bluuebunny/crossref_metadata_2025 huggingface dataset:
The response of skin friction, wall heat transfer and pressure drop to wall waviness in the presence of buoyancy
Authors: Rao C. N. B. , Sastri K. S.
Published: September 2002

Laminar natural convection flow and heat transfer of a viscous incompressible fluid confined between two long vertical wavy walls has been analysed taking the fluid properties constant and variable. In particular, attention is restricted to estimate the effects of viscous dissipation and wall waviness on the flow and heat transfer characteristics. Use has been made of a linearization technique to simplify the governing equations and of Galerkin′s method in the solution. The solutions obtained for the velocity and the temperature‐fields hold good for all values of the Grashof number and wave number of the wavy walls.
Observation on the foundation of kinetic theory of gases
Authors: Basu U. , Dutta M.
Published: September 2002

This paper deals with the study of the mathematical foundation of the Kinetic theory of gases. The significance of the Boltzmann model for a system of particles treated by classical mechanics is briefly explained. An apparent, but inherent difficulty in this model is pointed out.
Almost convex metrics and Peano compactifications
Authors: Dickman R. F.
Published: September 2002

Let (X, d) denote a locally connected, connected separable metric space. We say the X is S‐metrizable provided there is a topologically equivalent metric ρ on X such that (X, ρ) has Property S, i.e., for any ϵ > 0, X is the union of finitely many connected sets of ρ‐diameter less than ϵ. It is well‐known that S‐metrizable spaces are locally connected and that if ρ is a Property S metric for X, then the usual metric completion of (X, ρ) is a compact, locally connected, connected metric space; i.e., is a Peano compactification of (X, ρ). In an earlier paper, the author conjectured that if a space (X, d) has a Peano compactification, then it must be S‐metrizable. In this paper, that conjecture is shown to be false; however, the connected spaces which have Peano compactificatons are shown to be exactly those having a totally bounded, almost convex metric. Several related results are given.
A Pólya “shire” theorem for functions with algebraic singularities
Authors: Shaw J. K. , Prather C. L.
Published: September 2002

The classical “shire” theorem of Pólya is proved for functions with algebraic poles, in the sense of L. V. Ahlfors. A function f(z) is said to have an algebraic pole at z0 provided there is a representation , where p and N are positive integers and A(z) is analytic at z0. For p = 1, the proof given reduces to an entirely new proof of the shire theorem. New quantitative results are given on how zeros of the successive derivatives migrate to the final set.
Absolute continuity, singularity and product measures
Authors: Johnson Roy A.
Published: September 2002

Conditions are given under which a product of two semifinite measures is absolutely continuous or weakly singular with respect to another product of two semifinite measures. A Lebesgue type decomposition theorem is proved for certain product measures so that the resulting measures are themselves product measures.
On singularities of capillary surfaces in the absence of gravity
Authors: Roytburd V.
Published: September 2002

We study numerical solutions to the equation of capillary surfaces in
trapezoidal domains in the absence of gravity when the boundary contact angle declines from 90° to some critical value. We also discuss a result on the behavior of solutions in more general domains that confirms numerical calculations.
The n‐dimensional distributional Mellin transformation
Authors: Sinha Sunil Kumar
Published: September 2002

The n‐dimensional distributional Mellin transformation is developed using the testing function space Mc,d and its dual The standard theorems on analyticity, uniqueness and continuity are proved. A necessary and sufficient condition for a function to be an n‐dimensional Mellin transformation is proved by the help of a boundedness property for distribution in . Some operational transform formulas are also introduced.
A class of orthogonal polynomials of a new type
Authors: Dutta M. , Manocha Kanchan Prabha
Published: September 2002

The purpose of this paper is to study a class of polynomials associated with a class of m differential equations, where λ is fixed, n is a variable parameter, m is fixed positive integer and ν is a non‐negative integer <m. We also obtain all the important properties of this class of polynomials including Rodrigues′ formulas, generating function, and recurrence relations. Several special cases of
interest are obtained from our analysis.
A note of almost continuous mappings and Baire spaces
Authors: Tong Jing Cheng
Published: September 2002

We prove the following theorem: THEOREM. Let Y be a second countable, infinite R0‐space. If there are countably many open sets 01, 02, …, 0n, … in Y such that 01⫋02⫋…⫋0n⫋…, then a topological space X is a Baire space if and only if every mapping f : X → Y is almost continuous on a dense subset of X. It is an improvement of a theorem due to Lin and Lin [2].
Unbounded functions in the unit disk
Authors: Sons L. R.
Published: September 2002

A survey is made of results related to the value distribution of functions which are meromorphic or analytic in the unit disc and have unbounded growth according to some specific growth indicator.
On the structure of a triangle‐free infinite‐chromatic graph of Gyarfas
Authors: Eggan Larry , Harary Frank
Published: September 2002

Gyárfás has recently constructed an elegant new example of a triangle‐free infinite graph G with infinite chromatic number. We analyze its structure by studying the properties of a nested family of subgraphs Gn whose union is G.
On contact CR‐submanifolds of sasakian manifolds
Authors: Matsumoto Koji
Published: September 2002

Recently, K.Yano and M.Kon [5] have introduced the notion of a contact
CR‐submanifold of a Sasakian manifold which is closely similar to the one of a CR‐submanifold of a Kaehlerian manifold defined by A. Bejancu [1].

In this paper, we shall obtain some fundamental properties of contact CR‐submanifolds of a Sasakian manifold. Next, we shall calculate the length of the second
fundamental form of a contact CR‐product of a Sasakian space form (THEOREM 7.4). At last, we shall prove that a totally umbilical contact CR‐submanifold satisfying certain conditions is totally geodesic in the ambient manifold (THEOREM 8.1).
On a generalization of close‐to‐convexity
Authors: Noor K. Inayat
Published: September 2002

A class Tk of analytic functions in the unit disc is defined in which the concept of close‐to‐convexity is generalized. A necessary condition for a function f to belong to Tk, raduis of convexity problem and a coefficient result are solved in this paper.
On a property of probabilistic context‐free grammars
Authors: Chaudhuri R. , Rao A. N. V.
Published: September 2002

It is proved that for a probabilistic context‐free language L(G), the population density of a character (terminal symbol) is equal to its relative density
in the words of a sample S from L(G) whenever the production probabilities of the grammar G are estimated by the relative frequencies of the corresponding productions in the sample.
On the lattice theory of function semi‐norms
Authors: Schochetman I. E. , Tsui S. K.
Published: September 2002

We consider the lattice of function semi‐norms over a measure space,
as well as certain distinguished subsets. We determine which subsets are sublattices and, in turn, which of these are Dedekind complete. We also investigate the extent to which the distributive and DeMorgan Laws are valid in this setting.
Subclasses of close‐to‐convex functions
Authors: Silvia E. M.
Published: September 2002

Let 𝒦[C, D], −1 ≤ D < C ≤ 1, denote the class of functions g(z), g(0) = g′(0) − 1 = 0, analytic in the unit disk U = {z : |z| < 1} such that 1 + (zg″(z)/g′(z)) is subordinate to (1 + Cz)/(1 + Dz), z ϵ U. We investigate the subclasses of close‐to‐convex functions f(z), f(0) = f′(0) − 1 = 0, for which there exists g ϵ 𝒦[C, D] such that f′/g′ is subordinate to (1 + Az)/(1 + Bz), −1 ≤ B < A ≤ 1. Distortion and rotation theorems and coefficient bounds are obtained. It is also shown that these classes are preserved under certain integral operators.
On certain constactions in finitistic spaces
Authors: Deo Satya , Singh Mohan
Published: September 2002

Since the product of two finitistic spaces need not be finitistic, and also because a continuous closed image of a finitistic space need not be finitistic, it is natural to enquire whether or not the class of finitistic spaces in closed under the formation of cones, reduced cones, suspensions, reduced suspensions, adjunction spaces, mapping cylinders, mapping cones, joins and smash products. In this paper we prove that all of the above constructs, except joins and smash products, of finitistic spaces are finitistic. The joins and smash products of finitistic spaces, however, need not be finitistic. We find sufficient conditions under which these are also finitistic.
A note on a paper by S. Haber
Authors: Mercer A. McD.
Published: September 2002

A technique used by S. Haber to prove an elementary inequality is applied
here to obtain a more general inequality for convex sequences.
A note on an extension of Lindelöf′s theorem to meromorphic functions
Authors: Salmassi Mohammad
Published: September 2002

S. M. Shah [3] has given an extension of Lindelöf′s Theorem to meromorphic functions. He also obtained an expression for the characteristic function of a meromorphic function of integer order. In this note we give estimates for log|f(reiθ)| of such functions.
Value distribution and the Lemma of the logarithmic derivative on polydiscs
Authors: Stoll Wilhelm
Published: September 2002

Value distribution is developed on polydiscs with the special emphasis that the value distribution function depend on a vector variable. A Lemma of the logarithmic derivative for meromorphic functions on polydiscs is derived. Here the Bergman boundary of the polydiscs is approached along cones of any dimension and exceptional sets for such an approach are defined.
Supremum norm differentiability
Authors: Leonard I. E. , Taylor K. F.
Published: September 2002

The points of Gateaux and Fréchet differentiability of the norm in C(T, E) are obtained, where T is a locally compact Hausdorff space and E is a real Banach space. Applications of these results are given to the space ℓ∞(E) of all bounded sequences in E and to the space B(ℓ1, E) of all bounded linear operators from ℓ1 into E
On a class of polynomials associated with the paths in a graph and its application to minimum nodes disjoint path coverings of graphs
Authors: Farrell E. J.
Published: September 2002

Let G be a graph. With every path α of G let us associate a weight wα With every spanning subgraph C of G consisting of paths α1, α2, …, αk, let us associate the weight

urn:x-wiley:01611712:media:ijmm202385:ijmm202385-math-0001

.
The path polynomial of G is

urn:x-wiley:01611712:media:ijmm202385:ijmm202385-math-0002

,
where the summation is taken over all the spanning subgraphs of G whose components are paths. Some basic properties of these polynomials are given. The polynomials are then used to obtain results about the minimum number of node disjoint path coverings in graphs.
Some invariant theorems on geometry of Einstein non‐symmetric field theory
Authors: Shu-Lin Liu , Sen-Lin Xu
Published: September 2002

This paper generalizes Einstein′s theorem. It is shown that under the
transformation

urn:x-wiley:01611712:media:ijmm140940:ijmm140940-math-0001

,
curvature tensor , Ricci tensor Sik(U), and scalar curvature S(U) are all invariant, where Λ = Λjdxj is a closed 1‐differential form on an n‐dimensional manifold M.

It is still shown that for arbitrary U, the transformation that makes curvature tensor (or Ricci tensor Sik(U)) invariant

urn:x-wiley:01611712:media:ijmm140940:ijmm140940-math-0004

must be TΛ transformation, where V (its components are ) is a second order differentiable covariant tensor field with vector value.
On mixed finite element techniques for elliptic problems
Authors: Noor M. Aslam
Published: September 2002

The main aim of this paper is to consider the numerical approximation of
mildly nonlinear elliptic problems by means of finite element methods of mixed type. The technique is based on an extended variational principle, in which the constraint of interelement continuity has been removed at the expense of introducing a Lagrange multiplier.

It is shown that the saddle point, which minimizes the energy functional over the product space, is characterized by the variational equations. The eauivalence is used in deriving the error estimates for the finite element approximations. We give an example of a mildly nonlinear elliptic problem and show how the error estimates can be obtained from the general results.
The regularity series of a Cauchy space
Authors: Kent Darrell C.
Published: September 2002

This study extends the notion of regularity series from convergence spaces to Cauchy spaces, and includes an investigation of related topics such as that T2 and T3 modifications of a Cauchy space and their behavior relative to certain types of quotient maps. These concepts are applied to obtain a new characterization of Cauchy spaces which have T3 completions.
Strict topoligies in non‐Archimedean function spaces
Authors: Katsaras A. K.
Published: September 2002

Let F be a non‐trivial complete non‐Archimedean valued field. Some locally F‐convex topologies, on the space Cb(X, E) of all bounded continuous functions from a zero‐dimensional topological space X to a non‐Archimedean locally F‐convex space E, are studied. The corresponding dual spaces are also investigated.
Estimates for capacities and traces of potentials
Authors: Maz′ja V. G. , Preobrazenskii S. P.
Published: September 2002

It is shown that “isoperimetric” inequalities, relating measures and capacities, hold for all sets in ℝn if they are valid for all balls. As a corollary, the necessary and sufficient conditions for the continuity of some imbeddings of M. Riesz and Bessel potential spaces are obtained. The introduction contains a survey of known results on inequalities of Sobolev type.
On coefficients of path polynomials
Authors: Farrell E. J.
Published: September 2002

Explicit formulae, in terms of sugraphs of the graph, are given for the first six coefficients of the simple path polynomial of a graph. From these, explicit formulae are deduced for the number of hamiltonian paths in graphs with up to six nodes. Also simplified expressions are given for the number of ways of covering the nodes of some families of graphs with k paths, for certain values of k.
The Poulsen simplex is not a tensor product
Authors: Armstrong Thomas E.
Published: September 2002

It is shown that the Poulsen simplex is not a projective tensor product of non‐trivial Ghoquet simplexes.
Uniqueness of solution of a singular heat equation
Authors: Young Eutiquio C.
Published: September 2002

Some uniqueness results for the singular heat equation are presented in this paper.
On the Korteweg‐de Vries equation: an associated equation
Authors: Schlereth Eugene P. , Rodin Ervin Y.
Published: September 2002

The purpose of this paper is to describe a relationship between the Korteweg‐de Vries (KdV) equation

urn:x-wiley:01611712:media:ijmm237357:ijmm237357-math-0001

and another nonlinear partial differential equation of the form

urn:x-wiley:01611712:media:ijmm237357:ijmm237357-math-0002

The second equation will be called the Associated Equation (AE) and the connection between the two will be explained. By considering AE, explicit solutions to KdV will be obtained. These solutions include the solitary wave and the cnoidal wave solutions. In addition, similarity solutions in terms of Airy functions and Painlevé transcendents are found. The approach here is different from the Inverse Scattering Transform and the results are not in the form of solutions to specific initial value problems, but rather in terms of solutions containing arbitrary constants.
Integrability of derivations of classical solutions of Dirichlet′s problem for an elliptic equation
Authors: Hassan M. I.
Published: September 2002

The present work is concerned with integrability properties of derivatives of classical solutions of Dirichlet′s problem for a linear second‐order elliptic equation Lu = f. With the aid of special weighted Hilbert spaces of locally square integrable functions, we determine the nature of singularities that f can have near the boundary, in order that such classical solutions are in the Sobolev space W1. By means of an example it is shown that the obtained result is exact.
Some torsion theoretical characterizations of rings
Authors: Ahsan Javed
Published: September 2002

Rings whose torsion free modules are quasi‐injective, quasi‐projective or coflat have been characterized in the context of certain torsion theories.
On rank 5 projective planes
Authors: Bachmann Otto
Published: September 2002

In this paper we continue the study of projective planes which admit collineation groups of low rank (Kallaher [1] and Bachmann [2,3]). A rank 5 collineation group of a projective plane ℙ of order n ≠ 3 is proved to be flag‐transitive. As in the rank 3 and rank 4 case this implies that is ℙ not desarguesian and that n is (a prime power) of the form m4 if m is odd and n = m2 with m ≡ 0mod4 if n is even. Our proof relies on the classification of all doubly transitive groups of finite degree (which follows from the classification of all finite simple groups).
Representation of functions as the Post‐Widder inversion operator of generalized functions
Authors: Manandhar R. P. , Debnath L.
Published: September 2002

A study is made of the Post‐Widder inversion operator to a class of generalized functions in the sense of distributional convergence. Necessary and sufficient conditions are proved for a given function to have the representation as the rth operate of the Post‐Widder inversion operator of generalized functions. Some representation theorems are also proved. Certain results concerning the testing function space and its dual are established. A fundamental theorem regarding the existence of the real inversion operator (1.6) with r = 0 is proved in section 4. A classical inversion theory for the Post‐Widder inversion operator with a few other theorems which are fundamental to the representation theory is also developed in this paper.
Separation metrics for real‐valued random variables
Authors: Taylor Michael D.
Published: September 2002

If W is a fixed, real‐valued random variable, then there are simple and easily satisfied conditions under which the function dW, where dW(X, Y) = the probability that W “separates” the real‐valued random variables X and Y, turns out to be a metric. The observation was suggested by work done in [1].
On a non‐self adjoint expansion formula
Authors: Naylor D.
Published: September 2002

This paper develops a formula of inversion for an integral transform of the kind similar to that associated with the names of Kontorovich and Lebedev except that the kernel involves the Neumann function Yu(kr) and the variable r varies over the infinite interval a ≤ r < ∞ where a > 0 The transform is useful in the investigation of functions that satisfy the Helmholtz equation and a condition of radiation at infinity. The formula established is expressed entirely in terms of series expansions and replaces earlier inversion formulas that require the evaluation of contour integrals.
Coincidence theorems for some multivalued mappings
Authors: Rhoades B. E. , Singh S. L. , Kulshrestha Chitra
Published: September 2002

Two coincidence theorems in a metric space are proved for a multi‐valued mapping that commutes with a single‐valued mapping and satisfies a general multi‐valued contraction type condition.
A remark on the r‐th mean differentiability
Authors: Stamatelos George D.
Published: September 2002

This paper is concerned with the r‐th mean differentiability. In the mathematical developments regarding the asymptotic expansion and the asymptotic distribution of the likelihood function, there arises the question whether the assumptions made on the model imply differentiability in the r′‐th mean of the underlying random functions, for integer values r′ < r. The present paper provides an answer to this question and also gives the explicit form of the derivatives in the r′‐th mean involved.
Finite dimensionality in scole of Banach algebras
Authors: Takahasi Sin-Ei
Published: September 2002

It is shown that if the socle soc(A) of a semisimple Banach algebra A is norm‐closed, then soc(A) is already finite dimensional. The proof makes use of the Al‐Moajil theorem. However it is remarked that our main theorem is an extension of the Al‐Moajil′s.
A construction of the general relativistic Boltzmann equation
Authors: Dolan P. , Zenios A. C.
Published: September 2002

Our work depends essentially on the notion of a one‐particle seven‐dimensional state‐space. In constructing a general relativistic theory we assume that all measurable quantities arise from invariant differential forms. In this paper, we study only the case when instantaneous, binary, elastic collisions occur between the particles of the gas. With a simple model for colliding particles and their collisions, we derive the kinetic equation, which gives the change of the distribution function along flows in state‐space.
Unsteady free convection of a stagnation point of attachment on an isothermal surface
Authors: Ingham D. B. , Merkin J. H. , Pop I.
Published: September 2002

The time development free convection flow near a three‐dimensional stagnation point of attachment on an isothermal surface is studied at large Grashof numbers. A small time solution and an accurate numerical method is described for determining the solution of the time‐dependent boundary‐layer equations. For a range of values of parameter c, which describes the local geometry, the development of the various physical properties of the flow are calculated and compared with their values at small and large values of time. In another range of values of c the numerical results suggest the development of a singularity in the boundary‐layer equations at a finite value of time. An anlysis is presented which is consistent with the numerical results and confirms the presence of this singularity.
Almost contact metric 3‐submersions
Authors: Watson Bill
Published: September 2002

An almost contact metric 3‐submersion is a Riemannian submersion, π from an almost contact metric manifold onto an almost quaternionic manifold which commutes with the structure tensors of type (1, 1);i.e., π*φi = Jiπ*, for i = 1, 2, 3. For various restrictions on ∇φi, (e.g., M is 3‐Sasakian), we show corresponding limitations on the second fundamental form of the fibres and on the complete integrability of the horizontal distribution. Concommitantly, relations are derived between the Betti numbers of a compact total space and the base space. For instance, if M is 3‐quasi‐Saskian (dΦ = 0), then b1(N) ≤ b1(M). The respective φi‐holomorphic sectional and bisectional curvature tensors are studied and several unexpected results are obtained. As an example, if X and Y are orthogonal horizontal vector fields on the 3‐contact (a relatively weak structure) total space of such a submersion, then the respective holomorphic bisectional curvatures satisfy: . Applications to the real differential geometry of Yarg‐Milis field equations are indicated based on the fact that a principal SU(2)‐bundle over a compactified realized space‐time can be given the structure of an almost contact metric 3‐submersion.
Multiparameter extrapolation and deflation methods for solving equation systems
Authors: Hallett A. J. Hughes
Published: September 2002

Most models in economics and the applied sciences are solved by first order iterative techniques, usually those based on the Gauss‐Seidel algorithm. This paper examines the convergence of multiparameter extrapolations (accelerations) of first order iterations, as an improved approximation to the Newton method for solving arbitrary nonlinear equation systems. It generalises my earlier results on single parameter extrapolations. Richardson′s generalised method and the deflation method for detecting successive solutions in nonlinear equation systems are also presented as multiparameter extrapolations of first order iterations. New convergence results are obtained for those methods.
On the convergence of Fourier series
Authors: de Souza Geraldo Soares
Published: September 2002

We define the space . Each bn is a special p‐atom, that is, a real valued function, defined on (−π, π], which is either b(t) = 1/2π or , where I is an interval in (−π, π], L is the left half of I and R is the right half. |I| denotes the length of I and XE the characteristic function of E. Bp is endowed with the norm , where the infimum is taken over all possible representations of f. Bp is a Banach space for 1/2 < p < ∞. Bp is continuously contained in Lp for 1 ≤ p < ∞, but different. We have THEOREM. Let 1 < p < ∞. If f ∈ Bp then the maximal operator maps Bp into the Lorentz space L(p, 1) boundedly, where Sn(f, x) is the nth‐sum of the Fourier Series of f.
Some generating functions of modified Bessel polynomials from theview point of Lie group
Authors: Chongdar Asit Kumar
Published: September 2002

In this paper we have derived a class of bilateral generating relation for modified Bessel polynomials from the view point of Lie group. An application of our theorem is also pointed out.

Corrigendum: Some generating functions of modifed Bessel polynomials from the view point of Lie groupdx.doi.org/10.1155/S0161171286000790
Reducible functional differential equations
Authors: Shah S. M. , Wiener Joseph
Published: September 2002

This is the first part of a survey on analytic solutions of functional differential equations (FDE). Some classes of FDE that can be reduced to ordinary differential equations are considered since they often provide an insight into the structure of analytic solutions to equations with more general argument deviations. Reducible FDE also find important applications in the study of stability of differential‐difference equations and arise in a number of biological models.
A trace theorem for Caloric functions
Authors: Mhaskar H. N.
Published: September 2002

Given a solution of the heat equation in an open strip, we state necessary and sufficient conditions for the existence of a boundary function in a given weighted Banach space. We then investigate the relationship between the smoothness of this boundary function and the growth of the solution of the heat equation.
A charaterization of closed maps using the whyburn construction
Authors: Stallings Yvonne O.
Published: September 2002

In this paper we modify the Whyburn construction for a continuous function f : X → Y. If the range is first countable, we get a characterization of closed maps; namely, the constructions are the same if and only if the map is closed.
Function theory for a beltrami algebra
Authors: Case B. A.
Published: September 2002

Complex functions are investigated which are solutions of an elliptic system of partial differential equations associated with a real parameter function. The functions f associated with a particualr parameter function g on a domain D form a Beltrami algebra denoted by the pair (D, g) and a function theory is developed in this algebra. A strong conformality property holds for all functions in a (D, g) algebra. For g ≡ |z| = r the algebra (D, r) is that of the analytic functions.
Analytic representation of the distributional finite Hankel transform
Authors: Singh O. P. , Pathak Ram S.
Published: September 2002

Various representations of finite Hankel transforms of generalized functions are obtained. One of the representations is shown to be the limit of a certain family of regular generalized functions and this limit is interpreted as a process of truncation for the generalized functions (distributions). An inversion theorem for the gereralized finite Hankel transform is established (in the distributional sense) which gives a Fourier‐Bessel series representation of
generalized functions.
A generalized Meijer transformation
Authors: Rao G. L. N. , Debnath L.
Published: September 2002

In a series of papers [1‐6], Kratzel studies a generalized version of the classical Meijer transformation with the Kernel function (st) νη(q, ν + 1;  (st)q). This transformation is referred to as GM transformation which reduces to the classical Meijer transform when q = 1. He also discussed a second generalization of the Meijer transform involving the Kernel function which reduces to the Meijer function when n = 2 and the Laplace transform when n = 1. This is called the Meijer‐Laplace (or ML) transformation. This paper is concerned with a study of both GM and ML transforms in the distributional sense. Several properties of these transformations including inversion, uniqueness, and analyticity are discussed in some detail.
On Legendre numbers
Authors: Haggard Paul W.
Published: September 2002

The Legendre numbers, an infinite set of rational numbers are defined from the associated Legendre functions and several elementary properties are presented. A general formula for the Legendre numbers is given. Applications include summing certain series of Legendre numbers and evaluating certain integrals. Legendre numbers are used to obtain the derivatives of all orders of the Legendre polynomials at x = 1.
Ordered Cauchy spaces
Authors: Kent D. C. , Vainio R.
Published: September 2002

This paper is concerned with the notion of “ordered Cauchy space” which is given a simple internal characterization in Section 2. It gives a discription of the category of ordered Cauchy spaces which have ordered completions, and a construction of the “fine completion functor” on this category. Sections 4 through 6 deals with certain classes of ordered Cauchy spaces which have ordered completions; examples are given which show that the fine completion does not preserve such properties as uniformizability, regularity, or total boundedness. From these results, it is evident that a further study of ordered Cauchy completions is needed.
Study of nonlinear wave processes in plasmas using the formalism of a special Lorntz transformation for a space‐independent fram
Authors: Paul S. N. , Chakraborty B. , Debnath L.
Published: September 2002

A study is made of nonlinear waves in plasmas using the formalism of a special Lorentz transformation for a space‐independent frame, S′. This special transformation is used to transform the space‐time dependent equations in a cold, relativistic, magnetized plasma to the S′ frame. Then the transformed equations are employed to derive the expressions for the Lagrangian and the Hamiltonian in the S′ frame. The Lagrengian and the Hamiltonian for a strong circularly polarized laser beam have also been obtained in the S′ frame. The exact form of the nonlinear dispersion relation is derived for circularly polarized waves. Then the results for the frequency and the wave number shifts of these waves in a cold, magnetized relativistic plasma are obtained with some Discussion on the nature of the frequency
shifts. Finally, numerical results are presented for the radiation of Nd‐glass laser in dense plasmas.
Local energy decay for waves governed by a system of nonlinear Shrödinger equations in a nonuniform medium
Authors: Lin J. E.
Published: September 2002

We show that the local energy of a smooth localized solution to a system of coupled nonlinear Shrödinger equations in a certain nonuniform medium decays to zero as the time approaches infinity.
Diagonalization of a self‐adjoint operator acting on a Hilbert module
Authors: Saworotnow Parfeny P.
Published: September 2002

For each bounded self‐adjoint operator T on a Hilbert module H over an H*‐algebra A there exists a locally compact space m and a certain A‐valued measure μ such that H is isomorphic to L2(μ) ⊗ A and T corresponds to a multiplication with a continuous function. There is a similar result for a commuting family of normal operators. A consequence for this result is a representation theorem for generalized stationary processes.
Methods of constructing hyperfields
Authors: Massouros Ch. G.
Published: September 2002

In this paper we introduce a class of hyperfields which contains non quotient
hyperfields. Thus we give a negative answer to the question of whether every hyperfield is isomorphic to a quotient of a field K by some subgroup G of its multiplicative group.
On a function related to Ramanujan′s Tau function
Authors: Ewell John A.
Published: September 2002

For the function ψ = ψ12, defined by , the author derives two simple formulas. The simpler of these two formulas is expressed
solely in terms of the well‐known sum‐of‐divisors function.
On k‐traid sequences
Authors: Gupta Hansraj , Singh K.
Published: September 2002

At the conference of the Indian Mathematical Society held at Allahabad in December 1981, S. P. Mohanty and A. M. S. Ramasamy pointed out that the three numbers 1, 2, 7, have the following property: the product of any two of them increased by 2 is a perfect square. They then showed that there is no fourth integer which hsares this property with all of them. They used Pell′s equation and the theory of quadratic residues to prove their statement. In this paper,
we show that their statement holds for a very large set of triads and our proof of the statement is very simple.
Functorial properties of the lattice of functional semi‐norms
Authors: Schochetman I. E. , Tsui S. K.
Published: September 2002

Given a measureable transformation between measure spaces, we determine when such gives rise to a mapping between the corresponding lattice of function semi‐norms. We further determine when this mappings preserves norms and observe that it does preserve certain other important properties. We next establish a functorial connection between measure spaces and lattice. Finally, we show that the above lattice mapping does not commute with the associate construction.
An Extension of a result of Csiszar
Authors: Cerrito P. B.
Published: September 2002

We extend the results of Csiszar (Z. Wahr. 5(1966) 279‐295) to a topological semigroup S. Let μ be a measure defined on S. We consider the value of . First. we show that the value of α is either zero or one. If α = 1, we show that there exists a sequence of elements {an} In S such that converges vaguely to a probability measure where δ denotes point mass. In particular, we apply the results to inverse and matrix semigroups.
Singularity methods for magnetohydrodynamics
Authors: Alawneh A. D. , Shawagfeh N. T.
Published: September 2002

Singular solutions for linearized MHD equations based on Oseen approximations have been obtained such as Oseenslet. Oseenrotlet, mass source, etc. By suitably distributing these singular solutions along the axes of symmetry of an axially symmetric bodies, we derive the approximate values for the velocity fields, the force and the momentum for the case of translational and rotational motions of such bodies in a steady flow of an incompressible viscous and magnetized fluid.
Global magnetofluidostatic fields (an unsolved PDE problem)
Authors: Surdo C. Lo
Published: September 2002

A satisfactory theory of the Global MagnetoFluidoStatic (GMFS) Fields, where symmetric and non‐symmetric configurations can be dealt with on the same footing, has not yet been developed. However the formulation of the Nowhere‐Force‐Free, Local‐Global MFS problem about a given smooth isobaric toroidal surface 𝒮0 (actually, a degenerate initial‐value problem) can be weakened so as to include certain generalized solutions as formal power series in a “natural” transverse coordinate. lt is reasonable to conjecture that these series converge, for sufficiently smooth data on 𝒮0. in the same function space which their coefficients belong to (in essence, a complete linear space over the 2‐torus).
A group theoretic approach to generalized harmonic vibrations in a one dimensional lattice
Authors: Boyd J. N. , Raychowdhury P. N.
Published: September 2002

Beginning with a group theoretical simplification of the equations of motion for harmonically coupled point masses moving on a fixed circle, we obtain the natural frequencies of motion for the array. By taking the number of vibrating point masses to be very large, we obtain the natural frequencies of vibration for any arbitrary, but symmetric, harmonic coupling of the masses in a one dimensional lattice. The result is a cosine series for the square of the frequency, where , j ∈ {1, 2, 3, …, N} and a(ℓ) depends upon the attractive force constant between the j‐th and (j + ℓ)‐th masses. Lastly, we show that these frequencies will be propagated by wave forms in the lattice.
Finite difference methods for computing eigenvalues of fourth order boundary value problems
Authors: Usmani Riaz A.
Published: September 2002

This brief report 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 linear differential equation y(4) + (p(x) − λq(x))y = 0. These methods are derived from the formula

urn:x-wiley:01611712:media:ijmm608690:ijmm608690-math-0001

Numerical results are included to demonstrate practical usefulness of our methods.
Fourier transforms of Dini‐Lipschitz functions
Authors: Younis M. S.
Published: September 2002

It is well known that if Lipschitz conditions of a certain order are imposed on a function f(x), then these conditions affect considerably the absolute convergence of the Fourier series and Fourier transforms of f. In general, if f(x) belongs to a certain function class, then the Lipschitz conditions have bearing as to the dual space to which the Fourier coefficients and transforms of f(x) belong. In the present work we do study the same phenomena for the wider Dini‐Lipschitz class as well as for some other allied classes of functions.
On the distributional Stieltjes transformation
Authors: Nikolic-Despotovic D. , Takaci A.
Published: September 2002

This paper is concerned with some general theorems on the distributional Stieltjes transformation. Some Abelian theorems are proved.
Analytic solutions of nonlinear neutral and advanced differential equatios
Authors: Wiener Joseph , Debnath Lokenath , Shah S. M.
Published: September 2002

A study is made of local existence and uniqueness theorems for analytic solutions of nonlinear differential equations of neutral and advanced types. These results are of special interest for advanced eauations whose solutions, in general, lose their margin of smoothness. Furthermore, existence of entire solutions is established for linear advanced differential systems with polynomial coefficients.
Conservation laws for shallow water waves on a sloping beach
Authors: Akyildiz Yilmaz
Published: September 2002

Shallow water waves are governed by a pair of non‐linear partial differential equations. We transfer the associated homogeneous and non‐homogeneous systems, (corresponding to constant and sloping depth, respectively), to the hodograph plane where we find all the non‐simple wave solutions and construct infinitely many polynomial conservation laws. We also establish correspondence between conservation laws and hodograph solutions as well as Bäcklund transformations by using the linear nature of the problems on the hodogrpah plane.
A digraph equation for homomorphic images
Authors: Girse Robert D. , Gillman Richard A.
Published: September 2002

The definitions of a homomorphism and a contraction of a graph are generalized to digraphs. Solutions are given to the graph equation .
Trigonometric identities
Authors: Baica Malvina
Published: September 2002

In this paper the author obtains new trigonometric identities of the form which are derived as a result of relations in a cyclotomic field ℛ(ρ), where ℛ is the field of rationals and ρ is a root of unity.

Those identities hold for every positive integer p ≥ 3 and any proof avoiding cyclotomic fields could be very difficult, if not insoluble. Two formulas

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stated only by Gauss in a slightly different form without a proof, are obtained and used in this paper in order to give some numeric applications of our new trigonometric identities.
On the operator equation α + α−1 = β + β−1
Authors: Thaheem A. B.
Published: September 2002

Let α, β be ∗‐automorphisms of a von Neumann algebra M satisfying the operator equation α + α−1 = β + β−1. In this paper we use new techniques (which are useful in noncommutative situations as well) to provide alternate proofs of the results:‐ If α, β commute then there is a central projection p in M such that α = β on MP and α = β−1 on M(1 − P); If M = B(H), the algebra of all bounded operators on a Hilbert space H, then α = β or α = β−1.
On polynomial equations in Banach space, perturbation techniques and applications
Authors: Argyros Ioannis K.
Published: September 2002

We use perturbation techniques to solve the polynomial equation in Banach
space. Our techniques provide more accurate information on the location of solutions and yield existence and uniqueness in cases not covered before. An example is given to justify our method.
On the complementary factor in a new congruence algorithm
Authors: Hilton Peter , Pedersen Jean
Published: September 2002

In an earlier paper the authors described an algorithm for determining the quasi‐order, Qt(b), of tmodb, where t and b are mutually prime. Here Qt(b) is the smallest positive integer n such that tn = ±1modb, and the algorithm determined the sign (−1)  ϵ ,  ϵ  = 0, 1, on the right of the congruence. In this sequel we determine the complementary factor F such that tn − (−1)  ϵ  = bF, using the algorithm rather that b itself. Thus the algorithm yields, from knowledge of b and t, a rectangular array

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The second and third rows of this array determine Qt(b) and  ϵ ; and the last 3 rows of the array determine F. If the first row of the array is multiplied by F, we obtain a canonical array, which also depends only on the last 3 rows of the given array; and we study its arithmetical properties.
Lamb′s plane problem in a thermo‐elastic micropolar medium with stretch
Authors: Chadha T. K. , Kumar Rajneesh , Bebnath Lokenath
Published: September 2002

A study is made of the Lamb plane problem in a thermo‐elastic micropolar medium with the effect of stretch. The problem is solved for an arbitrary, normal load distribution by using the double Fourier transform. The displacement components, force stress, couple stress, vector first moment and the temperature field are determined for a half space subjected to an arbitrary normal load. Two special cases of a horizontal force and a torque which are oscillating with a frequency ω have been investigated. It is shown that results of this analysis reduce to those without stretch.

Corrigendum to “Lamb′s plane problem in a thermo-elastic micropolar medium with stretch”dx.doi.org/10.1155/S0161171288000936
Riccati equations
Authors: Williams Lloyd K.
Published: September 2002

In this paper we find closed form solutions of some Riccati equations. Attention is restricted to the scalar as opposed to the matrix case. However, the ones considered have important applications to mathematics and the sciences, mostly in the form of the linear second‐order ordinary differential equations which are solved herewith.
On coefficient bounds of a certain class of p‐valent λ‐spiral functions of order α
Authors: Aouf M. K.
Published: September 2002

Let , denote the class of functions analytic in U = {z : |z| < 1}, which satisfy for z = reiθ ∈ U

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,
w(z) is analytic in U with w(0) = 0 and |w(z)|≦|z| for z ∈ U. In this paper we obtain the bounds of an and we maximize over the class Sλ(A, B, p, α) for complex values of μ.
Some properties of Jordan‐Ehlers spacetime
Authors: Mohanty G. , Panigrahi U. K.
Published: September 2002

It is shown that for cylindrically symmetric Jordan‐Ehlers spacetime, either
the charged scalar meson field associated with meson rest mass M or the charged perfect fluid cannot be the source for generating gravitation.
Resonance classes of measures
Authors: De Squire Maria Torres
Published: September 2002

We extend F. Holland′s definition of the space of resonant classes of functions, on the real line, to the space R(Φpq) (1≦p, q≦∞) of resonant classes of measures, on locally compact abelian groups. We characterize this space in terms of transformable measures and establish a realatlonship between R(Φpq) and the set of positive definite functions for amalgam spaces. As a consequence we answer the conjecture posed by L. Argabright and J. Gil de Lamadrid in their work on Fourier analysis of unbounded measures.
Generalized Laplace transform with matrix variables
Authors: Joshi R. M. , Joshi J. M. C.
Published: September 2002

In the present paper we have extended generalized Laplace transforms of Joshi to the space of m × m symmetric matrices using the confluent hypergeometric function of matrix argument defined by Herz as kernel. Our extension is given by

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The convergence of this integral under various conditions has also been discussed.
The real and complex inversion theorems for the transform have been proved and it has also been established that Hankel transform of functions of matrix argument are limiting cases of the generalized Laplace transforms.
Consequences of a sextuple‐product identity
Authors: Ewell John A.
Published: September 2002

A sextuple‐product identity, which essentially results from squaring the
classical Gauss‐Jacobi triple‐product identity, is used to derive two trigonometrical identities. Several special cases of these identities are then presented and discussed.
Recent developments on the Stieltjes transform of generalized functions
Authors: Pathak Ram Sankar , Debnath Lokenath
Published: September 2002

This paper is concerned with recent developments on the Stieltjes transform
of generalized functions. Sections 1 and 2 give a very brief introduction to the
subject and the Stieltjes transform of ordinary functions with an emphasis to the
inversion theorems. The Stieltjes transform of generalized functions is described
in section 3 with a special attention to the inversion theorems of this transform.
Sections 4 and 5 deal with the adjoint and kernel methods used for the development of
the Stieltjes transform of generalized functions. The real and complex inversion
theorems are discussed in sections 6 and 7. The Poisson transform of generalized
functions, the iteration of the Laplace transform and the iterated Stieltjes transfrom
are included in sections 8, 9 and 10. The Stieltjes transforms of different
orders and the fractional order integration and further generalizations of the
Stieltjes transform are discussed in sections 11 and 12. Sections 13, 14 and 15 are
devoted to Abelian theorems, initial‐value and final‐value results. Some applications
of the Stieltjes transforms are discussed in section 16. The final section deals with
some open questions and unsolved problems. Many important and recent references are
listed at the end.
On measure repleteness and support for lattice regular measures
Authors: Bachman George , Stratigos P. D.
Published: September 2002

The present paper is mainly concerned with establishing conditions which
.assure that all lattice regular measures have additional smoothness properties or
that simply all two‐valued such measures have such properties and are therefore Dirac
measures. These conditions are expressed in terms of the general Wallman space. The
general results are then applied to specific topological lattices, yielding new conditions
for measure compactness, Borel measure compactness, clopen measure repleteness,
strong measure compactness, etc. In addition, smoothness properties in the
general setting for lattice regular measures are related to the notion of support,
and numerous applications are given.