such those of G. I. Targonski [
Proc. Amer. Math. Soc.
18 (1967)(3)], V. B. Korotkov [
Sib. Math. J.
11 (1970)(1)], and J. Weidmann [
Manuscripta Math.
(1970)(2)]. In the present paper, we study a certain class of these operators in the Hilbert space

L^{2}\left(X,\mu\right)

. Precisely, we give necessary and sufficient conditions so that they possess equal defeciency indices. Such operators find their applications in the theory of random variable approximation.
On the Limiting Regularity Result of some Nonlinear Elliptic Equations
Authors: Alaoui M. Kbiri , Meskine D. , Souissi A.
Published: December 2009

We shall prove the limiting regularity

W_0^{1,\frac{N(p-1)}{N-1}}(\Omega )

of solutions of some nonlinear elliptic problems with right hand side in

LLog^{\alpha}L(\Omega)

and

\alpha \geq \frac{N - 1}{N}

. Also, an improved regularity is given when

\alpha < \frac{N - 1}{N}

.
On the Riemann–Hilbert Problem with a Piecewise Constant Matrix
Authors: Mityushev Vladimir V. , Rogosin Sergei V.
Published: December 2009

A constructive solution to the Riemann–Hilbert boundary value problem as well as to the

\mathbb C

-linear conjugation problem (or Riemann problem) with a special piecewise constant matrix for a multiply connected domain is obtained. The result is based on a vector generalization of the scalar method of functional equations in complex domain and on application of the Christoffel–Schwarz transformation of the half-plane onto a circular polygon.
Implicit Difference Methods for Quasilinear Differential Functional Equations on the Haar Pyramid
Authors: Kepczyńska A.
Published: December 2009

We present a new class of numerical methods for quasilinear first order partial functional differential equations. The numerical methods are difference schemes which are implicit with respect to the time variable. The existence of approximate solutions is proved by using a theorem on difference inequalities. The proof of the stability is based on a comparison technique with nonlinear estimates of the Perron type for given operators. Numerical experiments are presented. Results obtained in this paper can be applied to differential integral problems and to equations with deviated variables.
Iterative Approximation for a Boundary Value Problem Arising for the Electrical Potential on a Cylindrical Double Layer
Authors: Appell Jürgen , Chen Chur-Jen , Tseng Shiojenn , Väth Martin
Published: December 2009

Building on Banach's contraction mapping principle, we give existence, uniqueness, and approximation theorems for a boundary value problem on an unbounded domain arising in the mathematical modelling of the electrical potential in a cylindrical double layer.
Kernel Dimension of Singular Integral Operators with Piecewise Continuous Coefficients on the Unit Circle
Authors: Rogozhin A. , Silbermann Bernd
Published: December 2009

In this paper we propose a method to compute the kernel dimension of a Fredholm singular integral operator

aP+bQ

with piecewise continuous coefficients

a, b.

We show that the kernel dimension can be extracted from the singular value behavior of a polynomial collocation method. The results are illustrated by numerical experiments.
Fibre Picard Operators on Gauge Spaces and Applications
Authors: Rus I. A. , Petrusel A. , Serban M. A.
Published: December 2009

The purpose of this paper is to prove some fibre Picard operator principles in gauge spaces. As application, the differentiability with respect to parameters of the solution of a Volterra functional-integral equation is discussed.
Regularity of Minimizers of some Variational Integrals with Discontinuity
Authors: Ragusa Maria Alessandra , Tachikawa Atsushi
Published: December 2009

We prove regularity properties in the vector valued case for minimizers of variational integrals of the form

\mathcal A(u) = \int_\Omega A(x,u,Du)\,dx

where the integrand

A(x,u,Du)

is not necessarily continuous respect to the variable

x,

grows polinomially like

|\xi|^p,

p \geq 2.
Global Smooth Solutions of Viscous Compressible Real Flows with Density-Dependent Viscosity
Authors: Qin Xulong , Yao Zheng-an
Published: December 2009

We consider an initial boundary problem of viscous, compressible, heat-conducting real fluids with density-dependent viscosity. More precisely, we assume that the viscosity

\mu(\rho)=\rho^{\lambda}

, where

\rho

is the density of flows and

\lambda

is a positive constant. The equations of state for the real flows depend nonlinearly upon the temperature and the density unlike the linear dependence for the perfect flows. We prove the global existence (uniqueness) of smooth solutions under the hypotheses:

\lambda \in \big(2(\gamma-1),\frac12\big]

and

1\leq \gamma <\frac54

, which improves a previous result. In particular, we also show that no vacuum will be developed provided the initial density is far away from vacuum.
Description of Pointwise Multipliers in Pairs of Besov Spaces $B_1^k(\mathbb{R}^n)$
Authors: Shaposhnikova Tatyana
Published: December 2009

Necessary and sufficient conditions for a function to be a multiplier mapping the Besov space

B_1^m(\mathbb R^n)

into the Besov space

B_1^l(\mathbb R^n)

with integer

l

and

m

,

0<l\leq m

, are found. It is shown that multipliers between

B_1^m(\mathbb R^n)

and

B_1^l(\mathbb R^n)

form the space of traces of multipliers between the Sobolev classes

W_1^{m+1}(\mathbb R^{n+1}_+)

and

W_1^{l+1}(\mathbb R^{n+1}_+)

.
Invertibility of Matrix Wiener–Hopf plus Hankel Operators with Symbols Producing a Positive Numerical Range
Authors: Castro L. P. , Silva A. S.
Published: December 2009

We characterize left, right and both-sided invertibility of matrix Wiener–Hopf plus Hankel operators with possibly different Fourier symbols in the Wiener subclass of the almost periodic algebra. This is done when a certain almost periodic matrix-valued function (constructed from the initial Fourier symbols of the Hankel and Wiener–Hopf operators) admits a numerical range bounded away from zero. The invertibility characterization is based on the value of a certain mean motion. At the end, an example of a concrete Wiener–Hopf plus Hankel operator is studied in view of the illustration of the proposed theory.
Non-Trivial Self-Similar Extinction Solutions for a 3D Hele–Shaw Suction Problem
Authors: Prokert Georg , Vondenhoff E.
Published: December 2009

We show the existence of noncircular, self-similar solutions to the three-dimensional Hele–Shaw suction problem with surface tension regularisation up to complete extinction. In an appropriate scaling, these solutions are found as bifurcation solutions to a nonlocal elliptic equation of order three. The bifurcation parameter is the ratio of the suction speed and the surface tension coefficient.
On the Mathematical Analysis and Numerical Approximation of a System of Nonlinear Parabolic PDEs
Authors: Kačur J. , Malengier B. , Van Keer R.
Published: December 2009

In this paper we consider a boundary value problem for a system of 2 nonlinear parabolic PDEs e.g. arising in the context of ﬂow and transport in porous media. The ﬂow model is based on tho nonlinear Richard’s equation problem and is combined with the transport equation through saturation and Darcy’s velocity (discharge) terms. The convective terms are approximated by means of the method of characteristics initiated by P. Pironneau [Num. Math. 38 (1982), 871–885] and R. Douglas and T. F. Russel [SIAM J. Num. Anal. 19 (1982), 309–332]. The nonlinear terms in Richard’s equation are approximated by means of a relaxation scheme applied by W. Jäger and J. Kačur [RAIRO Model. Math. Anal. Num. 29 (1995), 605–627] and J. Kačur [IMA J. Num. Anal. 19 (1999), 119–154; SIAM J. Num. Anal. 39 (1999), c 290–316]. The convergence of the approximation method is proved.
Variable Order Diﬀerential Equations with Piecewise Constant Order-Function and Diﬀusion with Changing Modes
Authors: Umarov Sabir , Steinberg Stanly
Published: December 2009

In this paper diﬀusion processes with changing modes are studied involving the variable order partial diﬀerential equations. We prove the existence and uniqueness theorem of a solution of the Cauchy problem for fractional variable order (with respect to the time derivative) pseudo-diﬀerential equations. Depending on the parameters of variable order derivatives short or long range memories may appear when diﬀusion modes change. These memory eﬀects are classiﬁed and studied in detail. Processes that have distinctive regimes of diﬀerent types of diﬀusion depending on time are ubiquitous in the nature. Examples include diﬀusion in a heterogeneous media and protein movement in cell biology.
Polymorphisms in KCNE1 or KCNE3 are not associated with Ménière disease in the Caucasian population
Authors: Campbell Colleen A. , Della Santina Charley C. , Meyer Nicole C. , Smith Nancy B. , Myrie Oluwaseun A. , Stone Edwin M. , Fukushima Kuni , Califano Joseph , Carey John P. , Hansen Marlan R. , Gantz Bruce J. , Minor Lloyd B. , Smith Richard J.H.
Published: December 2009

Ménière disease (MD) is a complex disorder of unknown etiology characterized by the symptom triad of vertigo, sensorineural hearing loss, and tinnitus. Its reported incidence is 1–2 per 1,000 in Caucasians and 0.03–0.37 per 1,000 in Japanese. Doi et al. [Doi et al. (2005); ORL J Otorhinolaryngol Relat Spec 67:289–293] recently reported that two single nucleotide polymorphisms (SNPs) in KCNE1 and KCNE3 are associated with MD in Japanese subjects. Consistent with this possibility, these two genes encode potassium channels that are expressed in the stria vascularis and endolymphatic sac, respectively, and their role in ion transport suggests that they may be important in inner ear homeostasis. To establish whether a similar association exists in the Caucasian MD population, we sequenced the coding regions and exon–intron boundaries of both genes in 180 Caucasian persons with MD and 180 matched Caucasian controls. Neither of the two reported SNPs was significantly associated with MD when compared to the Caucasian controls (KCNE1, P = 0.55; KCNE3, P = 0.870). Comparison of allele frequencies between the Japanese MD population and our study population revealed no significant difference between groups (KCNE1, P = 0.90; KCNE3, P = 0.862), suggesting that the significant differences reported in the Japanese study arose from their control population. Six additional SNPs in both KCNE1 and KCNE3 were genotyped and none was associated with MD. Population stratification within our MD and Caucasian control population was excluded. Our data show that SNPs in KCNE1 and KCNE3 are not associated with MD in Caucasians. © 2009 Wiley‐Liss, Inc.
Loss of N‐acetylglucosamine‐1‐phosphotransferase gamma subunit due to intronic mutation in GNPTG causes mucolipidosis type III gamma: Implications for molecular and cellular diagnostics
Authors: Pohl Sandra , Encarnacão Marisa , Castrichini Monica , Müller‐Loennies Sven , Muschol Nicole , Braulke Thomas
Published: December 2009

Mucolipidosis type III gamma (MLIII, pseudo‐Hurler polydystrophy) is a rare autosomal recessive disorder where the activity of the multimeric GlcNAc‐1–phosphotransferase is reduced and formation of the mannose 6‐phosphate (M6P) recognition marker on lysosomal enzymes is impaired. In this disease, the targeting of lysosomal enzymes is affected resulting in their hypersecretion, and an intracellular deficiency of multiple hydrolases. We report the biochemical and molecular diagnosis of MLIII in three siblings, aged 17, 15, and 14 years, who presented with joint pain and progressive joint stiffness. In addition to missorting of newly synthesized lysosomal protease cathepsin D, there were low levels of M6P‐containing proteins in cell extracts and media of cultured fibroblasts of the Patients. Direct sequencing identified a novel homozygous mutation in intron 7, IVS7‐10G>A, of the GNPTG gene, which encodes the γ‐subunit of the GlcNAc‐1–phosphotransferase. This mutation created a cryptic 3′‐splice site resulting in a frameshift and premature translational termination (p.V176GfsX18). The GNPTG mRNA levels were markedly reduced in Patients' fibroblasts indicating that the intronic mutation mediates mRNA decay, which was confirmed by absence of the γ‐subunit protein. These data contribute to an efficient diagnostic strategy to identify Patients with MLIII gamma and characterize their biochemical defect in fibroblasts. © 2009 Wiley‐Liss, Inc.
Various types of LRP5 mutations in four patients with osteoporosis‐pseudoglioma syndrome: Identification of a 7.2‐kb microdeletion using oligonucleotide tiling microarray
Authors: Narumi Satoshi , Numakura Chikahiko , Shiihara Takashi , Seiwa Chizuru , Nozaki Yasuyuki , Yamagata Takanori , Momoi Mariko Y. , Watanabe Yoriko , Yoshino Makoto , Matsuishi Toyojiro , Nishi Eriko , Kawame Hiroshi , Akahane Tsutomu , Nishimura Gen , Emi Mitsuru , Hasegawa Tomonobu
Published: December 2009

Osteoporosis‐pseudoglioma syndrome (OPS; OMIM 259770) is an autosomal‐recessive genetic disorder characterized by severe osteoporosis and visual disturbance from childhood. Biallelic mutations in the low‐density lipoprotein receptor‐related protein 5 gene (LRP5) have been frequently detected, while a subset of patients had only one or no detectable mutation. We report on the clinical and molecular findings of four unrelated Japanese patients with the syndrome. The four patients had typical skeletal and ocular phenotypes of OPS, namely severe juvenile osteoporosis and early‐onset visual disturbance, with or without mental retardation. We undertook standard PCR‐based sequencing for LRP5 and found four missense mutations (p.L145F, p.T244M, p.P382L, and p.T552M), one nonsense mutation (p.R1534X), and one splice site mutation (c.1584+1G>A) among four OPS patients. Although three patients had two heterozygous mutations, one had only one heterozygous splice site mutation. In this patient, RT‐PCR from lymphocytic RNA demonstrated splice error resulting in 63‐bp insertion between exons 7 and 8. Furthermore, the patient was found to have only mutated RT‐PCR fragment, implying that a seemingly normal allele did not express LRP5 mRNA. We then conducted custom‐ designed oligonucleotide tiling microarray analyses targeted to a 600‐kb genome region harboring LRP5 and discovered a 7.2‐kb microdeletion encompassing exons 22 and 23 of LRP5. We found various types of LRP5 mutations, including an exon‐level deletion that is undetectable by standard PCR‐based mutation screening. Oligonucleotide tiling microarray seems to be a powerful tool in identifying cryptic structural mutations. © 2009 Wiley‐Liss, Inc.
A novel UBE3A truncating mutation in large Tunisian Angelman syndrome pedigree
Authors: Abaied L. , Trabelsi M. , Chaabouni M. , Kharrat M. , Kraoua L. , M'rad R. , Tebib N. , Maazoul F. , Chaabouni H.
Published: December 2009

We identified in a large Tunisian pedigree a novel UBE3A frameshift mutation in exon 16 coding region, and we expect that the resulting UBE3A truncated protein in our patients is non‐functional since the mutation implies the catalytic region of the enzyme. The family includes 14 affected patients born from four sisters. This mutation was found in all surviving affected individuals and their mothers pointing out the importance of genetic counseling possibility in Angelman syndrome (AS). All patients had severe mental retardation with epilepsy and microcephaly. Minor clinical expression variation was observed among the investigated patients. The severity of clinical expression is related to the detected molecular variation: deletion of 15 bp and insertion of 7 bp. These results are concordant with the gene expression observed in previously reported individuals with AS and truncated UBE3A protein. © 2009 Wiley‐Liss, Inc.
Brief communication: Patterns of linkage disequilibrium and haplotype diversity at Xq13 in six Native American populations
Authors: Wang Sijia , Bedoya Gabriel , Labuda Damian , Ruiz‐Linares Andres
Published: December 2009

Comparative studies of linkage disequilibrium (LD) can provide insights into human demographic history. Here, we characterize LD in six Native American populations using seven microsatellite markers in Xq13, a region of the genome extensively studied in populations around the world. Native Americans show relatively low diversity and high LD, in agreement with recent genome‐wide survey and a scenario of sequential founder effects accompanying human population dispersal around the globe. LD in Native Americans is similar to that observed in some recently described small population isolates and higher than in large European isolates (e.g., Finns), which have been extensively analyzed in medical genetics studies. Haplotype analyses are consistent with a colonization of the New World by a differentiated East Asian population, followed by extensive genetic drift in the Americas. Am J Phys Anthropol, 2010. © 2009 Wiley‐Liss, Inc.
Prehistorical East–West admixture of maternal lineages in a 2,500‐year‐old population in Xinjiang
Authors: Zhang Fan , Xu Zhi , Tan Jingze , Sun Yuefeng , Xu Bosong , Li Shilin , Zhao Xin , Zhou Hui , Gong Guoqiang , Zhang Jun , Jin Li
Published: December 2009

As an area of contact between Asia and Europe, Central Asia witnessed a scenario of complex cultural developments, extensive migratory movements, and biological admixture between West and East Eurasians. However, the detanglement of this complexity of diversity requires an understanding of prehistoric contacts of the people from the West and the East on the Eurasia continent. We demonstrated the presence of genetic admixture of West and East in a population of 35 inhabitants excavated in Gavaerk in southern Xinjiang and dated 2,800–2,100 years before present by analyzing their mitochondrial DNA variations. This result indicates that the initial contact of the East and the West Eurasians occurred further east than Central Asia as early as 2,500 years ago. Am J Phys Anthropol, 2010. © 2009 Wiley‐Liss, Inc.
Brief communication: Captive gorillas are right‐handed for bimanual feeding
Authors: Meguerditchian Adrien , Calcutt Sarah E. , Lonsdorf Elizabeth V. , Ross Stephen R. , Hopkins William D.
Published: December 2009

Predominance of right‐handedness has historically been considered as a hallmark of human evolution. Whether nonhuman primates exhibit population‐level manual bias remains a controversial topic. Here, we investigated the hypothesis that bimanual coordinated activities may be a key‐behavior in our ancestors for the emergence and evolution of human population‐level right‐handedness. To this end, we collected data on hand preferences in 35 captive gorillas (Gorilla gorilla) during simple unimanual reaching and for bimanual coordinated feeding. Unimanual reaching consisted of grasping food on the ground, while bimanual feeding consisted of using one hand for holding a food and processing the food item by the opposite hand. No population‐level manual bias was found for unimanual actions but, in contrast, gorillas exhibited a significant population‐level right‐handedness for the bimanual actions. Moreover, the degree of right‐handedness for bimanual feeding exceeds any other known reports of hand use in primates, suggesting that lateralization for bimanual feeding is robust in captive gorillas. The collective evidence is discussed in the context of potential continuity of handedness between human and nonhuman primates. Am J Phys Anthropol 2010. © 2009 Wiley‐Liss, Inc.
Dopamine‐dependent motor learning: Insight into levodopa's long‐duration response
Authors: Beeler Jeff A. , Cao Zhen Fang Huang , Kheirbek Mazen A. , Ding Yunmin , Koranda Jessica , Murakami Mari , Kang Un Jung , Zhuang Xiaoxi
Published: December 2009

Objective

Dopamine (DA) is critical for motor performance, motor learning, and corticostriatal plasticity. The relationship between motor performance and learning, and the role of DA in the mediation of them, however, remain unclear.

Methods

To examine this question, we took advantage of PITx3‐deficient mice (aphakia mice), in which DA in the dorsal striatum is reduced by 90%. PITx3‐deficient mice do not display obvious motor deficits in their home cage, but are impaired in motor tasks that require new motor skills. We used the accelerating rotarod as a motor learning task.

Results

We show that the deficiency in motor skill learning in PITx3(−/−) is dramatic and can be rescued with levodopa treatment. In addition, cessation of levodopa treatment after acquisition of the motor skill does not result in an immediate drop in performance. Instead, there is a gradual decline of performance that lasts for a few days, which is not related to levodopa pharmacokinetics. We show that this gradual decline is dependent on the retesting experience.

Interpretation

This observation resembles the long‐duration response to levodopa therapy in its slow buildup of improvement after the initiation of therapy and gradual degradation. We hypothesize that motor learning may play a significant, underappreciated role in the symptomatology of Parkinson disease as well as in the therapeutic effects of levodopa. We suggest that the important, yet enigmatic long‐duration response to chronic levodopa treatment is a manifestation of rescued motor learning. ANN NEUROL 2010;67:639–647
Effect of apolipoprotein E on biomarkers of amyloid load and neuronal pathology in Alzheimer disease
Authors: Vemuri Prashanthi , Wiste Heather J. , Weigand Stephen D. , Knopman David S. , Shaw Leslie M. , Trojanowski John Q. , Aisen Paul S. , Weiner Michael , Petersen Ronald C. , Jack Clifford R. ,   Alzheimer's Disease Neuroimaging Initiative
Published: December 2009

Objective

To study the effect of apolipoprotein E ϵ4 status on biomarkers of neurodegeneration (atrophy on magnetic resonance imaging [MRI]), neuronal injury (cerebrospinal fluid [CSF] t‐tau), and brain Aβ amyloid load (CSF Aβ1–42) in cognitively normal subjects (CN), amnestic subjects with mild cognitive impairment (aMCI), and patients with Alzheimer disease (AD).

Methods

We included all 399 subjects (109 CN, 192 aMCI, 98 AD) from the Alzheimer's Disease Neuroimaging Initiative study with baseline CSF and MRI scans. Structural Abnormality Index (STAND) scores, which reflect the degree of AD‐like anatomic features on MRI, were computed for each subject.

Results

A clear ϵ4 allele dose effect was seen on CSF Aβ1–42 levels within each clinical group. In addition, the proportion of the variability in Aβ1–42 levels explained by APOE ϵ4 dose was significantly greater than the proportion of the variability explained by clinical diagnosis. On the other hand, the proportion of the variability in CSF t‐tau and MRI atrophy explained by clinical diagnosis was greater than the proportion of the variability explained by APOE ϵ4 dose; however, this effect was only significant for STAND scores.

Interpretation

Low CSF Aβ1–42 (surrogate for Aβ amyloid load) is more closely linked to the presence of APOE ϵ4 than to clinical status. In contrast, MRI atrophy (surrogate for neurodegeneration) is closely linked with cognitive impairment, whereas its association with APOE ϵ4 is weaker. The data in this paper support a model of AD in which CSF Aβ1–42 is the earliest of the 3 biomarkers examined to become abnormal in both APOE carriers and noncarriers. ANN NEUROL 2010;67:308–316
Covalent functionalization of multiwalled carbon nanotubes with polybutadiene
Authors: Chen Hongbiao , Xiong Hua , Gao Yong , Li Huaming
Published: December 2009

Covalent functionalization of multiwalled carbon nanotubes (MWNTs) with polybutadiene was accomplished by coupling of isocyanate‐decorated MWNTs with hydroxyl‐terminated polybutadiene (HTPB) in dry toluene. The MWNT precursor, isocyanate‐functionalized MWNTs, was prepared by directly reacting commercial hydroxyl functionalized MWNTs with excess toluene 2,4‐diisocyanate (TDI). HTPBs with different molecular weights (Mn = 1900, 2600, and 3600 g/mol) were subjected to this coupling reaction, resulting in the formation of polymer functionalized MWNTs. FTIR spectroscopy was utilized to follow the introduction and consumption of isocyanate groups on the MWNTs. Thermogravimetric analysis (TGA) indicated that HTPB was successfully grafted onto MWNT surface, with the final products having a polymer weight percentage of around 30 wt %. Transmission electron microscopy (TEM) was utilized to image the polymer functionalized MWNTs, showing relatively uniform polymer coatings presented on the surface of MWNTs. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2010