bluuebunny/crossref_metadata_2025 huggingface dataset:
Commutativity theorems for rings with constraints on commutators
Authors: Abujabal Hamza A. S.
Published: September 2002

In this paper, we generalize some well‐known commutativity theorems for
associative rings as follows: Let n > 1, m, s, and t be fixed non‐negative integers such that
s ≠ m − 1, or t ≠ n − 1, and let R be a ring with unity 1 satisfying the polynomial identity
ys[xn, y] = [x, ym]xt for all y ∈ R. Suppose that (i) R has Q(n) (that is n[x, y] = 0 implies
[x, y] = 0); (ii) the set of all nilpotent elements of R is central for t > 0, and (iii) the set of
all zero‐divisors of R is also central for t > 0. Then R is commutative. If Q(n) is replaced by
m and n are relatively prime positive integers, then R is commutative if extra constraint is
given. Other related commutativity results are also obtained.
Ultrabornological structures
Authors: Murali V.
Published: September 2002

The purpose of this note is to extend Warner′s idea of
bornological structures to cover non‐locally convex situations and to
develop a framework unifying several variations on an ultrabornological
theme (for example, ultrabornological spaces, o‐ultrabornological spaces,
i‐ultrabornological algebras). We do this by first generalising the concept
of a structure on a vector space as defined by Warner.
Some formulas of L. Carlitz on Hermite polynomials
Authors: Chatterjea S. K. , Ali S. M. Eaqub
Published: September 2002

We have used the idea of ‘quasi inner product’ introduced by L. R.
Bragg in 1986 to consider generating series

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studied by L. Carlitz in 1963. The pecularity of the series is that there is (n!) 2
in the denominator, which has a striking deviation from the usuaI generating series
containing n! in the denominator. Our generating function for the said generating
series is quite different from that of Carlitz, but somewhat analogous to generating
integrals derived by G. N. Watson (Higher Transcendental function Vol.III, P 271‐272
for the case of Legendre, Gegenbauer and Jacobi polynomials.
On the stepanov almost periodic solution of a second‐order infinitesimal generator differential equation
Authors: Rao Aribindi Satyanarayan
Published: September 2002

The Stepanov almost periodic solution of a certain second‐order differential equation in a reflexive Banach space is shown to be almost periodic.
Shock waves and Cerenkov radiation in electromagnetic substratum
Authors: Wilhelm H. E.
Published: September 2002

The EM fields of charged particles moving with velocity v in a physical vacuum with
wave carrier (substratum) are determined by means of the generalized, Galilei covariant Maxwell
equations for inertial frames ∑. with substratum flow w. In this Galilean approach, all velocities
have absolute meaning relative to the substratum rest frame ∑o, and the relative velocity of material
particles is given by the linear Galilean relation vG = v1 − v2, permitting in principle superluminal
relative velocities |vG| > co. Inter alias, the possibility of EM shock waves and Cerenkov radiation
in the vacuum substratum is discussed. Experiments are proposed to test the theoretical
predictions.
A non‐uniqueness theorem in the theory of Voronoi sets
Authors: Jones M.
Published: September 2002

It is shown that two distinct, bounded, open subsets of ℝ2 may possess the
same Voronoi set.
Notes on sufficient conditions for a graph to be Hamiltonian
Authors: Paul Michael Joseph , Shershin Carmen Baytan , Shershin Anthony Connors
Published: September 2002

The first part of this paper deals with an extension of Dirac′s Theorem to
directed graphs. It is related to a result often referred to as the Ghouila‐Houri
Theorem. Here we show that the requirement of being strongly connected in the hypothesis
of the Ghouila‐Houri Theorem is redundant.

The Second part of the paper shows that a condition on the number of edges for a
graph to be hamiltonian implies Ore′s condition on the degrees of the vertices.
On approximation in the Lp‐norm by Hermit interpolation
Authors: Guohua Min
Published: September 2002

Lp‐approximation by the Hermite interpolation based on the zeros of the Tchebycheff polynomials of the first kind is considered. The corresponding result of Varma and Prasad [1] is generalized and perfected.
Type and cotype of some Banach spaces
Authors: Mastylo Mieczyslaw
Published: September 2002

Type and cotype are computed for Banach spaces generated by some positive sublinear operators and Banach function spaces. Applications of the results yield that under certain assumptions Clarkson′s inequalities hold in these spaces.
On θ‐C‐open sets
Authors: Baker C. W.
Published: September 2002

The properties of the collection of complements of θ‐closures of sets in a topological space are investigated in this paper. A strong continuity condition is defined in terms of these sets. Some applications to H‐closed spaces and Katetov spaces are given.
Analytic solution of Riccati equations occurring in open‐loop Nash multiplayer differential games
Authors: Jódar L. , Navarro E.
Published: September 2002

In this paper we present explicit analytic solutions of coupled Riccati matrix differential systems appearing in open‐loop Nash games. Two different cases are considered. Firstly, by means of appropriate algebraic transformations the problem is decoupled so that an explicit solution of the problem is available. The second is based on the existence of a solution of a rectangular Riccati type algebraic matrix equation associated with the problem.
Existence of equilibrium states of hollow elastic cylinders submerged in a fluid
Authors: Elgindi M. B. M. , Yen D. H. Y.
Published: September 2002

This paper is concerned with the existence of equilibrium states of thin‐walled elastic, cylindrical shell fully or partially submerged in a fluid. This problem obviously serves as a model for many problems with engineering importance. Previous studies on the deformation of the shell have assumed that the pressure due to the fluid is uniform. This paper takes into consideration the non‐uniformity of the pressure by taking into account the effect of gravity. The presence of a pressure gradient brings additional parameters to the problem which in turn lead to the consideration of several boundary value problems.
Semi‐simplicity of a proper weak H*‐algebra
Authors: Saworotnow Parfeny P.
Published: September 2002

A weak right H*‐algebra is a Banach algebra A which is a Hilbert space and which has a dense subset Dr with the property that for each x in Dr there exists xr such that (yx, z) = (y, zxr) for all y, z in A. It is shown that a proper (each xr is unique) weak right H*‐algebra is semi‐simple. Also there is an example of weak right H*‐algebra which is not a left H*‐algebra.
A note on a functional inequality
Authors: Alzer Horst
Published: September 2002

We prove: If r1, …, rk are (fixed) positive real numbers with , then the only entire solutions φ : ℂ → ℂ of the functional inequality

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are φ(z) = czn, where c is a complex number and n is a positive integer.
On strictly convex and strictly 2‐convex 2‐normed spaces II
Authors: Lin C.-S.
Published: September 2002

In this paper a new duality mapping is defined, and it is our object to show that there is a similarity among these three types of characterizations of a strictly convex 2‐normed space. This enables us to obtain more new results along each of two types of characterizations. We shall also investigate a strictly 2‐convex 2‐normed space in terms of the above two different types.
Some results on convergence rates for probabilities of moderate deviations for sums of random variables
Authors: Li Deli , Wang Xiangchen , Rao M. Bhaskara
Published: September 2002

Let X, Xn, n ≥ 1 be a sequence of iid real random variables, and , n ≥ 1. Convergence rates of moderate deviations are derived, i.e., the rate of convergence to zero of certain tail probabilities of the partial sums are determined. For example, we obtain equivalent conditions for the convergence of series only under the assumptions convergence that EX = 0 and EX2 = 1, where φ and ψ are taken from a broad class of functions. These results generalize and improve some recent results of Li (1991) and Gafurov (1982) and some previous work of Davis (1968). For b ∈ [0, 1] and ϵ > 0, let

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The behaviour of Eλϵ,b as ϵ ↓ 0 is also studied.
On dual integral equations arising in problems of bending of anisotropic plates
Authors: Aggarwala B. D. , Nasim C.
Published: September 2002

In this paper we consider dual integral equations, which arise in boundary value problems of bending of anisotropic plates. The function involved in these equations is a linear combination of elementary function, which turns out to be a particular case of a class of Fourier kernels, [2]. The method used here for solving the equations is some what similar to the method used for solving dual integral equations of Titchmarsh type, [1].
Some absolutely effective product methods
Authors: Dikshit H. P. , Fridy J. A.
Published: September 2002

It is proved that the product method A(C, 1), where (C, 1) is the Cesàro arithmetic mean matrix, is totally effective under certain conditions concerning the matrix A. This general result is applied to study absolute Nörlund summability of Fourier series and other related series.
Integral representations of generalized Lauricella hypergeometric functions
Authors: Tuan Vu Kim , Buschman R. G.
Published: September 2002

The generalized hypergeometric function was introduced by Srivastava and Daoust. In the present paper a new integral representation is derived. Similarly new integral representations of Lauricella and Appell function are obtained.
Recurrent points and discrete points for elementary amenable groups
Authors: Nassar Mostafa
Published: September 2002

Let βG be the Stone‐Cech compactification of a group G, AG the set of all almost periodic points in βG, KG = cℓ[⋃{suppμφ : φ ∈ LIM(G)}] and RG the set of all recurrent points in βG. In this paper we will study the relationships between KG and RG, and between AG and RG. We will show that for any infinite elementary amenable group G, AG⫋RG and RG − KG ≠ ϕ.
On complete convergence in a Banach space
Authors: Kuczmaszewska Anna , Szynal Dominik
Published: September 2002

Sufficient conditions are given under which a sequence of independent random elements taking values in a Banach space satisfy the Hsu and Robbins law of large numbers. The complete convergence of random indexed sums of random elements is also considered.
Completely positive linear operators for Banach spaces
Authors: Yang Mingze
Published: September 2002

Using ideas of Pisier, the concept of complete positivity is generalized in a different direction in this paper, where the Hilbert space ℋ is replaced with a Banach space and its conjugate linear dual. The extreme point results of Arveson are reformulated in this more general setting.
On the speed of convergence of iteration of a function
Authors: Drobot Vladimir
Published: September 2002

Let fn(x) be the nth iterate of a function in some interval [0, c]. It is known that if f(x) ~ x − xα, α > 1, then fn(x) ~ Ana for some A and a. In this paper we prove a converse of this theorem: The rate of convergence of the iterates determines the form of a function.
On quasi‐ideals of semirings
Authors: Dönges Christoph
Published: September 2002

Several statements on quasi‐ideals of semirings are given in this paper, where these semirings may have an absorbing element O or not. In Section 2 we characterize regular semirings and regular elements of semi‐rings using quasi‐ideals (cf. Thms. 2.1, 2.2 and 2.7). In Section 3 we deal with (O−)minimal and canonical quasi‐ideals. In particular, if the considered semiring S is semiprime or quasi‐reflexive, we present criterions which allow to decide easily whether an (O−)minimal quasi‐ideal of S is canonical (cf. Thms. 3.4 and 3.8). If S is an arbitrary semiring, we prove that for (O−)minimal left and right ideals L and R of S the product 〈RL〉⫅L ⋂ R is either {O} or a canonical quasi‐ideal of S (Thm. 3.9). Moreover, for each canonical quasi‐ideal Q of a semiring S and each element a ∈ S, Qa is either {O} or again a canonical quasi‐ideal of S (Thm. 3.11), and the product 〈Q1Q2〉 of canonical quasi‐ideals Q1, Q2 of S is either {O} or again a canonical quasi‐ideal of S (Thm. 3.12). Corresponding results to those given here for semirings are mostly known as well for rings as for semigroups, but often proved by different methods. All proofs of our paper, however, apply simultaneously to semirings, rings and semigroups (cf. Convention 1.1), and we also formulate our results in a unified way for these three cases. The only exceptions are statements on semirings and semigroups without an absorbing element O, which cannot have corresponding statements on rings since each ring has its zero as an absorbing element.
On a class of third order neutral delay differential equations with piecewise constant argument
Authors: Papaschinopoulos Garyfalos
Published: September 2002

In this paper we study existence, uniqueness and asymptotic stability of the solutions of a class of third order neutral delay differential equations with piecewise constant argument.
Error analysis of dynamical models in epidemiology
Authors: Pokhariyal G. P. , Rodrigues A. J.
Published: September 2002

In this paper we conduct the error analysis of two models used to simulate the disease profiles in plant pathogen epidemics. The role of the various model parameters is discussed in relation to accuracy
A remark on the slice map problem
Authors: Chō Muneo , Huruya Tadasi
Published: September 2002

It is shown that there exist a σ‐weakly closed operator algebra , generated by finite rank operators and a σ‐weakly closed operator algebra generated by compact operators such that the Fubini product contains properly .
Decomposition of openness
Authors: Baker C. W.
Published: September 2002

In this note weak openness and almost openness are used to develop two decompositions of openness. Two additional conditions related to openness also are developed.
Finite completely primary rings in which the product of any two zero divisors of a ring is in its coefficient subring
Authors: Alkhamees Yousif
Published: September 2002

According to general terminology, a ring R is completely primary if its set of zero divisors J forms an ideal. Let R be a finite completely primary ring. It is easy to establish that J is the unique maximal ideal of R and R has a coefficient subring S (i.e. R/J isomorphic to S/pS) which is a Galois ring. In this paper we give the construction of finite completely primary rings in which the product of any two zero divisors is in S and determine their enumeration. We also show that finite rings in which the product of any two zero divisors is a power of a fixed prime p are completely primary rings with either J2 = 0 or their coefficient subring is with n = 2 or 3. A special case of these rings is the class of finite rings, studied in [2], in which the product of any two zero divisors is zero.
Some results on invariant approximation
Authors: Carbone Antonio
Published: September 2002

In this paper results on Invariant approximations, extending and unifying earlier results are given. Several interesting results are derived as corollaries.
CR‐submanifolds of a locally conformal Kaehler space form
Authors: Shahid M. Hasan
Published: September 2002

(Bejancu [1,2]) The purpose of this paper is to continue the study of CR‐submanifolds, and in particular of those of a locally conformal Kaehler space form (Matsumoto [3]). Some results on the holomorphic sectional curvature, D‐totally geodesic, D1‐totally geodesic and D1‐minimal CR‐submanifolds of locally conformal Kaehler (1.c.k.)‐space from are obtained. We have also discussed Ricci curvature as well as scalar curvature of CR‐submanifolds of .
Effect of torsion in a helical pipe flow
Authors: Vasudevaiah M. , Patturaj R.
Published: September 2002

The problem of fully developed steady viscous incompressible flow in a helical pipe is studied. The predicted analytical expression in the literature for the flow rate is improved. The present result shows a reduction in the flow rate with increasing torsion, for a given curvature. Qualitatively this effect of torsion is seen to cause equivelocity contours in the normal section of the pipe, to undergo shear.
Some results on biorthogonal polynomials
Authors: Ruedemann Richard W.
Published: September 2002

Some biorthogonal polynomials of Hahn and Pastro are derived using a polynomial modification of the Lebesgue measure dθ combined with analytic continuation. A result is given for changing the measures of biorthogonal polynomials on the unit circle by the multiplication of their measures by certain Laurent polynomials.
Bundles of Banach algebras
Authors: Kitchen J. W. , Robbins D. A.
Published: September 2002

We study bundles of Banach algebras π : A → X, where each fiber Ax = π−1({x}) is a Banach algebra and X is a compact Hausdorff space. In the case where all fibers are commutative, we investigate how the Gelfand representation of the section space algebra Γ(π) relates to the Gelfand representation of the fibers. In the general case, we investigate how adjoining an identity to the bundle π : A → X relates to the standard adjunction of identities to the fibers.
Locally compact semi‐algebras generated by a commuting operator family
Authors: Nandakumar N. R. , Vandermee Cornelis V.
Published: September 2002

Conditions are provided for the local compactness of the closed semi‐algebra generated by a finite collection of commuting bounded linear operators with equibounded iterates in terms of their joint spectral properties.
Several identities in statistical mechanics
Authors: Hirschhorn M. D.
Published: September 2002

In an earlier paper concerning a solvable Inodel in statistical mechanics, Miwa and Jimbo state a theta‐function identity which they have checked to the 200th power, but of which they do not have a proof. The main objective of this note is to provide such a proof.
A note on p‐solvable and solvable finite groups
Authors: Khazal R. , Mukherjee N. P.
Published: September 2002

The notion of normal index is utilized in proving necessary and sufficient conditions for a group G to be respectively, p‐solvable and solvable where p is the largest prime divisor of |G|. These are used further in identifying the largest normal p‐solvable and normal solvable subgroups, respectively, of G.
Approximate inertial manifolds for nonlinear parabolic equations via steady‐state determining mapping
Authors: You Yuncheng
Published: September 2002

For nonlinear parabolic evolution equations, it is proved that, under the assumptions of local
Lipschitz continuity of nonlinearity and the dissipativity of semiflows, there exist approximate inertial
manifolds (AIM) in the energy space and that the approximate inertial manifolds are constructed as the
graph of the steady‐state determining mapping based on the spectral decomposition. It is also shown that
the thickness of the exponentially attracting neighborhood of the AIM converges to zero at a fractional
power rate as the dimension of the AIM increases. Applications of the obtained results to Burgers′
equation, higher dimensional reaction‐diffusion equations, 2D Ginzburg‐Landau equations, and axially
symmetric Kuramoto‐Sivashinsky equations in annular domains are included.
Operator equations, separation of variables and relativistic alterations
Authors: Hermann Robert A.
Published: September 2002

In this paper, a simple and unified method is developed that predicts the relativistic
alterations of physical measures when the behavior of a natural system is characterized by means
of a specific operator equation. Separation of variables is the simple underlying procedure.
Oriented 6‐dimensional submanifolds in the octonians, III
Authors: Hashimoto Hideya
Published: September 2002

In this paper, we classify 6‐dimensional almost Hermitian submanifolds in the
octonians 𝕆 according to the classification introduced by A. Gray and L. Hervella. We give new
examples of quasi‐Käthler and ∗‐Einstein submanifolds in 𝕆. Also, we prove that a 6‐dimensional
weakly ∗‐Einstein Hermitian submanifold in 𝕆 is totally geodesic.
Reflection of internal waves by sand ripples
Authors: Mandal Samiran , Basu Uma
Published: September 2002

An investigation is made to study the diffraction of a train of time harmonic
progressive waves propagating along the surface of separation of two superposed fluids which are
laterally unbounded, the upper fluid being extended infinitely upwards, the lower fluid being of
finite depth with sand ripples at the bottom. The first order correction to the velocity potential
for the problem of diffraction of interface waves in the presence of bottom deformation is
obtained by integral transform technique after introduction of a linear frictional term in the
kinematic boundary condition at the surface of separation following Lamb (1932), and the
reflection and transmission coefficients are estimated for a patch of sand ripples.
A survey of partial differential equations with piecewise continuous arguments
Authors: Wiener Joseph , Debnath Lokenath
Published: September 2002

Some work is described and new topics are posed on initial and boundary‐value
problems for partial differential equations whose arguments have intervals of constancy. These
equations are of considerable theoretical and applied interest.
On the spectrum of the negative Laplacian for general doubly‐connected bounded domains
Authors: Zayed E. M. E. , Younis A. I.
Published: September 2002

This paper is devoted to asymptotic formulas for functions related with the spectrum
of the standard Laplace operator in two and three dimensional bounded doubly connected domains
with impedance boundary conditions, where the impedances are assumed to be positive functions.
Moreover, asymptotic expressions for the difference of eigenvalues related to impedance boundary
value problems with different impedances are derived. Further results may be obtained.
Algorithmic aspects of bipartite graphs
Authors: Bakonyi Mihály , Varness Erik M.
Published: September 2002

We generalize previous work done by Donald J. Rose and Robert E. Tarjan [2],
who developed efficient algorithms for use on directed graphs. This paper considers an edge
elimination process on bipartite graphs, presenting several theorems which lead to an algorithm
for computing the minimal fill‐in of a given ordered graph.
Classical quotient rings of generalized matrix rings
Authors: Poole David G. , Stewart Patrick N.
Published: September 2002

An associative ring R with identity is a generalized matrix ring with idempotent
set E if E is a finite set of orthogonal idempotents of R whose sum is 1. We show that, in the
presence of certain annihilator conditions, such a ring is semiprime right Goldie if and only if eRe
is semiprime right Goldie for all e ∈ E, and we calculate the classical right quotient ring of R.
On Generic submanifolds of a locally conformal Kahler manifold with parallel canonical structures
Authors: shahid M. Hasan , Sharfuddin A.
Published: September 2002

The study of CR‐submanifolds of a Kähler manifold was
initiated by Bejancu [1]. Since then many papers have appeared on
CR‐submanifolds of a Kähler manifold. Also, it has been studied that
generic submanifolds of Kähler manifolds [2] are generalisations of
holomorphic submanifolds, totally real submanifolds and
CR‐submanifolds of Kähler manifolds. On the other hand, many examples
C2 of generic surfaces in which are not CR‐submanifolds have been
given by Chen [3] and this leads to the present paper where we obtain
some necessary conditions for a generic submanifolds in a locally
conformal Kähler manifold with four canonical strucrures, denoted by
P, F, t and f, to have parallel P, F and t. We also prove that for a
generic submanifold of a locally conformal Kähler manifold, F is
parallel iff t is parallel.
Non‐homogeneous Markov chains with a finite state space and a Doeblin type theorem
Authors: Chattopadhyay Rita
Published: September 2002

Doeblin [1] considered some classes of finite state nonhomogeneous Markov chains
and studied their asymptotic behavior. Later Cohn [2] considered another class of such Markov
chains (not covered earlier) and obtained Doeblin type results. Though this paper does not
present the best possible results, the method of proof will be of interest to the reader. It is
elementary and based on Hajnal′s results on products of nonnegative matrices.
Properties of the modulus of continuity for monotonous convex functions and applications
Authors: Gal Sorin Gheorghe
Published: September 2002

For a monotone convex function f ∈ C[a, b] we prove that the modulus of
continuity w(f; h) is concave on [a, b] as function of h. Applications to approximation theory are
obtained.
Some properties of starlike functions with respect to symmetric‐conjugate points
Authors: Al-Amiri Hassoon , coman Dan , Mocanu Petru T.
Published: September 2002

Let A be tile class of all analytic functions in the unit disk U such that f(0) = f′(0) − 1 = 0. A function f ∈ A is called starlike with respect to 2n symmetric‐conjugate points
if Rezf′(z)/fn(z) > 0 for z ∈ U, where

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,
ω = exp(2πi/n]. This class is denoted by , and was studied in [1]. A sufficient condition for
starlikeness with respect to symmetric‐conjugate points is obtained. In addition, images of some
subclasses of under the integral operator I : A → A, I(f) = F where

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and g ∈ A is given are determined.
A note on Quasi and Bi‐ideals in Ternary semigroups
Authors: Dixit V. N. , Dewan Sarita
Published: September 2002

In this paper we have studied the properties of Quasi‐ideals and Bi‐ideals
in ternary semi groups. We prove that every quasi‐ideal is a bi‐ideal in T
but the converse is not true in general by giving several example in different
context.
Best approximation and fixed points in strong M‐starshaped metric spaces
Authors: Al-Thagafi M. A.
Published: September 2002

We introduced strong M‐starshaped metric spaces. For these spaces, we obtained
two fixed‐point theorems generalizing a result of W. G. Dotson, and two theorems extending and
subsuming several known results on the existence of fixed points of best approximation.
Fourier‐like kernels as solutions of Ode′s
Authors: Aggarwala B. D.
Published: September 2002

In this paper, we generate asymmetric Fourier kernels as solutions of
ODE′s. These kernels give many previously known kernels as special cases. Several
applications are considered.
Outer measures associated with lattice measures and their application
Authors: Traina Charles
Published: September 2002

Consider a set X and a lattice ℒ of subsets of X such that ϕ, X ∈ ℒ. M(ℒ) denotes
those bounded finitely additive measures on A(ℒ) which are studied, and I(ℒ) denotes those elements
of M(ℒ) which are 0 − 1 valued. Associated with a μ ∈ M(ℒ) or a μ ∈ Mσ(ℒ) (the elements of M(ℒ)
which are σ‐smooth on ℒ) are outer measures μ′ and μ″. In terms of these outer measures various
regularity properties of μ can be introduced, and the interplay between regularity, smoothness, and
measurability is investigated for both the 0 − 1 valued case and the more general case. Certain results
for the special case carry over readily to the more general case or with at most a regularity assumption
on μ′ or μ″, while others do not. Also, in the special case of 0 − 1 valued measures more refined
notions of regularity can be introduced which have no immediate analogues in the general case.
The best approximation and an extension of a fixed point theorem of F. E. Browder
Authors: Sehgal V. M. , Singh S. P.
Published: September 2002

In this paper, the KKM
principle has been used to obtain a theorem on the best
approximation of a continuous function with respect to an affine map. The main result provides
extensions of some well‐known fixed point theorems.
Approximation by weighted means of Walsh‐Fourier series
Authors: Móricz F. , Rhoades B. E.
Published: September 2002

We study the rate of approximation to functions in Lp and, in particular, in Lip(α, p) by weighted means of their Walsh‐Fourier series, where α > 0 and 1 ≤ p ≤ ∞. For the case p = ∞, Lp is interpreted to be CW, the collection of uniformly W continuous functions over the unit interval [0, 1). We also note that the weighted mean kernel is quasi‐positive, under fairly general conditions.
Comparison and oscillation results for delay difference equations with oscillating coefficients
Authors: Yan Weiping , Yan Jurang
Published: September 2002

In this paper we consider the oscillation of the delay difference equation with oscillating coefficients

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Some comparison and oscillation results are obtained.
Univalence for convolutions
Authors: Silverman Herb
Published: September 2002

The radius of univalence is found for the convolution f∗g of functions f ∈ S (normalized univalent functions) and g ∈ C (close‐to‐convex functions). A lower bound for the radius of univalence is also determined when f and g range over all of S. Finally, a characterization of C provides an inclusion relationship.
Proper shape invariants: Tameness and movability
Authors: Čerin Zvonko
Published: September 2002

We study geometric properties of topological spaces called proper ‐tameness,
proper ‐tameness, and proper Nℬ‐movability, where ℬ and C denote classes of spaces. They
are related to proper ‐tameness and proper Mℬ‐movability from [5] and could be regarded
as their dual forms. All three are invariants of a recently invented author′s proper shape
theory and are described by the use of proper multi‐valued functions. We explore their basic
properties and prove several results on their preservation under proper maps.
Contra‐continuous functions and strongly S‐closed spaces
Authors: Dontchev J.
Published: September 2002

In 1989 Ganster and Reilly [6] introduced and studied the notion of LC‐continuous
functions via the concept of locally closed sets. In this paper we consider a stronger form of
LC‐continuity called contra‐continuity. We call a function f : (X, τ) → (Y, σ) contra‐continuous if the
preimage of every open set is closed. A space (X, τ) is called strongly S‐closed if it has a finite dense
subset or equivalently if every cover of (X, τ) by closed sets has a finite subcover. We prove that contra‐continuous
images of strongly S‐closed spaces are compact as well as that contra‐continuous, β‐continuous images of S‐closed spaces are also compact. We show that every strongly S‐closed space
satisfies FCC and hence is nearly compact.
Chain Conditions on Semirings
Authors: Mukherjee T. K. , Sen M. K. , Ghosh Shamik
Published: September 2002

In this paper we characterize the class of semirings S for which the semirings of
square matrices Mn(S) over S are (left) k‐artinian. Also an analogue of the Hilbert basis theorem for
semirings is obtained.

Corrigendum to “Chain conditions on semirings”dx.doi.org/10.1155/S0161171297000550
Common fixed point theorems for compatible mappings
Authors: Taş Kenan , Telci Mustafa , Fisher Brian
Published: September 2002

By using a compatibility condition due to Jungck we establish some common fixed
point theorems for four mappings on complete and compact metric spaces These results also generalize
a theorem of Sharma and Sahu.
A fixed point theorem for generalized metric spaces
Authors: Rhoades B. E.
Published: September 2002

In this paper we prove two fixed point theorems for the generalized metric spaces
introduced by Dhage.
Pexider functional equations‐their fuzzy analogs
Authors: Deeba Elias , De Korvin André , Xie Shishen
Published: September 2002

In this paper we shall interpret and study the Pexider functional equations in the
context of Fuzzy Set Theory. In particular, we shall present a general procedure for obtaining the
fuzzy analog of the Pexider functional equations and then solve the resulting equations.
Integrated cosine functions
Authors: Zheng Quan
Published: September 2002

In order to the second order Cauchy problem (CP2) : x″(t) = Ax(t), x(0) = x ∈ D(An), x″(0) = y ∈ D(Am) on a Banach space, Arendt and Kellermann recently introduced
the integrated cosine function. This paper is concerned with its basic theory, which contain some
properties, perturbation and approximation theorems, the relationship to analytic integrated semigroups,
interpolation and extrapolation theorems.
On the shift operators
Authors: Aggour M. M.
Published: September 2002

The purpose of this paper is to show that the weighted s‐shift operators and so the weighted shift and the right shift operators have the SVEP, but the left shift operator has not. Also, if T, S ∈ B(X) are quasi‐similar operators then, it is shown that T has the SVEP iff S has the SVEP. Finally, the paper shows that the right and left shift operators are not decomposable
Extension sets for real analytic functions and applications to Radon transforms
Authors: Arguedas Vernor , Estrada Ricardo
Published: September 2002

The real analytic character of a function f(x, y) is determined from its behavior along
radial directions fθ(s) = f(scosθ, ssinθ) for θ ∈ E, where E is a small set. A support theorem for
Radon transforms in the plane is proved. In particular if fθ extends to an entire function for θ ∈ E and
f(x, y) is real analytic in ℝ2 then it also extends to an entire function in ℂ2.
Compactifying a convergence space with functions
Authors: André Robert P.
Published: September 2002

A convergence space is a set together with a convergence
structure. In this paper we discuss
a method of constructing compactifications on a class of convergence
spaces by use of functions.
Strictly barrelled disks in inductive limits of quasi‐(LB)‐spaces
Authors: Bosch Carlos , Gilsdorf Thomas E.
Published: September 2002

A strictly barrelled disk B in a Hausdorff locally convex space E is
a disk such that the linear span of B with the topology of the Minkowski
functional of B is a strictly barrelled space. Valdivia′s closed graph theorems
are used to show that closed strictly barrelled
disk in a quasi‐(LB)‐space is
bounded. It is shown that a locally strictly
barrelled quasi‐(LB)‐space is
locally complete. Also, we show that a regular
inductive limit of quasi‐(LB)‐spaces is locally complete if and only if each closed bounded disk is a strictly
barrelled disk in one of the constituents.
Application on local discrete expansion
Authors: Abd El-Monsef M. E. , Kozae A. M. , Abo Khadra A. A.
Published: September 2002

The process of changing a topology by some types of
its local discrete expansion preserves
s‐closeness, S‐closeness, semi‐compactness, semi‐Ti, semi‐Ri, i ∈ {0, 1, 2}, and extremely disconnectness.
Via some other forms of such above replacements one can have topologies which satisfy
separation axioms the original topology does not have.
Lattice separation, coseparation and regular measures
Authors: Figueres Maurice C.
Published: September 2002

Let X be an arbitrary non‐empty set, and let ℒ, ℒ1, ℒ2
be lattices of subsets of X
containing
ϕ and X. 𝒜(ℒ) designates the algebra generated by ℒ and M(ℒ), these finite, non‐trivial,
non‐negative finitely additive measures on 𝒜(ℒ). I(ℒ) denotes those elements of M(ℒ) which assume
only the values zero and one. In terms of a μ ∈ M(ℒ) or I(ℒ), various outer measures are introduced.
Their properties are investigated. The interplay of
measurability, smoothness of μ, regularity of μ and
lattice topological properties on these outer measures is also investigated.

Finally, applications of these outer measures to separation type
properties between pairs of
lattices ℒ1, ℒ2 where ℒ1 ⊂ ℒ2 are developed. In
terms of measures from I(ℒ), necessary and sufficient
conditions are established for ℒ1 to semi‐separate ℒ2, for ℒ1 to separate ℒ2, and finally for ℒ1 to coseparate ℒ2.
Homomorphisms of ergodic group actions and conjugacy of skew product actions
Authors: Reyes Edgar N.
Published: September 2002

Let G be a locally compact group acting ergodically on X. We discuss relationships
between homomorphisms on the measured groupoid X × G, conjugacy of skew product extensions,
and similarity of measured groupoids. To do this, we describe
the structure of homomorphisms on
X × G
whose restriction to an extension given by
a skew product action is the trivial homomorphism.
Remarks on recent fixed point theorems for compatible maps
Authors: Singh S. L. , Chadha V. , Mishra S. N.
Published: September 2002

Following Gerald Jungck′s formulation of compatibility of
maps, several interesting fixed
point theorems for such maps have
been obtained, wherein at least one of the maps is continuous. The
main purpose of this note is to avoid the continuity condition
from some of the main results of Jungck et al.
Axisymmetric Lamb′s problem in a semi‐infinite micropolar viscoelastic medium
Authors: Biswas P. K. , Sengupta P. R. , Debnath Lokenath
Published: September 2002

A study is made of the axisymmetric problem of wave
propagation under the influence of
gravity in a micropolar viscoelastic semi‐infinite
medium when a time varying axisymmetric loading is
applied on the surface of the medium. Special attention is
given to the effects of gravity which induces a
kind of initial stress of a hydrostatic nature on the wave propagation.
Common fixed point theorems and applications
Authors: Pathak Hemant Kumar , Chang Shih Sen , Cho Yeol Je , Jung Jong Soo
Published: September 2002

The purpose of this paper is to discuss the existence of common fixed points for
mappings in general quasi‐metric spaces. As applications, some common fixed point theorems for
mappings in probabilistic quasi‐metric spaces are given. The results presented in this paper generalize
some recent results.
Localization and summability of multiple Hermite series
Authors: Karadzhov G. E. , El-Adad E. E.
Published: September 2002

The multiple Hermite series in Rn are investigated by the Riesz summability
method of order α > (n − 1)/2. More precisely, localization theorems for some classes of functions
are proved and sharp sufficient conditions are given. Thus the classical Szegö results are extended
to the n‐dimensional case. In particular, for these classes of functions the localization principle
and summability on the Lebesgue set are established.
A hypercontinuous hypersmooth Schwarzschild line element transformation
Authors: Herrmann Robert A.
Published: September 2002

In this paper, a new derivation for one of the black hole line elements is given since
the basic derivation for this line element is flawed mathematically. This derivation postulates
a transformation procedure that utilizes a transformation function that is modeled by an ideal
nonstandard physical world transformation process that yields a connection between an exterior
Schwarzschild line element and distinctly different interior line element. The transformation is an
ideal transformation in that in the natural world the transformation is conceived of as occurring
at an unknown moment in the evolution of a gravitationally collapsing spherical body with radius
greater than but near to the Schwarzsclfild radius. An ideal transformation models this transformation
in a manner independent of the objects standard radius. It yields predicted behavior
based upon a Newtonian gravitational field prior to the transformation, predicted behavior after
the transformation for a field internal to the Schwarzschild surface and predicted behavior with
respect to field alteration processes during the transformation.
On the Diophantine equation x2 + 2k = yn
Authors: Arif S. Akhtar , Abu Muriefah Fadwa S.
Published: September 2002

By factorizing the equation x2 + 2k = yn, n ≥ 3, k‐even, in the field Q(i), various
theorems regarding the solutions of this equation in rational integers are proved. A conjecture regarding
the solutions of this equation has been put forward and proved to be true for a large class of values of k
and n.
On strong form of Arzela convergence
Authors: Ewert Janina
Published: September 2002

We define some new type of convergence of nets of functions which is formulated in
terms of open covers. It preserves continuity and under some assumptions implies (or coincides with) the
Arzela quasi‐uniform convergence. Furthermore, the introduced strong convergence is used for
characterization of compactness and regularity of a topological space.
A class of generalized best approximation problems in locally convex linear topological spaces
Authors: Samanta Hora Krishna
Published: September 2002

In this paper a class of generalized best approximation problems is formulated in locally
convex linear topological spaces and is solved, using standard results of locally convex linear topological
spaces.
On normally flat Einstein submanifolds
Authors: Verstraelen Leopold , Zafindratafa Georges
Published: September 2002

The purpose of this paper is to study the second fundamental form of some submanifolds
Mn in Euclidean spaces 𝔼m which have flat normal connection. As such, Theorem gives precise
expressions for the (essentially 2) Weingarten maps of all 4‐dimensional Einstein submanifolds in 𝔼6,
which are specialized in Corollary 2 to the Ricci flat submanifolds. The main part of this paper deals with
flat submanifolds. In 1919, E. Cartan proved that every flat submanifold of dimension ≤3 in a
Euclidean space is totally cylindrical. Moreover, he asserted without proof the existence of flat nontotally
cylindrical submanifolds of dimension >3 in Euclidean spaces. We will comment on this
assertion, and in this respect will prove, in Theorem 3, that every flat submanifold Mn with flat normal
connection in 𝔼m is totally cylindrical (for all possible dimensions n and m).
Noninclusion theorems for summability matrices
Authors: Fridy J. A.
Published: September 2002

For both ordinary convergence and ℓ1‐summability explicit sufficient conditions on a
matrix have long been known that ensure that the summability method is strictly stronger than the identity
map. The main results herein show that a matrix that satisfies those conditions can be included by
another matrix only if the other matrix satisfies those same conditions.
Inequalities via Lagrange multipliers
Authors: Sulaiman W. T.
Published: September 2002

An easy method is obtained to prove many inequalities using Lagrange mutipliers.
On the distance between two Chebyshev sets in Banach spaces
Authors: El-Sayed Wagdy G.
Published: September 2002

The paper answers a question concerning the distance between two Chebyshev sets in
some Banach spaces.
Covariant and contravariant approaches to topology
Authors: Dydak Jerzy
Published: September 2002

This paper is an exposition of results contained in [2]. The purpose of [2] is
to present a way of viewing of basic topology which unifies quite a few results and concepts
previously seemed not related (quotient maps, product topology, subspace topology, separation
axioms, topologies on function spaces, dimension, metrizability). The basic idea is that in order
to investigate an unknown space X, one either maps known spaces to X or maps X to known
spaces.
The dimension of the boundary of the Lévy Dragon
Authors: Duvall P. , Keesling J.
Published: September 2002

In this paper we describe the computations done by the authors in determining the
dimension of the boundary of the Lévy Dragon. A general theory was developed for calculating the
dimension of a self‐similar tile and the theory was applied to this particular set. The computations were
challenging. It seemed that a matrix which was 215 × 215 would have to be analyzed. It was possible to reduce the analysis to a 752 × 752 matrix. At last it was seen that if λ
was the largest eigenvalue of a
certain 734 × 734 matrix, then Perron‐Frobenius theory played an important role
in analyzing this matrix.
Wavelet transforms in generalized Fock spaces
Authors: Schmeelk John , Takači Arpad
Published: September 2002

A generalized Fock space is introduced as it was developed by Schmeelk [1‐5],
also Schmeelk and Takači [6‐8]. The wavelet transform is then extended to this generalized
Fock space. Since each component of a generalized Fock functional is a generalized function,
the wavelet transform acts upon the individual entry much the same as was developed by
Mikusinski and Mort [9] based upon earlier work of Mikusinski and Taylor [10]. It is then
shown that the generalized wavelet transform applied to a member of our generalized Fock
space produces a more appropriate functional for certain appfications.
Local connectivity and maps onto non‐metrizable arcs
Authors: Nikiel J. , Treybig L. B. , Tuncali H. M.
Published: September 2002

Three classes of locally connected continua which admit sufficiently many maps
onto non‐metric arcs are investigated. It is proved that all continua in those classes are continuous
images of arcs and, therefore, have other quite nice properties.
Regular and singular perturbations of upper semicontinuous differential inclusion
Authors: Donchev Tzanko , Angelov Vasil
Published: September 2002

In the paper we study the continuity properties of the solution set of upper
semicontinuous differential inclusions in both regularly and singularly perturbed case. Using a
kind of dissipative type of conditions introduced in [1] we obtain lower semicontinuous dependence
of the solution sets. Moreover new existence result for lower semicontinuous differential inclusions
is proved.
The fractal structure of limit set of solution space of a doubly periodic Ricatti equation
Authors: Guan Ke-Ying
Published: September 2002

The limit set of the Kleinian group of a given doubly periodic Riccati equation is proved
to have a fractal structure if the parameter δ(λ) of the equation is greater than , and a possible
Hausdorff dimension is suggested to the limit set.
On prime and semiprime near‐rings with derivations
Authors: Argaç Nurcan
Published: September 2002

Let N be a semiprime right near‐ring, A a subset of N such that 0 ∈ A and AN⫅A, and d a derivation of N The purpose of this paper is to prove that if d acts as a homomorphism on A or as an anti‐homomorphism on A, then d(A) = {0}.
θ‐Almost summable sequences
Authors: Nuray Fatih
Published: September 2002

King[3] introduced and examined the concepts of almost A‐summable sequence,
almost conservative matrix and almost regular matrix By following King, in this paper we introduce
and examine the concepts of θ‐almost A‐summable sequence, θ‐almost conservative matrix and θ‐almost regular matrix
On α‐convex functions of order β
Authors: Fukui Seiichi
Published: September 2002

In 1969 Mocanu [1] introduced and studied a new class of analytic functions consisting of
α‐convex functions. Many mathematicians have studied and shown the properties of this class. Now we
will define new classes like that Mocanu class and then investigate and give some results. The class of α‐convex functions of order β partially includes Mocanu′s class.
Subcontra‐continuous functions
Authors: Baker C. W.
Published: September 2002

A weak form of contra‐continuity, called subcontra‐continuity, is introduced. It is
shown that subcontra‐continuity is strictly weaker than contra‐continuity and stronger than both
subweak continuity and sub‐LC‐continuity. Subcontra‐continuity is used to improve several results in
the literature concerning compact spaces.
On lattice‐topological properties of general Wallman spaces
Authors: Vlad Carmen
Published: September 2002

Let X be an arbitrary set and ℒ
a lattice of subsets of X such that ϕ,X ∈ ℒ.𝒜(ℒ) is the
algebra generated by ℒ and I(ℒ) consists of all zero‐one valued finitely additive measures on
𝒜(ℒ). Various subsets of and I(ℒ) are considered and certain lattices are investigated as well as the topology of
closed sets generated by them. The lattices are investigated for normality, regularity, repleteness and
completeness. The topologies are similarly discussed for various properties such as
T2 and Lindelöf.
α‐Scattered spaces
Authors: Rose David A.
Published: September 2002

α‐scattered spaces, spaces whose α‐topology is scattered, are introduced and used
to slightly extend a recent result of A. V. Arhangel′skii and P. J. Collins [1]. Strong irresolvability of
J. Foran and P. Liebnitz [6], is also characterized in terms ofthe α‐topology, and it is shown that a recent
theorem of Julian Dontchev [5] in essence maximally extends the Arhangel′skii‐Collins result.