bluuebunny/crossref_metadata_2025 huggingface dataset:
Modified logarithmic Sobolev inequalities in null curvature
Authors: Gentil Ivan , Guillin Arnaud , Miclo Laurent
Published: December 2011

We present a new logarithmic Sobolev inequality adapted to a log-concave measure on

\mathbb{R}

between the exponential and the Gaussian measure. More precisely, assume that

\Phi

is a symmetric convex function on

\mathbb{R}

satisfying

(1+\varepsilon)\Phi(x)\leq {x}\Phi'(x)\leq(2-\varepsilon)\Phi(x)

for

x\geq 0

large enough and with

\varepsilon\in ]0,1/2]

. We prove that the probability measure on

\mathbb{R}

\mu_\Phi(dx)=e^{-\Phi(x)}/Z_\Phi dx

satisfies a modified and adapted logarithmic Sobolev inequality: there exist three constants

A,B,C>0

such that for all smooth functions

f>0

,

\mathbf{Ent}_{\mu_\Phi}{\left(f^2\right)}\leq A\int H_{\Phi}\left(\frac{f'}{f}\right)f^2d\mu_\Phi,

with

H_{\Phi}(x)= \left\{ \begin{array}{l} x^2 \text{ if }\left|x\right|< C,\\ \Phi^*\left(Bx\right) \text{ if }\left|x\right|\geq C, \end{array} \right.

where

\Phi^*

is the Legendre–Fenchel transform of

\Phi

.
The volume near the zeroes of a smooth function
Authors: Batchourine Pavel , Fefferman Charles
Published: December 2011

We show that if a smooth function that never vanishes to infinite order, then the set of points within the distance

\delta

from the zeroes of this function has volume

O(\delta).
On monochromatic solutions of equations in groups
Authors: Cameron Peter J. , Cilleruelo Javier , Serra Oriol
Published: December 2011

We show that the number of monochromatic solutions of the equation

x_1^{\alpha_1}x_2^{\alpha_2}\cdots x_r^{\alpha_r}=g

in a

2

-coloring of a finite group

G

, where

\alpha_1,\ldots,\alpha_r

are permutations and

g\in G

, depends only on the cardinalities of the chromatic classes but not on their distribution. We give some applications to arithmetic Ramsey statements.
The Geometric Traveling Salesman Problem in the Heisenberg Group
Authors: Ferrari Fausto , Franchi Bruno , Pajot Hervé
Published: December 2011

In the Heisenberg group

{\mathbb H}

(endowed with its Carnot-Carathéodory structure), we prove that a compact set

E \subset {\mathbb H}

which satisfies an analog of Peter Jones' geometric lemma is contained in a rectifiable curve. This quantitative condition is given in terms of Heisenberg

\beta

numbers which measure how well the set

E

is approximated by Heisenberg straight lines.
Equation de Navier-Stokes avec densité et viscosité variables dans l’espace critique
Authors: Abidi Hammadi
Published: December 2011

In this article, we show that the Navier-Stokes system with variable density and viscosity is locally well-posed in the Besov space

\dot B^{\frac{N}{p}}_{p\,1}(\R^N)\times\big(\dot B^{\frac{N}{p}-1}_{p\,1}(\R^N)\big)^N,

for

1 < p\leq N

when the initial density approaches a strictly positive constant. This result generalizes the work by R. Danchin for the case where the viscosity is constant and

p=2

(see [Danchin, R.: Density-dependent incompressible viscous fluids in critical spaces. Proc. Roy. Soc. Edinburgh Sect. A 133 (2003), 1311-1334.]). Moreover, we prove existence and uniqueness in the Sobolev space\arriba{2}

H^{\frac{N}{2}+\alpha}(\R^N)\times\big(H^{\frac{N}{2}-1+\alpha}(\R^N)\big)^N

for

\alpha>0,

generalizing R. Danchin's result for the case where viscosity is constant (see [Danchin, R.: Local and global well-posedness results for flows of inhomogeneous viscous fluids. Adv. Differential Equations 9 (2004), 353-386.]).
The fractional maximal operator and fractional integrals on variable $L^p$ spaces
Authors: Capone Claudia , Cruz-Uribe David , Fiorenza Alberto
Published: December 2011

We prove that if the exponent function

p(\cdot)

satisfies log-Hölder continuity conditions locally and at infinity, then the fractional maximal operator

M_\alpha

,

0 < \alpha < n

, maps

L^{p(\cdot)}

to

L^{q(\cdot)}

, where

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

. We also prove a weak-type inequality corresponding to the weak

(1,n/(n-\alpha))

inequality for

M_\alpha

. We build upon earlier work on the Hardy-Littlewood maximal operator by Cruz-Uribe, Fiorenza and Neugebauer [The maximal function on variable

L^p

spaces. Ann. Acad. Sci. Fenn. Math. 28 (2003), 223-238]. As a consequence of these results for

M_\alpha

, we show that the fractional integral operator

I_\alpha

satisfies the same norm inequalities. These in turn yield a generalization of the Sobolev embedding theorem to variable

L^p

spaces.
Smooth rough paths and applications to Fourier analysis
Authors: Hara Keisuke , Lyons Terry J.
Published: December 2011

We show rough path estimates for smooth

L^p

functions whose derivatives are in

L^q

. We also give applications to Fourier analysis.
Some asymptotic properties of the hybrids of empirical and partial-sum processes
Authors: Alvarez-Andrade Sergio
Published: December 2011

The motivation of this paper is to study some properties of the local times (when it exists) of the hybrids of empirical and partial-sum processes defined by

\bar{A}_n(t)=\sum_{1\leq i \leq n} H(X_i)1_{\{X_i\leq t\}} \epsilon_i, \quad - \infty< t<\infty ,

namely by using knowing results on empirical process and Brownian local times.
Flux terms and Robin boundary conditions as limit of reactions and potentials concentrating at the boundary
Authors: Arrieta José M. , Jiménez-Casas Angela , Rodríguez-Bernal Aníbal
Published: December 2011

We analyze the limit of the solutions of an elliptic problem when some reaction and potential terms are concentrated in a neighborhood of a portion

\Gamma

of the boundary and this neighborhood shrinks to

\Gamma

as a parameter goes to zero. We prove that this family of solutions converges in certain Sobolev spaces and also in the sup norm, to the solution of an elliptic problem where the reaction term and the concentrating potential are transformed into a flux condition and a potential on

\Gamma

.
Comparison of the classical BMO with the BMO spaces associated with operators and applications
Authors: Deng Donggao , Duong Xuan Thinh , Sikora Adam , Yan Lixin
Published: December 2011

Let

L

be a generator of a semigroup satisfying the Gaussian upper bounds. A new

{\rm BMO}_L

space associated with

L

was recently introduced in [Duong, X. T. and Yan, L.: {New function spaces of BMO type, the John-Nirenberg inequality, interpolation and applications}. \textit{Comm. Pure Appl. Math.} {\bf 58} (2005), 1375-1420] and [Duong, X. T. and Yan, L.: {Duality of Hardy and BMO spaces associated with operators with heat kernels bounds}. \textit{J. Amer. Math. Soc.} {\bf 18} (2005), 943-973]. We discuss applications of the new

{\rm BMO}_L

spaces in the theory of singular integration. For example we obtain

{\rm BMO}_L

estimates and interpolation results for fractional powers, purely imaginary powers and spectral multipliers of self adjoint operators. We also demonstrate that the space

{\rm BMO}_L

might coincide with or might be essentially different from the classical BMO space.
Bound state solutions for a class of nonlinear Schrödinger equations
Authors: Bonheure Denis , Van Schaftingen Jean
Published: December 2011

We deal with the existence of positive bound state solutions for a class of stationary nonlinear Schrödinger equations of the form $$ -\varepsilon^2\Delta u + V(x) u = K(x) u^p,\qquad x\in\mathbb{R}^N,

where

V, K

are positive continuous functions and

p > 1

is subcritical, in a framework which may exclude the existence of ground states. Namely, the potential

V

is allowed to vanish at infinity and the competing function

K

does not have to be bounded. In the \\emph{semi-classical limit}, i.e. for

\varepsilon\sim 0

, we prove the existence of bound state solutions localized around local minimum points of the auxiliary function

\mathcal{A} = V^\theta K^{-\frac{2}{p-1}}

, where

\theta=(p+1)/(p-1)-N/2

. A special attention is devoted to the qualitative properties of these solutions as

\varepsilon$ goes to zero.
Entropy methods for reaction-diffusion equations: slowly growing a-priori bounds
Authors: Desvillettes Laurent , Fellner Klemens
Published: December 2011

In the continuation of [Desvillettes, L., Fellner, K.: Exponential Decay toward Equilibrium via Entropy Methods for Reaction-Diffusion Equations. J. Math. Anal. Appl. 319 (2006), no. 1, 157-176], we study reversible reaction-diffusion equations via entropy methods (based on the free energy functional) for a 1D system of four species. We improve the existing theory by getting 1) almost exponential convergence in

L^1

to the steady state via a precise entropy-entropy dissipation estimate, 2) an explicit global

L^{\infty}

bound via interpolation of a polynomially growing

H^1

bound with the almost exponential

L^1

convergence, and 3), finally, explicit exponential convergence to the steady state in all Sobolev norms.
Soluble products of connected subgroups
Authors: Gállego M. Pilar , Hauck Peter , Pérez-Ramos M. Dolores
Published: December 2011

The main result in the paper states the following: For a finite group

G=AB

, which is the product of the soluble subgroups

A

and

B

, if

\langle a,b \rangle

is a metanilpotent group for all

a\in A

and

b\in B

, then the factor groups

\langle a,b \rangle F(G)/F(G)

are nilpotent,

F(G)

denoting the Fitting subgroup of

G

. A particular generalization of this result and some consequences are also obtained. For instance, such a group

G

is proved to be soluble of nilpotent length at most

l+1

, assuming that the factors

A

and

B

have nilpotent length at most

l

. Also for any finite soluble group

G

and

k\geq 1

, an element

g\in G

is contained in the preimage of the hypercenter of

G/F_{k-1}(G)

, where

F_{k-1}(G)

denotes the (

k-1

)th term of the Fitting series of

G

, if and only if the subgroups

\langle g,h\rangle

have nilpotent length at most

k

for all

h\in G

.
Global infinite energy solutions of the critical semilinear wave equation
Authors: Germain Pierre
Published: December 2011

We consider the critical semilinear wave equation

(NLW)_{2^*-1} \;\;\; \left\{ \begin{aligned} \square u + |u|^{2^*-2} u & = 0 \\ u_{|t=0} & = u_0 \\ \partial_t u_{|t=0} & = u_1 \, \,, \end{aligned} \right.

set in

\mathbb{R}^d

,

d \geq 3

, with

2^* = \frac{2d}{d-2} \,\cdotp

Shatah and Struwe [Shatah, J. and Struwe, M.: Geometric wave equations. Courant Lecture Notes in Mathematics 2. New York University, Courant Institute of Mathematical Sciences. American Mathematical Society, RI, 1998] proved that, for finite energy initial data (ie if

(u_0,u_1) \in \dot{H}^1 \times L^2

), there exists a global solution such that

(u,\partial_t u)\in \mathcal{C}(\mathbb{R},\dot{H}^1 \times L^2)

. Planchon [Planchon, F.: Self-similar solutions and semi-linear wave equations in Besov spaces. J. Math. Pures Appl. (9) 79 (2000), no. 8, 809-820] showed that there also exists a global solution for certain infinite energy initial data, namely, if the norm of

(u_0,u_1)

in

\dot{B}^1_{2,\infty} \times \dot{B}^0_{2,\infty}

is small enough. In this article, we build up global solutions of

(NLW)_{2^*-1}

for arbitrarily big initial data of infinite energy, by using two methods which enable to interpolate between finite and infinite energy initial data: the method of Calderón, and the method of Bourgain. These two methods give complementary results.
Non-uniqueness in a free boundary problem
Authors: Bennewitz Björn
Published: December 2011

We show that a result of Lewis and Vogel on uniqueness in a free boundary problem for the

p

-Laplace operator is sharp in two dimensions.
Quasilinear equations with natural growth
Authors: Arcoya David , Martínez-Aparicio Pedro J.
Published: December 2011

We study the existence of positive solution

w\in H_0^1(\Omega)

of the quasilinear equation

-\Delta w+ g(w)|\nabla w|^2=a(x)

,

x\in \Omega

, where

\Omega

is a bounded domain in

\mathbb R^N

,

0\leq a\in L^\infty (\Omega )

and

g

is a nonnegative continuous function on

(0,+\infty)

which may have a singularity at zero.
Notes on the roots of Steiner polynomials
Authors: Henk Martin , Hernández Cifre María A.
Published: December 2011

We study the location and the size of the roots of Steiner polynomials of convex bodies in the Minkowski relative geometry. Based on a problem of Teissier on the intersection numbers of Cartier divisors of compact algebraic varieties it was conjectured that these roots have certain geometric properties related to the in- and circumradius of the convex body. We show that the roots of 1-tangential bodies fulfill the conjecture, but we also present convex bodies violating each of the conjectured properties.
The Walsh model for $M_2^*$ Carleson
Authors: Demeter Ciprian , Lacey Michael T. , Tao Terence , Thiele Christoph
Published: December 2011

We study the Walsh model of a certain maximal truncation of Carleson's operator related to the Return Times Theorem.
Fitting a $C^m$-Smooth Function to Data II
Authors: Fefferman Charles , Klartag Bo'az
Published: December 2011

We exhibit efficient algorithms to perform the following task: Given a function

f

defined on a finite subset

E \subset \mathbb R^n

, compute a

C^m

function

F

on

\mathbb R^n

, with a controlled

C^m

norm, that approximates

f

on the subset

E

.
A variant of compressed sensing
Authors: Matei Basarab , Meyer Yves
Published: December 2011

The famous Nyquist-Shannon sampling theorem has been recently improved by A. Olevskii and A. Ulanovskii. The present contribution is aimed at bridging the gap between their advance on irregular sampling and what is named "compressed sensing" in signal processing.
Universal Taylor series with maximal cluster sets
Authors: Bernal-González L. , Bonilla A. , Calderón-Moreno M. C. , Prado-Bassas J. A.
Published: December 2011

We link the overconvergence properties of certain Taylor series in the unit disk to the maximality of their cluster sets, so connecting outer wild behavior to inner wild behavior. Specifically, it is proved the existence of a dense linear manifold of holomorphic functions in the disk that are, except for zero, universal Taylor series in the sense of Nestoridis and, simultaneously, have maximal cluster sets along many curves tending to the boundary. Moreover, it is constructed a dense linear manifold of universal Taylor series having, for each boundary point, limit zero along some path which is tangent to the corresponding radius. Finally, it is proved the existence of a closed infinite dimensional manifold of holomorphic functions enjoying the two-fold wild behavior specified at the beginning.
A signed measure on rough paths associated to a PDE of high order: results and conjectures
Authors: Levin Daniel , Lyons Terry J.
Published: December 2011

Following old ideas of V. Yu. Krylov we consider the possibility that high order differential operators of dissipative type and constant coefficients might be associated, at least formally, with signed measures on path space in the same way that Wiener measure is associated with the Laplacian. There are fundamental difficulties with this idea because the measure would always have locally infinite mass. However, this paper provides evidence that if one considers equivalence classes of paths corresponding to distinct parameterisations of the same path, the measures might really exist on this quotient space. Precisely, we consider the measures on piecewise linear paths with given time partition defined using the semigroup associated to the differential operator and prove that these measures converge in distribution when the test functions on path space are the iterated integrals of the paths. Given a "random" piecewise-linear path, we evaluate its "expected" signature in terms of an explicit tensor series in the tensor algebra. Our approach uses an integration by parts argument under very mild conditions on the polynomial corresponding to the PDE of high order.
Random fractals and tree-indexed Markov chains
Authors: Durand Arnaud
Published: December 2011

We study the size properties of a general model of fractal sets that are based on a tree-indexed family of random compacts and a tree-indexed Markov chain. These fractals may be regarded as a generalization of those resulting from the Moran-like deterministic or random recursive constructions considered by various authors. Among other applications, we consider various extensions of Mandelbrot’s fractal percolation process.
Hölder exponents of arbitrary functions
Authors: Ayache Antoine , Jaffard Stéphane
Published: December 2011

The functional class of Hölder exponents of continuous function has been completely characterized by P. Andersson, K. Daoudi, S. Jaffard, J. Lévy Véhel andY. Meyer [1, 2, 6, 9]; these authors have shown that this class exactly corresponds to that of the lower limits of the sequences of nonnegative continuous functions. The problem of determining whether or not the H¨older exponents of discontinuous (and even unbounded) functions can belong to a larger class remained open during the last decade. The main goal of our article is to show that this is not the case: the latter H¨older exponents can also be expressed as lower limits of sequences of continuous functions. Our proof mainly relies on a “wavelet-leader” reformulation of a nice characterization of pointwise Hölder regularity due to P. Anderson.
Estimates for the $X$-ray transform restricted to 2-manifolds
Authors: Erdoğan M. Burak , Oberlin Richard
Published: December 2011

We prove almost sharp mixed-norm estimates for the

X

-ray transform restricted to lines whose directions lie on certain well-curved two dimensional manifolds.
On the Conley decomposition of Mather sets
Authors: Bernard Patrick
Published: December 2011

In the context of Mather’s theory of Lagrangian systems, we study the decomposition in chain-transitive classes of the Mather invariant sets. As an application, we prove, under appropriate hypotheses, the semi-continuity of the so-called Aubry set as a function of the Lagrangian.
Taylor Formula on step two Carnot Groups
Authors: Arena Gabriella , Caruso Andrea O. , Causa Antonio
Published: December 2011

In the setting of step two Carnot groups we give an explicit representation of Taylor polynomial in terms of a suitable basis of the real vector space of left invariant differential operators, acting pointwisely on monomials like the ordinary Euclidean iterated derivations.
Measure of submanifolds in the Engel group
Authors: Le Donne Enrico , Magnani Valentino
Published: December 2011

We find all intrinsic measures of

C^{1,1}

smooth submanifolds in the Engel group, showing that they are equivalent to the corresponding

d

-dimensional spherical Hausdorff measure restricted to the submanifold. The integer

d

is the degree of the submanifold. These results follow from a different approach to negligibility, based on a blow-up technique.
Singular integrals in nonhomogeneous spaces: $L^2$ and $L^p$ continuity from Hölder estimates
Authors: Bramanti Marco
Published: December 2011

We present a result of

L^p

continuity of singular integrals of Calderón-Zygmund type in the context of bounded nonhomogeneous spaces, well suited to be applied to problems of a priori estimates for partial differential equations. First, an easy and selfcontained proof of

L^2

continuity is got by means of

C^{\alpha}

continuity, thanks to an abstract theorem of Krein. Then

L^p

continuity is derived adapting known results by Nazarov-Treil-Volberg about singular integrals in nonhomogeneous spaces.
End-point estimates and multi-parameter paraproducts on higher dimensional tori
Authors: Workman John T.
Published: December 2011

Analogues of multi-parameter multiplier operators on

\mathbb{R}^d

are defined on the torus

\mathbb{T}^d

. It is shown that these operators satisfy the classical Coifman-Meyer theorem. In addition,

L(\log L)^n

end-point estimates are proved.
Topological and analytical properties of Sobolev bundles. II. Higher dimensional cases
Authors: Isobe Takeshi
Published: December 2011

We define various classes of Sobolev bundles and connections and study their topological and analytical properties. We show that certain kinds of topologies (which depend on the classes) are well-defined for such bundles and they are stable with respect to the natural Sobolev topologies. We also extend the classical Chern-Weil theory for such classes of bundles and connections. Applications related to variational problems for the Yang-Mills functional are also given.
Elliptic equations in the plane satisfying a Carleson measure condition
Authors: Dindoš Martin , Rule David J.
Published: December 2011

In this paper we settle (in dimension

n=2

) the open question whether for a divergence form equation

\div (A\nabla u) = 0

with coefficients satisfying certain minimal smoothness assumption (a Carleson measure condition), the

L^p

Neumann and Dirichlet regularity problems are solvable for some values of

p\in (1,\infty)

. The related question for the

L^p

Dirichlet problem was settled (in any dimension) in 2001 by Kenig and Pipher [Kenig, C.E. and Pipher, J.: The Dirichlet problem for elliptic equations with drift terms. Publ. Mat. 45 (2001), no. 1, 199-217].
Maps from Riemannian manifolds into non-degenerate Euclidean cones
Authors: Mari Luciano , Rigoli Marco
Published: December 2011

Let

M

be a connected, non-compact

m

-dimensional Riemannian manifold. In this paper we consider smooth maps

\varphi: M \rightarrow \mathbb{R}^n

with images inside a non-degenerate cone. Under quite general assumptions on

M

, we provide a lower bound for the width of the cone in terms of the energy and the tension of

\varphi

and a metric parameter. As a side product, we recover some well known results concerning harmonic maps, minimal immersions and Kähler submanifolds. In case

\varphi

is an isometric immersion, we also show that, if

M

is sufficiently well-behaved and has non-positive sectional curvature,

\varphi(M)

cannot be contained into a non-degenerate cone of

\mathbb{R}^{2m-1}

.
Global existence for the primitive equations with small anisotropic viscosity
Authors: Charve Frédéric , Ngo Van-Song
Published: December 2011

In this paper, we consider the primitive equations with zero vertical viscosity, zero vertical thermal diffusivity, and the horizontal viscosity and horizontal thermal diffusivity of size

\varepsilon^\alpha

where

0 < \alpha < \alpha_0

. We prove the global existence of a unique strong solution for large data provided that the Rossby number is small enough (the rotation and the vertical stratification are large).
Construction of multi-soliton solutions for the $L^2$-supercritical gKdV and NLS equations
Authors: Côte Raphaël , Martel Yvan , Merle Frank
Published: December 2011

Multi-soliton solutions, i.e. solutions behaving as the sum of

N

given solitons as

t \to +\infty

, were constructed for the

L^2

critical and subcritical (NLS) and (gKdV) equations in previous works (see [Merle, F.: Construction of solutions with exactly

k

blow-up points for the Schrödinger equation with critical nonlinearity. Comm. Math. Phys. 129 (1990), no. 2, 223-240], [Martel, Y.: Asymptotic

N

-soliton-like solutions of the subcritical and critical generalized Korteweg-de Vries equations. Amer. J. Math. 127 (2005), no. 5, 1103-1140] and [Martel, Y. and Merle, F.: Multi solitary waves for nonlinear Schrödinger equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 23 (2006), 849-864]). In this paper, we extend the construction of multi-soliton solutions to the

L^2

supercritical case both for (gKdV) and (NLS) equations, using a topological argument to control the direction of instability.
Strong $A_\infty$-weights are $A_\infty$-weights on metric spaces
Authors: Korte Riikka , Kansanen Outi Elena
Published: December 2011

We prove that every strong

A_\infty

-weight is a Muckenhoupt weight in Ahlfors-regular metric measure spaces that support a Poincaré inequality. We also explore the relations between various definitions for

A_\infty

-weights in this setting, since some of these characterizations are needed in the proof of the main result.
The $\varepsilon$-strategy in variational analysis: illustration with the closed convexification of a function
Authors: Hiriart-Urruty Jean-Baptiste , López Marco A. , Volle Michel
Published: December 2011

In this work, we concentrate our interest and efforts on general variational (or optimization) problems which do not have solutions necessarily, but which do have approximate solutions (or solutions within

\varepsilon > 0

). We shall see how to recover all the (exact) minimizers of the relaxed version of the original problem (by closed-convexification of the objective function) in terms of the

\varepsilon

-minimizers of the original problem. Applications to two approximation problems in a Hilbert space setting will be shown.
Partial regularity for subquadratic parabolic systems by $\mathcal{A}$-caloric approximation
Authors: Scheven Christoph
Published: December 2011

We establish a partial regularity result for weak solutions of nonsingular parabolic systems with subquadratic growth of the type

\partial_t u - \mathrm{div} a(x,t,u,Du) = B(x,t,u,Du),

where the structure function

a

satisfies ellipticity and growth conditions with growth rate

\frac{2n}{n+2} < p < 2

. We prove Hölder continuity of the spatial gradient of solutions away from a negligible set. The proof is based on a variant of a harmonic type approximation lemma adapted to parabolic systems with subquadratic growth.
Auslander bounds and homological conjectures
Authors: Wei Jiaqun
Published: December 2011

Inspired by recent works on rings satisfying Auslander’s conjecture, we study invariants, called Auslander bounds, and prove that they have strong relations to some homological conjectures.
On the interplay between Lorentzian Causality and Finsler metrics of Randers type
Authors: Caponio Erasmo , Javaloyes Miguel Angel , Sánchez Caja Miguel
Published: December 2011

We obtain some results in both Lorentz and Finsler geometries, by using a correspondence between the conformal structure (Causality) of standard stationary spacetimes on

M = \mathbb{R} \times S

and Randers metrics on

S

. In particular: (1) For stationary spacetimes: we give a simple characterization of when

\mathbb{R} \times S

is causally continuous or globally hyperbolic (including in the latter case, when

S

is a Cauchy hypersurface), in terms of an associated Randers metric. Consequences for the computability of Cauchy developments are also derived. (2) For Finsler geometry: Causality suggests that the role of completeness in many results of Riemannian Geometry (geodesic connectedness by minimizing geodesics, Bonnet-Myers, Synge theorems) is played by the compactness of symmetrized closed balls in Finslerian Geometry. Moreover, under this condition we show that for any Randers metric

R

there exists another Randers metric

\tilde R

with the same pregeodesics and geodesically complete. Even more, results on the differentiability of Cauchy horizons in spacetimes yield consequences for the differentiability of the Randers distance to a subset, and vice versa.
Product kernels adapted to curves in the space
Authors: Casarino Valentina , Ciatti Paolo , Secco Silvia
Published: December 2011

We establish

L^p

-boundedness for a class of operators that are given by convolution with product kernels adapted to curves in the space. The

L^p

bounds follow from the decomposition of the adapted kernel into a sum of two kernels with singularities concentrated respectively on a coordinate plane and along the curve. The proof of the

L^p

-estimates for the two corresponding operators involves Fourier analysis techniques and some algebraic tools, namely the Bernstein-Sato polynomials. As an application, we show that these bounds can be exploited in the study of

L^p-L^q

estimates for analytic families of fractional operators along curves in the space.
The Ecological Approach in Tobacco-Control Practice: Health Promotion Practitioner Characteristics Related to Using the Ecological Approach
Authors: Lévesque Lucie , Richard Lucie , Potvin Louise
Published: December 2011

Purpose.

To identify cognitive factors and personal characteristics related to the integration of the ecological approach in the everyday practice of health promotion practitioners.

Design.

Sociodemographic, cognitive, and behavior data were collected using a cross-sectional mail survey.

Setting.

Information was collected from regional public health organizations (n = 129) in the 10 Canadian provinces.

Subjects.

Health promotion practitioners involved in tobacco-control programming for youth (n = 524) comprised of 81% women with a mean age of 39 years.

Measures.

Attempts to integrate ecological strategies (i.e., interpersonal, organizational, and policy change) into tobacco-control practice were based on three self-report items. Six scales assessed knowledge, values, and normative beliefs about the ecological approach as well as perceived need for, effectiveness of, and competency regarding using the ecological approach.

Results.

The survey response rate was 80%. Stepwise discriminant analyses revealed four predictors (p < .001) contributing to the function solution concerning practitioner attempts to target the interpersonal environment: perceived competency, training discipline, years doing health promotion, and gender. Three predictors (p < . 001) contributed to each of the function solutions concerning practitioner attempts to target the organizational environment (perceived competency, perceived effectiveness, and normative beliefs) and practitioner attempts at policy change (perceived competency, knowledge, and normative beliefs).

Conclusions.

Tobacco-control practitioners who perceive themselves as having the skills to develop and/or implement interventions targeting a person's environment are more likely to target the environment for change.
Is Hypercholesterolemia a Risk Factor and Should it Be Treated in the Elderly?
Authors: Hall Kathleen M. , Luepker Russell V.
Published: December 2011

Purpose.

The 1993 National Cholesterol Education Program guidelines recommend cholesterol screening for elderly patients with and without known coronary heart disease. This review summarizes clinical trial evidence from the medical literature that addresses cholesterol treatment in the elderly.

Data Sources.

References were obtained from a MEDLINE search, bibliographies, metaanalyses, and review articles.

Study Inclusion and Exclusion Criteria.

Randomized, controlled clinical trials, including all lipid intervention trials with elderly participants or subgroup analyses of the elderly designed to measure major cardiovascular disease endpoints, were selected.

Data Extraction Methods.

A MEDLINE search of all clinical trials using key search terms yielded 1360 references. Journal titles and abstracts were reviewed for all references by one of us (K.M.H.). A full journal review was undertaken for 41 references to clinical trials. Five clinical trials fulfilled all criteria and represented unique data.

Data Synthesis.

A MEDLINE search (from 1966 to January 2000) and bibliography reviews yielded five important clinical trials with analyses of elderly participants. Data are presented in text form and a summary table.

Major Conclusions.

Clinical trial evidence supports treating hyperlipidemia in elderly persons for secondary prevention of coronary heart disease. Evidence from four secondary prevention trials demonstrated that major coronary heart disease risk decreased by 25% to 30% in elderly subjects treated for 5 years. Unanswered questions include cholesterol treatment for primary prevention in the elderly, gender effect, and benefit of treatment in persons older than 70.
Cigarette Smoking among the Elderly: Disease Consequences and the Benefits of Cessation
Authors: Burns David M.
Published: December 2011

Synopsis.

The disease consequence of smoking occurs disproportionately among the elderly because of the long duration of cumulative injury or change that underlies the bulk of tobacco-caused disease. Older smokers are less likely than younger smokers to attempt quitting, but they are more likely to be successful in the attempts that they do make to quit. Excess absolute rates of disease incidence and mortality due to smoking increase steadily with increasing age and duration of smoking, and there is little evidence to suggest that the disease consequences of smoking diminish among the elderly. Although cardiovascular disease is the most common cause of excess mortality among younger smokers, lung cancer is the largest cause of excess smoking-related mortality over the age of 60 years; and at older ages the excess death rate from chronic obstructive lung disease equals that for cardiovascular disease. Because of the dramatic increases in smoking-related excess mortality with advancing age, approximately 70% of the 400,000 or more deaths occur among those over age 60 years. The benefits of cessation are proportionately somewhat less among the elderly and may manifest more slowly than among younger smokers, but cessation remains the most effective way of altering smoking-induced disease risks at all ages, including those over the age of 60 years.
Role of iron and organic carbon in mass‐specific light absorption by particulate matter from Louisiana coastal waters
Authors: Estapa Margaret L. , Boss Emmanuel , Mayer Lawrence M. , Roesler Collin S.
Published: December 2011

We investigated the influences of organic content and mineralogical composition on light absorption by mostly mineral suspended particles in aquatic and coastal marine systems. Mass‐specific absorption spectra of suspended particles and surface sediments from coastal Louisiana and the lower Mississippi and Atchafalaya rivers were measured with a centered sample‐mount integrating sphere and analyzed in conjunction with organic carbon (OC), hydrochloric acid— (HCl‐) extractable iron, and dithionite‐extractable iron contents. Compositions and absorption properties were comparable to published values for similar particles. Dithionite‐extractable iron was strongly correlated with absorption at ultraviolet (UV) and blue wavelengths, while OC and HCl‐extractable iron were weakly but positively correlated. Oxidative removal of OC from sediments caused small and variable changes in absorption, while dithionite extraction of iron oxides strongly reduced absorption. Shoulders in the absorption spectra corresponded to absorption bands of iron oxide minerals, and their intensities were well correlated to dithionite‐extractable iron contents of the samples. These findings support a primary role for iron oxide and hydroxide minerals in the mass‐specific absorption of mostly inorganic particles from the terrestrially influenced coast of Louisiana. Riverine particles had higher dithionite‐extractable iron contents and iron oxide‐specific absorption features than did marine particles, consistent with current knowledge regarding differential transport of particulate iron oxides and hydroxides through estuarine salinity gradients and reductive alteration of these oxide phases on the Louisiana shelf. The quantifiable dependence of UV absorption features on iron oxide content suggests that, under certain conditions, in situ hyperspectral absorption measurements could be designed to monitor water‐column iron mineral transport and transformation.
Choroidal and Photoreceptor Layer Thickness in Myopic Population
Authors: Chen Wei , Wang Zhitao , Zhou Xuefen , Li Bin , Zhang Hong
Published: December 2011

Purpose

This study examined the profile of the choroidal thickness and photoreceptor layer thickness (PRLT) in healthy myopia subjects, with an attempt to find the connection between change of the choroidal thickness and retinal thickness changes.

Methods

A total of 64 study participants (64 eyes) were divided into 3 groups in terms of their refractive status: normal sight group (+1.0 D˜−1.0 D), mild or moderate myopia group (−1.0 D˜−6.0 D), high myopia group (>−6.0 D). The fovea and parafoveal region (the region of 6 mm diameter of the fovea as center) of the images were selected by spectral domain optical coherence tomography. A circle of retinal pigment epithelium (RPE) layer simulated by applying the least square curve fitting technique was obtained. Along the vertical direction of the RPE layer, choroidal thickness (choroidal thickness involved the total thickness at the fovea and parafoveal), PRLT, retinal thickness (RT), ganglion layer thickness (GLT), and retinal nerve fiber layer thickness (RNFLT) in the fovea (PRLT-f, RT-f) or in the parafoveal region (PRLT-pf, RT-pf, GLT and RNFLT) were calculated by Image J software manually.

Results

As compared with group 1, PRLT-pf, RT-pf, and choroidal thickness were significantly reduced (p<0.05) in group while no significant difference was found in PRLT-f, RT-f, GLT, and RNFLT between the 2 groups. Both univariate and forward multivariate linear regression analysis showed that PRLT-pf and choroidal thickness intertwined obviously.

Conclusions

In high myopia subjects, not only choroidal thickness, but also photoreceptor layer thickness in the parafoveal region decreased significantly. On the basis of neuron vascular unit theory, the change in choroidal thickness is significantly related to the alternation in PRLT and vice versa.
Results of Rapid Needs Assessments in Rural and Urban Iowa Following Large-scale Flooding Events in 2008
Authors: Quinlisk Patricia , Jones Mary J. , Bostick Nathan A. , Walsh Lauren E. , Curtiss Rebecca , Walker Robert , Mercer Steve , Subbarao Italo
Published: December 2011

Background: On June 8 and 9, 2008, more than 4 inches of rain fell in the Iowa-Cedars River Basin causing widespread flooding along the Cedar River in Benton, Linn, Johnson, and Cedar Counties. As a result of the flooding, there were 18 deaths, 106 injuries, and over 38 000 people displaced from their homes; this made it necessary for the Iowa Department of Health to conduct a rapid needs assessment to quantify the scope and effect of the floods on human health.

Methods: In response, the Iowa Department of Public Health mobilized interview teams to conduct rapid needs assessments using Geographic Information Systems (GIS)-based cluster sampling techniques. The information gathered was subsequently employed to estimate the public health impact and significant human needs that resulted from the flooding.

Results: While these assessments did not reveal significant levels of acute injuries resulting from the flood, they did show that many households had been temporarily displaced and that future health risks may emerge as the result of inadequate access to prescription medications or the presence of environmental health hazards.

Conclusions: This exercise highlights the need for improved risk communication measures and ongoing surveillance and relief measures. It also demonstrates the utility of rapid needs assessment survey tools and suggests that increasing use of such surveys can have significant public health benefits.

(Disaster Med Public Health Preparedness. 2011;5:287–292)
Highly Efficient and Chemoselective Ruthenium‐Catalyzed Hydrosilylation of Aldehydes
Authors: Do Youngshil , Han Junghoon , Rhee Young Ho , Park Jaiwook
Published: December 2011

The highly chemoselective hydrosilylation of aldehydes was achieved using a ruthenium catalyst activated by a household fluorescent light (30 W) at or below room temperature. The hydrosilylation was almost exclusive to aldehydes over ketones and olefins.
Rhodium‐Catalyzed Enantioselective Intramolecular [4+2] Cycloaddition using a Chiral Phosphine‐Phosphite Ligand: Importance of Microwave‐Assisted Catalyst Conditioning
Authors: Falk Anna , Fiebig Lukas , Neudörfl Jörg‐Martin , Adler Andreas , Schmalz Hans‐Günther
Published: December 2011

The use of modular α,α,α′,α′‐tetraaryl‐1,3‐dioxolane‐4,5‐dimethanol (TADDOL)‐ and 1,1′‐bi‐2‐naphthol (BINOL)‐derived phosphine‐phosphite ligands (L2*) in the asymmetric rhodium‐catalyzed intramolecular [4+2] cycloaddition (“neutral” Diels–Alder reaction) of (E,E)‐1,6,8‐decatriene derivatives (including a 4‐oxa and a 4‐aza analogue) was investigated. Initial screening of a small ligand library led to the identification of a most promising, TADDOL‐derived ligand bearing a phenyl group adjacent to the phosphite moiety at the arene backbone. In the course of further optimization studies, the formation of a new, more selective catalyst species during the reaction time was observed. By irradiating the pre‐catalyst with microwaves prior to substrate addition high enantioselectivities (up to 93% ee) were achieved. The new cyclization protocol was successfully applied to all three substrates investigated to give the bicyclic products in good yield and selectivity. 31P NMR and ESI‐MS measurements indicated the formation of a [Rh(L2*)2]+ species as the more selective (pre‐) catalyst.
Polyaniline nanofibers supported on titanium as templates for immobilization of Pd nanoparticles: A new electro‐catalyst for hydrazine oxidation
Authors: Hosseini M. G. , Zeynali S. , Momeni M. M. , Najjar R.
Published: December 2011

Palladium nanoparticles (Pd‐NPs)/polyaniline (PAni)/titanium (Ti) catalysts were prepared using electroless deposition of Pd‐NPs on PAni matrixes coated on Ti substrate. PAni/Ti electrodes were synthesized by electro‐polymerization of aniline on Ti. The morphology of Pd‐NPs on PAni/Ti electrodes were characterized by scanning electron microscopy technique and results indicated that Pd‐NPs were uniformly dispersed on the surface of PAni film. The electro‐catalytic properties of Pd‐NPs/PAni/Ti catalysts toward oxidation of hydrazine were investigated by different electrochemical methods and results showed that Pd‐NPs/PAni/Ti catalysts have high electrochemical activity. In addition, the mechanism of hydrazine electrochemical oxidation catalyzed by Pd‐NPs/PAni/Ti was investigated. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011
Hollow poly(N‐isopropylacrylamide)‐co‐poly(acrylic acid) microgels with high loading capacity for drugs
Authors: Chen Ying , Chen Yongbing , Nan Jingya , Wang Chunpeng , Chu Fuxiang
Published: December 2011

A convenient approach has been developed for the preparation of microsize hydrogels composed of crosslinked poly(acrylic acid) (PAA) and poly(N‐isopropylacrylamide) (PNIPAm). First, semi‐interpenetration polymer networks of hydropropylcellulose (HPC) and PNIPAm‐co‐PAA copolymer are formed through the copolymerization and crosslinking of monomer acrylic acid and N‐isopropylacrylamide in HPC aqueous solution. After the selective removal of HPC from networks due to ionization of PAA units and disruption of hydrogen bonding with increasing pH, PNIPAm‐co‐PAA microgels are obtained, whose volume is confirmed to be responsive to both temperature and pH. Doxorubicin hydrochloride (Dox) can be encapsulated in PNIPAm‐co‐PAA microgels with high drug loading driven by the electrostatic interaction, and a sustained‐release characteristic of Dox from the microgels is observed under physiological pH value and temperature. In vitro cell experiments, the drug‐loaded microgels can be taken up by LoVo cells and release their payload in cell cytoplasm without loss of drug efficacy. This indicates that PNIPAm‐co‐PAA microgels might be a potential drug delivery carriers especially for water‐soluble or polypeptide drugs. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011
Study of morphological and mechanical performance of amine‐cured glassy epoxy–clay nanocomposites
Authors: Mouloud A. , Cherif R. , Fellahi S. , Grohens Y. , Pillin I.
Published: December 2011

The effect of three different alkylammonium‐modified montmorillonite on morphological and mechanical properties of glassy epoxy‐amine nanocomposites is reported. Small amounts of clays <10 phr (part per hundred of resin) were used in each system of nanocomposite. The morphology of the prepared nanocomposites was performed by means of X‐ray diffraction and transmission electron microscopy. Differential scanning calorimetry (DSC) was used to investigate the glass transition temperatures (Tg). Mechanical properties were based on tensile characteristics (Young's modulus), impact strength, and fracture toughness. The measured moduli were compared to theoretical predictions. Scanning electron microscopy was used to study the morphological structure of the fracture surfaces of impacted specimens. It was found that at a low content of 2 phr (1.2 wt %) of nanoclays, the impact strength and the fracture toughness were improved by 77 and 90% respectively, comparatively to the neat epoxy, whereas DSC revealed a reduction of the Tg of nanocomposites. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011
Interleukin‐21 modulates Th1 and Th17 responses in giant cell arteritis
Authors: Terrier Benjamin , Geri Guillaume , Chaara Wahiba , Allenbach Yves , Rosenzwajg Michelle , Costedoat‐Chalumeau Nathalie , Fouret Pierre , Musset Lucile , Benveniste Olivier , Six Adrien , Klatzmann David , Saadoun David , Cacoub Patrice
Published: December 2011

Objective

Giant cell arteritis (GCA) is a large‐vessel vasculitis of unknown origin. Recent findings indicate that at least 2 separate lineages of CD4+ T cells, Th1 and Th17 cells, participate in vascular inflammation. The pathways driving these T cell differentiations are incompletely understood, but may provide novel therapeutic targets. This study was undertaken to identify cytokines involved in the pathogenesis of GCA.

Methods

Thirty GCA patients fulfilling the American College of Rheumatology criteria, with active disease or disease in remission, and 30 age‐matched controls were included. Levels of 27 cytokines were determined in culture supernatants, and flow cytometric analysis of peripheral blood mononuclear cells (PBMCs) and immunohistochemical analysis of temporal artery samples were performed.

Results

Multiparametric analysis of cytokines produced by PBMCs associated with GCA disease activity identified a signature involving interleukin‐2 receptor (IL‐2R), IL‐12, interferon‐γ (IFNγ), IL‐17A, IL‐21, and granulocyte–macrophage colony‐stimulating factor (GM‐CSF). An expansion of Th1 and Th17 cells and a decrease in Treg cells were observed in the peripheral blood of patients with active GCA. An expansion of IL‐21–producing CD4+ T cells was also observed in patients with active GCA and correlated positively with Th17 and Th1 cell expansion. Immunohistochemical analysis revealed IFNγ, IL‐17A, and IL‐21 expression within inflammatory infiltrates. Stimulation of purified CD4+ T cells with IL‐21 increased Th1 and Th17 cell frequencies and decreased FoxP3 expression. In contrast, blockade of IL‐21 using IL‐21R‐Fc markedly decreased the production of IL‐17A and IFNγ and increased FoxP3 expression.

Conclusion

Our findings indicate that IL‐21 plays a critical role in modulating Th1 and Th17 responses and Treg cells in GCA, and might represent a potential target for novel therapy.