bluuebunny/crossref_metadata_2025 huggingface dataset:
Submodules of secondary modules
Authors: Atani Shahabaddin Ebrahimi
Published: September 2002

Let R be a commutative ring with nonzero identity. Our
objective is to investigate representable modules and to examine
in particular when submodules of such modules are representable.
Moreover, we establish a connection between the secondary modules
and the pure‐injective, the Σ‐pure‐injective, and the prime modules.
Graded radical W type Lie algebras I
Authors: Nam Ki-Bong
Published: September 2002

We get a new ℤ‐graded Witt type simple Lie algebra
using a generalized polynomial ring which is the radical extension
of the polynomial ring F[x] with the exponential function ex.
q‐hyperelliptic compact nonorientable Kleinsurfaces without boundary
Authors: Bujalance J. A. , Estrada B.
Published: September 2002

Let X be a nonorientable Klein surface (KS in short), that is a
compact nonorientable surface with a dianalytic structure defined
on it. A Klein surface X is said to be q‐hyperelliptic if and only if there exists an involution Φ on X (a dianalytic homeomorphism of order
two) such that the quotient X/〈Φ〉 has algebraic genus q. q‐hyperelliptic nonorientable KSs without boundary
(nonorientable Riemann surfaces) were characterized by means of
non‐Euclidean crystallographic groups. In this paper, using that
characterization, we determine bounds for the order of the
automorphism group of a nonorientable q‐hyperelliptic Klein surface X such that X/〈Φ〉 has no boundary and
prove that the bounds are attained. Besides, we obtain the
dimension of the Teichmüller space associated to this type of surfaces.
Generalized Beltrami flows and other closed‐form solutions of an unsteady viscoelastic fluid
Authors: Labropulu F.
Published: September 2002

We study flows of an unsteady non‐Newtonian fluid by assuming the form of the vorticity a priori. The two forms that have been considered are ∇2ψ = F(t)ψ + G(t), which is known as the generalized Beltrami flow and ∇2ψ = f(t)ψ + g(t)y.
Cut points in abcohesive, aposyndetic, and semi‐locally connected spaces
Authors: John David A. , So Shing S.
Published: September 2002

In 1941, F. B. Jones introduced aposyndesis, which generalizes
the concept of semi‐local connectedness defined earlier by G. T. Whyburn (1942), in the study of continuum theory. Using Jones′s idea, D. A. John (1993) defined abcohesiveness as a generalization of aposyndesis and studied the A‐sets in abcohesive spaces. In this paper, some properties of abcohesive spaces are studied and a number of results by B. Lehman (1976) and Whyburn (1942, 1968) are generalized; sufficient conditions for the existence of two nodal sets are established as well.
Common fixed point theorems for a weak distance in complete metric spaces
Authors: Ume Jeong Sheok , Yi Sucheol
Published: September 2002

Using the concept of a w‐distance, we obtain common fixed point theorems on complete metric spaces. Our results generalize the corresponding theorems of Jungck, Fisher, Dien, and Liu.
The Galois algebras and the Azumay Galois extensions
Authors: Szeto George , Xue Lianyong
Published: September 2002

Let B be a Galois algebra over a commutative ring R with Galois group G, C the center of B, K = {g ∈ G | g(c) = c for all  c ∈ C}, Jg{b ∈ B | bx = g(x)b for all x ∈ B} for each g ∈ K, and BK = (⊕∑g∈K Jg). Then BK is a central weakly Galois algebra with Galois group induced by K. Moreover, an Azumaya Galois extension B with Galois group K is characterized by using BK.
Typically real logharmonic mappings
Authors: Abdulhadi Zayid
Published: September 2002

We consider logharmonic mappings of the form defined on the unit disk U which are typically real. We obtain representation theorems and distortion theorems. We determine the radius of univalence and starlikeness of these mappings. Moreover, we derive a geometric characterization of such mappings.
Continuous and Lp estimates for the complex Monge‐Ampère equation on bounded domains in ℂn
Authors: Darko Patrick W.
Published: September 2002

Continuous solutions with continuous data and Lp solutions with Lp data are obtained for the complex Monge‐Ampère equation on bounded domains, without requiring any smoothness of the domains.
Existance theroms for the matrix Riccati equation W′ + WP(t)W + Q(t) = 0
Authors: Jones Robert A.
Published: September 2002

Sufficient conditions are established for the matrix Riccati equation to have a symmetric solution on a given interval. The criteria involve integral conditions on the coefficient matrices of the Riccati equation. The present results are compared with previously known results.
The conjugate of a singular functional differentialoperator
Authors: Hall L. M.
Published: September 2002

An explicit representation of the conjugate of a singular functional differential operator is given. Some theorems and their corollaries are proven.
On L1‐convergence of Walsh‐Fourier series
Authors: Onneweer C. W.
Published: September 2002

Let G denote the dyadic group, which has as its dual group the Walsh(‐Paley) functions. In this paper we formulate a condition for functions in L1(G) which implies that their Walsh‐Fourier series converges in L1(G)‐norm. As a corollary we obtain a Dini‐Lipschitz‐type theorem for L1(G) convergence and we prove that the assumption on the L1(G) modulus of continuity in this theorem cannot be weakened. Similar results also hold for functions on the circle group T and their (trigonometric) Fourier series.
A note on Riemann integrability
Authors: Beer G. A.
Published: September 2002

In this note we define Riemann integrabillty for real valued functions defined on a compact metric space accompanied by a finite Borel measure. If the measure of each open ball equals the measure of its corresponding closed ball, then a bounded function is Riemann integrable if and only if its set of points of discontinuity has measure zero.
On the definition of a close‐to‐convex function
Authors: Goodman A. W. , Saff E. B.
Published: September 2002

The standard definition of a close‐to‐convex function involves a complex numerical factor eiβ which is on occasion erroneously replaced by 1. While it is known to experts in the field that this replacement cannot be made without essentially changing the class, explicit reasons for this fact seem to be lacking in the literature. Our purpose is to fill this gap, and in so doing we are lead to a new coefficient problem which is solved for n = 2, but is open for n > 2.
Generalized Whittaker′s equations for holonomic mechanicalsystems
Authors: Hussain Munawar
Published: September 2002

In this paper the classical theorem “a conservative holonomic dynamic system is invariantly connected with a certain differential form” is generalized to group variables. This general theorem is then used to reduce the order of a Hamiltonian system by the use of the integral of energy. Equations of motion of the reduced system so obtained are derived which are the so‐called generalized Whittaker′s equations. Finally an example is given as an application of the theory.
Some analogues of Knopp’s core theorem
Authors: Maddox I. J.
Published: September 2002

Inequalities between certain functionals on the space of bounded real sequences are considered. Such inequalities being analogues of the classical theorem of Knopp on the core of a sequence. Also, a result is given on infinite matrices of bounded linear operators acting on bounded sequences in a Banach space.
Rings with involution whose symmetric elements are central
Authors: Lim Taw Pin
Published: September 2002

In a ring R with involution whose symmetric elements S are central, the skew‐symmetric elements K form a Lie algebra over the commutative ring S. The classification of such rings which are 2‐torsion free is equivalent to the classification of Lie algebras K over S equipped with a bilinear form f that is symmetric, invariant and satisfies [[x, y], z] = f(y, z)x − f(z, x)y. If S is a field of char ≠2, f ≠ 0 and dimK > 1 then K is a semisimple Lie algebra if and only if f is nondegenerate. Moreover, the derived algebra K′ is either the pure quaternions over S or a direct sum of mutually orthogonal abelian Lie ideals of dim≤2.
Ranked solutions of the matric equation A1X1 = A2X2
Authors: Porter A. Duane , Mousouris Nick
Published: September 2002

Let GF(pz) denote the finite field of pz elements. Let A1 be s × m of rank r1 and A2 be s × n of rank r2 with elements from GF(pz). In this paper, formulas are given for finding the number of X1,X2 over GF(pz) which satisfy the matric equation A1X1 = A2X2, where X1 is m × t of rank k1, and X2 is n × t of rank k2. These results are then used to find the number of solutions X1, …, Xn, Y1, …, Ym, m, n > 1, of the matric equation A1X1 … Xn = A2Y1 … Ym.
The radius of convexity of certain analytic functions II
Authors: Ratti J. S.
Published: September 2002

In [2], MacGregor found the radius of convexity of the functions f(z) = z + a2z2 + a3z3 + …, analytic and univalent such that |f′(z) − 1| < 1. This paper generalized MacGregor′s theorem, by considering another univalent function g(z) = z + b2z2 + b3z3 + … such that for |z| < 1. Several theorems are proved with sharp results for the radius of convexity of the subfamilies of functions associated with the cases: g(z) is starlike for |z| < 1, g(z) is convex for |z| < 1, Re{g′(z)} > α(α = 0, 1/2).
An analytic solution of the non‐linear equation ∇2λ(r) = f(λ) and its application to the ion‐atmosphere theory of strong electrolytes
Authors: Bagchi S. N.
Published: September 2002

For a long time the formulation of a mathematically consistent statistical
mechanical theory for a system of charged particles had remained a formidable unsolved problem. Recently, the problem had been satisfactorily solved, (see Bagchi [1] [2]) ,by utilizing the concept of ion‐atmosphere and generalized Poisson‐Boltzmann (PB) equation. Although the original Debye‐Hueckel (DH) theory of strong electrolytes [3] cannot be accepted as a consistent theory, neither mathematically nor physically, modified DH theory, in which the exclusion volumes of the ions enter
directly into the distribution functions, had been proved to be mathematically consistent. It also yielded reliable physical results for both thermodynamic and transport properties of electrolytic solutions. Further, it has already been proved by the author from theoretical considerations (cf. Bagchi [4])as well as from a posteriori verification (see refs. [1] [2]) that the concept of ion‐atmosphere and the use of PB equation retain their validities generally. Now during the past 30 years, for convenice of calculations, various simplified versions of the original Dutta‐Bagchi distribution function (Dutta & Bagchi [5])had been used successfully in modified DH theory of solutions of strong electrolytes. The primary object of this extensive study, (carried out by the author during 1968‐73), was to decide a posteriori by using the exact analytic solution of the relevant PB equation about the most suitable, yet theoretically consistent, form of the distribution function. A critical analysis of these results eventually led to the formulation of a new approach to the statistical mechanics of classical systems, (see Bagchi [2]), In view of the uncertainties inherent in the nature of the system to be discussed below, it is believed that this voluminous work, (containing 35 tables and 120 graphs), in spite of its legitimate simplifying assumptions, would be of great assistance to those who are interested in studying the properties of ionic solutions from the standpoint of a physically and mathematically consistent theory.
A note of equivalence classes of matrices over a finite field
Authors: Brawley J. V. , Mullen Gary L.
Published: September 2002

Let denote the algebra of m × m matrices over the finite field Fq of q elements, and let Ω denote a group of permutations of Fq. It is well known that each ϕϵΩ can be represented uniquely by a polynomial ϕ(x)ϵFq[x] of degree less than q; thus, the group Ω naturally determines a relation ∼ on as follows: if then A ~ B if ϕ(A) = B for some ϕϵΩ. Here ϕ(A) is to be interpreted as substitution into the unique polynomial of degree <q which represents ϕ.

In an earlier paper by the second author [1], it is assumed that the relation ∼ is an equivalence relation and, based on this assumption, various properties of the relation are derived. However, if m ≥ 2, the relation ∼ is not an equivalence relation on . It is the purpose of this paper to point out the above erroneous assumption, and to discuss two ways in which hypotheses of the earlier paper can be modified so that the results derived there are valid.
An ordered set of Nörlund means
Authors: Defranza J.
Published: September 2002

Nörlund methods of summability are studied as mappings from ℓ1 into ℓ1. Those Nörlund methods that map ℓ1 into ℓ1 are characterized. Inclusion results are given and a class of Nörlund methods is shown to form an ordered abelian semigroup.
A result on co‐chromatic graphs
Authors: Farrell E. J.
Published: September 2002

A sufficient condition for two graphs with the same number of nodes to have the same chromatic polynomial is given.
A characterization of pseudocompactness
Authors: Misra Prabduh Ram , Vinodkumar
Published: September 2002

It is proved here that a completely regular Hausdorff space X is pseudocompact if and only if for any continuous function f from X to a pseudocompact space (or a compact space) Y, f*ϕ is z‐ultrafilter whenever ϕ is a z‐ultrafilter on X.
On some extensions of the accelerated overrelaxation (AOR) theory
Authors: Hadjidimos A. , Yeyios A.
Published: September 2002

This paper extends the convergence theory of the Accelerated Overrelaxation (AOR) method to cases analogous to those considered first by Ostrowski and then by Varga in connection with the Successive Overrelaxation (SOR) method. Among others, the Ostrowski Theorem, some of the theorems by Varga on the extensions of the SOR theory, and some recent results by Niethammer and by the authors are obtained as special cases of the work presented in this paper. In addition, several points are raised which suggest further research.
Algebras with actions and automata
Authors: Kühnel W. , Pfender M. , Meseguer J. , Sols I.
Published: September 2002

In the present paper we want to give a common structure theory of left action, group operations, R‐modules and automata of different types defined over various kinds of carrier objects: sets, graphs, presheaves, sheaves, topological spaces (in particular: compactly generated Hausdorff spaces). The first section gives an axiomatic approach to algebraic structures relative to a base category B, slightly more powerful than that of monadic (tripleable) functors. In section 2 we generalize Lawveres functorial semantics to many‐sorted algebras over cartesian closed categories. In section 3 we treat the structures mentioned in the beginning as many‐sorted algebras with fixed “scalar” or “input” object and show that they still have an algebraic (or monadic) forgetful functor (theorem 3.3) and hence the general theory of algebraic structures applies. These structures were usually treated as one‐sorted in the Lawvere‐setting, the action being expressed by a family of unary operations indexed over the scalars. But this approach cannot, as the one developed here, describe continuity of the action (more general: the action to be a B‐morphism), which is essential for the structures mentioned above, e.g. modules for a sheaf of rings or topological automata. Finally we discuss consequences of theorem 3.3 for the structure theory of various types of automata. The particular case of algebras with fixed “natural numbers object” has been studied by the authors in [23].
Integrity basis for a second‐order and a fourth‐order tensor
Authors: Betten Josef
Published: September 2002

In this paper a scalar‐valued isotropic tensor function is considered, the variables of which are constitutive tensors of orders two and four, for instance, characterizing the anisotropic properties of a material. Therefore, the system of irreducible invariants of a fourth‐order tensor is constructed. Furthermore, the joint or simultaneous invariants of a second‐order and a fourth‐order tensor are found. In a similar way one can construct an integrity basis for a tensor of order greater than four, as shown in the paper, for instance, for a tensor of order six.
Stability implications on the asymptotic behavior of nonlinear systems
Authors: Chiou Kuo-Liang
Published: September 2002

In this paper we generalize Bownds′ Theorems (1) to the systems and . Moreover we also show that there always exists a solution X(t) of for which limt→∞sup‖X(t)‖ > o( = ∞) if there exists a solution Y(t) for which limt→∞sup‖Y(t)‖ > o( = ∞).
On some fixed point theorems in Banach spaces
Authors: Pai D. V. , Veeramani P.
Published: September 2002

In this paper, some fixed point theorems are proved for multi‐mappings as well as a pair of mappings. These extend certain known results due to Kirk, Browder, Kanna, Ćirić and Rhoades.
Axial shear modulus of a fiber‐reinforced composite with random fiber cross‐sections
Authors: Bose S. K. , Debnath L.
Published: September 2002

A study is made of the effective axial shear modulus of a fiber reinforced material with random fiber cross‐sections so that the micromechanics is governed by stochastic differential equations. A coarse‐graining procedure is adopted to investigate the macroscopic behavior of the material. This analysis leads to the formula for the effective axial shear modulus

urn:x-wiley:01611712:media:ijmm471593:ijmm471593-math-0001

where μ1 and μ2 are the shear modulus of the matrix and fibers respectively and c is the concentration of the fibers less that 0.5. For c > 0.5, the fiber and matrix moduli are to be interchanged and c is to be replaced by 1 − c. The results of this study are compared with those of the theory of fibre reinforced materials. Finally, a numerical example is presented with graphical representation.
The chromatic index of cyclic Steiner 2‐designs
Authors: Colbourn Charles J. , Colbourn Marlene J.
Published: September 2002

The number of colours needed to colour the blocks of a cyclic Steiner 2‐design S(2, k, v) is at most v.
Heat transfer between a fluid and a plate: multidimensional Laplace transformation methods
Authors: Buschman R. G.
Published: September 2002

Multidimensional Laplace transformations are used to obtain the surface
temperature and the surface heat flux of a plate with a fluid flowing across it without solving the complete boundary value problem. It is also shown that the constant initial and boundary values can be relaxed and the method still applies. The solution to the boundary value problem at points away from the surface can be treated similarly
Advanced differential equations with piecewise constant argument deviations
Authors: Shah S. M. , Wiener Joseph
Published: September 2002

Functional differential equations of advanced type with piecewise constant
argument deviations are studied. They are closely related to impulse, loaded and, especially, to difference equations, and have the structure of continuous dynamical systems within intervals of unit length.
Propagation of elastic waves in DNA
Authors: Mukherjee Sunil , Sarkar Saumyendra Nath , Raychaudhuri Probhas , Mazumdar Sunil Kumar
Published: September 2002

The mathematical analyses of longitudinal and torsional elastic waves transmitted along DNA molecule undergoing Brownian motion in solution are presented. Longitudinal vibrations in DNA are shown to be responsible for drug intercalation and breathing. The near neighbor exclusion mode of drug intercalation is explained. Torsional oscillations in DNA are shown to be responsible for conformation transitions from a right handed to a left handed form, depending on sequence specificity in high salt concentration.
A helly number for unions of two boxes in R2
Authors: Breen Marilyn
Published: September 2002

Let S be a polygonal region in the plane with edges parallel to the coordinate axes. If every 5 or fewer boundary points of S can be partitioned into sets A and B so that conv A ⋃  conv B⫅S, then S is a union of two convex sets, each a rectangle. The number 5 is best possible.

Without suitable hypothesis on edges of S, the theorem fails. Moreover, an example reveals that there is no finite Helly number which characterizes arbitrary unions of two convex sets, even for polygonal regions in the plane.
More on the Schur group of a commutative ring
Authors: Mollin R. A.
Published: September 2002

The Schur group of a commutative ring, R, with identity consists of all classes in the Brauer group of R which contain a homomorphic image of a group ring RG for some finite group G. It is the purpose of this article to continue an investigation of this group which was introduced in earlier work as a natural generalization of the Schur group of a field. We generalize certain facts pertaining to the latter, among which are results on extensions of automorphisms and decomposition of central simple algebras into a product of cyclics. Finally we introduce the Schur exponent of a ring which equals the well‐known Schur index in the global or local field case.
Extensions of some formulae of A. Selberg
Authors: Spiro Claudia A.
Published: September 2002

This paper is concerned with estimating the number of positive integers up to some bound (which tends to infinity), such that they have a fixed number of prime divisors, and lie in a given arithmetic progression. We obtain estimates which are uniform in the number of prime divisors, and at the same time, in the modulus of the arithmetic progression. These estimates take the form of a fixed but arbitrary number of main terms, followed by an error term.
Approximation of irrationals
Authors: Baica Malvina
Published: September 2002

The author uses a new modification of Jacobi‐Perron Algorithm which holds for complex fields of any degree (abbr. ACF), and defines it as Generalized Euclidean Algorithm (abbr. GEA) to approximate irrationals.

This paper deals with approximation of irrationals of degree
n = 2, 3, 5. Though approximations of these irrationals in a variety of patterns are known, the results are new and practical, since there is used an algorithmic method.
Constructions of positive commutative semigroups on the plane, II
Authors: Farley Reuben W.
Published: September 2002

A positive semiroup is a topological semigroup containing a subsemigroup
N isomorphic to the multiplicative semigroup of nonnegative real numbers, embedded as
a closed subset of E2 in such a way that 1 is an identity and 0 is a zero. Using results in Farley [1] it can be shown that positive commutative semigroups on the plane constructed by the techniques given in Farley [2] cannot contain an infinite number of two dimensional groups. In this work an example of such a semigroup will be constructed which does, however, contain an infinite number of one dimensional groups. Also, some preliminary results are given here concerning what types of semilattices of idempotent elements are possible for positive commutative semigroups on E2. In particular, we will show that there is a unique positive commutative semigroup on E2 which is the union of connected groups and which contains five idempotent elements. Also, we will show that such semigroups having nine idempotent elements are not unique by constructing an example of such a semigroup with nine idempotent elements whose semilattice of idempotent elements is not “symmetric” and hence which is not isomorphic to the semigroup with nine idempotent elements constructed in Farley [2].
A singular boundary value problem for neutral equations
Authors: Angelov Vasil G.
Published: September 2002

Using some previous results of the author and Kirk‐Schöneberg,
theorems for the existence and uniqueness of an absolutely continuous solution of a singular boundary value problem for neutral equations have been proved.
On the order of exponential growth of the solution of the linear difference equation with periodic coefficient in Banach space
Authors: Hussein H. Attia
Published: September 2002

An equation of the form y − A(t)y = f(t) is considered, where , and the necessary and sufficient criteria for the exponential growth of the solution of this equation is obtained.
A note on periodic solutions of functional differential equations
Authors: Chang S. H.
Published: September 2002

The existence of periodic solution for a certain functional differential equation with quasibounded nonlinearity is established.
On fixed points of set‐valued directional contractions
Authors: Park Sehie
Published: September 2002

Using equivalent formulations of Ekeland′s theorem, we improve fixed point theorems of Clarke, Sehgal, Sehgal‐Smithson, and Kirk‐Ray on directional contractions by giving geometric estimations of fixed points.
Compatible mappings and common fixed points
Authors: Jungck Gerald
Published: September 2002

A generalization of the commuting mapping concept is introduced. Properties of this “weakened commutativity” are derived and used to obtain results which generalize a theorem by Park and Bae, a theorem by Hadzic, and others.
On a generalization of the corona problem
Authors: Gentili Graziano , Struppa Daniele C.
Published: September 2002

Let g, f1, …, fm ∈ H∞(Δ). We provide conditions on f1, …, fm in order that |g(z)| ≤ |f1(z)| + …+|fm(z)|, for all z in Δ, imply that g, or g2, belong to the ideal generated by f1, …, fm in H∞.
Co‐convexial reflector curves with applications
Authors: Al-Rashed Abdallah M. , Zaheer Neyamat
Published: September 2002

The concept of reflector curves for convex compact sets of reflecting type in the complex plane was introduced by the authors in a recent paper (to appear in J. Math. Anal. and Appln.) in their attempt to solve a problem related to Stieltjes and Van Vleck polynomials. Though, in the said paper, certain convex compact sets (e.g. closed discs, closed line segments and the ones with polygonal boundaries) were shown to be of reflecting type, it was only conjectured that all convex compact sets are likewise. The present study not only proves this conjecture and establishes the corresponding results on Stleltjes and Van Vleck polynomials in its full generality
as proposed earlier by the authors, but it also furnishes a more general family of curves sharing the properties of confocal ellipses.
On quasi‐convex functions and related topics
Authors: Noor Khalida Inayat
Published: September 2002

Let S be the class of functions f which are analytic and univalent in the unit disc E with f(0) = 0, f′(0) = 1. Let C, S* and K be the classes of convex, starlike and close‐to‐convex functions respectively. The class C* of quasi‐convex functions is defined as follows:

Let f be analytic in E and f(0), f′(0) = 1. Then f ϵ C* if and only if there exists a g ϵ C such that, for z ϵ E

urn:x-wiley:01611712:media:ijmm491830:ijmm491830-math-0001

.

In this paper, an up‐to‐date complete study of the class C* is given. Its basic properties, its relationship with other subclasses of S, coefficient problems, arc length problem and many other results are included in this study. Some related classes are also defined and studied in some detail.
Convergence theorems for Banach space valued integrable multifunctions
Authors: Papageorgiou Nikolaos S.
Published: September 2002

In this work we generalize a result of Kato on the pointwise behavior of a weakly convergent sequence in the Lebesgue‐Bochner spaces . Then we use that result to prove Fatou′s type lemmata and dominated convergence theorems for the Aumann integral of Banach space valued measurable multifunctions. Analogous convergence results are also proved for the sets of integrable selectors of those multifunctions. In the process of proving those convergence theorems we make some useful observations concerning the Kuratowski‐Mosco convergence of sets.
On coincidence theorems for a family of mappings in convex metric spaces
Authors: Hadzic Olga
Published: September 2002

In this paper, a theorem on common fixed points for a family of mappings defined on convex metric spaces is presented. This theorem is a generalization of the well known fixed point theorem proved by Assad and Kirk. As an application a common fixed point theorem in metric spaces with a convex structure is obtained.
Poisson stability in product of dynamical systems
Authors: Kumar A. , Bhagat R. P.
Published: September 2002

This paper deals with Poisson stable and distal dynamical system. It is shown that the product of Poisson stable motions is a Poisson stable motion in dynamical systems.
Dynamics of multilayered orthotropic viscoelastic plates of Maxwell solids
Authors: Roy P. Pal , Debnath L.
Published: September 2002

This paper is concerned with a simplified dynamical analysis of orthotropic viscoelastic plates that are made up of an arbitrary number of layers each of which is a Maxwell type solid. This study includes the case where some or all the layers are themselves constituted by thinly laminated materials with couple stresses. The recurrence equations for the shear stresses are obtained for an arbitrary number of layers and then applied to plates with two or three layers. The viscoelastic damping effect is determined by the process of linearization and then illustrated by a plate composed of one, two or three layers. It is found that the damping increases with anisotropy and wave number. These results are shown by graphical representations.
Recent results in hyperring and hyperfield theory
Authors: Nakassis Anastase
Published: September 2002

This survey article presents some recent results in the theory of hyperfields and hyperrings, algebraic structures for which the sum of two elements is a subset of the structure. The results in this paper show that these structures cannot always be embedded in the decomposition of an ordinary structure (ring or field) in equivalence classes and that the structural results for hyperfields and hyperrings cannot be derived from the corresponding results in field and ring theory.
A generalization of the global limit theorems of R. P. Agnew
Authors: Rosalsky Andrew
Published: September 2002

For distribution functions {Fn, n ≥ 0}, the relationship between the weak convergence of Fn to F0 and the convergence of ∫Rϕ(|Fn − F0|)dx to 0 is studied where ϕ is a nonnegative, nondecreasing function. Sufficient and, separately, necessary conditions are given for the latter convergence thereby generalizing the so‐called global limit theorems of Agnew wherein ϕ(t) = |t|r. The sufficiency results are shown to be sharp and, as a special case, yield a global version of the central limit theorem for independent random variables obeying the Liapounov condition. Moreover, weak convergence of distribution functions is characterized in terms of their almost everywhere limiting behavior with respect to Lebesgue measure on the line.

Addendum: A generalization of the global limit theorems of R. P. Agnewdx.doi.org/10.1155/S0161171288000699
A pair of biorthogonal polynomials for the Szegö‐Hermite weight function
Authors: Thakare N. K. , Madhekar M. C.
Published: September 2002

A pair of polynomial sequences and where is of degree n in xk and is of degree m in x, is constructed. It is shown that this pair is biorthogonal with respect to the Szegö‐Hermite weight function |x|2μexp(−x2), (μ > −1/2) over the interval (−∞, ∞) in the sense that

urn:x-wiley:01611712:media:ijmm292373:ijmm292373-math-0005

urn:x-wiley:01611712:media:ijmm292373:ijmm292373-math-0006

where m, n = 0, 1, 2, … and k is an odd positive integer.

Generating functions, mixed recurrence relations for both these sets are obtained. For k = 1, both the above sets get reduced to the orthogonal polynomials introduced by professor Szegö.
Non archimedean metric induced fuzzy uniform spaces
Authors: Lowen R. , Srivastava A. K. , Wuyts p.
Published: September 2002

It is shown that the category of non‐Archimedean metric spaces with 1‐Lipschitz
maps can be embedded as a coreflective non‐bireflective subcategory in the category
of fuzzy uniform spaces. Consequential characterizations of topological and uniform
properties are derived.
On a class of polynomials associated with the Cliques in a graph and its applications
Authors: Farrell E. J.
Published: September 2002

The clique polynomial of a graph is defined. An explicit formula is then
derived for the clique polynomial of the complete graph. A fundamental theorem and a
reduction process is then given for clique polynomials. Basic properties of the
polynomial are also given. It is shown that the number theoretic functions defined
by Menon are related to clique polynomials. This establishes a connection between
the clique polynomial and decompositions of finite sets, symmetric groups and
analysis.
On (J, pn) summability of Fourier series
Authors: Mazhar S. M.
Published: September 2002

In this note two theorems have been established. The first one deals with
the summability (J, pn) of a Fourier series while the second on concerns with the
summability of the first derived Fourier series. These results include, as a special
case, certain results of Nanda [1].
Linear and Riccati matrix equations
Authors: Williams Lloyd K.
Published: September 2002

In this paper we find exact solutions for linear ordinary differential equations
of any order when they are given in matrix form, as well as for classes of Riccati
matrix equations with two or three arbitrary matrix coefficients. Other nonlinear systems
of triangular form are also solved completely.
Application of decomposition to hyperbolic, parabolic, and elliptic partial differential equations
Authors: Adomian G.
Published: September 2002

The decomposition method is applied to examples of hyperbolic, parabolic,
and elliptic partial differential equations without use of linearizatlon techniques.
We consider first a nonlinear dissipative wave equation; second, a nonlinear equation
modeling convectlon‐diffusion processes; and finally, an elliptic partial differential
equation.
Notes on certain class of analytic functions with negative coefficients
Authors: Owa Shigeyoshi , Sekine Tadayuki , Yaguchi Teruo , Nunokawa Mamoru , Pashkouleva Donka
Published: September 2002

The object of the present paper is to show the extreme points of the class
A(n,Bk) consisting of analytic functions with negative coefficients and the support
points of the subclass A *(n,Bk) of A(n,Bk).
On anti‐commutative semirings
Authors: Ratti J. S. , Lin Y. F.
Published: September 2002

An anticommutative semiring is completely characterized
by the types of multiplications that are permitted. It is shown
that a semiring is anticommutative if and only if it is a product
of two semirings R1
and R2
such that R1 is left multiplicative and
R2 is right multiplicative.
Generalizing the arithmatic geometric mean — a hapless computer experiment
Authors: Peetre Jaak
Published: September 2002

The paper discusses the asymptotic behavior of generalizations of the Gauss′s arithmetic‐geometric mean, associated with the names Meissel (1875) and Borchardt (1876). The ”hapless computer experiment” in the title refers to the fact that the author at an earlier stage thought that one had genuine asymptotic formulae but it is now shown that in general ”fluctuations” are present. However, no very conclusive results are obtained so the paper ends in a conjecture concerning the special rôle of the algorithms of Gauss and Borchardt. The paper discusses the asymptotic behavior of generalizations of the Gauss′s arithmetic‐geometric mean, associated with the names Meissel (1875) and Borchardt (1876). The ”hapless computer experiment” in the title refers to the fact that the author at an earlier stage thought that one had genuine asymptotic formulae but it is now shown that in general ”fluctuations” are present. However, no very conclusive results are obtained so the paper ends in a conjecture concerning the special rôle of the algorithms of Gauss and Borchardt.
Fixed point theorems for compatible multi‐valued and single‐valued mappings
Authors: Kaneko Hideaki , Sessa Salvatore
Published: September 2002

The notion of compatibility for point‐to‐point mappings recently defined by
Jungck is generalized to include multi‐valued mappings. This idea is used to establish a fixed
point theorem for a generalized contractive multi‐valued mapping and a single‐valued mapping.
A generalized Frattini subgroup of a finite group
Authors: Bhattacharya Prabir , Mukherjee N. P.
Published: September 2002

For a finite group G and an arbitrary prime p, let SP(G) denote the intersection of all maximal subgroups M of G such that [G:M] is both composite and not divisible by p; if no such M exists we set SP(G) = G. Some properties of G are considered involving SP(G). In particular, we obtain a characterization of G when each M in the definition of SP(G) is nilpotent.
On the number of solutions of some integral equations arising in radiative transfer
Authors: Argyros Ioannis K.
Published: September 2002

We discuss the number of solutions of some nonlinear integral equations
arising in the theories of radiative transfer, neutron transport and in the kinetic
theory of gases.
On the number of cut‐vertices in a graph
Authors: Hopkins Glenn , Staton William
Published: September 2002

A connected graph with n vertices contains no more than cutvertices
of degree r. All graphs in which the bound is achieved are described. In
addition, for graphs of maximum degree three and minimum δ, best possible bounds are
obtained for δ=1, 2, 3.
Conservation laws for incompressible fluids
Authors: Caviglia G. , Morro A.
Published: September 2002

By means of a direct approach, a complete set of conservation laws for incompressible
fluids is determined. The problem is solved in the material (Lagrangian) description and the results
are eventually rewritten in the spatial (Eulerian) formulation. A new infinite family of conservation
laws is determined, besides those for linear momentum, angular momentum, energy and helicity.
Kelvin principle for a class of singular equations
Authors: Altin Abdullah , Young Eutiquio C.
Published: September 2002

The classical Kelvin principle concerns invariance of solutions of the Laplace equation with respect to inversion in a sphere. By employing a hyperbolic‐polar coordinate system, the principle is extended to cover a class of singular equations, which include the ultrahyperbolic equation.
Regularity of “F ” method of summability of sequences
Authors: Wei Yu Chuen
Published: September 2002

This paper is to develop theorems concerning the REGULARITY of the method
“F” which is more general than Cesaro′s, Able′s and Riemann′s methods In the
theory of summabillty.
On coarse‐grained entropy and mixing in statistical mechanics
Authors: Chakrabarti C. G.
Published: September 2002

The object of the paper If the study the roles of non‐equillbrium entropy
and mixing of phases in the statistical characterization of the coarse‐grained
interpretation of the irreversible approach to statistical equilibrlum of an isolated
system.
Locally closed sets and LC‐continuous functions
Authors: Ganster M. , Reilly I. L.
Published: September 2002

In this paper we introduce and study three different notions of generalized
continuity, namely LC‐irresoluteness, LC‐continuity and sub‐LC‐continuity. All three
notions are defined by using the concept of a locally closed set. A subset S of a
topological space X is locally closed if it is the intersection of an open and a
closed set. We discuss some properties of these functions and show that a function
between topological spaces is continuous if and only if it is sub‐LC‐continuous and
nearly continuous in the sense of Ptak. Several examples are provided to illustrate
the behavior of these new classes of functions.
*—Inductive limits and partition of unity
Authors: Murali V.
Published: September 2002

In this note we define and discuss some properties of partition of unity on
*‐inductive limits of topological vector spaces. We prove that if a partition of unity exists
on a *‐inductive limit space of a collection of topological vector spaces, then it is
isomorphic and homeomorphic to a subspace of a *‐direct sum of topological vector spaces.
The uniform boundedness principle for order bounded operators
Authors: Swartz Charles
Published: September 2002

Under appropriate hypotheses on the spaces, it is shown that a sequence
of order bounded linear operators which is pointwise order bounded is uniformly
order bounded on order bounded subsets. This result is used to establish a
Banach‐Steinhaus Theorem for order bounded operators.
Some properties and applications of the stuttering generalized waring distribution
Authors: Panaretos J.
Published: September 2002

The Stuttering Generalized Waring Distribution arises in connection
with sampling from an urn that contains balls of two colours (black and
white) and it can be thought of as an intermingling of generalized Waring
streams (Panaretos and Xekalaki [4]).

Because of its application potential a study of its properties
would be worthwhile. In this paper it is shown that it can be obtained
as a mixture of the generalized Poisson distribution. It is also
demonstrated that, in an urn scheme, increasing the number of balls in the
urn in an appropriate fashion one can end up with a Poisson type or a
negative blnomial type sampling distribution as an approximation
to the stuttering generalized Waring distribution.
Some series whose coefficients involve the value ζ(n) for $n$n odd
Authors: Bragg L. R.
Published: September 2002

By using two basic formulas for the digamma function, we derive a variety
of series that involve as coefficients the values (2n + 1), n = 1, 2, ⋯, of the
Riemann‐zeta function. A number of these have a combinatorial flavor which we also
express in a trignometric form for special choices of the underlying variable. We
briefly touch upon their use in the representation of solutions of the wave equation.
The closed neighborhood and filter conditions in solid sequence spaces
Authors: Johnson, P. D.
Published: September 2002

Let E be a topological vector space of scalar sequences, with topology τ;
(E,τ) satisfies the closed neighborhood condition iff there is a basis of
neighborhoods at the origin, for τ, consisting of sets whlch are closed with respect
to the topology π of coordinate‐wise convergence on E; (E,τ) satisfies the filter
condition iff every filter, Cauchy with respect to τ, convergent with respect
to π, converges with respect to τ.

Examples are given of solid (definition below) normed spaces of sequences which
(a) fail to satisfy the filter condition, or (b) satisfy the filter condition, but not
the closed neighborhood condition. (Robertson and others have given examples
fulfilling (a), and examples fulfilling (b), but these examples were not solid, normed
sequence spaces.) However, it is shown that among separated, separable solid
pairs (E,τ), the filter and closed neighborhood conditions are equivalent, and
equivalent to the usual coordinate sequences constituting an unconditional Schauder
basis for (E,τ). Consequently, the usual coordinate sequences do constitute an
unconditional Schauder basis in every complete, separable, separated, solid
pair (E,τ).
A topological lattice on the set of multifunctions
Authors: Papadopoulos Basil K.
Published: September 2002

Let X be a Wilker space and M(X,Y) the set of continuous multifunctions
from X to a topological space Y equipped with the compact‐open topology. Assuming
that M(X,Y) is equipped with the partial order ⊂ we prove that (M(X,Y), ⊂)
is a
topological V‐semilattice. We also prove that if X is a Wilker normal space and
U(X,Y) is the set of point‐closed upper semi‐continuous multifunctlons equipped with
the compact‐open topology, then (U(X,Y), ⊂) is a topological lattice.
Periodic Boehmians
Authors: Nemzer Dennis
Published: September 2002

A class of generalized functions, called periodic Boehmians, on the unit
circle, is studied. It is shown that the class of Boehmians contain all Beurling
distributions. An example of a hyperfunctlon that is not a Boehmian is given. Some
growth conditions on the Fourier coefficients of a Boehmian are given. It is shown
that the Boehmians, with a given complete metric topological vector space topology, is
not locally bounded.
Exchange PF‐rings and almost PP‐rings
Authors: Al-Ezeh H.
Published: September 2002

Let R be a commutative ring with unity. In this paper, we prove that R is an almost PP–PM–ring if and only if R is an exchange PF–ring. Let X be a completely regular Hausdorff space, and let βX be the Stone Čech compactification of X. Then we prove that the ring C(X) of all continuous real valued functions on X is an almost PP–ring if and only if X is an F–space that has an open basis of clopen sets. Finally, we deduce that the ring C(X) is an almost PP–ring if and only if C(X) is a U–ring, i.e. for each f ε C(X), there exists a unit u ε C(X) such that f = u|f|.
Transmission of obliquely incident surface waves through a narrow gap
Authors: Mandal B. N. , Kundu P. K.
Published: September 2002

This note is concerned with the transmission of a train of surface water waves obliquely incident on a thin plane vertical barrier with a narrow gap. Within the framework of the linearized theory of water waves, the problem is reduced to the solution of an integral equation which is solved approximately. The transmission and reflection co–efficients are also obtained approximately and represented graphically against the different angles of incidence for fixed wave numbers.
Bounds for the mean square error of reliability estimation from gamma distribution in presence of an outlier observation
Authors: Ghitany M. E. , Laverty W. H.
Published: September 2002

In this paper we discuss the behavlor of the statistic
, the uniformly
minimum variance unbiased (UMVU) estimate for the reliability of gamma distribution
with unknown scale parameter σ when an outlier observation is present. Given the
outlier effect on σ, we determine bounds for the mean and mean square error (MSE) of
R(t). A semi‐Bayesian approach is discussed when the outlier effect on σ
is treated
as a random variable having a prior distribution of beta type. Results of the
exponential distribution (Sinha [1]) are given as particular cases of our results.
Sublinear functionals ergodicity and finite invariant measures
Authors: Das G. , Patel B. K.
Published: September 2002

By introducing a sublinear functional involving infinite matrices, we establish
its connection with ergodicity and measure preserving transformation. Further,
we characterize the existence of a finite invariant measure by means of a condition involving
the above sublinear functional.
Space time manifolds and contact structures
Authors: Duggal K. L.
Published: September 2002

A new class of contact manifolds (carring a global non‐vanishing timelike vector field) is introduced to establish a relation between spacetime manifolds and contact structures. We show that odd dimensional strongly causal (in particular, globally hyperbolic) spacetimes can carry a regular contact structure. As examples, we present a causal spacetime with a non regular contact structure and a physical model [Gödel Universe] of Homogeneous contact manifold. Finally, we construct a model of 4‐dimensional spacetime of general relativity as a contact CR‐submanifold.
Abelian theorem for the Stieltjes transform of distributions
Authors: Stanković Bogoljub
Published: September 2002

First, a definition is given of the Stieltjes transform of distributions which contains some well‐known. Then, a structural theorem for distributions having S‐asymptotic is proved. This makes possible to prove two theorems of the Abelian type valued for Stieltjes transforms of distributions given in different ways.
The Dittert′s function on a set of nonnegative matrices
Authors: Hwang Suk Geun , Sohn Mun-Gu , Kim Si-Ju
Published: September 2002

Let Kn denote the set of all n × n nonnegative matrices with entry sum n. For X ∈ Kn with row sum vector (r1, …, rn), column sum vector (c1, …, cn), Let . Dittert′s conjecture asserts that ϕ(X) ≤ 2 − n!/nn for all X ∈ Kn with equality iff X = [1/n]n×n. This paper investigates some properties of a certain subclass of Kn related to the function ϕ and the Dittert′s conjecture.
A proof of Pollaczek‐Spitzer identity
Authors: Paramasamy S.
Published: September 2002

In this note we derive a proof of Pollaczek‐Spitzer identity using a generalization of Takacs ballot theorem.