bluuebunny/crossref_metadata_2025 huggingface dataset:
Solvability of a fourth order boundary value problem with periodic boundary conditions
Authors: Gupta Chaitan P.
Published: September 2002

Fourth order boundary value problems arise in the study of the equilibrium of an elastaic beam under an external load. The author earlier investigated the existence and uniqueness of the solutions of the nonlinear analogues of fourth order boundary value problems that arise in the equilibrium of an elastic beam depending on how the ends of the beam are supported. This paper concerns the existence and uniqueness of solutions of the fourth order boundary value problems with periodic boundary conditions.
Compatible mappings and common fixed points (2)
Authors: Jungck Gerald
Published: September 2002

A common fixed point theorem of S.L. and S.P. Singh is generalized by weakening commutativity hypotheses and by increasing the number of functions involved.
On the dissipation layer of radial bearings
Authors: Ayeni R. O. , Okoya S. S. , Agorzie C. J.
Published: September 2002

The dissipation boundary layer of certain radial bearings is identified. It is shown that, under certain conditions, the temperature outside this layer is constant.
An inverse problem for biharmonic equation
Authors: Ramm A. G.
Published: September 2002

An inhomogeneity immersed in a medium is found from the measurements of the elastic field on the surface of the medium.
A quasitopos containing CONV and MET as full subcategories
Authors: Lowen E. , Lowen R.
Published: September 2002

We show that convergence spaces with continuous maps and metric spaces with
contractions, can be viewed as entities of the same kind. Both can be characterized by a limit function λ which with each filter ℱ associates a map λℱ from the underlying set to the extended positive real line. Continuous maps and contractions can both be characterized as limit function preserving maps.

The properties common to both the convergence and metric case serve as a basis for
the definition of the category, CAP. We show that CAP is a quasitopos and that, apart from the categories CONV, of convergence spaces, and MET, of metric spaces, it also contains the category AP of approach spaces as nicely embedded subcategories.
S‐asymptotic expansion of distributions
Authors: Stanković Bogoljub
Published: September 2002

This paper contains first a definition of the asymptotic expansion at infinity of distributions belonging to , named S‐asymptotic expansion, as also its properties and application to partial differential equations.
Note on Legendre numbers
Authors: Sitaramachandrarao R. , Davis B. R.
Published: September 2002

The definition and basic properties of Legendre Numbers are reviewed here. We then develop some new properties and identities involving sums of Legendre Numbers, including clarification of a statement in the paper of Haggard [1].
Nonparametric minimal surfaces in R3 whose boundaries have a jump discontinuity
Authors: Lancaster Kirk E.
Published: September 2002

Let Ω be a domain in R2 which is locally convex at each point of its boundary except possibly one, say (0, 0), ϕ be continuous on ∂Ω/{(0, 0)} with a jump discontinuity at (0, 0) and f be the unique variational solution of the minimal surface equation with boundary values ϕ. Then the radial limits of f at (0, 0) from all directions in Ω exist. If the radial limits all lie between the lower and upper limits of ϕ at (0, 0), then the radial limits of f are weakly monotonic; if not, they are weakly increasing and then decreasing (or the reverse). Additionally, their behavior near the extreme directions is examined and a conjecture of the author′s is proven.
An application of stress energy tensor to the vanishing theorem of differential forms
Authors: Cai Kairen
Published: September 2002

The author applies the stress energy of differential forms to study the vanishing theorems of the Liouville type. It is shown that for a large class of underlying manifolds such as the Euclidean n‐space, the complex n‐space, and the complex hyperbolic space form, if any vector bundle valued p‐form with conservative stress energy tensor is of finite norm or slowly divergent norm, then the p‐form vanishes. This generalizes the recent results due to Hu and Sealey.
Convergence of the solutions for the equation
Authors: Afuwape Anthony Uyi
Published: September 2002

This paper is concerned with differential equations of the form

urn:x-wiley:01611712:media:ijmm326851:ijmm326851-math-0002

where a, b are positive constants and the functions g, h and p are continuous in their respective arguments, with the function h not necessarily differentiable. By introducing a Lyapunov function, as well as restricting the incrementary ratio η−1{h(ζ + η) − h(ζ)}, (η ≠ 0), of h to a closed sub‐interval of the Routh‐Hurwitz interval, we prove the convergence of solutions for this equation. This generalizes earlier results.
Maximal subalgebra of Douglas algebra
Authors: Gullory Carroll J.
Published: September 2002

When q is an interpolating Blaschke product, we find necessary and sufficient conditions for a subalgebra B of to be a maximal subalgebra in terms of the nonanalytic points of the noninvertible interpolating Blaschke products in B. If the set M(B) ⋂ Z(q) is not open in Z(q), we also find a condition that guarantees the existence of a factor q0 of q in H∞ such that B is maximal in . We also give conditions that show when two arbitrary Douglas algebras A and B, with A⫅B have property that A is maximal in B.
Pythagorean triangles of equal areas
Authors: Baica Malvina
Published: September 2002

The main intent in this paper is to find triples of Rational Pythagorean Triangles (abbr. RPT) having equal areas. A new method of solving a2 + ab + b2 = c2 is to set a = y − 1, b = y + 1, y ∈ N − {0, 1} and get Pell′s equation c2 − 3y2 = 1. To solve a2 − ab − b2 = c2, we set , b = y − 1, y ≥ 2, y ∈ N and get a corresponding Pell′s equation. The infinite number of solutions in Pell′s equation gives rise to an infinity of solutions to a2 ± ab + b2 = c2. From this fact the following theorems are proved.

Theorem 1 Let c2 = a2 + ab + b2, a + b > c > b > a > 0, then the three RPT‐s formed by (c, a), (c, b), (a + b, c) have the same area S = abc(b + a) and there are infinitely many such triples of RPT.

Theorem 2 Let c2 = a2 − ab + b2, b > c > a > 0, then the three RPT‐s formed by (b, c), (c, a), (c, b − a) have the same area S = abc(b − a) and there are infinitely many such triples of RPT.
Time‐evolution of a caustic
Authors: Ari Nasit , Gorman Arthur D.
Published: September 2002

The Lagrange manifold formalism is adapted to study the time‐evolution of caustics associated with high frequency wave propagation in media with both spatial and temporal inhomogenities.
Prime valued polynomials and class numbers of quadratic fields
Authors: Mollin Richard A.
Published: September 2002

It is the purpose of this paper to give a survey of the relationship between the class number one problem for real quadratic fields and prime‐producing quadratic polynomials; culminating in an overview of the recent solution to the class number one problem for real quadratic fields of Richaud‐Degert type. We conclude with new conjectures, questions and directions.
Ultraregular inductive limits
Authors: Kucera Jan
Published: September 2002

An inductive limit E = indlim En is ultraregular if it is regular and each set B ⊂ En, which is bounded in E, is also bounded in En. A necessary and sufficient condition for ultraregularity of E is given provided each En is an LF‐space which is closed in En+1.
Eigenvalues of the time—dependent fluid flow problem I
Authors: Zayed El-Sayed M. , Elshehawey El-Sayed F.
Published: September 2002

The direct and inverse boundary value problems for the linear unsteady viscous fluid flow through a closed conduit of a circular annular cross‐section Ω with arbitrary time‐dependent pressure gradient under the third boundary conditions have been investigated.
Problem of mathematical deduction of the existence of black holes
Authors: Chin Yuan-Shun
Published: September 2002

The mathematical proof of existence of Black Hole is based on the assumption of mass being independent of speed. Considering the effect of special relativity of the dependence of mass with speed there is no Black hole.
Note on certain subclass of close‐to‐convex functions of order α
Authors: Owa Shigeyoshi , Aouf M. K. , Nasr M. A.
Published: September 2002

The object of the present paper is to show a result for functions belonging to the class R(α) which is the subclass of close‐to‐convex functions in the unit disk U.
Principal toroidal bundles over Cauchy‐Riemann products
Authors: Abatangelo L. Maria , Dragomir Sorin
Published: September 2002

The main result we obtain is that given π : N → M a Ts‐subbundle of the generalized Hopf fibration over a Cauchy‐Riemann product i : M⊆ℂPn, i.e. j : N⊆H2n+s is a diffeomorphism on fibres and , if s is even and N is a closed submanifold tangent to the structure vectors of the canonical ℊ‐structure on H2n+s then N is a Cauchy‐Riemann submanifold whose Chen class is non‐vanishing.
An iteration technique and commutativity of rings
Authors: Abujabal H. A. S. , Khan M. S.
Published: September 2002

Through much shorter proofs, some new commutativity theorems for rings with unity have been obtained. These results either extend or generalize a few well‐known theorems. Our method of proof is based on an iteration technique.
A note on complex L1‐predual spaces
Authors: Das Mrinal Kanti
Published: September 2002

Some characterizations of complex L1‐predual spaces are proved.
Ring homomorphisms on H(G)
Authors: Nandakumar N. R.
Published: September 2002

It is shown that a ring homomorphism on H(G), the algebra of analytic functions on a regular region G in the complex plane, is either linear or conjugate linear provided that the ring homomorphism takes the identity function into a nonconstant function.
Fourier transforms in generalized Fock spaces
Authors: Schmeelk John
Published: September 2002

A classical Fock space consists of functions of the form,

urn:x-wiley:01611712:media:ijmm629657:ijmm629657-math-0001

where ϕ0 ∈ C and ϕq ∈ L2(R3q), q ≥ 1. We will replace the ϕq, q ≥ 1 with q‐symmetric rapid descent test functions within tempered distribution theory. This space is a natural generalization of a classical Fock space as seen by expanding functionals having generalized Taylor series. The particular coefficients of such series are multilinear functionals having tempered distributions as their domain. The Fourier transform will be introduced into this setting. A theorem will be proven relating the convergence of the transform to the parameter, s, which sweeps out a scale of generalized Fock spaces.
An integral involving the generalized zeta function
Authors: Elizalde E. , Romeo A.
Published: September 2002

A general value for , for a, b positive reals, is derived in terms of the Hurwitz ζ function. That expression is checked for a previously known special integral, and the case where a is a positive integer and b is half an odd integer is considered. The result finds application in calculating the numerical value of the derivative of the Riemann zeta function at the point −1, a quantity that arises in the evaluation of determinants of Laplacians on compact Riemann surfaces.
A coupled magneto‐thermo‐elastic problem in a perfectly conducting elastic half‐space with thermal relaxation
Authors: Roy-Choudhuri S. K. , Chatterjee Gargi
Published: September 2002

In the present paper we consider the magneto‐thermo‐elastic wave produced by a thermal shock in a perfectly conducting elastic half‐space. Here the Lord‐Shulman theory of thermoelasticity [1] is used to account for the interaction between the elastic and thermal fields. The solution obtained in analytical form reduces to those of Kaliski and Nowacki [2] when the coupling between the temperature and strain fields and the relaxation time are neglected. The results also agree with those of Massalas and DaLamangas [3] in absence of the thermal relaxation time.
An application of Miller and Mocanu′s result
Authors: Owa Shigeyoshi , Wu Zhworen
Published: September 2002

The object of the present paper is to give an application of Miller and Mocanu′s result for a certain integral operator.
Some fixed point iteration procedures
Authors: Rhoades B. E.
Published: September 2002

This paper provides a survey of iteration procedures that have been used to
obtain fixed points for maps satisfying a variety of contractive conditions. The author does
not claim to provide complete coverage of the literature, and admits to certain biases in the
theorems that are cited herein. In spite of these shortcomings, however, this paper should be
a useful reference for those persons wishing to become better acquainted with the area.
Properties of α‐expansions of topologies
Authors: Rose David A.
Published: September 2002

The results of O. Njåstad for α‐topologies together with the results of P. L. Sharma for anti‐compact
perfect Hausdorff spaces are combined to produce several counterexamples in one space.
An inverse eigenvalue problem for an arbitrary multiply connected bounded region in R2
Authors: Zayed E. M. E.
Published: September 2002

The basic problem is to determine the geometry of an arbitrary multiply connected bounded
region in R2 together with the mixed boundary conditions, from the complete knowledge of the eigenvalues
for the Laplace operator, using the asymptotic expansion of the spectral function as t → 0.
Finite‐infinite range inequalities in the complex plane
Authors: Mhaskar H. N.
Published: September 2002

Let E⫅C be closed, ω be a suitable weight function on E, σ be a positive
Borel measure on E. We discuss the conditions on ω and σ which ensure the existence of
a fixed compact subset K of E with the following property. For any p, 0 < P ≤ ∞, there
exist positive constants c1, c2 depending only on E, ω, σ and p such that for every integer
n ≥ 1 and every polynomial P of degree at most n,

urn:x-wiley:01611712:media:ijmm729523:ijmm729523-math-0001

.
In particular, we shall show that the support of a certain extremal measure is, in some
sense, the smallest set K which works. The conditions on σ are formulated in terms of
certain localized Christoffel functions related to σ.
A discrete Stochastic Korovkin theorem
Authors: Anastassiou George A.
Published: September 2002

In this article we give a sufficient condition for the pointwise −− in
the first mean Korovkin property on B0(P), the space of stochastic processes with
real state space and countable index set Γ and bounded first moments.
Oscillation criteria in neutral equations of n order with variable coefficients
Authors: Georgiou D. A. , Qian C.
Published: September 2002

Consider the n‐order neutral delay differential equation

urn:x-wiley:01611712:media:ijmm261263:ijmm261263-math-0001

where P,Q ∈ C[[t0, ∞), ℝ] and the delays τ and σ are nonnegative real numbers. In this paper we
examined the oscillatory behavior of the solutions of the above equation using techniques which
allow the relaxation of the restrictions which has been introduced previously. We illustrate new
type of conditions which improve and extend known results, by relaxing hypotheses that P is
constant and Q is τ‐periodic.
Lucas numbers of the form PX2, where P is prime
Authors: Robbins Neville
Published: September 2002

Let Ln denote the nth Lucas number, where n is a natural number.
Using elementary techniques, we find all solutions of the equation: Ln = px2
where p is prime and p < 1000.
A novel interpretation of least squares solution
Authors: Chan Jack-Kang
Published: September 2002

We show that the well‐known least squares (LS) solution of an overdetermined system of linear equations is a convex combination of all the non‐trivial solutions weighed by the squares of the corresponding
denominator determinants of the Cramer′s rule. This Least Squares Decomposition (LSD) gives an alternate statistical interpretation of least squares, as well as another geometric meaning. Furthermore, when the singular values of the matrix of the overdetermined system are not small, the LSD may be able to provide flexible solutions. As an illustration, we apply the LSD to interpret the LS‐solution in the problem of source localization.
Some results on certain subclasses of analytic functions involving generalized hypergeometric functions and Hadamard product
Authors: Noor Khalida Inayat
Published: September 2002

By using a certain linear operator defined by a Hadamard product or convolution, several interesting subclasses of analytic functions in the unit disc are introduced and some unifying relationships between them are established. A variety of characterization results involving a certain functional and some general functions of hypergeometric type are investigated for these classes.
The approximation property of some vector valued Sobolev‐Slobodeckij spaces
Authors: Bosch Carlos , Pérez-Esteva Salvador , Motos Joaquín
Published: September 2002

In this paper we consider the Sobolev‐Slobodeckij spaces Wm,p(ℜn, E) where E is a strict (LF)‐space, m ∈ (0, ∞)\ℕ and p ∈ [1, ∞). We prove that Wm,p(ℜn, E) has the approximation property provided E has it, furthermore if E is a Banach space with the strict approximation property then Wm,p(ℜn, E) has this property.
One‐dimensional game of life and its growth functions
Authors: Ahmadi Mohammad H.
Published: September 2002

We start with finitely many 1′s and possibly some 0′s in between. Then each entry in the other rows is obtained from the Base 2 sum of the two numbers diagonally above it in the preceding row. We may formulate the game as follows: Define d1,j recursively for 1, a non‐negative integer, and j an arbitrary integer by the rules:

urn:x-wiley:01611712:media:ijmm525863:ijmm525863-math-0001

urn:x-wiley:01611712:media:ijmm525863:ijmm525863-math-0002

urn:x-wiley:01611712:media:ijmm525863:ijmm525863-math-0003

Now, if we interpret the number of 1′s in row i as the coefficient ai of a formal power series, then we obtain a growth function, . It is interesting that there are cases for which this growth function factors into an infinite product of polynomials. Furthermore, we shall show that this power series never represents a rational function.
Generalized Green′s functions for higher order boundary value matrix differential systems
Authors: Villanueva R. J. , Jodar L.
Published: September 2002

In this paper, a Green′s matrix function for higher order two point boundary value differential matrix problems is constructed. By using the concept of rectangular co‐solution of certain algebraic matrix equation associated to the problem, an existence condition as well as an explicit closed form expression for the solution of possibly not well‐posed boundary value problems is given avoiding the increase of the problem dimension.
Elementary sequences
Authors: Beslin Scott J.
Published: September 2002

Explicit finite algebraic formulas are given for some well‐known sequences, including complements of polynomial sequences.
A note on the free convection boundary layer on a vertical surface with prescribed heat flux at small Prandtl number
Authors: Merkin J. H. , Kumaran V.
Published: September 2002

It is shown that for a particular case of the surface heat flux the equations for small Prandtl number have simple analytical solutions. These are presented and compared with numerical solutions of the general equations.
Spaces of compact operators which are M‐ideals in L(X, Y)
Authors: Cho Chong-Man
Published: September 2002

Suppose X and Y are reflexive Banach spaces. If K(X, Y), the space of all compact linear operaters from X to Y is an M‐ideal in L(X, Y), the space of all bounded linear operators from X to Y, then the second dual space K(X,Y)** of K(X, Y) is isometrically isomorphic to L(X, Y).
Connections between the matching and chromatic polynomials
Authors: Farrell E. J. , Whitehead Earl Glen
Published: September 2002

The main results established are (i) a connection between the matching and chromatic polynomials and (ii) a formula for the matching polynomial of a general complement of a subgraph of a graph. Some deductions on matching and chromatic equivalence and uniqueness are made.
A method of summability of Lagrange interpolation
Authors: Mache Detlef H.
Published: September 2002

The author uses in this paper a technique from numerical integration (see [9]) to get a discretely defined operator, which is a modification of the Lagrange operator. Therefore we improve with the linear summation method a result presented in [12] and we also point out a solution for a problem of P.L.Butzer in the proceedings of the Budapest conference in 1980.
Compatible mappings and common fixed points revisited
Authors: Jungck Gerald
Published: September 2002

A fixed point theorem involving a Meir‐Keeler type contraction principle is refined by diminishing continuity requirements.
A result of commutativity of rings
Authors: Gupta Vishnu
Published: September 2002

In this paper we prove the following:

THEOREM. Let n > 1 and m be fixed relatively prime positive integers and k is any non‐negative integer. If R is a ring with unity 1 satisfying xk[xn, y] = [x, ym] for all x, y ∈ R then R is commutative.
A mixed boundary value problem for Laplace′s equation involving a nearly circular disk
Authors: Chakrabarti A. , Manna D. P.
Published: September 2002

The electrostatic problem of a nearly circular disk charged to a unit potential is considered for its solution as it serves as the most important and symbolic mixed boundary value problem for Laplace′s equation with the aid of which many complicated mixed boundary value problems arising in elasticity and fluid dynamics can be handled for solution. The method used involves the utility of Green′s second identity, Abel′s integral equations and their inversions, along with a suitably designed perturbation scheme involving the small parameter ϵ(>0) occurring in the geometrical representation of the boundary of the nearly circular disk.
Vector‐valued means and weakly almost periodic functions
Authors: Zhang Chuanyi
Published: September 2002

A formula is set up between vector‐valued mean and scalar‐valued means that enables us translate many important results about scalar‐valued means developed in [1] to vector‐valued means. As applications of the theory of vector‐valued means, we show that the definitions of a mean in [2] and [3] are equivalent and the space of vector‐valued weakly almost periodic functions is admissible.
An oscillation criterion for inhomogeneous Stieltjes integro‐differential equations
Authors: El-Sayed M. A.
Published: September 2002

The aim of the paper is to give an oscillation theorem for inhomogeneous Stieltjes integro‐differential equation of the form . The paper generalizes the author′s work [2].
Common fixed point theorems for sequences of fuzzy mappings
Authors: Lee B. S. , Cho S. J.
Published: September 2002

In this paper, we define g‐contractive and g‐contractive type fuzzy mappings and prove common fixed point theorems for sequences of fuzzy mappings on a complete metric linear space.
Regular measures and normal lattices
Authors: Vlad Carmen
Published: September 2002

In this paper, we investigate M(ℒ) in case ℒ is a normal lattice of subsets of X and we extend the results to ℒ1, ℒ2‐lattices of subsets of X, such that ℒ1 ⊂ ℒ2 and ℒ1 separates ℒ2. We define the outer measures μ′ and μ″ which prove very useful in proving some of the above results.
Product involutions with 0 or 1‐dimensional fixed point sets on orientable handlebodies
Authors: Nelson Roger B.
Published: September 2002

Let h be an involution with a 0 or 1‐dimensional fixed point set on an orientable handlebody M. We show that obvious necessary conditions for fibering M as A × I so that h = τ × r with τ an involution of A and r reflection about the midpoint of I also turn out to be sufficient. We also show that such a product involution is determined by its fixed point set.
Wiener Tauberian theorems for vector‐valued functions
Authors: Parthasarathy K. , Varma Sujatha
Published: September 2002

Different versions of Wiener′s Tauberian theorem are discussed for the generalized group algebra L1(G, A) (of integrable functions on a locally compact abelian group G taking values in a commutative semisimple regular Banach algebra A) using A‐valued Fourier transforms. A weak form of Wiener′s Tauberian property is introduced and it is proved that L1(G, A) is weakly Tauberian if and only if A is. The vector analogue of Wiener′s L2‐span of translates theorem is examined.
Pascal type properties of Betti numbers
Authors: de Alwis Tilak
Published: September 2002

In this paper, we will describe the Pascal Type properties of Betti numbers of ideals associated to n‐gons. These are quite similar to the properties enjoyed by the Pascal′s Triangle, concerning the binomial coefficients. By definition, the Betti numbers βt(n) of an ideal I associated to an n‐gon are the ranks of the modules in a free minimal resolution of the R‐module R/I, where R is the polynomial ring k[x1, x2, …, xn]. Here k is any field and x1, x2, …, xn are indeterminates. We will prove those properties using a specific formula for the Betti numbers.
Measures of Lindelof and separability in approach spaces
Authors: Baekeland R. , Lowen R.
Published: September 2002

In this paper we introduce the notions of separability and Lindelöf in approach spaces and investigate their behaviour under products and subspaces.
Fixed point theorems for non‐self maps I
Authors: Hicks Troy L. , Saliga Linda Marie
Published: September 2002

Suppose f : C → X where C is a closed subset of X. Necessary and sufficient conditions are given for f to have a fixed point. All results hold when X is complete metric space. Several results hold in a much more general setting.
Estimates for the Cauchy matrix of perturbed linear impulsive equation
Authors: Simeonov P. S. , Bainov D. D.
Published: September 2002

Estimates for the Cauchy matrix of a perturbed linear impulsive equation are obtained for given estimates for the Cauchy matrix of the corresponding unperturbed linear impulsive equation.
Arbitrary squeeze flow between two disks
Authors: Rukmani R. , Usha R.
Published: September 2002

A viscous incompressible fluid is contained between two parallel disks with arbitrarily shrinking width h(τ). The solution is obtained as a power series in a single nondimensional parameter (squeeze number) S, for small values of S in contrast to the multifold series solution obtained by Ishizawa in terms of an infinite set of nondimensional parameters. The gap width h(τ) is obtained for different states: when the top disk moves with constant velocity, constant force or constant power.
The strong WCD property for Banach spaces
Authors: Wilkins Dave
Published: September 2002

In this paper, we introduce weakly compact version of the weakly countably
determined (WCD) property, the strong WCD (SWCD) property. A Banach space X is said to
be SWCD if there s a sequence (An) of weak ∗ compact subsets of X∗∗ such that if K ⊂ X is
weakly compact, there is an (nm) ⊂ N such that . In this case, (An) is called a
strongly determining sequence for X. We show that SWCG⇒SWCD and that the converse does
not hold in general. In fact, X is a separable SWCD space if and only if (X, weak) is an ℵ0‐space.
Using c0 for an example, we show how weakly compact structure theorems may be used to
construct strongly determining sequences.
Gliding hump properties and some applications
Authors: Boos Johann , Fleming Daniel J.
Published: September 2002

In this not we consider several types of gliding bump properties for a sequence space E
and we consider the various implications between these properties. By means of examples we show that
most of the implications are strict and they afford a sort of structure between solid sequence spaces and
those with weakly sequentially complete β‐duals. Our main result is used to extend a result of Bennett and
Kalton which characterizes the class of sequence spaces E with the properly that E ⊂ SF, whenever F is
a separable FK space containing E where SF denotes the sequences in F having sectional convergence.
This, in turn, is used to identify a gliding humps property as a sufficient condition for E to be in this
class.
On chains and posets within the power set of a continuum
Authors: Matthews P. T. , McMaster T. B. M.
Published: September 2002

Transfinite induction is employed to construct a copy of an arbitrary partially‐ordered
set of cardinality at most c within the power set (quasi‐ordered by sub‐chain
embeddability) of the real line.
Topological properties and matrix transformations of certain ordered generalized sequence spaces
Authors: Gupta Manjul , Kaushal Kalika
Published: September 2002

In this note, we carry out investigations related to the mixed
impact of ordering and topological structure of a locally convex solid
Riesz space (X,τ) and a scalar valued sequence space λ, on the vector
valued sequence space λ(X) which is formed and topologized with the help
of λ and X, and vice versa. Besides,we also characterize o‐matrix transformations
from c(X), ℓ∞(X) to themselves, cs(X) to c(X) and derive necessary
conditions for a matrix of linear operators to transform ℓ1(X) into a
simple ordered vector valued sequence space Λ(X).
Existence theorems for a second order m‐point boundary value problem at resonance
Authors: Gupta Chaitan P.
Published: September 2002

Let f : [0, 1] × R2 → R be function satisfying Caratheodory′s conditions and e(t) ∈ L1[0, 1]. Let η ∈ (0, 1), ξi ∈ (0, 1), ai ≥ 0, i = 1, 2, …, m − 2, with , 0 < ξ1 < ξ2 < …<ξm−2 < 1 be given. This paper is concerned with the problem of existence of a solution
for the following boundary value problems

urn:x-wiley:01611712:media:ijmm650928:ijmm650928-math-0002

Conditions for the existence of a solution for the above boundary value problems are given
using Leray Schauder Continuation theorem.
Convex functions and the rolling circle criterion
Authors: Srinivas V. , Juneja O. P. , Kapoor G. P.
Published: September 2002

Given 0 ≤ R1 ≤ R2 ≤ ∞, CVG(R1, R2) denotes the class of
normalized convex functions f in the unit disc U, for which ∂f(U)
satisfies a Blaschke Rolling Circles Criterion with radii R1 and R2.
Necessary and sufficient conditions for R1 = R2, growth and
distortion theorems for CVG(R1, R2) and rotation theorem for the
class of convex functions of bounded type, are found.
The T‐statistically convergent sequences are not an FK‐space
Authors: Kline Jeannette
Published: September 2002

In ths note show that under certain restrictions on a nonnegative regular summability
matrix T, the space of T‐statistically convergent sequences cannot be endowed with locally convex
FK topology.
Cone valued Lyapunov functions and Lipschitz stability of nonlinear systems of differential equations
Authors: Akinyele Olusola
Published: September 2002

We introduce a new comparison result which will be an important tool when we
apply cone valued Lyapunov like functions. We also introduce new concepts of ϕ0‐uniform Lipschitz
stability and (λ, λ, ϕ0)‐practical stability and employ our comparison result to carry out stability
analysis of nonlinear systems. Our results are also applicable to nonlinear perturbed systems.
On completely 0‐simple semigroups
Authors: Ho Yue-Chan Phoebe
Published: September 2002

Let S be a completely 0‐simple semigroup and F be an algebraically closed field.
Then for each 0‐minimal right ideal M of S, M = B ∪ C ∪ {0}, where B is a right group and C
is a zero semigroup. Also, a matrix representation for S other than Rees matrix is found for the
condition that the semigroup ring R(F, S) is semisimple Artinian.
On the surjectivity of linear transformations
Authors: Damlakhi M. , Anandam V.
Published: September 2002

Let B be a reflexive Banach space, X a locally convex space and T : B → X (not necessarily bounded) linear transformation. A necessary and sufficient condition is obtained so that for a given v ∈ X there is a solution for the equation Tu = v. This result is used to discuss the existence of an Lp‐weak solution of Du = v where D is a differential operator with smooth coefficients and v ∈ Lp.
Fractional derivatives of holomorphic functions on bounded symmetric domains of Cn
Authors: Lou Zengjian
Published: September 2002

Let f ∈ H(Bn). f|β| denotes the βth fractional derivative of f. If f|β| ∈ Ap,q,α(Bn), we show that

(I) , then f ∈ As,t,α(Bn), and , ,

(II) If , then f ∈ B(Bn) and

(III) If , then especially If β = 1 then where Bn is the unit ball of Cn.
A new criterion for starlike functions
Authors: Yi Ling , Ding Shusen
Published: September 2002

In this paper we shall get a new criterion for starlikeness, and the hypothesis of this criterion is much weaker than those in [1] and [2].
On matrix convexity of the Moore‐Penrose inverse
Authors: Mond B. , Pečarić J. E.
Published: September 2002

Matrix convexity of the Moore‐Penrose inverse was
considered in the recent literature.
Here we give some converse inequalities as well as further generalizations.
A representation of bounded commutative BCK‐algebras
Authors: Abujabal H. A. S. , Aslam M. , Thaheem A. B.
Published: September 2002

In this note, we prove a representation
theorem for bounded commutative BCK‐algebras.
Lattices of fuzzy objects
Authors: Sangalli Arturo A. L.
Published: September 2002

The collection of fuzzy subsets of a set
X forms a complete lattice
that extends the complete lattice 𝒫(X) of crisp subsets of X. In this paper, we
interpret this extension as a special case of the fuzzification
of an arbitrary
complete lattice A. We show how to construct a complete lattice F(A, L)
the L‐fuzzificatio
of A, where L
is the valuation lattice that extends A while
preserving all suprema and infima. The fuzzy
objects in F(A, L)
may be interpreted as the sup‐preserving maps from A
to the dual of L. In particular,
each complete lattice coincides with its 2‐fuzzification, where 2 is the twoelement
lattice. Some familiar fuzzifications (fuzzy subgroups, fuzzy subalgebras,
fuzzy topologies, etc.) are special cases of our construction. Finally,
we show that
the binary relations on a set X may be seen as the fuzzy subsets of X with
respect to the valuation lattice 𝒫(X).
A curious integral
Authors: Masson David R.
Published: September 2002

A double integral which came from a cohomology calculation is evaluated
explicitly using the properties of  3F2 and  2F1 hypergeometric functions.
On the growth of the spectral measure
Authors: Boumenir A.
Published: September 2002

We are concerned with the asymptotics of the spectral measure associated with a
self‐adjoint operator. By using comparison techniques we shall show that the eigenfunctionals of
L2 are close to the eigenfunctionals L1 if and only if dΓ1 ≈ dΓ2 as λ → ∞.
Convergence of Ishikawa iterates of generalized nonexpansive mappings
Authors: Ghosh M. K. , Debnath L.
Published: September 2002

This paper is concerned with the convergence of Ishikawa iterates of generalized
nonexpansive mappings in both uniformly convex and strictly convex Banach spaces. Several fixed point
theorems are discussed.
A shooting method for singular nonlinear second order Volterra integro‐differential equations
Authors: Shaw R. E. , Garey L. E.
Published: September 2002

The method of parallel shooting will be employed to solve nonlinear second order singular
Volterra integro‐differential equations with two point boundary conditions.
Fourier transform of hn(x + p)hn(x − p)
Authors: Ismail Mourad E. H. , Stempak Krzystztof
Published: September 2002

We evaluate Fourier transform of a function with Hermite polynomials involved.
An elementary proof is based on a combinatorial formula for Hermite polynomials.
Longest cycles in certain bipartite graphs
Authors: Wong Pak-Ken
Published: September 2002

Let G be a connected bipartite graph with bipartition (X, Y) such that |X| ≥ |Y|(≥2),
n = |X| and m = |Y|. Suppose, for all vertices x ∈ X and y ∈ Y, dist(x, y) = 3 implies
d(x) + d(y) ≥ n + 1. Then G contains a cycle of length 2m. In particular, if m = n, then G is
hamiltomian.
L1 spaces fail a certain aapproximative property
Authors: Kamal Aref
Published: September 2002

In this paper the author studies some cases of Banach space that does not have the
property P1. He shows that if X = ℓ1 or L1(μ) for some non‐purely atomic measure μ, then X does not
have the property P1. He also shows that if
X = ℓ∞ or C(Q) for some infinite compact Hausdorff space
Q, then X* does not have the property P1.
Nearly conconcentric Korteweg‐de Vries equation and periodic traveling wave solution
Authors: Chen Yunkai
Published: September 2002

The generalized nearly concentric Korteweg‐de Vries equation is considered. The author converts the equation into the power Kadomtsev‐Petviashvili equation
. Solitary wave solutions and cnoidal wave solutions are
obtained. The cnoidal wave solutions are shown to be representable as infinite sums of solitons by using
Fourier series expansions and Poisson′s summation formula.
On common fixed and periodic points of commuting functions
Authors: Alikhani-Koopaei Aliasghar
Published: September 2002

It is known that two commuting continuous functions on an interval need not have
a common fixed point. It is not known if such two functions have a common periodic point. In
this paper we first give some results in this direction. We then define a new contractive condition,
under which two continuous functions must have a unique common fixed point.
Fourier transforms of Lipschitz functions on the hyperbolic plane H2
Authors: Younis M. S.
Published: September 2002

The purpose of the present work is to study the order of magnitude of the Fourier
transforms for large λ
of complex‐valued functions f(z)
sating certain Lipschitz conditions in
the non‐Euclidean hyperbolic plane H2.
Calculating norms in the spaces l∞(Γ)/c0(Γ) and l∞(Γ)/c(Γ)
Authors: Sznajder Roman
Published: September 2002

We explicitly compute norms in the quotient spaces
l∞(Γ)/c0(Γ) and l∞(Γ)/c(Γ).
Equicontinuity of iterates of circle maps
Authors: Valaristos Antonios
Published: September 2002

Let f be a continuous map of the circle to itself. Necessary and sufficient conditions are given for the family ofiterates
to be equicontinuous.
A sampling theorem associated with boundary‐value problems with not necessarily simple eigenvalues
Authors: Annaby Mahmoud H. , Hassan Hassan A.
Published: September 2002

We use a new version of Kramer′s theorem to derive a sampling theorem associated
with second order boundary‐value problems whose eigenvalues are not necessarily simple.
On a new absolute summability method
Authors: Sulaiman W. T.
Published: September 2002

A theorem concerning some new absolute summability method is proved. Many other
results, some of them known, are deduced.
Weak regularity of probability measures
Authors: Siegel Dale
Published: September 2002

This paper examines smoothness attributes of probability measures on lattices which
indicate regularity, and then discusses weaker forms of regularity; specifically, weakly regular and
vaguely regular. They are obtained from commonly used outer measures, and we study them mainly for
the case of
M(ℒ) or for those components of M(ℒ) with added smoothness prerequisites. This is a
generalization of many concepts presented in my earlier paper (see [1]).
Integrability of doubly‐periodic Riccati equation
Authors: Ling Ma , Ke-Ying Guan
Published: September 2002

By the structure of solvable subgroup of SL(2, ℂ)
(see [1]), the integrability and
properties of solutions of a Riccati equation with an elliptic function coefficient, which is related to a
Fuchsian equation on the torus T2,is studied.
Numerical solution of integral equations with finite part integrals
Authors: Ashour Samir A.
Published: September 2002

We obtain convergence rates for several algorithms that solve a
class of Hadamard singular integral equations using the general theory of approximations for unbounded operators.
Marcinkiewicz‐type strong law of large numbers for double arrays of pairwise independent random variables
Authors: Hong Dug Hun , Hwang Seok Yoon
Published: September 2002

Let {Xij} be a double sequence of pairwise independent random variables. If P{|Xmn| ≥ t} ≤ P{|X| ≥ t} for all nonnegative real numbers t and , for 1 < p < 2, then we prove that

urn:x-wiley:01611712:media:ijmm690634:ijmm690634-math-0002

Under the weak condition of E|X|plog+|X| < ∞, it converges to 0 in L1. And the results can be generalized to an r‐dimensional array of random variables under the conditions , respectively, thus, extending Choi and Sung′s result [1] of the one‐dimensional case.
Limit sets in product of semi‐dynamical
Authors: Bhagat Ramjee Prasad
Published: September 2002

Continuing the study of the properties of Poisson stability and
distality [4], we mention the conditions under which Ωx(x) = ΠΩα(xα), α ∈ I and thus, the product of Poisson stable motions remains Poisson stable in the product system.
The Diophantine equation x2 + 2k = yn, II
Authors: E. Cohn J. H.
Published: September 2002

New results regarding the full solution of the diophantine equation x2 + 2k = yn in positive integers are obtained. These support a previous conjecture, without providing a complete proof.
Six‐dimensional considerations of Einstein′s connection for the first two classes. I. The recurrence relations in 6‐g‐UFT
Authors: Chung Kyung Tae , Yang Gye Tak , Hwang In Ho
Published: September 2002

Lower dimensional cases of Einstein′s connection were already investigated by many authors for n = 2, 3, 4, 5. This paper is the first part of the following series of two papers, in which we obtain a surveyable tensorial representation of 6‐dimensional Einstein′s connection in terms of the unified field tensor, with main emphasis on the derivation of powerful and useful recurrence relations which hold in 6‐dimensional Einstein′s unified field theory (i.e., 6‐g‐UFT):

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

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

All considerations in these papers are restricted to the first and
second classes only, since the case of the third class, the simplest case, was already studied by many authors.
Bounded and L2‐solutions to a second order nonlinear differential equation with a square integrable forcing term
Authors: Kroopnick Allan
Published: September 2002

This paper presents two theorems concerning the nonlinear differential equation x″ + c(t)f(x)x′ + a(t, x) = e(t), where e(t) is a continuous square‐integrable function. The first theorem gives sufficient conditions when all the solutions of this equation are bounded while the second theorem discusses when all the solutions are in L2[0, ∞).
On decomposable pseudofree groups
Authors: Scevenels Dirk
Published: September 2002

An Abelian group is pseudofree of rank ℓ if it belongs to the extended genus of ℤℓ, i.e., its localization at every prime p is isomorphic to . A pseudofree group can be studied through a sequence of rational matrices, the so‐called sequential representation. Here, we use these sequential representations to study the relation between the product of extended genera of free Abelian groups and the extended genus of their direct sum. In particular, using sequential representations, we give a new proof of a result by Baer, stating
that two direct sum decompositions into rank one groups of a completely decomposable pseudofree Abelian group are necessarily equivalent. On the other hand, sequential representations can also be used to exhibit examples of pseudofree groups having nonequivalent direct sum decompositions into indecomposable groups. However, since this cannot occur when using the notion of near‐isomorphism rather than isomorphism, we conclude our work by giving a characterization of near‐isomorphism for pseudofree groups in terms of their sequential representations.
Notes on Fréchet spaces
Authors: Hong Woo Chorl
Published: September 2002

First, we introduce sequential convergence structures and characterize Fréchet spaces and continuous functions in Fréchet spaces using these structures. Second, we give sufficient conditions for the expansion of a topological space by the sequential closure operator to be a Fréchet space and also a sufficient condition for a simple expansion of a topological space
to be Fréchet. Finally, we study on a sufficient condition that a sequential space be Fréchet, a weakly first countable space be first countable, and a symmetrizable space be semi‐metrizable.
Smoothness conditions on measures using Wallman spaces
Authors: Traina Charles
Published: September 2002

In this paper, X denotes an arbitrary nonempty set, ℒ a lattice of subsets of X with ∅, X ∈ ℒ, A(ℒ) is the algebra generated by ℒ and M(ℒ) is the set of nontrivial, finite, and finitely additive measures on A(ℒ), and MR(ℒ) is the set of elements of M(ℒ) which are ℒ‐regular. It is well known that any μ ∈ M(ℒ) induces a finitely additive measure on an associated Wallman space. Whenever is countably additive.

We consider the general problem of given μ ∈ MR(ℒ), how do properties of imply smoothness properties of μ? For instance, what conditions on are necessary and sufficient for μ to be σ‐smooth on ℒ, or strongly σ‐smooth on ℒ, or countably additive? We consider in discussing these questions either of two associated Wallman spaces.
Solvability of quasilinear elliptic equations with strong dependence on the gradient
Authors: Žubrinić Darko
Published: September 2002

We study the problem of existence of positive, spherically symmetric strong solutions of quasilinear elliptic equations involving p‐Laplacian in the ball. We allow simultaneous strong dependence of the right‐hand side on both the unknown function and its gradient. The elliptic problem is studied by relating it to the corresponding singular ordinary integro‐differential equation. Solvability range is obtained in the form of simple inequalities involving the coefficients describing the problem.
We also study a posteriori regularity of solutions. An existence result is formulated for elliptic equations on arbitrary bounded domains in dependence of outer radius of domain.
Local exact controllability of the age‐dependent population dynamics with diffusion
Authors: Ainseba Bedr′eddine , Anita Sebastian
Published: September 2002

We investigate the local exact controllability of a linear age
and space population dynamics model where the birth process is
nonlocal. The methods we use combine the Carleman estimates for
the backward adjoint system, some estimates in the theory of
parabolic boundary value problems in L k
and the Banach fixed
point theorem.
On projection constant problems and the existence of metric projections in normed spaces
Authors: El-Shobaky Entisarat , Ali Sahar Mohammed , Takahashi Wataru
Published: September 2002

We give the sufficient conditions for the existence of a metric
projection onto convex closed subsets of normed linear spaces
which are reduced conditions than that in the case of reflexive
Banach spaces and we find a general formula for the projections
onto the maximal proper subspaces of the classical Banach spaces
l p, 1 ≤ p < ∞
and c 0. We also give the sufficient
and necessary conditions for an infinite matrix to represent a
projection operator from l p, 1 ≤ p < ∞
or c 0 onto
anyone of their maximal proper subspaces.
An Ambrosetti‐Prodi‐type problem for an elliptic system ofequations via monotone iteration method and Leray‐Schauder degree theory
Authors: Filho D. C. de Morais
Published: September 2002

In this paper we employ the Monotone Iteration Method and the Leray‐Schauder
Degree Theory to study an ℝ2‐parametrized system of elliptic
equations. We obtain a curve dividing the plane into two regions. Depending
on which region the parameter is, the system will or will not have solutions.
This is an Ambrosetti‐Prodi‐type problem for a system of equations.
Carleson embeddings
Authors: Heiming Helmut J.
Published: September 2002

In this paper we discuss several operator ideal properties for so
called Carleson embeddings of tent spaces into specific L q(μ)‐spaces, where μ is a Carleson measure on the complex unit disc. Characterizing absolutely
q‐summing, absolutely continuous and
q‐integral Carleson embeddings in terms of the underlying measure is our main topic. The presented results extend and integrate results especially known for composition operators on Hardy spaces as well as embedding theorems for function spaces of similar kind.