bluuebunny/crossref_metadata_2025 huggingface dataset:
INVESTIGATION INTO THE INFLUENCE OF FLAME RETARDANT ADDITIVES ON SOME FIRE PROPERTIES OF POLYESTER MATERIALS APPLYING SMALL-SCALE TESTING TECHNIQUES
Authors: Półka Marzena , Gałaj Jerzy , Karpovič Zbignev
Published: September 2013

In order to investigate the impact of some inorganic additive flame retardants on the selected fire properties of the materials based on polyester resin Polimal 1033 APy, small-scale fire testing techniques have been used. Seven samples have been studied: unmodified PES, PES modified with MoO3 (7, 14 and 21 wt%) and PES modified with Sb2O3 (7, 14 and 21 wt%). The following flammable properties of materials have been determined: the heat of combustion (HOC), the ignition temperature of volatile thermal decomposition products (Tig), self-ignition temperature and oxygen index. A cone calorimeter method has been used for determining heat release rate (HRR), mass loss, specific extinction area (SEA) and other combustion parameters. The toxicological analysis of combustion products has been conducted. Based on the obtained results, the following conclusions have been made: (1) MoO3 and Sb2O3 added to the studied material change its flammable properties and fire parameters. It can be indicated by higher HOC, higher Tig and self-ignition temperature, as well as by lower HRR and SEA. Modified materials become safer in terms of fire hazard. (2) A significant reduction in HRRmax of approx. 40% in the content of 7 wt% has been observed. The lowest HRRmaxof approximately 300 kW/m2 and 450 kW/m2 have been obtained for 21 wt% in a range of 200–600 s at 30 kW/m2 and 100–400 s at 50 kW/m2 respectively. Except for a sample containing 7 wt% of Sb2O3, a clear local reduction in HRR (from 50 to 150 kW/m2), in case of all modified samples has been noticed. (3) Sb2O3 has a greater impact on the thermostability of the studied materials compared to MoO3 in all cases of heat flux density and additive concentrations. The effectiveness of Sb2O3, as a flame retardant is the most evident at 21 wt%.
CRITICAL DEPTH OF NORMAL CRACKS IN REINFORCED CONCRETE BEAMS OF RECTANGULAR CROSS-SECTION
Authors: Jokūbaitis Vidmantas , Juknevičius Linas
Published: September 2013

The evaluation of stress state of longitudinal tensile reinforcement is highly important while examining the technical state of under-reinforced concrete structures. The appearance of yield stress in tensile reinforcement could be treated as the start of incipient failure of the flexural structure. The state of tensile reinforcement of flexural reinforced concrete structures could be examined by observing the properties of normal cracks. This paper presents the analysis of the relationship between various parameters of a normal crack during its development. Some elements of fracture mechanics are used for analysis of stress state in flexural reinforced concrete members. The analytical data are compared to the experimental results, and the adjustment functions are proposed for flexural beams of certain cross section shape, dimensions and reinforcing ratio.
Inflammation and Hypertension in Rheumatoid Arthritis
Authors: Manavathongchai Siriporn , Bian Aihua , Rho Young Hee , Oeser Annette , Solus Joseph F. , Gebretsadik Tebeb , Shintani Ayumi , Stein C. Michael
Published: September 2013

Objective.

Hypertension (HTN), a common modifiable cardiovascular risk factor, is more common in patients with rheumatoid arthritis (RA), but the underlying mechanisms are unclear. We examined the hypothesis that mediators of inflammation and markers of cardiovascular risk are associated with HTN in RA.

Methods.

We compared measures of inflammation [serum C-reactive protein (CRP), tumor necrosis factor alpha (TNF-α), interleukin 6 (IL-6), homocysteine, and leptin concentrations] and insulin resistance [homeostasis model assessment index (HOMA)] in RA patients with (n = 90) and without HTN (n = 79). HTN was defined as blood pressure ≥ 140/90 mm Hg or treatment with antihypertensive therapy. The independent association of markers of interest with HTN was examined using multivariable logistic regression.

Results.

Patients with HTN were significantly older and had longer disease duration than those without HTN (both p < 0.001). Concentrations of homocysteine [11.1 (8.5–13.5) μmol/l vs 9.3 (7.8–11.0) μmol/l] were significantly higher in patients with HTN (p < 0.001). After adjustment for age, sex, race, smoking, body mass index, and corticosteroid and nonsteroidal antiinflammatory drugs (NSAID) use, increased concentrations of homocysteine (OR 2.9, 95% CI: 1.5–5.5, p = 0.001), and leptin (OR 2.0, 95% CI: 1.0–3.8, p = 0.046) were significantly associated with HTN, but the 28-joint Disease Activity Score, IL-6, CRP, TNF-α, and HOMA index were not (all p > 0.05).

Conclusion.

HTN in patients with RA is not associated with generalized systemic inflammation or insulin resistance, but is associated with increasing concentrations of homocysteine and leptin. The pathogenesis of HTN in RA may involve pathways more regularly associated with fat and vascular homeostasis.
RETRACTED: Social identity, ethnicity and the gospel of reconciliation
Authors: Goroncy Jason A.
Published: September 2013

This article attends to the relationship between our ethnic, social and cultural identities, and the creation of the new communal identity embodied in the Christian community. Drawing upon six New Testament texts – Ephesians 2:11–22; Galatians 3:27–28, 1 Corinthians 7:17–24 and 10:17, 1 Peter 2:9–11 and Revelation 21:24–26 – it is argued that the creation of a new and prime identity in Christ does not abrogate other creaturely identities, even as it calls for the removal of such as boundary markers. Catholicity, in other words, is intrinsically related to the most radical particularity, and demands an ongoing work of discernment and of judgement vis-à-vis the gospel itself. Those baptised into Christ are now to live in the reality of Christ who is both the boundary and centre of their existence, a boundary which includes all humanity in its cultural, ethnic, gendered, social and historical particularities.*This article has been retracted at the request of the Editor-in-Chief. Reason: It has come to light that sections of text in this article were inadvertently copied verbatim from an unpublished source without permission. This article has been removed for legal reasons. Apologies are offered to the readers of the journal. Copies for archival purposes can be obtained from submissions@hts.org.za
Assessment of acquired immune response to Rhipicephalus appendiculatus tick infestation in different goat breeds
Authors: Gopalraj Jeyanthi B.P. , Clarke Francoise C. , Donkin Edward F.
Published: September 2013

Changes in serum gamma globulin levels, numbers of replete female ticks and engorged tick mass were used as parameters to monitor the acquired immune response (antibody mediated immune response) elicited by Rhipicephalus appendiculatus adult tick infestations. Three consecutive Rhipicephalus appendiculatus adult tick infestations were applied to South African Indigenous goats (Nguni), Saanen goats and cross-bred goats (Saanen goats crossed with South African Indigenous goats [Nguni]) under laboratory conditions. During the three consecutive Rhipicephalus appendiculatus adult tick infestations the serum gamma globulin levels increased in all three breeds, whilst the mean replete female tick numbers and engorged tick mass decreased. Even though all three goat breeds exhibited an acquired immune response, the South African Indigenous goats (Nguni) response was significantly higher than that of the Saanen and cross-bred goats. However, the acquired immune response elicited by Saanen goats was significantly lower when compared with cross-bred goats.
A dual-process model of diversity outcomes: The case South African police service in the Pretoria area
Authors: Jackson Leon T.B. , Van de Vijver Fons J.R. , Molokoane Davey H.
Published: September 2013

Orientation: The study addresses the question of how employees of the South African Police Service (SAPS) cope with intercultural relations in an increasingly diverse organisation.Research purpose: A dual-process model of diversity outcomes was tested in which a distinction is made between a positive (work-related) stream that links positive diversity conditions through active coping to work outcomes and a relatively independent health related) stream of negative antecedents, mediating passive coping skills and ill-health related outcomes.Motivation for the study: To test the viability of a dual-process model to understand diversity outcomes in the workplace.Research design, approach and methods: A convenience sample (n= 158) was recruited from members of the SAPS in Gauteng, using a cross-sectional design. Instruments used in previous acculturation research were adapted to measure contextual factors, coping and diversity outcomes.Main findings: A very good fit for the proposed hypothetical model was found. Approach coping partially mediated the relationship between positive acculturation conditions and the subjective experience of work success whereas avoidance coping fully mediated the relationship between discrimination, and ill-health symptoms are related to ill-health symptoms.Practical/managerial implications: Mainstream-facilitating conditions and discrimination influence individual coping styles, which in turn impact on ill-health and the subjective experience of work success. In addition, ill-health also impacts negatively on work-success experiences amongst the sampled SAPS members. It would thus make sense for the SAPS to sanction discrimination.Contribution/value added: A variation of the mediated dual-process model for diversity (Jackson & Van de Vijver, in press), using coping strategies as mediators was supported. The model adds new insights in diversity in organisations.
Daniel 9 as part of an apocalyptic book?
Authors: Nel Marius
Published: September 2013

Daniel 9 relates how Daniel studies the Hebrew Holy Scriptures and finds the prophecy of Jeremiah that Jerusalem will lie desolate for seventy years. He reacts by devoting himself to prayer and fasting in order to remind God of this promise of restoring his people. The better part of the chapter is dedicated to the contents of his prayer. During the prayer, the man, Gabriel, appears with the intent to give Daniel an understanding of the meaning of the seventy years, which is the measure of the punishment of Israel�s transgression and sin and which will end with eternal righteousness, when the Holy of Holies will be anointed. The Book of Daniel consists of two sections: the tales of the first six chapters and the visions of the last six chapters. This article asked the question: what role does Daniel 9 play as a part of the apocalyptic section of the book? Is Daniel�s prayer and Gabriel�s revelation apocalyptically conditioned? Why did the author or compiler include it in the book and, especially, in the second, apocalyptic section of the book? The conclusion of this article was that Daniel 9 was placed intentionally by the compiler in the latter half of the book because of the revelation about the seventy weeks, which is in line with the last three chapters� indication of the end times and Israel�s elevation to become the ruler of the earth. Several arguments were formulated to support this conclusion.
On Arithmetic Monodromy Representations of Eisenstein Type in Fundamental Groups of Once Punctured Elliptic Curves
Authors: Nakamura Hiroaki
Published: September 2013

We discuss certain arithmetic invariants arising from the monodromy representation in fundamental groups of a family of once punctured elliptic curves of characteristic zero. An explicit formula in terms of Kummer properties of modular units is given to describe these invariants. In the complex analytic model, the formula turns out to feature generalized Dedekind–Rademacher functions as the main periodic part of the invariant.
Nakajima Varieties and Repetitive Algebras
Authors: Leclerc Bernard , Plamondon Pierre-Guy
Published: September 2013

We realize certain graded Nakajima varieties of finite Dynkin type as orbit closures of repetitive algebras of Dynkin quivers. As an application, we show that the perverse sheaves introduced by Nakajima to describe irreducible characters of quantum loop algebras are isomorphic to the intersection cohomology sheaves of these orbit closures.
Positivity for Cluster Algebras of Rank 3
Authors: Lee Kyungyong , Schiffler Ralf
Published: September 2013

We prove the positivity conjecture for skew-symmetric coefficient-free cluster algebras of rank 3.
Boundary value problems and integral operators for the bi-Laplacian in non-smooth domains
Authors: Mitrea Irina , Mitrea Marius
Published: September 2013

In this paper we explore the effectiveness of the classical method of layer potentials in the treatment of boundary value problems for the bi-Laplacian formulated in arbitrary Lipschitz domains, Lipschitz domains whose outward unit normal has small mean-oscillations, and domains of class

\mathcal C^1

.
Coerciveness Property for a Class of Non-Smooth Functionals
Authors: Motreanu Dumitru , Motreanu Viorica V.
Published: September 2013

The paper establishes a general coerciveness property for a class of non-smooth func-tionals satisfying an appropriate Palais-Smale condition. This result is obtained by applying an abstract principle supplying qualitative information concerning the asymptotic behaviour of a non-smooth functional. Comparison with other results in this field is provided.
A Topological Fixed-Point Index Theory for Evolution Inclusions
Authors: Bader R.
Published: September 2013

In the paper we construct a topological fixed-point theory for a class of set-valued maps which appears in natural way in boundary value problems for differential inclusions. Our construction is based upon the notion of (

U, V

)-approximation in the sense of Ben-El-Mechaiekh and Deguire. As applications we consider initial-value problems for nonlinear evolution inclusions of the type

x'(t) \in –A(t,x(t)) + F(t, x(t))

|x(0) = x_0

where the operator

A

satisfies various monotonicity assumptions and

F

is an upper semicontinuous set-valued perturbation.
Blow-Up and Convergence Results for a One-Dimensional Non-Local Parabolic Problem
Authors: Rougirel A.
Published: September 2013

Considering a one-dimensional non-local semilinear parabolic problem, it is shown that blow-up in finite time occurs for suitable large initial conditions. The asymptotic behavior of global solutions corresponding to small initial conditions is also investigated. Their convergence in

H^1

-norm to a well determinated stationary solution is proved.
On the Fredholm Property of the Stokes Operator in a Layer-Like Domain
Authors: Nazarov Sergei A. , Pileckas K.
Published: September 2013

The Stokes problem is studied in the domain

\Omega \subset \mathbb R^3

coinciding with the layer

\Pi = {x = (y,z) : y = (y_1, y_2) \in (0,1)}

outside some ball. It is shown that the operator of such problem is of Fredholm type; this operator is defined on a certain weighted function space

\mathcal D^l_{\beta} (\Omega­

) with norm determined by a stepwise anisotropic distribution of weight factors (the direction of

z

is distinguished). The smoothness exponent

l

is allowed to be a positive integer, and the weight exponent

\beta

is an arbitrary real number except for the integer set

\mathbb Z

where the Fredholm property is lost. Dimensions of the kernel and cokernel of the operator are calculated in dependence of

\beta

. It turns out that, at any admissible

\beta

, the operator index does not vanish. Based on the generalized Green formula, asymptotic conditions at infinity are imposed to provide the problem with index zero.
Conditional Stability of a Real Inverse Formula for the Laplace Transform
Authors: Saitoh S. , Kim Tuan Vu , Yamamoto Masahiro
Published: September 2013

We establish a conditional stability estimate of a real inverse formula for the Laplace transform of functions under the assumption that the Bergman-Selberg norms of the Laplace transform of those functions are uniformly bounded. The rate of the stability estimate is shown to be of logarithmic order.
On Inequalities of Korn, Friedrichs, Magenes-Stampacchia-Necas and Babuska-Aziz
Authors: Tiero A.
Published: September 2013

The equivalence between the inequalities of Korn, Friedrichs, Magenes-Stampacchia-Necas and Babuska-Aziz is derived using some elementary properties of the gradient, divergence and curl operators implied by these inequalities.
Some Series over the Product of Two Trigonometric Functions and Series Involving Bessel Functions
Authors: Stankovic Miomir S. , Vidanovic Mirjana V. , Trickovic Slobodan B.
Published: September 2013

The sum of the series

S_{\alpha} = S_{\alpha} s,a,b,f(y),g(x) = \sum^\infty_{n=1} \frac {(s)^{n–1}f (an – b)y g (an–b)x}{(an–b)^{\alpha}}

involving the product of two trigonometric functions is obtained using the sum of the series

\sum^\infty_{n=1} \frac {(s)^{(n–1)} f((an–b)x)}{(an–b)^\alpha} = \frac {c\pi}{2\Gamma (\alpha) f (\frac {\pi \alpha}{2})} x^{\alpha–1} + \sum^\infty_{i=0} (–1)^i \frac {F(\alpha – 2i – \delta)}{(2i + \delta)!} x^{2i+\delta}

whose terms involve one trigonometric function. The first series is represented as series in terms of the Riemann zeta and related functions, which has a closed form in certain cases. Some applications of these results to the summation of series containing Bessel functions are given. The obtained results also include as special cases formulas in some known books. We further show how to make use of these results to obtain closed form solutions of some boundary value problems in mathematical physics.
The Generalized Riemann Problem of Linear Conjugation for Non-Homogeneous Polyanalytic Equations of Order $n$ in $W_{n,p}(D)$
Authors: Mshimba Ali Seif
Published: September 2013

We consider a non-homogeneous polyanalytic partial differential equation of order

n

in a simply-connected domain

D

with smooth boundary

\partial D

in the complex plane

\mathbb C

. Initially we transform the given equation into an equivalent system of integro-differential equations and then find the general solution of the former in

W_{n,p} (D)

. Next we pose and prove the solvability of a generalized Riemann problem of linear conjugation to the differential equation. This is effected by first reducing the Riemann problem to a corresponding one for a polyanalytic function. The latter is solved by first transforming it into

n

classical Riemann problems of linear conjugation for

n

holomorphic functions expressed in terms of the analytic functions which define the polyanalytic function. The solution of the classical Riemann problem is available in the literature.
A Semilinear Furi-Martelli-Vignoli Spectrum
Authors: Appell Jürgen , De Pascale Espedito , Vignoli A.
Published: September 2013

In this note we extend a spectrum which was introduced by Furi, Martelli and the third author in 1978 for continuous nonlinear maps

F

to a certain new spectrum for a “semilinear pair” (

L, F

), with

L

being a linear Fredholm operator of index zero, and

F

being nonlinear and continuous.
A Note on Degenerate Variational Problems with Linear Growth
Authors: Bildhauer M.
Published: September 2013

Given a class of strictly convex and smooth integrands

f

with linear growth, we consider the minimization problem

\int_{\Omega} f \bigtriangledown u) dx \rightarrow

min and the dual problem with maximizer

\sigma

. Although degenerate problems are studied, the validity of the classical duality relation is proved in the following sense: there exists a generalized minimizer

u* \in BV (\Omega; \mathbb R^N)

of the original problem such that

\sigma (x) = \bigtriangledown f (\bigtriangledown^a u*)

holds almost everywhere, where

\bigtriangledown^a u*

denotes the absolutely continuous part of

\bigtriangledown u*

with respect to the Lebesgue measure. In particular, this relation is also true in regions of degeneracy, i.e. at points

x

such that

D^2f(\bigtriangledown ^a u*(x)) = 0

. As an application, we can improve the known regularity results for the dual solution.
Entropy Solution for a Hyperbolic Equation
Authors: Bernard Sévérine
Published: September 2013

Nonlinear hyperbolic systems of conservation laws play a central role in Science and Engineering, and their mathematical theory as well as their numerical approximation have made recent significative progress. This paper deals with the existence and uniqueness of an entropy solution of the Cauchy problem for the quasi-linear equation

u-t + a(f(u))_x = 0

in one space dimension, where

a

is a non-smooth coefficient.
$C^{1,\alpha}$ Local Regularity for the Solutions of the $p$-Laplacian on the Heisenberg Group for $2≤p<1+\sqrt5$
Authors: Marchi Silvana
Published: September 2013

We prove local Hölder continuity of the homogeneous gradient for weak solutions

u \in W^{1,p}_{loc}

of the

p

-Laplacian on the Heisenberg group

\mathbb H^n

for

2≤p<1+\sqrt 5

.
Existence and Regularity Results for Non-Negative Solutions of some Semilinear Elliptic Variational Inequalities via Mountain Pass Techniques
Authors: Girardi Mario , Mastroeni Loretta , Matzeu Michele
Published: September 2013

The main result stated in the present paper is the existence of a non-negative solution for a semilinear variational inequality through the use of some estimates for the Mountain-Pass critical points obtained for the penalized equations associated with the variational inequality. The positivity of the solution is achieved through a regularity result and the strong maximum principle.
Free Boundary Problem for a One-Dimensional Transport Equation
Authors: Kuttler Christina
Published: September 2013

For a linear transport equation in one space dimension with speeds in a compact interval and a general symmetric kernel for the change of velocity a problem with free boundary (Stefan problem) is stated. The case of constant speed corresponds to a Stefan problem for the damped wave equation (telegraph equation). Existence and uniqueness of the free boundary is shown, and the connection to the classical Stefan problem (parabolic limit) is exhibited.
Asymptotical Behavior of Solutions of Nonlinear Elliptic Equations in $\mathrm R^N$
Authors: Grillot Michèle , Grillot Philippe
Published: September 2013

In this paper we study the behavior near infinity of non-negative solutions

u \in C^2(\mathbb R^N)

of the semi-linear elliptic equation

– \Delta u+u^q – u^p =0

where

q \in (0, 1), p > q

and

N ≥2

. Especially, for a non-negative radial solution of this equation we prove the following alternative:

\qquad

either

u

has a compact support

\qquad

or

u

tends to one at infinity.Moreover, we prove that if a general solution is sufficiently small in some sense, then it is compactly supported. To prove this result we use some inequalities between the solution and its spherical average at a shift point and consider a differential inequality. Finally, we prove the existence of non-trivial solutions which converge to one at infinity.
On Bernis’ Interpolation Inequalities in Multiple Space Dimensions
Authors: Grün Günther
Published: September 2013

In spatial dimensions

d < 6

, we derive estimates of the form

\int_{\Omega} u^{n–4} |\nabla u|^6 + \int_{\Omega} u^{n–2}|\nabla u|^2|D^2u|^2 ≤ C \int_{\Omega} u^n|\nabla \Delta u|^2

for functions

u \in H^2 (\Omega)

with vanishing normal derivatives on the boundary

\partial \Omega

. These inequalities imply that

\int_{\Omega}|\nabla \Delta u \frac {n+2}{2} |^2

can be controlled by

\int _{\Omega} u^n| \nabla\Delta u|^2

. This observation will be a key ingredient for the proof of certain qualitative results – e.g. finite speed of propagation or occurrence of a waiting time phenomenon – for solutions to fourth order degenerate parabolic equations like the thin film equation. Our result generalizes – in a slightly modified way – estimates in one space dimension which were obtained by F. Bernis.
On a New Type of Eisenstein Series in Clifford Analysis
Authors: Kraußhar Rolf Sören
Published: September 2013

In this paper we deduce a recursion formula for the partial derivatives of the fundamental solution of the generalized Cauchy-Riemann operator in

\mathbb R^{k+1}

in terms of permutational products. These functions generalize the classical negative power functions to Clifford analysis. We exploit them to introduce a new generalization of the classical complex analytic Eisenstein series on the half-plane to higher dimensions satisfying the generalized Cauchy-Riemann differential equation. Under function-theoretical and number-theoretical aspects we investigate their Fourier series expansion in which multiple divisor sums and certain generalizations of the Riemann zeta function play a crucial role.
Differential-Functional Inequalities for Bounded Vector-Valued Functions
Authors: Herzog Gerd
Published: September 2013

For the space

\mathbb R^n

ordered by a cone and some functions

f : \mathbb R^{n+mn} \to \mathbb R^n

and

h_1, ..., h_m : \mathbb R \to \mathbb R

we consider differential-functional inequalities of the type

v'' + cv' + f v,v(_1), ..., v(h_m) ≤ u'' + cu' + f u, u(h_1), ..., u(h_m)

and conclude

u ≤ v

under suitable conditions on

u, v, h_k

and

f

. The result can be applied to obtain existence and uniqueness results for differential-functional boundary value problems of the form

u'' + cu' + f u, u(h_1), ..., u(h_m) = q

with

u \in C^2 (\mathbb R, \mathbb R^n)

bounded.
Special First Order Systems in Clifford Analysis and Resolutions
Authors: Sabadini Irene , Sommen Franciscus
Published: September 2013

In this paper we present and discuss to some extent a number of first order systems of partial differential operators with constant coefficients which arise naturally within the language of Clifford analysis. We also present resolutions for certain examples.
Local Existence Result of the Dopant Diffusion in Arbitrary Space Dimensions
Authors: Bader R. , Merz W.
Published: September 2013

In this paper we consider the pair diffusion process in more than two spatial dimensions. In this case we are able to prove just a local existence result, since it is not possible to deduce global a priori estimates for the equations as it can be done in the two-dimensional case. The model includes a nonlinear system of reaction-drift-diffusion equations, a nonlinear ordinary differential equation in Banach spaces and an elliptic equation for the electrostatic potential. The local existence result is based on the fixed point theorem of Schauder.
Stably Solvable Maps are Unstable under Small Perturbations
Authors: Furi Massimo
Published: September 2013

We show that the set of stably solvable maps from an infinite dimensional Banach space

E

into itself is not open in the topological space

C(E)

of the continuous selfmaps of

E

. The question of whether or not this set is open is related to nonlinear spectral theory and was posed in [7].
Extremal Solutions for a Class of Unilateral Problems
Authors: Huy Nguyen Bich , Thanh Nguyen Duy , Thanh Tran Dinh
Published: September 2013

We apply a fixed point theorem for increasing operators in ordered Banach spaces to prove the existence of extremal (i.e. maximal or minimal) solutions for the variational inequality

\langle Av, w – v\rangle ≥ \int _\Omega f(x, v)(w–v)dx

where

A

is the

p

-Laplacian and

f(x,u) = F(x,u,u)

with

F(x,u,v)

being a function, non-decreasing in

u

and non-increasing in

v

.
On the Solutions of a Quadratic Integral and an Integral-Differential Equation
Authors: von Wolfersdorf Lothar
Published: September 2013

An integral equation and a related integral-differential equation of first order over

\mathbb R_+

with a quadratic integral term representing the so-called autocorrelation of the unknown function is dealt with. For both equations the general solution is constructed and estimated in the

L^2

-norm. Further, the asymptotic behaviour and the stability of the solution are investigated.
A General Inverse Problem for a Memory Kernel in One-Dimensional Viscoelasticity
Authors: Janno Jaan , von Wolfersdorf Lothar
Published: September 2013

A general inverse problem for the identification of a memory kernel in viscoelasticity in one space dimension is dealt with, where the kernel is represented by a finite sum of products of known spatially dependent functions and unknown time-dependent functions. Using the Laplace transform method an existence and uniqueness theorem for the memory kernel is proved.
Stability Phenomenon for Generalizations of Algebraic Differential Equations
Authors: Barsegian G. , Begehr Heinrich , Laine Ilpo
Published: September 2013

Certain stability properties for meromorphic solutions

w(z) = u(x,y) + i v(x,y)

of partial differential equations of the form

\sum^m–{t=0}f_t(w^2)^{m–t} = 0

are considered. Here the coefficients

f_t

are functions of

x, y

, of

u,v

and the partial derivatives of

u,v

. Assuming that certain growth conditions for the coefficients

f_t

are valid in the preimage under

w

of five distinct complex values, we find growth estimates, in the whole complex plane, for the order

\rho (w)

and the unintegrated Ahlfors-Shimizu characteristic

A(r,w)

.
On Topological Singular Set of Maps with Finite 3-Energy into $S^3$
Authors: Pakzad M.R.
Published: September 2013

We prove that the topological singular set of a map in

W^{1,3} (M, \mathbb S^3)

is the boundary of an integer-multiplicity rectifiable current in

M

, where

M

is a closed smooth manifold of dimension greater than 3 and

\mathbb S^3

is the three-dimensional sphere. Also, we prove that the mass of the minimal integer-multiplicity rectifiable current taking this set as the boundary is a strongly continuous functional on

W^{1,3} (M, \mathbb S^3)

.
Results on Balanced Products of Distributions in Colombeau Algebra
Authors: Damyanov B.
Published: September 2013

Various products of distributions with coinciding point singularities are derived when the products are ’balanced’ so that their sum is a generalized function which is associated to a distribution. These products follow the idea of a known result on distributional products published by Jan Mikusinski in 1966. The results in the present paper are obtained in the Colombeau algebra of generalized functions, which provides an efficient tool for dealing with nonlinear problems of Schwartz distributions.
Tensor Algebras and Displacement Structure II: Non-Commutative Szegö Polynomials
Authors: Constantinescu Tiberiu , Johnson J. L.
Published: September 2013

In this paper we continue to explore the connection between tensor algebras and displacement structure. We focus on recursive orthonormalization and we develop an analogue of the Szegö-type theory of orthogonal polynomials in the unit circle for several non-commuting variables. Thus we obtain recurrence equations and Christoffel-Darboux formulas for Szegö polynomials in several non-commuting variables, as well as a Favard type result. Also, we continue to study a Szegö-type kernel for the

N

-dimensional unit ball of an infinite-dimensional Hilbert space.
On Resonant Differential Equations with Unbounded Non-Linearities
Authors: Krasnosel'skii A. M. , Kuznetsov N. A. , Rachinskii D.
Published: September 2013

We present a method to study asymptotically linear degenerate problems with sublinear unbounded non-linearities. The method is based on the uniform convergence to zero of projections of non-linearity increments onto some finite-dimensional spaces. Such convergence was used for the analysis of resonant equations with bounded non-linearities by many authors. The unboundedness of nonlinear terms complicates essentially the analysis of most problems: existence results, approximate methods, systems with parameters, stability, dissipativity, etc. In this paper we present statements on projection convergence for unbounded non-linearities and apply them to various resonant asymptotically linear problems: existence of forced periodic oscillations and unbounded sequences of such oscillations, existence of unbounded solutions, sharp analysis of integral equations with simple degeneration of the linear part (a scalar two-point boundary value problem is considered as an example), existence of non-trivial cycles for higher order autonomous ordinary differential equations, and Hopf bifurcations at infinity.
Exact Solution of a System of Generalized Hopf Equations
Authors: Joseph K.T.
Published: September 2013

In this paper we construct explicit solutions for initial value problem for a system of first order equations. When

n = 1

, this system is just the standard Hopf equation in conservative form. When

n > 1

, the system is non-conservative. We use the vanishing viscosity method to construct solutions. As the system is non-conservative we use Volpert product and the algebra of generalized Colombeau functions to make sense of the products which appear in the equations.
Comparison of Non-Commutative 2- and $p$-Summing Operators from $B(l_2)$ into $OH$
Authors: Mezrag L.
Published: September 2013

In the theory of

p

-summing operators studied by Pietsch we know that

\pi_2(C(K),H) = \pi_p(C(K),H)

for any Hilbert space

H

and any

p

such that

2 < p < +\infty

. In this paper we prove that this equality is not true in the same notion generalized by Junge and Pisier to operator spaces, i.e.

\pi_{l_2} (Bl_2), OH) (=\pi^0_2(B(l_2),OH)) \neq \pi_{l_p}(B(l_2),OH)

.
A Unified Approach to Linear Differential Algebraic Equations and their Adjoints
Authors: Balla K. , März Roswitha
Published: September 2013

Instead of a single matrix occurring in the standard setting, the leading term of the linear differential algebraic equation is composed of a pair of well matched matrices. An index notion is proposed for the equations. The coefficients are assumed to be continuous and only certain subspaces have to be continuously differentiable. The solvability of lower index problems is proved. The solution representations are based on the solutions of certain inherent regular ordinary differential equations that are uniquely determined by the problem data. The assumptions allow for a unified treatment of the original equation and its adjoint. Both equations have the same index and are solvable simultaneously. Their fundamental solution matrices satisfy a relation that generalizes the classical Lagrange identity.
On Oscillation of a Differential Equation with Infinite Number of Delays
Authors: Berezansky Leonid , Braverman Elena
Published: September 2013

For a scalar delay differential equation

\dot{x}(t) + \sum^\infty_{k=1} a_k(t)x(h_k(t)) = 0 \; \; \; (H_k(t) ≤ t)

a connection between the following four properties is established:
A Certain Series Associated with Catalan’s Constant
Authors: Adamchik V.S.
Published: September 2013

A parametric class of series generated by integration of complete elliptic integrals

\sum^\infty_{–r \neq k=0} \frac{\bigl(\begin{smallmatrix} 2k\\ k \end{smallmatrix} \bigr)}{(k+r)16^k}

is valuated in closed form. Alternative proofs to results of Ramanujan and others are given. Also, a particular case of the Saalschützian hypergeometric series

_4F_3(1)

is derived.
The Set of Divergent Infinite Products in a Banach Space is $\sigma$-Porous
Authors: Reich Simeon , Zaslavski Alexander J.
Published: September 2013

Let

K

be a bounded closed convex subset of a Banach space. We study several convergence properties of infinite products of non-expansive self-mappings of

K

. In our recent work we have considered several spaces of sequences of such self-mappings. Endowing them with appropriate topologies, we have shown that the infinite products corresponding to generic sequences converge. In the present paper we prove that the subsets consisting of all sequences of mappings with divergent infinite products are not only of the first Baire category, but also

\sigma

-porous.
On the Spectral Radius of Convolution Dilation Operators
Authors: Didenko Victor D. , Korenovskyy A.A. , Lee S.L.
Published: September 2013

Convolution dilation operators with non-compactly supported kernels are considered and effective formulae for their spectral radii are found. The formulae depend on the behaviour of the eigenvalues of the dilation matrix.
On a Similarity Boundary Layer Equation
Authors: Brighi B.
Published: September 2013

The purpose of this paper is to study the autonomous third order nonlinear differential equation

f'''+ \frac{m+1}{2} f f'' – mf'^2 = 0

on

(0, \infty)

, subject to the boundary conditions

f(0) = a \in \mathbb R, f'(0) = 1

and

f'(t) \rightarrow 0

as

t \rightarrow \infty

. This problem arises when looking for similarity solutions to problems of boundary-layer theory in some contexts of fluids mechanics, as free convection in porous medium or flow adjacent to a stretching wall. Our goal here is to investigate by a direct approach this boundary value problem as completely as possible, say studying existence or non-existence and uniqueness or non-uniqueness of solutions according to the values of the real parameter m. In particular, we will emphasize similarities and differences between the cases

a = 0

and

a \neq 0

in the boundary condition

f(0) = a

.
On the Problem of Periodic Evolution Inclusions of the Subdifferential Type
Authors: Bader R. , Papageorgiou Nikolaos S.
Published: September 2013

We examine nonlinear periodic evolution inclusions of the subdifferential type and prove two existence theorems: one for the "non-convex, lower semicontinuous" problem and the other for the "convex,

h

-upper semicontinuous" problem. Our method of proof is based on the theory of nonlinear operators of monotone type and on multi-valued analysis. We also present three examples from partial and ordinary differential inclusions, illustrating the applicability of our work.
Some Remarks on Complementarity Problems in a Hilbert Space
Authors: Carbone Antonio , Zabrejko P. P.
Published: September 2013

We present a new approach to the analysis of solvability properties for complementarity problems in a Hilbert space. This approach is based on the Skrypnik degree which, in the case of mappings in a Hilbert space, is essentially more general in comparison with the classical Leray-Schauder degree. Namely, the Skrypnik degree allows us to obtain some new results about solvability of complementarity problems in the infinite-dimensional case. The case of generalized solutions is also considered.
On the Asymptotics of Nonlinear Difference Equations
Authors: Berg Lothar
Published: September 2013

Solutions of nonlinear difference equations of second order are investigated with respect to their asymptotic behaviour. In particular, seven conjectures of Kulenović and Ladas concerning rational difference equations are verified.
On the Representation of Generalized Analytic Vectors
Authors: Berglez Peter
Published: September 2013

This paper is concerned with the representation of generalized analytic vectors which are defined as solutions of certain elliptic systems of linear first-order partial differential equations in two complex variables. For the explicite representation of solutions we give integral operators of Vekua type as well as differential operators of Bauer type which map holomorphic vectors onto the set of solutions. For the existence of the differential operators we give a necessary and sufficient condition. We discuss properties of these operators and show how to construct the kernels of the integral operators using the differential operators. Finally we present examples for systems of differential equations for which all the solutions can be represented explicitely.
On the Operator-Valued Nevanlinna-Pick Problem
Authors: Ionescu A.
Published: September 2013

In this note we construct a specific Schur-Nevanlinna type algorithm that will be used in describing more precisely the solutions of the operator-valued Nevanlinna-Pick problem with the so-called method of Weyl circles. We also present an approach to the Pick criterion in the operator-valued setting.
Degenerate Stieltjes Moment Problem and Associated $J$-Inner Polynomials
Authors: Bolotnikov Vladimir
Published: September 2013

In this paper we consider the truncated Stieltjes matrix moment problem when the so-called information matrices are degenerate and describe the set of all solutions in terms of the linear fractional transformation using the fundamental matrix inequality method.
On a Class of Nonlinear Convolution Equations
Authors: von Wolfersdorf Lothar , Janno Jaan
Published: September 2013

By means of weighted norms existence and uniqueness theorems are proved for some classes of nonlinear convolution equations in Lebesgue spaces

L_p

and spaces

C

of continuous functions. The applicability of the theorems is shown by examples
Degenerate Parabolic Differential Equations of Fourth Order and a Plasticity Model with Non-Local Hardening
Authors: Grün Günther
Published: September 2013

By the means of energy estimates we prove existence and non-negativity results for degenerate parabolic partial differential equations of fourth order in arbitrary space dimensions. In addition, we present an elasto-viscoplastic model of Norton-Hoff type with isotropic, non-local hardening which takes the formation of dislocation patterns during plastic deformation into consideration. Finally, we give an existence result for this model.
A Variational Approach to Boundary Value Problems for a Class of Nonlinear Systems of Mixed Type
Authors: Gittel H.-P.
Published: September 2013

Transonic small disturbance theory in two dimensions leads to a nonlinear first-order system of mixed type. For such systems corresponding variational problems are formulated. These minimum problems are studied on closed sets of admissible functions satisfying certain boundedness constraints and entropy conditions. Existence theorems can be proved though the functionals need not be convex and the given sets are not compact. Furthermore, some properties of minimizers are derived.
A Fully Discrete Galerkin Method for Integral and Pseudo differential Equations on Closed Curves
Authors: Kelle O. , Vainikko Gennadi
Published: September 2013

We propose a cheep fully discrete version of the trigonometric Galerkin method of optimal accuracy order for integral and pseudodifferential equations on closed curves. A practical implementation of the method leads to a band system of linear algebraic equations. The error analysis is based on a thorough study of related integral operators in Sobolev spaces of periodic functions.
On the Discrete Spectrum of Ordinary Differential Operators in Weighted Function Spaces
Authors: Müller-Pfeiffer Erich , Jiong Sun
Published: September 2013

The investigations deal with the spectrum of ordinary differential equations of order

2n

where the underlying Hubert space is weighted. Especially, conditions on the coefficients are given such that the spectra are discrete.
Maximal Elements and Coincident Points for Couple-Majorized Mappings in Product Topological Vector Spaces
Authors: Deguire P. , Yuan Xian-Zhi
Published: September 2013

By introducing a concept called ’couple-majorized mapping’ in product topoogical vector spaces we establish existence theorems of maximal elements for couple.majorized set-valued families with arbitrary index set. As applications, some component coincidence and fixed points theorems are given which could be regarded as product extension version of the Fan-Browder fixed point theorem and related coincidence theorems. Finally, a coincidence theorem is used to derive the Sion minimax inequality in the case of two functions.
Conformally Covariant Operators in Clifford Analysis
Authors: Ryan John
Published: September 2013

Following recent work of Peetre and Qian, the conformal covariance of convolution operators involving the fundamental solutions to iterates of the Dirac operator in Euclidean space is described using Vahlen matrices. This conformal covariance is applied to a number of problems, including Dirichlet problems over unbounded domains.
Existence and Uniqueness of a Regular Solution of the Cauchy- Dirichlet Problem for Doubly Nonlinear Parabolic Equations
Authors: Ivanov A.V.
Published: September 2013

Existence and uniqueness of some Holder continuous generalized solution of Cauchy-Dirichlet problem for a class of degenerate or singular quasilinear parabolic equations is established. Similar equations arise in the study of turbulent filtration of a gas or a fluid through porous media.
An Example for Different Associated Spaces in the Case of Pseudoanalytic Functions
Authors: Yüksel U.
Published: September 2013

The theory of solving initial-value problems in associated spaces makes it possible to solve initial-value problems with more general initial functions. In many cases the associated space is not uniquely determined, i.e. there exist various so-called co-associated spaces in which initial-value problems can be solved. The present paper is aimed at giving an example to this fact.
On a Biquaternionic Bag Model
Authors: Kravchenko Vladislav V.
Published: September 2013

There is considered a biquaternionic reformulation of a linear bag model describing the phenomenon of quarks confinement. The problem reduces to a boundary singular integral equation associated with the biquaternionic hyperholomorphic function theory which allows to study the invertibility and Fredholmness of the bag model.
A Classification of Special Riemannian 3-Manifolds with Distinct Constant Ricci Eigenvalues
Authors: Kowalski O. , Prüfer Friedbert
Published: September 2013

All Riemannian 3-manifolds with distinct constant Ricci eigenvalues and satisfying some additional geometrical conditions are classified in an explicit form. One obtains locally homogeneous spaces and two different classes of locally non-homogeneous spaces in this way.
The Transient Lubrication Problem as a Generalized Hele-Shaw Type Problem
Authors: Bayada G. , Boukrouche M. , Talibi M. El-A.
Published: September 2013

The aim of this paper is to bridge the gap between Hele-Shaw theory and lubrication theory. A first generalization of the Hele-Shaw problem is considered for which existence, uniqueness and regularity theorems are given. Then taking shear effects into account, lubrication fluid mixture approach has to be used, inducing a new formulation of the initial problem. Connection of the two kind of problems are then given, establishing Ilele-Shaw phenomena as a particular case of lubrication problem on a mathematical basis.
Hölder Inequalities and Sharp Embeddings in Function Spaces of $B^s_{pq}$ and $F^s_{pq}$ Type
Authors: Sickel Winfried , Triebel Hans
Published: September 2013

Besides assertions on sharp embeddings of

B^s_{pq}

and

F^s_{pq}

we give necessary and sufficient conditions on the parameters

s,p,q,p_1,q_1,p_2,q_2

for the Hölder type inequalities

\| f \cdot g | B^s_{pq} \| ≤ c \| f | B^s_{p_1q_1} \| \| g | B^s_{p_2q_2}

and

\| f \cdot g | F^s_{pq} \| ≤ c \| f | F^s_{p_1q_1} \| \| g | F^s_{p_2q_2}

to hold.
Gauss’ and Related Inequalities
Authors: Varošanec S. , Pečarić J.
Published: September 2013

Let

g : [a,b] \to \mathbb R

be a non-negative increasing differentiable function and

f : [a,b] \to \mathbb R

a non-negative function such that the quotient

f/g’

is non-decreasing. Then the function

Q(r) = (r+ 1) \int^b_a g(x)^r f(x)dx

is log-concave. If

g(a) = 0, b \in (a, \infty]

and the quotient

f/g’

is non-increasing, then the function

Q

is log-convex.
On a Comparison Theorem for Second Order Nonlinear Ordinary Differential Equations
Authors: Rudek Th.
Published: September 2013

We present a comparison theorem for second order nonlinear differential equations of the form

(R(t)w(x(t))x’(t))’ + p(t)f(x(t)) = 0 \ \ \ (t \in [t_0, \beta],\beta ≤ \infty)

where

p

is a continuous function on

[t_0, \beta)

without any restriction on its sign.
On Continuous Capacities
Authors: Brzezina M.
Published: September 2013

Let

(X, W)

be a balayage space,

\gamma

a Choquet capacity on

X

,

\beta(E)

the essential base of

E \subset X

and, for a compact set

K \subset X, \alpha (K) = \gamma (\beta(K))

. Then some properties of the set function

\alpha

are investigated. In particular, it is shown when

\alpha

is the Choquet capacity. Further, some relation a to the so-called continuous capacity deduced from a kernel on

X

is given. At last, some open problems from the book [1] by G. Anger are solved.