bluuebunny/crossref_metadata_2025 huggingface dataset:
On a subclass of α‐convex λ‐spiral functions
Authors: Al-Oboudi F. M. , Hidan M. M.
Published: September 2002

Let H denote the class of functions which are analytic in the unit disc Δ = {z : |z| < 1}. In this paper, we introduce the class
of functions f ∈ H with f(z)f′(z)/z ≠ 0, satisfying for z ∈ Δ : {(eiλ − αcosλ)(zf′(z)/f(z)) + αcosλ(1 + zf″(z)/f′(z))}≺cosλ((1 + Az)/(1 + Bz)) + isinλ, where ≺ denotes subordination, α and λ are real numbers, |λ| < π/2
and
−1 ≤ B < A ≤ 1. Functions in
are shown to be λ‐spiral like and hence univalent. Integral representation, coefficients bounds, and other results are given.
On hypersurfaces in a locally affine Riemannian Banach manifold
Authors: Lashin El-Said R. , Mersal Tarek F.
Published: September 2002

We prove that an essential hypersurface of second order in an
infinite dimensional locally affine Riemannian Banach manifold is
a Riemannian manifold of constant nonzero curvature.
Adjoint regular rings
Authors: Heatherly Henry E. , Tucci Ralph P.
Published: September 2002

Let R be a ring. The circle operation is the operation
a∘b = a + b − ab, for all a, b ∈ R. This operation
gives rise to a semigroup called the adjoint semigroup
or circle semigroup of R. We investigate rings in
which the adjoint semigroup is regular. Examples are given which
illustrate and delimit the theory developed.
On certain quasi‐complemented and complemented Banach algebras
Authors: Wong Pak-Ken
Published: September 2002

In this paper, we continue the study of quasi‐complemented algebras and complemented algebras. The former are generalizations of the latter and were introduced in [4] and studied in [4] and [11]. Some results are proved.
The effect of random scale changes on limits of infinitesimalsystems
Authors: Brockett Patrick L.
Published: September 2002

Suppose S = {{Xnj,    j = 1, 2, …, kn}} is an infinitesimal system of random variables whose centered sums converge in law to a (necessarily infinitely divisible) distribution with Levy representation determined by the triple (γ, σ2, M). If {Yj,    j = 1, 2, …} are independent indentically distributed random variables independent of S, then the system S′ = {{YjXnj, j = 1, 2, …, kn}} is obtained by randomizing the scale parameters in S according to the distribution of Y1. We give sufficient conditions on the distribution of Y in terms of an index of convergence of S, to insure that centered sums from S′ be convergent. If such sums converge to a distribution determined by , then the exact relationship between (γ, σ2, M) and is established. Also investigated is when limit distributions from S and S′ are of the same type, and conditions insuring products of random variables belong to the domain of attraction of a stable law.
On generation and propagation of tsunamis in a shallowrunning ocean
Authors: Debnath Lokenath , Basu Uma
Published: September 2002

A theory is presented of the generation and propagation of the two and the three dimensional tsunamis in a shallow running ocean due to the action of an arbitrary ocean floor or ocean surface disturbance. Integral solutions for both two and three dimensional problems are obtained by using the generalized Fourier and Laplace transforms. An asymptotic analysis is carried out for the investigation of the principal features of the free surface elevation. It is found that the propagation of the tsunamis depends on the relative magnitude of the given speed of the running ocean and the wave speed of the shallow ocean. When the speed of the running ocean is less than the speed of the shallow ocean wave, both the two and the three dimensional free surface elevation represent the generation and propagation of surface waves which decay asymptotically as for the two dimensional case and as t−1 for the three dimensional tsunamis. Several important features of the solution are discussed in some detail. As an application of the general theory, some physically realistic ocean floor disturbances are included in this paper.
Convexity, boundedness, and almost periodicity for differential equations in Hillbert space
Authors: Goldstein Jerome A.
Published: September 2002

There are three kinds of results. First we extend and sharpen a convexity inequality of Agmon and Nirenberg for certain differential inequalities in Hilbert space. Next we characterize the bounded solutions of a differential equation in Hilbert space involving and arbitrary unbounded normal operator. Finally, we give a general sufficient condition for a bounded solution of a differential equation in Hilbert space to be almost periodic.
Strong boundedness of analytic functions in tubes
Authors: Carmichael Richard D.
Published: September 2002

Certain classes of analytic functions in tube domains TC = ℝn + iC in n‐dimensional complex space, where C is an open connected cone in ℝn, are studied. We show that the functions have a boundedness property in the strong topology of the space of tempered distributions g′. We further give a direct proof that each analytic function attains the Fourier transform of its spectral function as distributional boundary value in the strong (and weak) topology of g′.
On the overconvergence of certain series
Authors: Blambert M. , Parvatham R.
Published: September 2002

In this work, we consider certain class of exponential series with polynomial coefficients and study the properties of convergence of such series. Then we consider a subclass of this class and prove certain theorems on the overconvergence of such a series, which allow us to determine the conditions under which the boundary of the region of convergence of this series is a natural boundary for the function f defined by this series.
The group of homomorphisms of abelian torsion groups
Authors: Legg M. W.
Published: September 2002

Let G and A be abelian torsion groups. In[5], R. S. Pierce develops a complete set of invariants for Hom(G, A). To compute these invariants he introduces, and uses extensively, the group of small homomorphisms of G into A. Also, using some of Pierce′s methods, Fuchs characterizes this group in [1]. Our purpose in this paper is to characterize Hom(G, A) in what seems to be a more natural manner than either of the treatments just mentioned.
Gelfand pairs and spherical functions
Authors: Dieudonné Jean
Published: September 2002

This is a summary of the lectures delivered on Special Functions and Linear Representation of Lie Groups at the NSF‐CBMS Research Conference at East Carolina University in March 5‐9, 1979. The entire lectures will be published by the American Mathematical Society as a conference monograph in Mathematics.
A graph and its complement with specified properties I: connectivity
Authors: Akiyama Jin , Harary Frank
Published: September 2002

We investigate the conditions under which both a graph G and its complement possess a specified property. In particular, we characterize all graphs G for which G and both (a) have connectivity one, (b) have line‐connectivity one, (c) are 2‐connected, (d) are forests, (e) are bipartite, (f) are outerplanar and (g) are eulerian. The proofs are elementary but amusing.
The (16, 16, 2) designs
Authors: Assmus, Jr E. F. , Salwach Chester J.
Published: September 2002

Elementary techniques of algebraic coding theory are here used to discuss the three biplanes with k = 6. These three designs are intimately related to the (16, 11) extended binary Hamming code and to one another; we systematically investigate these relationships.

We also exhibit each of the three designs as difference sets.
The stieltjes transform of distributions
Authors: Tiwari U. N. , Pandey J. N.
Published: September 2002

In the present work, two complex inversion formulas of Byrne and Love for generalized Stieltjes transformation are shown to be valid for a class of distributions. This is accomplished by transfering the complex inversion formulas on the testing function space of a class of distributions and then showing that the limiting process in the resulting formula converges in the topology of the testing function space.
On Hausdorff compactifications of non‐locally compact spaces
Authors: Hatzenbuhler James , Mattson Don A.
Published: September 2002

Let X be a completely regular, Hausdorff space and let R be the set of points in X which do not possess compact neighborhoods. Assume R is compact. If X has a compactification with a countable remainder, then so does the quotient X/R, and a countable compactificatlon of X/R implies one for X − R. A characterization of when X/R has a compactification with a countable remainder is obtained. Examples show that the above implications cannot be reversed.
Completion functors for Cauchy spaces
Authors: Fric R. , Kent D. C.
Published: September 2002

Completion functors are constructed on various categories of Cauchy spaces by forming the composition of Wyler′s completion functor with suitable modification functors.
Generation of SH‐type waves in layered anisotropic elastic media
Authors: Pal P. C. , Debnath Lokenath
Published: September 2002

A study is made of the generation of SH‐type waves at the free surface of a layered anisotropic elastic medium due to an impulsive stress discontinuity moving with uniform velocity along the interface of the layered medium. The exact solution for the displacement function is obtained by the Laplace and Fourier transforms combined with the modified Cagniard method. The numerical results for an important special case at two different distances are shown graphically. The results of the present study are found to be in excellent agreement with those of isotropic elastic media.
On block irreducible forms over Euclidean domains
Authors: Clark W. Edwin , Liang J. J.
Published: September 2002

In this paper a general canonical form for elements in a ring Euclidean with respect to a real valuation is established. It is also shown that this form is unique and minimal thus gives the arithmetical weight of an element with respect to a radix.
On the block structure of PBIB designs
Authors: Chandak M. L.
Published: September 2002

Let denote the set having any treatment θ and its n1 first associates in a PBIB design with m(≥2) associate classes. A theorem on distribution of the elements of this set among the blocks of the block design is proved and results related to certain well known association schemes of three associate classes are obtained.
A covering theorem for odd typically‐real functions
Authors: Merkes E. P.
Published: September 2002

An analytic function f(z) = z + a2z2 + … in |z| < 1 is typically‐real if Imf(z)Imz ≥ 0. The largest domain G in which each odd typically‐real function is univalent (one‐to‐one) and the domain ⋂f(G) for all odd typically real functions f are obtained.
A non‐linear hyperbolic equation
Authors: de Brito Eliana Henriques
Published: September 2002

In this paper the following Cauchy problem, in a Hilbert space H, is considered:

urn:x-wiley:01611712:media:ijmm732105:ijmm732105-math-0001

urn:x-wiley:01611712:media:ijmm732105:ijmm732105-math-0002

urn:x-wiley:01611712:media:ijmm732105:ijmm732105-math-0003

M and f are given functions, A an operator in H, satisfying convenient hypothesis, λ ≥ 0 and α is a real number.

For u0 in the domain of A and u1 in the domain of , if λ > 0, and u1 in H, when λ = 0, a theorem of existence and uniqueness of weak solution is proved.
Generalized random processes and Cauchy′s problem for some partial differential systems
Authors: El-Borai Mahmoud M.
Published: September 2002

In this paper we consider a parabolic partial differential system of the form DtHt = L(t, x, D)Ht. The generalized stochastic solutions Ht, corresponding to the generalized stochastic initial conditions H0 are given. Some properties concerning these generalized stochastic solutions are also obtained.
PIS for n‐coupled nonlinear systems
Authors: Dey S. K.
Published: September 2002

A numerical algorithm dealing with solutions of equations with one variable may not be extended to solve nonlinear systems with n unknowns. Even when such extensions are possible, properties of these two similar algorithms are, in general, different. In [2] a perturbed iterative scheme (PIS) has been developed to solve nonlinear equations with one variable. Its properties with regard to nonlinear systems were analyzed in [1]. Here these properties were extended to n‐coupled nonlinear systems.
A Lebesgue decomposition for elements in a topological group
Authors: Dence Thomas P.
Published: September 2002

Our aim is to establish the Lebesgue decomposition for strongly‐bounded elements in a topological group. In 1963 Richard Darst established a result giving the Lebesgue decomposition of strongly‐bounded elements in a normed Abelian group with respect to an algebra of projection operators. Consequently, one can establish the decomposition of strongly‐bounded additive functions defined on an algebra of sets. Analagous results follow for lattices of sets. Generalizing some of the techniques yield decompositions for elements in a topological group.
A completion functor for Cauchy groups
Authors: Fric R. , Kent D. C.
Published: September 2002

A completion functor is constructed on the category of completely normal Cauchy groups and Cauchy‐continuous homomorphisms. A competion functor is also obtained for a corresponding category of convergence groups.
On locally divided integral domains and CPI‐overrings
Authors: Dobbs David E.
Published: September 2002

It is proved that an integral domain R is locally divided if and only if each CPI‐extension of ℬ (in the sense of Boisen and Sheldon) is R‐flat (equivalently, if and only if each CPI‐extension of R is a localization of R). Thus, each CPI‐extension of a locally divided domain is also locally divided. Treed domains are characterized by the going‐down behavior of their CPI‐extensions. A new class of (not necessarily treed) domains, called CPI‐closed domains, is introduced. Examples include locally divided domains, quasilocal domains of Krull dimension 2, and qusilocal domains with the QQR‐property. The property of being CPI‐closed behaves nicely with respect to the D + M construction, but is not a local property.
On rank 4 projective planes
Authors: Bachmann O.
Published: September 2002

Let a finite projective plane be called rank m plane if it admits a collineation group G of rank m, let it be called strong rank m plane if moreover GP = G1 for some point‐line pair (P, 1). It is well known that every rank 2 plane is desarguesian (Theorem of Ostrom and Wagner). It is conjectured that the only rank 3 plane is the plane of order 2. By [1] and [7] the only strong rank 3
plane is the plane of order 2. In this paper it is proved that no strong rank 4 plane exists.
Spiral like integral operators
Authors: Bajpai Shyam K.
Published: September 2002

In this paper we investigate the Robertson‐Libera integral operators for the class of spiral like univalent and analytic functions. We find that special types of transformations preserve the class property. Our results generalize or sharpen the results recently obtained by Miller et al [7] and by Causey and White [3].
Yet another characterization of the sine function
Authors: Gervais Robert , Rubel Lee A.
Published: September 2002

In this expository paper, it is shown that if an entire function of exponential type vanishes at least once in the complex plane and if it has exactly the same number of zeros (counting multiplicities) as its second derivative, then this function must take the form Asin(Bz + C).
Convergence analysis of a perturbed iterative scheme (PIS) for solution of nonlinear systems
Authors: Dey S. K.
Published: September 2002

In the references [1, 2, 3] a perturbed iterative scheme (PIS) has been studied both theoretically and computationally to solve nonlinear equations. In this article a more general analysis of its convergence properties has been done
The star compactification
Authors: Richardson G. D. , Kent D. C.
Published: September 2002

The relationships between a convergence space and its star compactification
is studied. Special attention is given to lifting properties of this compactification. In particular, it is shown that a natural extension of any continuous function to the respective compactification spaces is θ‐continuous.
A theory of nonlinear wave loading on offshore structures
Authors: Debnath Lokenath , Rahman Matiur
Published: September 2002

A theoretical study is made of the nonlinear wave loading on offshore
structures using the diffraction theory of hydrodynamics. A nonlinear modification of the classical Morison equation, D ≡ Fℓ + FD for estimating wave forces on offshore structures is suggested in this paper. The modified equation is found in the form D ≡ Fℓ + Fnℓ + FD where Fnℓ ≡ Fd + Fw + Fq is the nonlinear contribution made up of the dynamic, waterline, and the quadratic forces associated with the irrotational‐flow part of the wave loading on structures. The study has then been applied to calculate the linear and the nonlinear wave loadings on a large vertical cylinder partially immersed in an ocean of arbitrary uniform depth. All the linear and nonlinear forces exerting on the cylinder are determined explicitly. A comparison is made between these two kinds of forces. Special attention is given to the nonlinear wave loadings on the cylinder. It is shown that all nonlinear effects come from the interaction between the body′s responses to the oncoming wave′s fluctuating velocity and its fluctuating extension. It is found that the nonlinear effects are dominated by the sum of the dynamic and waterline forces. The nonlinear correction to Morison′s equation increases with increasing kb where b is the characteristic dimension of the body and k is the wave number. This prediction is shown to be contrary to that of the linear diffraction theory which predicted that the Morison coefficient decreases with increasing kb. Several interesting results and limiting cases are discussed in some detail.
On free ring extensions of degree n
Authors: Szeto George
Published: September 2002

Nagahara and Kishimoto [1] studied free ring extensions B(x) of degree n for some integer n over a ring B with 1, where xn = b, cx = xρ(c) for all c and some b in B(ρ = automophism of  B), and {1, x … , xn−1} is a basis. Parimala and Sridharan [2], and the author investigated a class of free ring extensions called generalized quaternion algebras in which b = −1 and ρ is of order 2. The purpose of the present paper is to generalize a characterization of a generalized quaternion algebra to a free ring extension of degree n in terms of the Azumaya algebra. Also, it is shown that a one‐to‐one correspondence between the set of invariant ideals of B under ρ and the set of ideals of B(x) leads to a relation of the Galois extension B over an invariant subring under ρ to the center of B.
A divisibility property of binomial coefficients viewed as an elementary sieve
Authors: Hudson Richard H. , Williams Kenneth S.
Published: September 2002

The triangular array of binomial coefficients

urn:x-wiley:01611712:media:ijmm856269:ijmm856269-math-0001

is said to have undergone a j‐shift if the r‐th row of the triangle is shifted rj units to the right (r = 0, 1, 2, …). Mann and Shanks have proved that in a 2‐shifted array a column number c > 1 is prime if and only if every entry in the c‐th column is divisible by its row number. Extensions of this result to j‐shifted arrays where j > 2 are considered in this paper. Moreover, an analog of the criterion of Mann and Shanks [2] is given which is valid for arbitrary arithmetic progressions.
On an accelerated procedure of extrapolation
Authors: Yeyios A.
Published: September 2002

This paper presents some theoretical results concerning an extrapolation
method, based on a completely consistent linear stationary iterative method of first degree, for the numerical solution of the linear system Au = b.The main purpose of the paper is to find ranges for the extrapolation parameter, such that the extrapolation method converges independently of whether the original iterative method is convergent or not.
Elastodynamic singular points and their applications
Authors: Alawneh A. D. , Kanwal R. P.
Published: September 2002

Suitable singularites such as a dynamical Kelvin quadropole are defined
to study the dynamical displacements set up in an infinite homogeneous and isotropic elastic medium. Approximate solutions are presented up to terms which are of higher order than those known so far.
Generalized group algebras and their bundles
Authors: Schochetman I. E.
Published: September 2002

Our primary objective here is to extend the concept of Banach ∗‐algebraic bundle to the setting where the bundle product and involution are just measurable, i.e. not necessarily continuous. Our secondary objective is to introduce the ∗‐algebra operations into such a bundle by means of operator fields and study the smoothness of these operations in terms of the smoothness of the fields.
The compactum and finite dimensionality in Banach algebras
Authors: Al-Moajil Abdullah H.
Published: September 2002

Given a Banach algebra A, the compactum of A is defined to be the set of elements x ∈ A such that the operator a → xax is compact. General properties of the compactum and its relation to the socle of A are discussed. Characterizations of finite dimensionality of a semi‐simple Banach algebra are given in terms of the compactum and the socle of A.
The second coefficient of a function with all derivatives univalent
Authors: Sathaye A. , Shah S. M.
Published: September 2002

We consider the second coefficient of a class of functions, univalent and normalized, and with all derivatives univalent in the unit disk D, and improve on a known result. It is also shown that this bound is in a sense best possible.
On the periodic solutions of linear homogenous systems of differential equations
Authors: Bose A. K.
Published: September 2002

Given a fundamental matrix ϕ(x) of an n‐th order system of linear homogeneous differential equations Y′ = A(x)Y, a necessary and sufficient condition for the existence of a k‐dimensional (k ≤ n) periodic sub‐space (of period T) of the solution space of the above system is obtained in terms of the rank of the scalar matrix ϕ(t) − ϕ(0).
Instability through porous medium of two viscous superposed conducting fluids
Authors: Sharma R. C. , Thakur K. P.
Published: September 2002

The stability of the plane interface separating two viscous superposed conducting fluids through porous medium is studied when the whole system is immersed in a uniform horizontal magnetic field. The stability analysis is carried out for two highly viscous fluids of equal kinematic viscosities, for mathematical simplicity. It is found that the stability criterion is independent of the effects of viscosity and porosity of the medium and is dependent on the orientation and magnitude of the magnetic field. The magnetic field is found to stabilize a
certain wave number range of the unstable configuration. The behaviour of growth rates with respect to viscosity, porosity and medium permeability are examined analytically.
Some geometric properties of magneto‐fluid flows
Authors: Gangwar S. S. , Babu Ram
Published: September 2002

By employing an anholonomic description of the governing equations, certain geometric results are obtained for a class of non‐dissipative magnetofluid flows. The stream lines are geodesics on a normal congruence of the surfaces which are the Maxwellian surfaces.
Tensor products of commutative Banach algebras
Authors: Tewari U. B. , Dutta M. , Madan Shobha
Published: September 2002

Let A1, A2 be commutative semisimple Banach algebras and A1⊗∂A2 be their projective tensor product. We prove that, if A1⊗∂A2 is a group algebra (measure algebra) of a locally compact abelian group, then so are A1 and A2. As a consequence, we prove that, if G is a locally compact abelian group and A is a comutative semi‐simple Banach algebra, then the Banach algebra L1(G, A) of A‐valued Bochner integrable functions on G is a group algebra if and only if A is a group algebra. Furthermore, if A has the Radon‐Nikodym property, then the Banach algebra M(G, A) of A‐valued regular Borel measures of bounded variation on G is a measure algebra only if A is a measure algebra.
A characterization of singular endomorphisms of a barrelled Pták space
Authors: Franekić Damir
Published: September 2002

The concept of topological divisor of zero has been extended to endomorphisms
of a locally convex topological vector space (LCTVS). A characterization of singular endomorphisms, similar to that of Yood [1], is obtained for endomorphisms of a barrelled Pták (fully complete) space and it is shown that each such endomorphism is a topological divisor of zero. Furthermore, properties of the adjoint of an endomorphism are characterized in terms of topological divisors of zero, and the effect of change of operator topology on such a characterization is given.
A note on Gordan′s theorem over cone domains
Authors: Skarpness Brad , Sposito V. A.
Published: September 2002

This note presents a proof of Gordan′s Theorem over general closed, convex cone domains which follows in a natural way appealing to the standard definitions of closed convex cones and their respective polar cones.
On the partition property of measures on Pℋλ
Authors: Pelletier Donald H.
Published: September 2002

The partition property for measures on Pℋλ was formulated by analogy with a property which Rowbottom [1] proved was possessed by every normal measure on a measurable cardinal. This property has been studied in [2], [3], and [4]. This note summarizes [5] and [6], which contain results relating the partition property with the extendibility of the measure and with an auxiliary combinatorial property introduced by Menas in [4]. Detailed proofs will appear in [5] and [6].
Classification of injective factors: The wok of Alain Connes
Authors: Wright Steve
Published: September 2002

The fundamental results of A. Connes which determine a complete set of isomorphism classes for most injective factors are discussed in detail. After some introductory remarks which lay the foundation for the subsequent discussion, an historical survey of some of the principal lines of the investigation in the classification of factors is presented, culminating in the Connes‐Takesaki structure theory of type III factors. After a discussion of injectivity for finite factors, the main result of the paper, the uniqueness of the injective II1 factor, is deduced, and the structure of II∞ and type III injective factors is then obtained as corollaries of the main result.
Complete function spaces
Authors: Mccoy R. A.
Published: September 2002

A study is made of certain completeness properties of the space of all
continuous real‐valued functions on a space, where this function space has the compact‐open topology.
Effectiveness of transposed inverse sets in faber regions
Authors: Adepoju J. A. , Nassif M.
Published: September 2002

The effectiveness properties, in Faber regions, of the transposed inverse
of a given basic set of polynominals, are investigated in the present paper. A certain inevitable normalizing substitution, is first formulated, to be undergone by the given set to ensure the existence of the transposed inverse in the Faber region. The first main result of the present work (Theorem 2.1), on the one hand, provides a lower bound of the class of functions for which the normalized transposed inverse set is effective in the Faber region. On the other hand, the second main result (Theorem 5.2) asserts the fact that the normalized transposed inverse set of a simple set of polynomials, which is effective in a Faber region, should not necessarily be effective there.
The combinational structure of non‐homogeneous Markov chains with countable states
Authors: Mukherjea A. , Nakassis A.
Published: September 2002

Let P(s, t) denote a non‐homogeneous continuous parameter Markov chain with countable state space E and parameter space [a, b], −∞ < a < b < ∞. Let R(s, t) = {(i, j) : Pij(s, t) > 0}. It is shown in this paper that R(s, t) is reflexive, transitive, and independent of (s, t), s < t, if a certain weak homogeneity condition holds. It is also shown that the relation R(s, t), unlike in the finite state space case, cannot be expressed even as an infinite (countable) product of reflexive transitive relations for certain non‐homogeneous chains in the case when E is infinite.
Two dimentional lattice vibrations from direct product representations of symmetry groups
Authors: Boyd J. N. , Raychowdhury P. N.
Published: September 2002

Arrangements of point masses and ideal harmonic springs are used to model
two dimensional crystals. First, the Born cyclic condition is applied to a double chain composed of coupled linear lattices to obtain a cylindrical arrangement. Then the quadratic Lagrangian function for the system is written in matrix notation. The Lagrangian is diagonalized to yield the natural frequencies of the system. The transformation to achieve the diagonalization was obtained from group theorectic considerations. Next, the techniques developed for the double chain are applied to a square lattice. The square lattice is transformed into the toroidal Ising model. The direct product nature of the symmetry group of the torus reveals the transformation to diagonalize the Lagrangian for the Ising model, and the natural frequencies for the principal directions in the model are obtained in closed form.
Closed spectral measures in Fréchet spaces
Authors: Ricker W.
Published: September 2002

Closed spectral measures, which are often used in the theory of operators, have the desirable property that their L1‐space is complete. In this note criteria are given which assure the closedness of spectral measures acting in Fréchet spaces.
Generalized multitime expansions for equations with slowly varying coefficients
Authors: Levine L. E. , Obi W. C.
Published: September 2002

The successive terms in a uniformly valid multitime expansion of the solutions of constant coefficient differential equations containing a small parameter ϵ may be obtained without resorting to secularity conditions if the time scales ti = ϵit(i = 0, 1, …) are used. Similar results have been achieved in some cases for equations with variable coefficients by using nonlinear time scales generated from the equations themselves. This paper extends the latter approach to the general second order ordinary differential equation with slowly varying coefficients and examines the restrictions imposed by the method.
The Mehler‐Fock transform of general order and arbitrary index and its inversion
Authors: Nasim Cyril
Published: September 2002

An integral transform involving the associated Legendre function of zero order, , x ∈ [1, ∞), as the kernel (considered as a function of τ), is called Mehler‐Fock transform. Some generalizations, involving the function , where the order μ is an arbitrary complex number, including the case when μ = 0, 1, 2, … have been known for some time. In this present note, we define a general Mehler‐Fock transform involving, as the kernel, the Legendre function , of general order μ and an arbitrary index , t = σ + iτ, −∞ < τ < ∞. Then we develop a symmetric inversion formulae for these transforms. Many well‐known results are derived as special cases of this general form. These transforms are widely used for solving many axisymmetric potential problems.
Stable P and distal dynamical systems
Authors: Prasad S. S. , Kumar Anant
Published: September 2002

In this paper we study the behavior of dynamical systems in uniform space which are Poisson stable and distal. The main results are that the trajectories of such motions are closed and every almost periodic motion is stable P and distal. In complete uniform space, this motion is periodic, Lagrange stable and recurrent.
Fields of sets, set functions, set function integrals, and finite additivity
Authors: Appling William D. L.
Published: September 2002

This expository paper discusses, for set functions defined on a field of sets, some of the basic properties of set functions and set function integrals.
Rings all of whose additive group endomorphisms are left multiplications
Authors: Rosen Michael I. , shisha Oved
Published: September 2002

Motivated by Cauchy′s functional equation f(x + y) = f(x) + f(y), we study in §1 special rings, namely, rings for which every endomorphism f of their additive group is of the form f(x) ≡ ax. In §2 we generalize to R algebras (R a fixed commutative ring) and give a classification theorem when R is a complete discrete valuation ring. This result has an interesting consequence, Proposition 12, for the theory of special rings.
Weak continuity and almost continuity
Authors: Rose D. A.
Published: September 2002

Two relationships considered by Weston [1] for a pair of topologies on a set X are translated to a function setting. An attempt to characterize the two resulting types of functions leads to new characterizations of weak continuity and almost continuity. After showing that weak continuity and almost continuity are independent, interrelationships are sought. This leads to the definition of subweak continuity and a new characterization for almost openness. Finally, several published results are strengthened or slightly extended.
Periodic rings with commuting nilpotents
Authors: Abu-Khuzam Hazar , Yaqub Adil
Published: September 2002

Let R be a ring (not necessarily with identity) and let N denote the set of nilpotent elements of R. Suppose that (i) N is commutative, (ii) for every x in R, there exists a positive integer k = k(x) and a polynomial f(λ) = fx(λ) with integer coefficients such that xk = xk+1f(x), (iii) the set In = {x|xn = x} where n is a fixed integer, n > 1, is an ideal in R. Then R is a subdirect sum of finite fields of at most n elements and a nil commutative ring. This theorem, generalizes the “xn = x” theorem of Jacobson, and (taking n = 2) also yields the well known structure of a Boolean ring. An Example is given which shows that this theorem need not be true if we merely assume that In is a subring of R.
Commutativity theorems for rings and groups with constraints on commutators
Authors: Psomopoulos Evagelos
Published: September 2002

Let n > 1, m, t, s be any positive integers, and let R be an associative ring with identity. Suppose xt[xn, y] = [x, ym]ys for all x, y in R. If, further, R is n‐torsion free, then R is commutativite. If n‐torsion freeness of R is replaced by “m, n are relatively prime,” then R is still commutative. Moreover, example is given to show that the group theoretic analogue of this theorem is not true in general. However, it is true when t = s = 0 and m = n + 1.
The extending topologies
Authors: Clark Bradd , Schneider Victor
Published: September 2002

Let H be a topological group and a subgroup of G. A topology on G is called an extending topology if and only if it makes G a topological group and it induces the given topology on H. The set of all such topologies is studied.
Separation axioms for partially ordered convergence spaces
Authors: Vainio Reino
Published: September 2002

In partially ordered convergence spaces, separation axioms are introduced and then related to the concept of complete separatedness due to Nachbin as well as to connectedness concepts. A method to generate new separation axioms is studied.
Weak continuity and strongly closed sets
Authors: Rose D. A.
Published: September 2002

After demonstrating the usual product theorems for weakly continuous functions, strongly closed and extremely closed subsets are contrasted to support the conjecture that a product of faintly continuous functions need not be faintly continuous. Strongly closed sets are used to characterize Hausdorff spaces and Urysohn spaces, and with these characterizations two results obtained by T. Noiri are obtained by function‐theoretic means rather than by point‐set method.
The compactum of a semi‐simple commutative Banach algebra
Authors: Al-Moajil Abduliah H.
Published: September 2002

Let A be a commutative semi‐simple Banach algebra such that the set consisting of finite sums of elements from minimal left ideals coincides with that of finite sums of elements from minimal right ideals. Let S(A) (the socle of A) denote this set. Let C(A) denote the set of elements x in A such that the map a → xax is compact. It is shown that C(A) is the norm closure of S(A).
On some extensions of Hardy’s inequality
Authors: Imoru Christopher O.
Published: September 2002

We present in this paper some new integral inequalities which are related to Hardy′s inequality, thus bringing into sharp focus some of the earlier results of the author.

On some extensions of Hardy’s inequalitydx.doi.org/10.1155/S0161171286000261
A note on the estimation of the Poisson parameter
Authors: Chitgopekar S. S.
Published: September 2002

This paper considers the problem of estimating the mean of a Poisson
distribution when there are errors in observing the zeros and ones and obtains both the maximum likelihood and moments estimates of the Poisson mean and the error probabilities. It is interesting to note that either method fails to give unique estimates of these parameters unless the error probabilities are functionally related. However, it is equally interesting to observe that the estimate of the Poisson mean does not depend on the functional relationship between the error probabilities.
On topologies over rings
Authors: Fakhruddin Syed M.
Published: September 2002

In this note, we show that if a topology over a ring A satisfies a certain finiteness condition, then the Gabriel topology generated by can be explicitly constructed and it also satisfies the same finiteness condition.
Rings decomposed into direct sums of J‐rings and nil rings
Authors: Tominaga Hisao
Published: September 2002

Let R be a ring (not necessarily with identity) and let E denote the set of idempotents of R. We prove that R is a direct sum of a J‐ring (every element is a power of itself) and a nil ring if and only if R is strongly π‐regular and E is contained in some J‐ideal of R. As a direct consequence of this result, the main theorem of [1] follows.
The second continuous Jacobi transform
Authors: Deeba E. Y. , Koh E. L.
Published: September 2002

This paper continues the work started in [1]; a second continuous Jacobi transform is defined for suitable functions f(x). Properties of the transform are studied. In particular, the first continuous Jacobi transform in [1] and the second continuous Jacobi transform are shown to be inverse to each other. The paper concludes with an extension of Campbell′s sampling theorem [2].
Contractive mappings on a premetric space
Authors: Shen C. Y. , Sound A.
Published: September 2002

In this paper, we study the fixed point property of certain types of
contractive mappings defined on a premetric space. The applications of these results to topological vector spaces and to metric spaces are also discussed.
Some unsolved problems on meromorphic functions of uniformly bounded characteristic
Authors: Yamashita Shinji
Published: September 2002

The family UBC(R) of meromorphic functions of uniformly bounded characteristic in a Rieman surface R is defined in terms of the Shimizu‐Ahlfors characteristic function. There are some natural parallels between UBC(R) and BMOA(R), the family of holomorphic functions of bounded mean oscillation in R. After a survey some open problems are proposed in contrast with BMOA(R).
Characterization of convergence in fuzzy topological spaces
Authors: Lowen E. , Lowen R.
Published: September 2002

In a fuzzy topology on a set X, the limit of a prefilter (i.e. a filter in the lattice [0, 1] X) is calculated from the fuzzy closure. In this way convergence is derived from a fuzzy topology. In our paper we start with any rule “lim” which to any prefilter 𝔇 on X assigns, a function lim𝔇 ∈ [0, 1] X. We give necessary and sufficient conditions for the function 𝔇 → lim𝔇 in order that it can be derived from a fuzzy topology.
An edgeworth expansion for a sum of M‐Dependent random variables
Authors: Rhee Wan Soo
Published: September 2002

Given a sequence X1, X2, …, Xn of m‐dependent random variables with moments of order 3 + α (0 < α≦1), we give an Edgeworth expansion of the distribution of Sσ−1(S = X1 + X2 + …+Xn,  σ2 = ES2) under the assumption that E[exp(it Sσ1)] is small away from the origin. The result is of the best possible order.
θ‐regular spaces
Authors: Janković Dragan S.
Published: September 2002

In this paper we define a topological space X to be θ‐regular if every filterbase in X with a nonempty θ‐adherence has a nonempty adherence. It is shown that the class of θ‐regular topological spaces includes rim‐compact topological spaces and that θ‐regular H(i) (Hausdorff) topological spaces are compact (regular). The concept of θ‐regularity is used to extend a closed graph theorem of Rose [1]. It is established that an r‐subcontinuous closed graph function into a θ‐regular topological space is continuous. Another sufficient condition for continuity of functions due to Rose [1] is also extended by introducing the concept of almost weak continuity which is weaker than both weak continuity of Levine and almost continuity of Husain. It is shown that an almost weakly continuous closed graph function into a strongly locally compact topological space is continuous.
Random walk over a hypersphere
Authors: Joshi J. M. C.
Published: September 2002

In a recent paper the author had shown that a special case of S. M. Joshi
transform (so named after the author′s reverent father) of distributions

urn:x-wiley:01611712:media:ijmm357149:ijmm357149-math-0001

is a characteristic function of a spherical distribution. Using the methods developed in that paper; the problem of distribution of the distance CD, where C and D are points niformly distributed in a hypersphere, has been discussed in the present paper. The form of characteristic function has also been obtained by the method of projected distribution.
A generalization of Hammersley′s result has also been developed. The main purpose of the paper is to show that although the use of characteristic functions, using the method of Bochner, is available in problems of random walk yet distributional S. M. Joshi transform can be used as a natural tool has been proved for the first time in the paper.
A representation of Jacobi functions
Authors: Deeba E. Y. , Koh E. L.
Published: September 2002

Recently, the continuous Jacobi transform and its inverse are defined and studied in [1] and [2]. In the present work, the transform is used to derive a series representation for the Jacobi functions , −½ ≤ α, β ≤ ½, α + β = 0, and λ ≥ −½. The case α = β = 0 yields a representation for the Legendre functions and has been dealt with in [3]. When λ is a positive integer n, the representation reduces to a single term, viz., the Jacobi polynomial of degree n.
On pairwise S‐closed bitopological spaces
Authors: Mukherjee M. N.
Published: September 2002

The concept of pairwise S‐closedness in bitopological spaces has been introduced and some properties of such spaces have been studied in this paper.
Growth results for a subclass of Bazilevič functions
Authors: El-Ashwah Rabha Md. , Thomas D. K.
Published: September 2002

For α > 0, let B(α) be the class of regular normalized Bazilevič functions defined in the unit disc. Choosing the associated starlike function g(z) ≡ z gives a proper subclass B1(α) of B(α). For B(α), correct growth estimates in terms of the area function are unknown. Several results in this direction are given for B1(12).
Thin circular plate uniformaly loaded over a concentric elliptic path and supported on columns
Authors: Bassali W. A.
Published: September 2002

Within the limitations of the classical thin plate theory expressions are obtained for the small deflections of a thin isotropic circular plate uniformly loaded over a concentric ellipse and supported by four columns at the vertices of a rectangle whose sides are parallel to the axes of the ellipse. Formulae are given for the moments and shears at the centre of the plate and on the edge. Limiting cases are investigated.
Homomorphisms of complete n‐partite graphs
Authors: Girse Robert D.
Published: September 2002

It is shown that for every homomorphism ϕ of a graph G there exists a contraction θϕ on , the complement of G, such that if and only if G is a complete n‐partite graph.
On common fixed points of weakly commuting mappings andset‐valued mappings
Authors: Sessa S. , Fisher B.
Published: September 2002

Our main theorem establishes the uniqueness of the common fixed point of two set‐valued mappings and of two single‐valued mappings defined on a complete metric space,
under a contractive condition and a weak commutativity concept. This improves a theorem
of the second author.
On the existence of periodic and eventually periodic solutions of a fluid dynamic forced harmonic oscillator
Authors: Cooke Charlie H.
Published: September 2002

For certain flow regimes, the nonlinear differential equation , Y ≥ 0, G > 0 and constant, models qualitatively the behaviour of a forced, fluid dynamic, harmonic oscillator which has been a popular department store attraction. The device consists of a ball oscillating suspended in the vertical jet from a household fan. From the postulated form of the model, we determine sets of attraction and exploit symmetry properties of the system to show that all solutions are either initially periodic, with the ball never striking the fan, or else eventually approach a periodic limit cycle, after a sufficient number of bounces away from the fan.
A Diophantine system
Authors: Bremner Andrew
Published: September 2002

It is shown how to find all integers a, b such that a + b, a2 + b2 and a3 + b3 are simultaneously perfect squares.
Inclusions of Hardy Orlicz spaces
Authors: Khalil Roshdi
Published: September 2002

Let ϕ be a continuous positive increasing function defined on [0, ∞) such that ϕ(x + y) ≤ ϕ(x) + ϕ(y) and ϕ(0) = 0. The Hardy‐Orlicz space generated by ϕ is denoted by H(ϕ). In this paper, we prove that for ϕ ≠ ψ, if H(ϕ) = H(ψ) as sets, then H(ϕ) = H(ψ) as topological vector spaces. Some other results are given.
Stability analysis of linear multistep methods for delay differential equations
Authors: Bakke V. L. , Jackiewicz Z.
Published: September 2002

Stability properties of linear multistep methods for delay differential equations with respect to the test equation

urn:x-wiley:01611712:media:ijmm768965:ijmm768965-math-0001

0 < λ < 1, are investigated. It is known that the solution of this equation is bounded if and only if |a| < −b and we examine whether this property is inherited by multistep methods with Lagrange interpolation and by parametrized Adams methods.
Existence theorems for differential inclusions with nonconvex right hand side
Authors: Papageorgiou Nikolaos S.
Published: September 2002

In this paper we prove some new existence theorems for differential inclusions with a nonconvex right hand side, which is lower semicontinuous or continuous in the state variable, measurable in the time variable and takes values in a finite or infinite dimensional separable Banach space.
Decay of solutions of a system of nonlinear Klein‐Gordon equations
Authors: Ferreira José , Menzala Gustavo Perla
Published: September 2002

We study the asymptotic behavior in time of the solutions of a system of nonlinear Klein‐Gordon equations. We have two basic results: First, in the L∞(ℝ3) norm, solutions decay like 0(t−3/2) as t → +∞ provided the initial data are sufficiently small. Finally we prove that finite energy solutions of such a system decay in local energy norm as t → +∞.
Linear random boundary value problems containing weakly correlated forcing functions
Authors: Xia Ning-Mao
Published: September 2002

This paper concerns linear random boundary value problems that contain random variables In the boundary conditions and weakly correlated processes in the differential equations. When the correlation length ϵ is small the structure of the solution is pointed out, and the formulas for the density function of the solutions are derived. The discussion is given in terms of second order equations, but extensions to higher order problems are readily apparent.
Tauberian theorem for the distributional Stieltjes transformation
Authors: Nikolić-Despotović D. , Pilipović S.
Published: September 2002

In this paper we use the notion of L‐quasiasymptotic at infinity of distributions to obtain a final value Tauberian theorem for the distributional Stieltjes transformation.