bluuebunny/crossref_metadata_2025 huggingface dataset:
Space‐time caustics
Authors: Gorman Arthur D.
Published: September 2002

The Lagrange manifold (WKB) formalism enables the determination of the asymptotic series solution of linear differential equations modelling wave propagation in spatially inhomogeneous media at caustic (turning) points. Here the formalism is adapted to determine a class of asymptotic solutions at caustic points for those equations modelling wave propagation in media with both spatial and temporal inhomogeneities. The analogous Schrodinger equation is also considered.
On the complete integrability of an equation having solitons but not known to have a Lax pair
Authors: Roychowdhury A. , Mahato G.
Published: September 2002

It is usually assumed that a system having N‐soliton solutions is completely integrable. Here we have analyzed a set of equations occuring in case of capillary gravity waves. Though the system under discussion has N‐soliton solutions, it has yet to be shown that the system is completely integrable. No Lax pair is known for the system. Here we show that the system is not completely integrable in the sense of Ablowitz et al.
On the general solution of a functional equation connected to sum form information measures on open domain—III
Authors: Kannappan Pl. , Sahoo P. K.
Published: September 2002

In this series, this paper is devoted to the study of a functional equation connected with the characterization of weighted entropy and weighted entropy of degree β. Here, we find the general solution of the functional equation (2) on an open domain, without using 0‐probability and 1‐probability.
Graphs and projective plaines in 3‐manifolds
Authors: Heil Wolfgang , Negami Seiya
Published: September 2002

Proper homotopy equivalent compact P2‐irreducible and sufficiently large 3‐manifolds are homemorphic. The result is not known for irreducible 3‐manifolds that contain 2‐sided projective planes, even if one assumes the Poincaré conjecture. In this paper to such a 3‐manifold M is associated a graph G(M) that specifies how a maximal system of mutually disjoint non‐isotopic projective planes is embedded in M, and it is shown that G(M) is an invariant of the homotopy type of M. On the other hand it is shown that any given graph can be realized as G(M) for infinitely many irreducible and boundary irreducible M.

As an application it is shown that any closed irreducible 3‐manifold M that contains 2‐sided projective planes can be obtained from a P2‐irreducible 3‐manifold and P2 × S1 by removing a solid Klein bottle from each and gluing together the resulting boundaries: furthermore M contains an orientation preserving simple closed curve α such that any nontrivial Dehn surgery along α yields a P2‐irreducible 3‐manifold.
Numerical methods for approximating eigenvalues of boundary value problems
Authors: Usmani Kiaz A. , Isa Mohammad
Published: September 2002

This paper describes some new finite difference methods for the approximation of eigenvalues of a two point boundary value problem associated with a fourth order linear differential equation of the type . The smallest positive eigenvalue of some typical eigensystems is computed to demonstrate the practical usefulness of the numerical techniques developed.
Iterations converging to distinct solutions of some nonlinear operator equations in Banach space
Authors: Argyros Ioannis K.
Published: September 2002

We examine the solvability of multilinear equations of the form

urn:x-wiley:01611712:media:ijmm906809:ijmm906809-math-0001

where Mk is a k‐linear operator on a Banach space X and y ∈ X is fixed.
Character induction in p‐groups
Authors: Coloma Teresa L. Santa
Published: September 2002

Let G be a finite p‐group and let χ be an irreducible character of G. Then χ is monomial; that is, χ = λG, where λ is a linear character of some subgroup of G. We are interested in locating subgroups of G which induce the character χ.
Almost periodic motion in complete space
Authors: Kumar Anant
Published: September 2002

It is interesting that in a complete space an almost periodic motion is periodic if the null set ϕ is closed and if ϕ is not closed then every point of its trajectory is a limit point.
Cyclotomy of order 15 over GF(p2), p = 4, 11(mod15)
Authors: Friesen Christian , Muskat Joseph B. , Spearman Blair K. , Williams Kenneth S.
Published: September 2002

For primes p ≡ 4, 11(mod15) explicit formulae are obtained for the cyclotomic numbers of order 15 over GF(p2).
Decomposition solution for Duffing and Van der Pol oscillators
Authors: Adomian G.
Published: September 2002

The decomposition method is applied to solve the Duffing and Van der Pol oscillators without customary restrictive assumptions [1‐4] and without resort to perturbation methods.
Pseudo‐Sasakian manifolds endowed with a contact conformal connection
Authors: Goldberg Vladislav V. , Rosca Radu
Published: September 2002

Pseudo‐Sasakian manifolds endowed with a contact conformal connection are defined. It is proved that such manifolds are space forms , K < 0, and some remarkable properties of the Lie algebra of infinitesimal transformations of the principal vector field on are discussed. Properties of the leaves of a co‐isotropic foliation on and properties of the tangent bundle manifold having as a basis are studied.
Quasi‐adjoint third order difference equations: oscillatory and asymptotic behavior
Authors: Smith B.
Published: September 2002

In this paper, asymptotic properties of solutions of

urn:x-wiley:01611712:media:ijmm806976:ijmm806976-math-0001

are investigated via the quasi‐adjoint equation

urn:x-wiley:01611712:media:ijmm806976:ijmm806976-math-0002

A necessary and sufficient condition for the existence of oscillatory solutions of (E+) is given. An example showing that it is possible for (E+) to have only nonoscillatory solutions is also given.

Corrigendum: Quasi-adjoint third order difference equations: oscillatory and asymptotic behaviordx.doi.org/10.1155/S0161171287000747
A generalization of a theorem by Cheo and Yien concerning digital sums
Authors: Cooper Curtis N. , Kennedy Robert E.
Published: September 2002

For a non‐negative integer n, let s(n) denote the digital sum of n. Cheo and Yien proved that for a positive integer x, the sum of the terms of the sequence

urn:x-wiley:01611712:media:ijmm846161:ijmm846161-math-0001

is (4.5)xlogx + 0(x). In this paper we let k be a positive integer and determine that the sum of the sequence

urn:x-wiley:01611712:media:ijmm846161:ijmm846161-math-0002

is also (4.5)xlogx + 0(x). The constant implicit in the big‐oh notation is dependent on k.
An hypervaluation of a ring onto a totally orderednon‐cancellative semigroup without zero divisors
Authors: Papadopoulos John
Published: September 2002

In this paper we answer to a question posed by Marc KRANSER: It is possible to have a totally ordered noncancellative semigroup without zero divisors, and a ring hypervaluated by this semigroup? We were able to give a positive answer and provide an example.
On a generalization of Hausdorff space
Authors: Dutta Tapas
Published: September 2002

Here, a new separation axiom as a generalization of that of Hausdorff is introduced. Its simple consequences and relations with some other known separation axioms are studied. That a non‐indiscrete topological group satisfies this axiom is shown.
Holomorphic extension of generalizations of Hp functions. II
Authors: Carmichael Richard D.
Published: September 2002

In a previous article we have obtained a holomorphic extension theorem (edge of the wedge theorem) concerning holomorphic functions in tubes in ℂn which generalize the Hardy Hp functions for the cases 1 < p ≤ 2. In this paper we obtain a similar holomorphic extension theorem for the cases 2 < p < ∞.
On complex L1‐predual spaces
Authors: Das Mrinal Kanti
Published: September 2002

This paper contains some characterisations of complex L‐balls, including interpolation theorems which are analogs of Edward′s separation theorem for simplices.
Properties of some weak forms of continuity
Authors: Noiri Takashi
Published: September 2002

As weak forms of continuity in topological spaces, weak continuity [1], quasi continuity [2], semi continuity [3] and almost continuity in the sense of Husain [4] are well‐known. Recently, the following four weak forms of continuity have been introduced: weak quasi continuity [5], faint continuity [6], subweak continuity [7] and almost weak continuity [8]. These four weak forms of continuity are all weaker than weak continuity. In this paper we show that these four forms of continuity are respectively independent and investigate many fundamental properties of these four
weak forms of continuity by comparing those of weak continuity, semi continuity and almost continuity.
Gaps in the sequence n2ϑ(mod1)
Authors: Drobot Vladimir
Published: September 2002

Let ϑ be an irrational number and let {t} denote the fractional part of t. For each N let I0, I1, …, IN be the intervals resulting from the partition of [0, 1] by the points {k2ϑ}, k = 1, 2, …, N. Let T(N) be the number of distinct lengths these intervals can assume. It is shown that T(N) → ∞. This is in contrast to the case of the sequence {nϑ}, where T(N) ≤ 3.
Some limit theorems for ratios of transition probabilities
Authors: Chattopadhyay Rita
Published: September 2002

In this paper, infinite dimensional forward convergent stochastic chains have been considered in the framework of [1]. The main result of this paper deals with the observation that the total flow of probability from the C‐states to the T‐states is very small compared to that from the T‐states to the C‐states, if the chain is observed for a sufficiently long time. Some examples have been given to justify the assumptions involved.
Rayleigh wave scattering at the foot of a mountain
Authors: Deshwal P. S. , Mann K. K.
Published: September 2002

A theoretical study of scattering of seismic waves at the foot of a mountain is discussed here. A mountain of an arbitrary shape and of width a (0 ≤ x ≤ a, z = 0) in the surface of an elastic solid medium (z ≥ 0) is hit by a Rayleigh wave. The method of solution is the technique of Wiener and Hopf. The reflected, transmitted and scattered waves are obtained by inversion of Fourier transforms. The scattered waves behave as decaying cylindrical waves at distant points and have a large amplitude near the foot of the mountain. The transmitted wave decreases exponentially as its distance from the other end of the mountain increases.
Functional equation of a special Dirichlet series
Authors: Abou-Tair Ibrahim A.
Published: September 2002

In this paper we study the special Dirichlet series

urn:x-wiley:01611712:media:ijmm308272:ijmm308272-math-0001

This series converges uniformly in the half‐plane Re(s) > 1 and thus represents a holomorphic function there. We show that the function L can be extended to a holomorphic function in the whole complex‐plane. The values of the function L at the points 0, ±1, −2, ±3, −4, ±5, … are obtained. The values at the positive integers 1, 3, 5, … are determined by means of a functional equation satisfied by L.
Even perfect numbers and their Euler′s function
Authors: Asadulla Syed
Published: September 2002

The purpose of this article is to prove some results on even perfect numbers and on their Euler′s function. The results obtained are all straightforward deductions from well‐known elementary number theory.
An existence theorem for optimal control with nonstandard cost functionals
Authors: Mukherjee R. N. , Prasad Shiv
Published: September 2002

An existence theorem for optimal control is obtained for a general nonstandard cost functional of fractional type in this work. As an application of our result we can derive an existence theorem for optimal control given by M. B. Subrahamanyam for a cost functional, which is a ratio of two given integral cost functionals.
Generalization of certain subclasses of analytic functions
Authors: Sekine Tadayuki
Published: September 2002

We introduce the subclass Tj(n, m, α) of analytic functions with negative coefficients by the operator Dn. Coefficient inequalities and distortion theorems of functions in Tj(n, m, α) are determind. Further, distortion theorems for fractional calculus of functions in Tj(n, m, α) are obtained.
Rational choice function derived from a fuzzy preference
Authors: Kim Jin Bai , Kymn Kern O.
Published: September 2002

We shall prove that every fuzzy rational choice function is fuzzy regular (see Richter [6, p. 36] ), count the total number of the fuzzy rational choice ftmctions on a set of four elements and consider a semigroup of all fuzzy rational choice functions on a set.
New classification of analytic functions with negative coefficients
Authors: Owa Shigeyoshi , Obradović Milutin
Published: September 2002

New classification of analytic functions with negative coefficients is given by using the coefficients inequality, that is, new subclass A(p, n, Bk) of analytic functions with negative coefficient is defined. The object of the present paper is to prove various distortion theorems for functions in A(p, n, Bk), and for fractional calculus of functions belonging to A(p, n, Bk). Further, some properties of the class A(p, n, Bk) are shown.
On singular projective deformations of two second class totally focal pseudocongruences of planes
Authors: Goldberg Ludmila
Published: September 2002

Let be a projective deformation of the second order of two totally focal pseudocongruences L and of (m − 1)‐planes in projective spaces Pn and , 2m − 1 ≤ n < 3m − 1, and let K be a collineation realizing such a C. The deformation C is said to be weakly singular, singular, or α‐strongly singular, α = 3, 4, …, if the collineation K gives projective deformations of order 1, 2 or α of all corresponding focal surfaces of L and . It is proved that C is weakly singular and conditions are found for C to be singular. The pseudocongruences L and are identical if and only if C is 3‐strongly singular.
The semigroup of nonempty finite subsets of rationals
Authors: Spake Reuben
Published: September 2002

Let Q be the additive group of rational numbers and let ℛ be the additive semigroup of all nonempty finite subsets of Q. For X ∈ ℛ, define AX to be the basis of 〈X − min(X)〉 and BX the basis of 〈max(X) − X〉. In the greatest semilattice decomposition of ℛ, let 𝒜(X) denote the archimedean component containing X. In this paper we examine the structure of ℛ and determine its greatest semilattice decomposition. In particular, we show that for X, Y ∈ ℛ, 𝒜(X) = 𝒜(Y) if and only if AX = AY and BX = BY. Furthermore, if X is a non‐singleton, then the idempotent‐free 𝒜(X) is isomorphic to the direct product of a power joined subsemigroup and the group Q.
On star polynomials, graphical partitions and reconstruction
Authors: Farrell E. J. , de Matas C. M.
Published: September 2002

It is shown that the partition of a graph can be determined from its star polynomial and an algorithm is given for doing so. It is subsequently shown (as it is well known) that the partition of a graph is reconstructible from the set of node‐deleted subgraphs.
A note on the unique solvability of a class of nonlinear equations
Authors: Sen Rabindranath , Mukherjee Sulekha
Published: September 2002

The aim of the present note is to devise a simple criterion for the existence of the unique solution of a class of nonlinear equations whose solvability is taken for granted.
An identity for a class of arithmetical functions of two variables
Authors: Chidambaraswamy J. , Krishnaiah P. V.
Published: September 2002

For a positive integer r, let r∗ denote the quotient of r by its largest squarefree divisor (1∗ = 1). Recently, K. R. Johnson proved that

urn:x-wiley:01611712:media:ijmm180307:ijmm180307-math-0001

according as r∗|n or not where C(n, r) is the well known Ramanujan′s sum. In this paper, using a different method, we generalize (∗) to a wide class of arithmetical functions of 2 variables and deduce as special cases (∗) and similar formulae for several generalizations of Ramanujan′′s sum.
On sequences of contractive mappings and their fixed points
Authors: Imdad M. , Khan M. S. , Sessa S.
Published: September 2002

By using a condition of Reich, we establish two fixed point theorems concerning sequences of contractive mappings and their fixed points. A suitable example is also given.
Ring source potentials in two superposed fluids separeted by an inertial surface
Authors: Mandal B. N. , Kundu Krishna
Published: September 2002

The study of waves at the interface of two superposed fluids due to the presence of a vertical body of revolution requires the consideration of potentials due to horizontal ring sources submerged in one of the fluids. In this paper, the velocity potentials in the two fluids are computed due to a horizontal ring of sources of time‐dependent strength submerged in either of the fluids of a two‐fluid medium that are separated by an inertial surface.
Matrix transformations and convex spaces
Authors: Maddox I. J.
Published: September 2002

In a Hausdorff topological linear space we examine relations between r‐convexity and a condition on matrix transformations between null sequences. In particular, for metrizable spaces the condition implies r‐convexity. For locally bounded spaces the condition implies sequential completeness.
Ordered compactification of totally ordered spaces
Authors: Kent D. C. , Richmond T. A.
Published: September 2002

A complete description of the T2‐ordered compactifications of a totally ordered space X is given in terms of the simple and essential singularities.
Smooth structures on sphere bundles over spheres
Authors: Ajala Samuel Omoloye
Published: September 2002

In [1] R. De Sapio gave a classification of smooth structures of a p‐sphere bundle over a q‐sphere with one cross‐section and p < q. In [2] J. Munkres also gave a classification up to concordance of differential structures in the case where the bundle has at least two cross‐sections. In [3] R. Schultz gave a classification in the case p ≥ q. Here we will give a classification of the p‐sphere bundle over a q‐sphere without any cross‐section and p < q.
Some congruence properties of binomial coefficients and linear second order recurrences
Authors: Robbins Neville
Published: September 2002

Using elementary methods, the following results are obtained:(I) If p is prime, 0 ≤ m ≤ n, 0 < b < apn−m, and p∤ab, then ; If r, s are the roots of x2 = Ax − B, where (A, B) = 1 and D = A2 − 4B > 0, if , vn = rn + sn, and k ≥ 0, then (II) ; (III) If p is odd and p∤D, then ; (IV) .
Periodic solutions of Volterra integral equations
Authors: Islam M. N.
Published: September 2002

Consider the system of equations

urn:x-wiley:01611712:media:ijmm793746:ijmm793746-math-0001

and

urn:x-wiley:01611712:media:ijmm793746:ijmm793746-math-0002

Existence of continuous periodic solutions of (1) is shown using the resolvent function of the kernel k. Some important properties of the resolvent function including its uniqueness are obtained in the process. In obtaining periodic solutions of (1) it is necessary that the resolvent of k is integrable in some sense. For a scalar convolution kernel k some explicit conditions are derived to determine whether or not the resolvent of k is integrable. Finally, the existence and uniqueness of continuous periodic solutions of (1) and (2) are btained using the contraction mapping principle as the basic tool.
Completeness of regular inductive limits
Authors: Kucera Jan , McKennon Kelly
Published: September 2002

Regular LB‐space is fast complete but may not be quasi‐complete. Regular
inductive limit of a sequence of fast complete, resp. weakly quasi‐complete, resp.
reflexive Banach, spaces is fast complete, resp. weakly quasi‐complete, resp. reflexive
complete, space.
The diophantine equation ni + 1 = k(dn − 1)
Authors: Ligh Steve , Bourque Keith
Published: September 2002

The Diophantine equation of the title is solved for i = 3, 4
and an infinite
family of solutions were found for i ≥ 5.
Common fixed points of compatible mappings
Authors: Kang S. M. , Cho Y. J. , Jungck G.
Published: September 2002

In this paper, we present a common fixed point theorem for compatible mappings, which extends the results of Ding, Diviccaro‐Sessa and the third author.
A note on analytic measures
Authors: Asmar Nakhle
Published: September 2002

Let G be a compact Abelian group with character group X. Let S be a subset of X such that, for some real‐valued homomorphism ψ on X, the set S ⋂ ψ−1(]−∞, ψ(χ)]) is finite for all χ in X. Suppose that μ is a measure in M(G) such that vanishes off of S, then μ is absolutely continuous with respect to the Haar measure on G.
A note on Tauberian operators
Authors: Araujo Jesús , Martinez-Maurica J.
Published: September 2002

In this note we prove the existence of operators which are not Tauberian even though they satisfy properties about restrictions being Tauberian. The operators are defined on Banach spaces which contain a somewhat reflexive, non‐reflexive subspace. This gives an answer to a question proposed by R. Neidinger [1].
Weighted additive information measures
Authors: Sander Wolfgang
Published: September 2002

We determine all measurable functions I, G, L : [0, 1] → ℝ satisfying the functional equation for P ∈ Γn, Q ∈ Γm and for a fixed pair (n, m), n ≥ 3, m ≥ 3, where G(0) = L(0) = 0 and G(1) = L(1) = 1. This functional equation has interesting applications in information theory.
On a fixed point theorem of Fisher and Sessa
Authors: Jungck Gerald
Published: September 2002

A fixed point theorem of Fisher and Sessa is generalized by replacing the requirements of commutativity and nonexpansiveness by compatibility and continuity respectively.
Quasi‐bounded sets
Authors: Kucera Jan
Published: September 2002

It is proved in [1] & [2] that a set bounded in an inductive limit E = indlim En of Fréchet spaces is also bounded in some En iff E is fast complete. In the case of arbitrary locally convex spaces En every bounded set in a fast complete indlim En is quasi‐bounded in some En, though it may not be bounded or even contained in any En. Every bounded set is quasi‐bounded. In a Fréchet space every quasi‐bounded set is also bounded.
Explicit solutions of Fisher′s equation with three zeros
Authors: Abur-Robb M. F. K.
Published: September 2002

Explicit traveling wave solutions of Fisher′s equation with three simple zeros ut = uxx + u(1 − u)(u − a), a ∈ (0, 1), are obtained for the wave speeds suggested by pure analytic considerations. Two types of solutions are obtained: one type is of a permanent wave form whereas the other is not.
Stable matrices, the Cayley transform, and convergent matrices
Authors: Haynes Tyler
Published: September 2002

The main result is that a square matrix D is convergent () if and
only if it is the Cayley transform CA = (I − A) −1(I + A) of a stable matrix A, where a stable matrix
is one whose characteristic values all have negative real parts. In passing, the concept of
Cayley transform is generalized, and the generalized version is shown closely related to the
equation AG + GB = D. This gives rise to a characterization of the non‐singularity of the
mapping X → AX + XB. As consequences are derived several characterizations of stability
(closely related to Lyapunov′s result) which involve Cayley transforms.
On maximal measures with respect to a lattice
Authors: Camacho James
Published: September 2002

Outer measures are used to obtain measures that are maximal with respect to
a normal lattice. Alternate proofs are then given extending the measure theoretic
characterizations of a normal lattice to an arbitrary, non‐negative finitely additive
measure on the algebra generated by the lattice. Finally these general results are
used to consider σ‐smooth measures with respect to the lattice when further conditions
on the lattice hold.
On approximation of the solutions of delay differential equations by using piecewise constant arguments
Authors: Györi Istevan
Published: September 2002

By using the Gronwall Bellman inequality we prove some limit relations
between the solutions of delay differential equations with continuous arguments and the
solutions of some related delay differential equations with piecewise constant
arguments(EPCA). EPCA are strongly related to some discrete difference equations
arising in numerical analysis, therefore the results can be used to compute numerical
solutions of delay differential equations. We also consider the delay differential
equations of neutral type by applying a generalization of the Gronwall Bellman
inequality.
Solvability of a fourth‐order boundary value problem with periodic boundary conditions II
Authors: Gupta Chaitan P.
Published: September 2002

Let f : [0, 1] × R4 → R be a function satisfying Caratheodory′s conditions and
e(x) ∈ L1[0, 1]. This paper is concerned with the solvability of the fourth‐order fully quasilinear boundary
value problem

urn:x-wiley:01611712:media:ijmm908081:ijmm908081-math-0001

with u(0) − u(1) = u′(0) − u′(1) = u″(0) − u″(1) = u‴(0) − u‴(1) = 0. This problem was studied earlier by
the author in the special case when f was of the form f(x, u(x)), i.e., independent of u′(x), u″(x), u‴(x).
It turns out that the earlier methods do not apply in this general case. The conditions need to be related to
both of the linear eigenvalue problems
and with periodic boundary conditions.
On Hilbert polynomial of certain determinantal ideals
Authors: Udpikar Shrinivas G.
Published: September 2002

Let X = (Xij) be an m(1) by m(2) matrix whose entries Xij, 1 ≤ i ≤ m(1),
1 ≤ j ≤ m(2); are indeterminates over a field K. Let K[X] be the polynomial ring in
these m(1)m(2) variables over K. A part of the second fundamental theorem of
Invariant Theory says that the ideal I[p + 1] in K[X], generated by (p + 1) by (p + 1)
minors of X is prime. More generally in [1], Abhyankar defines an ideal I[p + a] in
K[X], generated by different size minors of X and not only proves its primeness but
also calculates the Hilbert function as well as the Hilbert polynomial of this
ideal. The said Hilbert polynomial is completely determined by certain integer valued
functions FD(m, p, a). In this paper we prove some important properties of these
integer valued functions.
Fixed points of multivalued nonexpansive maps
Authors: Husain T. , Latif Abdul
Published: September 2002

Fixed point theorems for multivalued contractive‐type and nonexpansive‐type
maps on complete metric spaces and on certain closed bounded convex subsets of
Banach spaces have been proved. They extend some known results due to Browder, Husain
and Tarafdar, Karlovitz and Kirk.
On the ideals of extended quasi‐nilpotent Banach algebras
Authors: Seddighin Morteza
Published: September 2002

Given a quasi‐nilpotent Banach algebra A, we will use the results of
Seddighin [2], to study the properties of elements which belong to a proper closed two
sided ideal of and . Here is the extension of A to a Banach Algebra with
identity.
Submanifolds of Euclidean space with parallel mean curvature vector
Authors: Ghazal Tahsin , Deshmukh Sharief
Published: September 2002

The object of the paper is to study some compact
submanifolds in the Euclidean space Rn whose mean curvature
vector is parallel in the normal bundle. First we prove that
there does not exist an n‐dimensional compact simply connected
totally real submanifold in R2n whose mean curvature vector is
parallel. Then we show that the n‐dimensional compact totally
real submanifolds of constant curvature and parallel mean
curvature in R2n are flat. Finally we show that compact
Positively curved submanifolds in Rn with parallel mean
curvature vector are homology spheres. The last result in
particular for even dimensional submanifolds implies that their
Euler poincaré characteristic class is positive, which for the
class of compact positively curved submanifolds admiting isometric
immersion with parallel mean curvature vector in Rn, answers the
problem of Chern and Hopf
Bounds for distribution functions of sums of squares and radial errors
Authors: Nelsen Roger B. , Schweizer Berthold
Published: September 2002

Bounds are found for the distribution function of the sum of squares X2 + Y2 where X and
Y are arbitrary continuous random variables. The techniques employed, which utilize copulas and their
properties, show that the bounds are pointwise best‐possible when X and Y are symmetric about 0 and
yield expressions which can be evaluated explicitly when X and Y have a common distribution function
which is concave on (0, ∞). Similar results are obtained for the radial error (X2 + Y2)1/2. The important
case where X and Y are normally distributed is discussed, and here best‐possible bounds on the circular
probable error are also obtained.
On the stationary vibrations of a rectangular plate subjected to stress prescribed partially at the circumference
Authors: El Sheikh M. G. , Khater A. H. , Callebaut D. K.
Published: September 2002

The stationary periodical problem of a vibrating rectangular plate, stressed at a segment
while fixed elsewhere at one of its edges, is considered. Using the finite Fourier transformation, the problem
is converted to a singular integral equation that in turn can be reduced to an infinite system of algebraic
equations. The truncation of the algebraic system is justified.
When in a multiplicative derivation additive?
Authors: Daif Mohamad Nagy
Published: September 2002

Our main objective in this note is to prove the following. Suppose R is a
ring having an idempotent element e(e ≠ 0,  e ≠ 1) which satisfies:

urn:x-wiley:01611712:media:ijmm275743:ijmm275743-math-0001

If d is any multiplicative derivation of R, then d is additive.
Stochastic orderings induced by star‐shaped functions
Authors: Krieger Henry A.
Published: September 2002

The non‐decreasing functions whicl are star‐shaped and supported above at each point
of a non‐empty closed proper subset of the real line induce an ordering, on the class of distribution
functions with finite first moments, that is strictly weaker than first degree stochastic
dominance and strictly stronger than second degree stochastic dominance. Several characterizations
of this ordering are developed, both joint distribution criteria and those involving
only marginals. Tle latter are deduced from a decomposition theorem, which reduces the
problem to consideration of certain functions which are star‐shaped on the complement of
an open interval.
On the three‐dimensional CR‐submanifolds of the six‐dimensional sphere
Authors: Bashir M. A.
Published: September 2002

We show that the six‐dimensional sphere does not admit three‐dimensionel totally
umbilical proper CR‐submanifolds.
Remarks on quasilinear evolutions equations
Authors: Rivera James E. Munoz
Published: September 2002

In this paper we study the existence result of classical solutions for the quasilinear equation , with initial data u(0) = u0, u(1) = u1 and homogeneous boundary conditions.
Some remarks on inequalities that characterize inner product spaces
Authors: Alonso Javier
Published: September 2002

The purpose of this paper is to obtain some new characterizations of inner product spaces in the line of the Jordan‐von Neumann identity and to make some remarks on similar known characterizations of Day, Delbosco, Rassias and Senechalle, among others.
On normal lattices and separation and semi‐separation of lattices
Authors: Schutz Robert W.
Published: September 2002

This present paper is concerned with two main conditions, that of normality of a lattice, and separation and semi‐separation of two lattices, both looked at using measure theoretic techniques. We look at each property using {0, 1} two valued measures and associated {0, 1} valued set functions.

For normal lattices we look at consequences of normality in terms of properties of their measures and closely allied set functions. For separation and semi‐separation of two lattices, we investigate the realtionship between regular measures of both lattices, define the notion of weak going up and look at this notion in terms of separation and semi‐separation. We then give necessary and sufficent conditions for semi‐separation in terms of equality of two set fuctions, derived from regular measures on the smaller lattice on the larger lattice.
Γ‐group congruences on regular Γ‐semigroups
Authors: Seth A.
Published: September 2002

In this paper a Γ‐group congruence on a regular Γ‐semigroup is defined, some equivalent expressions for any Γ‐group congruence on a regular Γ‐semigroup and those for the least Γ‐group congruence in particular are given.
Long range scattering with Stark effect and almost periodic potentials
Authors: White Denis A. W.
Published: September 2002

Spectral and scattering theory is discussed for the Stark effect Hamiltonians H0 = −(1/2)Δ − x1 and H = H0 + V where V is a long range perturbation. Most significantly, in one dimension, and for V consisting of a slowly decaying term and an almost periodic term, the two Hilbert space wave operators (of Isozaki and Kitada) are shown to exist and be complete by Enss′s time dependent method.
A note on ordered planes
Authors: Gamon Margaret A. , Kent D. C.
Published: September 2002

Necessary and sufficient conditions are given for the equivalence of the Nachbin and Wallman‐ordered compactification of an ordered plane.
Interpolation of natural cubic spline
Authors: Kumar Arun , Govil L. K.
Published: September 2002

From the result in [1] it follows that there is a unique quadratic spline which bounds the same area as that of the function. The matching of the area for the cubic spline does not follow from the corresponding result proved in [2]. We obtain cubic splines which preserve the area of the function.
Linear functionals on Orlicz sequence spaces without local convexity
Authors: Nowak Marian
Published: September 2002

The general form of continuous linear functionals on an Orlicz sequence space 1ϕ (non‐separable and non‐locally convex in general) is obtained. It is proved that the space hϕ is an M‐ideal in 1ϕ.
On subclasses of close‐to‐convex functions of higher order
Authors: Noor Khalida Inayat
Published: September 2002

The classes Tk(ρ), 0 ≤ ρ < 1, k ≥ 2, of analytic functions, using the class Vk(ρ) of functions of bounded boundary rotation, are defined and it is shown that the functions in these classes are close‐to‐convex of higher order. Covering theorem, arc‐length result and some radii problems are solved. We also discuss some properties of the class Vk(ρ) including distortion and coefficient results.
Bernoulli trials and permutation statistics
Authors: Rawlings Don
Published: September 2002

Several coin‐tossing games are surveyed which, in a natural way, give rise to “statistically” induced probability measures on the set of permutations of {1, 2, …, n} and on sets of multipermutations. The distributions of a general class of random variables known as binary tree statistics are also given.
An introduction of F‐graphs, a graph‐theoretic representation of natural numbers
Authors: Farrell E. J.
Published: September 2002

A special type of family graphs (F‐graphs, for brevity) are introduced. These are cactus‐type graphs which form infinite families under an attachment operation. Some of the characterizing properties of F‐graphs are discussed. Also, it is shown that, together with the attachment operation, these families form an infinite, commutative semigroup with unit element. Finally, it is shown that F‐graphs are graph‐theoretical representations of natural numbers.
Transient development of gravity waves for two layered fluids
Authors: Essawy A. H. , Faltas M. S.
Published: September 2002

The transient gravity waves generated by a harmonically oscillating wave maker immersed in two incompressible fluids, the upper fluid having a free surface, is considered. The resulting linearized initial value problem is solved using the method of generalized functions, and asymptotic analysis for large time and distance are given for the elevation.
A parabolic differential equation with unbounded piecewise constant delay
Authors: Wiener Joseph , Debnath Lokenath
Published: September 2002

A partial differential equation with the argument [λt] is studied, where [•] denotes the greatest integer function. The infinite delay t − [λt] leads to difference equations of unbounded order.
Two‐sided essential nilpotence
Authors: Eslami Esfandiar , Stewart Patrick
Published: September 2002

An ideal I of a ring A is essentially nilpotent if I contains a nilpotent ideal N of A such that J ⋂ N ≠ 0 whenever J is a nonzero ideal of A contained in I. We show that each ring A has a unique largest essentially nilpotent ideal EN(A). We study the properties of EN(A) and, in particular, we investigate how this ideal behaves with respect to related rings.
Almost γ‐continuous functions
Authors: Cammaroto F. , Noiri T.
Published: September 2002

In this paper, a new class of functions called “almost γ‐continuous” is introduced and their several properties are investigated. This new class is also utilized to improve some published results concerning weak continuity [6] and γ‐continuity [2].
A note on the support of right invariant measures
Authors: Tserpes N. A.
Published: September 2002

A regular measure μ on a locally compact topological semigroup is called right invariant if μ(Kx) = μ(K) for every compact K and x in its support. It is shown that this condition implies a property reminiscent of the right cancellation law. This is used to generalize a theorem of A. Mukherjea and the author (with a new proof) to the effect that the support of an r*‐invariant measure is a left group iff the measure is right invariant on its support.
An application of KKM‐map principle
Authors: Carbone A.
Published: September 2002

The following theorem is proved and several fixed point theorems and coincidence theorems are derived as corollaries. Let C be a nonempty convex subset of a normed linear space X, f : C → X a continuous function, g : C → C continuous, onto and almost quasi‐convex. Assume that C has a nonempty compact convex subset D such that the set

urn:x-wiley:01611712:media:ijmm571891:ijmm571891-math-0001

is compact.

Then there is a point y0 ∈ C such that ‖g(y0) − f(y0)‖ = d(f(y0), C).
Exact, approximate solutions and error bounds for coupled implicit systems of partial differential equations
Authors: Jódar Lucas
Published: September 2002

In this paper coupled implicit initial‐boundary value systems of second order partial differential equations are considered. Given a finite domain and an admissible error ϵ an analytic approximate solution whose error is upper bounded by ϵ in the given domain is constructed in terms of the data.
Radius problems for a subclass of close‐to‐convex univalent functions
Authors: Noor Khalida Inayat
Published: September 2002

Let P[A, B], −1 ≤ B < A ≤ 1, be the class of functions p such that p(z) is subordinate to . A function f, analytic in the unit disk E is said to belong to the class if, and only if, there exists a function g with such that , 0 ≤ β < 1 and z ∈ E. The functions in this class are close‐to‐convex and hence univalent. We study its relationship with some of the other subclasses of univalent functions. Some radius problems are also solved.
On the Cayley‐Hamilton property in abelian groups
Authors: Militello Robert R.
Published: September 2002

In this paper, the work of Casacuberta and Hilton on the class of abelian fg‐like groups is extended. These groups share much in common with the class of finitely generated abelian groups.
On commutativity of one‐sided s‐unital rings
Authors: Abujabal H. A. S. , Khan M. A.
Published: September 2002

The following theorem is proved: Let r = r(y) > 1, s, and t be non‐negative integers. If R is a left s‐unital ring satisfies the polynomial identity [xy − xsyrxt, x] = 0 for every x, y ∈ R, then R is commutative. The commutativity of a right s‐unital ring satisfying the polynomial identity [xy − yrxt, x] = 0 for all x, y ∈ R, is also proved.
Outer compositions of hyperbolic/loxodromic linear fractional transfomations
Authors: Gill John
Published: September 2002

It is shown, using classical means, that the outer composition of hyperbolic or loxodromic linear fractional transformations {fn}, where fn → f, converges to α, the attracting fixed point of f, for all complex numbers z, with one possible exception, z0. I.e.,

urn:x-wiley:01611712:media:ijmm210145:ijmm210145-math-0001

When z0 exists, Fn(z0) → β, the repelling fixed point of f. Applications include the analytic theory of reverse continued fractions.
Primary decomposition of torsion R[X]‐modules
Authors: Adkins William A.
Published: September 2002

This paper is concerned with studying hereditary properties of primary decompositions of torsion R[X]‐modules M which are torsion free as R‐modules. Specifically, if an R[X]‐submodule of M is pure as an R‐submodule, then the primary decomposition of M determines a primary decomposition of the submodule. This is a generalization of the classical fact from linear algebra that a diagonalizable linear transformation on a vector space restricts to a diagonalizable linear transformation of any invariant subspace. Additionally, primary decompositions are considered under direct sums and tensor product.
Some results on π‐solvable and supersolvable groups
Authors: Dutta T. K. , Bhattacharyya A.
Published: September 2002

For a finite group G, ϕp(G), Sp(G), L(G) and S𝒫(G) are generalizations of the Frattini subgroup of G. We obtain some results on π‐solvable, p‐solvable and supersolvable groups with the help of the structures of these subgroups.
Solving higher order Fuchs type differential systems avoiding the increase of the problem dimension
Authors: Navarro E. , Jódar L. , Company R.
Published: September 2002

In this paper, we develop a Frobenius matrix method for solving higher order systems of differential equations of the Fuchs type. Generalized power series solution of the problem are constructed without increasing the problem dimension. Solving appropriate algebraic matrix equations a closed form expression for the matrix coefficient of the series are found. By means of the concept of a k‐fundamental set of solutions of the homogeneous problem an explicit solution of initial value problems are given.
Solutions to Lyapunov stability problems of sets: nonlinear systems with differentiable motions
Authors: Grujic Ljubomir T.
Published: September 2002

Time‐invariant nonlinear systems with differentiable motions are considered. The algorithmic necessary and sufficient conditions are established in various forms for one‐shot construction of a Lyapunov function, for asymptotic stability of a compact invariant set and for the exact determination of the asymptotic stability domain of the invariant set.

The classical conditions are expressed in terms of existence of a system Lyapunov functions. The conditions of theorems presented herein are expressed via properties of the solution ? to , or of the solution ? to , for arbitrarily selected p?P(S; f) or p?P1(S; f), where families P(S; f) and P1(S; f) are well defined. The equation , or its equivalent , should be solved only for one selection of the function p.
Flows for chosen vorticity functions exact solutions of the Navier‐Stokes equations
Authors: Chandna O. P. , Oku-Ukpong E. O.
Published: September 2002

Solutions are obtained for the equations of the motion of the steady incompressible viscous planar generalized Beltrami flows when the vorticity distribution is given by ∇2ψ = ψ + f(x, y) for three chosen forms of f(x, y).
Extensions of Hardy‐Littlewood inequalities
Authors: Lou Zengjian
Published: September 2002

For a function f ∈ Hp(Bn), with f(0) = 0, we prove

(1) If 0 < p ≤ s,then

urn:x-wiley:01611712:media:ijmm679145:ijmm679145-math-0001

(2) If s ≤ p < ∞, then

urn:x-wiley:01611712:media:ijmm679145:ijmm679145-math-0002

where Rβf is the fractional derivative of f. These results generalize the known cases s = 2, β = 1 ([1]).
A criterion for p‐valently starlike functions
Authors: Owa Shigeyoshi , Nunokawa Mamoru , Fukui Seiichi
Published: September 2002

The object of the present paper is to prove a criterion for p‐valently starlike functions in the open unit disk.
Infinite products over visible lattice points
Authors: Campbell Geoffrey B.
Published: September 2002

About fifty new multivariate combinatorial identities are given, connected with partition theory, prime products, and Dirichlet series. Connections to Lattice Sums in Chemistry and Physics are alluded to also.
p‐systems in local Noether lattices
Authors: Johnson E. W. , Johnson Johnny A. , Taylor Monty B.
Published: September 2002

In this paper we introduce the concept of a p‐system in a local Noether lattice and obtain several characterizations of these elements. We first obtain a topological characterization and then a characterization in terms of the existence of a certain type of decreasing sequence of elements. In addition, p‐systems are characterized in quotient lattices and completions.
Zero‐sum partition theorems for graphs
Authors: Caro Y. , Krasikov I. , Roditty Y.
Published: September 2002

Let q = pn be a power of an odd prime p. We show that the vertices of every graph G can be partitioned into t(q) classes such that the number of edges in any induced subgraph 〈Vi〉 is divisible by q, where , and if q = 2n, then t(q) = 2q − 1.

In particular, it is shown that t(3) = 3 and 4 ≤ t(5) ≤ 5.
Minimal CR‐submanifolds of a six‐dimentional sphere
Authors: Shahid M. Hasan , Husain S. I.
Published: September 2002

We establish several formulas for a 3‐dimensional CR‐submanifold of a six‐dimensional
sphere and state some results obtained by making use of them.
Variational inequalities of strongly nonlinear elliptic operators of infinite order
Authors: El-Dessouky Adell T.
Published: September 2002

The present paper deals with the study of the solvability of variational inequalities
for strongly nonlinear elliptic operators of infinite order with liberal growth on the coefficients.
Asymptotic optimality of sequential designs for estimation
Authors: Rekab Kamel
Published: September 2002

This paper is concerned with the problem of allocating a fixed number of trials
between K independent populations from the exponential family, in order to estimate a linear
combination of the means with squared error loss. Introducing independent conjugate priors, a
batch sequential procedure is proposed and compared with the optimal.
On CR‐submanifolds of the six‐dimensional sphere
Authors: Bashir M. A.
Published: September 2002

We consider proper CR‐submanifolds of the six‐dimensional sphere S6. We prove
that S6 does not admit compact proper CR‐submanifolds with non‐negative sectional curvature
and integrable holomorphic distribution.
Direct sums of J‐rings and radical rings
Authors: Guo Xiuzhan
Published: September 2002

Let R be a ring, J(R) the Jacobson radical of R and P the set of potent
elements of R. We prove that if R satisfies (∗) given x, y in R there exist integers
m = m(x, y) > 1 and n = n(x, y) > 1 such that xmy = xyn and if each x ∈ R is
the sum of a potent element and a nilpotent element, then N and P are ideals and R = N ⊕ P. We also prove that if R satisfies (∗) and if each x ∈ R has a representation
in the form x = a + u, where a ∈ P and u ∈ J(R) ,then P is an ideal and R = J(R) ⊕ P.
Convolution of Hankel transform and its application to an integral involving Bessel functions of first kind
Authors: Tuan Vu Kim , Saigo Megumi
Published: September 2002

In the paper a convolution of the Hankel transform is constructed. The convolution is used
to the calculation of an integral containing Bessel functions of the first kind.
The atomic decomposition of harmonic functions satisfying certain conditions of integrability
Authors: Bogdan Krzysztof
Published: September 2002

Distributions on Euclidean spaces with derivatives of their Poisson integral satisfying
certain natural conditions of integrability are represented as sums of weighted atoms. The atomic
decomposition is obtained by means of the Calderón reproducing formula.
Completion of probabilistic normed spaces
Authors: Guillén Bernardo Lafuerza , Lallena José Antonio Rodríguez , Sempi Carlo
Published: September 2002

We prove that every probabilistic normed space, either according to the original
definition given by erstnev, or according to the recent one introduced by Alsina, Schweizer and
Sklar, has a completion.