bluuebunny/crossref_metadata_2025 huggingface dataset:
Fixed point theorems for generalized Lipschitzian semigroups
Authors: Jung Jong Soo , Thakur Balwant Singh
Published: September 2002

Let K be a nonempty subset of a p‐uniformly convex Banach space E, G a left reversible semitopological semigroup, and 𝒮 = {Tt : t ∈ G} a generalized Lipschitzian
semigroup of K into itself, that is, for s ∈ G, ‖Tsx − Tsy‖ ≤ as‖x − y‖ + bs(‖x − Tsx‖ + ‖y − Tsy‖) + cs(‖x − Tsy‖ + ‖y − Tsx‖), for x, y ∈ K where as, bs, cs > 0 such that there exists a t1 ∈ G such that bs + cs < 1 for all s≽t1. It is proved that if there exists a closed subset C of K such that for all x ∈ K, then 𝒮 with has a common fixed point, where α = lim sups(as + bs + cs)/(1 − bs − cs) and β = lim sups(2bs + 2cs)/(1 − bs − cs).
Convergent nets in abelian topological groups
Authors: Ledet Robert
Published: September 2002

A net in an abelian group is called a T‐net if there exists a Hausdorff group topology in which the net converges to 0. This
paper describes a fundamental system for the finest group
topology in which the net converges to 0. The paper uses this
description to develop conditions which insure there exists a
Hausdorff group topology in which a particular subgroup is dense
in a group. Examples given include showing that there are
Hausdorff group topologies on ℝn in which any
particular axis may be dense and Hausdorff group topologies on
the torus in which S1 is dense.
Global attractivity without stability for Liénard type systems
Authors: Mureşan Marian
Published: September 2002

We are concerned with some conditions such as the trivial solution of a planar system of differential equations (including the Liénard system) that is globally attractive but not
stable. We emphasize the connection with some nonoscillatory conditions. The results are related to the previous ones obtained by Hara in 1993.
On the Reidemeister torsion of rational homology spheres
Authors: Nicolaescu Liviu I.
Published: September 2002

We prove that the Modℤ
reduction of the Reidemeister
torsion of a rational homology 3‐sphere is naturally a ℚ/ℤ‐valued quadratic function uniquely determined by a ℚ/ℤ‐constant and the linking form.
Strictly webbed spaces and regularity properties of inductive limits
Authors: García-Martínez Armando
Published: September 2002

Sequentially complete, locally complete, locally Baire, and bornivorously webbed are equivalent for strictly webbed spaces. For inductive limits of strictly webbed spaces these properties
are equivalent. Moreover, they imply regularity.
Biorthogonal multiresolution analyses and decompositions of Sobolev spaces
Authors: Jouini Abdellatif , Trimèche Khalifa
Published: September 2002

The object of this paper is to construct extension operators in
the Sobolev spaces Hk(]−∞, 0]) and Hk([0, +∞[)(k ≥ 0). Then we use these extensions to get biorthogonal
wavelet bases in Hk(ℝ). We also give a construction in L2([−1, 1]) to see how to obtain boundaries functions.
Finite AG‐groupoid with left identity and left zero
Authors: Mushtaq Qaiser , Kamran M. S.
Published: September 2002

A groupoid G whose elements satisfy the left invertive law:
(ab)c = (cb)a is known as Abel‐Grassman′s groupoid (AG‐groupoid).
It is a nonassociative algebraic structure midway between a
groupoid and a commutative semigroup. In this note, we show that
if G is a finite AG‐groupoid with a left zero then, under
certain conditions, G without the left zero element is a commutative group.
Value distribution of certain differential polynomials
Authors: Lahiri Indrajit
Published: September 2002

We prove a result on the value distribution of differential
polynomials which improves some earlier results.
A sufficient condition for starlikeness of order α
Authors: Mocanu Petru T. , Oros Gh.
Published: September 2002

We obtain a sufficient condition for starlikeness of order α, |f′(z) − λ(f(z)/z) + λ − 1| < M = Mn(λ, α), where λ ∈ [0, 1], α ∈ [0, 1] and the function f(z) = z + an+1zn+1 + ⋯ is analytic in the unit disc U.
Exponential forms and path integrals for complexnumbers in n dimensions
Authors: Olariu Silviu
Published: September 2002

Two distinct systems of commutative complex numbers in n dimensions are described, of polar and planar types. Exponential
forms of n‐complex numbers are given in each case, which depend on
geometric variables. Azimuthal angles, which are cyclic variables,
appear in these forms at the exponent, and this leads to the
concept of residue for path integrals of n‐complex functions. The
exponential function of an n‐complex number is expanded in terms
of functions called in this paper cosexponential functions, which
are generalizations to n dimensions of the circular and
hyperbolic sine and cosine functions. The factorization of
n‐complex polynomials is discussed.
Computations of Nambu‐Poisson cohomologies
Authors: Monnier Philippe
Published: September 2002

We want to associate to an n‐vector on a manifold of dimension n a cohomology which generalizes the Poisson cohomology of a 2‐dimensional Poisson manifold. Two possibilities are given here. One of them, the Nambu‐Poisson cohomology, seems to be the most pertinent. We study these two cohomologies locally, in the case of germs of n‐vectors on 𝕜n(𝕜 = ℝ or ℂ).
On blockers in bounded posets
Authors: Matveev Andrey O.
Published: September 2002

Antichains of a finite bounded poset are assigned antichains playing a role analogous to that played by blockers in the Boolean lattice of all subsets of a finite set. Some properties of lattices of generalized blockers are discussed.
Pythagorean identity for polyharmonic polynomials
Authors: Fryant Allan , Vemuri Murali Krishna
Published: September 2002

Polyharmonic polynomials in n variables are shown to satisfy a
Pythagorean identity on the unit hypersphere. Application is made
to establish the convergence of series of polyharmonic
polynomials.
Matrix method for solving linear complex vector functional equations
Authors: Risteski Ice B.
Published: September 2002

We give a new matrix method for solving both homogeneous and
nonhomogeneous linear complex vector functional equations with
constant complex coefficients.
Classification of reduction invariants with improved backpropagation
Authors: Shamsuddin S. M. , Darus M. , Sulaiman M. N.
Published: September 2002

Data reduction is a process of feature extraction that transforms
the data space into a feature space of much lower dimension
compared to the original data space, yet it retains most of the
intrinsic information content of the data. This can be done by
using a number of methods, such as principal component analysis
(PCA), factor analysis, and feature clustering. Principal
components are extracted from a collection of multivariate cases
as a way of accounting for as much of the variation in that
collection as possible by means of as few variables as possible.
On the other hand, backpropagation network has been used
extensively in classification problems such as XOR problems,
share prices prediction, and pattern recognition. This paper
proposes an improved error signal of backpropagation network for
classification of the reduction invariants using principal
component analysis, for extracting the bulk of the useful
information present in moment invariants of handwritten digits,
leaving the redundant information behind. Higher order
centralised scale‐ invariants are used to extract features of
handwritten digits before PCA, and the reduction invariants are
sent to the improved backpropagation model for classification
purposes.
Fuzzy filters in BCI‐algebras
Authors: Lele C. , Wu C. , Mamadou T.
Published: September 2002

We introduce the notion of fuzzy filters and weak filters in
BCI‐algebras and discuss their properties. Then we establish some
relations among filters, fuzzy filters, and weak filters in
BCI‐algebras.
On the continuity of principal eigenvalues for boundary valueproblems with indefinite weight function with respect to radiusof balls in ℝN
Authors: Afrouzi Ghasem Alizadeh
Published: September 2002

We investigate the continuity of principal eigenvalues (i.e.,
eigenvalues corresponding to positive eigenfunctions) for the
boundary value problem −Δu(x) = λg(x)u(x), x ∈ BR(0); u(x) = 0, |x| = R, where BR(0) is a ball in ℝN, and g is a smooth function, and we show that and are continuous functions of R.
Effect of the radiative damping on magnetohydrodynamic waves in an isothermal medium
Authors: Alkahby Hadi , Talmadge Andrew , Jalbout Abraham
Published: September 2002

We investigate the effect of the heat radiation on the reflection
and dissipation of upward propagating waves in an isothermal
atmosphere. It is shown that the magnetic field produces a
totally reflecting layer. Consequently, the atmosphere can be
divided into two distinct regions. In the lower region, the
solution can be written as a linear combination of an upward and
a downward propagating wave, and in the upper region the
solution, which satisfies the upper boundary condition, decays
exponentially or behaves like a constant. These two regions are
connected by a region in which the reflection and
transmission of the waves takes place. Moreover, the heat
radiation affects only the lower region and changes the sound
speed from the adiabatic value to the isothermal one. The
reflection coefficient and the attenuation factor of the
amplitude of the waves are derived for all values of the heat
radiation coefficient. Finally, the conclusions are presented in
connection with the heating process of the solar atmosphere.
A generalized beta function and associated probability density
Authors: Ben Nakhi Y. , Kalla S. L.
Published: September 2002

We introduce and establish some properties of a generalized form
of the beta function. Corresponding generalized incomplete beta
functions are also defined. Moreover, we define a new probability
density function (pdf) involving this new generalized beta
function. Some basic functions associated with the pdf, such as
moment generating function, mean residue function, and hazard rate
function are derived. Some special cases are mentioned. Some
figures for pdf, hazard rate function, and mean residue life
function are given. These figures reflect the role of shape and
scale parameters.
Derivations in Banach algebras
Authors: Park Kyoo-Hong , Jung Yong-Soo , Bae Jae-Hyeong
Published: September 2002

We present some conditions which imply that a derivation on a
Banach algebra maps the algebra into its Jacobson radical.
The de Rham theorem for the noncommutative complex of Cenkl and Porter
Authors: Mejias Luis Fernando
Published: September 2002

We use noncommutative differential forms (which were first introduced by Connes) to construct a noncommutative version of the complex of Cenkl and Porter Ω∗,∗(X) for a simplicial set X. The algebra Ω∗,∗(X) is a differential graded algebra with a filtration Ω∗,q(X) ⊂ Ω∗,q+1(X), such that Ω∗,q(X) is a ℚq‐module, where ℚ0 = ℚ1 = ℤ and ℚq = ℤ[1/2, …, 1/q] for q > 1. Then we use noncommutative versions of the Poincaré lemma and Stokes′ theorem to prove the noncommutative tame de Rham theorem: if X is a simplicial set of finite type, then for each q ≥ 1 and any ℚq‐module M, integration of forms induces a natural isomorphism of ℚq‐modules I : Hi(Ω∗,q(X), M) → Hi(X; M) for all i ≥ 0. Next, we introduce a complex of noncommutative tame de Rham currents Ω∗,∗(X) and we prove the noncommutative tame de Rham theorem for homology: if X is a simplicial set of finite type, then for each q ≥ 1 and any ℚq‐module M, there is a natural isomorphism of ℚq‐modules I : Hi(X; M) → Hi(Ω∗,q(X), M) for all i ≥ 0.
One‐sided complements and solutions of the equation aXb = c in semirings
Authors: Blyumin Sam L. , Golan Jonathan S.
Published: September 2002

Given multiplicatively‐regular elements a and b in a semiring
R, and given an element c of R, we find a complete set of solutions to the equation aXb = c. This result is then extended to equations over matrix semirings.
Consecutive evaluation of Euler sums
Authors: Boyadzhiev Khristo N.
Published: September 2002

We describe a simple method for a consecutive evaluation of the
Euler sums S(r, p), r = 1, 2, … in terms of zeta values.
Solving some nonlinear equations by successive approximations
Authors: Kalinde Albert K.
Published: September 2002

The iterations scheme generated by an infinite sequence of
operators satisfying some contractive conditions in a complete
metric space is used to solve some integral equations of
Hammerstein type.
Unsteady flow induced by variable suction on a porous disk rotating eccentrically with a fluid at infinity
Authors: Ghosh A. K. , Paul S. , Debnath Lokenath
Published: September 2002

We study the effect of variable suction or blowing on the flow of
an incompressible viscous fluid due to noncoaxial rotations of a
porous disk and a fluid at infinity. The inquiries are made about
the components of fluid velocity and the shear stress at the
disk. It is found that the effect of uniform suction or blowing
on the flow is enhanced in the presence of variable suction or
blowing.
A combinatorial commutativity property for rings
Authors: Bell Howard E. , Klein Abraham A.
Published: September 2002

We study commutativity in rings R with the property that for a fixed positive integer n, xS = Sx for all x ∈ R and all
n‐subsets S of R.
Generalized transversely projective structure on a transversely holomorphic foliation
Authors: Biswas Indranil
Published: September 2002

The results of Biswas (2000) are extended to the situation of
transversely projective foliations. In particular, it is shown
that a transversely holomorphic foliation defined using everywhere
locally nondegenerate maps to a projective space
ℂℙn, and whose transition functions are given
by automorphisms of the projective space, has a canonical
transversely projective structure. Such a foliation is also
associated with a transversely holomorphic section of N⊗−k
for each k ∈ [3, n + 1], where N is the normal bundle to
the foliation. These transversely holomorphic sections are also
flat with respect to the Bott partial connection.
Global geometric structures associated with dynamical systems admitting normal shift of hypersurfaces in Riemannian manifolds
Authors: Sharipov Ruslan A.
Published: September 2002

One of the ways of transforming hypersurfaces in Riemannian manifold is to move their points along some lines. In Bonnet construction of geodesic normal shift, these points move along
geodesic lines. Normality of shift means that moving hypersurface
keeps orthogonality to the trajectories of all its points. Geodesic lines correspond to the motion of free particles if the points of hypersurface are treated as physical entities obeying Newton′s second law. An attempt to introduce some external force F acting on the points of moving hypersurface in Bonnet construction leads to the theory of dynamical systems admitting a normal shift. As appears in this theory, the force field F of dynamical system should satisfy some system of partial differential equations. Recently, this system of equations was integrated, and explicit formula for F was obtained. But this formula is local. The main goal of this paper is to reveal global geometric structures associated with local expressions for F given by explicit formula.
Almost sure central limit theorems for strongly mixing and associated random variables
Authors: Gonchigdanzan Khurelbaatar
Published: September 2002

We prove an almost sure central limit theorem (ASCLT) for
strongly mixing sequence of random variables with a slightly slow
mixing rate α(n) = O((loglogn)−1−δ). We also
show that ASCLT holds for an associated sequence of random
variables without a stationarity assumption.
On weighted spaces without a fundamental sequence of bounded sets
Authors: Olaleru J. O.
Published: September 2002

The problem of countably quasi‐barrelledness of weighted spaces of continuous functions, of which there are no results in the
general setting of weighted spaces, is tackled in this paper.
This leads to the study of quasi‐barrelledness of weighted spaces
in which, unlike that of Ernst and Schnettler (1986), though with
a similar approach, we drop the assumption that the weighted
space has a fundamental sequence of bounded sets. The study of
countably quasi‐barrelledness of weighted spaces naturally leads
to definite results on the weighted (DF)‐spaces for those
weighted spaces with a fundamental sequence of bounded sets.
Contractive curves
Authors: Bonifant Araceli , Dabija Marius
Published: September 2002

We discuss the dynamics of the correspondences associated to
those plane curves whose local sections contract the Poincaré
metric in a hyperbolic planar domain.
Exceptional smooth Bol loops
Authors: Sbitneva Larissa V.
Published: September 2002

One new class of smooth Bol loops, exceptional Bol loops, is introduced and studied. The approach to the Campbell‐Hausdorff
formula is outlined. Bol‐Bruck loops and Moufang loops are exceptional which justifies our consideration.
Cohomology of the variational complex in the class of exterior forms of finite jet order
Authors: Sardanashvily Gennadi
Published: September 2002

We obtain the cohomology of the variational complex on the infinite‐order jet space of a smooth fiber bundle in the class of exterior forms of finite jet order. In particular, this provides a solution of the global inverse problem of the calculus of variations of finite order on fiber bundles.
Moment Lyapunov exponent of delay differential equations
Authors: Fofana M. S.
Published: September 2002

The aim of this paper is to establish a connecting thread through
the probabilistic concepts of pth‐moment Lyapunov exponents, the integral averaging method, and Hale′s reduction approach for delay dynamical systems. We demonstrate this connection by studying the stability of perturbed deterministic and stochastic differential equations with fixed time delays in the displacement and derivative functions. Conditions guaranteeing stable and unstable solution response are derived. It is felt that the connecting thread provides a unified framework for the stability study of delay differential equations in the deterministic and stochastic sense.
Normal Lie subsupergroups and non‐abelian supercircles
Authors: Baguis P. , Stavracou T.
Published: September 2002

We propose and study an appropriate analog of normal Lie subgroups in the supergeometrical context. We prove that the ringed space obtained taking the quotient of a Lie supergroup by a normal Lie subsupergroup, is still a Lie supergroup. We show how one can construct Lie supergroup structures over topologically nontrivial Lie groups and how the previous property of normal Lie subsupergroups can be used, in order to explicitly obtain the coproduct, counit, and antipode of these structures. We illustrate the general theory by carrying out the previous constructions over the circle, which leads to non‐abelian super generalizations of the circle.
Null distribution of multiple correlation coefficient under mixture normal model
Authors: Ali Hydar , Nagar Daya K.
Published: September 2002

The multiple correlation coefficient is used in a large variety
of statistical tests and regression problems. In this article, we
derive the null distribution of the square of the sample multiple
correlation coefficient, R2, when a sample is drawn from a mixture of two multivariate Gaussian populations. The moments of 1 − R2 and inverse Mellin transform have been used to derive the density of R2.
A higher‐order method for nonlinear singular two‐point boundary value problems
Authors: Furati K. M. , El-Gebeily M. A.
Published: September 2002

We present a finite difference method for a general class of nonlinear singular two‐point boundary value problems. The order of convergence of the method for such a general class of problems is higher than the previous reported methods. The method yields a fourth‐order convergence for the special case p(x) = w(x) = xα, α ≥ 1.
Harmonicity of horizontally conformal maps and spectrum of the Laplacian
Authors: Yun Gabjin
Published: September 2002

We discuss the harmonicity of horizontally conformal maps and
their relations with the spectrum of the Laplacian. We prove that if Φ : M → N is a horizontally conformal map such that the tension field is divergence free, then Φ is harmonic. Furthermore, if N is noncompact, then Φ must be constant. Also we show that the projection of a warped product manifold onto the first component is harmonic if and only if the warping function is constant. Finally, we describe a characterization for a horizontally conformal map with a constant dilation preserving an eigenfunction.
Projective representations of quivers
Authors: Park Sangwon
Published: September 2002

We prove that

is a projective representation of a quiver Q = •→• if and only if P1 and P2 are projective left R‐modules, f is an injection, and f (P 1) ⊂ P 2 is a summand. Then, we generalize the result so that a representation of a quiver Q = •→•→•⋯•→•→• is projective representation if and only if each Mi is a projective left R‐module and the representation is a direct sum of projective representations.
On a weak form of weak quasi‐continuity
Authors: Baker C. W.
Published: September 2002

A weak form of weak quasi‐continuity, which we call subweak
quasi‐continuity, is introduced. It is shown that subweak
quasi‐continuity is strictly weaker than weak quasi‐continuity. Subweak
quasi‐continuity is used to strengthen several results in the
literature concerning weak quasi‐continuity. Specifically, results
concerning the graph, graph function, and restriction of a weakly
quasi‐continuous function are extended slightly. Also, a result
concerning weakly quasi‐continuous retractions is strengthened.
The Hausdorff dimension and exact Hausdorff measure of random recursive sets with overlapping
Authors: Guo Hongwen , Hu Dihe
Published: September 2002

We weaken the open set condition and define a finite intersection
property in the construction of the random recursive sets. We prove that this larger class of random sets are fractals in the sense of Taylor, and give conditions when these sets have positive and finite Hausdorff measures, which in certain extent generalize some of the known results, about random recursive fractals.
Asymptotic Hölder absolute values
Authors: Garcia E. Muñoz
Published: September 2002

We prove that asymptotic Hölder absolute values are Hölder
equivalent to classical absolute values. As a corollary we obtain
a generalization of Ostrowski′s theorem and a classical theorem by E. Artin. The theorem presented implies a new, more flexible, definition of classical absolute value.
A note on Riesz elements in C*‐algebras
Authors: Legg David
Published: September 2002

It is known that every Riesz operator R on a Hilbert space can be written R = Q + C, where C is compact and both Q and CQ‐QC are quasinilpotent. This result is extended to a general C*‐algebra setting.
A class of generalized uniform asymptotic expansions
Authors: Obi Wilson C.
Published: September 2002

In [1] E. L. Reiss obtained a multivariable expansion of the problem L[y] ≡ y″ + 2ϵy′ + y = 0, t > 0; y(0; ϵ) = 0, y′(0, ϵ) = 1 by means of a technique which does not employ the traditional method of using a secularity condition in obtaining higher order approximations. In this paper Reiss′ technique is formalized and new results are established.
Graphs which have pancyclic complements
Authors: Straight H. Joseph
Published: September 2002

Let p and q denote the number of vertices and edges of a graph G, respectively. Let Δ(G) denote the maximum degree of G, and the complement of G. A graph G of order p is said to be pancyclic if G contains a cycle of each length n, 3 ≤ n ≤ p. For a nonnegative integer k, a connected graph G is said to be of rank k if q = p − 1 + k. (For k equal to 0 and 1 these graphs are called trees and unicyclic graphs, respectively.)

In 1975, I posed the following problem: Given k, find the smallest positive integer pk, if it exists, such that whenever G is a rank k graph of order p ≤ pk and Δ(G) < p − 2 then is pancyclic. In this paper it is shown that a result by Schmeichel and Hakiml (2) guarantees that pk exists. It is further shown that for k = 0, 1, and 2, pk = 5, 6, and 7, respectively.
Complete residue systems in the ring of matricesof rational integers
Authors: Shiue Jau-Shyong , Hwang Chie-Ping
Published: September 2002

This paper deals with the characterizations of the complete residue system mod.   G, where G is any n × n matrix, in the ring of n × n matrices.
Uniform approximation by incomplete polynomials
Authors: Saff E. B. , Varga R. S.
Published: September 2002

For any θ with 0 < θ < 1, it is known that, for the set of all incomplete polynomials of type θ, i.e, , to have the Weierstrass property on [aθ, 1], it is necessary that

urn:x-wiley:01611712:media:ijmm401670:ijmm401670-math-0002

In this paper, we show that the above inequalities are essentially sufficient as well.
Characteristic approximation properties of quadratic irrationals
Authors: Jurkat W. B. , Peyerimhoff A.
Published: September 2002

Some characteristic approximation properties of quadratic irrationals are studied in this paper. It is shown that the limit points of the sequence δn form a subset C(x), and D(x) can be generated from C(x) in a relatively simple way. Another proof of Lekkerkerker′s theorem
is given using relations between δn−1, δn, δn+1 which are independent of x and n.
Viscous damping of gravity waves over a permeable bed
Authors: Puri K. K.
Published: September 2002

The damping of gravity waves over the surface of a layer of viscous fluid which overlies a porous bed saturated with the same fluid is studied. It is shown that viscosity may not be the dominant influence in the damping mechanism; the damping effects due to percolation in the fixed bed may be of the same or even higher order than those due to viscosity.
Submatrices of summability matrices
Authors: Fridy J. A.
Published: September 2002

It is proved that a matrix that maps ℓ1 into ℓ1 can be obtained from any regular matrix by the deletion of rows. Similarly, a conservative matrix can be obtained by deletion of rows from a matrix that preserves boundedness. These techniques are also used to derive a simple sufficient condition for a matrix to sum an unbounded sequence.
Dentable functions and radially uniform quasi‐convexity
Authors: Looney Carl G.
Published: September 2002

In this paper we give a further result which states sufficient conditions for the theory of convergence of minimizing sequences to be applicable, develop the theory further, and give an application.
Some results on composition operators on ℓ2
Authors: Singh R. K. , Gupta D. K. , Komal B. S.
Published: September 2002

A necessary and sufficient condition for a bounded operator to be a
composition operator is investigated in this paper. Normal, quasi‐hyponormal, paranormal composition operators are characterised.
Isomorphs of a class of Queueing systems
Authors: Ghosal A. , Madan Sudhir
Published: September 2002

Restricted isomorphism between two queueing systems implies that they have equivalent distribution function for at least one (but not all) output elements (e.g. waiting time, queue size, idle time, etc.). Quasi‐isomorphism implies an approximate equivalence. Most of the single‐server queueing systems can be approximated by a quasi‐isomorphic system which has a gamma inter‐arrival and gamma service distributions (Ep/Eq/1).

This paper deals with the derivation of simpler isomorphs (in quasi‐restricted sense) for such gamma‐gamma (Ep/Eq/1) systems.
An invitation on the study of univalent and multivalent functions
Authors: Goodman A. W.
Published: September 2002

We begin with the basic definition and some very simple examples from the theory of univalent functions. After a brief look at the literature, we survey the progress that has been made on certain problems in this field. The article ends with a few open questions.
Remainders of power series
Authors: McCall J. D. , Fricke G. H. , Beyer W. A.
Published: September 2002

Suppose has radius of convergence R and . Suppose |z1| < |z2| < R, and T is either z2 or a neighborhood of z2. Put S = {N | σN(z1) > σN(z) for zϵT}. Two questions are asked: (a) can S be cofinite? (b) can S be infinite? This paper provides some answers to these questions. The answer to (a) is no, even if T = z2. The answer to (b) is no, for T = z2 if liman = a ≠ 0. Examples show (b) is possible if T = z2 and for T a neighborhood of z2.
A stability theory for perturbed differential equations
Authors: Gordon Sheldon P.
Published: September 2002

The problem of determining the behavior of the solutions of a perturbed
differential equation with respect to the solutions of the original unperturbed differential equation is studied. The general differential equation considered is

urn:x-wiley:01611712:media:ijmm589604:ijmm589604-math-0001

and the associated perturbed differential equation is

urn:x-wiley:01611712:media:ijmm589604:ijmm589604-math-0002

.

The approach used is to examine the difference between the respective solutions F(t, t0, x0) and G(t, t0, y0) of these two differential equations. Definitions paralleling the usual concepts of stability, asymptotic stability, eventual stability, exponential stability and instability are introduced for the difference G(t, t0, y0) − F(t, t0, x0) in the case where the initial values y0 and x0 are sufficiently close. The principal mathematical technique employed is a new modification of Liapunov′s Direct Method which is applied to the difference of the two solutions. Each of the various stabillty‐type properties considered is then shown to be guaranteed by the existence of a Liapunov‐type function with appropriate properties.
Modifications of the continuation method for the solution of systems of nonlinear equations
Authors: Lindfield G. R. , Simpson D. C.
Published: September 2002

Modifications are proposed to the Davidenko‐Broyden algorithm for the solution of a system of nonlinear equations. The aim of the modifications is to reduce the overall number of function evaluations by limiting the number of function evaluations for any one subproblem. To do this alterations are made to the strategy used in determining the subproblems to be solved. The modifications are compared with other methods for a wide range of test problems, and are shown to significantly reduce the number of function evaluations for the difficult problems. For the easier problems the modified method is equivalent to the Davidenko‐Broyden algorithm.
Convergence of weighted sums of independent random variables and an extension to Banach space‐valued random variables
Authors: Padgett W. J. , Taylor R. L.
Published: September 2002

Let {Xk} be independent random variables with EXk = 0 for all k and let {ank : n ≥ 1,  k ≥ 1} be an array of real numbers. In this paper the almost sure convergence of , n = 1, 2, …, to a constant is studied under various conditions on the weights {ank} and on the random variables {Xk} using martingale theory. In addition, the results are extended to weighted sums of random elements in Banach spaces which have Schauder bases. This extension provides a convergence theorem that applies to stochastic processes which may be considered as random elements in function spaces.
Nonlinear interaction of waves in a hot inhomogeneous magnetized plasma
Authors: Khan Tara Prasad , Das Mahadeb , Debnath Lokenath
Published: September 2002

This study is concerned with the theory of parametric coupling of waves in a hot inhomogeneous magnetized plasma in which the temperature gradient has been taken into account. The general dispersion relation and the polarization of the ordinary and the extra‐ordinary wave modes are discussed. The eigen‐mode solutions of the coupled differential equations for the wave amplitudes are obtained in the terms of the so called three wave interaction matrix elements. The theory of nonlinear wave‐wave interactions, which has been extended to the case of an
inhomogeneous magnetized plasma, is used to determine the threshold value of the electric field and the frequency shift. The results of this paper are also compared with the other known results. It is shown that the findings of this study are in excellent agreement with the results of earlier investigators.
Generalization of sum representation functional equations‐I
Authors: Kannappan Pl. , Sathyabhama V.
Published: September 2002

This paper contains the solution of a functional equation which is a generalization of a functional equation arising in a characterization of directed divergence and inaccuracy.
A pointwise contraction criteria for the existence of fixed points
Authors: Sehgal V. M.
Published: September 2002

Let S be a subset of a metric space (X, d) and T : S → X be a mapping. In this paper, we define the notion of lower directional increment QT(x, y] of T at x ∈ S in the direction of y ∈ X and give sufficient conditions for T to have a fixed point when QT(x, Tx] < 1 for each x ∈ S. The results herein generalize the recent theorems of Clarke (Caned. Math. Bull. Vol. 21(1), 1978, 7‐11) and also improve considerably some earlier results.
Uniform stability of linear multistep methods in Galerkin procedures for parabolic problems
Authors: Gekeler Eckart
Published: September 2002

Linear multistep methods are considered which have a stability region S and are D‐stable on the whole boundary ∂S ⊂ S of S. Error estimates are derived which hold uniformly for the class of initial value problems Y′ = AY + B(t), t > 0, Y(0) = Y0 with normal matrix A satisfying the spectral condition Sp(ΔtA) ⊂ S, Δt time step, Sp(A) spectrum of A. Because of this property, the result can be applied to semidiscrete systems arising in the Galerkin approximation of parabolic problems. Using known results of the Ritz theory in elliptic boundary value problems error bounds for Galerkin multistep procedures are then obtained in this way.
On the Knuth semi‐fields
Authors: Hughes D. R. , Kallaher M. J.
Published: September 2002

We consider three of Knuth′s four classes of semi‐fields Knuth [11] namely, those having dimension 2 over a nucleus and show that the autotopism group is solvable (Corollary 4.12). This generalizes a result of Hughes [5]. We also show that for semi‐fields of dimension 2 over a nucleus, the number of pairwise non‐isomorphic isotopic images is at least 5 (Corollary 5.1.1). This generalizes a result in [10].
Remark on functions with all derivatives univalent
Authors: Lachance M.
Published: September 2002

An attractive conjecture is discounted for the class of normalized univalent functions whose derivatives are also univalent.
Mean‐periodic functions
Authors: Berenstein Carlos A. , Taylor B. A.
Published: September 2002

We show that any mean‐periodic function f can be represented in terms of exponential‐polynomial solutions of the same convolution equation f satisfies, i.e., u∗f = 0(μ ∈ E′(ℝn)). This extends to n‐variables the work of L. Schwartz on mean‐periodicity and also extends L. Ehrenpreis′ work on partial differential equations with constant coefficients to arbitrary convolutors. We also answer a number of open questions about mean‐periodic functions of one variable. The basic ingredient is our work on interpolation by entire functions in one and several complex variables.
On the Hankel determinants of close‐to‐convex univalent functions
Authors: Noor K. Inayat
Published: September 2002

The rate of growth of Hankel determinant for close‐to‐convex functions is determined. The results in this paper are best possible.
A topological property of β(N)
Authors: Nakassis Anastase
Published: September 2002

In this paper we prove that the Stone‐Cech‐compactification of the natural numbers does not admit a countable infinite decomposition into subsets homeomorphic to each other and to the said compactification.
Mazur spaces
Authors: Wilansky Albert
Published: September 2002

A Mazur space is a locally convex topological vector space X such that every fϵXs is continuous where Xs is the set of sequentially continuous linear functionals on X; Xs is studied when X is of the form C(H), H a topological space, and when X is the weak * dual of a locally convex space. This leads to a new classification of compact T2 spaces H, those for which the weak * dual of C(H) is a Mazur space. An open question about Banach spaces with weak * sequentially compact dual ball is settled: the dual space need not be Mazur.
Some conditions on fixed rings
Authors: Reiter Edna E.
Published: September 2002

This paper deals with a question about the ascending and descending chain conditions on two‐sided ideals. Using the ideas of the skew group ring, certain results for two‐sided ideals are proved.
Oscillation in second order functional equations with deviating arguments
Authors: Singh Bhagat
Published: September 2002

For the pair of functional equations

urn:x-wiley:01611712:media:ijmm174267:ijmm174267-math-0001

and

urn:x-wiley:01611712:media:ijmm174267:ijmm174267-math-0002

sufficient conditions have been found to cause all solutions of equation (A) to be oscillatory. These conditions depend upon a positive solution of equation (B).
A generalization of contraction principle
Authors: Ghosh K. M.
Published: September 2002

In this paper, a generalized mean value contraction is introduced. This contraction is an extension of the contractions of earlier researchers and of the generalized mean value non‐expansive mapping. Using the generalized mean value contraction, some fixed point theorems are discussed.
Absolute continuity and hyponormal operators
Authors: Putnam C. R.
Published: September 2002

Let T be a completely hyponormal operator, with the rectangular representation T = A + iB, on a separable Hilbert space. If 0 is not an eigenvalue of T* then T also has a polar factorization T = UP, with U unitary. It is known that A, B and U are all absolutely continuous operators. Conversely, given an arbitrary absolutely continuous selfadjoint A or unitary U, it is shown that there exists a corresponding completely hyponormal operator as above. It is then shown that these ideas can be used to establish certain known absolute continuity properties of various unitary operators by an appeal to a lemma in which, in one interpretation, a given unitary operator is regarded as a polar factor of some completely hyponormal operator. The unitary operators in question are chosen from a number of sources: the F. and M. Riesz theorem, dissipative and certain mixing transformations in ergodic theory, unitary dilation theory, and minimal normal extensions of subnormal contractions.
A simple characterization of the trace‐class of operators
Authors: Saworotnow Parfeny P.
Published: September 2002

The trace‐class (τc) of operators on a Hilbert space is characterized in terms of existence of certain centralizers.
On K‐transform
Authors: Nasim C.
Published: September 2002

Using a combination of infinite order linear differential operators and integral operators, the inversion of K‐transform is established. Inversion procedures for Laplace transform and Potential transform are derived as special cases.
Note on a role for entire functions of the classes P and P*
Authors: Prather C. L.
Published: September 2002

We use the B and B* operators of Levin on the Classes P and P* and a comparison principle to prove a Gauss‐Lucas Theorem for differential operators. The connection with the determination of final sets for differential operators is then clarified.
Continuity of multiplication of distributors
Authors: Kucera Jan , Mckennon Kelly
Published: September 2002

In a reference book for distributions [1], it is shown that the multiplication
(u, f) ↦ uf on C∞ × 𝒟′, as well as on 𝒪M × 𝒮′, is hypocontinuous. We show here that in both cases it is discontinuous.
A distributional representation of strip analytic functions
Authors: Mitrović Dragiŝa
Published: September 2002

A strip analytic function converging in the D′ topology to certain boundary values (from the interior of the strip) is represented as the difference of two generalized Cauchy integrals.
Some remarks on certain classes of semilattices
Authors: Murty P. V. Ramana , Murty M. Krishna
Published: September 2002

In this paper the concept of a ∗‐semilattice is introduced as a generalization to distributive ∗‐lattice first introduced by Speed [1]. It is shown that almost all the results of Speed can be extended to a more eneral class of distributive ∗‐semilattices. In pseudocomplemented semilattices and distributive semilattices the set of annihilators of an element is an ideal in the sense of Grätzer [2]. But it is not so in general and thus we are led to the definition of a weakly distributive semilattice. In §2 we actually obtain the interesting corollary that a modular ∗‐semilattice is weakly distributive if and only if its dense filter is neutral. In §3 the concept of a sectionally pseudocomplemented semilattice is introduced in a natural way. It is proved that given a sectionally pseudocomplemented semilattice there is a smallest quotient of it which is a sectionally Boolean algebra. Further as a corollary to one of the theorems it is obtained that a sectionally pseudocomplemented semilattice with a dense element becomes a ∗‐semilattice. Finally a necessary and sufficient condition for a ∗‐semilattice to be a pseudocomplemented semilattice is obtained.
Smallest cubic and quartic graphs with a given number of cutpoints and bridges
Authors: Chartrand Gary , Saba Farrokh , Cooper John K. , Harary Frank , Wall Curtiss E.
Published: September 2002

For positive integers b and c, with c even, satisfying the inequalities b + 1 ≤ c ≤ 2b, the minimum order of a connected cubic graph with b bridges and c cutpoints is computed. Furthermore, the structure of all such smallest cubic graphs is determined. For each positive integer c, the minimum order of a quartic graph with c cutpoints is calculated. Moreover, the structure and number of all such smallest quartic graphs are determined.
On Bellman‐Bihari integral inequalities
Authors: Young Eutiquio C.
Published: September 2002

Integral inequalities of the Bellman‐Bihari type are established for integrals involving an arbitrary number of independent variables.
Spectral inequalities involving the sums and products of functions
Authors: Chong Kong-Ming
Published: September 2002

In this paper, the notation ≺ and ≺≺ denote the Hardy‐Littlewood‐Pólya spectral order relations for measurable functions defined on a fnite measure space (X, Λ, μ) with μ(X) = a, and expressions of the form f≺g and f≺≺g are called spectral inequalities. If f, g ∈ L1(X, Λ, μ), it is proven that, for some b ≥ 0, whenever , here δ and ι respectively denote decreasing and increasing rearrangement. With the particular case b = 0 of this result, the Hardy‐Littlewood‐Pólya‐Luxemburg spectral inequality fg≺≺δfδg for 0 ≤ f, g ∈ L1(X, Λ, μ) is shown to be a consequence of the well‐known but seemingly unrelated spectral inequality f + g≺δf + δg (where f, g ∈ L1(X, Λ, μ)), thus giving new proof for the former spectral inequality. Moreover, the Hardy‐Littlewood‐Pólya‐Luxemburg spectral inequality is also tended to give and for not necessarily non‐negative f, g ∈ L1(X, Λ, μ).
On elations in semi‐transitive planes
Authors: Johnson N. L.
Published: September 2002

Let π be a semi‐transitive translation plane of even order with reference to the subplane π0. If π admits an affine elation fixing π0 for each axis in π0 and the order of π0 is not 2 or 8, then π is a Hall plane.
Probability in quantum mechanics
Authors: Gilson J. G.
Published: September 2002

By using a fluid theory which is an alternative to quantum theory but from which the latter can be deduced exactly, the long‐standing problem of how quantum mechanics is related to stochastic processes is studied. It can be seen how the Schrödinger probability density has a relationship to time spent on small sections of an orbit, just as the probability density has in some classical contexts.
On the positive solutions of a higher order functional differential equation with a discontinuity
Authors: Graef John R. , Spikes Paul W. , Grammatikopoulos Myron K.
Published: September 2002

The n‐th order nonlinear functional differential equation

urn:x-wiley:01611712:media:ijmm769678:ijmm769678-math-0001

is considered; necessary and sufficient conditions are given for this equation to have: (i) a positive bounded solution x(t) → B > 0 as t → ∞; and (ii) all positive bounded solutions converging to 0 as t → ∞. Other results on the asymptotic behavior of solutions are also given. The conditions imposed are such that the equation with a discontinuity

urn:x-wiley:01611712:media:ijmm769678:ijmm769678-math-0002

is included as a special case.
A fixed point theorem for contraction mappings
Authors: Sehgal V. M.
Published: September 2002

Let S be a closed subset of a Banach space E and f : S → E be a strict contraction mapping. Suppose there exists a mapping h : S → (0, 1] such that (1 − h(x))x + h(x)f(x) ∈ S for each x ∈ S. Then for any x0 ∈ S, the sequence {xn} in S defined by xn+1 = (1 − h(xn))xn + h(xn)f(xn), n ≥ 0, converges to a u ∈ S. Further, if ∑h(xn) = ∞, then f(u) = u.
The solution of the functional equation of D′Alembert′s type for commutative groups
Authors: Rukhin A. L.
Published: September 2002

A functional equation of the form , where functions ϕ1, ϕ2, αi, βi, i = 1, …, n are defined on a commutative group, is solved. We also obtain conditions for the solutions of this equation to be matrix elements of a finite dimensional representation of the group.
Information sets as permutation cycles for quadratic residue codes
Authors: Jenson Richard A.
Published: September 2002

The two cases p = 7 and p = 23 are the only known cases where the automorphism group of the [p + 1,    (p + 1)/2] extended binary quadratic residue code, O(p), properly contains PSL(2, p). These codes have some of their information sets represented as permutation cycles from Aut(Q(p)). Analysis proves that all information sets of Q(7) are so represented but those of Q(23) are not.
Bazilevic functions of type β
Authors: Noor K. Inayat
Published: September 2002

In this paper, a new coefficient result for the Bazileviĉ functions of type β is obtained.
Zeros of smallest modulus of functions resembling exp(z)
Authors: Stolarsky Kenneth B.
Published: September 2002

To determine (in various senses) the zeros of the Laplace transform of a signed mass distribution is of great importance for many problems in classical analysis and number theory. For example, if the mass consists of finitely many atoms, the transform is an exponential polynomial. This survey studies what is known when the distribution is a probability density function of small variance, and examines in what sense the zeros must have large moduli. In particular, classical results on Bessel function zeros, of Szegö on zeros of partial sums of the exponential, of I. J. Schoenberg on k‐times positive functions, and a result stemming from Graeffe′s method, are all presented from a unified probabilistic point of view.
Uniformizable Cauchy spaces
Authors: Lowen-Colebunders Eva
Published: September 2002

A family C of filters on a set X is uniformizable if there is a uniformity on X such that C is its collection of Cauchy filters. Using the theory of completions and Cauchy continuous maps for Cauchy spaces, we obtain characterizations of uniformizable Cauchy spaces. In particular, given a Cauchy structure C on X we investigate under what conditions the filter is a uniformity and C is its collection of Cauchy filters. This problem is treated using Cauchy covering systems.
A theorem on “localized” self‐adjointness of Shrödinger operators with ‐potentials
Authors: Cycon Hans L.
Published: September 2002

We prove a result which concludes the self‐adjointness of a Schrödinger operator from the self‐adjointness of the associated “localized” Schrödinger operators having ‐Potentials.
Subsemi‐Eulerian graphs
Authors: Suffel Charles , Tindell Ralph , Hoffman Cynthia , Mandell Manachem
Published: September 2002

A graph is subeulerian if it is spanned by an eulerian supergraph. Boesch, Suffel and Tindell have characterized the class of subeulerian graphs and determined the minimum number of additional lines required to make a subeulerian graph eulerian.

In this paper, we consider the related notion of a subsemi‐eulerian graph, i.e. a graph which is spanned by a supergraph having an open trail containing all of its lines. The subsemi‐eulerian graphs are characterized and formulas for the minimum number of required additional lines are given. Interrelationships between the two problems are stressed as well.