bluuebunny/crossref_metadata_2025 huggingface dataset:
Convolution algebras arising from Sturm‐Liouville transforms and applications
Authors: Huffman Jason P. , Heatherly Henry E.
Published: September 2002

A regular Sturm‐Liouville eigenvalue problem gives rise to a related linear integral transform. Churchill has shown how such an integral transform yields, under certain circumstances, a
generalized convolution operation. In this paper, we study the properties of convolution algebras arising in this fashion from a regular Sturm‐Liouville problem. We give applications of these
convolution algebras for solving certain differential and integral equations, and we outline an operational calculus for classes of such equations.
Remarks on a paper by Silverman
Authors: Singh Vikramaditya
Published: September 2002

We improve a result in Silverman′s paper (1999) and answer a
question he posed. We also consider a similar problem and obtain
sufficient conditions for starlikeness.
p‐adic difference‐difference Lotka‐Volterra equation and ultra‐discrete limit
Authors: Matsutani Shigeki
Published: September 2002

We study the difference‐difference Lotka‐Volterra equations in
p‐adic number space and its p‐adic valuation version. We point out that the structure of the space given by taking the
ultra‐discrete limit is the same as that of the p‐adic valuation space. Since ultra‐discrete limit can be regarded as a
classical limit of a quantum object, it implies that a correspondence between classical and quantum objects might be associated with valuation theory.
A note on the countable union of prime submodules
Authors: Pournaki M. R. , Tousi M.
Published: September 2002

Let M be a finitely‐generated module over a Noetherian ring R. Suppose 𝔞 is an ideal of R and let N = 𝔞M and 𝔟 = Ann(M/N). If 𝔟⫅J(R), M is complete with respect to the 𝔟‐adic topology, is a countable family of prime submodules of M, and x ∈ M, then x + N⫅∪i≥1Pi implies that x + N⫅Pj for some i ≥ 1. This extends a theorem of Sharp and Vámos concerning prime ideals to prime
submodules.
Annihilating polynomials for quadratic forms
Authors: Lewis David W.
Published: September 2002

This is a short survey of the main known results concerning annihilating polynomials for the Witt ring of quadratic forms over a field.
Constructing irreducible polynomials with prescribed level curves over finite fields
Authors: Caragiu Mihai
Published: September 2002

We use Eisenstein′s irreducibility criterion to prove that there
exists an absolutely irreducible polynomial P(X, Y) ∈ GF(q)[X, Y] with coefficients in the finite field GF(q) with q elements, with prescribed level curves Xc : = {(x, y) ∈ GF(q)2 | P(x, y) = c}.
Description of the structure of singular spectrum for Friedrichs model operator near singular point
Authors: Iakovlev Serguei I.
Published: September 2002

The study of the point spectrum and the singular continuous one is reduced to investigating the structure of the real roots set of an analytic function with positive imaginary part M(λ). We prove a uniqueness theorem for such a class of analytic functions.
Combining this theorem with a lemma on smoothness of M(λ) near its real roots permits us to describe the density of the singular
spectrum.
On chiral differential operators over homogeneous spaces
Authors: Gorbounov Vassily , Malikov Fyodor , Schechtman Vadim
Published: September 2002

We give a classification and construction of chiral algebras of differential operators over semisimple algebraic groups G and over homogeneous spaces G/N and G/P where N is a nilpotent and P a parabolic subgroup.
Some sequence spaces and statistical convergence
Authors: Savaş E.
Published: September 2002

We introduce the strongly (V, λ)‐convergent sequences and give the relation between strongly (V, λ)‐convergence and strongly (V, λ)‐convergence with respect to a modulus.
Initial‐boundary value problem with a nonlocal condition for a viscosity equation
Authors: Bouziani Abdelfatah
Published: September 2002

This paper deals with the proof of the existence, uniqueness, and continuous dependence of a strong solution upon the data, for an initial‐boundary value problem which combine Neumann and integral conditions for a viscosity equation. The proof is based on an energy inequality and on the density of the range of the linear operator corresponding to the abstract formulation of the studied problem.
Random fixed point theorems for asymptotic 1‐set contraction operators
Authors: Vijayaraju P.
Published: September 2002

Random fixed point theorems for condensing, 1‐set contraction selfless are known. But no random fixed point theorem for more general asymptotic 1‐set contraction selfmaps is yet available.
The purpose of this paper is to prove random fixed point theorems
for such maps.
Coefficient inequalities for certain analytic functions
Authors: Nishiwaki Junichi , Owa Shigeyoshi
Published: September 2002

For real α(α > 1), we introduce subclasses M(α) and N(α) of analytic functions f(z) with f(0) = 0 and f′(0) = 1 in U. The object of the present paper is to consider
the coefficient inequalities for functions f(z) to be in the classes M(α) and N(α). Further, the bounds of α for functions f(z) to be starlike in U are considered.
Projective algorithms for solving complementarity problems
Authors: Haddad Caroline N. , Habetler George J.
Published: September 2002

We present robust projective algorithms of the von Neumann type
for the linear complementarity problem and for the generalized
linear complementarity problem. The methods, an extension of
Projections Onto Convex Sets (POCS) are applied to a class of
problems consisting of finding the intersection of closed
nonconvex sets. We give conditions under which convergence occurs
(always in 2 dimensions, and in practice, in higher dimensions)
when the matrices are P‐matrices (though not necessarily
symmetric or positive definite). We provide numerical results
with comparisons to Projective Successive Over
Relaxation (PSOR).
Certain convex harmonic functions
Authors: Kim Yong Chan , Jahangiri Jay M. , Choi Jae Ho
Published: September 2002

We define and investigate a family of complex‐valued harmonic
convex univalent functions related to uniformly convex analytic
functions. We obtain coefficient bounds, extreme points,
distortion theorems, convolution and convex combinations for this
family.
Fuzzy properties in fuzzy convergence spaces
Authors: Jäger Gunther
Published: September 2002

Based on the concept of limit of prefilters and residual
implication, several notions in fuzzy topology are fuzzyfied in
the sense that, for each notion, the degree to which it is
fulfilled is considered. We establish therefore theories of
degrees of compactness and relative compactness, of closedness,
and of continuity. The resulting theory generalizes the
corresponding “crisp” theory in the realm of fuzzy convergence
spaces and fuzzy topology.
Boundedness and monotonicity of principal eigenvalues for boundary value problems with indefinite weight functions
Authors: Afrouzi G. A.
Published: September 2002

We study the principal eigenvalues (i.e., eigenvalues corresponding to positive eigenfunctions) for the boundary value problem: −Δu(x) = λg(x)u(x), x ∈ D; (∂u/∂n)(x) + αu(x) = 0, x ∈ ∂D, where Δ is the standard Laplace operator, D is a bounded domain with smooth boundary, g : D → ℝ is a smooth function which changes sign on D and
α ∈ ℝ. We discuss the relation between α and the principal eigenvalues.
Periodicity in distribution. I. Discrete systems
Authors: Dorogovtsev A. Ya.
Published: September 2002

We consider the existence of periodic in distribution
solutions to the difference equations in a Banach space. A random
process is called periodic in distribution if all its
finite‐dimensional distributions are periodic with respect to
shift of time with one period. Only averaged characteristics of a
periodic process are periodic functions. The notion of the
periodic in distribution process gave adequate description for
many dynamic stochastic models in applications, in which dynamics
of a system is obviously nonstationary. For example, the
processes describing seasonal fluctuations, rotation under impact
of daily changes, and so forth belong to this type. By now, a considerable
number of mathematical papers has been devoted to periodic and
almost periodic in distribution stochastic processes. We
give a survey of the theory for certain classes of the linear
difference equations in a Banach space. A feature of our treatment
is the analysis of the solutions on the whole of axis. Such an
analysis gives simple answers to the questions about solution
stability of the Cauchy problem on +∞, solution stability
of analogous problem on −∞, or of existence solution for
boundary value problem and other questions about global behaviour
of solutions. Examples are considered, and references to
applications are given in remarks to appropriate theorems.
A model for dip‐coating of a two liquid mixture
Authors: O′Brien S. B. G. , Hayes M.
Published: September 2002

We consider a thin film flow where a flat substrate is coated
with a mixture of two miscible liquids, of equal viscosity, and
develop a model to predict the evolving coating thicknesses. The
developed model can, under certain circumstances, be used as an
approximation for the dip‐coating of a liquid suspension of a
viscous volatile liquid and solid solute as occurs in many
industrial applications.
Generalized solutions describing singularity interaction
Authors: Danilov V. G.
Published: September 2002

We present a new method for constructing solutions
to nonlinear evolutionary equations describing
the propagation and interaction of nonlinear waves.
Impulsive functional‐differential equations with nonlocalconditions
Authors: Akça Haydar , Boucherif Abdelkader , Covachev Valéry
Published: September 2002

The existence, uniqueness, and continuous dependence of a mild
solution of an impulsive functional‐differential evolution
nonlocal Cauchy problem in general Banach spaces are studied.
Methods of fixed point theorems, of a C0 semigroup of operators and the Banach contraction theorem are applied.
Estimates for the norms of solutions of delay difference systems
Authors: Medina Rigoberto
Published: September 2002

We derive explicit stability conditions for delay difference
equations in ℂn (the set of n complex vectors) and estimates for the size of the solutions are derived. Applications to partial difference equations, which model diffusion and reaction processes, are given.
New versions of the Nyman‐Beurling criterion for the Riemann hypothesis
Authors: Báez-Duarte Luis
Published: September 2002

Let ρ(x) = x − [x], χ = χ(0,1), λ(x) = χ(x)logx, and M(x) = ΣK≤x μ(k), where μ is the Möbius function. Norms are in Lp(0, ∞), 1 < p < ∞. For M1(θ) = M(1/θ) it is noted that ξ(s) ≠ 0 in ℜs > 1/p is equivalent to for all r ∈ (1, p). The space ℬ is the linear space generated by the functions x ↦ ρ(θ/x) with θ ∈ (0, 1]. Define . For all p ∈ (1, ∞) we prove the following theorems: (I) implies , and implies for all r ∈ (1, p). (II) implies ξ(s) ≠ 0 in ℜs ≥ 1/p, and ξ(s) ≠ 0 in ℜs ≥ 1/p implies for all r ∈ (1, p).
On hypergeometric generalized negative binomial distribution
Authors: Ghitany M. E. , Al-Awadhi S. A. , Kalla S. L.
Published: September 2002

It is shown that the hypergeometric generalized negative binomial distribution has moments of all positive orders, is overdispersed, skewed to the right, and leptokurtic. Also, a three‐term recurrence relation for computing probabilities from the considered distribution is given. Application of the distribution to entomological field data is given and its goodness‐of‐fit is demonstrated.
Global pinching theorems of submanifolds in spheres
Authors: Cai Kairen
Published: September 2002

Let M be a compact embedded submanifold with parallel mean
curvature vector and positive Ricci curvature in the unit sphere
S n+p(n ≥ 2 , p ≥ 1). By using the Sobolev
inequalities of P. Li (1980) to Lp estimate for the square length
σ of the second fundamental form and the norm of a tensor
Φ, related to the second fundamental form, we set up some
rigidity theorems. Denote by ‖σ‖p the Lp norm of
σ and H the constant mean curvature of M. It is shown that there is a constant C depending only on n, H, and k where (n − 1) k is the lower bound of Ricci curvature such that if
‖σ‖ n/2 < C, then M is a totally umbilic hypersurface in the sphere S n+1.
On the irregularity of the distribution of the sums of pairs of odd primes
Authors: Giordano George
Published: September 2002

Let P2(n) denote the number of ways of writing n as a sum of two odd primes. We support a conjecture of Hardy and Littlewood concerning P2(n) by showing that it holds in a certain “average” sense. Thereby showing the irregularity of P2(n).
Some results on fixed point theorems for multivalued mappings in complete metric spaces
Authors: Ume Jeong Sheok , Lee Byung Soo , Cho Sung Jin
Published: September 2002

Using the concept of w‐distance, we improve some well‐known fixed point theorems.
A minimization theorem in quasi‐metric spaces and its applications
Authors: Ume Jeong Sheok
Published: September 2002

We prove a new minimization theorem in quasi‐metric spaces, which improves the results of Takahashi (1993). Further, this theorem
is used to generalize Caristi′s fixed point theorem and Ekeland′s
ϵ‐variational principle.
Complete residue systems in the quadratic domain Z(e2πi/3)
Authors: Bergum Gerald E.
Published: September 2002

Several representations for a complete residue system in the Euclidean domain Z(ω) are presented in this paper.
Maps of manifolds with indefinite metrics preservingcertain geometrical entities
Authors: Kulkarni R. S.
Published: September 2002

It is shown that (i) a diffeomorphism of manifolds with indefinite metrics preserving degenerate r‐plane sections is conformal, (ii) a sectional curvature‐preservlng diffeomorphism of manifolds with indefinite metrics of dimension ≥4 is generically an isometry.
On the Meijer transformation
Authors: Conlan J. , Koh E. L.
Published: September 2002

Recently [8], an operational calculus for the operator Bμ = t−μDt1+μD with −1 < μ < ∞ was developed via the algebraic approach [4], [13], [15]. This paper gives the integral transform version. In particular, a differentiation theorem and a convolution theorem are proved.
Nonlinear differential equations and algebraic systems
Authors: Williams Lloyd K.
Published: September 2002

In this paper we obtain the general solution of scalar, first‐order differential equations. The method is variation of parameters with asymptotic series and the theory of partial differential equations.The result gives us a form like a differential quotient requiring only that a limit be taken. Like the familiar expression for the solution of linear, first order, ordinary equations, it is the same in all cases.
A simplification of D′Alarcao′s idempotent separating extensionsof inverse semigroups
Authors: Edwards Constance C.
Published: September 2002

In [2] D′Alarcao states necessary and sufficient conditions for the attainment of an idempotent‐separating extension of an inverse semigroup. To do this D′Alarcao needed essentially three mappings satisfying thirteen conditions. In this paper we show that one can achieve the same results with two mappings satisfying eight conditions.
Quasi‐convex univalent functions
Authors: Noor K. Inayat , Thomas D. K.
Published: September 2002

In this paper, a new class of normalized univalent functions is introduced. The properties of this class and its relationship with some other subclasses of univalent functions are studied. The functions in this class are close‐to‐convex.
On a class of continous flow
Authors: Mogollon Ramon
Published: September 2002

This paper involves characterizations of a class of continuous flows. The flows considered are those in which the positive prolongation of each point coincides with the trajectory through the point. The characterizations are based on the theory of prolongation.
Wronskians and subspaces of certain fourth order differential equations
Authors: Etgen G. J. , Taylor Willie E.
Published: September 2002

The objectives of the paper are to study the behavior of Wronskians of solutions of the fourth order differential equations and to relate this behavior with the oscillations of these equations, as well as to the structure of the subspaces of the solution spaces of the equations.
Closed form bound‐state perturbation theory
Authors: Rose Ollie J. , Adler Carl G.
Published: September 2002

The perturbed Schrödinger eigenvalue problem for bound states is cast into integral form using Green′s Functions. A systematic algorithm is developed and applied to the resulting equation giving rise to approximate solutions expressed as functions of the given perturbation parameter. As a by‐product, convergence radii for the traditional Rayleigh‐Schrödinger and Brillouin‐Wigner perturbation theories emerge in a natural way.
Damping of waves due to a soluble film
Authors: Puri K. K.
Published: September 2002

The damping of avity waves, forming on the surface of a layer of viscous, incompressible fluid which rests on top of a porous medium, is studied. It is assumed that the ′free′ surface of the fluid has a thin film of soluble material adsorbed on it and the relaxation time for the equilibrium of the film is negligible in comparison to the free surface oscillations. The damping coefficient of the waves is calculated as a function of the parameters associated with the surfactant and the permeability.
Binomial expansions modulo prime powers
Authors: Haggard Paul W. , Kiltinen John O.
Published: September 2002

In this note a result is given and proved concerning binomial expansions modulo prime powers. In the proof congruence modulo prime powers is generalized to the rational numbers via valuations.
The convolution‐induced topology on L∞(G) and linearly dependent translates in L1(G)
Authors: Crombez G. , Govaerts W.
Published: September 2002

Given a locally compact Hausdorff group G, we consider on L∞(G) the τc‐topology, i.e. the weak topology under all convolution operators induced by functions in L1(G). As a major result we characterize the trigonometric polynomials on a compact group as those functions in L1(G) whose left translates are contained in a finite‐dimensional set. From this, we deduce that τc is different from the w∗‐topology on L∞(G) whenever G is infinite. As another result, we show that τc coincides with the norm‐topology if and only if G is discrete. The properties of τc are then studied further and we pay attention to the τc‐almost periodic elements of L∞(G).
Some remarks on the stability analysis in Robe′s three body problem
Authors: Meire R.
Published: September 2002

An improved technique is presented for the stability analysis of Robe′s 3‐body problem which gives more accurate results for the transition curves in the parameter plane than does Robe′s paper.

A novel property of the system of differential equations describing the motion is used, which reduces the computer time by more than 50%.
A generalization of some fixed point theorems of K. M. Ghosh
Authors: Rhoades B. E.
Published: September 2002

This note establishes the following result. Let T be a selfmap of a normed linear space E. For 0 < λ ≤ 1, define Tλx = λx + (1 − λ)Tx for each x in E. If, in addition, S = TTλ satisfies any contractive definition strong enough to guarantee that S has a unique fixed point u in E, and, if TTλu = TλTu, then u is the unique fixed point for T.
On a pair of random generalized non‐linear contractions
Authors: Achari J.
Published: September 2002

A fixed point theorem for a pair of random generalized non‐linear contraction
mappings involving four points of the space under consideration is proven. It is shown that this result includes the result of Lee and Padgett [1]. Also an application of the result is given.
Seminormal graded rings and weakly normal projective varieties
Authors: Leahy John V. , Vitulli Marie A.
Published: September 2002

This paper is concerned with the seminormality of reduced graded rings and the weak normality of projective varieties. One motivation for this investigation is the study of the procedure of blowing up a non‐weakly normal variety along its conductor ideal.
On fundamental sets over a finite field
Authors: Abbas Yousef , Liang Joseph J.
Published: September 2002

A partition over finite field is defined and each equivalence class is constructed and represented by a set called the fundamental set. If a primitive element is used to construct the addition table over these fundamental sets then all additions over the field can be computed. The number of partitions is given for some finite fields.
Extensions of the Heisenberg‐Weyl inequality
Authors: Heinig H. P. , Smith M.
Published: September 2002

In this paper a number of generalizations of the classical Heisenberg‐Weyl uncertainty inequality are given. We prove the n‐dimensional Hirschman entropy inequality (Theorem 2.1) from the optimal form of the Hausdorff‐Young theorem and deduce a higher dimensional uncertainty inequality (Theorem 2.2). From a general weighted form of the Hausdorff‐Young theorem, a one‐dimensional weighted entropy inequality is proved and some weighted forms of the Heisenberg‐Weyl inequalities are given.
A simultaneous solution to two problems on derivatives
Authors: Cater F. S.
Published: September 2002

Let A be a nonvoid countable subset of the unit interval [0, 1] and let B be an Fσ‐subset of [0, 1] disjoint from A. Then there exists a derivative f on [0, 1] such that 0 ≤ f ≤ 1, f = 0 on A, f > 0 on B, and such that the extended real valued function 1/f is also a derivative.
Continuous dependence of boundary values for semiinfinite interval ordinary differential equations
Authors: Eberly David H.
Published: September 2002

Certain elliptic equations arising in catalysis theory can be transformed into ordinary differential equations on the interval (0, ∞). The solutions to these problems usually depend on parameters ρ ∈ ℝn, say u(t, ρ). For certain types of nonlinearities, we show that the boundary value is continuous on compact sets of the variable ρ. As a consequence, bifurcation results for the elliptic equation are obtained.
A regular graph of girth 6 and valency 11
Authors: Wong P. K.
Published: September 2002

Let f(11, 6) be the number of vertices of an (11, 6)‐cage. By giving a regular graph of girth 6 and valency 11, we show that f(11, 6) ≤ 240. This is the best known upper bound for f(11, 6).
Simulation of continuously deforming parabolic problems by Galerkin finite‐elements method
Authors: Halabi Yahia S.
Published: September 2002

A general numerical finite element scheme is described for parabolic problems with phase change wherein the elements of the domain are allowed to deform continuously. The scheme is based on the Galerkin approximation in space, and finite difference approximation for the time derivatives. The numerical scheme is applied to the two‐phase Stefan problems associated with the melting and solidification of a substance. Basic functions based on Hermite polynomials are used to allow exact specification of flux‐latent heat balance conditions at the phase boundary. Numerical results obtained by this scheme indicates that the method is stable and produces an accurate solutions for the heat conduction problems with phase change; even when large time steps used. The method is quite general and applicable for a variety of problems involving transition zones and deforming regions, and can be applied for one multidimensional problems.
On a variation of Sands′ method
Authors: Obaid Evelyn E.
Published: September 2002

A subset of a finite additive abelian group G is a Z‐set if for all a ∈ G, na ∈ G for all n ∈ Z. The group G is called “Z‐good” if in every factorization G = A ⊕ B, where A and B are Z‐sets at least one factor is periodic. Otherwise G is called “Z‐bad.”

The purpose of this paper is to investigate factorizations of finite ablian groups which arise from a variation of Sands′ method. A necessary condition is given for a factorization G = A ⊕ B, where A and B are Z‐sets, to be obtained by this variation. An example is provided to show that this condition is not sufficient. It is also shown that in general all factorizations G = A ⊕ B, where A and B are Z‐sets, of a “Z‐good” group do not arise from this variation of Sands′ method.
The semigroup of nonempty finite subsets of integers
Authors: Spake Reuben
Published: September 2002

Let Z be the additive group of integers and g the semigroup consisting of all nonempty finite subsets of Z with respect to the operation defined by

urn:x-wiley:01611712:media:ijmm461819:ijmm461819-math-0001

For X ∈ g, define AX to be the basis of 〈X − min(X)〉 and BX the basis of 〈max(X) − X〉. In the greatest semilattice decomposition of g, let α(X) denote the archimedean component containing X and define α0(X) = {Y ∈ α(X) : min(Y) = 0}. In this paper we examine the structure of g and determine its greatest semilattice decomposition. In particular, we show that for X, Y ∈ g, α(X) = α(Y) if and only if AX = AY and BX = BY. Furthermore, if X ∈ g is a non‐singleton, then the idempotent‐free α(X) is isomorphic to the direct product of the (idempotent‐free) power joined subsemigroup α0(X) and the group Z.
On the Affine Weyl group of type
Authors: Albar Muhammad A.
Published: September 2002

We study in this paper the affine Weyl group of type , [1]. Coxeter [1] showed that this group is infinite. We see in Bourbaki [2] that is a split extension of Sn, the symmetric group of degree n, by a group of translations and of lattice of weights. is one of the crystallographic Coxeter groups considered by Maxwell [3], [4].

We prove the following:

THEOREM 1. is a split extension of Sn by the direct product of (n − 1) copies of Z.

THEOREM 2. The group is soluble of derived length 3, is soluble of derived length 4. For n > 4, the second derived group coincides with the first and so is not soluble for n > 4.

THEOREM 3. The center of is trivial for n ≥ 3.
Abelian theorems for Whittaker transforms
Authors: Carmichael Richard D. , Pathak R. S.
Published: September 2002

Initial and final value Abelian theorems for the Whittaker transform of functions and of distributions are obtained. The Abelian theorems are obtained as the complex variable of the transform approaches 0 or ∞ in absolute value inside a wedge region in the right half plane.
A measure of mutual divergence among a number of probability distributions
Authors: Kapur J. N. , Kumar Vinod , Kumar Uma
Published: September 2002

The principle of optimality of dynamic programming is used to prove three
major inequalities due to Shannon, Renyi and Holder. The inequalities are then used to obtain some useful results in information theory. In particular measures are obtained to measure the mutual divergence among two or more probability distributions.
Srinivasa Ramanujan (1887‐1920) and the theory of partitions of numbers and statistical mechanics a centennial tribute
Authors: Debnath Lokenath
Published: September 2002

This centennial tribute commemorates Ramanujan the Mathematician and
Ramanujan the Man. A brief account of his life, career, and remarkable mathematical contributions is given to describe the gifted talent of Srinivasa Ramanujan. As an example of his creativity in mathematics, some of his work on the theory of partition of numbers has been presented with its application to statistical mechanics.
Some theorems on generalized polars with arbitrary weight
Authors: Zaheer Neyamat , Khan Aijaz A.
Published: September 2002

The present paper, which is a continuation of our earlier work in Annali di Mathematica [1] and Journal Math. Seminar [2] (EγEUθPIA), University of Athens, Greece, deals with the problem of determining sufficiency conditions for the nonvanishing of generalized polars (with a vanishing or nonvanishing weight) of the product of abstract homogeneous polynomials in the general case when the factor polynomials have been preassigned independent locations for their respective null‐sets. Our main theorems here fully answer this general problem and include in them, as special cases, all the results on the topic known to date and established by Khan, Marden and Zaheer (see Pacific J. Math. 74 (1978), 2, pp. 535‐557, and the papers cited above). Besides, one of the main theorems leads to an improved version of Marden′s general theorem on critical points of rational functions of the form f1f2 … fp/fp+1 … fq, fi being complex‐valued polynomials of degree ni.
On generalized heat polynomials
Authors: Nasim C.
Published: September 2002

We consider the generalized heat equation of nth order . If the initial temperature is an even power function, then the heat transform with the source solution as the kernel gives the heat polynomial. We discuss various properties of the heat polynomial and its Appell transform. Also, we give series representation of the heat transform when the initial temperature is a power function.
Nowhere dense sets and real‐valued functions with closed graphs
Authors: Baggs Ivan
Published: September 2002

Closed and nowhere dense subsets which coincide with the points of
discontinuity of real‐valued functions with a closed graph on spaces which are not
necessarily perfectly normal are investigated. Certain Gδ
subsets of completely
regular and normal spaces are characterized. It is also shown that there exists a
countable connected Urysohn space X with the property that no closed and nowhere
dense subset of X coincides with the points of discontinuity of a real‐valued
function on X with a closed graph.
A note on weakly θ‐continuous functions
Authors: Mršević M. , Reilly I. L.
Published: September 2002

Recently a new class of functions between topological spaces, called weakly
θ‐continuous functions, has been introduced and studied. In this paper we show how an
appropriate change of topology on the domain of a weakly θ‐continuous function reduces
it to a weakly continuous function. This paper examines some of the consequences of
this result.
A bounded consistency theorem for strong summabilities
Authors: Chun C. S. , Freedman A. R.
Published: September 2002

The study of R‐type summability methods is continued in this paper by
showing that two such methods are identical on the bounded portion of the strong
summability field associated with the methods. It is shown that this “bounded
consistency” applies for many non‐matrix methods as well as for regular matrix methods.
Bieberback functions and periodic distributions
Authors: Karunakaran V.
Published: September 2002

This paper deals with a correspondence between the periodic distributions
and holomorphic functions. Periodic distributions whose “negative” Fourier
coefficients are zero are characterised as the boundary values of certain holomorphic
functions.
Conformal vector fields in symmetric and conformal symmetric spaces
Authors: Sharma Ramesh
Published: September 2002

Consequences of the existence of conformal vector fields in (locally)
symmetric and conformal symmetric spaces, have been obtained. An attempt has
been made for a physical interpretation of the consequences in the framework of
general relativity.
Abelian group in a topos of sheaves: torsion and essential extensions
Authors: Bhutani Kiran R.
Published: September 2002

We investigate the properties of torsion groups and their essential
extensions in the category AbShL of Abellan groups in a topos of sheaves on a
locale. We show that every torsion group is a direct sum of its p‐primary components
and for a torsion group A, the group [A,B] is reduced for any Bε
AbShL.. We give an
example to show that in AbShL the torsion subgroup of an injective group need not be
injective. Further we prove that if the locale is Boolean or finite then essential
extensions of torsion groups are torsion. Finally we show that for a first countable
hausdorff space X essential extensions of torsion groups in AbSh0(X) are torsion iff X
is discrete.
On coding theorem connected with ‘useful’ entropy of order‐β
Authors: Jain Priti , Tuteja R. K.
Published: September 2002

Guiasu and Picard [1] introduced the mean length for ‘useful’ codes. They called this length as the ‘useful’ mean length. Longo [2] has proved a noiseless coding theorem for this ‘useful’ mean length. In this paper we will give two generalizations of ‘useful’ mean length. After then the noiseless coding theorems are proved using these two generalizations.
Products of stochastic matrices and applications
Authors: Cohn Harry
Published: September 2002

This paper deals with aspects of the limit behaviour of products
of nonidentical finite or countable stochastic matrices (Pn). Applications
are given to nonhomogeneous Markov models as positive chains, some classes of
finite chains considered by Doeblin and weakly ergodic chains.
Some applications of Schwarz Lemma for operators
Authors: Mishra Akshaya Kumar
Published: September 2002

A generalized Schwarz lemma and some Harnack type inequalities for operators
have been obtained in this paper.
Pseudo‐analytic finite partition approach to temperature distribution problem in Human limbs
Authors: Saxena V. P. , Bindra J. S.
Published: September 2002

The main object of this paper is to Introduce the Pseudo Analytic Finite
Partition method and to illustrate its use in solving physiological heat distribution
problems pertaining to limbs and similar body organs. A two dimensional circular
region resembling the cross section of a human or animal limb is considered. The
biological properties are assumed to vary along the radial direction. The theoretical
model incorporates the effect of blood mass flow and metabolic heat generation. The
region is divided into annular sub‐regions and Ritz variational finite element method
is applied along the radial direction, while for the angular direction, Fourier Series
has been used due to uniformity in each annular part.
A note on influence of subgroup restrictions in finite group structure
Authors: Khazal R. , Mukherjee N. P.
Published: September 2002

The structure of a finite group under specific restrictions respectively on
its maximal, minimal and prime power subgroups has been investigated in this paper.
A variational formalism for the eigenvalues of fourth order boundary value problems
Authors: Hajj Adnan A.
Published: September 2002

This paper describes a variational approach for computing eigenvalues of a
two point boundary value problem associated with coupled second order equations to which
a fourth order linear differential equation is reduced. An attractive feature of this
approach is the technique of enforcing the boundary conditions by the variational functional.
Consequently, the expansion functions need not satisfy any of them.
Uniqueness and stability of solutions for a type of parabolic boundary value problem
Authors: Gonzalez-Velasco Enrique A.
Published: September 2002

We consider a boundary value problem consisting of the one‐dimensional
parabolic equation , where g, h and q are functions of x, subject to
some general boundary conditions. By developing a maximum principle for the boundary
value problem, rather than the equation, we prove the uniqueness of a nonnegative
solution that depends continuously on boundary values.
Some aspects of ion‐acoustic whistlers in the ionosphere in the presence of negative ions
Authors: Sur A. K. , Das G. C. , Chakraborty B. , Paul S. N. , Debnath L.
Published: September 2002

A study is made of the propagation of ion‐acoustic whistlers in the
atmosphere including the effects of negative ions. The dispersion relation, phase and
group velocities of whistlers are discussed. It is shown that the presence of
negative ions introduces a critical frequency which, for equal ionic masses, is equal
to the ion‐cyclotron frequency. Special attention is given to the group travel time
of whistlers at mid‐latitude and equator so that the role of negative ions on the
group travel time can be determined. The cyclotron damping of whistlers in the
presence of negative ions has been studied. The velocity distribution, total
attenuation and the induced magnetic field are calculated from the temporal as well as
spatial cyclotron damping. It is suggested that the attenuation of whistlers may
cause heating of the ionosphere. It is also indicated that the measurement of the
group travel time from its source to the observer at the satellite would help to
diagnose the ionospheric parameters. The results of the analysis are presented by
several graphical presentations.
Pareto optimality for nonlinear infinite dimensional control systems
Authors: Avgerinos Evgenios P. , Papageorgiou Nikolaos S.
Published: September 2002

In this note we establish the existence of Pareto optimal solutions for nonlinear, infinite dimensional control systems with state dependent control constraints and an integral criterion taking values in a separable, reflexive Banach lattice. An example is also presented in detail. Our result extends earlier ones obtained by Cesari and Suryanarayana.
A note on some spaces Lγ of distributions with Laplace transform
Authors: Esteva Salvador Pérez
Published: September 2002

In this paper we calculate the dual of the spaces of distributions Lγ introduced in [1]. Then we prove that Lγ is the dual of a subspace of C∞(ℝ).
On ultraconnected spaces
Authors: Mathew P. M.
Published: September 2002

In this paper, we study some properties of ultraconnected spaces and show that ultraconnected spaces are maximal ultraconnected and minimal . We also introduce the notion of F‐connected spaces, topological spaces wich are both hyperconnected and ultraconnected and characterize compact maximal F‐connected topologies on a set.
On Fréchet theorem in the set of measure preserving functions over the unit interval
Authors: Chou So-Hsiang , Nguyen Truc T.
Published: September 2002

In this paper, we study the Fréchet theorem in the set of measure preserving functions over the unit interval and show that any measure preserving function on [0, 1] can be approximated by a sequence of measure preserving piecewise linear continuous functions almost everywhere. Some application is included.
Boundary value problems in time for wave equations on RN
Authors: Smiley M. W. , Fink A. M.
Published: September 2002

Let Lλ denote the linear operator associated with the radially symmetric form of the wave operator together with the side conditions of decay to zero as r = ‖x‖ → +∞ and T‐periodicity in time. Thus , when there are N space variables. For δ, R, T > 0 let DT,R = (0, T) × (R, +∞) and denote the weighted L2 space with weight function exp(δr). It is shown that Lλ is a Fredholm operator from dom(Lλ) ⊂ L2(D) onto with non‐negative index depending on λ. If [2πj/T]2 < λ ≤ [2π(j+1)/T]2 then the index is 2j + 1. In addition it is shown that Lλ has a bounded partial inverse , with all spaces weighted by the function exp(δr). This provides a key ingredient for the analysis of nonlinear problems via the method of alternative problems.
On the existence of the solution of Burgers′ equation for n ≤ 4
Authors: Boules Adel N.
Published: September 2002

In this paper a proof of the existence of the solution of Burgers′ equation for n ≤ 4 is presented. The technique used is shown to be valid for equations with more general types of nonlinearities than is present in Burgers′ equation.
Regular eigenvalue problem with eigenparameter contained in the equation and the boundary conditions
Authors: Zayed E. M. E. , Ibrahim S. F. M.
Published: September 2002

The purpose of this paper is to establish the expansion theorem for a regular right‐definite eigenvalue problem for the Laplace operator in Rn, (n ≥ 2) with an eigenvalue parameter λ contained in the equation and the Robin boundary conditions on two “parts” of a smooth boundary of a simply connected bounded domain.
On probalistic normed spaces under τT,L
Authors: Ying Mingsheng
Published: September 2002

We introduce the operation ⊛L copulative with τT,L to define PN space under τT,L and establish some basic properties of probabilistic seminorms and norms under τT,L. Finally, we discuss so‐called L‐simple spaces.
Solution of an integral equation with a logarithmic kernel
Authors: Sampath C. , Jain D. J.
Published: September 2002

A simple independent integral equation technique is presented to solve an integral equation with a logarithmic kernel which governs solutions of many two‐dimensional Dirichlet boundary value problems involving two coplanar and parallel infinite strips. The technique is further illustrated by an example.
Induced measures on Wallman spaces
Authors: Yallaoui El-Bachir
Published: September 2002

Let X be an abstract set and ℒ a lattice of subsets of X. To each lattice‐regular measure μ, we associate two induced measures and on suitable lattices of the Wallman space IR(ℒ) and another measure μ′ on the space . We will investigate the reflection of smoothness properties of μ onto , and μ′ and try to set some new criterion for repleteness and measure repleteness.
Properties of solutions to a second order nonlinear differential equation
Authors: Kroopnick Allan J.
Published: September 2002

In this note, we show when all solutions to the nonlinear differential equation x″ + c(t)f(x)g(x′)x′ + a(t, x) = 0 are bounded. Furthermore, the solutions are either oscillatory or monotonic and asymptotically stable.
Some properties of the functional equation
Authors: Chambers Li. G.
Published: September 2002

A discussion is given of some of the properties of the functional
Volterra Integral equation

urn:x-wiley:01611712:media:ijmm142513:ijmm142513-math-0002

and of the corresponding multidimensional equation. Sufficient conditions are
given for the uniqueness of the solution, and an iterational process is provided
for the construction of the solution, together with error estimates. In addition
bounds are provided on the solution. The results obtained are illustrated by
means of the pantograph equation.
Universally catenarian domains of D + M type, II
Authors: Dobbs David E. , Fontana Marco
Published: September 2002

Let T be a domain of the form K + M, where K is a field and M is a maximal ideal
of T. Let D be a subring of K such that R = D + M is universally catenarian. Then D is
universally catenarian and K is algebraic over k, the quotient field of D. If [K : k] < ∞, then T is
universally catenarian. Consequently, T is universally catenarian if R is either Noetherian or a
going‐down domain. A key tool establishes that universally going‐between holds for any domain
which is module‐finite over a universally catenarian domain.
An extension of Helson‐Edwards theorem to Banach Modules
Authors: Takahasi Sin-Ei
Published: September 2002

An extension of the Helson‐Edwards theorem for the group algebras to Banach
modules over commutative Banach algebras is given. This extension can be viewed as a
generalization of Liu‐Rooij‐Wang′s result for Banach modules over the group algebras.
Vieta′s triangular array and a related family of polynomials
Authors: Robbins Neville
Published: September 2002

If n ≥ 1, let the nth row of an infinite triangular array consist of entries
, where .

We develop some properties of this array, which was discovered by Vieta. In addition, we prove
some irreducibility properties of the family of polynomials .

These polynomials, which we call Vieta polynomials, are related to Chebychev polynomials of the
first kind.
On separation of lattices
Authors: Szeto Mabel
Published: September 2002

Separation properties of a lattice of subsets of an arbitrary set or separation
properties between a pair of such lattices have strong implications on the associated lattice regular
measures and conversely. A number of such relationships are investigated and applications given to
topological lattices in a topological space.
A flag transitive plane of order 49 and its translation complement
Authors: Rao M. L. Narayana , Satyanarayana K. , Rao K. M. Arjuna
Published: September 2002

The translation complement of the flag transitive plane of order 49 [Proc. Amer. Math. Soc. 32 (1972), 256‐262] constructed by Rao is computed. It is shown that
the flag transitive group itself is the translation complement and it is a solvable
group of order 600.
Approximation by double Walsh polynomials
Authors: Móricz Ferenc
Published: September 2002

We study the rate of approximation by rectangular partial sums, Cesàro means, and de la Vallée Poussin means of double Walsh‐Fourier series of a function in a homogeneous Banach space X. In particular, X may be Lp(I2), where 1≦p < ∞ and I2 = [0, 1) × [0, 1), or CW(I2), the latter being the collection of uniformly W‐continuous functions on I2. We extend the results by Watari, Fine, Yano, Jastrebova, Bljumin, Esfahanizadeh and Siddiqi from univariate to multivariate cases. As by‐products, we deduce sufficient conditions for convergence in Lp(I2)‐norm and uniform convergence on I2 as well as characterizations of Lipschitz classes of functions. At the end, we raise three problems.
On polynomial EPr matrices
Authors: Meenakshi Ar. , Anandam N.
Published: September 2002

This paper gives a characterization of EPr‐λ‐matrices. Necessary and sufficient conditions are determined for (i) the Moore‐Penrose inverse of an EPr‐λ‐matrix to be an EPr‐λ‐matrix and (ii) Moore‐Penrose inverse of the product of EPr‐λ‐matrices to be an EPr‐λ‐matrix. Further, a condition for the generalized inverse of the product of λ‐matrices to be a λ‐matrix is determined.
Semi‐topological properties
Authors: Nayar Bhamini M. P. , Arya S. P.
Published: September 2002

A property preserved under a semi‐homeomorphism is said to be a semi‐topological property. In the present paper we prove the following results: (1) A topological property P is semi‐topological if and only if the statement (X, 𝒯) has P if and only if (X, F(𝒯)) has P′ is true where F(𝒯) is the finest topology on X having the same family of semi‐open sets as (X, 𝒯), (2) If P is a topological property being minimal P is semi‐topological if and only if for each minimal P space (X, 𝒯), 𝒯 = F(𝒯).
Hankel complementary integral transformations of arbitrary order
Authors: Linares M. Linares , Pérez J. M. R. Mendez
Published: September 2002

Four selfreciprocal integral transformations of Hankel type are defined through

urn:x-wiley:01611712:media:ijmm681761:ijmm681761-math-0001

where i = 1, 2, 3, 4; μ ≥ 0; α1(x) = x1+2μ, ℊ1,μ(x) = x−μJμ(x), Jμ(x) being the Bessel function of the first kind of order μ; α2(x) = x1−2μ, ℊ2,μ(x) = (−1)μx2μℊ1,μ(x); α3(x) = x−1−2μ, ℊ3,μ(x) = x1+2μℊ1,μ(x), and α4(x) = x−1+2μ, ℊ4,μ(x) = (−1)μxℊ1,μ(x). The simultaneous use of transformations ℋ1,μ, and ℋ2,μ, (which are denoted by ℋμ) allows us to solve many problems of Mathematical Physics involving the differential operator Δμ = D2 + (1 + 2μ)x−1D, whereas the pair of transformations ℋ3,μ and ℋ4,μ, (which we express by ) permits us to tackle those problems containing its adjoint operator , no matter what the real value of μ be. These transformations are also investigated in a space of generalized functions according to the mixed Parseval equation

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which is now valid for all real μ.
On k‐ideals of semirings
Authors: Sen M. K. , Adhikari M. R.
Published: September 2002

Certain types of ring congruences on an additive inverse semiring are characterized with the help of full k‐ideals. It is also shown that the set of all full k‐ideals of an additively inverse semiring in which addition is commutative forms a complete lattice which is also modular.
Fixed point theorems for d‐complete topological spaces I
Authors: Hicks Troy L.
Published: September 2002

Generalizations of Banach′s fixed point theorem are proved for a large class of non‐metric spaces. These include d‐complete symmetric (semi‐metric) spaces and complete quasi‐metric spaces. The distance function used need not be symmetric and need not satisfy the triangular inequality.
On the lower semi‐continuity of the set valued metric projection
Authors: Sejeeni Fowzi Ahmad
Published: September 2002

The lower semi‐continuity of best approximation operators from Banach lattices on to closed ideals is investigated. Also the existence of best approximation to sub‐function modules of function modules is proved. The order intersection properties of cells are studied and used to prove the above results.