bluuebunny/crossref_metadata_2025 huggingface dataset:
Hypersurfaces in a conformally flat space with curvature collineation
Authors: Duggal K. L. , Sharma R.
Published: September 2002

We classify the shape operators of Einstein and pseudo Einstein hypersurfaces in a
conformally flat space with a symmetry called curvature collineation. We solve the fundamental
problem of finding all possible forms of non‐diagonalizable shape operators. A physical example
of space‐time with matter is presented to show that the energy condition has direct relation with
the diagonalizability of shape operator.
Some sufficient conditions for univalence
Authors: Singh Sukhjit
Published: September 2002

A new subclass R(α), 0 ≤ α ≤ 1, of the class St(1/2) the class of
starlike functions of order 1/2 is introduced and it is shown that R(α) is closed
with respect to the Hadamard product of analytic functions. Some sufficient
conditions for the normalized regular functions to be univalent in the unit disk E are
given.
Ordinary dichotomy and perturbations of the coefficient matrix of the linear impulsive differential equation
Authors: Milev N. V. , Bainov D. D.
Published: September 2002

In the present paper it is proved that the ordinary dichotomy is preserved under
perturbations of the coefficient matrix of the linear impulsive differential equation.
Covering of radial segments for domains bounded by k‐circles
Authors: Inoue Tetsuo
Published: September 2002

Some theorems on radial segments is studied for ring domains bounded by k‐circles.
A note on Bazilevič functions
Authors: Halim S. A. , Thomas D. K.
Published: September 2002

For α > 0, let B1(α) be the class of normalized analytic functions defined in the open
unit disc D satisfying Re(f(z)/z) α−1f′(z) > 0 for z ∈ D. The sharp lower bound for Re(f(z)/z) α is
obtained and the result is generalized to some iterated integral operators.
Fixed points and continuity for multivalued mappings
Authors: Hicks Troy , Rhoades B. E.
Published: September 2002

Many of the contractive definitions do not require continuity of the map. However, in a previous paper the second author has shown in [1] that, in most cases, the function is continuous at a fixed point. In this paper we show that the same behavior is exhibited for many multivalued mappings.
Nonlinear random operator equations and inequalities in Banach spaces
Authors: Karamolegos Antonios , Kravvaritis Dimitrios
Published: September 2002

In this paper we give some new existence theorems for nonlinear random equations and inequalities involving operators of monotone type in Banach spaces. A random Hammerstein integral equation is also studied. In order to obtain random solutions we use some results from the existing deterministic theory as well as from the theory of measurable multifunctions and, in particular, the measurable selection theorems of Kuratowski/Ryll‐Nardzewski and of Saint‐Beuve.
On the oscillatory properties of the solutions of a class of integro‐differential equations of neutral type
Authors: Bainov D. D. , Myshkis A. D. , Zahariev A. I.
Published: September 2002

In the present paper the oscillatory properties of the solutions of the equation

urn:x-wiley:01611712:media:ijmm163126:ijmm163126-math-0001

are investigated where n ≥ 1, L is an operator of the difference type, It ⊂ ℝ, K : DK → ℝ, DK⫅ℝ3, x : [αx, ∞] → ℝ. Under natural conditions imposed on L, It and K it is proved that for n even all ultimately nonzero solutions oscillate and for n odd they either oscillate or tend to zero as t → ∞.
A queueing system with a fixed accumulation level, random server capacity and capacity dependent service time
Authors: Dshalalow Jewgeni H. , Tadj Lotfi
Published: September 2002

This paper introduces a bulk queueing system with a single server processing groups of customers of a variable size. If upon completion of service the queueing level is at least r the server takes a batch of size r and processes it a random time arbitrarily distributed. If the queueing level is less than r the server idles until the queue accumulates r customers in total. Then the server capacity is generated by a random number equals the batch size taken for service which lasts an arbitrarily distributed time dependent on the batch size.

The objective of the paper is the stationary distribution of queueing process which is studied via semi‐regenerative techniques. An ergodicity criterion for the process is established and an explicit formula for the generating function of the distribution is obtained.
Oscillation and non‐oscillation of some neutral differential equations of odd order
Authors: Lalli B. S. , Zhang B. G.
Published: September 2002

An existence criterion for nonoscillatory solution for an odd order neutral differential equation is provided. Some sufficient conditions are also given for the oscillation of solutions of some nth order equations with nonlinearity in the neutral term.
Computer two dimensional maps of loop soliton lattice systems using the new approach to the no integrability Aesthetic field equations
Authors: Muraskin M.
Published: September 2002

We show that there are varieties of somewhat different loop soliton lattices when we specify an integration path in No Integrability Aesthetic Field Theory. These are illustrated using two dimensional computer maps. We have previously studied several such systems using the new approach to non‐integrable systems developed in previous papers. [1‐3]. The results of these earlier papers indicated that the solitons were rearranged by the new integration scheme in an erratic looking manner. However, we were restricted to regions close to the origin in these studies. With additional computer time made available and the use of tapes to store large amounts of information we have studied the above loop soliton systems and have been able to map considerable larger regions of the x, y plane. Symmetries for locations of the planar maxima and minima have been uncovered within a particular quadrant, although the symmetry found is not as great as the lattice. The type symmetry found is not maintained when more than one quadrant is involved. We also
study a system that can be looked at as a perturbation of a loop lattice system. A brief discussion of the background material appears in the appendix.
Totally real surfaces in CP2 with parallel mean curvature vector
Authors: Al-Gwaiz M. A. , Deshmukh Sharief
Published: September 2002

It has been shown that a totally real surface in CP2 with parallel mean curvature vector and constant Gaussian curvature is either flat or totally geodesic.
Measure‐theoretic characterizations of hereditarily‐normal spaces
Authors: Hertzlinger Joseph
Published: September 2002

In this paper we characterize hereditarily‐normal spaces in terms of the measure‐theoretic properties of
the lattice of closed sets. We then generalize from that lattice to other lattices. We apply the results to extremally‐disconnected spaces.
An extension of Horn′s theorem for a space of locally integrable functions
Authors: Henriquez Hernan R. , Hernandez Eduardo A.
Published: September 2002

In this paper we extend the fixed point theorem of Horn′s to the space of locally integrable functions from (−∞, 0] into a Banach space X.
An infinite version of the Pólya enumeration theorem
Authors: Bekes Robert A.
Published: September 2002

Using measure theory, the orbit counting form of Pólya′s enumeration theorem is extended to countably infinite discrete groups.
Unordered Love in infinite directed graphs
Authors: Johnson Peter D.
Published: September 2002

A digraph D = (V, A) has the Unordered Love Property (ULP) if any two different vertices have a unique common outneighbor. If both (V, A) and (V, A−1) have the ULP, we say that D has the SDULP.

A love‐master in D is a vertex ν0 connected both ways to every other vertex, such that D − ν0 is a disjoint union of directed cycles.

The following results, more or less well‐known for finite digraphs, are proven here for D infinite: (i) if D is loopless and has the SDULP, then either D has a love‐master, or D is associable with a projective plane, obtainable by taking V as the set of points and the sets of outneighbors of vertices as the lines; (ii) every projective plane arises from a digraph with the SDULP, in this way.
Complete lift of a structure satisfying FK − (−)K+1F = 0
Authors: Das Lovejoy S.
Published: September 2002

The idea of f‐structure manifold on a differentiable manifold was initiated and developed by Yano [1], Ishihara and Yano [2], Goldberg [3] and among others. The horizontal and complete lifts from a differentiable manifold Mn of class C∞ to its cotangent bundles have been studied by Yano and Patterson [4,5]. Yano and Ishihara [6] have studied lifts of an f‐structure in the tangent and cotangent bundles. The purpose of this paper is to obtain integrability conditions of a structure satisfying FK − (−)K+1F = 0 and FW − (−)W+1F ≠ 0 for 1 < W < K, in the tangent bundle.
θ‐R‐continuous functions
Authors: Baker C. W.
Published: September 2002

A strong form of continuity, called θ‐R‐continuity, is introduced. It is shown that θ‐R‐continuity is stronger than R‐continuity. Relationships between θ‐R‐continuity and various closed graph properties are investigated. Additional properties of θ‐R‐continuous functions are established.
On the ME‐manifold in n‐*g‐UFT and its conformal change
Authors: Chung Kyung Tae , Eun Gwang Sik
Published: September 2002

An Einstein′s connection which takes the form (3.1) is called an ME‐connection. A generalized n‐dimensional Riemannian manifold Xn on which the differential geometric structure is imposed by a tensor field *gλν through a unique ME‐connection subject to the conditions of Agreement (4.1) is called *g‐ME‐manifold and we denote it by *g‐MEXn. The purpose of the present paper is to introduce this new concept of *g‐MEXn and investigate its properties. In this paper, we first prove a necessary and sufficient condition for the unique existence of ME‐connection in Xn, and derive a surveyable tensorial representation of the ME‐connection. In the second, we investigate the conformal change of *g‐MEXn and present a useful tensorial representation of the conformal change of the ME‐connection.
Dynamics of the radix expansion map
Authors: Goertzel Ben , Bowman Harold , Baker Richard
Published: September 2002

The chaotic dynamics of the map ϕ(x) = (βx + α)(mod1) are studied using Parry′s β‐expansion. It is shown that for 1 < β < 2, a ≥ 0, the number of periodic points of period n is 0(βn).
On the application of Newton′s and Chord methods to bifurcation problems
Authors: Elgindi M. B. M.
Published: September 2002

This paper is concerned with the applications of Newton′s and chord methods in the computations of the bifurcation solutions in a neighborhood of a simple bifurcation point for prescribed values of the bifurcation parameter.
On a subclass of C1 functions for which the Lagrange interpolation yields the Jackson order of approximation
Authors: Li Xin
Published: September 2002

We continue the investigation initiated by Mastroianni and Szabados on question whether Jackson′s order of approximation can be attained by Lagrange interpolation for a wide class of functions. Improving a recent result of Mastroianni and Szabados, we show that for a subclass of C1 functions the local order of approximation given by Lagrange interpolation can be much better (of at least ) than Jackson′s order.
A class of bounded starlike functions
Authors: Silverman Herb
Published: September 2002

We consider functions f(z) = z + … that are analytic in the unit disk and satisfy there the inequality Re(f′(z) + zf″(z)) > α, α < 1. We find extreme points and then determine sharp lower bounds on Ref′(z) and Re(f(z)/z). Sharp results for the sequence of partial sums are also found.
On a generalization of Hankel kernel
Authors: Nasim C. , Aggarwala B. D.
Published: September 2002

We consider an expression involving the Bessel function, the Neumann function and the MacDonald function and discover various combinations of these functions which are Fourier kernels or conjugate Fourier kernels. Also a large number of integration formulae are established involving these kernels.
A generalized formula of Hardy
Authors: Campbell Geoffrey B.
Published: September 2002

We give new formulae applicable to the theory of partitions. Recent work suggests they also relate to quasi‐crystal structure and self‐similarity. Other recent work has given continued fractions for the type of functions herein. Hardy originally gave such formulae as ours in early work on gap power series which led to his and Littlewood′s High Indices Theorem. Over a decade ago, Mahler and then others proved results on irrationality of decimal fractions applicable to types of functions we consider.
On the existence and uniqueness problems of solutions for set‐valued and single‐valued nonlinear operator equations in probabilistic normed spaces
Authors: Chang Shih-Sen , Cho Yeol Je , Wang Fan
Published: September 2002

In this paper, we introduce the concept of more general probabilistic contractors in probabilistic normed spaces and show the existence and uniqueness of solutions for set‐valued and single‐valued nonlinear operator equations in Menger probabilistic normed spaces.
Remarks on the existence and decay of the nonlinear beam equation
Authors: Rivera Jaime E. Mũnoz
Published: September 2002

We will consider a class of nonlinear beam equation and we will prove the existence and decay weak
solution
Fixed point of nonexpansive type and K‐multivalued maps
Authors: Latif Abdul , Husain Taqdir , Beg Ismat
Published: September 2002

Some fixed point theorems for nonexpansive type and K‐multivalued mappings are proved. Also the strong convergence of sequences of iterates of multivalued type maps is established.
Strictly extreme and strictly exposed points
Authors: Qiu Jing Hui , McKennon Kelly
Published: September 2002

The notions of strictly extreme and strictly exposed are introduced. Their properties are discussed, examples are given, and inter‐relationships investigated. In particular it is proved that, for separable normed spaces, the strictly extreme points are just the strictly exposed points.
Characteristic polynomials of some weighted graph bundles and its application to links
Authors: Sohn Moo Young , Lee Jaeun
Published: September 2002

In this paper, we introduce weighted graph bundles and study their characteristic polynomial. In particular, we show that the characteristic polynomial of a weighted ‐bundles over a weighted graph G? can be expressed as a product of characteristic polynomials two weighted graphs whose underlying graphs are G As an application, we compute the signature of a link whose corresponding weighted graph is a double covering of that of a given link.
First passage processes in Queuing system MX/Gr/1 with service delay discipline
Authors: Abolnikov Lev , Dshalalow Jewgeni H. , Dukhovny Alexander M.
Published: September 2002

This article deals with a general single‐server bulk queueing system with a server waiting until the queue will reach level r before it starts processing customers. If at least r customers are available the server takes a batch of the fixed size r of units for service. The input stream is assumed to be a compound Poisson process modulated by a semi‐Markov process and with a multilevel control of service time.

The authors evaluate the steady state probabilities of the queueing processes with discrete and continuous time parameter preliminarily establishing necessary and sufficient conditions for the ergodicity of the processes. The authors use the recent results on the first excess level processes to explicitly find all characteristics of the named processes. Some characteristics of the input process, service cycle, intensity of the system, and both idle and busy periods are also found. The results obtained in the article are illustrated by numerous examples.
Semiprime SF‐rings whose essential left ideals are two‐sided
Authors: Jule Zhang , Xhianneng Du
Published: September 2002

It is proved that if R is a semiprime ELT‐ring and every simple right R‐module is flat then R is regular. Is R regular if R is a semiprime ELT‐ring and every simple right R‐module is flat? In this note, we give a positive answer to the question.
Relative injectivity and CS‐modules
Authors: Kamal Mahmoud Ahmed
Published: September 2002

In this paper we show that a direct decomposition of modules M ⊕ N, with N homologically independent to the injective hull of M, is a CS‐module if and only if N is injective relative to M and both of M and N are CS‐modules. As an application, we prove that a direct sum of a non‐singular semisimple module and a quasi‐continuous module with zero socle is quasi‐continuous. This result is known for quasi‐injective modules. But when we confine ourselves to CS‐modules we need no conditions on their socles. Then we investigate direct sums of CS‐modules which are pairwise relatively inective. We show that every finite direct sum of such modules is a CS‐module. This result is known for quasi‐continuous modules. For the case of infinite direct sums, one has to add an extra condition. Finally, we briefly discuss modules in which every two direct summands are relatively inective.
Asymptotic behavior of solutions of nonlinear functional differential equations
Authors: Jung Jong Soo , Park Jong Yeoul , Kang Hong Jae
Published: September 2002

Using the properties of almost nonexpansive curves introduced by B. Djafari Rouhani, we study the asymptotic behavior of solutions of nonlinear functional differential equation du(t)/dt + Au(t) + G(u)(t)?f(t), where A is a maximal monotone operator in a Hilbert space H, f?L1(0, 8 : H) and is a given mapping.
On complete convergence of the sum of a random number of a stable type P random elements
Authors: Adler André , Volodin Andrey
Published: September 2002

Complete convergence for randomly indexed normalized sums of random
elements of the form is established. The random elements {Xn} belong to
a type p stable space and are assumed to be independent, but not necessarily identically
distributed. No assumptions are placed on the joint distributions of the stopping times
{Tn}.
Some subregular germs for p‐adic Sp4(F)
Authors: Yangkon Kim , Kwangho So
Published: September 2002

Shalika′s unipotent regular germs were found by the authors in the case of G = Sp4(F).
Next, subregular germs are also desirable, for at least f(1) is constructible in another form for any
smooth function f by using Shalika germs. Some of them were not so hard as expected although to
find all of them is still not done explicitly.
Outer measures and weak regularity of measures
Authors: Siegel Dale
Published: September 2002

This paper investigates smoothness properties of probability measures on
lattices which imply regularity, and then considers weaker versions of regularity; in particular,
weakly regular, vaguely regular, and slightly regular. They are derived from commonly
used outer measures, and we analyze them mainly for the case of I(ℒ) or for those elements
of I(ℒ) with added smoothness conditions.
Effect of gravity on visco‐elastic surface waves in solids involving time rate of strain and stress of higher order
Authors: Das Tapan Kumar , Sengupta P. R. , Debnath Lokenath
Published: September 2002

A study is made of the surface waves in a higher order visco‐elastic solid involving time
rate of change of strain and stress under the influence of gravity. A fairly general equation for the wave
velocity is derived. This equation is used to examine various kinds of surface waves including Rayleigh
waves, Love waves and Stoneley waves. It is shown that the corresponding classical results follow from
this analysis in the absence of gravity and viscosity.
On outer measures and semi‐separation of lattices
Authors: Schutz Robert W.
Published: September 2002

This present paper is concerned with set functions related to {0, 1} two valued measures.
These set functions are either outer measures or have many of the same characteristics. We investigate their
properties and look at relations among them. We note in particular their association with the semi‐separation of lattices.

To be more specific, we define three set functions μ″, μ′, and related to μ ϵ I(L) the {0, 1} two
valued set functions defined on the algebra generated by the lattice of sets L st μ is a finitely additive
monotone set function for which μ(ϕ) = 0. We note relations among them and properties they possess.ln
particular necessary and sufficient conditions are given for the semi‐separation of lattices in terms of
equality of set functions over a lattice of subsets.

Finally the notion of I‐lattice is defined, we look at some properties of these with certain other side
conditions assume, and end with an application involving semi‐separation and I‐lattices.
A boundary value problem with a discontinuous coefficient and containing a spectral parameter in the boundary condition
Authors: Darwish A. A.
Published: September 2002

A singular non‐self‐adjoint boundary value problem is considered. This problem
has a discontinuous coefficient with a spectral parameter in the boundary condition. Some
solutions of the eigenvalue equation are given. The discrete spectrum is studied and the
resolvent is obtained. Formulation of the adjoint problem is deduced and hence the continuous
spectrum of the considered problem is given. Furthermore, the spectrum of the adjoint problem
is investigated.
A selection and a fixed point theorem and an equilibrium point of an abstract economy
Authors: Husain T. , Tarafdar E.
Published: September 2002

A selection theorem and a fixed point theorem are proved. The fixed point theorem
is then applied to prove the existence of an equilibrium point of an abstract economy.
On a general Hyers‐Ulam stability result
Authors: Borelli Costanz , Forti Gian Luigi
Published: September 2002

In this paper, we prove two general theorems about Hyers‐Ulam stability of
functional equations. As particular cases we obtain many of the results published in the last ten
years on the stability of the Cauchy and quadratic equation.
A weak invariance principle and asymptotic stability for evolution equations with bounded generators
Authors: Chukwu E. N. , Smoczynski P.
Published: September 2002

If V is a Lyapunov function of an equation du/dt = u′ = Zu in a Banach space then
asymptotic stability of an equilibrium point may be easily proved if it is known that sup(V′) < 0 on
sufficiently small spheres centered at the equilibrium point. In this paper weak asymptotic stability is
proved for a bounded infinitesimal generator Z under a weaker assumption V′ ≤ 0 (which alone
implies ordinary stability only) if some observability condition, involving Z and the Frechet derivative
of V′, is satisfied. The proof is based on an extension of LaSalle′s invariance principle, which yields
convergence in a weak topology and uses a strongly continuous Lyapunov function. The theory is
illustrated with an example of an integro‐differential equation of interest in the theory of chemical
processes. In this case strong asymptotic stability is deduced from the weak one and explicit sufficient
conditions for stability are given. In the case of a normal infinitesimal generator Z in a Hilbert
space, strong asymptotic stability is proved under the following assumptions Z*+Z is weakly
negative definite and Ker Z = {0}. The proof is based on spectral theory.
Stability of nonlinear systems under constantly acting perturbations
Authors: Liu Xinzhi , Sivasundaram S.
Published: September 2002

In this paper, we investigate total stability, attractivity and uniform stability in
terms of two measures of nonlinear differential systems under constant perturbations. Some sufficient
conditions are obtained using Lyapunov′s direct method. An example is also worked out.
Approximating common fixed points of families of quasi‐nonexpansive mappings
Authors: Ghosh M. K. , Debnath Lokenath
Published: September 2002

This paper deals with a family of quasi‐nonexpansive mappings in a uniformly convex
Banach space, and the convergence of iterates generated by this family. A fixed point theorem for two
quasi‐nonexpansive mappings is then proved. This theorem is then extended for a finite family of quasinonexpansive
mappings. It is shown that Ishikawa′s [1] result follows as special cases of results proved
in this paper.
Acoustic‐gravity waves in a viscous and thermally conducting isothermal atmosphere
Authors: Alkahby H. Y.
Published: September 2002

In this paper we will investigate the effect of Newtonian cooling on the propagation
of acoustic‐gravity waves in a viscous and thermally conducting isothermal atmosphere for large
Prandtl number and for an arbitrary values of Newtonian cooling coefficient. This problem leads
to a singular perturbation problem which is solved by matching inner and outer approximations.
It is shown that the viscosity creates an absorbing and reflecting layer. Below it the oscillatory
process is adiabatic, for small Newtonian cooling coefficient, and above it the solution will decay
to constant before it is influenced by the effect of the thermal conductivity. Newtonian cooling is
a volume effect and influences mainly the lower adiabatic region, in which it causes attenuation in
the amplitude of the wave. Finally it is shown that when Newtonian cooling coefficient goes to
infinity it acts directly to eliminate the temperature perturbation associated with the wave and the
attenuation factor in the amplitude of the wave. Accordingly the wavelength changes to the one
consistent with the Newtonian sound speed. The reflection coefficient and the attenuation factor of
the amplitude of the wave are derived for all values of Newtonian cooling coefficient.
The law of the iterated logarithm for exchangeable random variables
Authors: Zhang Hu-Ming , Taylor Robert L.
Published: September 2002

In this note, necessary and sufficient conditions for laws of the iterated logarithm
are developed for exchangeable random variables.
Complemented subspaces of p‐adic second dual Banach spaces
Authors: Kiyosawa Takemitsu
Published: September 2002

Let K be a non‐archimedean non‐trivially valued complete field. In this
paper we study Banach spaces over K. Some of main results are as follows:
(1) The Banach space has an orthocomplemented subspace linearly homeomorphic
to c0.
(2) The Banach space has an orthocomplemented subspace linearly homeomorphic
to l∞.
Coefficient subrings of certain local rings with prime‐power characteristic
Authors: Sumiyama Takao
Published: September 2002

If R is a local ring whose radical J(R) is nilpotent and R/J(R) is a commutative field
which is algebraic over GF(p), then R has at least one subring S such that , where each Si, is
isomorphic to a Galois ring and S/J(S) is naturally isomorphic to R/J(R). Such subrings of R are mutually
isomorphic, but not necessarily conjugate in R.
On certain classes of meromorphically starlike functions
Authors: Cho Nak Eun , Kim Ji A.
Published: September 2002

The object of the present paper is to introduce a new class ∑n(α) of meromorphic
functions defined by a multiplier transformation and to investigate some properties for the class ∑n(α)
Further we study integrals of functions in ∑n(α).
Generalized totally disconnectedness
Authors: Dorsett Charles
Published: September 2002

In this paper totally disconnectedness is generalized to maximal disconnectedness, which is investigated,
and additional properties of totally disconnectedncss and 0‐dimensional are given.
Fréchet algebras generated by certain of their elements
Authors: Ouzomgi S. , Redlin L. , Watson S.
Published: September 2002

We consider F‐algebras A that are generated by elements of the form z, , where e is the identity. If A has no topclogical divisors of zero we show that A is
isomorphic to H(Ω), where Ω is finitely connected region. We also study F‐algebras in which
{e, z, z−1, z2, z−2, …} is basis.
Quasiminimal distal function space and its semigroup compactification
Authors: Pandian R. D.
Published: September 2002

Quasiminimal distal function on a semitopological semigroup is
introduced. The concept of right topological semigroup compactification is
employed to study the algebra of quasiminimal distal functions. The universal
mapping property of the quasiminimal distal compactification is obtained.
Differentiable semigroups are Lie groups
Authors: Holmes John P. , Anderson Mitch
Published: September 2002

We present here a modern, detailed proof to the following theorem which was introduced
by Garrett Birkhoff [1] in 1938. If S is a local semigroup with neighborhood of 1 homeomorphic to a
Banach space and with multiplication strongly differentiable at 1, then S is a local Lie Group. Although
this theorem is more than 50 years old and remains the strongest result relating to Hilbert′s fifth problem
in the infinite dimensional setting, it is frequently overlooked in favor of weaker results. Therefore, it
is the goal of the authors here to clarify its importance and to demonstrate a proofwhich is more accessible
to contemporary readers than the one offered by Birkhoff.
On the K‐th extension of the Sieve of eratosthenes
Authors: Quesada Antonio R.
Published: September 2002

The Sieve of Eratosthenes has been recently extended by excluding the multiples
of 2, 3, and 5 from the initial set, and finding the additive rules that give the positions of the
multiples of the remaining primes. We generalize these results. For a given k we let the initial
set Sk consists of natural numbers relatively prime to the first k primes, and find the rules
governing the positions of the multiples of the remaining elements.
Singular boundary value problems for quasi‐differential equations
Authors: Eloe Paul W. , Henderson Johnny
Published: September 2002

Solutions are obtained of boundary value problems for Lny + f(x, L0y, …, Ln−2y), satisfying L2y(0) = Ln−1y(1) = 0, 0 ≤ i ≤ n − 2, where Li, denotes the ith
quasiderivative, and where f(x, y1, …, yn−1) has singularities at yi = 0, 1 ≤ i ≤ n − 1.
Surface temperature determination from Borehole measurements: Regularization and error estimates
Authors: Le Tran Thi , Navarro Milagros
Published: September 2002

The authors consider the problem of determining the temperature distribution u(x, t) on
the half‐line x = 0, t > 0, from measurements at an interior point, for all t > 0. As is well‐known, this is
an ill‐posed problem Using the Tikhonov method, the authors give a regularized solution, and assuming
the (unknown) exact solution is in Hα(ℝ), α > 0. They give an error estimate of the order 1/(1n1/ ϵ )α
for ϵ  → 0, where ϵ  > 0 is a bound on the measurement error.
Two inequalities for means
Authors: Sandor J.
Published: September 2002

We prove two new inequalities for the identric mean and a mean related to the arithmetic
and geometric mean of two numbers.
A characterization of the Rogers q‐hermite polynomials
Authors: Al-Salam Waleed A.
Published: September 2002

In this paper we characterize the Rogers q‐Hermite polynomials as the only orthogonal
polynomial set which is also 𝒟q‐Appell where 𝒟q is the Askey‐Wilson finite difference
operator.
Constructive solution of coupled second order delay differential equations with variable coefficients
Authors: Villanueva R. J. , Hervas A. , Ferrer M. V.
Published: September 2002

In this paper, we study initial value problems for coupld second order delay differential
equations with variable coefficients. By means of the application of the method of steps and
the method of Frobenius, the exact solution of the problem is constrcted. Then, in a bounded
domain, a finite analytic solution with error bounds is provided. Given an admissible error ϵ we
give the number of terms to be taken in the infinite series exact solution so that the approximation
error be smaller than in the bounded domain.
Regularization and asymptotic expansion of certain distributions defined by divergent series
Authors: Estrada Ricardo
Published: September 2002

The regularization of the distribution . which gives a regularized value to the divergent series is obtained in several spaces of test functions. The asymptotic expansion as ϵ → 0+of series of the type is also obtained.
A new analogue of Gauss′ functional equation
Authors: Haruki Hiroshi , Rassias Themistocles M.
Published: September 2002

Gauss established a theory on the functional equation (Gauss′ functional equation)

urn:x-wiley:01611712:media:ijmm248590:ijmm248590-math-0001

,
where f : R+ × R+ → R is an unknown function of the above equation.

In this paper we treat the functional equation

urn:x-wiley:01611712:media:ijmm248590:ijmm248590-math-0002

where f : R+ × R+ → R is an unknown function of this equation.

The purpose of this paper is to prove new results on this functional equation by following
the theory of Gauss′ functional equation.
Perfect maps in compact (countably compact) spaces
Authors: Garg G. L. , Goel Asha
Published: September 2002

In this paper, among other results, characterizations of perfect maps in compact Hausdorff(Fréchet,
countably compact, Hausdorff) spaces are obtained.
Point‐valued mappings of sets
Authors: Insall Matt
Published: September 2002

Let X be a metric space and let CB(X) denote the closed bounded subsets of X with the
Hausdorff metric. Given a complete subspace Y of CB(X), two fixed point theorems, analogues of results
in [1], are proved, and examples are given to suggest their applicability in practice.
Stability of ψ‐additive mappings: applications to nonlinear analysis
Authors: Isac George , Rassias Themistocles M.
Published: September 2002

The Hyers‐Ulam stability of mappings is in development and several authors have remarked interesting applications of this theory to various mathematical problems. In this paper some applications in nonlinear analysis are presented, especially in fixed point theory. These kinds of applications seem not to have ever been remarked before by other authors.
Complex and distributional weights for sieved ultraspherical polynomials
Authors: Charris Jairo A. , Soriano Felix H.
Published: September 2002

Contour integral and distributional orthogonality of sieved ultraspherical polynomials are established for values of the parameters outside the natural range of orthogonality by positive measures on the real line. A general representation theorem for moment functionals is included.
On non‐parallel s‐structures
Authors: Xenos Philippos J. , Karatsobanis John N.
Published: September 2002

Using algebraic topology, we find out the number of all non‐parallel s‐structures
which an n‐dimensional Euclidean space En admits. The obtaining results are generalized on a manifold
M which is CW‐complex.
The regular open‐open topology for function spaces
Authors: Porter Kathryn F.
Published: September 2002

The regular open‐open topology, Troo, is introduced, its properties for spaces of
continuous functions are discussed, and Troo is compared to Too, the open‐open topology. It is then
shown that Troo on H(X), the collection of all self‐homeomorphisms on a topological space, (X, T),
is equivalent to the topology induced on H(X) by a specific quasi‐uniformity on X, when X is a
semi‐regular space.
A characterization of point semiuniformities
Authors: Montgomery Jennifer P.
Published: September 2002

The concept of a uniformity was developed by A.
Well and there have been several generalizations. This
paper defines a point semiuniformity and gives necessary
and sufficient conditions for a topological space to be
point semiuniformizable. In addition, just as uniformities
are associated with topological groups, a point
semiuniformity is naturally associated with a semicontinuous
group. This paper shows that a point semiuniformity
associated with a semicontinuous group is a uniformity
if and only if the group is a topological group.
Another note on Levine′s decomposition of continuity
Authors: Rose David A. , Mimna Roy A. , Janković Dragan
Published: September 2002

Several decompositions of continuity each stronger than Norman Levine′s are found
improving results of J. Chew and J. Tong, as well as of the first two named authors above.
Outer measures, measurability, and lattice regular measures
Authors: Ponnley J.
Published: September 2002

Let X be an arbitrary non‐empty set, and ℒ a lattice of subsets of X such that
∅, X ∈ ℒ. 𝒜(ℒ) denotes the algebra generated by ℒ and I(ℒ) those zero‐one valued, non‐trivial, finitely
additive measures on 𝒜(ℒ)Iσ(ℒ) denotes those elements of I(ℒ) that are σ‐smooth on ℒ, and IR(ℒ)
denotes those elements of I(ℒ) that are ℒ‐regular while . In terms of those and
other subsets of I(ℒ), various outer measures are introduced, and their properties are investigated. Also,
the interplay between the measurable sets associated with these outer measures, regularity properties of
the measures, smoothness properties of the measures, and lattice topological properties are thoroughly
investigated‐ yielding new results for regularity or weak regularity of these measures, as well as
domination on a lattice of a suitably given measure by a regular one Finally, elements of Iσ(ℒ) are fully
characterized in terms of induced measures on a certain generalized Wallman space.
Oblique interface‐wave diffraction by a small bottom deformation in two superposed fluids
Authors: Mandal B. N. , Basu U.
Published: September 2002

The problem of diffraction of oblique interface‐waves by a small bottom
deformation of the lower fluid in two superposed fluids has been investigated here assuming linear theory
and invoking a simplified perturbation analysis. First order corrections to the velocity potentials in the
two fluids are obtained by using the Green′s integral theorem in a suitable manner. The transmission and
reflection coefficients are evaluated approximately. These reduce to the known results for a single fluid
in the absence of the upper fluid.
Extreme points and convolution properties of some classes of multivalent functions
Authors: Ahuja O. P.
Published: September 2002

This paper deals with the extreme points of closed convex hulls of the classes of
multivalent functions related to Ruscheweyh derivatives and then these are used to determine the
coefficient bounds. Finally, we investigate convolution conditions and other properties of the functions in
these classes.
On the distributional orthogonality of the general Pollaczek polynomials
Authors: Charris Jairo A. , Soriano Felix H.
Published: September 2002

A distributional representation of the moment functional of the general Pollaczek
polynomials is established. This representation holds for a wider range of parameters than the
representation by a positive measure.
A uniform estimate for the rate of convergence in the multidimensional central limit theorem for homogeneous Markov chains
Authors: Gharib M.
Published: September 2002

In this paper a uniform estimate is obtained for the remainder term in the central
limit theorem (CLT) for a sequence of random vectors forming a homogeneous Markov chain with
arbitrary set of states. The result makes it possible to estimate the rate of convergence in the CLT
without assuming the finiteness of the absolute third moment of the transition probabilities. Some
consequences are also proved.
Monotone and convex H*‐algebra valued functions
Authors: Saworotnow Parfeny P.
Published: September 2002

Classical theorems about monotone and convex functions are generalized to the case of H*‐algebra valued functions.

Also there are new examples of a vector measure.
Bounded functions starlike with respect to symmetrical points
Authors: Al-Oboudi Fatima M.
Published: September 2002

Let P[A, B], −1 ≤ B < A ≤ 1, be the class of functions p analytic in the unit disk E with p(0) = 1 and subordinate to . In this paper we define and study the classes of functions starlike with respect to symmetrical points. A function f analytic in E and given by is said to be in if and only if, for z ∈ E, . Basic results on are studied such as coefficient bounds, distortion and rotation theorems, the analogue of the Polya‐Schoenberg conjecture and others.
Generating new classes of orthogonal polynomials
Authors: Branquinho Amílcar , Marcellán Francisco
Published: September 2002

Given a sequence of monic orthogonal polynomials (MOPS), {Pn}, with respect
to a quasi‐definite linear functional u, we find necessary and sufficient conditions on the parameters
an and bn
for the sequence

urn:x-wiley:01611712:media:ijmm657910:ijmm657910-math-0001

to be orthogonal. In particular, we can find explicitly the linear functional v such that the new
sequence is the corresponding family of orthogonal polynomials. Some applications for Hermite
and Tchebychev orthogonal polynomials of second kind are obtained.

We also solve a problem of this type for orthogonal polynomials with respect to a Hermitian
linear functional.
The Θ‐transformation of certain positive linear operators
Authors: Lupaş Aleandru , Mache Detlef H.
Published: September 2002

The intention of this paper is to describe a construction method for
a new sequence
of linear positive operators, which enables us to get a pointwise order of approximation regarding
the polynomial summator operators which have best
properties of approximation.
Deformation of domain and the limit of the variational eigenvalues of semilinear elliptic operators
Authors: Shibata Tetsutaro
Published: September 2002

We consider the semilinear elliptic eigenvalue problem

urn:x-wiley:01611712:media:ijmm431709:ijmm431709-math-0001

The asymptotic behavior of the variational eigenvalues μ = μn(r, α) obtained by Ljusternik‐Schnirelman
theory is studied when the domain Ω0 is deformed continuously. We also consider the cases that
Vol(Ωr) → 0, ∞ as r → ∞.
Topological properties of generalized Wallman spaces and lattice relations
Authors: Allan James A.
Published: September 2002

Let X be an abstract set and ℒ be a lattice of subsets of X. Associated with the
pair (X, ℒ) are a variety of Wallman‐type topological
spaces. Some of these spaces generalize very
important topological spaces such as the Stone‐Čech
compactification, the real compactification, etc. We
consider the general setting and investigate how the properties of ℒ reflect over to the general Wallman
Spaces and conversely. Completeness properties of the lattices in
the Wallman Spaces are investigated,
as well as the interplay of topological properties
of these spaces such as T2, regularity and Lindelöf with ℒ.
Some counterexamples and properties on generalizations of Lindelöf spaces
Authors: Cammaroto Filippo , Santoro Grazia
Published: September 2002

In this paper we give some significative
counterexamples to prove that some well known
generalizations of Lindelöf property are proper. Also we
give some new results, we introduce and study
the almost regular‐Lindelof spaces as a generalization of
the almost‐Lindelöf spaces and as a new and
significative application of the quasi‐regular open subsets of [1].
Univalent functions maximizing Re[f(ζ1) + f(ζ2)]
Authors: Hibschweiler Intisar Qumsiyeh
Published: September 2002

We study the problem maxh∈Sℜ[h(z1) + h(z2)] with z1, z2 in Δ. We show that
no rotation of the Koebe function is a solution for this problem
except possibly its real rotation,
and only when or z1, z2 are both real, and are in a neighborhood of the x‐axis. We prove
that if the omitted set of the extremal function f is part of a straight line that passes through
f(z1) or f(z2)
then f is the Koebe function or its real rotation. We
also show the existence of
solutions that are not unique and are different from
the Koebe function or its real rotation. The
situation where the extremal value is equal to zero can occur
and it is proved, in this case, that
the Koebe function is a solution if and only if z1 and z2
are both real numbers and z1z2 < 0.
The dual space of β(Γ)
Authors: Nemzer Dennis
Published: September 2002

The space of Boehmians with Δ‐convergence is a complete topological vector space in
which the topology is induced by an invariant metric. We show that the dual space of the space of periodic
Boehmians can be identified with the class of trigonometric polynomials.
Relations between exponential laws for spaces of C∞‐functions
Authors: Biström Peter
Published: September 2002

In this paper we prove that some new as well as some already existing exponential
laws for spaces of C∞‐ and holomorphic functions can all be generated from one general
exponential law.
On the semi‐inner product in locally convex spaces
Authors: Chang Shih-Sen , Chen Yu-Qing , Lee Byung Soo
Published: September 2002

The purpose of this paper is to introduce the concept of semi‐inner products in locally
convex spaces and to give some basic properties.
On quadruple integral equations involving trigonometric kernels
Authors: Aggarwala B. D.
Published: September 2002

A general technique is developed for the solution of quadruple integral equations
involving trigonometric kernels. Four such sets are solved explicitly. Application is made to the
problem of three‐collinear cracks in linear plane elasticity.
Acoustic‐gravity waves in a viscous and thermally conducting isothermal atmosphere (part III: for arbitrary Prandtl number)
Authors: Alkahby Hadi Yahya
Published: September 2002

In this paper we will investigate the combined effect of Newtonian cooling, viscosity and
thermal condition on upward propagating acoustic waves in an isothermal atmosphere. In part one of this
series we considered the case of large Prandtl number, while in part two we investigated the case of small
Prandtl number. In those parts we examined only the limiting cases, i.e. the cases of small and large
Prandtl number, and it is more interesting to consider the case of arbitrary Prandtl number, which is the
subject of this paper, because it is a better representative model. It is shown that if the Newtonian
cooling coefficient is small compared to the frequency of the wave, the effect of the thermal conduction is
dominated by that of the viscosity. Moreover, the solution can be written as a linear combination of an
upward and a downward propagating wave with equal wavelengths and equal damping factors. On the
other hand if Newtonian cooling is large compared to the frequency of the wave the effect of thermal
conduction will be eliminated completely and the atmosphere will be transformed from the adiabatic form
to an isothermal. In addition, all the linear relations among the perturbations quantities will be modified.
It follows from the above conclusions and those of the first two parts, that when the effect of Newtonian
cooling is negligible thermal conduction influences the propagation of the wave only in the case of small
Prandtl number.
Random processes with convex coordinates on triangular graphs
Authors: Boyd J. N. , Raychowdhury P. N.
Published: September 2002

Probabilities for reaching specified destinations and expectation values for
lengths for random walks on triangular arrays of points and edges are computed. Probabilities
and expectation values are given as functions of the convex (barycentric) coordinates of the
starting point.
Hearing the shape of a compact Riemannian manifold with a finite number of piecewise impedance boundary conditions
Authors: Zayed E. M. E.
Published: September 2002

The spectral function , where are the eigenvalues of the
negative Laplace‐Beltrami operator −Δ, is studied for a compact Riemannian manifold Ω of dimension
“k” with a smooth boundary ∂Ω, where a finite number of piecewise impedance boundary conditions
on the parts ∂Ωi(i = 1, …, m) of the boundary ∂Ω can be considered, such that
, and γi(i = 1, …, m) are assumed to be smooth functions which are not strictly positive.
On radii of starlikeness and convexity for convolutions of starlike functions
Authors: Ling Yi , Ding Shusen
Published: September 2002

In this paper, we obtain the radiuses of univalence, starlikeness and convexity
for convolutions of starlike functions.
Two elementary commutativity theorems for generalized boolean rings
Authors: Gupta Vishnu
Published: September 2002

In this paper we prove that if R is a ring with 1 as an identity element in which xm − xn ∈ Z(R) for all x ∈ R and fixed relatively prime positive integers m and n, one of which is even, then R is commutative. Also we prove that if R is a 2‐torsion free ring with 1 in which for all x ∈ R and fixed positive integer n and non‐negative integer k, then R is commutative.