bluuebunny/crossref_metadata_2025 huggingface dataset:
Commutativity and structure of rings with commuting nilpotents
Authors: Abu-Khuzam Hazar , Yaqub Adil
Published: September 2002

Let R be a ring and let N denote the set of nilpotent elements of R. Let Z denote the center of R. Suppose that (i) N is commutative, (ii) for every x in R there exists x′ϵ < x> such that x − x2x′ϵN, where  denotes the subring generated by x, (iii) for every x, y in R, there exists an integer n = n(x, y) ≥ 1 such that both (xy) n − (yx) n and (xy) n+1 − (yx) n+1 belong to Z. Then R is commutative and, in fact, R is isomorphic to a subdirect sum of nil commutative rings and local commutative rings. It is further shown that both conditions in hypothesis (iii) are essential. The proof uses the structure theory of rings along with some earlier results of the authors.
On iterative solution of nonlinear functional equations in a metric space
Authors: Sen Rabindranath , Mukherjee Sulekha
Published: September 2002

Given that A and P as nonlinear onto and into self‐mappings of a complete metric space R, we offer here a constructive proof of the existence of the unique solution of the operator equation Au = Pu, where u ∈ R, by considering the iterative sequence Aun+1 = Pun (u0 prechosen, n = 0, 1, 2, …). We use Kannan′s criterion [1] for the existence of a unique fixed point of an operator instead of the contraction mapping principle as employed in [2]. Operator equations of the form Anu = Pmu, where u ∈ R, n and m positive integers, are also treated.
On the Ritt order of a certain class of functions
Authors: Parvatham R. , Thangamani J.
Published: September 2002

The authors introduce the notions of Ritt order and lower order to
functions defined by the series where (λn) is a D‐sequence and fn(s) are entire functions of bounded index.
An amenability property of algebras of functions on semidirect products of semigroups
Authors: Lerner Bao-Ting
Published: September 2002

Let S1 and S2 be semitopological semigroups, S1 τ  S2 a semidirect product. An amenability property is established for algebras of functions on S1 τ  S2. This result is used to decompose the kernel of the weakly almost periodic compactification of S1 τ  S2 into a semidirect product.
A class of hyperrings and hyperfields
Authors: Krasner Marc
Published: September 2002

Hyperring is a structure generalizing that of a ring, but where the addition is not a composition, but a hypercomposition, i.e., the sum x + y of two elements, x, y, of a hyperring H is, in general, not an element but a subset of H. When the non‐zero elements of a hyperring form a multiplicative group, the hyperring is
called a hyperfield, and this structure generalizes that of a field. A certain class of hyperfields (residual hyperfields of valued fields) has been used by the author [1] as an important technical tool in his theory of approximation of complete valued fields by sequences of such fields. Tne non‐commutative theory of hyperrings (particularly Artinian) has been studied in depth by Stratigopoulos [2].

The question arises: How common are hyperrings? We prove in this paper that a
conveniently defined quotient R/G of any ring R by any normal subgroup G of its multiplicative semigroup is always a hyperring which is a hyperfield when R is a field. We ask: Are all hyperrings isomorphic to some subhyperring of a hyperring belonging to the class just described?
Isomorphisms of semigroups of transformations
Authors: Murti A. Sita Rama
Published: September 2002

If M is a centered operand over a semigroup S, the suboperands of M containing zero are characterized in terms of S‐homomorphisms of M. Some properties of centered operands over a semigroup with zero are studied.

A Δ‐centralizer C of a set M and the semigroup S(C, Δ) of transformations of M over C are introduced, where Δ is a subset of M. When Δ = M, M is a faithful and irreducible centered operand over S(C, Δ). Theorems concerning the isomorphisms of semigroups of transformations of sets Mi over Δi‐centralizers Ci, i = 1, 2 are obtained, and the following theorem in ring theory is deduced: Let Li, i = 1, 2 be the rings of linear transformations of vector spaces (Mi, Di) not necessarily finite dimensional. Then f is an isomorphism of L1 → L2 if and only if there exists a 1 − 1 semilinear transformation h of M1 onto M2 such that fT = hTh−1 for all T ∈ L1.
Path decompositions of chains and circuits
Authors: Farrell E. J.
Published: September 2002

Expressions for the path polynomials (see Farrell [1]) of chains and circuits
are derived. These polynomials are then used to deduce results about node disjoint path decompositions of chains and circuits. Some results are also given for decompositions in which specific paths must be used.
Some fixed point theorems for Hardy‐Rogers type mappings
Authors: Rhoades B. E. , Sessa S. , Khan M. S. , Khan M. D.
Published: September 2002

The first result establishes a fixed point theorem for three maps of a complete metric space. The contractive definition is a generalization of that of Hardy and Rogers, and the commuting condition of Jungck is replaced by the concept of weakly commuting. The other results are extensions of some theorems of Kannan.
On a class of fourth order linear recurrence equations
Authors: Cheng Sui-Sun
Published: September 2002

This paper is concerned with sequences that satisfy a class of fourth order linear recurrence equations. Basic properties of such sequences are derived. In addition, we discuss the oscillatory and nonoscillatory behavior of such sequences.
A class of completely regular spaces
Authors: Eklund Patrik E.
Published: September 2002

In this paper we investigate topologies with ultrafilters having bases of open sets. It is shown that these topologies are completely regular. All results are obtained by using Richardson′s compactification of convergence spaces. We also prove a non‐existance of a dense convergence space compactification with lifting property.
Contact co‐isotropic CR submanifolds of a pseudo‐Sasakian manifold
Authors: Goldberg Vladislav V. , Rosca Radu
Published: September 2002

It is proved that any co‐isotropic submanifold M of a pseudo‐Sasakian manifold is a CR submanifold (such submanfolds are called CICR submanifolds) with involutive vertical distribution ν1. The leaves M1 of D1 are isotropic and M is ν1‐totally geodesic. If M is foliate, then M is almost minimal. If M is Ricci D1‐exterior recurrent, then M receives two contact Lagrangian foliations. The necessary and sufficient conditions for M to be totally minimal is that M be contact D1‐exterior recurrent.
A note on generalized harmonic‐Cesàro summability
Authors: Hiorkawa Hiroshi
Published: September 2002

This note shows that conjectures proposed by G. Das and P.C. Mohapatra [1] on inclusion relations between two generalized Harmonic‐Cesàro methods of summability, are true.
Invariant manifolds and alternative approaches to reductive perturbation theory: dissipative systems
Authors: Morris Hedley C. , Sheil Derek , Dodd Roger
Published: September 2002

This paper is concerned with the limiting process known as Reductive Perturbation Theory. A new view of both conventional reductive perturbation theory and the higher order theory of Kodama is presented for a general class of dissipative systems. An alternative Iterative approach to the determination of higher order corrections is outlined.
Bifurcation for the solutions of equations involving set valued mappings
Authors: Tarafdar E. U. , Thompson H. B.
Published: September 2002

This paper is devoted to a generalization of the bifurcation theorem of
Karsnosel′skii and Rabinowitz to the set valued situation.
Transformations which preserve convexity
Authors: Fontenot Robert A. , Proschan Frank
Published: September 2002

Let C be the class of convex nondecreasing functions f : [0, ∞) → [0, ∞) which satisfy f(0) = 0. Marshall and Proschan [1] determine the one‐to‐one and onto functions ψ : [0, ∞) → [0, ∞) such that g = ψ∘f∘ψ−1 belongs to C whenever f belongs to C. We study several natural models for multivariate extension of the Marshall‐Proschan result. We show that these result in essentially a restatement of the original Marshall‐Proschan characterization.
On locally conformal Kähler space forms
Authors: Matsumoto Koji
Published: September 2002

An m‐dimensional locally conformal Kähler manifold (l.c.K‐manifold) is characterized as a Hermitian manifold admitting a global closed l‐form αλ (called the Lee form) whose structure satisfies

urn:x-wiley:01611712:media:ijmm569581:ijmm569581-math-0002

,
where ∇λ denotes the covariant differentiation with respect to the Hermitian metric gμλ, , and the indices ν, μ, …, λ run over the range 1, 2, …, m.

For l. c. K‐manifolds, I. Vaisman [4] gave a typical example and T. Kashiwada ([1],
[2],[3]) gave a lot of interesting properties about such manifolds.

In this paper, we shall study certain properties of l. c. K‐space forms. In §2, we shall mainly get the necessary and sufficient condition that an l. c. K‐space form is an Einstein one and the Riemannian curvature tensor with respect to gμλ will be expressed without the tensor field Pμλ. In §3, we shall get the necessary and sufficient condition that the length of the Lee form is constant and the sufficient condition that a compact l. c. K‐space form becomes a complex space form. In the last §4, we shall prove that there does not exist a non‐trivial recurrent l. c. K‐space form.
On the spectrum of weakly almost periodic solutions of certain abstract differential equations
Authors: Rao Aribindi Satyanarayan , Dube L. S.
Published: September 2002

In a sequentially weakly complete Banach space, if the dual operator of a linear operator A satisfies certain conditions, then the spectrum of any weakly almost periodic solution of the differential equation u′ = Au + f is identical with the spectrum of f except at the origin, where f is a weakly almost periodic function.
Strong laws of large numbers for arrays of row‐wise exchangeable random elements
Authors: Taylor Robert Lee , Patterson Ronald Frank
Published: September 2002

Let {Xnk, 1 ≤ k ≤ n, n ≤ 1} be a triangular array of row‐wise exchangeable random elements in a separable Banach space. The almost sure convergence of , is obtained under varying moment and distribution conditions on the random elements. In particular, strong laws of large numbers follow for triangular arrays of random elements in(Rademacher) type p separable Banach spaces. Consistency of the kernel density estimates can be obtained in this setting.
On center‐like elements in rings
Authors: Fisher Joe W. , Fahmy Mohamed H.
Published: September 2002

In a paper with a similar title Herstein has considered the structure of prime rings which contain an element a which satisfies either [a, x] n = 0 or is in the center of R for each x in R. We consider the structure of rings which contain an element a which satisfies powers of certain higher commutators. The two types which we consider are (1) or is in the center of R for all x1, x2, …, xm in R and (2) for all x1, x2, …, xm in R. We obtain results similar to those obtained by Herstein; however, in some cases we must strengthen the hypotheses.

Also we consider a third type (3) for all x in R and extend results of Herstein and Giambruno.
Boundary value problems for differential equations with reflection of the argument
Authors: Wiener Joseph , Aftabizadeh A. R.
Published: September 2002

Linear and nonlinear boundary value problems for differential equations
with reflection of the argument are considered.
The diophantine equation r2 + r(x + y) = kxy
Authors: Utz W. R.
Published: September 2002

The Diophantine equation of the title is solved in integers.
Perturbations of normally solvable nonlinear operators, I
Authors: Ray William O. , Walker Anita M.
Published: September 2002

Let X and Y be Banach spaces and let ℱ and 𝒢 be Gateaux differentiable mappings from X to Y In this note we study when the operator ℱ + 𝒢 is surjective for sufficiently small perturbations 𝒢 of a surjective operator ℱ The methods extend previous results in the area of normal solvability for nonlinear operators.
On the strong matrix summability of derived Fourier series
Authors: Mishra K. N. , Srivastava R. S. L.
Published: September 2002

Strong summability with respect to a triangular matrix has been defined and applied to derived Fourier series yielding a result which extends some known results under a general criterion
Distribution of LRC for testing sphericity of a complex multivariate Gaussian model
Authors: Nagar D. K. , Jain S. K. , Gupta A. K.
Published: September 2002

In this paper, exact null distribution of the likelihood ratio criterion for testing sphericity structure in a complex multivariate normal covariance matrix is obtained in computable series form. The method of inverse Mellin transform and contour integration has been used. Certain special cases are given explicitly in terms of the hypergeometric functions.
A variant of a fixed point theorem of Browder‐Fan and Reich
Authors: Sehgal V. M.
Published: September 2002

Let S be a convex, weakly compact subset of a locally convex Hausdorff space (E, τ) and f : S → E be a continuous multifunction from its weak topology ω to τ. let ρ be a continuous seminorm on (E, τ) and for subsets A, B of E let p(A, B) = inf{p(x − y) : x ϵ A, y ϵ B}. In this paper, sufficient conditions are developed for the existence of an x ϵ S satisfying p(x, fx) = p(fx, S). The result is then used to prove several fixed point theorems.
On orderability of topological groups
Authors: Rangan G.
Published: September 2002

A necessary and sufficient condition for a topological group whose topology
can be induced by a total order compatible with the group structure is given and such groups are called ordered or orderable topological groups. A separable totally disconnected ordered topological group is proved to be non‐archimedean metrizable while the converse is shown to be false by means of an example. A necessary and sufficient condition for a no‐totally disconnected locally compact abelian group to be orderable is also given.
Diophantine equations and identities
Authors: Baica Malvina
Published: September 2002

The general diophantine equations of the second and third degree are far from being totally solved. The equations considered in this paper are

urn:x-wiley:01611712:media:ijmm317827:ijmm317827-math-0001

Infinitely many solutions of each of these equations will be stated explicitly, using the results from the ACF discussed before.

It is known that the solutions of Pell′s equation are well exploited. We include it here because we shall use a common method to solve these three above mentioned equations and the method becomes very simple in Pell′s equations case.

Some new third and fifth degree combinatorial identities are derived from units in algebraic number fields.
On a subclass of Bazilevič functions
Authors: Thomas D. K.
Published: September 2002

Let B(α) be the class of normalised Bazilevič functions of type α > 0 with respect to the starlike function g. Let B1(α) be the subclass of B(α) when g(z) ≡ z. Distortion theorems and coefficient estimates are obtained for functions belonging to B1(α).
An algebraic characterization of complete inner product spaces
Authors: Istratescu Vasile I.
Published: September 2002

We present a characterization of complete inner product spaces using en involution on the set of all bounded linear operators on a Banach space. As a metric conditions we impose a “multiplicative” property of the norm for hermitain operators. In the second part we present a simpler proof (we believe) of the Kakutani and Mackney theorem on the characterizations of
complete inner product spaces. Our proof was suggested by an ingenious proof of a similar result obtained by N. Prijatelj.
Two‐dimensional source potentials in a two‐fluid medium for the modified Helmholtz′s equation
Authors: Mandal B. N. , Chakrabarti R. N.
Published: September 2002

Velocity potentials describing the irrotational infinitesimal motion of two superposed inviscid and incompressible fluids under gravity with a horizontal plane of mean surface of separation, are derived due to a vertical line source present in either of the fluids, whose strength, besides being harmonic in time, varies sinusiodally along its length. The technique of deriving the potentials here is an extension of the technique used for the case of only time harmonic vertical line source. The present case is concerned with the two‐dimensional modified Helmholtz′s equation while the previous is concerned with the two‐dimensional Laplace′s equation.
Notes on almost‐periodicity in topological vector spaces
Authors: N′guérékata Gaston Mandata
Published: September 2002

A study is made of almost‐periodic functions in topological vector spaces with applications to abstract differential equations.
Concepts of generalized bounded variation and the theory of Fourier series
Authors: Avdispahić M.
Published: September 2002

The aim of this article is to unify a large part of present knowledge about the behaviour of Fourier series of functions of generalized bounded variation. The connections between various concepts are discussed, particular attention being payed to those due to Waterman and Chanturiya. Exploiting the existing interactions and utilizing the power of one or another approach to some typical questions of the Fourier theory, a number of previously unnoticed results are obtained in the course of this exposition.
Certain near‐rings are rings, II
Authors: Bell Howard E.
Published: September 2002

We investigate distributively‐generated near‐rings R which satisfy one of the following conditions: (i) for each x, y ∈ R, there exist positive integers m, n for which xy = ymxn; (ii) for each x, y ∈ R, there exists a positive integer n such that xy = (yx)n. Under appropriate additional hypotheses, we prove that R must be a commutative ring.
A topology for automata II
Authors: Srivastava Arun K. , Shukla Wagish
Published: September 2002

A topology on the state set of an automaton is considered and it is shown that under this topology, genetically closed subsets and primaries, in the sense of Bavel [1] turn out to be precisely the regular closed subsets and minimal regular closed subsets respectively. The concept of a compact automaton is introduced and it is indicated that it can be viewed as a generalization of a finite automaton. Included also is an observation showing that our topological considerations can help recover some of the results of Dörfler [2].
On collineation groups of translation planes of order q4
Authors: Jha V. , Johnson N. L.
Published: September 2002

Let P be an affine translation plane of order q4 admitting a nonsolvable group G in its translation complement. If G fixes more than q + 1 slopes, the structure of G is determined. In particular, if G is simple then q is even and G = L2(2s) for some integer s at least 2.
p‐representable operators in Banach spaces
Authors: Khalil Roshdi
Published: September 2002

Let E and F be Banach spaces. An operator T ∈ L(E, F) is called p‐representable if there exists a finite measure μ on the unit ball, B(E*), of E* and a function g ∈ Lq(μ, F), , such that

urn:x-wiley:01611712:media:ijmm746286:ijmm746286-math-0002

for all x ∈ E. The object of this paper is to investigate the class of all p‐representable operators. In particular, it is shown that p‐representable operators form a Banach ideal which is stable under injective tensor product. A characterization via factorization through Lp‐spaces is given.
Cohyponormal operators with the single valued extension property
Authors: Lange Ridgley , Wang Shengwang
Published: September 2002

It is proved that in order to find a nontrivial hyperinvariant subspace for a cohyponormal operator it suffices to make the further assumption that the operator have the single‐valued extension property.
Diffeomorphism groups of connected sum of a product of spheres and classification of manifolds
Authors: Ajala Samuel Omoloye
Published: September 2002

In [1] and [2] a classification of a manifold M of the type (n, p, 1) was given where Hp(M) = Hn−p(M) = ℤ is the only non‐trivial homology groups. In this paper we give a complete classification of manifolds of the type (n, p, 2) and we extend the result to manifolds of type (n, p, r) where r is any positive integer and p = 3, 5, 6, 7mod(8).
On Bazilevic functions
Authors: Noor Khalida I. , Al-Bany Sumayya A.
Published: September 2002

Let B(β) be the class of Bazilevic functions of type β(β > 0). A function f ϵ B(β) if it is analytic in the unit disc E and , where g is a starlike function. We generalize the class B(β) by taking g to be a function of radius rotation at most kπ(k ≥ 2). Archlength, difference of coefficient, Hankel determinant and some other problems are solved for this generalized class. For k = 2, we obtain some of these results for the class B(β) of Bazilevic functions of type β.
An energy concerving modification of numerical methods for the integration of equations of motion
Authors: Labudde Robert A. , Greenspan Donald
Published: September 2002

In the integration of the equations of motion of a system of particles, conventional
numerical methods generate an error in the total energy of the same order as the truncation error. A simple modification of these methods is described, which results in exact conservation of the energy.
The Meijer transformation of generalized functions
Authors: Koh E. L. , Deeba E. Y. , Ali M. A.
Published: September 2002

This paper extends the Meijer transformation, Mμ, given by

urn:x-wiley:01611712:media:ijmm745171:ijmm745171-math-0001

,
where f belongs to an appropriate function space, μ ϵ (−1, ∞) and Kμ is the modified Bessel function of third kind of order μ, to certain generalized functions. A testing space is constructed so as to contain the Kernel, , of the transformation. Some properties of the kernel, function space and its dual are derived. The generalized Meijer transform, , is now defined on the dual space. This transform is shown to be analytic and an inversion theorem, in the distributional sense, is established.
Means with values in a Banach lattice
Authors: Chivukula R. Rao , Sarma I. Ramabhadra
Published: September 2002

Means, generalized means and invariant means (on a semigroup) with values
in a Banach lattice are defined and studied.
Finite p′‐nilpotent groups. II
Authors: Srinivasan S.
Published: September 2002

In this paper we continue the study of finite p′‐nilpotent groups that was started in the first part of this paper. Here we give a complete characterization of all finite groups that are not p′‐nilpotent but all of whose proper subgroups are p′‐nilpotent.
On some properties of polynomials rings
Authors: Al-Ezeh H.
Published: September 2002

For a commutative ring with unity R, it is proved that R is a PF‐ring if and only if the annihilator, , for each a ϵ R is a pure ideal in R, Also it is proved that the polynomial ring, R[X], is a PF‐ring if and only if R is a PF‐ring. Finally, we prove that R is a PP‐ring if and only if R[X] is a
PP‐ring.
Two‐point boundary value problems involving reflection of the argument
Authors: Gupta Chaitan P.
Published: September 2002

Two point boundary value problems involving reflection of the argument are
studied. The nonlinearity involved is allowed to cross asymptotically any number of eigenvalues of the associated linear eigenvalue problem as long as those crossings take place in subsets of sufficiently small measure.
Magnetohydrodynamic channel flow and variational principles
Authors: El-Hajj Adnan A.
Published: September 2002

This paper deals with magnetohydrodynamic channel flow problems. Attention is given to a variational principle where the boundary conditions are incorporated via a
suitable functional which is stationary at the solution of the given problem; the trial functions used for the approximate solution need not satisfy any of the given boundary conditions.
On M‐ideals in
Authors: Cho Chong-Man
Published: September 2002

For 1 < p, r < ∞, , {ni} bounded, the space K(X) of all compact operators on X is the only nontrivial M‐ideal in the space B(X) of all bounded linear operators on X.
Some generating functions of Laguerre polynomials
Authors: Thakurta Bidyut Kumar Guha
Published: September 2002

In this note a class of interesting generating relation, which is stated in the form of theorem, involving Laguerre polynomials is derived. Some applications of the theorem are also given here.
Transfer scattering matrix of non‐uniform surface acoustic wave transducers
Authors: Debnath N. C. , Roy T.
Published: September 2002

This paper is concerned with a general mathematical theory for finding the
admittance matrix of a three‐port non‐uniform surface acoustic wave (SAW) network characterized by n unequal hybrid sections. The SAW interdigital transducer and its various circuit model representations are presented in some detail. The Transfer scattering matrix of a transducer consisting of N non‐uniform sections modeled through the hybrid equivalent circuit is discussed. General expression of the scattering matrix elements for a N‐section SAW network is included. Based upon hybrid equivalent circuit model of one electrode section, explicit formulas for the scattering and transfer scattering matrices of a SAW transducer are obtained. Expressions of the transfer scattering matrix elements for the N‐section crossed‐field and in‐line model of SAW transducers are also derived as special cases. The matrix elements are computed in terms of complex frequency and thus allow for transient
response determinations. It is shown that the general forms presented here for the matrix elements are suitable for the computer aided design of SAW transducers.
The Lebesgue integral as a Riemann integral
Authors: Gonzalez-Velasco Enrique A.
Published: September 2002

The object of this paper is to develop a very direct theory of the Lebesgue
integral that is easily accessible to any audience familiar with the Riemann integral.
The sharpeness of some cluster set results
Authors: Rung D. C. , Obaid S. A.
Published: September 2002

We show that a recent cluster set theorem of Rung is sharp in a
certain sense. This is accomplished through the construction of an
interpolating sequence whose limit set is closed, totally disconnected and
porous. The results also generalize some of Dolzenko′s cluster set theorems.
Studies on the differential equations of enzyme kinetics. I. bimolecular scheme: simplified model
Authors: Marmasse Claude , Wiener Joseph
Published: September 2002

The main properties of the solution of the differential system of the model
are obtained by qualitative integration. The integral curve is compared with the
solutions given by the two classical approximations to the problem: it is shown that
the steady‐state approximation is to be preferred to the rapid equilibrium theory as
a general method and the conditions under which they will furnish accurate results
are discussed.
Strong laws of large numbers for arrays of rowwise independent random elements
Authors: Taylor Robert Lee , Hu Tien-Chung
Published: September 2002

Let {Xnk} be an array of rowwise independent random elements in a separable
Banach space of type p + δ with EXnk = 0 for all k, n. The complete convergence (and hence almost sure convergence) of , 1 ≤ p < 2, is obtained when {Xnk} are uniformly bounded by a random variable X with E|X|2p < ∞. When the array {Xnk} consists of i.i.d, random elements, then it is shown that converges completely to 0 if and only if .
Quadratic subfields on quartic extensions of local fields
Authors: Repka Joe
Published: September 2002

We show that any quartic extension of a local field of odd residue characteristic must contain an intermediate field. A consequence of this is that local fields of odd residue characteristic do not have extensions with Galois group A4 or S4. Counterexamples are given for even residue characteristic.
Summability methods based on the Riemann Zeta function
Authors: Chu Larry K.
Published: September 2002

This paper is a study of summability methods that are based on the Riemann Zeta function. A limitation theorem is proved which gives a necessary condition for a sequence x to be zeta summable. A zeta summability matrix Zt associated with a real sequence t is introduced; a necessary and sufficient condition on the sequence t such that Zt maps l1 to l1 is established. Results comparing the strength of the zeta method to that of well‐known summability methods are also investigated.
Two dimensional Laplace transforms of generalized hypergeometric functions
Authors: Dahiya R. S. , Jowhar I. H.
Published: September 2002

The object of this paper is to obtain new operational relations between the original and the image functions that involve generalized hypergeometric G‐functions.
Optimality and existence for Lipschitz equations
Authors: Henderson Johnny
Published: September 2002

Solutions of certain boundary value problems are shown to exist for the nth order differential equation y(n) = f(t, y, y′, …, y(n−1)), where f is continuous on a slab (a, b) × Rn and f satisfies a Lipschitz condition on the slab. Optimal length subintervals of (a, b) are determined, in terms of the Lipschitz coefficients, on which there exist unique solutions.
On some weak conditions of commutativity in common fixed point theorems
Authors: Imdad M. , Khan M. S. , Sessa S.
Published: September 2002

We generalize common fixed point theorems of Fisher and Sessa in complete metric spaces, using some conditions of weak commutativity between a set‐valued mapping and a single‐valued mapping. Suitable examples prove that these conditions do not imply each of the others.
Some results concerning exponential divisors
Authors: Hagis Peter
Published: September 2002

If the natural number n has the canonical form then is said to be an exponential divisor of n if bi|ai for i = 1, 2, …, r. The sum of the exponential divisors of n is denoted by σ(e)(n). n is said to be an e‐perfect number if σ(e)(n) = 2n; (m; n) is said to be an e‐amicable pair if σ(e)(m) = m + n = σ(e)(n); n0, n1, n2, … is said to be an e‐aliquot sequence if ni+1 = σ(e)(ni) − ni. Among the results established in this paper are: the density of the e‐perfect numbers is .0087; each of the first 10, 000, 000e‐aliquot sequences is bounded.
On rational solution of the state equation of a finite automaton
Authors: Chaudhuri R. , Höft H.
Published: September 2002

We prove that the necessary and sufficient condition for the state equation of a finite automaton M to have a rational solution is that the lexicographical Gödel numbers of the strings belonging to each of the end‐sets of M form an ultimately periodic set. A method of determining the existence of a rational solution of the state equation is also given.
on associative copulas uniformly close
Authors: Alsina C. , Ger R.
Published: September 2002

Associative copulas uniformly close are studied with detail. Some classical results of Ulam and Hyers as well as the representation theorem for associative functions play a fundamental role.
A note on certain subclass of close‐to‐convex functions
Authors: Owa Shigeyoshi , Liquan Liu , Ma Wancang
Published: September 2002

The object of the present paper is to show a result for functions belonging to class P′(1 − α, 0) which is a subclass of close‐to‐convex functions in the unit disk U.
On translativity of absolute Rogosinski‐Bernstein summability methods
Authors: Al-Madi Azmi K.
Published: September 2002

The paper is concerned with the problem of translativity of an absolute Rogosinski‐Bernstein summability methods (Bh); 0≦h≦1. The paper contains two results that when h; , |Bh| is translative and when h; , then |Bh| is not translative neither to the left nor to the right.
Computation of relative integral bases for algebraic number fields
Authors: Haghighi Mahmood
Published: September 2002

At first we are given conditions for existence of relative integral bases for extension (K; k) = n. Then we will construct relative integral bases for extensions , , .
A note on Bessel function dual integral equation with weight function
Authors: Mandal B. N.
Published: September 2002

An elementary procedure based on Sonine′s integrals has been used to reduce dual integral equations with Bessel functions of different orders as kernels and an arbitrary weight function to a Fredholm integral equation of the second kind. The result obtained here encompasses many results concerning dual integral equations with Bessel functions as kernels known in the literature.
A note on mass formula and Quark structure
Authors: Roy T.
Published: September 2002

A simple proof of the Gelmann‐Okubo mass formula for the baryon octet and decuplet is given in this note.
Some further results on Legendre numbers
Authors: Haggard Paul W.
Published: September 2002

The Legendre numbers, , are expressed in terms of those numbers, , in the previous column down to and in terms of those, , above but in the same column. Other results are given for numbers close to a given number. The limit of the quotient of two consecutive non‐zero numbers in any one column is shown to be −1. Bounds for the Legendre numbers are described by circles centered at the origin. A connection between Legendre numbers and Pascal numbers is exhibited by expressing the Legendre numbers in terms of combinations.
Subweakly α‐continuous functions
Authors: Rose David A.
Published: September 2002

In a recent paper by T. Noiri [1], a function f : X → Y is said to be weakly α‐continuous if f : Xα → Y is weakly continuous where Xα is the space X endowed with the α‐topolooy. Smilarly, we define subweak α‐continuity and almost α‐continuity and show that almost α‐continuity coincides with the almost continuity of T. Husain [2] and H. Blumberg [3]. This implies a functional tridecomposition of continuity using almost continuity and subweak α‐continuity.
The computation of the index of a Morse function at a critical point
Authors: Sakkalis Takis
Published: September 2002

A theoretical approach in computing the index of a Morse function at a critical point on a real non‐singular hypersurface V is given. As a consequence the Euler characteristic of V is computed. In the case where the hypersurface is polynomial and compact, a procedure is given that finds a linear function ℓ, whose restriction ℓ|V, is a Morse function on V.
Supersets for the spectrum of elements in extended Banach algebras
Authors: Seddighin Morteza
Published: September 2002

If A is a Banach Algebra with or without an identity, A can be always extended to a Banach algebra with identity, where is simply the direct sum of A and C, the algebra of complex numbers. In this note we find supersets for the spectrum of elements of .
On normal lattices and Wallman spaces
Authors: Eid George M.
Published: September 2002

Let X be an abstract set and Ω a lattice of subsets of X. The notion of Ω being mildly normal or slightly normal is investigated. Also, the general Wallman space with an alternate topology is investigated, and for Ω not necessarily disjunctive, an analogue of the Wallman space is constructed.
A decomposition into homeomorphic handlebodies with naturally equivalent involutions
Authors: Nelson Roger B.
Published: September 2002

Downing [6] extended the well‐known result that any closed 3‐manifold X contains a handlebody H such that c1(X − H) is homeomorphic to H in the case where X is a compact 3‐manifold with nonvoid boundary. We show that if X is a compact 3‐manifold with involution h having 2‐dimensional fixed point set, then X contains an h‐invariant handlebody H such that the involutions induced on H and c1(X − H) are naturally equivalent.
On the location of the zeros of analytic functions
Authors: Dewan K. K. , Govil N. K.
Published: September 2002

In this paper we obtain regions containing all the zeros of a class of analytic functions whose coefficients are subject to certain conditions. Our results sharpen some of the results known in this direction. Also we give some examples to show that in some cases the regions obtained by our results are considerably sharper than the regions obtained by known results.
On commutativity theorems for rings
Authors: Abujabal H. A. S. , Khan M. S.
Published: September 2002

Let R be an associative ring with unity. It is proved that if R satisfies the polynomial identity [xny − ymxn, x] = 0(m > 1, n ≥ 1), then R is commutative. Two or more related results are also obtained.
Strong oscillations for second order nonlinear functional differential equations
Authors: Yan Jurang
Published: September 2002

In this paper, we establish some strongly oscillation theorems for nonlinear second order functional differential equation

urn:x-wiley:01611712:media:ijmm685169:ijmm685169-math-0001

without assuming that g(t) is retarded or advanced.
Splaying a search tree in preorder takes linear time
Authors: Chaudhuri R. , Höft H.
Published: September 2002

In this paper we prove that if the nodes of an arbitrary n‐node binary search tree T are splayed according to the preorder sequence of T then the total time is O(n). This is a special case of the splay tree traversal conjecture of Sleator and Tarjan [1].
A necessary and sufficient condition for uniqueness of solutions of singular differential inequalities
Authors: Lair Alan V.
Published: September 2002

The author proves that the abstract differential inequality in which the linear operator A(t) = M(t) + N(t), M symmetric and N antisymmetric, is in general unbounded, ω(t) = t−2ψ(t)‖u(t)‖2 + ‖M(t)u(t)‖‖u(t)‖ and γ is a positive constant has a nontrivial solution near t = 0 which vanishes at t = 0 if and only if . The author also shows that the second order differential inequality in which has a nontrivial solution near t = 0 such that u(0) = u′(0) = 0 if and only if either or . Some mild restrictions are placed on the operators M and N. These results extend earlier uniqueness theorems of Hile and Protter.
On close‐to‐convex functions of complex order
Authors: Al-Amiri H. S. , Fernando Thotage S.
Published: September 2002

The class S*(b) of starlike functions of complex order b was introduced and studied by M.K. Aouf and M.A. Nasr. The authors using the Ruscheweyh derivatives introduce the class K(b) of functions close‐to‐convex of complex order b, b ≠ 0 and its generalization, the classes Kn(b) where n is a nonnegative integer. Here S*(b) ⊂ K(b) = K0(b). Sharp coefficient bounds are determined for Kn(b) as well as several sufficient conditions for functions to belong to Kn(b). The authors also obtain some distortion and covering theorems for Kn(b) and determine the radius of the largest disk in which every f ∈ Kn(b) belongs to Kn(1). All results are sharp.
Discrete quadratic splines
Authors: Rana Surendra Singh
Published: September 2002

In the present paper, we define a new class of discrete splines and study the existence, uniqueness, and convergence properties of discrete quadratic splines satisfying the Mean Averaging Condition.
On maximum‐entropy and related principles in statistical equilibrium
Authors: Chakrabarti C. G. , Mukhopadhyay V.
Published: September 2002

The paper aims to study the importance and equivalence of the principles of maximum‐entropy, and sufficient and stable inferences in the statistical characterization of the thermal equilibrium of a closed system.
The structure of homomorphisms from Banach algebras of differentiable functions into finite dimensional Banach algebras
Authors: Ngo Viet
Published: September 2002

We show that the structure of continuous and discontinuous homomorphisms from the Banach algebra Cn[0, 1] of n times continuously differentiable functions on the unit interval [0, 1] into finite dimensional Banach algebras is completely determined by higher point derivations.
A note on neighborhoods of analytic functions having positive real part
Authors: Walker Janice B.
Published: September 2002

Let P denote the set of all functions analytic in the unit disk D = {z||z| < 1} having the form with Re{p(z)} > 0. For δ ≥ 0, let Nδ(p) be those functions analytic in D with . We denote by P′ the class of functions analytic in D having the form with Re{[zp(z)]′} > 0. We show that P′ is a subclass of P and detemine δ so that Nδ(p) ⊂ P for p ∈ P′.
*‐Topological properties
Authors: Hamlett T. R. , Rose David
Published: September 2002

An ideal on a set X is a nonempty collection of subsets of X closed under the operations of subset (heredity) and finite unions (additivity). Given a topological space (X, τ) an ideal ℐ on X and A⊆X, ψ(A) is defined as ⋃{U ∈ τ : U − A ∈ ℐ}. A topology, denoted τ*, finer than τ is generated by the basis {U − I : U ∈ τ, I ∈ ℐ}, and a topology, denoted 〈ψ(τ)〉, coarser than τ is generated by the basis ψ(τ) = {ψ(U) : U ∈ τ}. The notation (X, τ, ϑ) denotes a topological space (X, τ) with an ideal ℐ on X. A bijection f : (X, τ, ℐ) → (Y, σ, J) is called a *‐homeomorphism if f : (X, τ*) → (Y, σ*) is a homeomorphism, and is called a ψ‐homeomorphism if f : (X, 〈ψ(τ)〉) → (Y, 〈ψ(σ)〉) is a homeomorphism. Properties preserved by *‐homeomorphisms are studied as well as necessary and sufficient conditions for a ψ
‐homeomorphism to be a *‐homeomorphism. The semi‐homeomorphisms and semi‐topological properties of Crossley and Hildebrand [Fund. Math., LXXIV (1972), 233‐254] are shown to be special case.
A note on maximally resolvable spaces
Authors: Tzannes V.
Published: September 2002

A.G. El′kin [1] poses the question as to whether any uncountable cardinal number can be the dispersion character of a Hausdorff maximally resolvable space.

In this note we prove that every cardinal number ℵ ≥ ℵ1 can be the dispersion character of a metric (hence, maximally resolvable) connected, locally connected space. We also proved that every cardinal number ℵ ≥ ℵ0 can be the dispersion character of a Hausdorff (resp. Urysohn, almost regular) maximally resolvable space X with the following properties: 1) Every continuous real‐valued function of X is constant, 2) For every point x of X, every open neighborhood U of x, contains an open neighborhood V of x such that every continuous real‐valued function of V is constant. Hence the space X is connected and locally connected and therefore there exists a countable connected locally connected Hausdorff (resp. Urysohn or almost regular) maximally resolvable space (not satisfying the first axiom of countability).
Generation of waves at an inertial surface due to explosions
Authors: Mandal B. N. , Ghosh N. K.
Published: September 2002

This paper is concerned with the generation of surface waves by an axially symmetric initial disturbance applied at an inertial surface in an ocean of finite depth. This initial disturbance can be either in the form of an impulse or an elevation or depression. The depression of the inertial surface is obtained as an infinite integral in each case. The method of stationary phase is applied to evaluate the integral for large values of time and distance.
An absolute continuity for positive operators on Banach lattices
Authors: Feldman W. , Piston C. , Piston Calvin E.
Published: September 2002

For positive operators on a Banach lattice, absolute contnuity
conditions are considered. An operator absolutely continuous with respect to
T is compared to sums of compositions of T together with orthomorphisms or in
special cases projections. Consequences For compact operators on functions
spaces C(X) are considered.
Dual integral equations involving Weber‐Orr transforms
Authors: Nasim C.
Published: September 2002

In this paper we consider dual integral equations involving inverse
Weber‐Orr transforms of the type , k = 0, 1, …. A general solution is
established using elementary methods. Many known results are derived as special cases.
Associated transforms for solution of nonlinear equations
Authors: Debnath Joyati , Debnath Narayan C.
Published: September 2002

Nonlinear multivariable differential or integrodifferential equations with terms of
mixed dimensionality can be solved using multidimensional Laplace transform. The special
technique used to find the inverse of the multidimensional Laplace transform is known as
the association of variables. In this paper, some basic theorems are developed for the theory
of association. Examples are presented for each theorem. Once the basic theorems are
established, it is possible to derive many useful ssociated pairs.
Some inequalities for maximum modules of polynomials
Authors: Govil N. K.
Published: September 2002

A well‐known result of Ankeney and Rivlin states that if p(z) is a polynomial of degree
n, such that p(z) ≠ 0 in |z| < 1, then . In this paper we prove
some generalizations and refinements of this result.
Property Q
Authors: Bandy C.
Published: September 2002

Some properties of property Q are stated, some new results are proved and implications
to totally metacompact and totally paracompact are obtained.
On isomorphisms and hyper‐reflexivity of closed subspace lattices
Authors: Deguang Han
Published: September 2002

There are some papers, such as [1], [2] and [3], in which some properties on
isomorphism of closed subspace lattices of Hilbert spaces were studied. In this short paper we will
point out that the hyper‐reflexivity of closed subspace lattice is invariant under isomorphism of
ξ(H1) on ξ(H2). We also proved that if T is in L(H) such that and ℱ is a hyper‐reflexive
subspace lattice, then ϕT(ℱ) ∪ {H} is hyper‐reflexive where ϕT is a homomorphism induced by T.
Generalizations of the primitive element theorem
Authors: Nikolopoulos Christos , Nikolopoulos Panagiotis
Published: September 2002

In this paper we generalize the primitive element theorem to the
generation of separable algebras over fields and rings. We prove that any
finitely generated separable algebra over an infinite field is generated by
two elements and if the algebra is commutative it can be generated by one
element. We then derive similar results for finitely generated separable
algebras over semilocal rings.
Groups of homeomorphisms and normal subgroups of the group of permutations
Authors: Ramachandran P. T.
Published: September 2002

In this paper, it is proved that no nontrivial proper normal subgroup of
the group of permutations of a set X can be the group of homeomorphisms of (X, T) for
any topology T on X.
Partial differential equations with piecewise constant delay
Authors: Wiener Joseph , Debnath Lokenath
Published: September 2002

The influence of certain discontinuous delays on the behavior of solutions to partial
differential equations is studied. In Section 2, the initial value problems (IVP) are discussed for differential
equations with piecewise constant argument (EPCA) in partial derivatives. A class of loaded partial
differential equations that arise in solving certain inverse problems is studied in some detail in Section 3.
Section 4 is devoted to obtain the solutions of IVP for linear partial differential equations with piecewise
constant delay by using integral transforms. Finally, an abstract Cauchy problem is discussed.
On the integrability of a K‐conformal killing equation in a Kaehlerian manifold
Authors: Takano Kazuhiko
Published: September 2002

We show that necessary and sufficient condition in order that K‐ conformal
Killing equation is completely integrable is that the Kaehlerian manifold K2m(m > 2) is of constant holomorphic sectional curvature.
Splaying a search tree in preorder takes linear time
Authors: Chaudhuri R. , Höft H.
Published: September 2002

In this paper we prove that if the nodes of an arbitrary n‐node binary
search tree T are splayed in the preorder sequence of T then the total time is O(n).
This is a special case of the splay tree traversal conjecture of Sleator and Tarjan.
A problem of thermal shock with thermal relaxation
Authors: Ramamurthy D. , Sharma A. V. Manohara
Published: September 2002

The problem of a semi‐infinite medium subjected to thermal shock on its
plane boundary is solved using the generalized theory of thermoelasticity. The
expressions for temperature, strain and stress are presented. The results are
exhibited graphically and compared with previous results.