bluuebunny/crossref_metadata_2025 huggingface dataset:
A Characterization of the Dependence of the Riemannian Metric on the Curvature Tensor by Young Symmetrizers
Authors: Fiedler Bernold
Published: September 2013

In differential geometry several differential equation systems are known which allow the determination of the Riemannian metric from the curvature tensor in normal coordinates. We consider two of such differential equation systems. The first system used by Gunther [8] yields a power series of the metric the coefficients of which depend on the covariant derivatives of the curvature tensor symmetrized in a certain manner. The second system, the so-called Herglotz relations [9], leads to a power series of the metric depending on symmetrized partial derivatives of the curvature tensor.We determine a left ideal of the group ring

\mathbb C (S_{r+4})

of the symmetric group

S_{r+4}

which is associated with the partial derivatives

\partial^{(r)} R

of the curvature tensor

R

of order

r

and construct a decomposition of this left ideal into three minimal left ideals using Young symmetrizers and the Littlewood-Richardson rule. Exactly one of these minimal left ideals characterizes the so-called essential part of

\partial^{(r)} R

on which the metric really depends via the Herglotz relations. We give examples of metrics with and without a non-essential part of

\partial^{(r)} R

. Applying our results to the covariant derivatives of the curvature tensor we can show that the algebra of tensor polynomials

\mathcal R

generated by

\triangledown_{(i_1} ... \triangledown_{i_r)} R_{ijkl}

and the algebra

\mathcal R^s

generated by

\triangledown_{(i_l} ... \triangledown_{i_r} R_{|k|i_{r+l^s r+2)}l}

fulfil

\mathcal R = \mathcal R^s

.
On Generating Orthogonal Polynomials for Discrete Measures
Authors: Fischer H.-J.
Published: September 2013

In the present paper, we derive an algorithm for computing the recurrence coefficients of orthogonal polynomials with respect to discrete measures. This means that the support of the measure is a finite set. The algorithm is based oniormulae of Nevai describing the transformation of recurrence coefficients, if we add a point mass to the measure of orthogonality (generalized to the case of discrete measures). The numerical condition of the problem as well as the stability properties of the new algorithm and of the well-known Stieltjes-procedure are investigated. As examples show, this new algorithm has stability properties similar to procedures based on the Lanczos algorithm.
On the Kernel of the Klein-Gordon Operator
Authors: Kravchenko Vladislav V. , Castillo P. R.
Published: September 2013

In this work with the aid of technics of quaternionic analysis we show that any solution of the Klein-Gordon equation can be represented via two solutions of the Dirac equation with the same mass. Moreover, the two functions corresponding to each solution of the Klein-Gordon equation are unique.
On a Theorem of Hernández and Nashed
Authors: Dörfner M.
Published: September 2013

We prove a theorem on the global invertibility of nonlinear maps in metric vector spaces. As corollaries our result yields a theorem of Hernández and Nashed, as well as the classical Banach-Mazur lemma and an invertibility criterion by Browder.
Variational Integrals on Orlicz–Sobolev Spaces
Authors: Fuchs Martin , Osmolovski V.
Published: September 2013

We consider vector functions

u : \mathbb R^n \supset \Omega \to \mathbb R^N

minimizing variational integrals of the form

\int_{\Omega} G(\triangledown u)dx

with convex density

G

whose growth properties are described in terms of an

N

-function

A : (0, \infty) \to (0, \infty)

with limsup

_{t \to \infty} A(t)t^{–2} < \infty

. We then prove - under certain technical assumptions on

G

- full regularity of

u

provided that

n = 2

, and partial

C^1

-regularity in the case

n ≥ 3

. The main feature of the paper is that we do not require any power growth of

G

.
Embedding Theorems for Sobolev-Besicovitch Spaces of Almost Periodic Functions
Authors: Iannacci R. , Bersani A.M. , Dell'Acqua G. , Santucci P.
Published: September 2013

We show embedding theorems of Sobolev type for Sobolev-Besicovitch spaces

H^{m,q}_{ap}

of almost periodic functions for any

q > 1

and, consequently, for spaces

W^{m,q}_{ap}

, with

q \in (1, 2)

. The fundamental tool for the proof of the main theorem is the Hausdorff-Young theorem for almost periodic functions.
On the Dirac Operator with an Electromagnetic Potential
Authors: Kravchenko Vladislav V.
Published: September 2013

A new approach based on the construction of some special biquaternionic projection operators is proposed for analysis and solution of the Dirac equation with electromagnetic potential. There is given an example of the application of this technique which allows us to find the solutions for some class of potentials.
On Strong Closure of Sets of Feasible States Associated with Families of Elliptic Operators
Authors: Zaytsev O.
Published: September 2013

The closure of sets of feasible states for systems of elliptic equations in the strong topology of the Cartesian product

[H^1_0 (\Omega)]^m

of Sobolev spaces is considered. For

m = 2

and

\Omega \subset \mathbb R^2

, it is shown that there is a family of linear elliptic operators of the type div

(\chi \mathcal A^1 + (1 - \chi)\mathcal A^2)\triangledown

, where

\chi

belongs to the set of all characteristic functions of measurable subsets of

\Omega

, such that there does not exist a larger family of operators of the type div

\mathcal A \triangledown

for which the sets of feasible states coincide with the closure of the original ones.
$L_p$-Theory of Boundary Integral Equations on a Contour with Inward Peak
Authors: Maz'ya Vladimir G. , Soloviev A.
Published: September 2013

Boundary integral equations of the second kind in the logarithmic potential theory - are studied under the assumption that the contour has an inward peak. For each equation we find a pair of function spaces such that the corresponding operator bijectively maps one of them onto another.
Approximation of Stochastic Differential Equations with Modified Fractional Brownian Motion
Authors: Grecksch Wilfried , Anh V.V.
Published: September 2013

The modified fractional Brownian motion is a special semimartingale. This stochastic process is suitable for studying the phenomenon of long-range dependence in a wide range of fields. This paper introduces stochastic differential equations with respect to modified fractional Brownian motion. The solution of these equations is approximated by a splitting method whose convergence in probability is proved. An application of this method to determine

\epsilon

-optimal controls for a stochastic control problem is also given.
Some Operator Ideals in Non-Commutative Functional Analysis
Authors: Fidaleo F.
Published: September 2013

We study classes of linear maps between operator spaces

E

and

F

which factorize through maps arising in a natural manner by the Pisier vector-valued non-commutative

L^p

-spaces

S_p[E]

based on the Schatten classes on the separable Hilbert space

\ell ^2

. These classes of maps, firstly introduced in [28] and called p-nuclear maps, can be viewed as Banach operator ideals in the category of operator spaces, that is in non-commutative (quantized) functional analysis. We also discuss some applications to the split property for inclusions of

W*

-algebras such as those describing the physical observables in Quantum Field Theory.
Asymptotic Behavior of $M$-Band Scaling Functions of Daubechies Type
Authors: Bi N. , Debnath L. , Sun Qiyu
Published: September 2013

This paper deals with the asymptotic behavior of

M

-band scaling functions

^M_N\phi

and

M

-band symbols

^M_NH

as

M \to \infty

for

N ≥ 2

. This is followed by pointwise convergence, and

L^p

-convergence

(1 ≤ p ≤ \infty)

of

^M_N\phi

, and the limit function

g

of

^M_N\phi

as

M \to \infty

.
On Nonlinear Model of the Vibrating Membrane
Authors: Iannelli A.
Published: September 2013

A nonlinear model describing the transversal motion of an elastic membrane is introduced and the corresponding equation is studied: An existence and uniqueness theorem for the global solution of the Cauchy-Dirichlet problem is proved
Free Boundary Value Problem for the Axisymmetric Fluid’s Flow with Surface Tension and Wedging Forces
Authors: Chthterbakov E.
Published: September 2013

A free boundary value problem with surface tension and wedging forces is consid-ered. From the mathematical point of view it leads to a boundary value problem in which the mean and Gauss curvatures appear in the boundary condition on the unknown surface. The variational problem is formulated and it is proved that its solution is the solution of the free boundary value problem. Infinite smoothness of the free surface is proved and it is also proved that the curve generating the free surface is analytic for some values of the problem parameters.
Explicit Calculation of Some Polynomials Introduced by W. Gautschi
Authors: Fischer H.-J.
Published: September 2013

In his classical by now investigation of the numerical condition of methods for computing orthogonal polynomials from modified moments, Gautschi introduced some poly-nomials defined by the nodes and weights of a Gaussian quadrature formula for the measure of orthogonality. We show that these polynomials can be calculated explicitly for Chebyshev weights of first, second and third kinds.
The Canonical Endomorphism for Infinite Index Inclusions
Authors: Fidaleo F. , Isola Tommaso
Published: September 2013

We give purely algebraic characterisations of the canonical endomorphism in in-teresting infinite index cases, continuing previous works of Longo and the authors. We apply these results when compact and discrete (but not necessarily finite-dimensional) Woronowicz algebras act alternately on the factors in the various levels of Jones’ tower. We characterise when the acting algebra is a Kac algebra.
Hyperbolic Functional-Differential Equations with Unbounded Delay
Authors: Kamont Zdzisław
Published: September 2013

The phase space-for quasilinear equations with unbounded delay is constructed. Carathéodory solutions of initial problems are investigated. A theorem on the existence, uniqueness and continuous dependence upon initial data is given. The method of bichar-acteristics and integral inequalities are used.
Existence and Uniqueness of Solutions to a Class of Stochastic Functional Partial Differential Equations via Integral Contractors
Authors: Turo Jan
Published: September 2013

Existence and uniqueness theorem for first order stochastic functional partial differential equations with the white noise as a coefficient is proved. In the proof the characteristics method and the concept of integral contractors are used.
On the Matrix Norm Subordinate to the Holder Norm
Authors: Albrecht J. , Klein P.P.
Published: September 2013

For non-negative matrices

P

the matrix norm subordinate to the Hölder norm of index

p

with

p \in (1,\infty)

is determined by an eigenvalue problem

T\alpha = \lambda \alpha

, where

T

is a homogeneous, strongly monotone operator.
Oblique Derivative Problems for Elliptic Systems of Second Order Equations in Infinite Domains
Authors: Begehr Heinrich , Wen Guochun
Published: September 2013

There are many problems in mechanics and physics, the mathematical models of which are some boundary value problems for nonlinear elliptic systems of first and second order equations in multiply connected domains including infinity. In this paper, we discuss oblique derivative problems for systems of second order equations.
Stability Rates for Linear Ill-Posed Problems with Compact and Non-Compact Operators
Authors: Hofmann Bernd , Fleischer G.
Published: September 2013

In this paper we deal with the ’strength’ of ill-posedness for ill-posed linear operator equations

Ax = y

in Hilbert spaces, where we distinguish according to M. Z. .Nashed the ill-posedness of type I if

A

is not compact, but we have

R(A) \neq \bar{R(A)}

for the range

R(A)

of

A

, and the ill-posedness of type II for compact operators

A

. From our considerations it seems to follow that-the problems with non-compact operators

A

are not ingeneral ’less’ ill-posed than the problems with compact operators. We motivate this statement by comparing the approximation and stability behaviour of discrete least-squares solutions and the growth rate of Galerkin matrices in both cases. Ill-posedness measures for compact operators

A

as discussed by B. Hofmann and U. Tautenhahn are derived from the decay rate of the non-increasing sequence of singular values of

A

. Since singular values do not exist for non-compact operators

A

, we introduce stability rates in order to have a common measure for the compact and non-compact cases. Properties of these rates are illustrated by means of convolution equations in the compact case and by means of equations with multiplication operators in thenon-compact case. Moreover, using increasing rearrangements of multiplier functions specific measures of ill-posedness called ill-posedness rates are considered for multiplication* operators. In this context, the character of sufficient conditions providing convergence rates of Tikhonov regularization are compared-for compact operators and multiplication. operators.
On the Low Wave Number Behavior of Two-Dimensional Scattering Problems for an Open Arc
Authors: Kress R.
Published: September 2013

The low wave number asymptotics for the solution of the Dirichlet problem for the two-dimensional Helmholtz equation in the exterior of an open arc is analyzed via a single-layer integral equation approach. It is shown that the solutions to the Dirichlet problem for the Helmholtz equation converge to a solution of the Dirichlet problem for the Laplace equation as the wave number tends to zero provided the boundary values converge.
On Optimal Regularization Methods for Fractional Differentiation
Authors: Tautenhahn Ulrich , Gorenflo Rudolf
Published: September 2013

In this paper we consider the following fractional differentiation problem: given noisy data

f^{\delta} L^2(\mathbb R)

to

f

, approximate the fractional derivative

u = D_{\beta} f \in L^2(\mathbb R)

for

\beta > 0

, which is the solution of the integral equation of first kind

(A_{\beta} u(x) = \frac{1}{\Gamma (\beta)} \int^x_{– \infty} \frac {u(t) dt}{(x–t)^{1– \beta}} = f(x)

. Assuming

\|f–f^{\delta} \|_{L^2(\mathbb R)} ≤ \delta

and

\| u \|_p ≤ E

(where

\| \cdot \|_p

denotes the usual Sobolev norm of order

p > 0

) we answer the question concerning the best possible accuracy for identifying

u

from the noisy data

f^{\delta}

. Furthermore, we discuss special regularization methods which realize this best possible accuracy.
Duality for Optimal Control-Approximation Problems with Gauges
Authors: Wanka Gert , Krallert U.
Published: September 2013

Looking for

m

state variables and

n

control variables such that the sum of the distance functions between the state variables and the control variables becomes minimal is called control-approximation problem. This problem is investigated under constraints. Moreover, the distances between the control variables themselves are taken into account. Powers of several gauges are chosen as distance functions. The considerations happen in Hausdorif locally convex topological real vector spaces.In particular, location problems of very general type (e.g. so-called multifacility problems) turn out to be special cases of such control-approximation problems.After the formulation of the primal control-approximation problem some considerations concerning gauges follow. Then a dual problem is given and weak and strong duality assertions are obtained.
Some Surprising Results on a One-Dimensional Elliptic Boundary Value Blow-Up Problem
Authors: Cheng Yuanji
Published: September 2013

In this paper we consider the one-dimensional elliptic boundary blow-up problem

\Delta_p u = f(u) \ \ (a < t < b)

u(a) = u(b) = +\infty

where

\Delta_p u = (|u'{t}|^{p–2} u'(t))'

is the usual

p

-Laplace operator. We show that the structure of the solutions can be very rich even for a simple function

f

which gives a leading that a similar result might hold also in higher dimensional spaces.
Mixed Boundary Value Problems for Nonlinear Elliptic Systems in n-Dimensional Lipschitzian Domains
Authors: Ebmeyer Carsten
Published: September 2013

Let

u : \Omega \to \mathbb R^n

be the solution of the nonlinear elliptic system

– \sum^n_{i=1} \partial_i F_i (x, \triangledown u) = f(x) + \sum^n_{i=1} \partial_i f_i (x),

where

\Omega \in \mathbb R^n

is a bounded domain with a piecewise smooth boundary (e.g.,

\Omega

is a polyhedron). It is assumed that a mixed boundary value condition is given. Global regularity results in Sobolev and in Nikolskii spaces are proven, in particular

[W^{s, 2} (\Omega)]^N

-regularity

(s < \frac{3}{2})

of

u

.
On Hammerstein Equations with Natural Growth Conditions
Authors: Moroz V. , Zabrejko P. P.
Published: September 2013

this paper we study a nonlinear Hammerstein integral equation by means of the direct variational method. Under certain "natural" growth conditions on the non-linearity we show that the existence of a local minimum for the energy functional implies the solvability of the original equation. In these settings the energy functional may be non-smooth on its domain and, moreover, operators in data may be non-compact. Some solvability and non-trivial solvability results for the original equation are given.
A New Minimal Point Theorem in Product Spaces
Authors: Göpfert Alfred , Tammer Chr. , Zălinescu C.
Published: September 2013

We derive a minimal point theorem for a subset

A

in a cone in product spaces under a weak assumption concerning the boundedness of the considered set

A

. Using this result we improve two vectorial variants of Ekeland’s variational principle. Finally, a new characterization of well-based cones is given.
Estimates for Quasiconformal Mappings onto Canonical Domains
Authors: Thao Vo Dang
Published: September 2013

In this paper we establish estimates for

K

-quasiconformal mappings

z = g(w)

of a domain bounded by two circles

|w| = 1, |w| = q

and

n

continua situated in

q < |w| < 1

onto a circular ring

Q(g) < |z| < 1

that has been slit along

n

arcs on the circles

|z| = R_j(g) (j = 1,... ,n)

such that

|z| = 1

and

|z| = Q

correspond to

|w| = 1

and

|w| = q

, respectively. The bounds in the estimates for

Q, R_j

and

|g(w)|

are explicitly given, most of them are optimal. They are deduced mainly from [17].
The Behaviour of the Eigenvalues for a Class of Operators Related to some Self-Affine Fractals in $\mathbb R^2$
Authors: Farkas W.
Published: September 2013

The obtaining of sharp estimates for the asymptotic behaviour of the eigenvalues of the (semi-elliptic) operator acting in the anisotropic Sobolev space

W_2^{(1,2)}(\Omega) = \{ u \in W_2^{(1,2)} (\Omega) : u|\partial \Omega = \frac{\partial u}{\partial x_2}| \partial \Omega = 0 \}

generated by the quadratic form

\int_{\Omega} f(\gamma) g (\gamma)d \mu (\gamma)

is investigated. Here

\mu

is an appropriate self-affine fractal measure on the unit disc

\Omega \subset \mathbb R^2

.
Nonlinear Hyperbolic Equations with Dissipative Temporal and Spatial Non-Local Memory
Authors: Mošna F. , Nečas Jindřich
Published: September 2013

The equation governing the evolution of a displacement vector in an elastic body with dissipative temporal and spatial non-local memory is considered. The memory term is generated by a singular but integrable kernel. The existence of a global weak solution to the associated initial- boundary problem is established by constructing Calerkin approximations and deriving a suitable energy estimate.
Homogenization of the Poisson Equation in a Thick Periodic Junction
Authors: Mel'nyk T.A.
Published: September 2013

A convergence theorem and asymptotic estimates as

\epsilon \to 0

are proved for a solution to a mixed boundary-value problem for the Poisson equation in a junction

\Omega_{\epsilon}

, of a domain

\Omega_0

and a large number

N^2

of

\epsilon

-periodically situated thin cylinders with thickness of order

\epsilon = O(\frac{1}{N})

. For this junction, we construct an extension operator and study its properties.
A System of Ordinary and Partial Differential Equations Describing Creep Behaviour of Thin-Walled Shells
Authors: Altenbach H. , Deuring P. , Naumenko K.
Published: September 2013

The article deals with a system of partial and ordinary differential equations de-scribing creep and damage processes in the material of thin-walled structures. It is shown that if set up in suitable Sobolev spaces, this system may be solved uniquely, locally in time.
Full $C^{1, \alpha}$-Regu1arity for Minimizers of Integral Functionals with $L$ log $L$-Growth
Authors: Mingione Giuseppe , Siepe F.
Published: September 2013

We consider the integral functional with nearly-linear growth

\int_{\Omega} |Du| \mathrm {log} (1+|Du|)dx

where

u : \Omega \subset \mathbb R^n \to \mathbb R^N (n ≥ 2, N ≥ 1)

and we prove that any local minimizer

u

has locally Hölder continuous gradient in the interior of

\Omega

thus excluding the presence of singular sets in

\Omega

. This functional has recently been considered by several authors in connection with variational models for problems from the theory of plasticity with logarithmic hardening. We also give extensions of this result to more general cases.
Oscillations of Certain Delay Integro-Differential Equations
Authors: Wang Y.H. , Zhang Binggen
Published: September 2013

In this paper, the oscillation of solutions of certain delay integro-differential systems are considered. Sufficient conditions for the non-existence of non-oscillatory solutions for these systems are obtained. Comparison results are obtained also.
On the Hubert Inequality
Authors: Mingzhe Gao
Published: September 2013

It is shown that the Hilbert inequality for double series can be improved by introducing the positive real number

\frac{1}{\pi^2} (\frac{s^2(b)}{\|a\|^2} + \frac{s^2(b)}{\|b\|^2})

where

s(x) = \sum^{\infty}_{n=1} \frac{x_n}{n}

and

\|x\|^2 = \sum^{\infty}_{n=1} x^2_n (x = a, b)

. The coefficient

\pi

of the classical Hilbert inequality is proved not to be the best possible if

\|a\|

or

\|b\|

is finite. A similar result for the Hubert integral inequality is also proved.
Recursion Formulae for $\sum^n_{m=1} m^k$
Authors: Guo Sen-Lin , Qi Feng
Published: September 2013

Using elementary approach and mathematical induction, several recursion formulae for

S_k(n) = \sum^n_{m=1} m^k

are presented which show that

S_{k+1}(n)

could be obtained from

S_k(n)

. A method and a formula of calculating Bernoulli numbers are proposed.
On $B$-Bounded Semigroups as a Generalization of $C_0$-Semigroups
Authors: Arlotti Luisa
Published: September 2013

this paper we consider the one-parameter family of linear operators that A. Belleni Morante recently introduced and called

B

-bounded semigroups. Such a family was studied by A. Belleni Morante himself and by J. Banasiak. Here we give a necessary and sufficient condition that a pair (

A, B

) of linear operators be the generator of a

B

-bounded semigroup. Our procedure is constructive and is equivalent to the Yosida procedure for the construction of a

C_0

-semigroup when

B = I

. We also show that our result represents a generalization of Banasiak’s result.
Exponential Stability of a Nonlinear Distributed Parameter System
Authors: Tervo Jouko , Nihtilä Markku
Published: September 2013

A nonlinear parabolic partial differential equation model describing the behaviour of a distributed parameter fixed-bed bioreactor is studied here. Exponential stability around the steady state solution for exponentially decaying deviations in the input and disturbance are proved via abstract formulation of the model as an evolution equation and by utilizing semigroup theory and asymptotic stability of the corresponding evolution operator.
Initial-Boundary Value Problem for Some Coupled Nonlinear Parabolic System of Partial Differential Equations Appearing in Thermodiffusion in Solid Body
Authors: Gawinecki Jerzy A. , Kacprzyk P. , Bar-Joseph B.
Published: September 2013

We prove a theorem about existence, uniqueness and regularity of the solution to an initial-boundary value problem for a nonlinear coupled parabolic system consisting of two equations. Such a system appears in the thermodiffusion in solid body. In our proof we use an energy method, methods of Sobolev spaces, semigroup theory and the Banach fixed point theorem.
Sobolev Inequalities on Sets with Irregular Boundaries
Authors: Kilpeläinen Tero , Malý Jan
Published: September 2013

We derive (weighted) Sobolev-Poincaré inequalities for

s

-John domains and

s

-cusp domains, both with optimal exponents. These results are obtained as consequences of a more comprehensive criterion.
$CM$-Selectors for Pairs of Oppositely Semicontinuous Multifunctions and Some Applications to Strongly Nonlinear Inclusions
Authors: Nguyen Hong Thai , Juniewicz M. , Zieminska J.
Published: September 2013

We present a new approximate joint selection theorem which unifies Michael’s theorem (1956) on continuous selections and Cellina’s theorem (1969) on continuous

\epsilon

-approximate selections. More precisely, we show that, given a convex-valued

H

-upper semicontinuous multifunction

F

and a convex-closed-valued lower semicontinuous multifunction

G

with

F(x) \bigcap G(x) \neq \emptyset

, one can find a continuous function

f

which is both a selection of

G

and an

\epsilon

-approximate selection of

F

. We also prove a parametric version of this theorem for multifunctions

F

and

G

of two variables

(s, u) \in \Omega \times X

where

\Omega

­ is a measure space. Using this selection theorem, we obtain an existence result for elliptic systems involving a vector Laplacian and a strongly nonlinear multi-valued right-hand side, subject to Dirichlet boundary conditions.
Asymptotically Stable Almost-Periodic Oscillations in Systems with Hysteresis Nonlinearities
Authors: Brokate M. , Collings I. , Pokrovskii A.V. , Stagnitti F.
Published: September 2013

We present some sufficient conditions for the asymptotic stability of forced almostperiodic oscillations in nonlinear systems subject to small hysteresis perturbations. The main technical restriction on hysteresis nonlinearity comes to a contraction-type property, which holds for some classical models of hysteresis. Also we require a special stability property of the unperturbed system in the sense of Lyapunov and the bounded input-bounded output.
Multiple Solutions for a System of $(n_i, p_i)$ Boundary Value Problems
Authors: Wong Patricia J.Y. , Agarwal R.P.
Published: September 2013

We consider the system of boundary value problems

\left.
\begin{align*}
&&u_1^{n_i}(t)+f_i(t,u_1(t),...,u_m(t))=0\\
&&u_i^{(j)}(0)=0\\
&&u_i^{(p_i)}(1)=0
\end{align*}
\right\}

for

t \in [0, 1], i = 1, ..., m

and

0 ≤ j ≤ n_i-2

where

n_i ≥ 2

and

1 ≤ p_i ≤n_i – 1

. Several criteria are offered for the existence of single and twin solutions of the system that are of fixed signs.
The Classical and the Modified Neumann Problems for the Inhomogeneous Pluriholomorphic System in Polydiscs
Authors: Mohammed A.
Published: September 2013

The classical Neumann problem for the inhomogeneous pluriholomorphic system in a polydisc is considered. Its solvability conditions and its solution are given. It is shown that the problem is not well-posed. To fix the solution the boundary condition is modified. For the modified problem the solvability conditions and the solution which is unique up to an arbitrary constant are explicitly given.
On Representations of Partial *-Algebras Based on $\mathfrak B$-Weights
Authors: Kürsten Klaus-Detlef , Wagner Elmar
Published: September 2013

A generalization of the

GNS

-representation is investigated that represents partial *-algebras as systems of operators acting on a partial inner product space (i.e.,

PIP

-space). It is based on possibly indefinite

\mathfrak B

-weights which are closely related to the positive

\mathfrak B

-weights introduced by J.-P. Antoine, Y. Soulet and C. Trapani. Some additional assumptions had to be made in order to guarantee the

GNS

-construction. Different partial products of operators on a

PIP

-space are considered which allow the

GNS

-construction under suitable conditions. Several examples illustrate the argumentation and indicate inherent problems.
A Non-Differentiability Result for the Inversion Operator between Sobolev Spaces
Authors: Farkas G. , Garay Barnabas M.
Published: September 2013

The order of differentiability of the inversion operator

\mathcal J

between certain spaces or manifolds of distributionally differentiable functions is shown to be sharp in the following sense. Up to a certain order

k

guaranted by inverse function arguments, the operator

\mathcal J

is everywhere differentiable and

\mathcal J^{(k)}

is continuous. On the other hand,

\mathcal J

is nowhere

k+1

times differentiable.
Capillary Surfaces in Non-Cylindrical Domains
Authors: Schindlmayr G.
Published: September 2013

This paper is concerned with the capillary problem in a class of non-cylindrical domains in

K \subset \mathbb R^{n+1}

obtained by scaling a bounded cross-section ­

\Omega \subset \mathbb R^n

along the vertical axis. The capillary surfaces are described in two different ways. In the first model, they are described as the boundary of a Caccioppoli set and in a second model, after transforming

K

to a cylinder, they are described as graphs of functions on

\Omega

­. The volume of the fluid is prescribed. For both models, the energy functional is derived and declared on the appropriate function space consisting of

BV

-functions. Main results are existence and a priori bounds of minimizers, using the direct methods in the calculus of variations. For the special case of a cone over the domain

\Omega

­, a criterion is given to assure that the tip is not filled with liquid. Another point of examination concerns modelling the volume restriction by means of a Lagrange multiplier.
On More General Lipschitz Spaces
Authors: Haroske Dorothee D.
Published: September 2013

The present paper deals with (logarithmic) Lipschitz spaces of type

\mathrm {Lip}^{(1,–\alpha)}_{p,q} (1 ≤ p ≤ \infty, 0 < q ≤ \infty, \alpha > \frac {1}{q})

. We study their properties and derive some (sharp) embedding results. In that sense this paper can be regarded as some continuation and extension of our papers [8, 9], but there are also connections with some recent work of Triebel concerning Hardy inequalities and sharp embeddings. Recall that the nowadays almost 'classical' forerunner of investigations of this type is the Brézis-Wainger result [6] about the 'almost' Lipschitz continuity of elements of the Sobolev spaces

H^{1+ \frac{n}{p}}_p (\mathbb R^n)

when

1 < p < \infty

.
On the Existence of $C^1$ Functions with Perfect Level Sets
Authors: D'Aniello Emma , Darji U.B.
Published: September 2013

Given a closed set

M \subset [0, 1]

of Lebesgue measure zero, we construct a

C^1

function

f

with the property that

f^{–1} ({y})

is a perfect set for every

y

in

M

.
A Multiplicity Fixed Point Theorem in Fréchet Spaces
Authors: O'Regan Donal
Published: September 2013

A new multiplicity result is presented for maps between Fréchet spaces. Our argument relies on fixed point results in Banach spaces together with a result on hemicompact maps. An application is also given to illustrate how the theory can be applied in practice.
Some Oscillation and Non-Oscillation Theorems for Fourth Order Difference Equations
Authors: Thandapani E. , Arockiasamy I.M.
Published: September 2013

Sufficient conditions are established for oscillation of all solutions of the fourth order difference equation

\Delta a_n \Delta (b_n \Delta (c_n \Delta y_n)) + q_n f (y_{n+1}) = h_n \\ (n \in \mathbb N_0)

where

\Delta

is the forward difference operator

\Delta y_n = y_{n+1} – y_n, \{a_n\}, \{b_n\}, \{c_n\}, \{q_n\}, \{h_n\}

are real sequences, and

f

is a real-valued continuous function. Also, sufficient conditions are provided which ensure that all non-oscillatory solutions of the equation approach zero as

n \to \infty

. Examples are inserted to illustrate the results.
Asymptotic Justification of the Conserved Phase-Field Model with Memory
Authors: Felli Veronica
Published: September 2013

We consider a conserved phase-field model with memory in which the Fourier heat conduction law is replaced by a constitutive assumption of Curtin-Pipkin type; the system is conserved in the sense that the initial mass of the order parameter is preserved during the evolution. We investigate a Cauchy-Neumann problem for this model which couples an integro-differential equation with a nonlinear fourth-order equation for the phase field. here we assume that the heat flux memory kernel has a decreasing exponential as principal part and we study the behaviour of solutions when this kernel converges to a Dirac mass. We show that the solution to the conserved phase-field model with memory converges to a solution to the phase-field problem without memory under suitable assumptions on the data.
Hysteresis in Filtration through Porous Media
Authors: Bagagiolo F. , Visintin Augusto
Published: September 2013

We study an evolution problem for filtration through porous media, accounting for hysteresis in the saturation versus pressure constitutive relation. We provide a weak formulation of the problem, assuming that the memory effect in the constitutive relation consists not only of a rate-independent component but also of a rate-dependent one. We prove an existence result, which also applies to the case where the hysteresis operator is of Preisach-type.
On a Simple System of Discrete Two-Scale Difference Equations
Authors: Berg Lothar , Krüppel Manfred
Published: September 2013

A special system of two discrete two-scale difference equations with polynomial solutions is investigated. For-the solutions, addition and subtraction theorems are established showing in particular the behaviour of the solutions for a great argument, as well as further relations and inequalities. Also, corresponding generating functions are constructed which imply explicit representations for the Solutions.
On a Local Lipschitz Constant of the Maps Related to $LU$-Decomposition
Authors: Balanov Z. , Krawcewicz Wieslaw , Kushkuley A. , Zabrejko P. P.
Published: September 2013

Let

M(n, \mathbb R)

be the set of real positive definite symmetric

(n \times n)

-matrices equipped with the Euclidean norm, and let

A \in M(n, \mathbb R)

. Let

L(n, \mathbb R)

be the set of all real non-degenerate lower-triangular

(n \times n)

-matrices equipped with the Euclidean norm, and let

L : M(n, \mathbb R) \to L(n, \mathbb R)

be a (differentiable) map assigning to a positive definite symmetric matrix its lower-triangular factor in the

LU

-decomposition. We give an effective upper estimate for

\|L’(A)\|

.
Some Properties of Legendre Functions and Related Applications
Authors: Chu Chie-Ping
Published: September 2013

Some properties of Legendre functions in an asymmetric interval (with respect to zero) with zero boundary values are obtained through variational methods. There are given some applications to the monotonicity and estimates of the first Dirichlet cigenvalue for moving bands on

S^2

.
Spatial Clustering of Aedes aegypti Related to Breeding Container Characteristics in Coastal Ecuador: Implications for Dengue Control
Authors: Schafrick Nathaniel H. , Milbrath Meghan O. , Berrocal Veronica J. , Wilson Mark L. , Eisenberg Joseph N. S.
Published: September 2013

Mosquito management within households remains central to the control of dengue virus transmission. An important factor in these management decisions is the spatial clustering of Aedes aegypti. We measured spatial clustering of Ae. aegypti in the town of Borbón, Ecuador and assessed what characteristics of breeding containers influenced the clustering. We used logistic regression to assess the spatial extent of that clustering. We found strong evidence for juvenile mosquito clustering within 20 m and for adult mosquito clustering within 10 m, and stronger clustering associations for containers ≥ 40 L than those < 40 L. Aedes aegypti clusters persisted after adjusting for various container characteristics, suggesting that patterns are likely attributable to short dispersal distances rather than shared characteristics of containers in cluster areas. These findings have implications for targeting Ae. aegypti control efforts.
The Comparative Study of Drotaverine Hydrochloride and Valethamate Bromide in First Stage of Labor
Authors: Palii Sudhir Babu , Akkupalli Vijaya Lakshmi , Maddi Suneetha
Published: September 2013

Objective

To evaluate and compare the effects of drotaverine and valethamate on cervical dilatation.

Materials and methods

Total of 100 patients (aged 20 to 30 years) including both primigravidae and multigravidae in first stage of labor, were divided randomly into two groups with 50 patients in each. The drotaverine (D) and valethamate (V) groups were given intravenously, 40 mg drotaverine hydrochloride to the former with every 2 hours for a maximum of 3 doses and 8 mg valethamate bromide to the latter with maximum of 6 doses half an hour apart.

Results

In primigravidae and multigravidae the average duration of active phase is shortened by 3 hours with 1.92 cm/ hour cervical dilatation in drotaverine group and 1 hour 45 minutes with 1.44 cm/hour in valethamate group (p-value < 0.05). There was no significant difference in the duration of second and third stages in both groups. No obstetrical complications or major side effects observed in both groups.

Conclusion

Drotaverine accelerates labor better than of valethamate. The reduction of pain during labor is better with drotaverine when compared with valethamate.

How to cite this article

Palii SB, Akkupalli VL, Maddi S. The Comparative Study of Drotaverine Hydrochloride and Valethamate Bromide in First Stage of Labor. J South Asian Feder Obst Gynae 2013;5(2):52-56.
Three ‘Delays’ as a Framework for Critical Analysis of Maternal Near Miss and Maternal Mortality
Authors: Yunus Saira , Kauser Shahnaz , Ali Shazia
Published: September 2013

Objective

The aim of the study was to assess the magnitude and causes of three delays and their possible implications for safe motherhood.

Methods

The cross-sectional prospective study was carried out over a period of 1 year from January to December 2010. All patients who fulfill the WHO criteria for maternal near miss and all cases of maternal death during this period were included in the study. The various factors responsible for the delays in accessing obstetrics care facilities at all the three levels were analyzed.

Results

During 1 year period there were 10,553 emergency admissions in labor room and there were 4538 deliveries, out of these 123 patients who fulfilled the WHO criteria for near miss were included in the study. 83% of patients (102) reported first delay in seeking care and the most common reason for delay was inability to judge the graveness of situation. After initial care there was a delay in reaching a facility with comprehensive obstetric care in 62% of cases (76 patients) and this delay was of around 6 to 8 hours. Once the patients reached Jinnah Hospital there was a delay in about 15 (12%) patients. There were 13 maternal deaths during this period of 1 year and there was a delay both at seeking initial care and referral by the initial care providers.

Conclusion

Delay in deciding to seek care (1st delay) was the major factors responsible for high maternal mortality and morbidity. So the role of community actors such as mothers in law, husbands, local healers and pharmacies and increased access to properly trained birth attendants need to be addressed if delays in reaching health facilities are to be shortened.

How to cite this article

Yunus S, Kauser S, Ali S. Three ‘Delays’ as a Framework for Critical Analysis of Maternal Near Miss and Maternal Mortality. J South Asian Feder Obst Gynae 2013;5(2):57-59.
LNG Emergency Contraceptive Pills: Risk Factor for Ectopic Pregnancy
Authors: Ghike Sunita , Somalwar Savita A , Joshi Sulbha A , Kawthalkar Anjali S , Jain Sheela H , Gawande Madhuri S
Published: September 2013

Hormonal emergency contraceptive drugs designed to prevent undesired pregnancy are available over the counter. In spite of availability of various contraceptive techniques, couple protection rate in our country is still inadequate. A large number of couples prefer to use emergency contraceptive pill instead of regular contraceptives. Though hormonal emergency contraceptives pills are highly effective and safe with fewer side effects, their failure rate is high when used in periovulatory period with increased chances of ectopic pregnancy.

How to cite this article

Jain SH, Ghike S, Gawande MS, Joshi SA, Kawthalkar AS, Somalwar SA. LNG Emergency Contraceptive Pills: Risk Factor for Ectopic Pregnancy. J South Asian Feder Obst Gynae 2013;5(2):87-88.
TASAS DE DEFORESTACIÓN EN SAN LUIS POTOSÍ, MÉXICO (1993-2007)
Authors: Miranda-Aragón Liliana , Treviño-Garza Eduardo J. , Jiménez-Pérez Javier , Aguirre-Calderón Oscar A. , González-Tagle Marco A. , Pompa-García Marín , Aguirre-Salado Carlos A.
Published: September 2013

Es importante conocer las tasas de deforestación para el diseño de programas regionales bajo el enfoque particular de Reducción de Emisiones por Degradación y Deforestación (REDD+). Con el propósito de estimar la tasa de deforestación del estado de San Luis Potosí, se realizó un análisis mediante intersección espacial de los mapas de vegetación y uso del suelo serie II (1993) y serie IV (2007). El estudio se enfocó en cuatro zonas biogeográficas: Altiplano, Centro, Media y Huasteca. La tasa de deforestación anual se calculó para cada zona: Altiplano (0.11 %), Centro (-0.12 %, recuperación), Media (0.16 %), y Huasteca (0.51 %). En las zonas áridas y semiáridas se detectó un cambio de matorral a pastizal; mientras que en la zona Huasteca, la selva fue la vegetación más afectada. A excepción de la Huasteca, las tasas de deforestación anuales fueron más bajas que la media nacional (0.43 % de 1976 a 2000). Estos resultados brindan información valiosa para focalizar esfuerzos orientados a detener el proceso de deforestación en San Luis Potosí.
ECOLOGÍA, APROVECHAMIENTO Y COMERCIALIZACIÓN DEL ORÉGANO (Lippia graveolens H. B. K.) EN MAPIMÍ, DURANGO
Authors: Granados-Sánchez Diódoro , Martínez-Salvador Martín , López-Ríos Georgina F. , Borja-De la Rosa Amparo , Rodríguez-Yam Gabriel A.
Published: September 2013

El orégano, Lippia graveolens H. B. K., es una planta adaptada a las condiciones de aridez con capacidad para prosperar bajo diversos grados de presión por la recolección. En Mapimí, Durango, la planta ha sido colectada y comercializada durante años y significa una fuente de ingresos para las familias que dependen de su recolección, aunque los comerciantes obtienen la mayor parte de los beneficios. En la región de Mapimí se evaluaron las diversas áreas productoras con el fin de establecer la dinámica e impacto del proceso de recolección y sus efectos sobre la planta. Para esto, se hicieron recorridos de campo, toma de muestras y delimitación de las áreas de distribución del orégano. También se analizó el proceso de producción y los canales de comercialización, a fin de diseñar una alternativa de manejo que garantice la sustentabilidad de la actividad. El proceso de producción y comercialización se estudió mediante la aplicación de entrevistas abiertas a productores, visitas de campo y visitas a las empresas beneficiadoras y comercializadoras, así como a los intermediarios que intervienen en diferentes etapas del proceso.
PRODUCCIÓN DE HOJARASCA Y RETORNO DE NUTRIENTES VÍA FLIAR EN UN MATORRAL DESÉRTICO MICRÓFILO EN EL NORESTE DE MÉXICO
Authors: González-Rodríguez Humberto , Ramírez-Lozano Roque G. , Cantú-Silva Israel , Gómez-Meza Marco V. , Cotera-Correa Mauricio , Carrillo-Parra Artemio , Marroquín-Castillo Jonathan J.
Published: September 2013

La caída de hojarasca y el contenido de macro (Ca, N, P, Mg y K) y microminerales (Fe, Mn y Zn) de las hojas se compararon en dos sitios durante 12 meses (septiembre 2008-agosto 2009). El sitio 1 se ubicó en la comunidad El Llano de La Soledad, Galeana, Nuevo León (1,863 m) y el sitio 2 en la comunidad San José del Alamito, Satillo, Coahuila (1,895 m). En cada sitio se colocaron, aleatoriamente, 10 canastas (1 m2) para la captura de hojarasca. La caída anual de hojarasca en el sitio 2 fue mayor (407 g·m-2·año-1) que en el sitio 1 (162 g·m-2·año-1). Las hojas representaron el 47.7 y 53.2 % en el sitio 1 y 2, respectivamente, seguido de ramas (24.6 y 20.3 %), estructuras reproductivas (21.3 y 20.2 %) y otros (4.3 y 7.6 %). La deposición de macro y microminerales fue mayor en el sitio 2 que en el sitio 1. Las diferencias espaciales y temporales, en la cantidad de hojarasca y el retorno de minerales, pudieron estar relacionadas con las temperaturas extremas, composición de la vegetación y propiedades químicas del suelo.
EFECTO DEL MANEJO FORESTAL EN LA DIVERSIDAD Y COMPOSICIÓN ARBÓREA DE UN BOSQUE TEMPLADO DEL NOROESTE DE MÉXICO
Authors: Hernández-Salas Javier , Aguirre-Calderón Óscar A. , Alanís-Rodríguez Eduardo , Jiménez-Pérez Javier , Treviño-Garza Eduardo J. , González-Tagle Marco A. , Luján-Álvarez Concepción , Olivas-García Jesús M. , Domínguez-Pereda L. Alfonso
Published: September 2013

En la presente investigación se evaluó el efecto de las prácticas silvícolas en la diversidad y composición de especies arbóreas de un bosque templado del noroeste de México. Para ello, 46 parcelas fueron evaluadas cada 10 años: 1986, 1996 y 2006. Se estimaron los índices de diversidad alfa y beta de la comunidad arbórea, y la abundancia, dominancia, frecuencia e índice de valor de importancia de cada especie (IVI). Los resultados muestran que el aprovechamiento forestal modifica la diversidad y composición del estrato arbóreo. La comunidad arbórea mantuvo el número de especies pero disminuyó en los índices de Margalef y Shannon-Wiener de diversidad alfa. La composición (diversidad beta) se modificó en 16 %. El género Pinus aumentó los valores relativos de abundancia, dominancia, frecuencia e índice de valor de importancia, mientras que el género Quercus decreció. Las especies de mayor importancia ecológica fueron P. arizonica y P. durangensis.
IDENTIFICACIÓN DE UN DERIVADO DE LANOSTEROL PROCEDENTE DEL HONGO CULTIVADO Pisolithus arhizus (Scop.) Rauschert
Authors: Márquez-Fernández Olivia , Herrera Eloy , Castellanos-Onorio Olaya , Estrada-Torres Arturo , Trigos Ángel
Published: September 2013

Los hongos micorrizógenos se encuentran en asociación con las raíces de muchas plantas, incluyendo casi todas las especies de árboles como la familia Pinaceae. Algunos derivados triterpénicos de lanosterol se han aislado tanto del micelio como de los cuerpos fructíferos del hongo ectomicorrizógeno Pisolithus arhizus. En el presente trabajo, se cultivó una cepa de la especie P. arhizus, aislada de bosques de pino en Oaxaca en condiciones de laboratorio, con el fin de determinar qué tipo de compuestos se pueden encontrar en una cepa mexicana cultivada bajo condiciones asimbióticas y sus posibles implicaciones ecológicas. Los resultados confirman que, en la fermentación líquida in vitro del micelio, la cepa aislada de los bosques de México presenta el mismo tipo de triterpenos sin funcionalidad con el carbono-23 como otras cepas procedentes de bosques de Europa y Brasil, a pesar de que se utilizó un medio de cultivo PDA en lugar del medio de cultivo Melin-Norkrans.