bluuebunny/crossref_metadata_2025 huggingface dataset:
Orthogonal Projection and Restricted Subordination of Hubert-Schmidt Operator-Valued Stationary Processes
Authors: Klotz L.
Published: September 2013

The paper contains two results on subordination of stationarily correlated Hilbert-Schmidt operator-valued stationary processes. First an explicit form of the spectral measure of the orthogonal projection of one process onto another is stated. On the basis of this result B. Fritzsche’s and B. Kirstein’s solution of the restricted subordination problem for finite-dimensional processes is generalized to Hilbert-Schmidt operator-valued processes.
Regularity Properties and Generalized Inverses of Delta-Related Operators
Authors: Castro L. P. , Speck Frank-Olme
Published: September 2013

As a central topic certain relations between operator matrices are investigated which are called delta relations. The main aim of these relations is to reduce questions about classes of operators without invertibility symbol to those which admit an invertibility symbol. Particular attention is devoted to the generalized inversion of such operators. Different kinds of relations are introduced in order to analyze the "information" contained in the symbols of the related operators. Several examples are considered and the theory is also applied to singular integral operators with Carleman shift. Asymptotic solutions of equations characterized by those operators are presented. The approach simplifies several known results, makes the theory more rigorous from the operator theoretic point of view, and allows further conclusions in a very compact form.
The Stokes System in Domains with Outlets of Bounded and Connected Cross-Sections
Authors: Passerini A. , Thäter G.
Published: September 2013

The Stokes system with prescribed fluxes is investigated. By smoothness assumptions on the boundary and by the boundedness of the diameters of the outlets it is ensured that the divergence equation in each bounded subdomain is solvable, the Poincaré inequality is valid and the constants in all the corresponding estimates are bounded

independently of the location

. We derive existence, uniqueness and regularity results in two different frameworks: On one hand we use weighted function spaces generated by

L^q

-norms,

1 < q < \infty

, where the weight is of exponential type and apply a technique of Maz’ya and Plamenevskii. On the other hand we use local spaces, since in order to solve the problem with non-zero flux it seems to us that to formulate results in local spaces is more adequate and physical senseful.
On Two-Point Right Focal Eigenvalue Problems
Authors: Wong Patricia J.Y. , Agarwal R.P.
Published: September 2013

We consider the boundary value problem

(–1)^{n–p}y^{(n} = \lambda F(t, y, y', \dots, y^{(p)} \ \ \ (n ≥ 2, t \in (0,1))

y^{(i)} (0) = 0 \ \ \ (0 ≤ i ≤ p–1)

y^{(i)} (1) = 0 \ \ \ (p ≤ i ≤ n–1)

where

\lambda > 0

and

1 ≤ p ≤ n–1

are fixed. The values of

\lambda

are characterized so that the boundary value problem has a positive solution. We also establish explicit intervals of

\lambda

. Examples are included to dwell upon the importance of the results obtained.
Semi-Infinite Transportation Problems
Authors: Voigt H.
Published: September 2013

An old set partitioning problem is treated as a special case of the Kantorovic-Monge transportation problem. This problem is then related to Klötzler’s transportation flow problems which allow the consideration of a local cost rate, instead of the constant cost rate in the Kantorovic-Monge problem. Three possibilities for the; numerical solution of the problem are discussed and briefly compared.
Finite Chainability, Locally Lipschitzian and Uniformly Continuous Functions
Authors: Marino G. , Lewicki Grzegorz , Pietramala P.
Published: September 2013

We present a notion of a finitely chainable subset of a metric space

X

. We show that

Y

is a finitely chainable subset of

X

if and only if

f(Y)

is a bounded subset of

\mathbb R

for any uniformly locally Lipschitzian or uniformly continuous real-valued function

f

on

X

. As a corollary we reprove the Atsuji theorem in a slightly stronger form.
Orlicz-Pettis Theorems for Multiplier Convergent Series
Authors: Swartz C. , Stuart C.
Published: September 2013

Orlicz-Pettis theorems have been established for multiplier convergent series where the multipliers come from

c_0

or

l^p (0 < p < \infty)

. We show that these results as well as the classical Orlicz-Pettis theorem are corollaries of a general result based on the fact that all of these multiplier spaces have the canonical unit vectors as a Schauder basis.
On Inequalities of Friedrichs and Babuska-Aziz in Dimension Three
Authors: Velte W.
Published: September 2013

1983, Horgan and Payne have published a paper entitled "On inequalities of Korn, Friedrichs and Babuska-Aziz". In that paper the two authors have proven a simple relation between the optimal constants occuring in the three inequalities under consideration. The analysis there is restricted to inequalities for functions of two variables only. In the present paper we will show that the results of Horgan and Payne concerning two of the inequalities have a counterpart in dimension three where, however, the situation is different in some aspects.
Uniqueness Results for the Full Frémond Model of Shape Memory Alloys
Authors: Chemetov Nikolai
Published: September 2013

In the paper we show two uniqueness results for problems related to the thermo-mechanical model proposed by Frémond, which describes the structural phase transitions in the shape memory alloys.
On Some Uniform Convexities and Smoothness in Certain Sequence Spaces
Authors: Cui Yunan , Hudzik Henryk , Pluciennik Ryszard
Published: September 2013

It is proved that any Banach space

X

with property

A^e_2

has property

A_2

and that a Banach space

X

is nearly uniformly smooth if and only if it is nearly uniformly *- smooth and weakly sequentially complete. It is shown that if

X

is a Köthe sequence space the dual of which contains no isomorphic copy of

l_1

and has property

A^e_2

, then

X

has the uniform Kadec-Klee property. Criteria for nearly uniformly convexity of Musielak-Orlicz spaces equipped with the Orlicz norm are presented. It is also proved that both properties nearly uniformly smoothness and nearly uniformly convexity for Musielak-Orlicz spaces equipped with the Luxemburg norm coincide with reflexivity. Finally, an interpretation of those results for Nakano spaces

l^{(p_i)} (1 < p_i < \infty)

is given.
Fourier Multipliers for Besicovitch Spaces
Authors: Grande R.
Published: September 2013

In this paper a generalization of some results from Fourier analysis on periodic function spaces to the almost periodic case is given. We consider almost periodic distributions which constitute a subclass of tempered distributions. Under suitable conditions on the spectrum

\Lambda \subset \mathbb R^s

, a distribution

T \in S'(\mathbb R^s)

is almost periodic if it can be represented as

\sum_{\lambda \in \Lambda} a_{\lambda} e^{i \lambda x}

, where the sequence

(a_{\lambda})_{\lambda \in \Lambda}

is tempered. The main result states that any Fourier multipliers for

L^q(\mathbb R^s)

of the Michlin-Hörmander type is also a Fourier multiplier for the Besicovich spaces

B^q_{ap} (\mathbb R^s, \Lambda)

, if it is restricted to the spectrum

\Lambda

. Finally, we prove that the Sobolev-Besicovich spaces

H^{N,q}_{sp} (\mathbb R^s, \Lambda)

coincide if

N \in \mathbb N

.
Balls in Constrained Urns and Cantor-Like Sets
Authors: Wirsching Günther J.
Published: September 2013

Let

A_n(k)

denote the number of different ways to distribute

k

indistinguishable balls into

n

constrained urns, with capacities

c_1,\cdots, c_n

. We consider the

normalized \ counting \ functions \ \varphi_n(x) = \gamma_nA_n(|\varrho x|)

, where

\varphi_n, \varrho_n > 0

are appropriate constants such that supp

(\varphi_n) = [0,1]

and

\int^1_0 \varphi_n (x)dx = 1

. It is shown here that, if

(c_n)_{n \in \mathbb N}

is

asymptotically \ geometric \ with \ weight \ q > \frac{3}{2}

, i.e. if

q^{–n}c_n

converges to some positive real number, then the functions

\varphi_n

converge to some

C^{\infty}

-function

\varphi

on

\mathbb R

. This function

\varphi

is the unique solution of the integral equation

\varphi(x) = \frac{q}{q–1} \int^{qx}{qx–q+1} \varphi (t)dt

satisfying supp

\varphi \in [0,1]

and

\int^1_0 \varphi(t)dt = 1

. Moreover, if

q > 2

, it is shown that

\varphi

is a polynomial on each interval outside a Cantor-like set in the interval [0, 1].
Domain Identification for a Nonlinear Elliptic Equation
Authors: Trong Dang Duc
Published: September 2013

It is proposed to identify the domain

\Omega \in \mathbb R^n

of a nonlinear elliptic equation subject to given Cauchy data on part of the known outer boundary

\Gamma

and to the zero condition on the unknown inner boundary

\gamma

. It is proved that under the assumption

\dot{\bar{\Omega}} = \Omega

, the domain

\Omega

is uniquely determined.
A Note on Convergence of Level Sets
Authors: Camilli Fabio
Published: September 2013

Given a sequence of functions

f_n

converging in some topology to a function

f

, in general the 0-level set of

f_n

does not give a good approximation of the one of

g

. In this paper we show that, if we consider an appropriate perturbation of the 0-level set of

f_n

, we get a sequence of sets converging to the 0-level set of

f

, where the type of set convergence depends on the type of convergence of

f_n

to

f

.
On Restriction Properties of Multiplication Operators
Authors: Plichko A. , Shevchik V.
Published: September 2013

A multiplication operator

A

acting in a rearrangement-invariant function space

E

is considered. Infinite dimensional subspaces

X

of

E

for which the restriction

A|X

is an isomorphism are described. Applications to multiplied trigonometric sequences in Banach function spaces are given.
On Evolution Equations for Moving Domains
Authors: Prokert Georg
Published: September 2013

We introduce a general framework for the description of the autonomous motion of closed surfaces which are diffeomorphic images of spheres. The governing surface motion laws are in general nonlocal and lead therefore to nonlocal evolution equations for a perturbation function on a fixed reference domain. Although this evolution equation is fully nonlinear, the invariance of the problem with respect to a certain class of reparametrizations and the corresponding chain rule allow a quasilinearization of the evolution equation. Hence, as far as short-time existence and uniqueness of the solution and stability of equilibria are concerned, the analysis of the problems is reduced to the study of their linearizations and the application of known techniques for quasilinear Cauchy problems. Using a priori estimates and Galerkin approximations in Sobolev spaces, both parabolic and first-order hyperbolic equations can be treated. In the case of parabolic problems, the smoothing property of the evolution can be proved.This general approach can be applied to a broad class of moving boundary problems. We will briefly discuss lIele-Shaw flow and Stokes flow driven by surface tension as well as classical Hele-Shaw flow with advancing liquid boundary as examples for parabolic evolutions.
Global Solution of Optimal Shape Design Problems
Authors: Fakharzadeh A. , Rubio J.E.
Published: September 2013

We consider optimal shape design problems defined by pairs of geometrical elements and control functions associated with linear or nonlinear elliptic equations. First, necessary conditions are illustrated in a variational form. Then by applying an embedding process, the problem is extended into a measure-theoretical one, which has some advantages. The theory suggests the development of a computational method consisting of the solution of a finite-dimensional linear programming problem. Nearly optimal shapes and related controls can thus be constructed. Two examples are also given.
Blow-Up in a Modified Constantin-Lax-Majda Model for the Vorticity Equation
Authors: Wegert Elias , Vasudeva Murthy A. S.
Published: September 2013

We propose a one-dimensional model for the vorticity equation involving viscos-ity. Complex methods are utilzed in order to study finite time blow-up of the solutions. In particular, it is shown that the blow-up time depends monotoneously on the viscosity.
Approximation of Levy-Feller Diffusion by Random Walk
Authors: Gorenflo Rudolf , Mainardi F.
Published: September 2013

After an outline of W. Feller’s inversion of the (later so called) Feller potential operators and the presentation of the semigroups thus generated, we interpret the two-level difference scheme resulting from the Grünwald-Letnikov discretization of fractional derivatives as a random walk model discrete in space and time. We show that by properly scaled transition to vanishing space and time steps this model converges to the continuous Markov process that we view as a generalized diffusion process. By re-interpretation of the proof we get a discrete probability distribution that lies in the domain of attraction of the corresponding stable Levy distribution. By letting only the time-step tend to zero we get a random walk model discrete in space but continuous in time. Finally, we present a random walk model for the time-parametrized Cauchy probability density.
Nonlinear Equations with Operators Satisfying Generalized Lipschitz Conditions in Scales
Authors: Janno Jaan
Published: September 2013

By means of the contraction principle we prove existence, uniqueness and stability of solutions for nonlinear equations

u + G_0[D, tL] + L(G_1 [D, u], G2[D, u]) = f

in a Banach space

E

, where

G_0, G_1 , G_2

satisfy Lipschitz conditions in scales of norms,

L

is a bilinear operator and

D

is a data parameter. The theory is applicable for inverse problems of memory identification and generalized convolution equations of the second kind.
Initial Dirichlet Problem for Half-Plane Diffraction: Global Formulae for its Generalized Eigenfunctions, Explicit Solution by the Cagniard-de Hoop Method
Authors: Meister E. , Rottbrand K.
Published: September 2013

This paper deals with time-dependent plane wave diffraction by a soft/soft Sommerfeld half-plane

\sum : x > 0, y = ±0

. The explicit solution is obtained as a time-convolution in two ways: The first is directly applying the Cagniard de Hoop method to the generalized Wiener-Hopf solution of the corresponding stationary problem due to Meister & Speck (1989). The second way makes use of the Laplace integral representation of the generalized eigenfunctions with respect to the spatial (Cartesian) variables derived by Ali Mehmeti in his habilitation thesis (1995) from formulae of Meister (1983). After deforming the path of.integration into the semi-infinte branch cut lines of the characteristic square root

\sqrt{\xi^2-k^2}

of the Helmholtzian, he obtains representations where real wave numbers may appear. But for convergence of the integrals one has to distinguish the cases

x ≥ 0

and

x < 0

, where the obstacle is present or not. We set the time Laplace variable

s = –ik

and recover the time domain functions for the diffracted field from the eigenfunctions of the stationary problem. There follows a global formula representation with polar coordinates having the diffracting edge of

\sum

as its center. The solution of the initial boundary value problem is seen to coincide with that obtained in the first way, indeed.
Property C for Ordinary Differential Equations and Applications to Inverse Scattering
Authors: Ramm A.G.
Published: September 2013

Property C, that is, completeness of the set of products of some solutions to Sturm-Liouville equations is proved. Several uniqueness theorems for various inverse scattering prob-lems are obtained in a very simple way with the help of property C. Two classical uniqueness results for inverse scattering problem on the half-axis and for the inverse spectral problem are proved in a very short new way. Earlier the author introduced property C for partial differential equations and used it extensively for proving uniqueness theorems for many inverse problems.
A Characterization of a Two-Weight Inequality for Discrete Two-Dimensional Hardy Operators
Authors: Rakotondratsimba Y.
Published: September 2013

We obtain a characterization of non-negative double sequences

V = V(n_1, n_2))_{n_1, n_2}

and

U = (U(n_1 ,n_2))_{n_1,n_2}

for which the two-dimensional discrete Hardy operator

\mathbb H

is bounded from

l^p(V)

into

l^q(U)

whenever

1 < p ≤ q < \infty

.
Existence Theorems for Boundary Value Problems for Strongly Nonlinear Elliptic Systems
Authors: Nguyen Hong Thai
Published: September 2013

Let

L

be a linear elliptic, a pseudomonotone or a generalized monotone operator (in the sense of F. E. Browder and I. V. Skrypnik), and let

F

be the nonlinear Nemytskij superposition operator generated by a vector-valued function

f

. We give two general existence theorems for solutions of boundary value problems for the equation

Lx = Fx

. These theorems are based on a new functional-theoretic approach to the pair

(L, F)

, on the one hand, and on recent results on the operator

F

, on the other hand. We treat the above mentioned problems in the case of strong non-linearity

F

, i.e. in the case of lack of compactness of the operator

L - F

. In particular, we do not impose the usual growth conditions on the nonlinear function

f

; this allows us to treat elliptic systems with rapidly growing coefficients or exponential non-linearities. Concerning solutions, we consider existence in the classical weak sense, in the so-called

L_{\infty}

-weakened sense in both Sobolev and Sobolev-Orlicz spaces, and in a generalized weak sense in Sobolev-type spaces which are modelled by means of Banach

L_{\infty}

-modules. Finally, we illustrate the abstract results by some applied problems occuring in nonlinear mechanics.
On Axially Symmetric Flows in $mathbb R^3$
Authors: Leonardi S. , Málek Josef , Nečas Jindřich , Pokorný Milan
Published: September 2013

We prove in a simpler as ususal way global-in-time existence of regular solutions to three-dimensional Navier-Stokes equations under the assumption that the flow is axially symmetric.
A Compactness Criterion of Mixed Krasnoselskii-Riesz Type in Regular ideal Spaces of Vector Functions
Authors: Väth Martin
Published: September 2013

We present a compactness criterion in ideal spaces of vector-valued functions. In the case of real functions, the criterion gives a precise formula for the measure of non-compactness. In the Lebesgue-Bochner spaces

L_p(\mathbb R^n, U)

the result can be interpreted as a Riesz compactness criterion and generalizes a theorem of Orlicz and Szufla.
On Some Dimension Problems for Self-Affine Fractals
Authors: Bernardi M.P. , Bondioli C.
Published: September 2013

We deal with self-affine fractals in

\mathbb R^2

. We examine the notion of affine dimension of a fractal proposed in [26]. To this end, we introduce a generalized affine Hausdorif dimension related to a family of Borel sets. Among other results, we prove that for a suitable class of self-affine fractals (which includes all the so-called general Sierpiñski carpets), under the "open set condition", the affine dimension of the fractal coincides - up to a constant - not only with its Hausdorif dimension arising from a non-isotropic distance

D_{\theta}

in

\mathbb R^2

, but also with the generalized affine Hausdorff dimension related to the family of all balls in

(\mathbb R^2, D{\theta})

. We conclude the paper with a comparison between this assertion and results already known in the literature.
Global Bifurcation Results for a Semilinear Biharmonic Equation on all of $\mathbb R^N$
Authors: Stavrakakis N.M. , Zographopoulos N.
Published: September 2013

We prove existence of positive solutions for the semilinear problem

(–\Delta)^2u = \lambda g(x)f(u), \ \ \ u(x) > 0 \ (x \in \mathbb R^N), \ \ \ \mathrm {lim}_{|x| \to +\infty} u(x) = 0

under the main hypothesis

N > 4

and

g \in L^{N/4}(\mathbb R^N)

. First, we employ classical spectral analysis for the existence of a simple positive principal cigenvalue for the linearized problem. Next, we prove the existence of a global continuum of positive solutions for the problem above, branching out from the first eigenvalue of the differential equation in the case that

f(u) = u

. This fact is achieved by applying standard local and global bifurcation theory. It was possible to carry out these methods by working between certain equivalent weighted and homogeneous Sobolev spaces.
Some Inequalities of the Incomplete Gamma and Related Functions
Authors: Qi Feng , Mei Jia-Qiang
Published: September 2013

In the article, many inequalities of the integrals

\int^{\infty}_x e^{–t^p} dt, \ \ \ \int^x_0 e^{–t^p}, \ \ \ \int^x_0 e^{t^p} dt

for

p > 0

, which are related to the incomplete gamma function, are established. The approach used in the paper could yield more particular inequalities of the above functions. Some known results are generalized, extended or refined.
Spatial Riemann Problem for Analytic Functions of Two Complex Variables
Authors: Begehr Heinrich , Dai D.Q.
Published: September 2013

The Riemann boundary value problem is discussed for analytic functions in poly-discs. Necessary and sufficient conditions for the existence of a finite number of solutions and a finite number of solvability conditions are derived.
On Direct Decomposition of the Space $\mathcal L_p(\Omega)$
Authors: Kähler Uwe
Published: September 2013

A direct decomposition of the space

\mathcal L_p(\Omega)

is obtained as a generalization of the orthogonal decomposition of the space

\mathcal L_2(\Omega)

, where one of the subspaces is the space of all monogenic

\mathcal L_p

-functions. Basic results about the orthogonal decomposition are carried over to this more general context. In the end a boundary value problem of the Stokes equations will be studied by a method based on this direct decomposition.
Acoustics of a Stratified Poroelastic Composite
Authors: Gilbert Robert P. , Panchenko Alexander
Published: September 2013

In this paper we discuss the acoustic boundary layer problem for a poroelastic seabed abutting onto a liquid half space. The problem is addressed using the method of homogenization where the microscopic equations are modelled after Burridge and Keller [5], Levy [10], and Panasenko [13]. A difference in our approach is that we do not consider the viscosity coefficients to be dependent on the pore size. To achieve continuity of displacement and stress at the interface to an arbitrary asymptotic order, we introduce correctors of two different types on each side. Then correctors of different types are matched across the interface.
A Real Inversion Formula for the Laplace Transform in a Sobolev Space
Authors: Amano Kazuo , Saitoh S. , Syarif A.
Published: September 2013

For the real-valued Sobolev-Hilbert space on

(0, \infty)

comprising absolutely continuous functions

F = F(t)

normalized by

F(0) = 0

and equipped with the inner product

(F_1, F_2) = \int^{\infty}_0 (F_1(t)F_2(t) + F'_1(t)F'_2(t))dt

we shall establish a real inversion formula for the Laplace transform.
Representation Formulas for Non-Symmetric Dirichlet Forms
Authors: Mataloni S.
Published: September 2013

As well-known, for

X

a given locally compact separable Hausdorff space,

m

a positive Radon measure on

X

with supp[

m

] =

X

and

C_0(X)

the space of all continuous functions with compact support on

X

the Beurling and Deny formula states that any regular Dirichlet form

(\bar{\mathcal E}, D(\bar{\mathcal E}))

on

L^2(X,m)

can be expressed as

\bar{\mathcal E} (u, v) = \bar{\mathcal E}^c (u,v) + \int_X uvk(dx) + \iint_{XxX–d} (u(x) - u(y))((v(x) - v(y))j(dx,dy)

for all

u,v \in D(\bar{\mathcal E} \cap C_0 (X)

where the symmetric Dirichiet form

\bar{\mathcal E}^c

, the symmetric measure

j(dx,dy)

and the measure

k(dx)

are uniquely determined by

\bar{\mathcal E}

. It is our aim to prove this formula in the non-symmetric case. For this we consider certain families of non-symmetric Dirichlet forms of diffusion type and show that these forms admit an integral representation involving a measure that enjoys some important functional properties as well as in the symmetric case.
Potential Type Operators on Curves with Vorticity Points
Authors: Rabinovich Vladimir S.
Published: September 2013

We study potential type operators on certain non-Lipschitz curves

\Gamma

. The curves under consideration are locally Lyapunov except for a finite set

F

of singular points. The normal vector

v(y)

to the curve

\Gamma

does not have a limit at the singular points and, moreover,

v(y)

may be an oscillating and rotating vector function in a neighborhood of the singular points. We establish a Fredholm theory of potential type operators in the spaces

L_{p,w} (\Gamma, \mathbb C^n)

where

p \in (1, \infty)

and

w

is a weight satisfying the Muckenhoupt condition.
A Kneser-Type Theorem for the Equation $x^{(m)} = f(t,x)$ in Locally Convex Spaces
Authors: Szukala A.
Published: September 2013

We shall give sufficient conditions for the existence of solutions of the Cauchy problem for the equation

x^{(m)} = f(t,x)

. We also prove that the set of these solutions is a continuum.
Geometry of Numerical Ranges in Locally $m$-Convex *-Algebras
Authors: Chryssakis Th.
Published: September 2013

In this paper we examine the symmetry of numerical ranges in a unital locally

m

-convex

C*

- algebra of a given element and its adjoint, with respect to a rotated real-axis, where the rotation angle depends on the value of the positive linear forms of the algebra (states) at the unit clement of the algebra.
Topological Structure of Solution Sets to Multi-Valued Asymptotic Problems
Authors: Andres J. , Gabor G. , Gorniewicz L.
Published: September 2013

Acydicity of solution sets-to asymptotic problems, when the value is prescribed either at the origin or at infinity, is proved for differential inclusions and discontinuous au-tonomous differential inclusions. Existence criteria showing that such sets are non-empty are obtained as well.
Monotonicity of the Number of Passages in Linear Chains and of the Basic Reproduction Number in Epidemic Models
Authors: Müller J. , Hadeler K.P.
Published: September 2013

models for infectious diseases, the basic reproduction number is the crucial parameter which determines the possibility of an outbreak. In simple situations it depends in a monotone way on the infectivity. Non-monotone behavior may occur in diseases where infectivity depends on time since infection and where transmission depends on social structure, as is shown by an example. A typical application is the HIV infection where transmission rates depend on existing pair bonds and infectivity changes drastically over time.For a class of epidemic models with pair formation models and infectivity depending on time since infection it is shown that the basic reproduction number is a monotone function of infectivity. This observation is a consequence of a general result on a class of cyclic linear reaction chains with tridiagonal structure for which it is shown that the number of passages depends in a monotone way on the rates.
Relaxation for Dirichlet Problems Involving a Dirichlet Form
Authors: Biroli Marco , Tchou N.
Published: September 2013

For a fixed Dirichlet form, we study the space of positive Borel measures (possibly infinite) which do not charge polar sets. We prove the density in this space of the set of the measures which represent varying, domains. Our method is constructive. For the Laplace operator, the proof was based on a pavage of the space. Here, we substitute this notion by that of

homogeneous covering

in the sense of Coiffman and Weiss.
De Rham’s Singular Function and Related Functions
Authors: Berg Lothar , Krüppel Manfred
Published: September 2013

For de Rham’s singular function we derive new properties, in particular some for-mulas which express its self-similarity. Inversions and compositions of de Rham’s function are considered as well as generalizations of de Rham’s functional equations which have a connection to the

(3n+1

)-iteration of Collatz.
Extension of the Bernstein Condition to Systems of Ordinary Differential Equations of General Form
Authors: Lepin A. Ja. , Myshkis A. D.
Published: September 2013

The Bernstein condition of boundedñess of the derivatives of an a priori bounded solution of a 2nd order ordinary differential equation is extended to systems in which each equation has its own order.
On Convolution Operators in the Spaces of Almost Periodic Functions and $L^p$ Spaces
Authors: Bruno G. , Pankov A.
Published: September 2013

We consider convolution operators generated by

L^1

functions in

L^p

spaces and various spaces of almost periodic functions. It turns out to be that if such an operator is invertible in one of these spaces, then it is invertible in all the spaces we consider. Further, we prove that any convolution has identical norms in many natural couples of function spaces.
On some Improperly Posed Problem for a Degenerate Nonlinear Parabolic Equation
Authors: Hayasida Kazuya
Published: September 2013

We consider the non-characteristic Cauchy problem for the degenerate nonlinear parabolic equation

|u|^{\alpha}u_t – \Delta u – \gamma |u|^{–\beta} u = 0

under some assumptions on

\alpha, \beta

and

\gamma

. The problem is improperly posed in the sense of Hadamard. We derive for such solutions an estimate in terms of the Cauchy data and a prescribed bound of the solution.
Weierstrass-Type Maximum Principle for Microstructure in Micromagnetics
Authors: Kružík Martin , Roubíček Tomáš
Published: September 2013

We derive necessary and sufficient optimality conditions for a relaxed (in terms of Young measures) variational problem governing steady states of ferromagnetic materials. Such conditions here stated in the form of a generalized Weierstrass maximum principle enable us to establish uniqueness of a solution in some specific situations and can also be used in efficient numerical algorithms solving the relaxed problems, for instance.
Local Existence of the Solution to the Initial-Boundary Value Problem in Nonlinear Thermodiffusion in Micropolar Medium
Authors: Gawinecki Jerzy A.
Published: September 2013

We prove a theorem about local existence (in time) of the solution to the first initial-boundary value problem for a nonlinear hyperbolic-parabolic system of eight coupled partial differential equations of second order describing the process of thermodiffusion in a three-dimensional micropolar medium. At first, we prove existence, uniqueness and regularity of the solution to this problem for the associated linearized system by using the Faedo-Galerkin method and semi-group theory. Next, we prove (basing on this theorem) an energy estimate for the solution to the linearized system by applying the method of Sobolev spaces. At last, by using the Banach fixed point theorem we prove that the solution of our nonlinear problem exists and is unique.
Non-Existence Results for a Semilinear Hyperbolic Problem with Boundary Condition of Memory Type
Authors: Kirane Mokhtar , Tatar Nasser-edine
Published: September 2013

We consider a problem which models the evolution of sound in a compressible fluid with reflection of sound at the surface of the material. Different methods such as the concavity method of Levine, the potential well method and an argument due to Tsutsumi are used to derive global non-existence theorems.
A Universal Constant for Exponential Riesz Sequences
Authors: Lindner A.M.
Published: September 2013

The aim of this paper is to study certain correlations between lower and upper bounds of exponential Riesz sequences, in particular between sharp lower and upper bounds, where we show that the product of the sharp bounds of an exponential Riesz sequence is bounded from above by a universal constant. The result is applied to the norms of coefficient and frame operators and their inverses.
Asymptotics of Zeros of the Wright Function
Authors: Luchko Yuri
Published: September 2013

The paper deals with the asymptotics of zeros of the Wright function

\phi (\rho, \beta; z) = \sum^{\infty}_{k=0} \frac{z^k}{k! \Gamma (\rho k + \beta)} \\ (\rho > –1)

in the case the parameter

\beta

is a real number. The exact formulae for the order, the type and the indicator function of the entire function

\phi (\rho, \beta ; z)

are given for

\rho > –1

. On the basis of these results and using the obtained distribution of the zeros of the Wright function it is shown to be a function of completely regular growth.
On the Method of Approximation by Families of Linear Polynomial Operators
Authors: Burinska Z. , Runovski Konstantin V. , Schmeisser Hans-Jürgen
Published: September 2013

It is shown that best approximation by trigonometric polynomials is achieved in average by families of linear polynomial operators in the

L_p

-metric for all

p, 0 < p < \infty

. This is compared with approximation by Fourier means and interpolation means which is restricted to

1 ≤ p ≤ \infty

and

p = \infty

, respectively.
Solvability of a Boundary Value Problem for Transonic Flow in a Nozzle
Authors: Kuz'min A.G.
Published: September 2013

A nonlinear perturbation problem for steady two-dimensional inviscid transonic flow in a nozzle is studied. The existence of a smooth solution to the problem is proved under the condition of positive acceleration of the given flow. The proof involves the method of singular perturbations for solving a linear problem associated with the nonlinear one. The technique for obtaining a priori estimates is simpler than that used in previous papers.
Some Definite Integrals Associated with the Riemann Zeta Function
Authors: Srivastava H.M. , Glasser M. Lawrence , Adamchik V.S.
Published: September 2013

The authors aim at deriving a family of series representations for

\zeta (2n + 1) (n \in \mathbb N)

by evaluating certain trigonometric integrals in several different ways. They also show how the results presented in this paper relate to those that were obtained in other works. Finally, some illustrative computational examples, using

Mathematica

(Version 4.0) for Linux, are considered.
On Ergodicity Coefficients of Infinite Stochastic Matrices
Authors: Rhodius Adolf
Published: September 2013

A class of ergodicity coefficients for infinite stochastic matrices is introduced and investigated with respect to connections to the well-known

\delta

-coefficient. The theory yields results on the behaviour of infinite products of stochastic matrices, in particular on inhomogeneous Markov chains and Markov systems.
A New Approach for Describing Electromagnetic Wave Propagation in Inhomogeneous Media
Authors: Kravchenko Vladislav V.
Published: September 2013

We propose a new approach for obtaining approximate solutions of Maxwell’s equations in inhomogeneous media. This work is based on the application of quaternionic analysis technique and consists of some approximate diagonalization of Maxwell’s equations. They are reduced to a pair of quaternionic equations which under some additional conditions can be solved exactly.
Semilinear Geometric Optics for Generalized Solutions
Authors: Wang Ya-Guang , Oberguggenberger Michael
Published: September 2013

This paper is devoted to the study of nonlinear geometric optics in Colombeau algebras of generalized functions in the case of Cauchy problems for semilinear hyperbolic systems in one space variable. Extending classical results, we establish a generalized variant of nonlinear geometric optics. As an application, a nonlinear superposition principle is obtained when distributional initial data are perturbed by rapid oscillations.
Univalent Functions with Range Restrictions
Authors: Kirsch Siegfried
Published: September 2013

Let

\Sigma

be the class of functions

f(z) = z + a_0 + a_{–1} z^{–1} + \cdots

analytic and univalent in

|z| > 1

. In this paper we investigate the problem to maximize

\mathfrak R a_{–1}

in two subclasses of

\Sigma

: (i) the class of all functions

f \in \Sigma

which omit two given values

±w_1 (0 < |w_1| < 2)

and (ii) the class of all functions

f \in \Sigma

with

a_0 = 0

which map onto regions of prescribed width

b_f = b (0 < b < 4)

in the direction of the imaginary axis. We solve these problems by applying a variational method to a coefficient problem in two subclasses of univalent Bieberbach-Eilenberg functions which are equivalent to these problems.
Insulin Resistance and Homocysteine Levels in Patients with Polycystic Ovarian Syndrome
Authors: Chari Suresh , Ghike Sunita , Gupta Madhur Mahesh , Chandankhede Manju
Published: September 2013

Objectives

To assess association in between insulin resistance and homocysteine levels in patients with polycystic ovarian syndrome (PCOS).

Methods

A case control study.

Setting

Hospital based.

Patients

Forty females diagnosed with PCOS were matched with 40 normal healthy controls.

Intervention

Blood samples for insulin, lipid profile, fasting glucose and homocysteine measurements.

Results

Our study suggests that PCOS patients have insulin resistance, dyslipidemia and hyperhomocysteinemia when compared with normal healthy controls.

Conclusion

To determine the short-term implications of reproductive performance and long-term implications regarding cardiovascular complications associated with PCOS the assessment of insulin resistance, lipid profile along with homocysteine levels in patients of PCOS is warranted.

How to cite this article

Gupta MM, Chari S, Chandankhede M, Ghike S. Insulin Resistance and Homocysteine Levels in Patients with Polycystic Ovarian Syndrome. J South Asian Feder Obst Gynae 2013;5(2):49-51.
Lateral Placentation by Ultrasonography: A Simple Predictor of Preeclampsia
Authors: Bhalerao Anuja , Kulkarni Sayali
Published: September 2013

Introduction

Preeclampsia is a disease of trophoblastic tissue. it is a complex clinical syndrome involving multiple organ systems and still remains the principle cause of maternal and perinatal morbidity and mortality. The search for an ideal predictive test is still on, and preventive measures for preeclampsia remain a challenging entity.

Aims and objectives:

1. To examine the relation between placental location and development of preeclampsia.

2. To study the pregnancy outcome in terms of mode of delivery and birth weight of all babies.

Research question

Does lateral placentation on ultrasonography at 20 to 24 weeks of gestation predict development of preeclampsia?

A detailed demographic history, gravidity, parity, history of abruption placenta, hypertension, preeclampsia, IUD, gestational diabetes were taken. General examination, including weight, blood pressure, vital signs was done. Detailed obstetric examination was done.

Ultrasonography was done for all women between 20 and 24 weeks of gestation, and placenta was classified as central when it was between the RT and LT side of uterus irrespective of being anterior, posterior or fundal. When 75% or more of placenta was on one side of midline, it was classified as lateral.

All women with central and lateral placenta were followed up till development of preeclampsia as per ACOG guidelines and later till delivery to see the outcome of pregnancy.

Observations

While recruiting, there was no bias on low-risk and high-risk groups but, at the end of the study, we found 182 women with high-risk factors and 281 women with low-risk factors.

A total of 71 pregnant women developed preeclampsia, of whom 52/71 (73.23%) had laterally situated placenta. This relationship seems to be significant. There was no relation of placental position and mode of delivary. The cesarean rate was 26.78% and normal delivaries being 73.21%. Of the cesareans, 76 (16.41%) were having centrally located placenta and 48 (10.36%) had laterally located placenta.

In our study, the sensitivity was 75, specificity was 81, the positive predictive value was 48 and the negative predictive value was 96.

Conclusion

As yet, there is no practical, acceptable and reliable method for screening for preeclampsia that has been thoroughly tested and tried.

In view of the results of our study, ultrasonography in pregnant woman during 20 to 24 weeks of gestation can be a easy, noninvasive, useful and cost-effective tool as a predictor of preeclampsia.

How to cite this article

Bhalerao AV, Kulkarni S, Somalwar S. Lateral Placentation by Ultrasonography: A Simple Predictor of Preeclampsia. J South Asian Feder Obst Gynae 2013;5(2): 68-71.
NATURACIÓN URBANA, UN DESAFÍO A LA URBANIZACIÓN
Authors: Urbano-López de Meneses Beatriz
Published: September 2013

La naturación urbana es la acción de incorporar la vegetación al medio urbano con el objetivo de amortiguar el desequilibrio entre la urbanización y la conservación del medio ambiente. Este artículo de revisión repasa los problemas ambientales, hidrológicos, de gestión de residuos, salubres y sociales que combate la naturación. Los sistemas respectivos se clasifican según la superficie naturada y la complejidad del sistema. Las capas básicas del sistema de naturación y los materiales que se emplean son analizados. Finalmente, se presentan las principales líneas de trabajo para el desarrollo e integración de los sistemas de naturación en la construcción de ciudades sostenibles.
CONTRACCIONES Y PROPIEDADES FÍSICAS DE ACACIA MANGIUM, TECTONA GRANDIS Y TERMINALIA AMAZONIA, MADERAS DE PLANTACIÓN EN COSTA RICA
Authors: Muñoz-Acosta Freddy , Moreno-Perez Pablo A.
Published: September 2013

De acuerdo con las normas ASTM D 2395-02 y D 143-94, se determinó la contracción total y normal en dirección radial (CR), tangencial (CT) y volumétrica (CV) y el coeficiente CT/ CR total y normal de Acacia mangium Willd., Tectona grandis L. f. y Terminalia amazonia A. Chev, maderas provenientes de plantación. También se determinaron algunas propiedades físicas como peso específico básico (PEB), PE12% y PEanhidro, densidad verde (DV) y normal (DN), punto de saturación de la fibra (PSF) y contenido de humedad (CH). Algunos criterios de clasificación, propuestos por otros investigadores, se aplicaron para categorizar la estabilidad dimensional y propiedades físicas de estas especies. Se encontró que la CR, CT, CV totales y CTtotal/CRtotal tienen diferencias significativas entre especies, al igual que las propiedades físicas PEB y PSF. El índice CTtotal/CRtotal indicó que T. grandis tiene mejor estabilidad dimensional. La relación lineal (R2= 0.7769) indicó que el PSF es un buen indicador de la magnitud de la CVtotal. Las especies de plantación de este estudio comparadas con las del bosque natural tienen estabilidad dimensional similar pero menor PEB.
Sources and photochemistry of volatile organic compounds in the remote atmosphere of western China: results from the Mt. Waliguan Observatory
Authors: Xue L. K. , Wang T. , Guo H. , Blake D. R. , Tang J. , Zhang X. C. , Saunders S. M. , Wang W. X.
Published: September 2013

Abstract. The chemistry of the natural atmosphere and the influence by long-range transport of air pollution are key issues in the atmospheric sciences. Here we present two intensive field measurements of volatile organic compounds (VOCs) in late spring and summer of 2003 at Mt. Waliguan (WLG, 36.28° N, 100.90° E, 3816 m a.s.l.), a baseline station in the northeast part of the Qinghai-Tibetan Plateau. Most VOC species exhibited higher concentrations in late spring than in summer. A typical diurnal variation was observed with higher nighttime levels, in contrast to results from other mountainous sites. Five different air masses were identified from backward trajectory analysis showing distinct VOC speciation. Air masses originating from the central Eurasian continent contained the lowest VOC levels compared to the others that were impacted by anthropogenic emissions from China and the Indian subcontinent. A photochemical box model based on the Master Chemical Mechanism (version 3.2) and constrained by a full suite of measurements was developed to probe the photochemistry of atmosphere at WLG. Our results show net ozone production from in situ photochemistry during both late spring and summer. Oxidation of nitric oxide (NO) by the hydroperoxyl radical (HO2) dominates the ozone production relative to the oxidation by the organic peroxy radicals (RO2), and the ozone is primarily destroyed by photolysis and reactions with the HOx (HOx = OH + HO2) radicals. Ozone photolysis is the predominant primary source of radicals (ROx = OH + HO2 + RO2), followed by the photolysis of secondary oxygenated VOCs and hydrogen peroxides. The radical losses are governed by the self and cross reactions among the radicals. Overall, the findings of the present study provide insights into the background chemistry and the impacts of pollution transport on the pristine atmosphere over the Eurasian continent.
Inverting for volcanic SO2 flux at high temporal resolution using spaceborne plume imagery and chemistry-transport modelling: the 2010 Eyjafjallajökull eruption case study
Authors: Boichu M. , Menut L. , Khvorostyanov D. , Clarisse L. , Clerbaux C. , Turquety S. , Coheur P.-F.
Published: September 2013

Abstract. Depending on the magnitude of their eruptions, volcanoes impact the atmosphere at various temporal and spatial scales. The volcanic source remains a major unknown to rigorously assess these impacts. At the scale of an eruption, the limited knowledge of source parameters, including time variations of erupted mass flux and emission profile, currently represents the greatest issue that limits the reliability of volcanic cloud forecasts. Today, a growing number of satellite and remote sensing observations of distant plumes are becoming available, bringing indirect information on these source terms. Here, we develop an inverse modelling approach combining satellite observations of the volcanic plume with an Eulerian regional chemistry-transport model (CHIMERE) to characterise the volcanic SO2 emissions during an eruptive crisis. The May 2010 eruption of Eyjafjallajökull is a perfect case study to apply this method as the volcano emitted substantial amounts of SO2 during more than a month. We take advantage of the SO2 column amounts provided by a vast set of IASI (Infrared Atmospheric Sounding Interferometer) satellite images to reconstruct retrospectively the time series of the mid-tropospheric SO2 flux emitted by the volcano with a temporal resolution of ~2 h, spanning the period from 1 to 12 May 2010. We show that no a priori knowledge on the SO2 flux is required for this reconstruction. The initialisation of chemistry-transport modelling with this reconstructed source allows for reliable simulation of the evolution of the long-lived tropospheric SO2 cloud over thousands of kilometres. Heterogeneities within the plume, which mainly result from the temporal variability of the emissions, are correctly tracked over a timescale of a week. The robustness of our approach is also demonstrated by the broad similarities between the SO2 flux history determined by this study and the ash discharge behaviour estimated by other means during the phases of high explosive activity at Eyjafjallajökull in May 2010. Finally, we show how a sequential IASI data assimilation allows for a substantial improvement in the forecasts of the location and concentration of the plume compared to an approach assuming constant flux at the source. As the SO2 flux is an important indicator of the volcanic activity, this approach is also of interest to monitor poorly instrumented volcanoes from space.