bluuebunny/crossref_metadata_2025 huggingface dataset:
A new Proof of Desingularization over fields of characteristic zero
Authors: Encinas Santiago , Villamayor U. Orlando
Published: December 2011

We present a proof of embedded desingularization for closed subschemes which does not make use of Hilbert–Samuel function and avoids Hironaka's notion of normal flatness (see also [17] page 224). Given a subscheme defined by equations, we prove that embedded desingularization can be achieved by a sequence of monoidal transformations; where the law of transformation on the equations defining the subscheme is simpler then that used in Hironaka's procedure.

This is done by showing that desingularization of a closed subscheme

X

, in a smooth sheme

W

, is achieved by taking an algorithmic principalization for the ideal

I(X)

, associated to the embedded scheme

X

. This provides a conceptual simplification of the original proof of Hironaka. This algorithm of principalization (of Log-resolution of ideals), and this new procedure of embedded desingularization discussed here, have been implemented in MAPLE.
Valuations in fields of power series
Authors: Herrera Govantes Francisco Javier , Olalla Acosta Miguel Ángel , Vicente Córdoba José Luis
Published: December 2011

This paper deals with valuations of fields of formal meromorphic functions and their residue fields. We explicitly describe the residue fields of the monomial valuations. We also classify all the discrete rank one valuations of fields of power series in two and three variables, according to their residue fields. We prove that all our cases are possible and give explicit constructions.
The Denef-Loeser series for toric surface singularities
Authors: Lejeune-Jalabert Monique , Reguera Ana J.
Published: December 2011

Let

H

denote the set of formal arcs going through a singular point of an algebraic variety

V

defined over an algebraically closed field

k

of characteristic zero. In the late sixties, J. Nash has observed that for any nonnegative integer

s

, the set

j^s(H)

of

s

-jets of arcs in

H

is a constructible subset of some affine space. Recently (1999), J. Denef and F. Loeser have proved that the Poincar\'{e} series associated with the image of

j^s(H)

in some suitable localization of the Grothendieck ring of algebraic varieties over

k

is a rational function. We compute this function for normal toric surface singularities.
Chains on the Eggers tree and polar curves
Authors: Wall C.T.C.
Published: December 2011

If

B

is a branch at

O\in\mathbb{C}^2

of a holomorphic curve, a Puiseux parametrisation

y=\psi(x)

of

B

determines "pro-branches" defined over a sector

|\mathrm{arg} x-\alpha| < \varepsilon

. The exponent of contact of two pro-branches is the (fractional) exponent of the first power of

x

where they differ. We first show how to use exponents of contact to give simple proofs of several well known results. For

C

the germ at

O

of a curve in

\mathbb{C}^2

, the Eggers tree

T_C

of

C

is defined. We also introduce combinatorial invariants (particularly, a certain 1-chain) on

T_C

. Any other germ

\Gamma

at

O

has contact with

C

measured by a unique point

X_{\Gamma}\in T_C

, and this determines the set of exponents of contact with

C

of any pro-branch of

\Gamma

. A simple formula establishes the converse, and this leads to a short proof of the theorem on decomposition of a transverse polar of

C

into parts

P_i

, where both the multiplicity of

P_i

, and the order of contact with

C

of each branch

Q

of

P_i

are explicitly given.
Elliptic Self-Similar Stochastic Processes
Authors: Benassi Albert , Roux Daniel
Published: December 2011

Let

M

be a random measure and

L

be an elliptic pseudo-differential operator on

\mathbb{R}^d

. We study the solution of the stochastic problem

LX=M

,

X(0)=0

when some homogeneity and integrability conditions are assumed. If

M

is a Gaussian measure the process

X

belongs to the class of Elliptic Gaussian Processes which has already been studied. Here the law of

M

is not necessarily Gaussian. We characterize the solutions

X

which are self-similar and with stationary increments in terms of the driving measure

M

. Then we use appropriate wavelet bases to expand these solutions and we give regularity results. In the last section it is shown how a percolation forest can help with constructing a self-similar Elliptic Process with non stable law.
Poissonian products of random weights: Uniform convergence and related measures
Authors: Barral Julien
Published: December 2011

The random multiplicative measures on

\mathbb{R}

introduced in Mandelbrot ([Mandelbrot 1996]) are a fundamental particular case of a larger class we deal with in this paper. An element

\mu

of this class is the vague limit of a continuous time measure-valued martingale

\mu _{t}

, generated by multiplying i.i.d. non-negative random weights, the

(W_M)_{M\in S}

, attached to the points

M

of a Poisson point process

S

, in the strip

H=\{(x,y)\in \mathbb{R}\times\mathbb{R}_+ ; 0 < y\leq 1\}

of the upper half-plane. We are interested in giving estimates for the dimension of such a measure. Our results give these estimates almost surely for uncountable families

(\mu ^{\lambda})_{\lambda \in U}

of such measures constructed simultaneously, when every measure

\mu^{\lambda}

is obtained from a family of random weights

(W_M(\lambda))_{M\in S}

and

W_M(\lambda)

depends smoothly upon the parameter

\lambda\in U\subset\mathbb{R}

. This problem leads to study in several sense the convergence, for every

s\geq 0

, of the functions valued martingale

Z^{(s)}_t: \lambda \mapsto \mu_{t}^{\lambda }([0,s])

. The study includes the case of analytic versions of

Z^{(s)}_t(\lambda)

where

\lambda\in\mathbb{C}^n

. The results make it possible to show in certain cases that the dimension of

\mu^{\lambda}

depends smoothly upon the parameter. When the Poisson point process is statistically invariant by horizontal translations, this construction provides the new non-decreasing multifractal processes with stationary increments

s\mapsto \mu ([0,s])

for which we derive limit theorems, with uniform versions when

\mu

depends on

\lambda

.
Singular Radon transforms and maximal functions under convexity assumptions
Authors: Seeger Andreas , Wainger Stephen
Published: December 2011

We prove variable coefficient analogues of results in [5] on Hilbert transforms and maximal functions along convex curves in the plane
Which values of the volume growth and escape time exponent are possible for a graph?
Authors: Barlow Martin T.
Published: December 2011

Let

\Gamma=(G,E)

be an infinite weighted graph which is Ahlfors

\alpha

-regular, so that there exists a constant

c

such that

c^{-1} r^\alpha\le V(x,r)\le c r^\alpha

, where

V(x,r)

is the volume of the ball centre

x

and radius

r

. Define the escape time

T(x,r)

to be the mean exit time of a simple random walk on

\Gamma

starting at

x

from the ball centre

x

and radius

r

. We say

\Gamma

has escape time exponent

\beta>0

if there exists a constant

c

such that

c^{-1} r^\beta \le T(x,r) \le c r^\beta

for

r\ge 1

. Well known estimates for random walks on graphs imply that

\alpha\ge 1

and

2 \le \beta \le 1+\alpha

. We show that these are the only constraints, by constructing for each

\alpha_0

,

\beta_0

satisfying the inequalities above a graph

\widetilde{\Gamma}

which is Ahlfors

\alpha_0

-regular and has escape time exponent

\beta_0

. In addition we can make

\widetilde{\Gamma}

sufficiently uniform so that it satisfies an elliptic Harnack inequality.
Multiplicative Square Functions
Authors: González María J. , Nicolau Artur
Published: December 2011

We study regularity properties of a positive measure in the euclidean space in terms of two square functions which are the multiplicative analogues of the usual martingale square function and of the Lusin area function of a harmonic function. The size of these square functions is related to the rate at which the measure doubles at small scales and determines several regularity properties of the measure. We consider the non-tangential maximal function of the logarithm of the densities of the measure in the dyadic setting, and of the logarithm of the harmonic extension of the measure, in the continuous setting. We relate the size of these maximal functions to the size of the corresponding square functions. Fatou type results,

L^p

estimates and versions of the Law of the Iterated Logarithm are proved. As applications we introduce a hyperbolic version of the Lusin Area function of an analytic mapping from the unit disc into itself, and use it to characterize inner functions. Another application to the theory of quasiconformal mappings is given showing that our methods can also be applied to prove a result by Din'kyn's on the smoothness of quasiconformal mappings of the disc.
On a subvariety of the moduli space
Authors: Cirre Francisco Javier
Published: December 2011

We give an explicit description of a non-normal irreducible subvariety of the moduli space of Riemann surfaces of genus

3

characterized by a non-cyclic group action. Defining equations of a family of curves representing non-normal points of this subvariety are computed. We also find defining equations of the family of hyperelliptic curves of genus

3

whose full automorphism group is

C_2\times C_4

. This completes the list of full automorphism groups of hyperelliptic curves.
The Cauchy problem for viscous shallow water equations
Authors: Wang Weike , Xu Chao-Jiang
Published: December 2011

In this paper we study the Cauchy problem for viscous shallow water equations. We work in the Sobolev spaces of index

s>2

to obtain local solutions for any initial data, and global solutions for small initial data.
Weighted Sobolev-Lieb-Thirring inequalities
Authors: Tachizawa Kazuya
Published: December 2011

We give a weighted version of the Sobolev-Lieb-Thirring inequality for suborthonormal functions. In the proof of our result we use

\varphi

-transform of Frazier-Jawerth.
A quantitative version of Krein’s Theorem
Authors: Fabian M. , Hájek P. , Montesinos Vicente , Zizler V.
Published: December 2011

A quantitative version of Krein’s Theorem on convex hulls of weak compact sets is proved. Some applications to weakly compactly generated Banach spaces are given.
Estimates of BMO type for singular integrals on spaces of homogeneous type and applications to hypoelliptic PDEs
Authors: Bramanti Marco , Brandolini Luca
Published: December 2011

Let us consider the class of “nonvariational uniformly hypoelliptic operators”:

Lu\equiv\sum_{i,j=1}^{q}a_{ij} (x) X_{i} X_{j} u

where:

X_1,X_2,\ldots,X_q

is a system of Hörmander vector fields in

\mathbb{R}^{n}

(

n>q

),

\{a_{ij}\}

is a

q\times q

uniformly elliptic matrix, and the functions

a_{ij} (x)

are continuous, with a suitable control on the modulus of continuity. We prove that:

\| X_{i} X_{j} u \|_{BMO(\Omega^{\prime})} \leq c \left\{\left\|Lu\right\|_{BMO(\Omega)} + \left\| u\right\|_{BMO(\Omega)} \right\}

for domains

\Omega^{\prime}\subset\subset\Omega

that are regular in a suitable sense. Moreover, the space

BMO

in the above estimate can be replaced with a scale of spaces of the kind studied by Spanne. To get this estimate, several results are proved, regarding singular and fractional integrals on general spaces of homogeneous type, in relation with function spaces of

BMO

type.
Completeness in $L^1 (\mathbb R)$ of discrete translates
Authors: Bruna Joaquim , Olevskii Alexander , Ulanovskii Alexander
Published: December 2011

We characterize, in terms of the Beurling-Malliavin density, the discrete spectra

\Lambda\subset\mathbb R

for which a generator exists, that is a function

\varphi\in L^1(\mathbb R)

such that its

\Lambda

-translates

\varphi(x-\lambda), \lambda\in\Lambda

, span

L^1(\mathbb R)

. It is shown that these spectra coincide with the uniqueness sets for certain analytic classes. We also present examples of discrete spectra

\Lambda\subset\mathbb R

which do not admit a single generator while they admit a pair of generators.
The Poisson’s problem for the Laplacian with Robin boundary condition in non-smooth domains
Authors: Lanzani Loredana , Méndez Osvaldo
Published: December 2011

Given a bounded Lipschitz domain

\Omega\subset {\mathbb R}^n

,

n\geq 3

, we prove that the Poisson's problem for the Laplacian with right-hand side in

L^p_{-t}(\Omega)

, Robin-type boundary datum in the Besov space

B^{1-1/p-t,p}_{p}(\partial \Omega)

and non-negative, non-everywhere vanishing Robin coefficient

b\in L^{n-1}(\partial \Omega)

, is uniquely solvable in the class

L^p_{2-t}(\Omega)

for

(t,\frac{1}{p})\in {\mathcal V}_{\epsilon}

, where

{\mathcal V}_{\epsilon}

(

\epsilon\geq 0

) is an open (

\Omega

,

b

)-dependent plane region and

{\mathcal V}_{0}

is to be interpreted ad the common (optimal) solvability region for all Lipschitz domains. We prove a similar regularity result for the Poisson's problem for the 3-dimensional Lamé System with traction-type Robin boundary condition. All solutions are expressed as boundary layer potentials.
Point fixe d’une application non contractante
Authors: Lemarié-Rieusset Pierre Gilles
Published: December 2011

We study a multilinear fixed-point equation in a closed ball of a Banach space where the application is

1

-Lipschitzian: existence, uniqueness, approximations, regularity.
A logarithmic Sobolev form of the Li-Yau parabolic inequality
Authors: Bakry Dominique , Ledoux Michel
Published: December 2011

We present a finite dimensional version of the logarithmic Sobolev inequality for heat kernel measures of non-negatively curved diffusion operators that contains and improves upon the Li-Yau parabolic inequality. This new inequality is of interest already in Euclidean space for the standard Gaussian measure. The result may also be seen as an extended version of the semigroup commutation properties under curvature conditions. It may be applied to reach optimal Euclidean logarithmic Sobolev inequalities in this setting. Exponential Laplace differential inequalities through the Herbst argument furthermore yield diameter bounds and dimensional estimates on the heat kernel volume of balls.
The Magic Square and Symmetric Compositions II
Authors: Elduque Alberto
Published: December 2011

The construction of Freudenthal's Magic Square, which contains the exceptional simple Lie algebras of types

F_4,E_6,E_7

and

E_8

, in terms of symmetric composition algebras is further developed here. The para-Hurwitz algebras, which form a subclass of the symmetric composition algebras, will be defined, in the split case, in terms of the natural two dimensional module for the simple Lie algebra

\mathfrak{sl}_2

. As a consequence, it will be shown how all the Lie algebras in Freudenthal's Magic Square can be constructed, in a unified way, using copies of

\mathfrak{sl}_2

and of its natural module.
Comparing homologies: Čech's theory, singular chains, integral flat chains and integral currents
Authors: De Pauw Thierry
Published: December 2011

We give a new proof of a Theorem of S. Mardešić, generalized by G. E. Bredon, that Čech and singular homology groups of certain locally connected spaces coincide. We use the chain complexes of integral flat chains (H. Whitney) and integral currents (H. Federer and W. H. Fleming) to define new homology groups of subsets of Euclidean space. We show these verify the axioms of Eilenberg and Steenrod, and we provide Lipschitz-flavored local connectedness conditions which guarantee these groups coincide with Čech's. Relations between these theories is relevant for the solvability and regularity of many geometric variational problems.
Wavelet construction of Generalized Multifractional processes
Authors: Ayache Antoine , Jaffard Stéphane , Taqqu Murad S.
Published: December 2011

We construct Generalized Multifractional Processes with Random Exponent (GMPREs). These processes, defined through a wavelet representation, are obtained by replacing the Hurst parameter of Fractional Brownian Motion by a sequence of continuous random processes. We show that these GMPREs can have the most general pointwise H#x00F6;lder exponent function possible, namely, a random H#x00F6;lder exponent which is a function of time and which can be expressed in the strong sense (almost surely for all

t

), as a

\liminf

of an arbitrary sequence of continuous processes with values in

[0,1]

.
On the Regularity Conditions for the Navier-Stokes and Related Equations
Authors: Chae Dongho
Published: December 2011

We obtain a regularity conditions for solutions of the 3D Navier-Stokes equations with fractional powers of the Laplacian, which incorporates the vorticity direction and its magnitude simultaneously. We find that regularity assumption of direction field of the vorticity compensates with the integrability condition for the magnitude of vorticity. The regularity of direction field is most naturally measured in terms of the Triebel-Lizorkin type of norms. This unifies and extends previous results in this direction of studies, where the geometric structure of the vortex stretching term is used to obtain refined regularity conditions, initiated by Constantin and Fefferman.
Integration Operators on Bergman Spaces with exponential weight
Authors: Dostanić Milutin R.
Published: December 2011

We study operators of the form

T_{g}f\left( z\right) =\int\nolimits_{0}^{z}f\left( \xi \right) \,g^{\prime }\left( \xi \right) \,d\left( \xi \right)

(

g

is an analytic function unity disc) on weighted Bergman spaces

L_{a}^{p}\left( w\right)

of the unit disc where symbol

g

is analytic function on the disc. For the case of

w(r) =\exp \Big( \frac{-a}{( 1-r)^{\beta }}\Big)\qquad \left( a>0, 0<\beta \leq 1\right)

it is shown that operator

T_{g}

is bounded (compact) on

L_{a}^{2}\left( w\right)

if and only if

\left( 1-\left\vert z\right\vert \right)^{\beta +1}\left\vert g^{\prime }\left( z\right) \right\vert =O\left( 1\right) \left( =o\left( 1\right) \right)

as

\left\vert z\right\vert \rightarrow 1-

, thus solving a problem formulated in [Aleman, A. and Siskakis, A.G.: Integration Operators on Bergman Spaces. Indiana Univ. Math. J. 46 (1997), no. 2, 337-356.].
Paraproducts with flag singularities I. A case study
Authors: Muscalu Camil
Published: December 2011

In this paper we prove

L^p

estimates for a tri-linear operator, whose symbol is given by the product of two standard symbols, satisfying the well known Marcinkiewicz-Hörmander-Mihlin condition. Our main result contains in particular the classical Coifman-Meyer theorem. This tri-linear operator is the simplest example of a large class of multi-linear operators, which we called \textit{paraproducts with flag singularities}.
The intrinsic square function
Authors: Wilson J. Michael
Published: December 2011

We show that the Lusin area function and essentially all of its real-variable generalizations are pointwise dominated by an \lq\lq intrinsic\rq\rq\ square function, and that this latter function is, for all practical purposes, no larger than a \lq\lq generic\rq\rq square function.
On uniqueness of automorphisms groups of Riemann surfaces
Authors: Leyton A. Maximiliano , Hidalgo Rubén A.
Published: December 2011

Let

\gamma, r, s

,

\geq 1

be non-negative integers. If

p

is a prime sufficiently large relative to the values

\gamma

,

r

and

s

, then a group

H

of conformal automorphisms of a closed Riemann surface

S

of order

p^{s}

so that

S/H

has signature

(\gamma,r)

is the unique such subgroup in

\mathrm{Aut}(S)

. Explicit sharp lower bounds for

p

in the case

(\gamma,r,s) \in \{(1,2,1),(0,4,1)\}

are provided. Some consequences are also derived.
Lipschitz conditions on the modulus of a harmonic function
Authors: Pavlović Miroslav
Published: December 2011

It is proved that if

u

is a real valued function harmonic in the open unit ball

\mathbb B_N\subset \mathbb R^N

and continuous on the closed ball, then the following conditions are equivalent, for

0 < \alpha < 1

:

The Lipschitz condition on

|u|^p

is also considered.
The Navier–Stokes equations in the critical Morrey–Campanato space
Authors: Lemarié-Rieusset Pierre Gilles
Published: December 2011

We shall discuss various points on solutions of the 3D Navier-Stokes equations from the point of view of Morrey-Campanato spaces (global solutions, strong-weak uniqueness, the role of real interpolation, regularity).
Littlewood-Paley-Stein theory for semigroups in UMD spaces
Authors: Hytönen Tuomas
Published: December 2011

The Littlewood-Paley theory for a symmetric diffusion semigroup

T^t

, as developed by Stein, is here generalized to deal with the tensor extensions of these operators on the Bochner spaces

L^p(\mu,X)

, where

X

is a Banach space. The

g

-functions in this situation are formulated as expectations of vector-valued stochastic integrals with respect to a Brownian motion. A two-sided

g

-function estimate is then shown to be equivalent to the UMD property of

X

. As in the classical context, such estimates are used to prove the boundedness of various operators derived from the semigroup

T^t

, such as the imaginary powers of the generator.
Strong $A_{\infty}$-weights and scaling invariant Besov capacities
Authors: Costea Șerban
Published: December 2011

This article studies strong

A_{\infty}

-weights and Besov capacities as well as their relationship to Hausdorff measures. It is shown that in the Euclidean space

{\mathbb{R}}^n

with

n\ge 2

, whenever

n-1 < s \le n

, a function

u

yields a strong

A_\infty

-weight of the form

w=e^{nu}

if the distributional gradient

\nabla u

has sufficiently small

||\cdot||_{{\mathcal L}^{s,n-s}}({\mathbb{R}}^n; {\mathbb{R}}^n)

-norm. Similarly, it is proved that if

2\le n < p < \infty

, then

w=e^{nu}

is a strong

A_\infty

-weight whenever the Besov

B_p

-seminorm

[u]_{B_p({\mathbb{R}}^n)}

of

u

is sufficiently small. Lower estimates of the Besov

B_p

-capacities are obtained in terms of the Hausdorff content associated with gauge functions

h

satisfying the condition

\int_0^1 h(t)^{p'-1} \frac{dt}{t} < \infty

.
The level 1 weight 2 case of Serre’s conjecture
Authors: Dieulefait Luis Victor
Published: December 2011

We prove Serre's conjecture for the case of Galois representations of Serre's weight

2

and level

1

. We do this by combining the potential modularity results of Taylor and lowering the level for Hilbert modular forms with a Galois descent argument, properties of universal deformation rings, and the non-existence of

p

-adic Barsotti-Tate conductor

1

Galois representations proved in [Dieulefait, L.: Existence of families of Galois representations and new cases of the Fontaine-Mazur conjecture. J. Reine Angew. Math. 577 (2004), 147-151].
A moduli approach to quadratic $\mathbb{Q}$-curves realizing projective mod $p$ Galois representations
Authors: Fernández Julio
Published: December 2011

For a fixed odd prime

p

and a representation

\varrho

of the absolute Galois group of

\mathbb{Q}

into the projective group

{\rm PGL}_2(\mathbb{F}_p)

, we provide the twisted modular curves whose rational points supply the quadratic

\mathbb{Q}

-curves of degree

N

prime to

p

that realize

\varrho

through the Galois action on their

p

-torsion modules. The modular curve to twist is either the fiber product of

X_0(N)

and

X(p)

or a certain quotient of Atkin-Lehner type, depending on the value of

N

mod

p

. For our purposes, a special care must be taken in fixing rational models for these modular curves and in studying their automorphisms. By performing some genus computations, we obtain as a by-product some finiteness results on the number of quadratic

\mathbb{Q}

-curves of a given degree

N

realizing

\varrho

.
Sums of Toeplitz products with harmonic symbols
Authors: Choe Boo Rim , Koo Hyungwoon , Lee Young Joo
Published: December 2011

On the Bergman space of the unit disk, we consider a class of operators which contain sums of finitely many Toeplitz products with harmonic symbols. We give characterizations of when an operator in that class has finite rank or is compact. Our results provide a unified way of treating several known results.
Rees algebras on smooth schemes: integral closure and higher differential operator
Authors: Villamayor U. Orlando
Published: December 2011

Let

V

be a smooth scheme over a field

k

, and let

\{I_n, n\geq 0\}

be a filtration of sheaves of ideals in

\mathcal{O}_V

, such that

I_0=\mathcal{O}_V

, and

I_s\cdot I_t\subset I_{s+t}

. In such case

\bigoplus I_n

is called a Rees algebra. A Rees algebra is said to be a differential algebra if, for any two integers

N > n

and any differential operator

D

of order

n

,

D(I_N)\subset I_{N-n}

. Any Rees algebra extends to a smallest differential algebra. There are two extensions of Rees algebras of interest in singularity theory: one defined by taking integral closures, and another by extending the algebra to a differential algebra. We study here some relations between these two extensions, with particular emphasis on the behavior of higher order differentials over arbitrary fields.
On the number of ovals of a symmetry of a compact Riemann surface
Authors: Bujalance Emilio , Cirre Francisco Javier , Gamboa José Manuel , Gromadzki Grzegorz
Published: December 2011

Let

X

be a symmetric compact Riemann surface whose full group of conformal automorphisms is cyclic. We derive a formula for counting the number of ovals of the symmetries of

X

in terms of few data of the monodromy of the covering

X\rightarrow X/G

, where

G=\mathrm{Aut}^\pm X

is the full group of conformal and anticonformal automorphisms of

X

.
Interpolation and Sampling for Generalized Bergman Spaces on finite Riemann surfaces
Authors: Schuster Alexander , Varolin Dror
Published: December 2011

We find sufficient conditions for a discrete sequence to be interpolating or sampling for certain generalized Bergman spaces on open Riemann surfaces. As in previous work of Bendtsson, Ortega-Cerdá, Seip, Wallsten and others, our conditions for interpolation and sampling are as follows: If a certain upper density of the sequence has value less that 1, then the sequence is interpolating, while if a certain lower density has value greater than 1, then the sequence is sampling. Unlike previous works, we introduce a family of densities all of which provide sufficient conditions. Thus we obtain new results even in classical cases, some of which might be useful in industrial applications. The main point of the article is to demonstrate the interaction between the potential theory of the Riemann surface and its interpolation and sampling properties.
Measure density and extendability of Sobolev functions
Authors: Hajłasz Piotr , Koskela Pekka , Tuominen Heli
Published: December 2011

We study necessary and sufficient conditions for a domain to be a Sobolev extension domain in the setting of metric measure spaces. In particular, we prove that extension domains must satisfy a measure density condition.
On the NLS dynamics for infinite energy vortex configurations on the plane
Authors: Bethuel Fabrice , Jerrard Robert L. , Smets Didier
Published: December 2011

We derive the asymptotical dynamical law for Ginzburg–Landau vortices in the plane under the Schrödinger dynamics, as the Ginzburg–Landau parameter goes to zero. The limiting law is the well-known point-vortex system. This result extends to the whole plane previous results of [Colliander, J. E. and Jerrard, R.L.: Vortex dynamics for the Ginzburg–Landau–Schrödinger equation. Internat. Math. Res. Notices 1998, no. 7, 333–358; Lin, F.-H. and Xin, J. X.: On the incompressible fluid limit and the vortex motion law of the nonlinear Schrödinger equation. Comm. Math. Phys. 200 (1999), 249–274] established for bounded domains, and holds for arbitrary degree at infinity. When this degree is non-zero, the total Ginzburg–Landau energy is infinite.
The linear fractional model on the ball
Authors: Bayart Frédéric
Published: December 2011

Given a holomorphic self-map

\varphi

of the ball of

\mathbb{C}^N

, we study whether there exists a map

\sigma

and a linear fractional transformation

A

such that

\sigma\circ\varphi=A\circ\sigma

. This is an important result when

N=1

with a great number of applications. We extend this result to the multi-dimensional setting for a large class of maps. Applications to commuting holomorphic self-maps are given.
Reflections of regular maps and Riemann surfaces
Authors: Melekoğlu Adnan , Singerman David
Published: December 2011

A compact Riemann surface of genus

g

is called an M-surface if it admits an anti-conformal involution that fixes

g+1

simple closed curves, the maximum number by Harnack's Theorem. Underlying every map on an orientable surface there is a Riemann surface and so the conclusions of Harnack's theorem still apply. Here we show that for each genus

g ϯ 1

there is a unique M-surface of genus

g

that underlies a regular map, and we prove a similar result for Riemann surfaces admitting anti-conformal involutions that fix

g

curves.
Almost classical solutions of Hamilton-Jacobi equations
Authors: Deville Robert , Jaramillo Jesús A.
Published: December 2011

We study the existence of everywhere differentiable functions which are almost everywhere solutions of quite general Hamilton-Jacobi equations on open subsets of

\mathbb R^d

or on

d

-dimensional manifolds whenever

d\geq 2

. In particular, when

M

is a Riemannian manifold, we prove the existence of a differentiable function

u

on

M

which satisfies the Eikonal equation

\Vert \nabla u(x) \Vert_{x}=1

almost everywhere on

M

.
Cyclic Blaschke products for composition operators
Authors: Gallardo-Gutiérrez Eva A. , Gorkin Pamela
Published: December 2011

In this work, cyclic Blaschke products for composition operators induced by disc automorphisms are studied. In particular, we obtain interpolating Blaschke products that are cyclic for nonelliptic automorphisms and we obtain a new characterization of Blaschke products that are not finite products of interpolating Blaschke products.
One-relator groups and proper 3-realizability
Authors: Cárdenas Manuel , Lasheras Francisco F. , Quintero Antonio , Repovš Dušan D.
Published: December 2011

How different is the universal cover of a given finite

2

-complex from a

3

-manifold (from the proper homotopy viewpoint)? Regarding this question, we recall that a finitely presented group

G

is said to be properly

3

-realizable if there exists a compact

2

-polyhedron

K

with

\pi_1(K) \cong G

whose universal cover

\tilde{K}

has the proper homotopy type of a PL

3

-manifold (with boundary). In this paper, we study the asymptotic behavior of finitely generated one-relator groups and show that those having finitely many ends are properly

3

-realizable, by describing what the fundamental pro-group looks like, showing a property of one-relator groups which is stronger than the QSF property of Brick (from the proper homotopy viewpoint) and giving an alternative proof of the fact that one-relator groups are semistable at infinity.
Gradings on the Albert algebra and on $\mathfrak{f}_4$
Authors: Draper Fontanals Cristina , Martín González Cándido
Published: December 2011

We study group gradings on the Albert algebra and on the exceptional simple Lie algebra

\frak{f}_4

over algebraically closed fields of characteristic zero. The immediate precedent of this work is [Draper, C. and Martin, C.: Gradings on

\frak{g}_2

. Linear Algebra Appl. 418 (2006), no. 1, 85-111] where we described (up to equivalence) all the gradings on the exceptional simple Lie algebra

\frak{g}_2

. In the cases of the Albert algebra and

\frak{f}_4

, we look for the nontoral gradings finding that there are only eight nontoral nonequivalent gradings on the Albert algebra (three of them being fine) and nine on

\frak{f}_4

(also three of them fine).
Asymptotic stability of solitons for the Benjamin-Ono equation
Authors: Kenig Carlos E. , Martel Yvan
Published: December 2011

In this paper, we prove the asymptotic stability of the family of solitons of the Benjamin-Ono equation in the energy space. The proof is based on a Liouville property for solutions close to the solitons for this equation, in the spirit of [Martel, Y. and Merle, F.: Asymptotic stability of solitons for subcritical generalized KdV equations. Arch. Ration. Mech. Anal. 157 (2001), 219-254], [Martel, Y. and Merle, F.: Asymptotic stability of solitons of the gKdV equations with a general nonlinearity. Math. Ann. 341 (2008), 391-427]. As a corollary of the proofs, we obtain the asymptotic stability of exact multi-solitons.
The Howe dual pair in Hermitean Clifford analysis
Authors: Brackx Fred , De Schepper Hennie , Eelbode David , Souček Vladimír
Published: December 2011

Clifford analysis offers a higher dimensional function theory studying the null solutions of the rotation invariant, vector valued, first order Dirac operator

\partial

. In the more recent branch Hermitean Clifford analysis, this rotational invariance has been broken by introducing a complex structure

J

on Euclidean space and a corresponding second Dirac operator

\partial_J

, leading to the system of equations

\partial f = 0 = \partial_J f

expressing so-called Hermitean monogenicity. The invariance of this system is reduced to the unitary group. In this paper we show that this choice of equations is fully justified. Indeed, constructing the Howe dual for the action of the unitary group on the space of all spinor valued polynomials, the generators of the resulting Lie superalgebra reveal the natural set of equations to be considered in this context, which exactly coincide with the chosen ones.
Universal objects in categories of reproducing kernels
Authors: Beltiţă Daniel , Galé José E.
Published: December 2011

We continue our earlier investigation on generalized reproducing kernels, in connection with the complex geometry of

C^*

- algebra representations, by looking at them as the objects of an appropriate category. Thus the correspondence between reproducing

(-*)

-kernels and the associated Hilbert spaces of sections of vector bundles is made into a functor. We construct reproducing

(-*)

-kernels with universality properties with respect to the operation of pull-back. We show how completely positive maps can be regarded as pull-backs of universal ones linked to the tautological bundle over the Grassmann manifold of the Hilbert space

\ell^2(\mathbb{N})

.
Tropical plane geometric constructions: a transfer technique in Tropical Geometry
Authors: Tabera Alonso Luis Felipe
Published: December 2011

The notion of geometric construction is introduced. This notion allows to compare incidence configurations both lying in the algebraic and the tropical plane. We provide sufficient conditions in a geometric construction to ensure that there is always an algebraic counterpart related by tropicalization. We also present some results to detect if this algebraic counterpart cannot exist. With these tools, geometric constructions are applied to transfer classical theorems to the tropical framework, we provide a notion of "constructible incidence theorem" and then several tropical versions of classical theorems are proved such as the converse of Pascal's, Fano's or Cayley-Bacharach theorems.
Multi-parameter Carnot-Carathéodory balls and the theorem of Frobenius
Authors: Street Brian
Published: December 2011

We study multi-parameter Carnot-Carathéodory balls, generalizing results due to Nagel, Stein and Wainger in the single parameter setting. The main technical result is seen as a uniform version of the theorem of Frobenius. In addition, we study maximal functions associated to certain multi-parameter families of Carnot-Carathéodory balls.
Sub-Riemannian geometry of parallelizable spheres
Authors: Godoy Molina Mauricio , Markina Irina
Published: December 2011

The first aim of the present paper is to compare various sub-Riemannian structures over the three dimensional sphere

S^3

originating from different constructions. Namely, we describe the sub-Riemannian geometry of

S^3

arising through its right action as a Lie group over itself, the one inherited from the natural complex structure of the open unit ball in

\mathbb{C}^2

and the geometry that appears when it is considered as a principal

S^1

-bundle via the Hopf map. The main result of this comparison is that in fact those three structures coincide. We present two bracket generating distributions for the seven dimensional sphere

S^7

of step 2 with ranks 6 and 4. The second one yields to a sub-Riemannian structure for

S^7

that is not widely present in the literature until now. One of the distributions can be obtained by considering the CR geometry of

S^7

inherited from the natural complex structure of the open unit ball in

\mathbb{C}^4

. The other one originates from the quaternionic analogous of the Hopf map.
Commercial Products That Convey Personal Health Information in Emergencies
Authors: Potini Vishnu C. , Weerasuriya Dilani N. , Lowery-North Douglas W. , Kellermann Arthur L.
Published: December 2011

Objective: Describe commercially available products and services designed to convey personal health information in emergencies.

Methods: The search engine Google®, supplemented by print ads, was used to identify companies and organizations that offer relevant products and services to the general market. Disease-specific, health system, and health plan-specific offerings were excluded. Vendor web sites were the primary sources of information, supplemented by telephone and e-mail queries to sales representatives. Perfect inter-rater agreement was achieved.

Results: Thirty-nine unique vendors were identified. Eight sell engraved jewelry. Three offer an embossed card or pamphlet. Twelve supply USB drives with various features. Eleven support password-protected web sites. Five maintain national call centers. Available media differed markedly with respect to capacity and accessibility. Quoted prices ranged from a one-time expenditure of $3.50 to an annual fee of $200. Associated features and annual fees varied widely.

Conclusion: A wide range of products and services exist to help patients convey personal health information. Health care providers should be familiar with their features, so they can access the information in a disaster or emergency.

(Disaster Med Public Health Preparedness. 2011;5:261–265)
Symptoms of Anxiety, Depression, and Posttraumatic Stress Among Survivors of the 2005 Pakistani Earthquake
Authors: Hashmi Shahrukh , Petraro Paul , Rizzo Tara , Nawaz Hafsa , Choudhary Rabeea , Tessier-Sherman Baylah , Kasl Stanislav , Nawaz Haq
Published: December 2011

Objectives: To assess and compare the prevalence of psychological morbidity among survivors of the 2005 northern Pakistan earthquake from Azad Kashmir and the Northwest Frontier Province (NWFP).

Methods: We conducted a cross-sectional study among randomly sampled survivors (N = 361) of the earthquake living in camps at the time of the interview, approximately 6 months after the earthquake.

Results: The prevalence of posttraumatic stress disorder (PTSD) symptoms in the total sample was 51.5% and the prevalence of individuals who received positive scores on the Hopkins Symptom Checklist (HSCL) was 75%. The prevalence rates for anxiety and depression symptoms were 77.3% and 70.9%, respectively. The prevalence in Azad Kashmir was 57.9% for PTSD and 79.8% for positive HSCL, and NWFP had 41.3% PTSD and 67.4% positive HSCL. Study subjects from Azad Kashmir were approximately 2 times as likely to have PTSD or a positive HSCL when compared to subjects from NWFP (odds ratio 1.95, confidence interval 1.27-3.0; P = .0024) and (odds ratio 1.91, confidence interval 1.18-3.1; P = .0085), respectively.

Conclusions: Nearly half of the northern Pakistan earthquake survivors had symptoms of PTSD. Six months after the incident, more than three-fourths exhibited symptoms of an anxiety disorder.

(Disaster Med Public Health Preparedness. 2011;5:293–299)
In Vitro Opioid Receptor Assays
Authors: Taylor David A.
Published: December 2011

Although opioid analgesics have been used for centuries, identification of opioid receptors and the ability of an opioid receptor antagonist to block natural pain processes prompted a search for endogenous opioid peptides. In vitro models were needed to characterize opioid activity in biological samples. The longitudinal muscle/myenteric plexus (LM/MP) of the guinea pig ileum was the classical in vitro assay system, but the development of the mouse vas deferens (MVD) assay provided another important model that could be employed. Both assays entail electrical stimulation of intramural nerves to produce muscle contractions of the target organ. The robust contractions of the LM/MP are inhibited by µ and κ opioid receptor agonists, while the more labile contractions of the MVD are inhibited by µ, κ, and δ opioid receptor agonists. These in vitro assay systems are useful for evaluating biological activity of unknown substances and studying the properties of drug tolerance and both are described in this unit. Curr. Protoc. Pharmacol. 55:4.8.1‐4.8.34. © 2011 by John Wiley & Sons, Inc.
Liquid Chromatography‐Mass Spectrometry Analysis of DNA Polymerase Reaction Products
Authors: Chowdhury Goutam , Guengerich F. Peter
Published: December 2011

This unit describes experimental and analytical procedures for characterizing the efficiency and fidelity of translesion DNA synthesis across various DNA damages by DNA polymerases in vitro. This procedure utilizes primer extension assays followed by LC‐MS and LC‐MS/MS analysis of the extension products. Detailed explanations for the analysis of the LC‐MS/MS data for deciphering the nucleotide sequences of the DNA fragments are also presented. This approach provides a significant improvement over conventional methods, as it allows detection of misincorporation, as well as frameshift products. Curr. Protoc. Nucleic Acid Chem. 47:7.16.1‐7.16.11. © 2011 by John Wiley & Sons, Inc.
Imaging efficiency of an X‐ray contrast agent‐incorporated polymeric microparticle
Authors: Ahn Sungsook , Jung Sung Yong , Lee Jin Pyung , Lee Sang Joon
Published: December 2011

Biocompatible polymeric encapsulants have been widely used as a delivery vehicle for a variety of drugs and imaging agents. In this study, X‐ray contrast agent (iopamidol) is encapsulated into a polymeric microparticle (polyvinyl alcohol) as a particulate flow tracer in synchrotron X‐ray imaging system. The physical properties of the designed microparticles are investigated and correlated with enhancement in the imaging efficiency by experimental observation and theoretical interpretation. The X‐ray absorption ability of the designed microparticle is assessed by Beer–Lambert–Bouguer law. Particle size, either in dried state or in solvent, primarily dominates the X‐ray absorption ability under the given condition, thus affecting imaging efficiency of the designed X‐ray contrast flow tracers. Copyright © 2011 John Wiley & Sons, Ltd.
Preferential Crystallization of a Helicene–Viologen Hybrid – An Efficient Method to Resolve [5]Helquat Enantiomers on a 20 g Scale
Authors: Vávra Jan , Severa Lukáš , Švec Pavel , Císařová Ivana , Koval Dušan , Sázelová Petra , Kašička Václav , Teplý Filip
Published: December 2011

The bistriflate salt of racemic [5]helquat 1 was found to form a conglomerate. Based on this finding, the preferential crystallization of this chiral helicene–viologen hybrid was developed to deliver pure enantiomers on a 20 g scale (10.5 g of each enantiomer). To the best of our knowledge, this is the largest amount of nonracemic helicene‐like compound obtained by preferential crystallization to date. The absolute configuration of the P enantiomer was confirmed by X‐ray crystal structure analysis. The chromatography‐free synthesis of racemic 1 on a multigram scale (30 g) is also presented as an entry point to this resolution study.
Phase and amplitude error indices for error quantification in pseudodynamic testing
Authors: Hessabi Reza Mirza , Mercan Oya
Published: December 2011

Real‐time pseudodynamic (PSD) and hybrid PSD testing methods are displacement controlled experimental techniques that are used to investigate the dynamic behaviour of complex and load rate‐dependent structures. Because the imposed command displacements are not predefined but generated during the test based on measured feedback, these methods are inherently prone to error propagation, which can affect the accuracy and even the stability of the entire experiment. As a result, to have these experimental methods as reliable tools, the accuracy of the test results needs to be assessed by carefully monitoring, and if possible, quantifying the errors involved. In this paper, phase and amplitude error indices (PAEI) are introduced to identify the experimental errors through uncoupled closed‐form equations. Unlike the indicators that have been previously introduced in the literature for error identification purposes, PAEI do not use test setup specific parameters in their formulation, and can quantify the errors independent of the amplitude of the command displacements. As such, PAEI can be used as standard tools for assessing the quality of the experiments performed in different laboratories or under different conditions. Additionally, because they can quantify the error, when implemented online, PAEI have the potential to be incorporated in the control law and thereby improve the actuator control during the tests. The formulation and implementation of PAEI are provided in this paper. The enhanced performance of the proposed indices is demonstrated by processing several different measured and command signals using PAEI and comparing the results with those revealed by the previous indicators. Copyright © 2011 John Wiley & Sons, Ltd.
How Popular Culture Texts Inform and Shape Students’ Discussions of Social Studies Texts
Authors: Hall Leigh A.
Published: December 2011

In this article, I examine how 6th‐grade students used pop culture texts to inform their understandings about social studies texts and shape their discussions of it. Discussions showed that students used pop culture texts in three ways when talking about social studies texts. First, students applied comprehension strategies to pop culture texts to help them interpret social studies texts. Second, students used pop culture texts as evidence to support their arguments about social studies texts. Finally, students used pop culture texts to shut down interpretations of social studies texts that they did not agree with and silence students who expressed alternative ideas.
Adult Learners’ Funds of Knowledge: The Case of an English Class for Parents
Authors: Larrotta Clarena , Serrano Arlene
Published: December 2011

This research is rooted in an approach that sees English learning and teaching as practices shaped by adults’ funds of knowledge and adult‐learning principles. We investigate how English‐literacy instruction can build on the funds of knowledge (life experiences, knowledge, skills, and learning habits) that adult learners bring with them. In addition, we explore how personal glossaries and storybooks help adults in their language‐learning journey. Data for the study were collected through field notes, interviews, and student products (personal glossaries and storybooks). Study participants are Spanish‐speaking adults enrolled in an English literacy class for parents. Participating adults’ funds of knowledge are identified and recommendations relevant for English‐literacy instructors are provided.
Putting service back into public service: The transformation of Botswana's immigration services
Authors: Hacker Stephen K. , Tsiane Segakweng N.
Published: December 2011

Poor customer service at Botswana's Department of Immigration and Citizenship placed its home ministry, Labour and Home Affairs, in the bottom tier of performance rankings and made it a frequent target of criticism. After identifying the root causes of the breakdown in service, the department's leaders used a transformational approach to sharply improve customer relations. Its key elements were a focus on the organization's quality culture, management intervention, on‐site improvement projects, and nontraditional engagements with staff. The awards and testimonials that followed demonstrate that a government organization that concentrates on improving the service‐mindedness of its staff can make rapid, profound, and sustainable gains in the delivery of customer service. © 2012 Wiley Periodicals, Inc.