bluuebunny/crossref_metadata_2025 huggingface dataset:
On exponential observability estimates for the heat semigroup with explicit rates
Authors: Miller Luc
Published: December 2009

This note concerns the final time observability inequality from an interior region for the heat semigroup, which is equivalent to the null-controllability of the heat equation by a square integrable source supported in this region. It focuses on exponential estimates in short times of the observability cost, also known as the control cost and the minimum energy function. It proves that this final time observability inequality implies four variants with roughly the same exponential rate everywhere (an integrated inequality with singular weights, an integrated inequality in infinite times, a sharper inequality and a Sobolev inequality) and some control cost estimates with explicit exponential rates concerning null-controllability, null-reachability and approximate controllability. A conjecture and open problems about the optimal rate are stated. This note also contains a brief review of recent or to be published papers related to exponential observability estimates: boundary observability, Schrödinger group, anomalous diffusion, thermoelastic plates, plates with square root damping and other elastic systems with structural damping.
Canonical surfaces in $\mathbb P^4$ with $p_g=p_a=5$ and $K^2=11$
Authors: Böhning Christian
Published: December 2009

In [Böh] a structure theorem for Gorenstein algebras in codimension 2 was obtained. In the first part of this article we give a geometric application and prove a structure theorem for good birational canonical projections of regular surfaces of general type with

p_g=5

to

\mathbb{P}^4

(Theorem 1.6). In the second part we show how this can be used to analyze the moduli space of canonical surfaces with

q=0

,

p_g=5

and

K^2=11

(Theorem 2.4).
Uniform convergence of the Lie–Dyson expansion with respect to the Planck constant
Authors: Bambusi Dario , Degli Espositi Mirko , Graffi Sandro
Published: December 2009

We prove that the Lie–Dyson expansion for the Heisenberg observables has a nonzero convergence radius in the variable

\epsilon t

which does not depend on the Planck constant

\hbar

. Here the quantum evolution

U_{\hbar,\epsilon}(t)

is generated by the Schrödinger operator defined by the maximal action in

L^2(\mathbb R^n)

of

-\hbar^2\Delta+\mathcal Q+\epsilon V

;

\mathcal Q

is a positive definite quadratic form on

\mathbb R^n

; the observables and

V

belong to a suitable class of pseudodifferential operators with analytic symbols. It is furthermore proved that, up to an error of order

\epsilon

, the time required for an exchange of energy between the unperturbed oscillator modes is exponentially long time independently of

\hbar

.
On the maximal order of a torsion point on a curve in $\mathbb G^n_m$
Authors: Corvaja Pietro , Zannier Umberto
Published: December 2009

Let

\mathcal C

be an irreducible algebraic curve in

\mathbb G_{\mathrm{m}}^2

; we are concerned with the maximal order

m=m(\mathcal C)

of a torsion point on

\mathcal C

. We suppose that

\mathcal C

is defined over a number field

k

, that it is not a translate of an algebraic subgroup by a torsion point, and we denote by

d

its degree and by

g

its genus. It is known that

m\ll_{k,\epsilon} d^{2+\epsilon}

for any

\epsilon >0

, which, as shown below, is nearly best-possible if only the degree is taken into account. Here, by means of a new method, we prove an upper bound (actually for curves in

\mathbb G_{\mathrm{m}}^n

) which implies in particular

m\ll_{k,\epsilon} \left(d \sqrt {d+g}\right)^{1+\epsilon}

. This gives back the above result and for small

g

it improves on it. The appearance of the genus seems to be a new feature in this kind of problems.
On a theorem of Schmid
Authors: Esposito Francesco , Maffei Andrea
Published: December 2009

We establish for which parabolic subgroups

P

of a simply connected and semisimple algebraic group

G

with unipotent radical

U

and Levi factor

H

the two rings

\mathbb k[G/H]^{U}

and

\mathbb k[U^-]

are isomorphic as

H

algebras. We show the relation of this problem with a Theorem of Schmid and we compare the multiplications in the rings

\mathbb k[U^-]

and

\mathbb k[G/H]

.
Hardy–Sobolev inequalities and hyperbolic symmetry
Authors: Castorina Daniele , Fabbri Isabella , Mancini Giovanni , Sandeep Kunnath
Published: December 2009

We discuss uniqueness and nondegeneracy of extremals for some wheighted Sobolev inequalities and give some applications to Grushin and scalar curvature type equations. The main theme is hyperbolic symmetry.
On the martingale problem associated to the $2D$ and $3D$ stochastic Navier–Stokes equations
Authors: Da Prato Giuseppe , Debussche Arnaud
Published: December 2009

In this paper we consider a Markov semigroup

(P_t)_{t\ge 0}

associated to

2D

and

3D

Navier–Stokes equations. In the two-dimensional case

P_t

is unique, whereas in the three-dimensional case (where uniqueness is not known) it is constructed as in [4] and [7].

For

d=2

, we explicit a core, identify the abstract generator of

(P_t)_{t\ge 0}

with the differential Kolmogorov operator

L

on this core and prove existence and uniqueness for the corresponding martingale problem. In dimension

3

, we are not able to prove a similar result and we explain the difficulties encountered. Nonetheless, we explicit a core for the generator of the transformed semigroup

(S_t)_{t\ge 0},

obtained by adding a suitable potential and then using the Feynman–Kac formula. Then we identify the abstract generator

(S_t)_{t\ge 0}

with a differential operator

N

on this core and prove uniqueness for the stopped martingale problem.
Systems of nonlinear Schrödinger equations. A survey
Authors: Ambrosetti Antonio
Published: December 2009

In this paper we survey some recent advances on various kind of systems of nonlinear Schrödinger equations. The arguments rely on critical point theory, the concentration compactness and perturbation methods.
Existence of hylomorphic solitary waves in Klein–Gordon and in Klein–Gordon–Maxwell equations
Authors: Benci Vieri , Fortunato Donato
Published: December 2009

This paper is devoted to the study of solitary waves whose existence is related to the ratio energy/charge. These solitary waves are called hylomorphic. This class includes the
Q
-balls, which are spherically symmetric solutions of the nonlinear Klein–Gordon equation (NKG), as well as solitary waves and vortices which occur, by the same mechanism, in the nonlinear Schrödinger equation and in gauge theories. It is proved an abstract theorem which allows to show the existence of hylomorphic solitary waves and vortices in the (NKG) and in the nonlinear Klein–Gordon–Maxwell equations (NKGM).
Explicit and Implicit Complementarity Problems in a Hilbert Space
Authors: Carbone Antonio , Zabrejko P. P.
Published: December 2009

We present some new results about solvability of implicit complementarity problems in a Hilbert space. We discuss two approaches. One of them is based on the usual change of variables and reduces the implicit complementarity problem to the explicit one. The second approach is based on the Skrypnik degree which, in the case of mappings in a Hilbert space, is essentially more general in comparison with the classical Leray-Schauder degree. In both cases, the solvability results are formulated in terms of auxiliary complementarity problems with parameter.
Expansions of Certain del bar Closed Forms via Fourier-Laplace Transform
Authors: Hatziafratis T.
Published: December 2009

We derive Laurent-type expansions of

\bar\partial

-closed

(0,n - 1)

-forms in certain domains in

\mathbb C^n

. These expansions involve the Bochner-Martinelli kernel and its derivatives and are based on the Fourier-Laplace transform.
Controllability Results for Evolution Inclusions with Non-Local Conditions
Authors: Benchohra M. , Gatsori E. P. , Górniewicz L. , Ntouyas S. K.
Published: December 2009

We prove controllability results for mild solutions defined on a compact real interval for first order differential evolution inclusions in Banach spaces with non-local conditions. By using suitable fixed point theorems we study the case when the multi-valued map has convex as well as non-convex values.
Delayed Loss of Stability in Systems with Degenerate Linear Parts
Authors: Rachinskii D. , Schneider K.
Published: December 2009

We study singularly perturbed scalar and planar differential equations with linear parts independent of time. The associated autonomous equations undergo a bifurcation of equilibria in the scalar case and the Hopf bifurcation in the case of planar systems at a bifurcation point where the zero equilibrium loses stability. We suggest natural sufficient conditions for the phenomenon of delayed loss of stability for the singularly perturbed equations and estimate the asymptotic delay. Bifurcation points, stability of the zero equilibrium, and the asymptotic delay are determined by superlinear terms in the expansions of the right-hand sides of the associated and singularly perturbed equations.
Michael Selection Problem in Hyperconvex Metric Spaces
Authors: Wu Xian
Published: December 2009

The Michael selection problem is researched in hyperconvex metric spaces. Our results show that the answer is "yes" for hyperconvex metric spaces and that the lower semicontinuity of the multi-valued mapping can be weakened. Moreover, as an application of our selection theorem, a fixed point theorem for locally-uniform weak lower semicontinuous multi-valued mappings is given.
Sequences of 0's and 1's. Classes of Concrete `big' Hahn Spaces
Authors: Boos Johann , Zeltser Maria
Published: December 2009

This paper continues the joint investigation by G. Bennett, J. Boos and T. Leiger [Studia Math. 149 (2002) 75–99] and J. Boos, T. Leiger and M. Zeltser [J. Math. Anal. Appl. 275 (2002) 883–899] of the extent to which sequence spaces are determined by the sequences of

0

's and

1

's that they contain. Bennett et al. proved that each subspace

E

of

\ell^\infty

containing the sequence

e = (1,1, \dots)

and the linear space

bs

of all sequences with bounded partial sums is a Hahn space, that is, an FK-space

F

contains

E

whenever it contains (the linear hull

\chi(E)

of) the sequences of

0

's and

1

's in

E

. In some sense these are ‘big’ subspaces of

\ell^\infty

. Theorem 2.6, one of the main results of this paper, tells us that this result remains true if we replace

bs

with suitably defined spaces

bs(N)

which are subspaces of

bs

when

N

is a finite partition of

\Bbb N

. As an application of the main result, two large families of closed subspaces

E

of

\ell^\infty

being Hahn spaces are presented: The bounded domain

E

of a weighted mean method (with positive weights) is a Hahn space if and only if the diagonal of the matrix defining the method is a null sequence; a similar result applies to the bounded domains of regular Nörlund methods. Since an FK-space

E

is a Hahn space if and only if

\chi(E)

is a dense barrelled subspace of

E

, by these results, a large class of concrete closed subspaces

E

of

\ell^\infty

such that

\chi(E)

is a dense barrelled subspace can be identified by really simple conditions. A further application gives a negative answer to Problem 7.1 in the paper mentioned above.
The Dirichlet Energy Integral on Intervals in Variable Exponent Sobolev Spaces
Authors: Harjulehto Petteri , Hästö Peter , Koskenoja Mika
Published: December 2009

We consider Dirichlet energy integral minimizers in variable exponent Sobolev spaces defined on intervals of the real line. We illustrate by examples that the minimizing question is interesting even in this case that is trivial in the classical fixed exponent space. We give an explicit formula for the minimizer, and some simple conditions for when it is convex, concave or Lipschitz continuous. The most surprising conclusion is that there does not exist a minimizer even for every smooth exponent.
Strict Equilibria of Multi-Valued Maps and Common Fixed Points
Authors: Gabor G.
Published: December 2009

We deal with strict equilibria of continuous multi-valued maps. This allows us to study the invariance problem for differential inclusions in non-invariant closed subsets of Euclidean spaces. We also give a new method in studying common fixed points of families of maps.
Explicit Upper Bound for Entropy Numbers
Authors: Hencl Stanislav
Published: December 2009

We give an explicit upper bound for the entropy numbers of the embedding

I\colon W^{r,p}(Q^l)\to C(\overline{Q^l})

where

Q^l=(-l,l)^m\subset \mathbb{R}^n

,

r\in\mathbb{N}

,

p\in(1,\infty)

and

r p>m

.
Tensor Algebras and Displacement Structure. III: Asymptotic Properties
Authors: Barakat Moe , Constantinescu Tiberiu
Published: December 2009

We continue to investigate some classes of Szegö type polynomials in several variables. We focus on asymptotic properties of these polynomials and we extend several classical results of G. Szegö to this setting.
Another Version of Maher's Inequality
Authors: Mecheri Salah
Published: December 2009

Let

H

be a separable infinite dimensional complex Hilbert space, and let

L(H)

denote the algebra of bounded linear operators on

H

into itself. Let

A=(A_{1},A_{2}...,A_{n})

,

B =(B_{1},B_{2}...,B_{n})

be n-tuples of operators in

L(H)

. We define the elementary operator

\Delta _{A,B}: L(H) \mapsto L(H)

by

\Delta _{A,B}(X)=\sum_{i=1}^{n}A_{i}XB_{i}-X.

In this paper we minimize the map

F_{p}(X)= \left\| T -\Delta _{A,B}(X) \right\| _{p}^{p}

, where

T\in \ker\Delta _{A,B}\cap C_{p}

, and we classify its critical points.
Hyperbolic Functional Differential Systems with Unbounded Delay
Authors: Koziel Slawomir
Published: December 2009

The phase space for quasilinear systems with unbounded delay is constructed. Caratheodory solutions to initial and mixed problems are investigated. Theorems on the local existence and continuous dependence upon initial or initial boundary functions are given. The fixed-point method and integral inequalities are used.
Uniform Convergence in Topological Groups
Authors: Aizpuru Antonio , Gutiérrez Dávila Antonio
Published: December 2009

We improve the Basic Matrix Theorem of Antosik-Swartz in the framework of topological groups. We also obtain an equivalent form of this generalization, which improves the Uniform Convergence Principle of Qu Wenbo and Wu Junde in Proc. Amer. Math. Soc. 130 (2002) 3283–3285.
Delta Waves for a Strongly Singular Initial-Boundary Hyperbolic Problem with Integral Boundary Condition
Authors: Kmit Irina
Published: December 2009

We investigate the existence and the singular structure of delta wave solutions to a semilinear hyperbolic equation with strongly singular initial and boundary conditions. The boundary conditions are given in nonlocal form with a linear integral operator involved. We construct a delta wave solution as a distributional limit of solutions to the regularized system. This determines the macroscopic behavior of the corresponding generalized solution in the Colombeau algebra G of generalized functions. We represent our delta wave as a sum of a purely singular part satisfying a linear system and a regular part satisfying a nonlinear system.
On the Unique Solvability of a Volevic System of Linear Equations with General Singularity
Authors: Lope Jose Ernie C. , Escaner IV José Maria L. , Arceo Carlene P.
Published: December 2009

We consider a Volevic system of linear partial differential equations with general singularity, for which we establish existence and uniqueness theorems that are analogues of the Cauchy–Kowalevsky and Holmgren Theorems. Our results are generalizations of those of J. Elschner [Beiträge Anal. 12 (1978) 185–198], J. E. C. Lope [J. Math. Sci. Univ. Tokyo 6 (1999) 527–538] and H. Tahara [J. Math. Soc. Japan 34 (1982) 279–288], which are in turn generalizations of the results of M. S. Baouendi and C. Goulaouic [Comm. Pure Appl. Math. 26 (1973) 455–475].
Global Regularity in Fractional Order Sobolev Spaces for the p-Laplace Equation on Polyhedral Domains
Authors: Ebmeyer Carsten , Liu Wenbin , Steinhauer Mark
Published: December 2009

The

p

-Laplace equation is considered for

p > 2

on a

n

-dimensional convex polyhedral domain under a Dirichlet boundary value condition. Global regularity of weak solutions in weighted Sobolev spaces and in fractional order Nikolskij and Sobolev spaces are proven.
Hardy-Littlewood Inequalities and Q_p-Spaces
Authors: Ren Guangbin , Kähler Uwe
Published: December 2009

We establish Hardy-Littlewood inequalities for monogenic and harmonic functions and consider their applications to the definition of Qp-spaces in Clifford analysis.
Approximative compactness and full rotundity in Musielak–Orlicz spaces and Lorentz–Orlicz spaces
Authors: Hudzik Henryk , Kowalewski Wojciech , Lewicki Grzegorz
Published: December 2009

We prove that approximative compactness of a Banach space

X

is equivalent to the conjunction of reflexivity and the Kadec–Klee property of

X

. This means that approximative compactness coincides with the drop property defined by Rolewicz in
Studia Math.
85 (1987), 25–35. Using this general result we find criteria for approximative compactness in the class of Musielak–Orlicz function and sequence spaces for both (the Luxemburg norm and the Amemiya norm) as well as critria for this property in the class of Lorentz–Orlicz spaces. Criteria for full rotundity of Musielak–Orlicz spaces are also presented in the case of the Luxemburg norm. An example of a reflexive strictly convex Köthe function space which is not approximatively compact and some remark concerning the compact faces property for Musielak–Orlicz spaces are given.
Fewer Convergence Conditions for the Halley Method
Authors: Ezquerro José Antonio , Hernández M.A.
Published: December 2009

We present a new semilocal convergence result of Newton-Kantorovich type for Halley's method, where fewer convergence conditions are required than all the existing ones until now.
Regularization of Hyperfunctions
Authors: Estrada Ricardo
Published: December 2009

We show that there are no continuous regularization procedures for the extension of hyperfunctions. We also show that there is a continuous projection operator from the space of hyperfunctions with support in a given compact set onto the subspace of hyperfunctions with support on a given \textsl{closed} subset if and only if the subset is a countable intersection of sets that are closed and open.
Composition Operators between $H^\infty$ and $\alpha$-Bloch Spaces on the Polydisc
Authors: Stevic Stevo
Published: December 2009

Let

U^n

be the unit polydisc of

{\mathbb C}^n

and

\varphi(z)=(\varphi_1(z),\ldots,\varphi_n(z))

a holomorphic self-map of

U^n.

Let

H(U^n)

denote the space of all holomorphic functions on

U^n,

H^\infty(U^n)

the space of all bounded holomorphic functions on

U^n,

and

{\cal B}^a(U^n),

a>0,

the

a

-Bloch space, i.e.,

{\cal B}^a(U^n)=\bigg\{ f\in H(U^n)\, |\, \|f\|_{{\cal B}^a}=|f(0)|+\sup\limits_{z\in U^n}\sum\limits^n_{k=1} \left|\frac{\partial f} {\partial z_k}(z)\right|\left(1- |z_k|^2\right)^a<+\infty\bigg\}.

We give a necessary and sufficient condition for the composition operator

C_{\\varphi}

induced by

\varphi

to be bounded and compact between

H^\infty(U^n)

and

a

-Bloch space

{\cal B}^a(U^n),

when

a\geq 1.
Elaboration of Some Results of Srivastava and Choi
Authors: Hailong Li , Toda Masayuki
Published: December 2009

In this paper we shall utilize some recent results of S. Kanemitsu, H. Kumagai, H. M. Srivastava and M. Yoshimoto in
Appl. Math. Comput.
154 (2004) on an asymptotic as well as an integral formula for the partial sum of the Hurwitz zeta-function, to elaborate on some results of Srivastava and Choi in
Series Associated with the Zeta and Related Functions
(Kluwer 2001), and in some cases to give improved generalizations thereof. More specifically, we shall give an asymptotic expansion of the sum of the values derivative of the digamma function. We shall also re-establish Bendersky–Adamchik's result and Elizalde's result.
The Hilbert Problem for Generalized Q-Holomorphic Functions
Authors: Hizliyel Sezayi
Published: December 2009

In this work, we extended classical Hilbert boundary value problem to generalized

Q

-holomorphic functions by replacing the condition that the solution vanishes at infinity by that the solution has a finite order of growth at infinity.
Logarithmic Interpolation Spaces between Quasi-Banach Spaces
Authors: Cobos Fernando , Fernández-Cabrera Luz M. , Manzano Antonio , Martínez Antón
Published: December 2009

Let

A_0

and

A_1

be quasi-Banach spaces with

A_0 \hookrightarrow A_1

. By means of a direct approach, we show that the interpolation spaces on

(A_0,A_1)

generated by the function parameter

t^\theta ( 1 + |\log t|)^{-b}

can be expressed in terms of classical real interpolation spaces. Applications are given to Zygmund spaces

L_p (\log L)_b (\Omega)

, Lorentz-Zygmund function spaces and operator spaces defined by using approximation numbers.
Extreme Points and Strong U-Points in Musielak–Orlicz Sequence Spaces Equipped with the Orlicz Norm
Authors: Cui Yunan , Hudzik Henryk , Wisla M. , Zou Mingxia
Published: December 2009

We give some criteria for extreme points and strong U-points in Musielak–Orlicz sequence spaces equipped with the Orlicz norm. It follows from these results that the notion of the strong U-point is essentially stronger than the notion of the extreme point in these spaces.
Uniqueness in Determining Polygonal Periodic Structures
Authors: Elschner Johannes , Yamamoto Masahiro
Published: December 2009

We consider the inverse problem of recovering a two-dimensional perfectly reflecting diffraction grating from scattered waves measured above the structure. We establish the uniqueness within the class of general polygonal grating profiles by a minimal number of incoming plane waves, without excluding Rayleigh frequencies and further geometric constraints on the profile. This extends and improves the uniqueness results of Elschner, Schmidt and Yamamoto [Inverse Problems 19 (2003), 779–787].
Bilinear Estimates Associated to the Schrödinger Equation with a Nonelliptic Principal Part
Authors: Onodera Eiji
Published: December 2009

We discuss bilinear estimates of tempered distributions in the Fourier restriction spaces for the two-dimensional Schödinger equation whose principal part is the d'Alembertian. We prove that the bilinear estimates hold if and only if the tempered distributions are functions.
Remarks on Generalized Contractions
Authors: Göhde Dietrich
Published: December 2009

The main result concerns an extension of Schauder's fixed point theorem to not necessarily continuous maps

T

which satisfy

\|Tx-Ty\| \le a \|x-y\|+b \max \{\|Tx-x\|, \|Ty-y\| \} \quad \text{with } a \ge 0, \; b \in (0,1)\,.
Attractor Bifurcation of Three-Dimensional Double-Diffusive Convection
Authors: Hsia Chun-Hsiung , Ma Tian , Wang Shouhong
Published: December 2009

In this article, we present a bifurcation analysis on the double-diffusive convection. Two pattern selections, rectangles and squares, are investigated. It is proved that there are two different types of attractor bifurcations depending on the thermal and salinity Rayleigh numbers for each pattern. The analysis is based on a newly developed attractor bifurcation theory, together with eigen-analysis and the center manifold reductions.
On Bernstein–Schnabl Operators on the Unit Interval
Authors: Altomare Francesco , Leonessa Vita , Rasa Ioan
Published: December 2009

In this paper we study the Bernstein-Schnabl operators associated with a continuous selection of Borel measures on the unit interval. We investigate their approximation properties by presenting several estimates of the rate of convergence in terms of suitable moduli of smoothness. We also study some shape preserving properties as well as the preservation of the convexity. Moreover we show that their iterates converge to a Markov semigroup whose generator is a degenerate second order elliptic differential operator on the unit interval. Qualitative properties of this semigroup are also investigated together with its asymptotic behaviour.
Resultants of Chebyshev Polynomials
Authors: Gishe Jemal , Ismail Mourad E. H.
Published: December 2009

Recently, K. Dillcher and K. B. Stolarsky [
Trans. Amer. Math. Soc.
357 (2004), 965–981] used algebraic methods to evaluate the resultant of two linear combinations of Chebyshev polynomials of the second kind. In this paper we give an alternative method of computing the same resultant and resultants of more general combinations of Chebyshev polynomials of the second kind. We also consider resultants of linear combinations of Chebyshev polynomials of the first kind.
Growth Estimates for the Gradient of an $H$-Surface Near Singular Points of the Boundary Configuration
Authors: Müller Frank
Published: December 2009

We provide estimates for the gradient growth of surfaces with prescribed mean curvature in

\mathbb{R}^3

near boundary points, which are mapped onto singular points of the boundary configuration. For corners of a Jordan arc, such estimates were provided by G. Dziuk [Analysis 1 (1981), 63–81]. We consider meeting points of a Jordan arc and a support manifold, as appearing in a partially free boundary problem (see G. Dziuk [Manuscr. Math. 35 (1981), 105–123] for the minimal surface case), and edge-type singularities of a support manifold. In subsequent papers, these results shall be used to derive asymptotic expansions of surfaces with prescribed mean curvature near such singular points.
Source Representation Strategy for Optimal Boundary Control Problems with State Constraints
Authors: Tröltzsch Fredi , Yousept I.
Published: December 2009

A state-constrained optimal boundary control problem governed by a linear elliptic equation is considered. In order to obtain the optimality conditions for the solutions to the model problem, a Slater assumption has to be made that restricts the theory to the two-dimensional case. This difficulty is overcome by a source representation of the control and combined with a Lavrentiev type regularization. Optimality conditions for the regularized problem are derived, where the corresponding Lagrange multipliers have

L^2

-regularity. By the spectral theorem for compact and normal operators, the convergence result of Tröltzsch and Yousept in [
Comput. Optim. Appl.
42 (2009), 43–66] is extended to a higher dimensional case. Moreover, the convergence for vanishing regularization parameter of the adjoint state associated with the regularized problem is shown. Finally, the uniform boundedness of the regularized Lagrange multipliers in

L^1(\Omega)

is verified by a maximum principle argument.
Eigenvalue Distribution of Semi-Elliptic Operators in Anisotropic Sobolev Spaces
Authors: Tamási Erika
Published: December 2009

We study the spectral properties of the compact non-negative self-adjoint operator

T=A^{-1}\circ \mathrm{tr}^\Gamma

acting in the anisotropic Sobolev space

H^{s,a}_2(\mathbb R^n)

and give two-sided estimates for the asymptotic behaviour of its eigenvalues

\lambda_k(T)

, where

A

is a semi-elliptic differential operator of type

Au(x)=(-1)^{s_1}\frac{\partial^{2s_1}u(x)}{\partial x_1^{2s_1}} + \cdots + (-1)^{s_n}\frac{\partial^{2s_n}u(x)}{\partial x_n^{2s_n}} + u(x),

and

\mathrm{tr}^{\Gamma}

a special trace operator on an anisotropic

d

-set

\Gamma

.
On a Class of Measures of Noncompactness in Banach Algebras and Their Application to Nonlinear Integral Equations
Authors: Banaś Józef , Olszowy Leszek
Published: December 2009

We introduce a class of measures of noncompactness in Banach algebras satisfying certain condition and we prove a ﬁxed point theorem for the product of two operators being contractions with respect to such measures of noncompactess. We also indicate measures of noncompactness in some Banach function algebras which satisfy the mentioned condition. The obtained results are applied to prove a few theorems on the existence of solutions of nonlinear integral equations in Banach algebras. Some characterizations of solutions of considered integral equations are also derived.
Chemical Bonding Assembly of Multifunctional Oxide Nanocomposites
Authors: Evans Gary , Duong Giap V. , Ingleson Michael J. , Xu Zhongling , Jones James T. A. , Khimyak Yaroslav Z. , Claridge John B. , Rosseinsky Matthew J.
Published: December 2009

The synthesis, functionalization and assembly of metal oxide nanoparticles BaTiO3 and CoFe2O4 is presented. The ferroelectric (BaTiO3) and ferromagnetic (CoFe2O4) oxide nanoparticle surfaces are directly functionalized via the anchoring of phosphonic acid and aminosilane molecules that engender the nanoparticles with terminal carboxylic acid and amine functional groups, respectively. These promote the electrostatic self‐assembly of the particles in non‐polar solvents and permit the synthesis of more chemically robust assemblies linked by the covalent amide bond via the addition of the chemical coupling agent N‐N′‐dicyclohexylcarbodiimide. This functionalization and assembly procedure is applied to two systems: the first comprised of 50 nm BaTiO3 and 10 nm CoFe2O4 particles and the second of 200 nm BaTiO3 and 12.5 nm CoFe2O4 particles. The latter composites possess magnetoelectric properties when processed into dense ceramics and, as a direct result of the assembly performed in solution, have a high degree of homogeneity between the ferroelectric and ferromagnetic phases. The developed functionalization and assembly procedure is considered to be adaptable to the preparation of other hybrid oxide nanomaterials with different property combinations.
Modeling of extraction behavior of docosahexaenoic acid ethyl ester by utilizing slug flow prepared by microreactor
Authors: Kamio Eiji , Seike Yu , Yoshizawa Hidekazu , Ono Tsutomu
Published: December 2009

The liquid–liquid extraction dynamics of an ethyl ester of docosahexaenoic acid (DHA‐Et) with silver ion was investigated. The kinetic model was derived according to the following stepwise processes: Diffusion of DHA‐Et across the organic film, complex‐formation between DHA‐Et and silver ion at the interface, and diffusion of extracted complex across the aqueous film. The kinetic parameters for the complex‐formation reaction were determined from the investigation with the stirred transfer cell. With the proposed model and determined parameters, we predicted the uptakes of DHA‐Et for the extraction system utilizing a slug flow prepared by a microchip. The calculated uptakes showed good correlation to the experimental data. The theoretical investigation suggested that the fast equilibration realized for the slug flow extraction system was due to the large specific interfacial area of the slug caused by the presence of wall film and the thin liquid film caused by the internal circulation. © 2009 American Institute of Chemical Engineers AIChE J, 2010
Left ventricular noncompaction: A rare disorder in adults and its association with 1p36 chromosomal anomaly
Authors: Dod Harvinder S. , Bhardwaj Ravindra , Hummel Marybeth , Morise Anthony P. , Batish Satdev , Warden Bradford E. , Beto Robert J. , Jain Abnash C.
Published: December 2009

We report on a case of a 25‐year‐old male with 1p36 deletion syndrome, who was diagnosed with left ventricular noncompaction (LVNC). The association of this rare chromosomal abnormality with LVNC is reported in the pediatric literature, but it has not previously been specifically reported in adults. It is important to diagnose this unclassified cardiomyopathy in the adult population with this chromosomal abnormality for appropriate management and treatment as highlighted in our case. © 2009 Wiley‐Liss, Inc.
Systematized organoid epidermal nevus with eccrine differentiation, multiple facial and oral congenital scars, gingival synechiae, and blepharophimosis: A novel epidermal nevus syndrome
Authors: Castori Marco , Annessi Giorgio , Castiglia Daniele , Buffa Vitaliano , Paradisi Andrea , Cascone Piero , Zambruno Giovanna , Grammatico Paola , Paradisi Mauro
Published: December 2009

Epidermal nevus syndrome is a clinically variable and genetically heterogeneous group of mosaic conditions characterized by the concurrence of extensive epidermal nevus with additional cutaneous and extracutaneous manifestations. This term groups together well‐characterized clinical entities, as well as dozens of apparently unique associations, which need further delineation. We report on a 23‐year‐old woman presenting the previously undescribed combination of widespread eccrine proliferation, multiple facial and oral pox‐like lesions, gingival synechiae, blepharophimosis, body asymmetry, and mental retardation. The patient has a healthy monozygotic twin. The eccrine proliferation is intermingled with areas of unaffected skin with a linear/segmental distribution on the limbs. The clinical presentation of such a complex phenotype fits well with the genetic mosaicism theory. The histologic findings, consisting of proliferation of immature to well‐formed eccrine duct‐like structures located in the deep dermis and interspersed with an abundant fibrous stroma constituted of horizontally oriented collagen fibers, seem a possible hallmark of this condition. © 2009 Wiley‐Liss, Inc.
A de novo 8.8‐Mb deletion of 21q21.1–q21.3 in an autistic male with a complex rearrangement involving chromosomes 6, 10, and 21
Authors: Haldeman‐Englert Chad R. , Chapman Kimberly A. , Kruger Hillary , Geiger Elizabeth A. , McDonald‐McGinn Donna M. , Rappaport Eric , Zackai Elaine H. , Spinner Nancy B. , Shaikh Tamim H.
Published: December 2009

We report here on a normal‐appearing male with pervasive developmental disorder who was found to have a de novo, apparently balanced complex rearrangement involving chromosomes 6, 10, and 21: 46,XY,ins(21;10)(q11.2;p11.2p13)t(6;21)(p23;q11.2). Further analysis by high‐density oligonucleotide microarray was performed, showing an 8.8‐Mb heterozygous deletion at 21q21.1–q21.3. Interestingly, the deletion is distal to the translocation breakpoint on chromosome 21. The deletion involves 19 genes, including NCAM2 and GRIK1, both of which are associated with normal brain development and function, and have been considered as possible candidate genes in autism and other neurobehavioral disorders. This case underscores the utility of genomewide microarray analysis for the detection of copy number alterations in patients with apparently balanced complex rearrangements and abnormal phenotypes. © 2009 Wiley‐Liss, Inc.
Genetic counseling for schizophrenia: A review of referrals to a provincial medical genetics program from 1968 to 2007
Authors: Hunter M.J. , Hippman Catriona , Honer William G. , Austin Jehannine C.
Published: December 2009

Recent studies have shown that individuals with schizophrenia and their family members are interested in genetic counseling, but few have received this service. We conducted an exploratory, retrospective study to describe (a) the population of individuals who were referred to the BC provincial medical genetics program for genetic counseling for a primary indication of schizophrenia, and (b) trends in number of referrals between 1968 and 2007. Referrals for a primary indication of schizophrenia were identified through the provincial program database. Charts were reviewed and the following information was recorded: discipline of referring physician, demographics, psychiatric diagnosis, referred individual's and partner's (if applicable) family history, and any current pregnancy history. Data were characterized using descriptive statistics. Our results showed that between 1968 and 2007, 288 referrals were made for a primary indication of schizophrenia. Most referrals were made: (a) for individuals who had a first‐degree family member with schizophrenia, rather than for affected individuals, (b) for preconception counseling, and (c) by family physicians (69%), with only 2% by psychiatrists. In conclusion, for British Columbia, individuals affected with schizophrenia and their family members are rarely referred for psychiatric genetic counseling. There is a need to identify barriers to psychiatric genetic counseling and develop strategies to improve access. © 2009 Wiley‐Liss, Inc.
Magnetic resonance angiography in reversible cerebral vasoconstriction syndromes
Authors: Chen Shih‐Pin , Fuh Jong‐Ling , Wang Shuu‐Jiun , Chang Feng‐Chi , Lirng Jiing‐Feng , Fang Ying‐Chen , Shia Ben‐Chang , Wu Jaw‐Ching
Published: December 2009

Objective

To investigate the evolution and clinical significance of vasoconstriction on magnetic resonance angiography (MRA) in patients with reversible cerebral vasoconstriction syndromes (RCVS).

Methods

Patients with RCVS were recruited and followed up with MRA examinations until normalization of vasoconstriction or for 6 months. The vasoconstriction severity of the major cerebral arterial segments (M1, M2, A1, A2, P1, P2, and basilar artery) was scored on a 5‐point scale: 0 (0–<10%), 1 (10–<25%), 2 (25–<50%), 3 (50–<75%), and 4 (≥75%). Subjects with at least 1 segment with a vasoconstriction score ≥2 were eligible for the study. Initial mean scores of single or combined arterial segments were used to predict ischemic complications.

Results

Seventy‐seven patients with RCVS (8 men/69 women; average age 47.7 ± 11.6 years) finished the study with a total of 225 MRAs performed. The mean number of arterial segments involved was 5.3 ± 3.0 in the initial MRA. Vasoconstriction scores reached their maximum 16.3 ± 10.2 days after headache onset, close to the average timing of headache resolution (16.7 ± 8.6 days). Vasoconstriction evolved in a parallel trend among different arterial segments. Seven (9.1%) patients developed posterior reversible encephalopathy syndromes (PRES). Six (7.8%) patients had ischemic stroke. A logistic regression model demonstrated that the M1–P2 combined score was associated with highest risk of PRES (odds ratio [OR], 11.6, p = 0.005) and ischemic stroke (OR, 3.4; p = 0.026).

Interpretation

MRA evaluation in patients with RCVS is valid. Vasoconstriction was pervasive and outlasted headache resolution. Vasoconstrictions in M1 and P2 are important determinants for PRES and ischemic stroke. ANN NEUROL 2010;67:648–656
Factorial experimental design on synthesis of functional core/shell polymeric nanoparticles via differential microemulsion polymerization
Authors: Norakankorn Chaiwat , Pan Qinmin , Rempel Garry L. , Kiatkamjornwong Suda
Published: December 2009

Functionalized core/shell nanoparticles of the co‐polymer of methyl methacrylate (MMA) and glycidyl methacrylate (GMA) could be polymerized by differential microemulsion polymerization, using a small amount of surfactant (the weight ratio of sodium dodecyl sulfate (SDS)/monomer is 1 : 24). The core/shell nanoparticles have a high conversion, high molecular weight, and small particle size (25–30 nm). The statistical analysis indicated that SDS, water, and the interactionbetween SDS and water have a significant positive interaction between the MMA conversion to form the core nanoparticles. For the core‐shell polymer, [GMA], [GMA]*[SDS], and [GMA]* [water] have significant negative effects on conversion; whereas [SDS] and [water], [SDS]*[water] and [GMA]*[SDS]*[water] have positive effects on the conversion to form core/shell nanoparticles. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2010
Influence of carbon nanotubes with different functional groups on the morphology and properties of PPO/PA6 blends
Authors: Shen Yu , Guo Zhenghong , Cheng Jie , Fang Zhengping
Published: December 2009

Carbon nanotubes with different functional groups were prepared and then incorporated into the poly(2,6‐dimethyl‐1,4‐phenylene oxide)/polyamide 6 (PPO/PA6) blend via melt blending. The influence of different carbon nanotubes on the morphology and properties of the blend was studied. The results show that addition of pristine CNTs, CNTs‐OH, CNTs‐NH2 leads to the evolution of the phase structure of PPO/PA6 (mass ratio: 60/40) blend from sea‐island to cocontinuous, whereas incorporation of CNTs‐COOH does not change the blend morphology due to serious aggregation of the carbon nanotubes. Incorporating different CNTs into PPO/PA6 blend increases the tensile modulus and storage modulus of the blends, whereas decreases slightly the tensile strength. At the same time, the glass transition temperatures (Tg) of PA6 and PPO are enhanced. ΔTg, the gap between the Tg of PA6 and PPO, decreases with the addition of carbon nanotubes due to the stronger interaction of carbon nanotubes with PA6 than PPO. A similar tendency was found in the storage modulus (G′) and complex viscosity (η*) of the composites. The dispersion state of different carbon nanotubes and their interaction with polymer components are different, which causes the different confinement effect to the macromolecular chains. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2010
Application of thermosetting organic solvent free polymer gel electrolyte in quasi‐solid‐state dye‐sensitized solar cell
Authors: Lan Zhang , Wu Jihuai , Lin Jianming , Huang Miaoliang
Published: December 2009

A kind of thermosetting organic solvent free polymer gel electrolyte with oligomer ethylene glycol as liquid phase was prepared and applied in quasi‐solid‐state dye‐sensitized solar cell (QS‐DSSC). The viscosity and the ionic conductivity of the polymer gel electrolyte are sensitive to the changed temperature. The photovoltaic performance of QS‐DSSC is also improved with the increased temperature due to the increased ionic conductivity and diffusion coefficient of iodide in polymer gel electrolyte. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2010
Equilibrium swelling of polystyrene by alkanes and carboxylic acids: A simple quantitative correlation model
Authors: Bernardo Gabriel , Vesely Drahosh
Published: December 2009

In this study, we show that the equilibrium saturation swelling of polystyrene by linear alkanes and linear carboxylic acids, as reported earlier (Bernardo and Vesely, Eur Polym J 2007, 43, 4983, Bernardo and Vesely, J Appl Polym Sci 2008, 110, 2393) can be correlated quantitatively using a model where only the alkyl‐chain lengths and the saturated vapor pressures of the organic liquids are considered. According to this model, at very low vapor pressures, the number of polystyrene monomer units per solvent molecule is directly proportional to the alkyl chain length of the solvent molecule under consideration. At higher vapor pressures, the number of polystyrene monomer units per solvent molecule tends to become independent of its alkyl chain length. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2010
Gelenke im Massivbau
Authors: Marx Steffen , Schacht Gregor
Published: December 2009

Gelenkige Verbindungen im Massivbau wurden bereits vor 130 Jahren entwickelt und seitdem in vielen Bauwerken erfolgreich eingesetzt. 1880 verwendete Köpke erstmalig so genannte Wälzgelenke beim Bau einer Naturstein‐Gewölbebrücke. Weitere Entwicklungen folgten zu Beginn des zwanzigsten Jahrhunderts vor allem in Frankreich durch Freyssinet (Betongelenke ohne Bewehrung des Gelenkhalses) und Mesnager (Betonfedergelenke). Die guten Erfahrungen bezüglich der Funktionalität und die wirtschaftlichen Vorteile führten in Frankreich zu einem intensiven Einsatz von Betongelenken, vor allem beim Bau von Stahlbetonbogenbrücken und von massiven Dreigelenkbögen für Hallentragwerke. Aber auch in Deutschland, in den USA und vor allem in der Schweiz wurden Betongelenke verwendet. Durch die Arbeiten von Fritz Leonhardt (Deutschland), E.O. Fessler (Schweiz) und G.D. Base (Großbritannien), welche bis heute international den Stand der Technik definieren, erlebten die Betongelenke in den sechziger Jahren eine Renaissance. Die Bemessungsregeln Leonhardts wurden im Rahmen eines Forschungsvorhabens hinsichtlich der heute bekannten Forschungserkenntnisse überarbeitet. Damit wird eine Bemessung von Betongelenken auf Basis des heute bauaufsichtlich eingeführten Regelwerks ermöglicht.

Concrete Hinges

Articulated connections consisting of concrete (concrete hinges) have already been developed 130 years ago and since then they were used successfully in many constructions. In 1880 Claus Köpcke (Dresden) was the first who used so called saddle bearings for a natural stone‐arched bridge. At the beginning of the 20th century further developments, especially in France by Freyssinet (concrete hinge without reinforcement in the throat of the hinge) and Mesnager (concrete hinge with heavy reinforcement in the throat of the hinge) have been made. The good experiences in the functionality and the economical advantages led to numerous use of concrete hinges in practice, especially in constructions of reinforced concrete arched bridges and threehinged arches for hall trusses. But concrete hinges were also used in Germany, in the USA and particularly in Switzerland. In the 1960 the works by Fritz Leonhardt (Germany), E.O. Fessler (Switzerland) and G.D. Base (Great‐Britain), which define the international state of the art till today, led to a renaissance of concrete hinges. The design rules given by Leonhardt have been adapted to the current state of knowledge within a research project. Therewith the design of concrete hinges based on the today established rules will be possible.
Daily ingestion of green tea catechins from adulthood suppressed brain dysfunction in aged mice
Authors: Unno Keiko , Ishikawa Yuichi , Takabayashi Fumiyo , Sasaki Toru , Takamori Nina , Iguchi Kazuaki , Hoshino Minoru
Published: December 2009

Oxidative damage is believed to be an important cause of senescence. We have previously found that green tea catechins (GT‐catechin), potent antioxidants, decrease oxidative damage to DNA and suppress brain dysfunction in aged senescence‐accelerated mice (SAMP10) when ingested from the age of 1 month to the age of 12 months. To clarify the effect of GT‐catechin on suppression of brain senescence, we investigated the effect of starting period to ingest GT‐catechin. Six‐ or 9‐month‐old SAMP10 mice were allowed free access to water containing 0.02% GT‐catechin. SAMP10 mice exhibit senescence characteristics such as shortened life span, atrophied forebrain and lowered learning and memory abilities. Learning ability was significantly higher in mice that ingested GT‐catechin from the age of 6 months to 12 months when compared with same‐aged control mice drank water without GT‐catechin. Starting GT‐catechin intake from the age of 9 months tended to improve learning ability. The ages of 6 and 9 months are thought to be adult and middle ages, respectively in SAMP10 mice. This result suggested that GT‐catechin was helpful in suppressing brain dysfunction with aging even when ingestion started at the adult age.
Folate deficiency followed by ionizing radiation perturbs hepatic dihydrofolate reducatse activity
Authors: Batra Vipen , Lakhmy Seetha , Devasagayam Thomas Paul Asir
Published: December 2009

There is lot of interest in the folate metabolism because of the essential role of folate coenzymes in nucleic acid synthesis. Gamma (γ) radiation is well known for inducing damage in the DNA. To counteract these damage, a variety of DNA repair pathways have evolved that require regular supply of DNA bases whose biosynthesis in turn depends on sufficient pools of folate dependent enzymes like dihydrofolate reductase (DHFR). In the present study, we examined the ionizing radiation mediated perturbation of DHFR activity in folate deficient and folate sufficient conditions. In folate deficient animals a potent inhibition of liver DHFR activity was observed. Our results showed that combination of folate starvation and ionizing radiation might adversely affect the DHFR activity, compared to their individual treatments. Measurement of apurinic/apyrimidinic sites (AP sites), a major type of DNA damage generated by radiation induced loss of purine and/or pyrimidine base, indicated a dose dependent DNA damage in folate deficient animals. In conclusion our data suggest an interactive role of folate deficiency and radiation injury in inhibiting DHFR activity.