bluuebunny/crossref_metadata_2025 huggingface dataset:
A plane vertical submerged barrier in surface water waves
Authors: Basu U. , Mandal B. N.
Published: September 2002

By a simple application of Green′s integral theorem, amplitude of the
radiated waves at infinity due to a line source in the presence of a fixed vertical plane barrier completely submerged in deep water is obtained.
The generalization and proof of Bertrand′s postulate
Authors: Giordano George
Published: September 2002

The purpose of this paper is to show that for 0 < r < 1 one can determine explicitly an x0 such that ∀x ≥ x0, ∃ at least one prime between rx and x. This is a generalization of Bertrand′s Postulate. Furthermore, the same procedures are used to show that if one can find upper and lower bounds for θ(x) whose difference is kxρ then ∃ a prime between x and x − Kxρ, where k, K > 0 are constants, 0 < ρ < 1 and , where p runs over the primes.
The space of Henstock integrable functions of two variables
Authors: Ostaszewski Krzysztof
Published: September 2002

We consider the space of Henstock integrable functions of two variables. Equipped with the Alexiewicz norm the space is proved to be barrelled. We give a partial description of its dual. We show by an example that the dual can′t be described in a manner analogous to the one‐dimensional case, since in two variables there exist functions whose distributional partials are measures and which are not multipliers for Henstock integrable functions.
Remarks on extreme eigenvalues of Toeplitz matrices
Authors: Pourahmadi Mohsen
Published: September 2002

Let f be a nonnegative integrable function on [−π, π], Tn(f) the (n + 1) × (n + 1) Toeplitz matrix associated with f and λ1,n its smallest eigenvalue. It is shown that the convergence of λ1,n to minf(0) can be exponentially fast even when f does not satisfy the smoothness condition of Kac, Murdoch and Szegö (1953). Also a lower bound for λ1,n corresponding to a large class of functions which do not satisfy this smoothness condition is provided.
Nonlinear integral inequality in two independent variables
Authors: Vaz P. T. , Deo S. G.
Published: September 2002

In this note, the authors obtain a generalization of the integral inequality of Bihari [1] to a nonlinear inequality in two independent variables. With the aid of this inequality a bound for the solution of a nonlinear partial differential equation is established.
Computation of displacements for nonlinear elastic beam models using monotone iterations
Authors: Korman Philip
Published: September 2002

We study displacement of a uniform elastic beam subject to various physically important boundary conditions. Using monotone methods, we discuss stability and instability of solutions. We present computations, which suggest efficiency of monotone methods for fourth order boundary value problems.
On the quasiuniqueness of solutions of degenerate equations in Hilbert space
Authors: Schuchman Vladimir
Published: September 2002

In this paper, we study the quasiuniqueness (i.e., f1≐f2 if f1 − f2 is flat, the function f(t) being called flat if, for any K > 0, t−kf(t) → 0 as t → 0) for ordinary differential equations in Hilbert space. The case of inequalities is studied, too.

The most important result of this paper is this:

THEOREM 3. Let B(t) be a linear operator with domain DB and B(t) = B1(t) + B2(t) where (B1(t)x, x) is real and Re(B2(t)x, x) = 0 for any x ∈ DB. Let for any x ∈ DB the following estimate hold:

urn:x-wiley:01611712:media:ijmm512093:ijmm512093-math-0001

urn:x-wiley:01611712:media:ijmm512093:ijmm512093-math-0002

. If u(t) is a smooth flat solution of the following inequality in the interval t ∈ I = (0, 1].

urn:x-wiley:01611712:media:ijmm512093:ijmm512093-math-0003

with non‐negative continuous function ϕ(t), then u(t) ≡ 0 in I. One example with self‐adjoint B(t) is given, too.
Modified Whyburn semigroups
Authors: Reynolds Beth Borel , Schneider Victor
Published: September 2002

Let f : X → Y be a continuous semigroup homomorphism. Conditions are given which will ensure that the semigroup X ∪ Y is a topological semigroup, when the modified Whyburn topology is placed on X ∪ Y.
Integrals of operator‐valued functions
Authors: Struble Raimond A.
Published: September 2002

Mikusinski‐type expansions of operator‐valued functions are discussed in some detail. As a natural part of the development, a kernel concept for operators is proposed and an elaborate system of convolution quotients in one and two variables is obtained.
Some conditions for finiteness of a ring
Authors: Bell Howard E.
Published: September 2002

Extending a result of Putcha and Yaqub, we prove that a non‐nil ring must be finite if it has both ascending chain condition and descending chain condition on non‐nil subrings. We also prove that a periodic ring with only finitely many non‐central zero divisors must be either finite or commutative.
On common fixed points of compatible mappings in metric and Banach spaces
Authors: Sessa S. , Rhoades B. E. , Khan M. S.
Published: September 2002

We prove a number of results concerning the existence of common fixed points of a family of maps satisfying certain contractive conditions in metric and Banach spaces. Results dealing with the stucture of the set of common fixed points of such maps are also given. Our work is an improvement upon the previously known results.
The Mackey convergence condition for spaces with webs
Authors: Gilsdorf Thomas E.
Published: September 2002

If each sequence converging to 0 in a locally convex space is also Mackey convergent to 0, that space is said to satisfy the Mackey convergence condition. The problem of characterizing those locally convex spaces with this property is still open. In this paper, spaces with compatible webs are used to construct both a necessary and a sufficient condition for a locally convex space to satisfy the Mackey convergence condition.
On convex functions of order α and type β
Authors: Ma Wancang
Published: September 2002

Owa [1] gave three subordination theorems for convex functions of order α and starlike functions of order α. Unfortunately, none of the theorems is correct. In this paper, similar problems are discussed for a generalized class and sharp results are given.
The Smirnov compactification as a quotient space of the Stone‐Čech compactification
Authors: McMaster T. B. M.
Published: September 2002

For a separated proximity space, a decomposition of the Stone‐Čech compactification is presented which produces the Smirnov compactification and its basic properties by elementary arguments without recourse to clusters or totally bounded uniformities.
Random fixed points and random differential inclusions
Authors: Papageorgiou Nikolaos S.
Published: September 2002

In this paper, first, we study random best approximations to random sets, using fixed point techniques, obtaining this way stochastic analogues of earlier deterministic results by Browder‐Petryshyn, KyFan and Reich. Then we prove two fixed point theorems for random multifunctions with stochastic domain that satisfy certain tangential conditions. Finally we consider a random differential inclusion with upper semicontinuous orientor field and establish the existence of random solutions.
Identification of waiting time distribution of M/G/1, Mx/G/1, GIr/M/1 queueing systems
Authors: Ghosal A. , Madan S.
Published: September 2002

This paper brings out relations among the moments of various orders of the waiting time of the 1st customer and a randomly selected customer of an arrival group for bulk arrivals queueing models, and as well as moments of the waiting time (in queue) for M/G/1 queueing system. A numerical study of these relations has been developed in order to find the (β1, β2) measures of waiting time distribution in a comutable form. On the basis of these measures one can look into the nature of waiting time distribution of bulk arrival queues and the single server M/G/1 queue.
On elastic waves in an thinly‐layered laminated medium with stress couples under initial stress
Authors: Roy P. Pal , Debnath L.
Published: September 2002

The present work is concerned with a simple transformation rule in finding out the composite elastic coefficients of a thinly layered laminated medium whose bulk properties are strongly anisotropic with a microelastic bending rigidity. These elastic coefficients which were not known completely for a layered laminated structure, are obtained suitably in terms of initial stress components and Lame′s constants λi, μi of initially isotropic solids. The explicit solutions of the dynamical equations for a prestressed thinly layered laminated medium under horizontal compression in a gravity field are derived. The results are discussed specifying the effects of hydrostatic, deviatoric and couple stresses upon the characteristic propagation velocities of shear and compression wave modes.
On an integral transform
Authors: Naylor D.
Published: September 2002

A formula of inversion is established for an integral transform whose kernel is the Bessel function Ju(kr) where r varies over the finite interval (0, a) and the order u is taken to be the eigenvalue parameter. When this parameter is large the Bessel function behaves for varying r like the power function ru and by relating the Bessel functions to their corresponding power functions the proof of the inversion formula can be reduced to one depending on the Mellin inversion theorem.
Multipliers on weighted Hardy spaces over certain totally disconnected groups
Authors: Kitada Toshiyuki
Published: September 2002

In this note, we consider the multipliers on weighted H1 spaces over totally disconnected locally compact abelian groups with a suitable sequence of open compact subgroups (Vilenkin groups). We first show an (H1, L1) multiplier result from which Onneweer′s theorem follows. We also give an (H1, H1) multiplier result under a condition of Baernstein‐Sawyer type.
A characterization of the algebra of holomorphic functions on a simply connected domain
Authors: Wang Derming , Watson Saleem
Published: September 2002

Let A be a singly‐generated ℱ‐algebra. It is shown that A isomorphic to H(Ω)
where Ω is a simply connected domain in ℂ if and only if A has no topological divisors of
zero. It follows from this that there are exactly three ℱ‐algebras (up to isomorphism) which
are singly generated and have no topological divisors of zero.
Modified boundary integral method for pressure driven MHD duct flow
Authors: Aggarwala B. D. , Ariel P. D.
Published: September 2002

In this paper, we investigate the flow of a viscous, Incompressible,
electrically conducting fluid through a rectangular duct in the presence of a magnetic
field, when one of the boundaries perpedicular to the magnetic field is partly
conducting and partly Insulating, by a modified Boundary Integral Method.

Three problems are considered (i) flow through an infinite channel, (ii) flow
through a rectangular duct when the conducting part is symmetrically situated, and
(iii) flow through a rectangular duct when the conducting part is arbltrarily
positioned.

Such problems have been studied before by asymptotic means for large values of M,
the Hartmann number. Hoverer, the present modification of the Boundary Integral
Method renders the problem computationally efficient and provides a reliable numerical
solution for all values of M. For large M, our coputation time decreases
significantly.
Measurable multifunctions and their applications to convex integral functionals
Authors: Papageorgiou Nikolaos S.
Published: September 2002

The purpose of this paper is to establish some new properties of set valued
measurable functions and of their sets of Integrable selectors and to use them to
study convex integral functionals defined on Lebesgue‐Bochner spaces. In this process
we also obtain a characterization of separable dual Banach spaces using multifunctions
and we present some generalizations of the classical “bang‐bang” principle to infinite
dimensional linear control systems with time dependent control constraints.
Operational calculs for the continuous Legendre transform with applications
Authors: Deeba E. Y. , Koh E. L.
Published: September 2002

This paper develops an operational calculus for the continuous Legendre transform
introduced and studied by Butzer, Stens and Wehrens [1]. It is an extension of the work done
by Churchill et al [2], [31 for the discrete case. In particular, a differentiation theorem and a
convolution theorem are proved and the results are applied to the solution of some boundary
value problems.
Theorems on association of variables in multidimensional Laplace transforms
Authors: Debnath Joyati , Debnath Narayan Chandra
Published: September 2002

The inverse of the multidimensional Laplace transform is often obtained by
the method of association of variables. In this paper, some basic theorems are
developed for evaluating the associated transform of certain types of transformed
functions. Many useful associated pairs can be produced with the aid of these
fundamental theorems. Several illustrative examples are included.
A note on rings with certain variables identities
Authors: Abu-Khuzam Hazar
Published: September 2002

It is proved that certain rings satisfying generalized‐commutator constraints of the form [xm, yn, yn, …, yn] = 0 with m and n depending on x and y, must have nil commutator ideal.
On first‐order differential operators with Bohr‐Neugebauer type property
Authors: Rao Aribindi Satyanarayan
Published: September 2002

We consider a differential equation u(t)‐Bu(t)=f(t), where the functions
u and f map the real line into a Banach space X and B: X →X is a bounded linear operator. Assuming that any Stepanov‐bounded solution u is Stepanov almost‐periodic when f is Bochner almost‐periodic, we establish that any Stepanov‐bounded solution u is
Bochner almost‐periodic when f is Stepanov almost‐periodic. Some examples are given in
which the operator ‐B is shown to satisfy our assumption.
Propagation of Rossby waves in stratified shear flows
Authors: Kandaswamy Palani G. , Selvi B. Tamil , Debnath Lokenath
Published: September 2002

A study is made of the propagation of Rossby waves in a stably stratified
shear flows. The wave equation for the Rossby waves is derived in an isothermal
atmosphere on a beta plane in the presence of a latitudinally sheared zonal flow. It
is shown that the wave equation is singular at five critical levels, but the wave
absorption takes place only at the two levels where the local relative frequency
equals in magnitude to the Brunt Vaisala frequency. This analysis also reveals that
these two levels exhibit valve effect by allowing the waves to penetrate them from one
side only. The absorption coefficient exp(2πμ) is determined at these levels. Both
the group velocity approach and single wave treatment are employed for the
investigation of the problem.
Flow of a dusty fluid due to Wavy motion of a wall for moderately large Reynolds numbers
Authors: Ramamurthy V. , Rao U. S.
Published: September 2002

The two‐dimensional flow of a dusty fluid induced by sinusoidal wavy motion
of an infinite wavy wall is considered for Reynolds numbers which are of magnitude
greater than unity. While the velocity components of the fluid and the dust particles
along the axial direction consist of a mean steady flow and a periodic flow, the
transverse components of both the fluid and the dust consist only of a periodic
flow. This is true both for the outer flow (the flow beyond the boundary layer) and
the inner flow (boundary layer flow). It is found that the mean steady flow is
proportional to the ratio 4π2a2/L2(a/L < <1)
, where a and L are the amplitude and the
wavelength of the wavy wall, respectively. Graphs of the velocity components, both
for the outer flow and the inner flow for various values of mass ‐ concentration of
the dust particles are drawn. It is found that the steady flow velocities of the
fluid and the dust particles approach to a constant value. Certain interesting
results regarding the axial and the transverse velocity components are also discussed.
On stability and boundedness of solutions of a certain fourth‐order delay differential equation
Authors: Okoronkwo Emmanuel O.
Published: September 2002

Using a Razumikhin ‐ type theorem, we deduce sufficient conditions that
guarantee the uniform asymptotic stability and boundedness of solutions of a scalar
real fourth‐order delay differential equation. The Lyapunov function constructed for
an ordinary fourth‐order differential equation is seen to work for the delay system.
Two constructions of the real numbers via alternating series
Authors: Knopfmacher Arnold , Knopfmacher John
Published: September 2002

Two further new methods are put forward for constructing the complete
ordered field of real numbers out of the ordered field of rational numbers. The
methods are motivated by some little known results on the representation of real
numbers via alternating series of rational numbers. Amongst advantages of the
methods are the facts that they do not require an arbitrary choice of "base" or
equivalence classes or any similar constructs. The methods bear similarities to
a method of construction due to Rieger, which utilises continued fractions.
A note on global existence for boundary value problems
Authors: Chyan Chuan J. , Henderson Johnny
Published: September 2002

Upper and lower solutions are used in establlsning global existence results for certain two–point boundary value problems for y‴ = f(x, y, y′, y″)
and y(n) = f(x, y, y′, …, y(n−1)).
Spatial numerical ranges of elements of Banach algebras
Authors: Gaur A. K. , Husain T.
Published: September 2002

In this paper, the notion of spatial numerical range of elements of Banach
algebras without identity is studied. Specifically, the relationship between spatial
numerical ranges, numerical ranges and spectra is investigated. Among other results,
it is shown that the closure of the spatial numerical range of an element of a Banach
algebra without Identity but wlth regular norm is exactly its numerical range as an
element of the unitized algebra. Futhermore, the closure of the spatial numerical
range of a hermitian element coincides with the convex hull of its spectrum. In
particular, spatial numerical ranges of the elements of the Banach algebra C0(X) are described.
Quasiasymptotic expansion of distributions from S+′ and the asymptotic expansion of the distributional Stieltjes transform
Authors: Pilipovic S.
Published: September 2002

By following the approach of Držoinov, Vladimirov and Zavialov we investigate
the quasiasymptotic expansion of distributions and give Abelian type results for the ordinar
asymptotic behaviour of the distributional Stieltjes transform of a distribution
with appropriate quasiasymptotic expansion.
Failure of random networks
Authors: Rhee Wansoo T.
Published: September 2002

This paper studies random failure of networks when we know the probability of
failure of each link but we know nothing about the intercorrelation of these failures. Without any
assumption on the structure of the network, we compute the probability that there still exists a
path from the source to the sink after the worst possible failure of the network.
On the δ‐continuous fixed point property
Authors: Cammaroto F. , Noiri T.
Published: September 2002

In this paper, we define and investigate the δ‐continuous retraction and the δ‐continuous fixed point property. Theorem 1 of Connell [11] and Theorem 3.4 of Arya and Deb [2] are improved.
A duality theorem for solutions of elliptic equations
Authors: Blanchet Pierre
Published: September 2002

Let L be a second order linear partial differential operator of elliptic type on a domain Ω of ℝm with coefficients in C∞(Ω). We consider the linear space of all solutions of the equation Lu = 0 on Ω with the topology of uniform convergence on compact subsets and describe the topological dual of this space. It turns out that this dual may be identified with the space of solutions of an adjoint equation near the boundary modulo the solutions of this adjoint equation on the entire domain.
Hodographic study of non‐Newtonian MHD aligned steady plane fluid flows
Authors: Nguyen P. V. , Chandna O. P.
Published: September 2002

A study is made of non‐Newtonian HHD aligned steady plane fluid flows to find exact solutions for various flow configurations. The equations of motion have been transformed to the hodograph plane. A Legendre‐transform function is used to recast the equations in the hodograph plane in terms of this transform function. Solutions for various flow configurations are obtained. Applications are investigated for the fluids of finite and infinite electrical conductivity bringing out the similarities and contrasts in the solutions of these types of fluids.
On semi‐homeomorphisms
Authors: Lee J. P.
Published: September 2002

In the first part of our work we show a condition for a semi‐homeomorphism in the sense of Crossley and Hildebrand (s.h.C.H) to be a semi‐homeomorphism in the sense of Biswas (s.h.B). Certain relevant examples are provided. Next, we define strong semi‐homeomorphisms Via nice restrictions of semi‐homeomorphisms (global condition) and we show that the new class of functions actually coincides with semi‐homeomorphisms. Then, in the third part we introduce local semi‐homeomorphisms (l.s.h.C.H.) via a corresponding local condition for restrictions. A few results pertaining to the preservation of some topological
properties under this new class of functions are examined.

On semi-homeomorphisms (corrigendum)dx.doi.org/10.1155/S016117129100114X
A note on one‐parameter groups of automorphisms
Authors: Thaheem A. B. , Mohammad Noor
Published: September 2002

Let {αt : t ∈ R} and {βt : t ∈ R} be two commuting one‐parameter groups of ∗‐automorphisms of a von Neumann algebra M such that αt + α−t = βt + β−t for all t ∈ R. The purpose of this note is to provide a simple and short proof of the central decomposition result: αt = βt on Mp and a αt = β−t on M(1 − p) for a central projection p ∈ M, without using the theory of spectral subspaces.
Time—periodic weak solutions
Authors: de Brito Eliana Henriques
Published: September 2002

In continuing from previous papers, where we studied the existence and uniqueness of the global solution and its asymptotic behavior as time t goes to infinity, we now search for a time‐periodic weak solution u(t) for the equation whose weak formulation in a Hilbert space H is

urn:x-wiley:01611712:media:ijmm464936:ijmm464936-math-0001

where: ′ = d/dt; (′) is the inner product in H; b(u, v), a(u, v) are given forms on subspaces U ⊂ W, respectively, of H; δ > 0, α ≥ 0, β ≥ 0 are constants and α + β > 0; G is the Gateaux derivative of a convex functional J : V ⊂ H → [0, ∞) for V = U, when α > 0 and V = W when α = 0, hence β > 0; v is a test function in V; h is a given function of t with values in H.

Application is given to nonlinear initial‐boundary value problems in a bounded domain of Rn.
Irresolute multifunctions
Authors: Popa V.
Published: September 2002

This paper considers a new class of multifunctions, the irresolute multifunctions. For the irresolute multifunctions we give some theorems of characterizations. Some relations between continuous multifunctions and irresolute multifunctions are established.
An inequality of W. L. Wang and P. F. Wang
Authors: Alzer Horst
Published: September 2002

In this note we present a proof of the inequality where Hn and Gn (resp. and ) denote the weighted harmonic and geometric means of x1, …, xn (resp. 1 − x1, …, 1 − xn) with xi ∈ (0, 1/2], i = 1, …, n.
Maximal subgroups of finite groups
Authors: Srinivasan S.
Published: September 2002

In finite groups maximal subgroups play a very important role. Results in the literature show that if the maximal subgroup has a very small index in the whole group then it influences the structure of the group itself. In this paper we study the case when the index of the maximal subgroups of the groups have a special type of relation with the Fitting subgroup of the group.
On the bounds of multivalently starlikeness and convexity
Authors: Owa Shigeyoshi , Nunokawa Mamoru
Published: September 2002

The object of the present paper is to prove some interesting results for the bounds of starlikeness and convexity of certain multivalent functions.
Inequalities for Walsh like random variables
Authors: Hajela D.
Published: September 2002

Let be a sequence of mean zero independent random variables. Let , and let [Yk] be the linear span of Yk. Assume δ ≤ |Xn| ≤ K for some δ > 0 and K > 0 and let for 1 < p < ∞. We show that for f ∈ [Ym] the following inequalities hold:

urn:x-wiley:01611712:media:ijmm346835:ijmm346835-math-0005

urn:x-wiley:01611712:media:ijmm346835:ijmm346835-math-0006

and
‖f‖2 ≤ C(4,m)2‖f‖1 ≤ C(4,m)2‖f‖2. These generalize various well known inequalities on Walsh functions.
Operational calculus and differential equations with infinitely smooth coefficients
Authors: Nemzer Dennis
Published: September 2002

A subring MF of the field of Mikusiński operators is constructed as a countable union space. Some topological properties of MF are investigated. Then, the product of an infinitely differentiable function and an element of MF is given and is used to investigate operational equations with infinitely smooth coefficients.
Fundamental theorem of Wiener calculus
Authors: Park Chull , Skoug David , Smolowitz Lawrence
Published: September 2002

In this paper we define and develop a theory of differentiation in Wiener space C[0, T]. We then proceed to establish a fundamental theorem of the integral calculus for C[0, T]. First of all, we show that the derivative of the indefinite Wiener integral exists and equals the integrand functional. Secondly, we show that certain functionals defined on C[0, T] are equal to the indefinite integral of their Wiener derivative.
Sublinear functionals and Knopp′s core theorem
Authors: Orhan C.
Published: September 2002

In this paper we are concerned with inequalities involving certain sublinear functionals on m, the space of real bounded sequences. Such inequalities being analogues of Knopp′s Core theorem.
Convexity preserving summability matrices
Authors: Selvaraj C. R.
Published: September 2002

The main result of this paper gives the necessary and sufficient conditions for the Abel matrices to preserve the convexity of sequences. Also, the higher orders of the Cesáro method are shown to be convexity‐preserving matrices.
On a family of weighted convolution algebras
Authors: Feichtinger Hans G. , Gürkanli A. Turan
Published: September 2002

Continuing a line of research initiated by Larsen, Liu and Wang [12], Martin and Yap [13], Gürkanli [15], and influenced by Reiter′s presentation of Beurling and Segal algebras in Reiter [2,10] this paper presents the study of a family of Banach ideals of Beurling algebras , G a locally compact Abelian group. These spaces are defined by weighted Lp‐conditions of their Fourier transforms. In the first section invariance properties and asymptotic estimates for the translation and modulation operators are given. Using these it is possible to characterize inclusions in section 3 and to show that two spaces of this type coincide if and only if their parameters are equal. In section 4 the existence of approximate identities in these algebras is established, from which, among other consequences, the bijection between the closed ideals of these algebras and those of the corresponding Beurling algebra is derived.
Orthodox Γ‐semigroups
Authors: Sen M. K. , Saha N. K.
Published: September 2002

Let M = {a, b, c, …} and Γ = {α, β, γ, …} be two non‐empty sets. M is called a Γ‐semigroup if aαb ∈ M, for α ∈ Γ and b ∈ M and (aαb)βc = aα(bβc), for all a, b, c ∈ M and for all α, β ∈ Γ. A semigroup can be considered as a Γ‐semigroup. In this paper we introduce orthodox Γ‐semigroups and extend different results of orthodox semigroups to orthodox Γ‐semigroups.
Some conditions for finiteness and commutativity of rings
Authors: Bell Howard E. , Guerriero Franco
Published: September 2002

We present several new sufficient conditions for a ring to be finite; we give two conditions which for periodic rings R imply that R must be either finite or commutative; and we study commutativity in rings with only finitely many non‐central subrings.
Hearing the shape of membranes: further results
Authors: Zayed E. M. E.
Published: September 2002

The spectral function , t > 0 where are the eigenvalues of the Laplacian in Rn, n = 2 or 3, is studied for a variety of domains. Particular attention is given to circular and spherical domains with the impedance boundary conditions on Γj (or Sj), j = 1, …, J where Γj and Sj, j = 1, …, J are parts of the boundaries of these domains respectively, while γj, j = 1, …, J are positive constants.
On generalizations of the series of Taylor, Lagrange, Laurent and Teixeira
Authors: Campos L. M. B. C.
Published: September 2002

The classical theorems of Taylor, Lagrange, Laurent and Teixeira, are extended from the representation of a complex function F(z), to its derivative F(ν)(z) of complex order ν, understood as either a ‘Liouville’ (1832) or a ‘Rieman (1847)’ differintegration (Campos 1984, 1985); these results are distinct from, and alternative to, other extensions of Taylor′s series using differintegrations (Osler 1972, Lavoie & Osler & Tremblay 1976). We consider a complex function F(z), which is analytic (has an isolated singularity) at ζ, and expand its derivative of complex order F(ν)(z), in an ascending (ascending‐descending) series of powers of an auxiliary function f(z), yielding the generalized Teixeira (Lagrange) series, which includes, for f(z) = z − ζ, the generalized Taylor (Laurent) series. The generalized series involve non‐integral powers and/or coefficients evaluated by fractional derivatives or integrals, except in the case ν = 0, when the classical theorems of Taylor (1715), Lagrange (1770), Laurent (1843) and Teixeira (1900) are regained. As an application, these generalized series can be used to generate special functions with complex parameters (Campos 1986), e.g., the Hermite and Bessel types.
On generalization of continued fraction of Gauss
Authors: Denis Remy Y.
Published: September 2002

In this paper we establish a continued fraction represetation for the ratio qf two basic bilateral hypergeometric series 2ψ2′s which generalize Gauss′ continued fraction for the ratio of two 2F1′s.
A commutativity theorem for left s‐unital rings
Authors: Abujabal Hamza A. S.
Published: September 2002

In this paper we generalize some well‐known commutativity theorems for associative rings as follows: Let R be a left s‐unital ring. If there exist nonnegative integers m > 1, k ≥ 0, and n ≥ 0 such that for any x, y in R, [xky − xnym, x] = 0, then R is commutative.
Remarks on a fixed‐point theorem of Gerald Jungck
Authors: Singh Maibam Ranjit
Published: September 2002

Jungck [1] obtained a fixed‐point theorem for a pair of continuous selfmappings on a complete metric space. Recently, Barada K. Ray [2] extended the theorem of Jungck [1] for three self‐mappings on a complete metric space. In the present paper we omit the continuity of the mapping used by Ray [2] and replace his four
conditions by a single condition. Our results so obtained generalize and/or unify fixed‐point theorems of Jungck [1], Ray [2], Rhoades [3], Ciric [4], Pal and Maiti [5], and Sharma and Yuel [6].
Example of a sequentially incomplete regular inductive limit of Banach spaces
Authors: Kucera Jan , McKennon Kelly
Published: September 2002

A sequentially incomplete regular inductive limit of a sequence of Banach spaces is constructed.
On point‐dissipative systems of differential equations with quadratic nonlinearity
Authors: Bose Anile K. , Cover Alan S. , Reneke James A.
Published: September 2002

The system x′ = Ax + f(x) of nonlinear vector differential equations, where
the nonlinear term f(x) is quadratic with orthogonality property xTf(x) = 0 for all x, is
point‐dissipative if uTAu < 0 for all nontrivial zeros u of f(x).
On the weak law of large numbers for normed weighted sums of I.I.D. random variables
Authors: Adler André , Rosalsky Andrew
Published: September 2002

For weighted sums of independent and identically distributed random variables
{Yn, n ≥ 1}, a general weak law of large numbers of the form is established where
{νn, n ≥ 1} and {bn, n ≥ 1} are statable constants. The hypotheses involve both the behavior of the tail of the
distribution of |Y1| and the growth behaviors of the constants {an, n ≥ 1} and {bn, n ≥ 1}. Moreover, a weak
law is proved for weighted sums indexed by random variables {Tn, n ≥ 1}. An example is presented
wherein the weak law holds but the strong law fails thereby generalizing a classical example.
On certain real hypersurfaces of quaternionic projective space
Authors: Perez Juan De Dios , Santos Florentino G.
Published: September 2002

We classify certain real hypersurfaces ot a quaternionic projective space satisfying
the condition σ(R(X, Y)SZ) = 0.
A note on the convolution and the product in D′ and S′
Authors: Kamiński A. , Rudnicki R.
Published: September 2002

Examples of tempered distibutions are shown such that the convolution and product exist in D′ and are tempered distributions, but they do not exist in S′. On
the other hand, there exist tempered distributions whose convolution or
product exist in D′ but are not tempered distributions.
Geometric presentations of classical knot groups
Authors: Erbland John , Guterriez Mauricio
Published: September 2002

The question addressed by thls paper is, how close is the tunnel number of
a knot to the minimum number of relators in a presentation of the knot group? A
dubious, but useful conjecture, is that these two invariants are equal. (The
analogous assertion applied to 3‐manifolds is known to be false. [1]). It has been
shown recently [2] that not all presentations of a knot group are “geometric”. The
main result in this paper asserts that the tunnel number is equal to the minimum
number of relators among presentations satisfying a somewhat restrictive condition,
that is, that such presentations are always geometric.
On a general convergence for Broyden like update method
Authors: Sen Rabindranath , Chattopadhyay Rini , Saha Tripti
Published: September 2002

The role of Broyden′s method as a powerful quasi‐Newton method for solving
unconstrained optimization problems or a system of nonlinear algebraic equations is
well known. We offer here a general convergence criterion for a method akin to
Broyden′s method in Rn. The approach is different from those of other convergence
proofs which are available only for the direct prediction methods.
A new proof of a theorem about generalized orthogonal polynomials
Authors: Mercer A. McD.
Published: September 2002

In this note it is shown that a fairly recent result on the asymptotic distribution of the zeros
of generalized polynomials can be deduced from an old theorem of G. Polya, using a minimum of orthogonal
polynomial theory.
On nonlinear variational inequalities
Authors: Noor Muhammed Aslam
Published: September 2002

The fixed point technique is used to prove the existence of a solution for a class of
nonlinear variational inequalities related with odd order constrained boundary value problems and
to suggest an iterative algorithm to compute the approximate solution.
A common fixed point theorem for two sequences of self‐mappings
Authors: Taniguchi Takeshi
Published: September 2002

In this paper a common fixed point theorem for two sequences of self‐mappings from
a complete metric space M to M is proved. Our theorem is a generalization of Hadzic′s fixed point
theorem[1].
Existence of solutions of boundary value problems for functional differential equations
Authors: Ntouyas S. K. , Tsamatos P. Ch.
Published: September 2002

In this paper, using a simple and classical application of the Leray‐Schauder
degree theory, we study the existence of solutions of the following boundary value
problem for functional differential equations

urn:x-wiley:01611712:media:ijmm271093:ijmm271093-math-0001

where f ∈ C([0, T] × Cr × ℝn, ℝn), h ∈ Cr, η ∈ ℝn and α, β, are real constants.
Thermo‐visco‐elastic Rayleigh waves under the influence of couple‐stress and gravity
Authors: Das Tapan Kumar , Sengupta P. R. , Debnath Lokenath
Published: September 2002

This paper is concerned with thermo‐visco‐elastic Rayleigh waves under the
influence of couple‐stresses and gravity. A more general phase velocity equation for these waves is
derived. It is shown that the phase velocity equation reduces to that of the classical elastic
Rayleigh waves in the absence of the couple‐stress parameter, viscosity and gravity.
On Lindelöf lattices and separation
Authors: Eid George M.
Published: September 2002

Let X be an abstract set and ℒ a lattice of subsets of X. Some general properties of
Lindelöf, regular as well as normal lattices are investigated for their measure implications and their
relationship to separation properties. Moreover, we show that the generalized Wallman replete
space and the generalized Wallman prime complete space are Lindelöf spaces if and only if certain
measure relationships hold on ℒ.
A note on best approximation and invertibility of operators on uniformly convex Banach spaces
Authors: Holub James R.
Published: September 2002

It is shown that if X is a uniformly convex Banach space and S a bounded linear operator on
X for which ‖I − S‖ = 1, then S is invertible if and only if . From this it follows that
if S is invertible on X then either (i) dist(I, [S]) < 1, or (ii) 0 is the unique best approximation to
I from [S], a natural (partial) converse to the well‐known sufficient condition for invertibility that
dist(I, [S]) < 1.
Generalized equivalence of matrices over Prüfer domains
Authors: DeMeyer Frank , Kakakhail Hainya
Published: September 2002

Two m × n matrices A, B over a commutative ring R are equivalent
in case there are invertible matrices P, Q over R with B = PAQ. While any m × n matrix over a principle ideal domain
can be diagonalized, the same is not true for Dedekind domains. The first author and T. J. Ford
introduced a coarser equivalence relation on matrices called homotopy and showed any m × n matrix
over a Dedekind domain is homotopic to a direct sum of 1 × 2 matrices. In this article give,
necessary and sufficient conditions on a Prüfer domain that any m × n matrix be homotopic to a
direct sum of 1 × 2 matrices.
On pairwise super continuous mappings in bitopological spaces
Authors: Khedr F. H. , Al-Shibani A. M.
Published: September 2002

The aim of this paper is to define and study super‐continuous mappings and some
other forms of continuity such as strong continuity, perfect continuity and complete continuity in
bitopological spaces and investigate the relations between these kinds of continuity and their effects
on some kinds of spaces.
On radii of convexity and starlikeness of some classes of analytic functions
Authors: Noor Khalida Inayat
Published: September 2002

Let P[A, B], −1 ≤ B < A ≤ 1, be the class of functions p such that p(z) is subordinate to
. Let P(α1) be the class of functions with positive real part greater than α1, 0 ≤ α1 ≤ 1. It is clear that
. The principal results in this paper are the determination of the radius of
β‐starlikeness and β‐convexity of f(z) with , when f(z) is restricted to certain classes of univalent
and analytic functions related vith P[A, B].
Continuous dependence and differentiation of solutions of finite difference equations
Authors: Henderson Johnny , Lee Linda
Published: September 2002

Conditions are given for the continuity and differentiability of solutions of initial value problems
and boundary value problems for the nth order finite difference equation, u(m + n) = f(m, u(m), u(m + 1), …, u(m + n − 1)), m ∈ ℤ.
An Arzela‐Ascoli type theorem for random functions
Authors: Noonan Joseph P. , Polchlopek Henry M.
Published: September 2002

A Theorem involving the convergence of random functions is presented. The Theorem is
based upon the Arzela‐Ascoli Theorem of Real Analysis. The development here may be useful in
transient or asymptotic analysis of random functions and linear systems theory.
Strong consistencies of the bootstrap moments
Authors: Hu Tien-Chung
Published: September 2002

Let X be a real valued random variable with E|X|r+δ < ∞ for some positive
integer r and real number, δ, 0 < δ ≤ r, and let {X, X1, X2, …} be a sequence of
independent, identically distributed random variables. In this note, we prove that,
for almost all w ∈ Ω, with probability 1. if for
some , where is the bootstrap rth sample moment of the bootstrap sample some
with sample size m(n) from the data set {X, X1, …, Xn} and μr is the rth moment of
X. The results obtained here not only improve on those of Athreya [3] but also the
proof is more elementary.
On a generalization of u‐means
Authors: Dubeau Francois
Published: September 2002

In this paper we present an extension of Bauer′s work about u‐means. We consider
a kind of composition of an admissible function u(x) (described by Bauer) and of a compatible
function ϕ(x). This construction allows us to define (u, ϕ)‐means. When ϕ(x) = x, the (u, ϕ)‐means
are the u‐means introduced by Bauer. The arithmetic, geometric and harmonic means are special
cases.
On multiparameter spectral theory
Authors: Debnath Lokenath , Verma Ram
Published: September 2002

A connection between the numerical range of the multipararneter linear system P(λ)
and the joint numerical range of the (commuting) separating operator system is given.
Nonsmooth analysis and optimization on partially ordered vector spaces
Authors: Reiland Thomas W.
Published: September 2002

Interval‐Lipschitz mappings between topological vector spaces are defined and compared with other Lipschitz‐type operators. A theory of generalized gradients is presented when both spaces are locally convex and the range space is an order complete vector lattice. Sample applications to the theory of nonsmooth optimization are given.
Almost complex surfaces in the nearly Kaehler S6
Authors: Deshmukh Sharief
Published: September 2002

It is shown that a compact almost complex surface in S6 is either totally geodesic or the minimum of its Gaussian curvature is less than or equal to 1/3.
Hodograph method in MHD orthogonal fluid flows
Authors: Nguyen P. V. , Chandna O. P.
Published: September 2002

Equations for steady plane MHD orthogonal flows of a viscous incompressible fluid of finite electrical conductivity are recast in the hodograph plane by using the Legendre transform function of the streamfunction. Three examples are studied to illustrate the developed theory. Solutions and geometries for these examples are determined.
A method of solving y(k) − f(x)y = 0
Authors: O′Hara P. J. , Osteen R. , Rodriguez R. S.
Published: September 2002

An alternative method is shown for solving the differential equation y(k) − f(x)y = 0 by means of series. Also included is a result for a sequence of functions which gives conditions under which .
Orthogonal bases in a topological algebra are Schauder bases
Authors: Bhatt Subbash J. , Deheri G. M.
Published: September 2002

In a topological algebra with separately continuous multiplication, the result quoted in the title is proved.
Remarks on derivations on semiprime rings
Authors: Daif Mohamad Nagy , Bell Howard E.
Published: September 2002

We prove that a semiprime ring R must be commutative if it admits a derivation d such that (i) xy + d(xy) = yx + d(yx) for all x, y in R, or (ii) xy − d(xy) = yx − d(yx) for all x, y in R. In the event that R is prime, (i) or (ii) need only be assumed for all x, y in some nonzero ideal of R.
Subclasses of uniformly starlike functions
Authors: Merkes Ed , Salmassi Mohammad
Published: September 2002

We study subclasses of the class of uniformly starlike functions which were recently introduced by A.W. Goodman. One new subclass is defined and it is shown that it shares many properties of the parent class.
Oscillation and nonoscillation theorems for some mixed difference equations
Authors: Smith B. , Taylor W. E.
Published: September 2002

In this paper we investigate the oscillatory and nonoscillatory behavior of solutions of certain mixed third and fourth order difference equations. Specific results are also obtained for the constant coefficient cases.
Asymptotics of regular convolution quotients
Authors: Stanković Bogoljub
Published: September 2002

The asymptotic behaviour of a class of generalized functions, named regular convolution quotients, has been defined and analysed. Some properties of such asymptotics, which can be useful in applications, have been proved.
Minimization of nonsmooth integral functionals
Authors: Papageorgiou Nikolaos S. , Papageorgiou Apostolos S.
Published: September 2002

In this paper we examine optimization problems involving multidimensional nonsmooth integral functionals defined on Sobolev spaces. We obtain necessary and sufficient conditions for optimality in convex, finite dimensional problems using techniques from convex analysis and in nonconvex, finite dimensional problems, using the subdifferential of Clarke. We also consider problems with infinite dimensional state space and we finally present two examples.
Some topologies on the set of lattice regular measures
Authors: Stratigos Panagiotis D.
Published: September 2002

We consider the general setting of A.D. Alexandroff, namely, an arbitrary set X and an arbitrary lattice of subsets of X, ℒ. 𝒜(ℒ) denotes the algebra of subsets of X generated by ℒ and MR(ℒ) the set of all lattice regular, (finitely additive) measures on 𝒜(ℒ).

First, we investigate various topologies on MR(ℒ) and on various important subsets of MR(ℒ), compare those topologies, and consider questions of measure repleteness whenever it is appropriate.

Then, we consider the weak topology on MR(ℒ), mainly when ℒ is δ and normal, which is the usual Alexandroff framework. This more general setting enables us to extend various results related to the special case of Tychonoff spaces, lattices of zero sets, and Baire measures, and to develop a systematic procedure for obtaining various topological measure theory results on specific subsets of MR(ℒ) in the weak topology with ℒ a particular topological lattice.
New representation of the non‐symmetric homogeneous bounded domains in ℂ4 and ℂ5
Authors: Tsagas Gr. , Dimou G.
Published: September 2002

This paper deals with the corresponding solvable Lie algebra to each of non‐symmetric homogeneous bounded domains in ℂ4 and ℂ5 by special set of matrices. Some interesting properties of Kähler manifolds are found. The theory of s‐structure on a complete Riemann manifold is also studied.
Lamb′s plane problem in a thermo‐visco‐elastic micropolar medium with the effect of gravity
Authors: Das Pravangsu Sekhar , Sengupta P. R. , Debnath Lokenath
Published: September 2002

A study is made of the Lamb plane problem in an infinite thermo‐visco‐elastic micropolar medium with the effect of gravity. The visco‐elasticity is characterized by the rate dependent theory of micro‐visco‐elasticity generalizing the classical Kelvin‐Voigt theory. The action of time harmonic loading is treated in detail. The solutions for the displacement fields, couple stresses and the temperature field are obtained in general and particular cases.
A characterization of the generalized Meijer transform
Authors: Deeba E. Y. , Koh E. L.
Published: September 2002

The purpose of the note is to prove a representation theorem for the generalized Meijer transform defined in [2]. In particular, we shall state and prove necessary and sufficient conditions for a function F(p) to be the generalized Meijer transform of a generalized function.
The second conjugate algebras of Banach algebras
Authors: Wong Pak-Ken
Published: September 2002

In this paper, we study Arens regularity of a Banach algebra A. In particular, we give characterizations for A to be Arens regular.
Radical classes of l‐groups
Authors: Ton Dao-Rong
Published: September 2002

The main results of this paper concern radical classes of l‐groups. In the sections 2‐3 the relationship between several radical classes of l‐groups are discussed and the characteristic properties for several radical mappings are given. In the sections 5‐6 we give nice concrete descriptions of some important radical classes of l‐groups using the structure theorems of a complete l‐group and an Archimedean l‐group.