bluuebunny/crossref_metadata_2025 huggingface dataset:
Bounds on the curvature for functions with bounded boundary rotation of order 1 − b
Authors: Nasr M. A.
Published: September 2002

Let Vk(1 − b), k ≥ 2 and b ≠ 0 real, denotes the class of locally univalent analytic functions in D = {z : |z| < 1} such that , z = reiθ ∈ D. In this note sharp bounds on the curvature of the image of |z| = r, 0 < r < 1, under a mapping f belonging to the class Vk(1 − b) have been obtained.
Note on the zeros of functions with univalent derivatives
Authors: Salmassi Mohammad
Published: September 2002

Let E denote the class of functions f(z) analytic in the unit disc D, normalized so that f(0) = 0 = f′(0) − 1, such that each f(k)(z), k ≥ 0 is univalent in D. In this paper we establish conditions for some functions to belong to class E.
Cyclotomic equations and square properties in rings
Authors: Fine Benjamin
Published: September 2002

If R is a ring, the structure of the projective special linear group PSL2(R) is used to investigate the existence of sum of square properties holding in R. Rings which satisfy Fermat′s two‐square theorem are called sum of squares rings and have been studied previously. The present study considers a related property called square property one. It is shown that this holds in an infinite class of rings which includes the integers, polynomial rings over many fields and Zpn where P is a prime such that −3 is not a square modp. Finally, it is shown that the class of sum of squares rings and the class satisfying square property one are non‐coincidental.
twistors and gauge fields
Authors: Sergeev A. G.
Published: September 2002

We describe briefly the basic ideas and results of the twistor theory. The main points: twistor representation of Minkowsky space, Penrose correspondence and its geometrical properties, twistor interpretation of linear massless fields, Yang‐Mills fields (including instantons and monopoles) and Einstein‐Hilbert equations.
The general quasi‐order algorithm in number theory
Authors: Hilton Peter , Pedersen Jean
Published: September 2002

This paper deals with a generalization of the Binary Quasi‐Order Theorem. This generalization involves a more complicated algorithm than (0.2)t. Some remarks are made on relative merits of two dual algorithms called the ψ‐algorithm and the ϕ‐algorithm. Some illustrative examples are given.
Generalized Ramsey numbers for paths in 2‐chromatic graphs
Authors: Meenakshi R. , Sundararaghavan P. S.
Published: September 2002

Chung and Liu have defined the d‐chromatic Ramsey number as follows. Let 1 ≤ d ≤ c and let . Let 1, 2, …, t be the ordered subsets of d colors chosen from c distinct colors. Let G1, G2, …, Gt be graphs. The d‐chromatic Ramsey number denoted by is defined as the least number p such that, if the edges of the complete graph Kp are colored in any fashion with c colors, then for some i, the subgraph whose edges are colored in the ith subset of colors contains a Gi. In this paper it is shown that where i ≤ j ≤ k < r(Pi, Pj), stands for a generalized Ramsey number on a 2‐colored graph and Pi is a path of order i.
The packing and covering of the complete graph I: the forests of order five
Authors: Roditty Y.
Published: September 2002

The maximum number of pairwise edge disjoint forests of order five in the complete graph Kn, and the minimum number of forests of order five whose union is Kn, are determined.
On an integral transform
Authors: Naylor D.
Published: September 2002

This paper establishes properties of a convolution type integral transform whose kernel is a Macdonald type Bessel function of zero order. An inversion formula is developed and the transform is applied to obtain the solution of some related integral equations.
On dual integral equations with Hankel kernel and an arbitrary weight function
Authors: Nasim C.
Published: September 2002

In this paper we deal with dual integral equations with an arbitrary weight function and Hankel kernels of distinct and general order. We propose an operational procedure, which depends on exploiting the properties of the Mellin transforms, and readily reduces the dual equations to a single equation. This then can be inverted by the Hankel inversion to give us an equation of Fredholm type, involving the unknown function. Most of the known results are then derived as special cases of our general result.
Certain subclasses of Bazilevič functions of type α
Authors: Owa Shigeyoshi , Obradović Milutin
Published: September 2002

Certain subclasses B(α, β) and B1(α, β) of Bazilevič functions of type α are introduced. The object of the present paper is to derive a lot of interesting properties of the classes B(α, β) and B1(α, β).
A note on the inverse function theorem of Nash and Moser
Authors: Lindstrom Mikael
Published: September 2002

The Nash‐Moser inverse function theorem is proved for different kind of differentiabilities.
An integral equation associated with linear homogeneous differential equations
Authors: Bose A. K.
Published: September 2002

Associated with each linear homogeneous differential equation of order n on the real line, there is an equivalent integral equation

urn:x-wiley:01611712:media:ijmm246569:ijmm246569-math-0002

which is satisfied by each solution f(x) of the differential equation.
On alpha‐close‐to‐convex functions of order beta
Authors: Nasr M. A.
Published: September 2002

Let Mβ(α)[α ≥ 0   and   β ≥ 0] denote the class of all functions

urn:x-wiley:01611712:media:ijmm540937:ijmm540937-math-0001

analytic in the unit disc U with f′(z)f(z)/z ≠ 0 and which satisfy for z = reiθ ∈ U the condition

urn:x-wiley:01611712:media:ijmm540937:ijmm540937-math-0002

for all θ2 > θ1. In this note we show that each f ∈ Mβ(α) is close‐to‐star of order β when 0 < β ≤ α.
On some results for ?‐spiral functions of order a
Authors: Obradovic Milutin , Owa Shigeyoshi
Published: September 2002

The results of various kinds concerning ?‐spiral functions of order a in the unit disk U are given in this paper. They represent mainly the generalizations of the previous results of the authors.
On some new N‐independent‐variable discrete inequalities of the Gronwall type
Authors: Yang En Hao
Published: September 2002

In this paper we shall establish some new discrete inequalities of the Gronwall type in N‐independent variables. They will have many applications for finite difference equations involving several independent variables and for numerical analysis. Their consequence for the case of N = 3, generalizes all of the known theorems obtained by Pachpatte and Singare in [1]. An example, to which those results established in [1] are inapplicable, is given here to convey the usefulness of the results obtained.
Nonlinear diffraction of water waves by offshore stuctures
Authors: Rahman Matiur , Debnath Lokenath
Published: September 2002

This paper is concerned with a variational formulation of a nonaxisymmetric water wave problem. The full set of equations of motion for the problem in cylindrical polar coordinates is derived. This is followed by a review of the current knowledge on analytical theories and numerical treatments of nonlinear diffraction of water waves by offshore cylindrical structures. A brief discussion is made on water waves incident on a circular harbor with a narrow gap. Special emphasis is given to the resonance phenomenon associated with this problem. A new theoretical analysis is also presented to estimate the wave forces on large conical structures. Second‐order (nonlinear) effects are included in the calculation of the wave forces on the conical structures. A list of important references is also given.
An application of the Ruscheweyh derivatives
Authors: Owa Shigeyoshi , Fukui Seiichi , Sakaguchi Koichi , Ogawa Shotaro
Published: September 2002

Let Dαf(z) be the Ruscheweyh derivative defined by using the Hadamard product of f(z) and z/(1−z)1+α. Certain new classes and Kα are introduced by virtue of the Ruscheweyh derivative. The object of the present paper is to establish several interesting properties of and Kα. Further, some results for integral operator Jc(f) of f(z) are shown.
A *‐mixing convergence theorem for convex set valued processes
Authors: de Korvin A. , Kleyle R.
Published: September 2002

In this paper the concept of a *‐mixing process is extended to multivalued maps from a probability space into closed, bounded convex sets of a Banach space. The main result, which requires that the Banach space be separable and reflexive, is a convergence theorem for *‐mixing sequences which is analogous to the strong law of large numbers. The impetus for studying this problem is provided by a model from information science involving the utilization of feedback data by a decision maker who is uncertain of his goals. The main result is somewhat similar to a theorem for real valued processes and is of interest in its own right.
Local behaviour of the derivative of a mid point cubic spline interpolator
Authors: Dikshit H. P. , Rana S. S.
Published: September 2002

In the present paper, we obtain an asymptotically precise estimate for the
derivative of the difference between the cubic spline interpolating at the mid points of a uniform partition and the function interpolated.
Asymptotic behavior of retarded differential equations
Authors: Yeh Cheh-Chih
Published: September 2002

Some integral criteria for the asymptotic behavior of oscillatory solutions of higher order retarded differential equations are given.
The power of powerful numbers
Authors: Mollin R. A.
Published: September 2002

In this note we discuss recent progress concerning powerful numbers, raise new questions and show that solutions to existing open questions concerning powerful numbers would yield advancement of solutions to deep, long‐standing problems such as Fermat′s Last Theorem. This is primarily a survey article containing no new, unpublished results.
On the solution of reaction‐diffusion equations with double diffusivity
Authors: Aggarwala B. D. , Nasim C.
Published: September 2002

In this paper, solution of a pair of Coupled Partial Differential equations is derived. These equations arise in the solution of problems of flow of homogeneous liquids in fissured rocks and heat conduction involving two temperatures. These equations have been considered by Hill and Aifantis, but the technique we use appears to be simpler and more direct, and some new results are derived. Also, discussion about the propagation of initial discontinuities is given and illustrated with graphs of some special cases.
Order compatibility for Cauchy spaces and convergence spaces
Authors: Kent D. C. , Vainio Reino
Published: September 2002

A Cauchy structure and a preorder on the same set are said to be compatible
if both arise from the same quasi‐uniform convergence structure on X. Howover, there are two natural ways to derive the former structures from the latter, leading
to strong and weak notions of order compatibility for Cauchy spaces. These in turn lead to characterizations of strong and weak order compatibility for convergence
spaces.
An operational procedure for Hankel type integrals
Authors: Nasim C.
Published: September 2002

In this paper, an operational procedure is established to evaluate Hankel type integrals. First, an operator L(θ), is constructed, which defines the integral. Then making use of some basic properties of this operator, an elementary procedure is developed for evaluating integrals for a special class of analytic functions. A few example are given to illustrate the technique.
A monotone path in an edge‐ordered graph
Authors: Bialostocki A. , Roditty Y.
Published: September 2002

An edge‐ordered graph is an ordered pair (G, f), where G is a graph and f is a bijective function, f : E(G) → {1, 2, …, |E(G)|}. A monotone path of length k in (G, f) is a simple path Pk+1 : v1v2 … vk+1 in G such that either f({vi, vi+1}) < f({vi+1, vi+2}) or f({vi, vi+1}) > f({vi+1, vi}) for i = 1, 2, …, k − 1.

It is proved that a graph G has the property that (G, f) contains a monotone path of length three for every f iff G contains as a subgraph, an odd cycle of length at least five or one of six listed graphs.
Matchings in hexagonal cacti
Authors: Farrell E. J.
Published: September 2002

Explicit recurrences are derived for the matching polynomials of the basic types of hexagonal cacti, the linear cactus and the star cactus and also for an associated graph, called the hexagonal crown. Tables of the polynomials are given for each type of graph. Explicit formulae are then obtained for the number of defect‐d matchings in the graphs, for various values of d. In particular, formulae are derived for the number of perfect matchings in all three types of graphs. Finally, results are given for the total number of matchings in the graphs.
Iterative methods for nonlinear quasi complementarity problems
Authors: Noor Muhammad Aslam
Published: September 2002

In this paper, we consider and study an iterative algorithm for finding the approximate solution of the nonlinear quasi complementarity problem of finding u ϵ k(u) such that

urn:x-wiley:01611712:media:ijmm786464:ijmm786464-math-0001

where m is a point‐to‐point mapping, T is a (nonlinear) continuous mapping from a real Hilbert space H into itself and k*(u) is the polar cone of the convex cone k(u) in H. We also discuss the convergence criteria and several special cases, which can be obtained from our main results.
On some classes of analytic functions
Authors: Noor Khalida I. , Madifer Haila
Published: September 2002

Let m1, m2 be any numbers and let be the class of functions of analytic in the unit disc E = {z : |z| < 1} for which

urn:x-wiley:01611712:media:ijmm671962:ijmm671962-math-0002

where S1 and S2 are analytic in E with . Moulis [1] gave a sufficient condition and a necessary condition on parameters m1 and m2 for the class to consist of univalent functions if S1 and S2 are taken to be convex univalent functions in E. In fact he proved that if where S1 and S2 are convex and , , 2|m1 + m2| ≤ 1, then f is univalent in E.

In this paper we consider the class in more general way and show that it contains the class of functions with bounded boundary rotation and many other classes related with it. Some coefficient results, arclength problem, radius of convexity and other problems are proved for certain cases. Our results generalize many previously known ones.
Two new finite difference methods for computing eigenvalues of a fourth order linear boundary value problem
Authors: Usmani Riaz A. , Sakai Manabu
Published: September 2002

This paper describes some new finite difference methods of order 2 and 4 for computing eigenvalues of a two‐point boundary value problem associated with a fourth
order differential equation of the form . Numerical results for two typical eigenvalue problems are tabulated to demonstrate practical usefulness of our methods.
Isometries of a function space
Authors: Vyas U. D.
Published: September 2002

It is proved here that an isometry on the subset of all positive functions of L1 ⋂ Lp(ℝ) can be characterized by means of a function h together with a Borel measurable mapping ϕ of ℝ, thus generalizing the Banach‐Lamparti theorem of Lp spaces.
M‐quasi‐hyponormal composition operators
Authors: Suri Pushpa R. , Singh N.
Published: September 2002

A necessary and sufficient condition is obtained for M‐quasi‐hyponormal composition operators. It has also been proved that the class of M‐quasi‐hyponormal composition operators coincides with the class of M‐paranormal composition operators. Existence of M‐hyponormal composition operators which are not hyponormal; and M‐quasihyponormal composition operators which are not M‐hyponormal and quasi‐hyponormal are also shown.
A generalized inversion formula for the continuous Jacobi transform
Authors: Zayed Ahmed I.
Published: September 2002

In this paper we extend the definition of the continuous Jacobi transform to a class of generalized functions and obtain a generalized inversion formula for it. As a by‐product of our technique we obtain a necessary and sufficient condition for an analytic function F(λ) in Reλ > 0 to be the continuous Jacobi transform of a generalized function.
Weakly recurrent and almost periodic points in βG
Authors: Nassar Mostafa
Published: September 2002

Let G be a group. We will study the relationship between AG and WRG. In Nassar [1] it has been shown that if G is a nontorsion group, then AG⫋RG. In this paper we will show that if G contains a subset A such that K.A is not left thick for each finite set K and A is not a finite union of thin sets, then AG⫋WRG.
The behavior of solutions of non‐linear differential equations in Hilbert space. I
Authors: Schuchman Vladimir
Published: September 2002

This paper deals with the behavior of solutions of ordinary differential equations in a Hilbert Space. Under certain conditions, we obtain lower estimates or upper estimates (or both) for the norm of solutions of two kinds of equations. We also obtain results about the uniqueness and the quasi‐uniqueness of the Cauchy problems of these equations. A method similar to that of Agmon‐Nirenberg is used to study the uniqueness of the Cauchy problem for the non‐degenerate linear case.
On extending endomorphisms to automorphisms
Authors: Levitz Hilbert , Nichols Warren
Published: September 2002

A monic endomorphism of a structure A can be extended to an automorphism of a larger structure A*. We investigate which properties are preserved by this process.
On behavior of solutions of non‐linear differential equations in Hilbert space II
Authors: Schuchman Vladimir
Published: September 2002

This paper deals with the behavior of solutions of non‐linear ordinary differntial equations in a Hilbert space with applications to non‐linear partial differential equations.
Convergence analysis of the iterative methods for quasi complementarity problems
Authors: Noor Muhammad Aslam
Published: September 2002

In this paper, we consider the iterative methods for the quasi complementarity problems of the form

urn:x-wiley:01611712:media:ijmm183086:ijmm183086-math-0001

where m is a point‐to‐point mapping and T is a continuous mapping from Rn into itself. The algorithms considered in this paper are general and unified ones, which include many existing algorithms as special cases for solving the complementarity problems.
On a nonolinear wave equation in unbounded domains
Authors: Vasconcellos Carlos Frederico
Published: September 2002

We study existence and uniqeness of the nonlinear wave equation

urn:x-wiley:01611712:media:ijmm473020:ijmm473020-math-0001

in unbounded domains. The above model describes nonlinear wave phenomenon in non‐homogeneous media. Our techniques ivolve fixed point arguments combined with the energy method.
Some applications of Legendre numbers
Authors: Haggard Paul W.
Published: September 2002

The associated Legendre functions are defined using the Legendre numbers. From these the associated Legendre polynomials are obtained and the derivatives of these polynomials at x = 0 are derived by using properties of the Legendre numbers. These derivatives are then used to expand the associated Legendre polynomials and xn in series of Legendre polynomials. Other applications include evaluating certain integrals, expressing polynomials as linear combinations of Legendre polynomials, and expressing linear combinations of Legendre polynomials as polynomials. A connection between Legendre and Pascal numbers is also given.
Some classes of alpha‐quasi‐convex functions
Authors: Noor Khalida Inayat
Published: September 2002

Let C[C, D], −1 ≤ D < C ≤ 1 denote the class of functions g, g(0) = 0, g′(0) = 1, analytic in the unit disk E such that is subordinate to , z ∈ E. We investigate some classes of Alpha‐Quasi‐Convex Functions f, with f(0) = f′(0) − 1 = 0 for which there exists a g ∈ C[C, D] such that is subordinate to , −1 ≤ B < A ≤ 1. Integral representation, coefficient bounds are obtained. It is shown that some of these classes are preserved under certain integral operators.
On generalized Rédei functions
Authors: Matthews R. , Lidl R.
Published: September 2002

A generalization of Rédei functions to polynomial vectors in n indeterminates over finite fields or residue class rings of integers is given by considering special types of polynomial vectors. Properties such as polynomial composition, change of basis, group structure and fixed points are studied together with applications in cryptography.
On barely continuous functions
Authors: Stephens Richard
Published: September 2002

The term barely continuous is a topological generalization of Baire‐1 according to F. Gerlits of the Mathematical Institute of the Hungarian Academy of Sciences, and thus worthy of further study. This paper compares barely continuous functions and continuous functions on an elementary level. Knowing how the continuity of the identity function between topologies on a given set yields the lattice structure for those topologies, the barely continuity of the identity function between topologies on a given set is investigated and used to add to the structure of that lattice. Included are certain sublattices generated by the barely continuity of the identity function between those topologies. Much attention is given to topologies on finite sets.
On solution of the integral equations for the potential problems of two circular‐strips
Authors: Sampath C. , Jain D. L.
Published: September 2002

Solutions are given to some singular integral equations which arise in two‐dimensional
Dirichlet and Newmann boundary value problems of two equal infinite coaxial circular strips in various branches of potential theory. For illustration, these solutions are applied to solve some boundary value problems in electrostatics, hydrodynamics, and expressions for the physical quantities of interest are derived.
Some roughness results concerning reducibility for linear difference equations
Authors: Papaschinopoulos Garyfalos
Published: September 2002

In this paper we prove first that the exponential dichotomy of linear difference equations is rough. Moreover we prove that if the coefficient matrix of a linear difference equation is almost periodic, then the Joint property of having an exponential dichotomy with a projection P and being reducible with P by an almost periodic kinematics similarity is rough.
Reduction of dimensionality in dynamic programming‐based solution methods for nonlinear integer programming
Authors: Ram Balasubramanian , Babu A. J. G.
Published: September 2002

This paper suggests a method of formulating any nonlinear integer programming problem, with any number of constraints, as an equivalent single constraint problem, thus reducing the dimensionality of the associated dynamic programming problem.
On Legendre numbers of the second kind
Authors: Haggard Paul W.
Published: September 2002

The Legendre numbers of the second kind, an infinite set of rational numbers, are defined from the associated Legendre functions. An explicit formula and a partial table for these numbers are given and many elementary properties are presented. A connection is shown between Legendre numbers of the first and second kinds. Extended Legendre numbers of the first and second kind are defined in a natural way and these are expressed in terms of those of the second and first kind, respectively. Two other sets of rational numbers are defined from the associated Legendre functions by taking derivatives and evaluating these at x = 0. One of these sets is connected to Legendre numbers of the first find while the other is connected to Legendre numbers of the second kind. Some series are also discussed.
A note on the spaces θM and
Authors: Bosch Carlos , Kucera Jan
Published: September 2002

The spaces θM and of multiplication and convolution operators on temperate distributions, together with their strong duals and θC, are Montel and distinguished.
On a global classical solution of a quasilinear hyperbolic equation
Authors: Ebihara Y. , Pereira D. C.
Published: September 2002

In this paper we establish the existence and uniqueness of global classical
solutions for the equation which arises in the study of the extensional vibrations of
thin rod, or torsional vibrations of thin rod.
On some fixed point theorems
Authors: Roux D. , Singh S. P.
Published: September 2002

In this paper we prove a fixed point theorem for inward mappings
uing a well‐known result of Ky Fan type in Hilbert space setting.
Viscosity solutions associated with impulse control problems for piecewise‐deterministic processes
Authors: Lenhart Suzanne M.
Published: September 2002

This paper considers existence and uniqueness results for viscosity solutions
of integro‐differential equations associated with the impulse control problem for piecewise‐deterministic
processes on bounded domains and on Rn.
Coincidence and fixed points of nonlinear Hybrid contractions
Authors: Singh Shyam Lal , Ha Ki Sik , Cho Yeol Je
Published: September 2002

In this Der, we show the existence of solutions of functional equations fx ∈ sx∩tx and
x=fx ∈ sx∩Tx under certain contraction and asymptotic regularity
conditions, where f, S and T are single‐valued and multl‐valued mappings on a metric
space, respectively. We also observe that MukherJee′s fixed point theorem for a
single‐valued mapping commuting with a multl‐valued mapping admits of a counterexample
and suggest some modifications. While doing so, we also answer an open
question raised in [I] and [2]. Moreover, our results extend and unify a multitude of
fixed point theorems for multi‐valued mappings.
On the continuity of the vector valued and set valued conditional expectations
Authors: Papageorgiou Nikolaos S.
Published: September 2002

In this paper we study the dependence of the vector valued conditional expectation (for both single valued and set valued random variables), on the σ–field and random variable that determine it. So we prove that it is continuous for the L1(X) convergence of the sub–σ–fields and of the random variables. We also present a sufficient condition for the L1(X)–convergence of the sub–σ–fields. Then we extend the work to the set valued conditional expectation using the Kuratowski–Mosco (K–M) convergence and the convergence in the Δ–metric. We also prove a property of the set valued conditional expectation.
On the exponential growth of solutions to non‐linear hyperbolic equations
Authors: Chi H. , Poorkarimi H. , Wiener J. , Shah S. M.
Published: September 2002

Existence‐uniqueness theorems are proved for continuous
solutions of some classes of non‐linear hyperbolic equations in
bounded and unbounded regions. In case of unbounded region, certain
conditions ensure that the solution cannot grow to infinity faster
than exponentially.
Sufficient conditions for spiral‐likeness
Authors: Silverman H.
Published: September 2002

Coefflcient conditions sufficient for splral‐likenss are found by
convolution methods. The order of starlikeness for such functions is also determined.
Second order parallel tensor in real and complex space forms
Authors: Sharma Ramesh
Published: September 2002

Levy′s theorem ‘A second order parallel symmetric non‐singular tensor
in a real space form is proportional to the metric tensor’ has been generalized by
showing that it holds even if one assumes the second order tensor to be parallel
(not necessarily symmetric and non‐singular) in a real space form of dimension
greater than two. Analogous result has been established for a complex space form.

It has been shown that an affine Killing vector field in a non‐flat complex space
form is Killing and analytic.
Quasi‐projective modules and the finite exchange property
Authors: Birkenmeier Gary F.
Published: September 2002

We define a module M to be directly refinable if whenever M=A+B,
there exists
and
such that
. Theorem. Let M be a quasi‐projective
module. Then M is directly refinable if and only if M has the finite
exchange property.
An analogue in certain unique factorization domains of the Euclid‐Euler theorem on perfect numbers
Authors: McDaniel Wayne L.
Published: September 2002

We show that there exists a natural extention of the sum of divisors function to all unique factorization domains F having a finite number of units such that if a perfect number in F is defined to be an integer η whose proper divisors sum to η, then the analogue of Euclid′s theorem giving the sufficient condition that an integer be an even perfect number holds in F, and an analogue of the Euclid‐Euler theorem giving the necessary and sufficient condition that an even integer be perfect holds in those domains having more than two units, i. e., in and .
On the structure of support point sets
Authors: Azoff E. , younis R.
Published: September 2002

Let X be a metrizable compact convex subset of a locally convex space. Using Choquet′s Theorem, we determine the structure of the support point set of X when X has countably many extreme points. We also characterize the support points of certain families of analytic functions.
Estimation of the scale parameter of gamma model in presence of outlier observations
Authors: Ghitany M. E.
Published: September 2002

This paper considers the Bayesian point estimation of the scale parameter for a two‐parameter gamma life‐testing model in presence of several outlier observations in the data. The Bayesian analysis is carried out under the assumption of squared error loss function and fixed or random shape parameter.
Bounded analytic functions and the little Bloch space
Authors: Attele Rohan
Published: September 2002

The radial limits of the weighted derivative of an bounded analytic function is considered.
On Pervin′s example concerning the connected‐open topology
Authors: McMaster T. B. M.
Published: September 2002

Irudayanathan and Naimpally [1] introduced a topology for function spaces (called the connected‐open topology) which has the property that the connected functions form a closed set provided that the codomain is completely normal. Pervin [2] gave an example showing that the proviso cannot be weakened to normality. The purpose of this note is to point out a lacuna in his demonstration, and to re‐establish the validity of the example.
Uniform Toeplitz matrices
Authors: Maddox I. J.
Published: September 2002

We characterize all infinite matrices of bounded linear operators on a Banach space which preserve the limits of uniformly convergent sequences defined on an infinite set. Also, we give a Tauberian theorem for uniform summability by the Kuttner‐Maddox matrix.
Analytic functions over valued fields
Authors: Bhaskaran R. , Karunakaran V.
Published: September 2002

Let K be a non‐archimedean, non‐trivially (rank 1) valued complete field. B, B0 denote the closed and open unit ball of K respectively. Necessary and sufficient conditions for analytic functions defined on B, B0 with values in K to be injective, necessary and sufficient conditions for fixed points, the problem of subordination are studied in this paper.
On Lamb′s plane problem in micropolar viscoelastic half‐space with stretch
Authors: Kumar Rajneesh , Gogna M. L. , Debnath Lokenath
Published: September 2002

A study is made of Lamb′s plane problem in micropolar viscoelastic half‐space with stretch. The viscoelasticity is characterized by the rate‐dependent theories of micro‐viscoelasticity generalizing the classical Kelvin‐Voigt theory. The displacement components, force stress, couple stress and vector first moment are obtained for a half‐space subjected to an arbitrary normal load. Two particular cases of a horizontal force and a torque which are time harmonic have been considered. Several limiting cases are obtained as special cases of the present analysis.
Solutions of an ordinary differential equation as a class of Fourier kernels
Authors: Aggarwala B. , Nasim C.
Published: September 2002

While there are various methods of generating Fourier kernels mentioned in the literature it is not so well recognized that Fourier kernels can be obtained as solutions of differential equations. In this note we define a class of Fourier kernels, which are solutions of a k ‐ fold Bessel equation.
On the coefficient domains of univalent functions
Authors: Elhosh M. M.
Published: September 2002

Coefficient domains for functions whose derivative has positive real part in the interior of an ellipse are given in this paper.
Biharmonic eigen‐value problems and Lp estimates
Authors: Gupta Chaitan P. , Kwong Ying C.
Published: September 2002

Biharmonic eigen‐values arise in the study of static equilibrium of an elastic body which has been suitably secured at the boundary. This paper is concerned mainly with the existence of and Lp‐estimates for the solutions of certain biharmonic boundary value problems which are related to the first eigen‐values of the associated biharmonic operators. The methods used in this paper consist of the a‐priori estimates due to Agmon‐Douglas‐Nirenberg and P. L. Lions along with the Fredholm theory for compact operators.
On the solution of some simple fractional differential equations
Authors: Campos L. M. B. C.
Published: September 2002

The differintegration or fractional derivative of complex order ν, is a generalization of the ordinary concept of derivative of order n, from positive integer ν = n to complex values of ν, including also, for ν = −n a negative integer, the ordinary n‐th primitive. Substituting, in an ordinary differential equation, derivatives of integer order by derivatives of non‐integer order, leads to a fractional differential equation, which is generally a integro‐differential equation. We present simple methods of solution of some classes of fractional differential equations, namely those with constant coefficients (standard I) and those with power type coefficients with exponents equal to the orders of differintegration (standard II). The fractional differential equations of standard I (II), both homogeneous, and inhomogeneous with exponential (power‐type) forcing, can be solved in the Liouville (Riemann) systems of differintegration. The standard I (II) is linear with constant (non‐constant) coefficients, and some results are also given for a class of non‐linear fractional differential equations (standard III).
Three dimensional Green′s function for ship motion at forward speed
Authors: Rahman Matiur
Published: September 2002

The Green′s function formulation for ship motion at forward speed contains double integrals with singularities in the path of integrations with respect to the wave number. In this study, the double integrals have been replaced by single integrals with the use of complex exponential integrals. It has been found that this analysis provides an efficient way of computing the wave resistance for three dimensional potential problem of ship motion with forward speed.
Remarks on quadratic equations in Banach space
Authors: Argyros Ioannis K.
Published: September 2002

We find new sufficient conditions for the uniqueness of solutions of quadratic and in general multilinear equations in a Banach space X, by assuming the existence of a certain limit of linear operators in a suitable subspace of X.
Mixed automorphic forms and differential equations
Authors: Lee Min Ho
Published: September 2002

We construct mixed automorphic forms associated to a certain class of nonhomogeneous linear ordinary differential equations. We also establish an isomorphism between the space of mixed automorphic forms of the second kind modulo exact forms nd a certain parabolic cohomology explicitly in terms of the periods of mixed automorphic forms.
On a pulsatile flow of a two‐phase viscous fluid in a tube of elliptic cross‐section
Authors: Ghosh A. K. , Khan A. R. , Debnath L.
Published: September 2002

A study is made of an unsteady flow of an incompressible viscous fluid with embedded small inert spherical particles contained in a tube of elliptic cross‐section due to a periodic pressure gradient acting along the length of the tube. The solutions for the fluid velocity and the particle velocity are obtained for large and
small times. It is shown that the effect of particles on the flow is significant in the small‐time solution while the large‐tlme solution shows no effect of the particles on the flow.
A note on finite group structure influenced by second and third maximal subgroups
Authors: Mukherjee N. P. , Khazal R.
Published: September 2002

The structure of a finite group having specified number of second and third maximal subgroups has been investigated in the paper.
On the joint numerical status and tensor products
Authors: Verma Ram , Debnath Lokenath
Published: September 2002

We prove a result on the joint numerical status of the bounded Hilbert space operators on the tensor products. The result seems to have nice applications in the multiparameter spectral theory.
On a theorem of H. Hopf
Authors: Sakkalis Takis
Published: September 2002

A simple proof of a theorem of H. Hopf [1], via Morse theory, is given.
Mackey convergence and quasi‐sequentially webbed spaces
Authors: Gilsdorf Thomas E.
Published: September 2002

The problem of characterizing those locally convex spaces satisfying the Mackey
convergence condition is still open. Recently in [4], a partial description was given using
compatible webs. In this paper, those results are extended by using quasi‐sequentially webbed
spaces (see Definition 1). In particular, it is shown that strictly barrelled spaces satisfy the Mackey
convergence condition and that they are properly contained in the set of quasi‐sequentially webbed
spaces. A related problem is that of characterizing those locally convex spaces satisfying the so‐called
fast convergence condition. A partial solution to this problem is obtained. Several
examples are given.

Corrigendum to
“Mackey convergence and quasi-sequentially webbed spaces”dx.doi.org/10.1155/S0161171291000820
Certain invariant subspaces for operators with rich eigenvalues
Authors: Seddighi Karim
Published: September 2002

For a connected open subset Ω of the plane and n a positive integer,
let Bn(Ω) be the space introduced by Cowen and Douglas. In this article we study the
spectrum of restrictions of T in order to obtain more information about the invariant
subspaces of T. When n = 1 and T ϵ B1(Ω) such that is a spectral set for T we
use the functional calculus we have developed for such operators to give some infinite
dimensional cyclic invariant subspaces for T.
Separable injectivity and C*‐tensor products
Authors: Huruya Tadasi , Kye Seung-Hyeok
Published: September 2002

Let A and B be C*‐algebras and let D be a C*‐subalgebra of B. We
show that if D is separably injective then the triple (A, B, D) verifies the slice map
conjecture. As an application, we prove that the minimal C*‐tensor product A ⊗ B is
separably injective if and only if both A and B are separably injective and either A or
B is finite‐dimensional.
On Galois projective group rings
Authors: Szeto George , Ma Linjun
Published: September 2002

Let A be a ring with 1, C the center of A and G′ an
inner automorphism group of A induced by {Uα in ​A/α in a finite
group G whose order is invertible}. Let be the fixed subring of
A under the action of G′.If A is a Galcis extension of with
Galois group G′ and C is the center of the subring then
and the center of is also C. Moreover, if
is Azumaya over C, then A is a projective group ring.
Semigroup compactifications by generalized distal functions and a fixed point theorem
Authors: Pandian R. D.
Published: September 2002

The notion of “Semigroup compactification” which is in a sense, a generalization of
the classical Bohr (almost periodic) compactification of the usual additive reals R,
has been studied by J. F. Berglund et. al. [2]. Their approach to the theory of
semigroup compactification is based on the Gelfand‐Naimark theory of commutative C* algebras,
where the spectra of admissible C*‐algebras, are the semigroup
compactifications. H. D. Junghenn′s extensive study of distal functions is from the
point of view of semigroup compactifications [5]. In this paper, extending Junghenn′s
work, we generalize the notion of distal flows and distal functions on an arbitrary
semitopological semigroup S, and show that these function spaces are admissible C*‐
subalgebras of C(S). We then characterize their spectra (semigroup compactifications)
in terms of the universal mapping properties these compactifications enjoy. In our
work, as it is in Junghenn′s, the Ellis semigroup plays an important role. Also,
relating the existence of left invariant means on these algebras to the existence of
fixed points of certain affine flows, we prove the related fixed point theorem.
On the semi‐sub‐hypergroups of a hypergroup
Authors: Massouros Ch. G.
Published: September 2002

In this paper we study some properties of the semi‐sub‐hypergroups and the
closed sub‐hypergroups of the hypergroups. We introduce the correlated elements and
the fundamental elements and we connect the concept antipodal of the latter with
Frattin′s hypergroup. We also present Helly′s Theorem as a corollary of a more
general Theorem.
On stability of additive mappings
Authors: Gajda Zbigniew
Published: September 2002

In this paper we answer a question of Th. M. Rassias concerning an extension of
validity of his result proved in [3].
On polynomial expansion of multivalent functions
Authors: Elhosh M. M.
Published: September 2002

Coefficient bounds for mean p‐valent functions, whose expansion in an
ellipse has a Jacobi polynomial series, are given in this paper.
Two countable Hausdorff almost regular spaces every contiunous map of which into every Urysohn space is constant
Authors: Tzannes V.
Published: September 2002

We construct two countable, Hausdorff, almost regular spaces
I(S), I(T) having the following properties: (1) Every continuous map of
I(S) (resp, I(T)) into every Urysohn space is constant (hence, both
spaces are connected). (2) For every point of I(S) (resp. of I(T)) and
for every open neighbourhood U of this point there exists an open
neighbourhood V of it such that V⫅U and every continuous map of V into
every Urysohn space is constant (hence both spaces are locally
connected). (3) The space I(S) is first countable and the space I(T) nowhere first countable. A consequence of the above is the construction
of two countable, (connected) Hausdorff, almost regular spaces with a
dispersion point and similar properties. Unfortunately, none of these
spaces is Urysohn.
On the degree of approximation of the Hermite and Hermite‐Fejer interpolation
Authors: Prasad J.
Published: September 2002

Here we find the order of convergence of the Hermite and Hermite‐Fejér interpolation polynomials constructed on the zeros of (1 − x2)Pn(x) where Pn(x) is the Legendre polynomial of degree n with normalization Pn(1) = 1.
R‐continuous functions
Authors: Konstadilaki-Savvapoulou Ch. , Janković D.
Published: September 2002

A strong form of continuity of functions between topological spaces is introduced and studied. It is shown that in many known results, especially closed graph theorems, functions under consideration are R‐continuous. Several results in the literature concerning strong continuity properties are generalized and/or improved.
Commutative rings with homomorphic power functions
Authors: Dobbs David E. , Kiltinen John O. , Orndorff Bobby J.
Published: September 2002

A (commutative) ring R (with identity) is called m‐linear (for an integer m ≥ 2) if (a+b)m = am + bm for all a and b in R. The m‐linear reduced rings are characterized, with special attention to the finite case. A structure theorem reduces the study of m‐linearity to the case of prime characteristic, for which the following result establishes an analogy with finite fields. For each prime p and integer m ≥ 2 which is not a power of p, there exists an integer s ≥ m such that, for each ring R of characteristic p, R is m‐linear if and only if for each r in R. Additional results and examples are given.
Comparison results and linearized oscillations for higher‐order difference equations
Authors: Ladas G. , Qian C.
Published: September 2002

Consider the difference equations

urn:x-wiley:01611712:media:ijmm412938:ijmm412938-math-0001

and

urn:x-wiley:01611712:media:ijmm412938:ijmm412938-math-0002

We establish a comparison result according to which, when m is odd, every solution of Eq.(1) oscillates provided that every solution of Eq.(2) oscillates and, when m is even, every bounded solution of Eq.(1) oscillates provided that every bounded solution of Eq.(2) oscillates. We also establish a linearized oscillation theorem according to which, when m is odd, every solution of Eq.(1) oscillates if and only if every solution of an associated linear equation

urn:x-wiley:01611712:media:ijmm412938:ijmm412938-math-0003

oscillates and, when m is even, every bounded solution of Eq.(1) oscillates if and only if every bounded solution of (*) oscillates.
Measuring static complexity
Authors: Goertzel Ben
Published: September 2002

The concept of pattern is introduced, formally defined, and used to analyze various measures of the complexity of finite binary sequences and other objects. The standard Kolmogoroff‐Chaitin‐Solomonoff complexity measure is considered, along with Bennett′s logical depth, Koppel′s sophistication′, and Chaitin′s analysis of the complexity of geometric objects. The pattern‐theoretic point of view illuminates the shortcomings of these measures and leads to specific improvements, it gives rise to two novel mathematical concepts‐‐orders of complexity and levels of pattern, and it yields a new measure of complexity, the structural complexity, which measures the total amount of structure an entity possesses.
A note on conservative measures on semigroups
Authors: Tserpes N. A.
Published: September 2002

Consider (S, B, μ) the measure space where S is a topological metric semigroup and μ a countably additive bounded Borel measure. Call μ conservative if all right translations tx : s → sx, x ∈ S (which are assumed closed mappings) are conservative with respect (S, B, μ) in the ergodic theory sense. It is shown that the semigroup generated by the support of μ is a left group. An extension of this result is obtained for σ‐finite μ.
Equiconvergence of some sequences of rational functions
Authors: Bokhari M. A. , Sharma A.
Published: September 2002

The phenomenon of equiconvergence was first observed by Walsh for two sequences of polynomial interpolants to a class of functions. Here we obtain analogues of Yuanren′s results for Walsh equiconvergence using rational functions as in Saff and Sharma. We extend this to Hermite interpolation and an earlier result of [1] is improved and corrected.
Derived length for arbitrary topological spaces
Authors: Jayanthan A. J.
Published: September 2002

The notion of derived length is as old as that of ordinal numbers itself. It is also known as the Cantor‐Bendixon length. It is defined only for dispersed (that is scattered) spaces. In this paper this notion has been extended in a natural way for all topological spaces such that all its pleasing properties are retained. In this process we solve a problem posed by V. Kannan. ([1] Page 158).
The zeros of as functions of order
Authors: Mercer A. McD.
Published: September 2002

If denotes the kth positive zero of the Bessel function , it has been shown recently by Lorch and Szego [2] that increases with ν in ν > 0 and that (with k fixed in 2, 3, …) increases in 0 < ν ≤ 3838. Furthermore, Wong and Lang have now extended the latter result, as well, to the range ν > 0. The present paper, by using a different kind of analysis, re‐obtains these conclusions as a special case of a more general result concerning the positive zeros of the function . Here, the constants a, b and c are subject to certain mild restrictions.
The nuclei and other properties of p‐primitive semifield planes
Authors: Cordero M.
Published: September 2002

In this article the nuclei of p‐primitive semifield planes are studied. The behavior of this class of planes under the operations of derivation, transposition and dualization is also analyzed.
On G‐finitistic spaces and related notions
Authors: Deo Satya , Andotra Janak Singh
Published: September 2002

Let X be a G‐space where G is a topological group. We show that X is G‐finitistic iff the orbit space X/G is finitistic. This result allows us to answer a question raised in [5] asking for an equivariant characterization of a non‐finitistic G‐space where G is a compact Lie group. For an arbitrary compact group G a simple characterization of G‐finitistic spaces has been obtained in terms of new notions of G‐compactness and G‐dimension.