bluuebunny/crossref_metadata_2025 huggingface dataset:
Algebraic obstructions to sequential convergence in Hausdorrf abelian groups
Authors: Clark Bradd , Cates Sharon
Published: September 2002

Given an abelian group G and a non‐trivial sequence in G, when will it be possible
to construct a Hausdroff topology on G that allows the sequence to converge? As one might expect
of such a naive question, the answer is far too complicated for a simple response. The purpose of
this paper is to provide some insights to this question, especially for the integers, the rationals, and
any abelian groups containing these groups as subgroups. We show that the sequence of squares
in the integers cannot converge to 0 in any Hausdroff group topology. We demonstrate that any
sequence in the rationals that satisfies a “sparseness” condition will converge to 0 in uncountably
many different Hausdorff group topologies.
Symmetric generating set of the groups A2n+1 and S2n+1 using Sn and an element of order two
Authors: Hammas A. M.
Published: September 2002

In this paper we will show how to generate in general A2n+1 and S2n+1 using a copy of
Sn and an element of order 2 in A2n+1 or S2n+1 for all positive integers n ≥ 2. We will also show how to
generate A2n+1 and S2n+1 symmetrically using n elements each of order 2.
Functional evolution equations with nonconvex lower semicontinuous multivalued perturbations
Authors: Ibrahim A. G.
Published: September 2002

In this paper we prove some existence theorems concerning the solutions and integral
solution for functional (delay) evolution equations with nonconvex lower semicontinuous multivalued
perturbations.
Finite bandwidth, long wavelength convection with boundary imperfectons: near‐resonant wavelength excitation
Authors: Riahi D. N.
Published: September 2002

Finite amplitude thermal convection with continuous finite bandwidth of long wavelength
modes in a porous layer between two horizontal poorly conducting walls is studied when spatially nonuniform
temperature is prescribed at the lower wall. The weakly nonlinear problem is solved by using
multiple scales and perturbation techniques. The preferred long wavelength flow solutions are
determined by a stability analysis. The case of near resonant wavelength excitation is considered to
determine the non‐modal type of solutions. It is found that, under certain conditions on the form of the
boundary imperfections, the preferred horizontal structure of the solutions is of the same spatial form as
that of the total or some subset of the imperfection shape function. It is composed of a multi‐modal
pattern with spatial variations over the fast variables and with non‐modal amplitudes, which vary over the
slow variables. The preferred solutions have unusual properties and, in particular, exhibit ‘kinks’ in
certain vertical planes which are parallel to the wave vectors of the boundary imperfections. Along
certain vertical axes, where some of these vertical planes can intersect, the solutions exhibit multiple
‘kinks’.
The solution of a singular integral equation with some applications in potential theory
Authors: Shawagfeh N. T.
Published: September 2002

An analytical solution is derived for a singular integral equation which governs some twodimensional
potential boundary value problems in a region exterior to n‐infinite co‐axial circular strips. An
application in electrostatics is discussed.
Separable subalgebras of a class of Azumaya algebras
Authors: Szeto George
Published: September 2002

Let S be a ring with 1, C the center of S, G a finite automorphism group of S of order n
invertible in S, and SG the subnng of elements of S fixed under each element in G. It is shown that the
skew group ring S*G is a G′‐Galois extension of that is a projective separable CG‐algebra where
G′ is the inner automorphism group of S*G induced by G if and only if S is a G‐Galois extension of SG
that is a projective separable CG‐algebra. Moreover, properties of the separable subalgebras of a
G‐Galois H‐separable extension S of SG are given when SG is a projective separable CG‐algebra.
Exponential stability for abstract linear autonomous functional differential equations with infinite delay
Authors: Liang Jin , Huang Falun , Xiao Tijun
Published: September 2002

Based on our preceding paper, this note is concerned with the exponential stability of the solution semigroup for the abstract linear autonomous functional differential equation

urn:x-wiley:01611712:media:ijmm549151:ijmm549151-math-0001

where L is a continuous linear operator on some abstract phase space B into a Banach space E. We prove that the solution semigroup of (∗) is exponentially stable if and only if the fundamental operator (∗) is exponentially stable and the phase space B is an exponentially fading memory space.
New existence of equilibria via connectedness
Authors: Im Sung Mo , Rim Dong Il , Kim Won Kyu
Published: September 2002

The purpose of this paper is to prove a new topological fixed point theorem by using the
connectedness property, and next existence of equilibria in generalized games are established as
applications.
Adams and Steenrod operators in dihedral homology
Authors: Gouda Y. Ch.
Published: September 2002

In this article, we define the Adam′s and Steenrod′s operators in the dihedral homology.
On new strengthened Hardy‐Hilbert′s inequality
Authors: Yang Bicheng , Debnath Lokenath
Published: September 2002

In this paper, a new inequality for the weight coefficient
ω(q, n) in the form

urn:x-wiley:01611712:media:ijmm854323:ijmm854323-math-0001

is proved. This is followed by a strengthened version ofthe Hardy‐Hilbert inequality.
An application of fixed point theorems in best approximation theory
Authors: Pathak H. K. , Cho Y. J. , Kang S. M.
Published: September 2002

In this paper, we give an application of Jungck’s fixed point theorem to best approximation theory, which extends the results of Singh and Sahab et al.
Asymptotic theory for a critical case for a general fourth‐order differential equation
Authors: Al-Hammadi A. S. A.
Published: September 2002

In this paper we identify a relation between the coefficients that represents a critical case
for general fourth‐order equations. We obtained the forms of solutions under this critical case.
Some properties of prereflexive subspaces of operators
Authors: Li Jiankui
Published: September 2002

In the paper, we define a notion of prereflexivity for subspaces, give several
equivalent conditions of this notion and prove that if S⫅L(H)
is prereflexive, then every σ‐weakly
closed subspace of S is prereflexive if and only if S
has the property WP(see definition
2.11). By our result, we construct a reflexive operator A
such that A ⊕ 0
is not prereflexive.
Effectiveness of similar sets of polynomials of two complex variables in polycylinders and in Faber regions
Authors: Sayyed K. A. M. , Metwally M. S.
Published: September 2002

In the present paper we investigate the effectiveness of similar sets of polynomials of two
complex variables in polycylinder and in Faber regions of the four dimensional space E4.
Generalized fractional calculus to a subclass of analytic functions for operators on Hilbert space
Authors: Kim Yong Chan , Choi Jae Ho , Lee Jin Seop
Published: September 2002

In this paper, we investigate some generalized results of applications of fractional integral
and derivative operators to a subclass of analytic functions for operators on Hilbert space.
Tag‐modules with complement submodules H‐pure
Authors: Singh Surjeet , Khan Mohd Z.
Published: September 2002

The concept of a QTAG‐module MR
was given by Singh [8]. The structure theory of such
modules has been developed on similar lines as that of torsion abelian groups. If a module MR is such
that M ⊕ M
is a QTAG‐module, it is called a strongly TAG‐module. This in turn leads to the concept of a
primary TAG‐module and its periodicity. In the present paper some decomposition theorems for those
primary TAG‐modules in which all h‐neat submodules are h‐pure are proved. Unlike torsion abelian
groups, there exist primary TAG‐modules of infinite periodicities. Such modules are studied in the last
section. The results proved in this paper indicate that the structure theory of primary TAG‐modules of
infinite periodicity is not very similar to that oftorsion abelian groups.
A note on the Boardman theorem
Authors: Lü Zhi , Zhou Chun-Lian
Published: September 2002

Let (T, Mn)
be a smooth involution on a closed n‐dimensional manifold with
. This paper gives three necessary and sufficient conditions that (T, Mn) is a bounding
involution.
Reflection and dissipation of oblique Alfvén waves in an isothermal atmosphere
Authors: Alkahby Hadi Yahya , Mahrous M. A.
Published: September 2002

In this article, we investigate the combined effects of viscosity and Ohmic electrical conductivity on upward and downward propagation oblique Alfvén waves in an isothermal atmosphere. It is shown that the presence and direction of the magnetic field play an important role in the structure and the heating mechanism of solar atmosphere. In addition, the atmosphere can be divided into two distinct regions connected by a transition region. In the
lower region, the solution can be written as a linear combination of an upward and a downward propagation wave with unequal wavelengths. In the upper region, the solution decays exponentially with the altitude. Moreover, the magnetic field creates a reflecting and a non‐absorbing transition region. On the contrary, the viscosity and Ohmic electrical conductivity produce a reflecting and an absorbing transition region. The nature of the transition region depends on the relative strength of the viscous diffusivity with respect to the resistive diffusivity and on the direction of the magnetic field. A unique solution is determined.
The reflection coefficient and damping factors are derived and the conclusions are discussed in connection with the nature of the heating mechanism of the solar atmosphere.
Recursive formulae for the multiplicative partition function
Authors: Kim Jun Kyo , Hahn Sang Guen
Published: September 2002

For a positive integer n, let f(n) be the number of essentially different ways of writing n as a product of factors greater than 1, where two factorizations of a positive integer are said to be essentially the same if they differ only in the order of the factors. This paper gives a recursive formula for the multiplicative partition function f(n).
Common fixed point theorems for semigroups on metric spaces
Authors: Huang Young-Ye , Hong Chung-Chien
Published: September 2002

This paper consists of two main results. The first one shows that
if S is a left reversible semigroup of selfmaps on a complete metric space (M, d) such that there is a gauge function φ for which d(f(x), f(y)) ≤ φ(δ(Of (x, y))) for f ∈ S and x, y in M, where δ(Of (x, y)) denotes the diameter of the orbit of x, y under f, then S has a unique common fixed point ξ in M and, moreover, for any f in S and x in M, the sequence of iterates {fn(x)} converges to ξ. The second result is a common fixed point theorem for a left reversible uniformly Lipschitzian semigroup of selfmaps on a bounded hyperconvex metric space (M, d).
Remarks on μ″‐measurbale sets: regularity, σ‐smootheness, and measurability
Authors: Vlad Carman
Published: September 2002

Let X be an arbitrary nonempty set and ℒ a lattice of subsets of X such that ϕ, X ∈ ℒ. 𝒜(ℒ) is the algebra generated by ℒ and ℳ(ℒ) denotes those nonnegative, finite, finitely additive measures μ on 𝒜(ℒ). I(ℒ) denotes the subset of ℳ(ℒ) of nontrivial zero‐one valued measures. Associated with μ ∈ I(ℒ) (or Iσ(ℒ)) are the outer measures μ′ and μ″ considered in detail. In addition, measurability conditions and regularity conditions are investigated and specific characteristics are given for , the set of μ″‐measurable sets. Notions of strongly σ‐smooth and vaguely regular measures are also discussed. Relationships between regularity, σ‐smoothness and measurability are investigated for zero‐one valued measures and certain results are extended to the case of a pair of lattices ℒ1, ℒ2 where ℒ1 ⊂ ℒ2.
Control subgroups and birational extensions of graded rings
Authors: Hussein Salah El Din S.
Published: September 2002

In this paper, we establish the relation between the concept of control subgroups and the class of graded birational algebras. Actually, we prove that if R = ⊕σ∈GRσ is a strongly G‐graded ring and H⊲G, then the embedding i : R(H)↪R, where R(H) = ⊕σ∈HRσ, is a Zariski extension if and only if H controls the filter ℒ(R − P) for every prime ideal P in an open set of the Zariski topology on R. This enables us to relate certain ideals of R and R(H) up to radical.
Six‐dimensional considerations of Einstein′s connection for the first two classes. II. The Einstein′s connection in 6‐g‐UFT
Authors: Chung Kyung Tae , Yang Gye Tak , Hwang In Ho
Published: September 2002

Lower dimensional cases of Einstein′s connection were already
investigated by many authors for n = 2, 3, 4, 5. In the following series of two papers, we present a surveyable tensorial
representation of 6‐dimensional Einstein′s connection in terms of the unified field tensor:

I. The recurrence relations in 6‐g‐UFT.

II. The Einstein′s connection in 6‐g‐UFT.

In our previous paper [2], we investigated some algebraic
structure in Einstein′s 6‐dimensional unified field theory (i.e., 6‐g‐UFT), with emphasis on the derivation of the recurrence relations of the third kind which hold in 6‐g‐UFT. This paper is a direct continuation of [2]. The purpose of the present paper is to prove a necessary and sufficient condition for a unique Einstein′s connection to exist in 6‐g‐UFT and to display a surveyable tensorial representation of 6‐dimensional Einstein′s connection in terms of the unified field tensor, employing the powerful recurrence relations of the third kind obtained in the first paper [2].

All considerations in this paper are restricted to the first and
second classes of the 6‐dimensional generalized Riemannian manifold
X6, since the case of the third class, the simplest case, was already studied by many authors.
On a class of univalent functions
Authors: Yang Dinggong , Liu Jinlin
Published: September 2002

We consider the class of univalent functions defined by the
conditions f(z)/z ≠ 0 and |(z/f(z))′​′| ≤ α, |z| < 1, where f(z) = z + ⋯ is analytic in |z| < 1 and 0 < α ≤ 2.
Tilings in topological spaces
Authors: Arenas F. G.
Published: September 2002

A tiling of a topological space X is a covering of X by sets (called tiles) which are the closures of their
pairwise‐disjoint interiors. Tilings of ℝ2 have received considerable attention (see [2] for a wealth of interesting examples and results as well as an extensive bibliography). On the other hand, the study of tilings of general topological spaces is just beginning (see [1, 3, 4, 6]). We give some generalizations for topological spaces of some results known for certain classes of tilings of topological vector spaces.
Double multipliers on topological algebras
Authors: Khan L. A. , Mohammad N. , Thaheem A. B.
Published: September 2002

The main purpose of this paper is to investigate some topological
properties of the double multiplier algebra on a topological algebra. Let Md(A) be the double multiplier algebra on a topological algebra A, and let u and s be the uniform and strong operator topologies on Md(A), respectively. It is shown, under some additional hypotheses on A, that

(1) Md(A) is u‐ and s‐complete;

(2) A is a u‐closed two‐sided ideal in Md(A);

(3) A is s‐dense in Md(A);

(4) s and u have the same bounded sets;

(5) each continuous onto homomorphism ϕ : A → B has a unique extension .
Existence of periodic traveling wave solutions to the generalized forced Boussinesq equation
Authors: Jones Kenneth L. , Chen Yunkai
Published: September 2002

The generalized forced Boussinesq equation, utt − uxx + [f(u)]xx + uxxxx = h0, and its periodic traveling wave solutions are considered. Using the transform
z = x − ωt, the equation is converted to a nonlinear ordinary differential equation with periodic boundary conditions. An equivalent relation between the ordinary differential equation and a Hammerstein type integral equation is then established by using the Green′s function method. This integral equation generates compact operators in a Banach space of real‐valued continuous
periodic functions with a given period 2T. The Schauder′s fixed point theorem is then used to prove the existence of solutions to the integral equation. Therefore, the existence of nonconstant
periodic traveling wave solutions to the generalized forced Boussinesq equation is established.
Sir James Lighthill and modern fluid mechanics: a memorial tribute
Authors: Debnath Lokenath
Published: September 2002

This memorial tribute commemorates Sir James Lighthill the man and the mathematical scientist. A brief biographical information is presented with my personal reminiscences. His major contributions to fluid mechanics with special reference to nonlinear dispersive waves are discussed. By any standards, his legacy of research and publications of six books and one hundred fifty papers will remain forever as a remarkable example of scholarly work.
Reidemeister torsion and integrable Hamiltonian systems
Authors: Fel′shtyn Alexander , Sánchez-Morgado Hector
Published: September 2002

In this paper, we compute the Reidemeister torsion of an isoenergetic surface for the integrable Hamiltonian system on the 4‐dimensional symplectic manifold. We use the spectral sequence defined by the filtration and following Floer‐Witten ideas we bring into play the orbits connecting the critical submanifolds.
Almost triangular matrices over Dedekind domains
Authors: Demeyer Frank , Kakakhail Haniya
Published: September 2002

Every matrix over a Dedekind domain is equivalent
to a direct sum of matrices A = (ai,j), where ai,j = 0 whenever j > i + 1.
Applications of Ruscheweyh derivatives and Hadamard product to analytic functions
Authors: Mogra M. L.
Published: September 2002

For given analytic functions in U = {z | |z| < 1} with λm ≥ 0, μm ≥ 0 and λm ≥ μm, let En(ϕ, ψ; A, B) be the class of analytic functions in U such that (f*Ψ)(z) ≠ 0 and

urn:x-wiley:01611712:media:ijmm978494:ijmm978494-math-0003

where is the nth Ruscheweyh derivative; ≪ and * denote subordination and the Hadamard product, respectively. Let T be the class of analytic functions in U of the form , and let En[ϕ, ψ; A, B] = En(ϕ, ψ; A, B)∩T. Coefficient estimates, extreme points, distortion theorems and radius of starlikeness and convexity are determined for functions in the class En[ϕ, ψ; A, B]. We also consider the quasi‐Hadamard product of functions in En[z/(1 − z), z/(1 − z); A, B] and En[z/(1−z)2, z/(1−z)2; A, B].
The relative dihedral homology of involutive algebras
Authors: Gouda Y. Gh.
Published: September 2002

Let f : A → B be a homomorphism of involutive algebras A, B. The purpose of this paper is to define a free involutive algebra resolution of algebra B over f and use it to define and study the relative dihedral homology.
Existence of global solution for a differential system with initial data in Lp
Authors: Bates Peter , Chen Fengxin , Wang Ping
Published: September 2002

In this paper, we study the system governing flows in the magnetic
field within the earth. The system is similar to the magnetohydrodynamic (MHD) equations. By establishing a new priori estimates and following Calderón′s procedure for the Navier Stokes equations [1], we obtained, for initial data in space Lp, the global in time existence and uniqueness of weak solution of the system subject to appropriate conditions.
A Picard‐Maclaurin theorem for initial value PDEs
Authors: Parker G. Edgar , Sochacki James S.
Published: September 2002

In 1988, Parker and Sochacki announced a theorem which proved that the Picard iteration, properly modified, generates the Taylor series solution to any ordinary differential equation (ODE) on ℜn with a polynomial generator. In this paper, we present an analogous theorem for partial differential equations (PDEs) with polynomial generators and analytic initial conditions. Since the domain of a solution of a PDE is a subset of ℜn, we identify one component of the domain to achieve the analogy with ODEs. The generator for the PDE must be a polynomial and autonomous with
respect to this component, and no partial derivative with respect to this component can appear in the domain of the generator. The initial conditions must be given in the designated component at zero and must be analytic in the nondesignated components. The power series solution of such a PDE, whose existence is guaranteed by the Cauchy theorem, can be generated to arbitrary degree by Picard iteration. As in the ODE case these conditions can be met,
for a broad class of PDEs, through polynomial projections.
Attractors of multivalued semiflows generated by differential inclusions and their approximations
Authors: Kapustian Alexei V. , Valero José
Published: September 2002

We prove the existence of global compact attractors for differential inclusions and obtain some results concerning the continuity and upper semicontinuity of the attractors for approximating and perturbed inclusions. Applications are given to a model of regional economic growth.
Multiple solutions for nonlinear discontinuous strongly resonant elliptic problems
Authors: Kourogenis Nikolaos C. , Papageorgiou Nikolaos S.
Published: September 2002

We consider quasilinear strongly resonant problems with discontinuous right‐hand side. To develop an existence theory we pass to a multivalued problem by, roughly speaking, filling in the gaps at the discontinuity points. We prove the existence of at least three nontrivial solutions. Our approach uses the nonsmooth critical point theory for locally Lipschitz functionals due to Chang (1981) and a generalized version of the Ekeland variational principle. At the end of the paper we show that the nonsmooth Palais‐Smale (PS)‐condition implies the coercivity of the
functional, extending this way a well‐known result of the “smooth” case.
Characterization of a class of functions using divided differences
Authors: Simeonov Plamen
Published: September 2002

We determine the class of functions, the divided difference of
which, at n distinct numbers, is a continuous function of the
product of these numbers.
Homoclinic solutions for linear and linearizable ordinary differential equations
Authors: Avramescu Cezar , Vladimirescu Cristian
Published: September 2002

Using functional arguments, some existence results for the
infinite boundary value problem are given. A solution of this problem is frequently called, from Poincaré, homoclinic.
Nonlinear ergodic theorems for asymptotically almost nonexpansive curves in a Hilbert space
Authors: Li Gang , Kim Jong Kyu
Published: September 2002

We introduce the notion of asymptotically almost nonexpansive
curves which include almost‐orbits of commutative semigroups of asymptotically nonexpansive type mappings and study the asymptotic behavior and prove nonlinear ergodic theorems for such curves. As applications of our main theorems, we obtain the results on the asymptotic behavior and ergodicity for a commutative semigroup of non‐Lipschitzian mappings with nonconvex domains in a Hilbert space.
Positive global solutions for a general model of size‐dependent population dynamics
Authors: Kato Nobuyuki
Published: September 2002

We study size‐structured population models of general type which
have the growth rate depending on the size and time. The local existence and uniqueness of the solution have been shown by Kato and Torikata (1997). Here, we discuss the positivity of the solution and global existence as well as L ∞ solutions.
(r, p)‐absolutely summing operators on the space C (T, X) and applications
Authors: Popa Dumitru
Published: September 2002

We give necessary and sufficient conditions for an operator on
the space C (T, X) to be (r, p)‐absolutely summing. Also we prove that the injective tensor product of an integral operator and an (r, p)‐absolutely summing operator is an
(r, p)‐absolutely summing operator.
Extension of the best approximation operator in Orlicz spaces and weak‐type inequalities
Authors: Favier Sergio , Zò Felipe
Published: September 2002

We consider an extension of the best approximation operator from
an Orlicz space L φ
to the space , where φ′
denotes the derivative of φ, and we prove a weak‐type inequality in this space. Further, we obtain some strong inequalities for suitable L ψ spaces.
Douglas algebras without maximal subalgebra and without minimal superalgebra
Authors: Guillory Carroll
Published: September 2002

We give several examples of Douglas algebras that do not have any maximal subalgebra. We find a condition on these algebras that
guarantees that some do not have any minimal superalgebra. We also
show that if A
is the only maximal subalgebra of a Douglas
algebra B, then the algebra A does
not have any maximal subalgebra.
On Milman’s moduli for Banach spaces
Authors: Maluta Elisabetta , Prus Stanisław , Szczepanik Mariusz
Published: September 2002

We show that infinite dimensional geometric moduli introduced by
Milman are strongly related to nearly uniform convexity and nearly uniform
smoothness. An application of those moduli to fixed point theory is given.
On periodic solutions of abstract differential equations
Authors: Eidelman Y. S. , Tikhonov I. V.
Published: September 2002

Let A
be a closed linear operator on a Banach space E.
We study periodic solutions of the differential equation
d Nu (t)/dt N = A u(t)
with an arbitrary integer N ≥ 1.
On the solvability of a system of wave and beam equations
Authors: Berkovits Juha
Published: September 2002

We prove new existence results for linearly coupled system of
wave and beam equations. The main concept is the matrix spectrum
which is a natural extension of standard definition. Using
invariant subspaces together with degree theoretic argument we
obtain information about the range of the abstract operator.
On the projection constants of some topological spaces and some applications
Authors: El-Shobaky Entisarat , Ali Sahar Mohammed , Takahashi Wataru
Published: September 2002

We find a lower estimation for the projection constant of the
projective tensor product X⊗ ∧Y
and the injective tensor product X⊗ ∨Y, we apply this
estimation on some previous results, and we also introduce a new
concept of the projection constants of operators rather than that
defined for Banach spaces.
Boundary value problems for second‐order partial differential equations with operator coefficients
Authors: Fayazov Kudratillo S. , Schock Eberhard
Published: September 2002

Let Ω T
be some bounded simply connected region in ℝ 2
with . We seek a function u(x, t)((x, t) ∈ Ω T)
with values in a Hilbert space H
which satisfies the equation ALu(x, t) = Bu(x, t) + f(x, t, u, u t), (x, t) ∈ Ω T, where A(x, t), B(x, t)
are families of linear operators
(possibly unbounded) with everywhere dense domain D
(D does
not depend on (x, t)) in H and
Lu(x, t) = u tt + a 11u xx + a 1u t + a 2u x. The values
u(x, t); ∂u(x, t)/∂n
are given in Γ 1. This problem is not in general well posed in the sense of
Hadamard. We give theorems of uniqueness and stability of the
solution of the above problem.
Free surface flow over an obstacle. Theoretical study of the fluvial case
Authors: Boukari D. , Djouadi R. , Teniou D.
Published: September 2002

The two‐dimensional stationary flow of a fluid over an obstacle
lying on the bottom of a stream is discussed. We take into
account the gravity and we neglect the effects of the surface
tension. An existence theory for the solution of this problem is
established by the implicit function theorem, for small obstacles
and Froude numbers in an interval included in ]0, 1[.
On Neumann hemivariational inequalities
Authors: Nikolaos Halidias
Published: September 2002

We derive a nontrivial solution for a Neumann noncoercive
hemivariational inequality using the critical point theory for
locally Lipschitz functionals. We use the Mountain‐Pass theorem
due to Chang (1981).
On the existence of solutions to a fourth‐order quasilinear resonant problem
Authors: Liu Shibo , Squassina Marco
Published: September 2002

By means of Morse theory we prove the existence of a nontrivial
solution to a superlinear p‐harmonic elliptic problem with
Navier boundary conditions having a linking structure around the
origin. Moreover, in case of both resonance near zero and
nonresonance at +∞ the existence of two nontrivial
solutions is shown.
Quasilinear elliptic systems of resonant type and nonlinear eigenvalue problems
Authors: de Nàpoli Pablo L. , Mariani M. Cristina
Published: September 2002

This work is devoted to the study of a quasilinear elliptic
system of resonant type. We prove the existence of infinitely
many solutions of a related nonlinear eigenvalue problem.
Applying an abstract minimax theorem, we obtain a solution of the
quasilinear system −Δpu = Fu(x,  u,  v),   − Δqv = F v(x,  u,  v), under conditions involving the first and the second eigenvalues.
Commutators in real interpolation with quasi‐power parameters
Authors: Fan Ming
Published: September 2002

The basic higher order commutator theorem is formulated for the real interpolation methods associated with the quasi‐power parameters, that is, the function spaces on which Hardy inequalities are valid. This theorem unifies and extends various results given by Cwikel, Jawerth, Milman, Rochberg, and others, and incorporates some results of Kalton to the context of commutator estimates for the real interpolation methods.
Existence theorems for elliptic hemivariational inequalities involving the p‐Laplacian
Authors: Kourogenis Nikolaos C. , Papageorgiou Nikolaos S.
Published: September 2002

We study quasilinear hemivariational inequalities involving the p‐Laplacian. We prove two existence theorems. In the first, we allow “crossing” of the principal eigenvalue by the generalized potential, while in the second, we incorporate problems at
resonance. Our approach is based on the nonsmooth critical point
theory for locally Lipschitz energy functionals.
Iterative solution of unstable variational inequalities on approximately given sets
Authors: Alber Y. I. , Kartsatos A. G. , Litsyn E.
Published: September 2002

The convergence and the stability of the iterative regularization method for solving variational inequalities with bounded nonsmooth properly monotone (i.e., degenerate) operators in Banach spaces are studied.
All the items of the inequality (i.e., the operator A, the “right hand
side” f and the set of constraints Ω) are to be perturbed.
The connection between the parameters of regularization and perturbations
which guarantee strong convergence of approximate solutions is established.
In contrast to previous publications by Bruck, Reich and the first author, we do not suppose
here that the approximating sequence is a priori bounded. Therefore the present
results are new even for operator equations in Hilbert and Banach
spaces. Apparently, the iterative processes for problems
with perturbed sets of constraints are being considered for the first time.
Approximating the zeros of accretive operators by the Ishikawaiteration process
Authors: Haiyun Zhou , Yuting Jia
Published: September 2002

Some strong convergence theorems are established for the Ishikawa iteration
processes for accretive operators in uniformly smooth Banach spaces.
Attractors of semigroups associated with nonlinear systems fordiffusive phase separation
Authors: Kenmochi Nobuyuki
Published: September 2002

We consider a model for diffusive phase transitions, for
instance, the component separation in a binary mixture. Our model is
described by two functions, the absolutete temperature θ : = θ(t, x) and the order parameter w : = w(t, x), which are governed by a system of two nonlinear parabolic PDEs. The order parameter
w is constrained to have double obstacles σ* ≤ w ≤ σ* (i.e., σ* and σ* are the threshold values of w). The objective of this paper is to discuss the semigroup {S(t)} associated with the phase separation model, and construct its global attractor.
Interior point control and observation for the wave equation
Authors: Khapalov A. Y.
Published: September 2002

This paper is concerned with the approximate and exact controllability
properties of the wave equation with interior point controls entering
via the concentrated force, the velocity of the displacement and the moment.
The emphasis is given to the moving point controls and their dual
observations whose advantages and disadvantages, versus the static ones,
are analyzed with respect to the space dimension, the duration of the
control time interval and the function spaces involved.
Bifurcation of the equivariant minimal interfaces in a hydromechanics problem
Authors: Borisovich A. Y. , Marzantowicz W.
Published: September 2002

In this work we study a deformation of the minimal interface of two fluids in a vertical tube under the presence of gravitation.
We show that a symmetry of the base of tube let us to apply
a method developed earlier by the first author and based
on the Crandall‐Rabinowitz bifurcation theorem.
Using the natural symmetry of the corresponding variational problem
defined by a symmetry of region and restricting the functional
to spaces of invariant functions we show the existence of bifurcation,
and describe its local picture,
for interfaces parametrized by the square and disc.
Embedding functions and their role in interpolation theory
Authors: Pustylnik Evgeniy
Published: September 2002

The embedding functions of an intermediate space A into a Banach couple
(A0, A1) are defined as its embedding constants into the couples
, ∀α, β > 0. Using these functions,
we study properties and interrelations of different intermediate spaces, give a new description of all real
interpolation spaces, and generalize the concept of weak‐type interpolation to
any Banach couple to obtain new interpolation theorems.
Stability of coupled systems
Authors: Khodja Farid Ammar , Benabdallah Assia , Teniou Djamel
Published: September 2002

The exponential and asymptotic stability are studied for certain coupled systems
involving unbounded linear operators and linear infinitesimal semigroup generators.
Examples demonstrating the theory are also given from the field of partial differential equations.
On the Mann and Ishikawa iteration processes
Authors: Haiyun Zhou , Yuting Jia
Published: September 2002

It is shown that a result of Chidume, involving the strong convergence of the Mann iteration process for continuous strongly accretive
operators, is actually a corollary to a result by Nevanlinna and Reich. It is then
shown that the Nevanlinna and Reich result can be extended to the case of an Ishikawa iteration process.
Nonlinear semigroups and the existence and stability of solutionsof semilinear nonautonomous evolution equations
Authors: Aulbach Bernd , Minh Nguyen Van
Published: September 2002

This paper is concerned with the existence and stability of solutions
of a class of semilinear nonautonomous evolution equations. A procedure
is discussed which associates to each nonautonomous equation the
so‐called evolution semigroup of (possibly nonlinear) operators.
Sufficient conditions for the existence and stability of solutions
and the existence of periodic oscillations are given in terms of the
accretiveness of the corresponding infinitesimal generator. Furthermore,
through the existence of integral manifolds for abstract evolutionary
processes we obtain a reduction principle for stability questions of mild
solutions. The results are applied to a class of partial functional
differential equations.
On a local degree for a class of multi‐valued vector fields ininfinite dimensional Banach spaces
Authors: Benkafadar N. M. , Gel′man B. D.
Published: September 2002

This paper is devoted to the development of a local degree for multi‐valued vector
fields of the form f − F. Here, f is a single‐valued,
proper, nonlinear, Fredholm, C1‐mapping
of index zero and F is a multi‐valued upper semicontinuous, admissible, compact
mapping with compact images. The mappings f and F are acting from a subset of a Banach space E into another Banach space E1. This local degree is used to
investigate the existence of solutions of a certain class of operator
inclusions.
A pointwise approximation theorem for linear combinations ofBernstein polynomials
Authors: Guo Shunsheng , Yue Shujie , Li Cuixiang , Yang Ge , Sun Yiguo
Published: September 2002

Recently, Z. Ditzian gave an interesting direct estimate for Bernstein
polynomials. In this paper we give direct and inverse results
of this type for linear combinations of Bernstein polynomials.
Flow invariance for perturbed nonlinear evolution equations
Authors: Bothe Dieter
Published: September 2002

Let X be a real Banach space, J = [0, a] ⊂ R, A : D(A) ⊂ X → 2X\ϕ an m‐accretive operator and f : J × X → X continuous. In this paper we obtain necessary and sufficient conditions for weak positive invariance (also called viability) of closed sets K ⊂ X for the evolution system
u′ + Au∍f(t, u)  on  J = [0, a].
More generally, we provide conditions under which this evolution system has
mild solutions satisfying time‐dependent constraints u(t) ∈ K(t) on J. This result is then applied to obtain global solutions of reaction‐diffusion systems with nonlinear diffusion, e.g. of type ut = ΔΦ(u) + g(u)  in  (0, ∞) × Ω,    Φ(u(t, ⋅))|∂Ω = 0,    u(0, ⋅) = u0 under certain assumptions on the setΩ ⊂ Rn the function Φ(u1, …, um) = (φ1(u1), …, φm(um)) and .
An abstract setting for differential Riccati equations in optimalcontrol problems for hyperbolic/Petrowski‐type P.D.E.′s withboundary control and slightly smoothing observation
Authors: Triggiani R.
Published: September 2002

We study, by the variational method, the Differential Riccati Equation
which arises in the theory of quadratic optimal control problems for
‘abstract hyperbolic’ equations (which encompass hyperbolic and
Petrowski‐type partial differential equations (P.D.E.) with boundary
control). We markedly relax, at the abstract level, the original
assumption of smoothing required of the observation operator by the
direct method of [D‐L‐T.1]. This is achieved, by imposing additional
higher level regularity requirements on the dynamics, which,
however, are always satisfied by the class of hyperbolic and
Petrowski‐type mixed P.D.E. problems which we seek to cover. To
appreciate the additional level of generality, and related technical
difficulties associate with it, it suffices to point out that in the
present treatment—unlike in [D‐L‐T.1]—the gain operator B*P(t) is no longer bounded between the state space Y and the control space U.
The abstract theory is illustrated by its application to a Kirchoff equation with one boundary control. This requires establishing new higher level interior and boundary regularity results.
Evolution semigroups for nonautonomous Cauchy problems
Authors: Nickel Gregor
Published: September 2002

In this paper, we characterize wellposedness of nonautonomous, linear Cauchy problems

urn:x-wiley:10853375:media:aaa632147:aaa632147-math-0001

on a Banach space X by the existence of certain evolution semigroups.

Then, we use these generation results for evolution semigroups
to derive wellposedness for nonautonomous Cauchy problems under some
“concrete” conditions. As a typical example, we discuss the so called “parabolic” case.
Local existence for a general model of size‐dependent population dynamics
Authors: Kato Nobuyuki , Torikata Hiroyuki
Published: September 2002

We shall investigate a size structured population dynamics with
aging and birth functions having general forms. The growth rate we deal with depends not only on the size but also on time. We show the existence of a local solution and continuous dependence on the initial data, which shows the uniqueness of the solution as well.
Variational inequalities for energy functionals with nonstandardgrowth conditions
Authors: Fuchs Martin , Gongbao Li
Published: September 2002

We consider the obstacle problem

urn:x-wiley:10853375:media:aaa495907:aaa495907-math-0001

for a given function and a bounded Lipschitz domain O in Rn. The growth properties of the convex integrand G are described in terms of a N‐function A : [0, 8)?[0, 8) with . If n = 3, we prove, under certain assumptions on G, C1,8‐partial regularity for the solution to the above obstacle problem. For the special case where A(t) = tln(1 + t) we obtain C1,a‐partial regularity when n = 4. One of the main features of the paper is that we do not require any power growth of G.
Uniform asymptotic normal structure, the uniform semi‐Opial property and fixed points of asymptotically regular uniformly lipschitzian semigroups. Part I
Authors: Budzyńska Monika , Kuczumow Tadeusz , Reich Simeon
Published: September 2002

In this paper we introduce the uniform asymptotic normal structure and the uniform semi‐Opial properties of Banach spaces. This part is devoted to a study of the spaces with these properties. We also compare them with those
spaces which have uniform normal structure and with spaces with WCS(X) > 1.
Rotationally invariant periodic solutions of semilinear wave equations
Authors: Schechter Martin
Published: September 2002

Under suitable conditions we are able to solve the semilinear wave
equation in any dimension. We are also able to compute the essential spectrum of the linear wave operator for the rotationally invariant periodic case.
Metric domains, holomorphic mappings and nonlinear semigroups
Authors: Reich Simeon , Shoikhet David
Published: September 2002

We study nonlinear semigroups of holomorphic mappings on certain domains in complex Banach spaces. We examine, in particular, their differentiability and their representations by exponential and other product formulas. In addition, we also construct holomorphic retractions onto the stationary point sets of such semigroups.
Brouwer degree, equivariant maps and tensor powers
Authors: Balanov Z. , Krawcewicz W. , Kushkuley A.
Published: September 2002

A construction of equivariant maps based on factorization through symmetric powers of a faithful representation is presented together with several examples of related equivariant maps. Applications to differential equations are also discussed.
The turnpike property for dynamic discrete time zero‐sum games
Authors: Zaslavski Alexander J.
Published: September 2002

We consider a class of dynamic discrete‐time two‐player zero‐sum games. We show that for a generic cost function and each initial state, there exists a pair of overtaking equilibria strategies over an infinite horizon. We also establish that for a generic cost function f, there exists a pair of stationary equilibria strategies (xf, yf) such that each pair of “approximate” equilibria strategies spends almost all of its time in a small neighborhood of (xf, yf).
On the degree theory for densely defined mappings of class (S+)L
Authors: Berkovits Juha
Published: September 2002

We introduce a new construction of topological degree for densely
defined mappings of monotone type. We also study the structure of the classes of mappings involved. Using the basic properties of the degree, we prove some abstract existence results that can be applied to elliptic problems.
Semilinear Volterra integrodifferential equations with nonlocal initial conditions
Authors: Aizicovici Sergiu , Mckibben Mark
Published: September 2002

We establish the global existence of mild solutions to a class of
nonlocal Cauchy problems associated with semilinear Volterra integrodifferential equations in a Banach space.
Evolutionary variational inequalities arising in quasistatic frictional contact problems for elastic materials
Authors: Motreanu Dumitru , Sofonea Mircea
Published: September 2002

We consider a class of evolutionary variational inequalities arising in quasistatic frictional contact problems for linear elastic materials. We indicate sufficient conditions in order to have the existence, the uniqueness and the Lipschitz continuous dependence of the solution with respect to the data, respectively. The existence of the solution is obtained using a time‐discretization method, compactness and lower semicontinuity arguments. In the study of the discrete problems we use a recent result obtained by the authors (2000). Further, we apply the abstract results in the study of a number of mechanical problems modeling the frictional contact between a deformable body and a foundation. The material is assumed to have linear elastic behavior and the processes are quasistatic. The first problem concerns a model with
normal compliance and a version of Coulomb′s law of dry friction, for which we prove the existence of a weak solution. We then consider a problem of bilateral contact with Tresca′s friction law and a problem involving a simplified version of Coulomb′s friction law. For these two problems we prove the existence, the uniqueness and the Lipschitz continuous dependence of the weak solution with respect to the data.
A boundary value problem in the hyperbolic space
Authors: Amster P. , Keilhauer G. , Mariani M. C.
Published: September 2002

We consider a nonlinear problem for the mean curvature equation
in the hyperbolic space with a Dirichlet boundary data g. We find solutions in a Sobolev space under appropriate conditions on
g.
Genetic Stabilization by p53 Involves Growth Regulatory and Repair Pathways
Authors: Wiesmüller Lisa
Published: September 2002

p53 performs a plethora of activities, which are directed towards the maintenance of the genomic integrity and constitute its universal role as a tumor suppressor. 1000 to 10000 latent p53 molecules are permanently available in order to monitor DNA exchange processes in mitotically growing cells. After the introduction of major DNA injuries the levels of posttranslationally modified p53 proteins rise, which in turn transcriptionally signal transient cell cycle arrest or apoptotic cell death, depending on the extent of damage. Taken together, p53 inhibits the manifestation of genomic instabilities at different control levels both during naturally occurring metabolic processes and in response to genotoxic treatments.
Olfactory Ensheathing Glia: Drivers of Axonal Regeneration in the Central Nervous System?
Authors: Moreno-Flores M. Teresa , Díaz-Nido Javier , Wandosell Francisco , Avila Jesús
Published: September 2002

Olfactory ensheathing glia (OEG) accompany olfactory growing axons in their entry to the adult mammalian central nervous system (CNS). Due to this special characteristic, considerable attention has been focused on the possibility of using OEG for CNS regeneration. OEG present a large heterogeneity in culture with respect to their cellular morphology and expressed molecules. The specific characteristics of OEG responsible for their regenerative properties have to be defined. These properties probably result from the combination of several factors: molecular composition of the membrane (expressing adhesion molecules as PSA‐NCAM, L1 and/or others) combined with their ability to reduce glial scarring and to accompany new growing axons into the host CNS. Their capacity to produce some neurotrophic factors might also account for their ability to produce CNS regeneration.
On the optimal exercise boundary for an American put option
Authors: Alobaidi Ghada , Mallier Roland
Published: September 2002

An American put option is a derivative financial instrument that
gives its holder the right but not the obligation to sell an
underlying security at a pre‐determined price. American options
may be exercised at any time prior to expiry at the discretion of
the holder, and the decision as to whether or not to exercise
leads to a free boundary problem. In this paper, we examine the
behavior of the free boundary close to expiry. Working directly
with the underlying PDE, by using asymptotic expansions, we are
able to deduce this behavior of the boundary in this limit.