bluuebunny/crossref_metadata_2025 huggingface dataset:
Admissible groups, symmetric factor sets, and simple algebras
Authors: Mollin R. A.
Published: September 2002

Let K be a field of characteristic zero and suppose that D is a K‐division algebra; i.e. a finite dimensional division algebra over K with center K. In Mollin [1] we proved that if K contains no non‐trivial odd order roots of unity, then every finite odd order subgroup of D* the multiplicative group of D, is cyclic. The first main result of this paper is to generalize (and simplify the proof of) the above. Next we generalize and investigate the concept of admissible groups. Finally we provide necessary and sufficient conditions for a simple algebra, with an abelian maximal subfield, to be isomorphic to a tensor product of cyclic algebras. The latter is achieved via symmetric factor sets.
Analysis of sectorial plates normally loaded over circular domains. II
Authors: Bassali Wadie A.
Published: September 2002

The method of images is applied to derive exact expressions for the deflections of unlimited wedge‐shaped plates the central parts of which are cut, when the plate is simply supported on the radial edges, elastically restrained or free along the circular edge and is acted upon by one of three types of normal loading distributed over the surface of a circular domain. Formulae for the bending and twisting moments along the circular edge are given. Limiting forms of the obtained solutions are considered.
On certain regular graphs of girth 5
Authors: O′keefe M. , Wong P. K.
Published: September 2002

Let f(v, 5) be the number of vertices of a (v, 5)‐cage (v ≥ 3). We give an upper bound for f(v, 5) which is considerably better than the previously known upper bounds. In particular, when v = 7, it coincides with the well‐known Hoffman‐ Singleton graph.
The general chain transform and self‐reciprocal functions
Authors: Nasim Cyril
Published: September 2002

A theory of a generalized form of the chain transforms of order n is developed, and various properties of these are established including the Parseval relation. Most known cases of the standard theory are derived as special cases. Also a theory of self‐reciprocal functions is given, based on these general chain transforms; and relations among various classes of self‐reciprocal functions are established.
Dispersive waves and caustics
Authors: Gorman Arthur D.
Published: September 2002

The Lagrange manifold (WKB) formalism enables the determination of the
asymptotic series solution of linear, non‐dispersive wave equations at turning points. The formalism is adapted to include those equations which model dispersive waves.
On the hadamard products of Schlicht functions and applications
Authors: Al-Amiri H. S.
Published: September 2002

We show that each of the schlicht classes of starlike, convex, close‐to‐convex
and strongly starlike with respect to symmetric points is invariant under the Hadamard product with the class of convex functions. The influence of certain operators over these classes is also investigated.
Iterated Stieltjes transform of generalized functions
Authors: Dube L. S.
Published: September 2002

The generalized S2‐transform of a member of f of a certain space of generalized functions is defined as

urn:x-wiley:01611712:media:ijmm928365:ijmm928365-math-0001

urn:x-wiley:01611712:media:ijmm928365:ijmm928365-math-0002

An inversion theorem for the transform is established interpreting the oonvergene in the weak distributional sense.
Generalized classes of starlike and convex functions of order α
Authors: Owa Shigeyoshi , Shen C. Y.
Published: September 2002

We have introduced, in this paper, the generalized classes of starlike and convex functions of order α by using the fractional calculus. We then proved some subordination theorems, argument theorems, and various results of modified Hadamard product for functions belonging to these classes. We have also established some properties about the generalized Libera operator defined on these classes of functions.
More on the Schur group of a commutative ring
Authors: Mollin R. A.
Published: September 2002

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

A locally conformal symplectic (l. c. s.) manifold is a pair (M2n, Ω) where M2n(n > 1)
is a connected differentiable manifold, and Ω a nondegenerate 2‐form on M such that (Uα‐ open subsets). , σα : Uα → ℝ, dΩα = 0. Equivalently, dΩ = ω∧Ω for some closed 1‐form ω. L. c. s. manifolds can be seen as generalized phase spaces of Hamiltonian dynamical systems since the form of the Hamilton equations is, in fact, preserved by homothetic canonical transformations. The paper discusses first Hamiltonian vector fields, and infinitesimal automorphisms (i. a.) on l. c. s. manifolds. If (M, Ω) has an i. a. X such that ω(X) ≠ 0, we say that M is of the first kind and Ω assumes the particular form Ω = dθ − ω∧θ. Such an M is a 2‐contact manifold with the structure forms (ω, θ), and it has a vertical 2‐dimensional foliation V. If V is regular, we can give a fibration theorem which shows that M is a T2‐principal bundle over a symplectic manifold. Particularly, V is regular for some homogeneous l. c. s, manifolds, and this leads to a general construction of compact homogeneous l. c. s, manifolds. Various related geometric results, including reductivity theorems for Lie algebras of i. a. are also given. Most of the proofs are adaptations of corresponding proofs in symplectic and contact geometry. The paper ends with an Appendix which states an analogous fibration theorem in Riemannian geometry.
On an asymptotic formula for the niven numbers
Authors: Cooper Curtis N. , Kennedy Robert E.
Published: September 2002

A Niven number is a positive integer which is divisible by its digital sum. A discussion of the possibility of an asymptotic formula for N(x) is given. Here, N(x) denotes the nmber of Niven numbers less than x. A partial result will be presented. This result will be an asymptotic formula for Nk(x) which denotes the number of Niven numbers less than x with digital sum k.
On certain inequalities for some regular functions in |z| < 1
Authors: Obradović Milutin
Published: September 2002

In this paper we give some inequalities for regular functions f(z) = z + a2z2 + … in |z| < 1 especially for starlike and convex functions of order α, 0 ≤ α < 1, To some extent those inequalities are the generalisations and improvements of the previous results given by Bernardi [1]. Some interesting consequences are given, too.
Tauberian conditions for Conull spaces
Authors: Connor J. , Snyder A. K.
Published: September 2002

The typical Tauberian theorem asserts that a particular summability method
cannot map any divergent member of a given set of sequences into a convergent sequence. These sets of sequences are typically defined by an “order growth” or “gap” condition. We establish that any conull space contains a bounded divergent member of such a set;
hence, such sets fail to generate Tauberian theorems for conull spaces.
On coefficients of circuit polynomials and characteristic polynomials
Authors: Farrell E. J.
Published: September 2002

Results are given from which expressions for the coefficients of the simple
circuit polynomial of a graph can be obtained in terms of subgraphs of the graph. From these are deduced parallel results for the coefficients of the characteristic polynomial of a graph. Some specific results are presented on the parities of the coefficients of characteristic polynomials. A characterization is then determined for graphs in which the number of sets of independent edges is always even. This leads to an interesting link between matching polynomials and characteristic polynomials. Finally explicit formulae are derived for the number of ways of covering two well known
families of graphs with node disjoint circuits, and for the first few coefficients of their characteristic polynomials.
The spaces OM and OC are ultrabornological a new proof
Authors: Kucera Jan
Published: September 2002

In [1] Laurent Schwartz introduced the spaces 𝒪M and of multiplication and convolution operators on temperate distributions. Then in [2] Alexandre Grothendieck used tensor products to prove that both 𝒪M and are bornological. Our proof of this property is more constructive and based on duality.
On mennicke groups of deficiency zero I
Authors: Albar Muhammad A.
Published: September 2002

The Mennicke group M(m, n, r) = 〈x, y, z, |xy = xm, yz = yn, zx = zr〉 is one of the few known 3‐generator groups of deficiency zero. Several cases of M(m, n, r) are studied.
On a fixed point theorem of Greguš
Authors: Fisher Brian , Sessa Salvatore
Published: September 2002

We consider two selfmaps T and I of a closed convex subset C of a Banach space X which are weakly commuting in X, i.e.

urn:x-wiley:01611712:media:ijmm191262:ijmm191262-math-0001

and satisfy the inequality

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for all x, y in C, where 0 < a < 1. It is proved that if I is linear and non‐expansive in C and such that IC contains TC, then T and I have a unique common fixed point in C.
Banach spaces of functions analytic in a polydisc
Authors: Hall Leon M.
Published: September 2002

This paper is concerned with functions of several complex variables analytic in the unit polydisc. Certain Banach spaces to which these functions might belong are defined and some relationships between them are developed. The space of linear functionals for the Banach space of functions analytic in the open unit polydisc and continuous on the unit torus is then described in terms of analytic functions using an extension of the Hadamard product.
On certain classes of p‐Valent functions
Authors: Aouf M. K.
Published: September 2002

Let (k ≥ 2, b ≠ 0 is any complex number, 0 ≤ α < p and |λ| < π/2) denote the class of functions analytic in U = {z : |z| < 1} having (p − 1) critical points in U and satisfying

urn:x-wiley:01611712:media:ijmm204023:ijmm204023-math-0003

In this paper we generalize both those functions f(z) which are p‐valent convex of order α, 0 ≤ α < p, with bounded boundary rotation and those p‐valent functions f(z) for which zf′(z)/p is λ‐spirallike of order α, 0 ≤ α < p.
On some spaces of summable sequences and their duals
Authors: de Souza Geraldo Soares , Golightly G. O.
Published: September 2002

Suppose that S is the space of all summable sequences α with and J the space of all sequences β of bounded variation with . Then for α in S and β in J ; this inequality leads to the description of the dual space of S as J. It, related inequalities, and their consequences are the content of this paper. In particular, the inequality cited above leads directly to the Stolz form of Abel′s theorem and provides a very simple argument. Also, some other sequence spaces are discussed.
Comparison theorems for fourth order differential equations
Authors: Etgen Garret J. , Taylor Willie E.
Published: September 2002

This paper establishes an apparently overlooked relationship between the pair of fourth order linear equations yiv − p(x)y = 0 and yiv + p(x)y = 0, where p is a positive, continuous function defined on [0, ∞). It is shown that if all solutions of the first equation are nonoscillatory, then all solutions of the second equation must be nonoscillatory as well. An oscillation criterion for these equations is also given.
A note on subordination
Authors: Owa Shigeyoshi
Published: September 2002

Suffridge showed a result for subordinate functions. The object of the present paper is to show some subordinate theorems with the aid of the result by Suffridge.
Thirty‐nine perfect numbers and their divisors
Authors: Asadulla Syed
Published: September 2002

The following results concerning even perfect numbers and their divisors are proved: (1) A positive integer n of the form 2p−1(2p − 1), where 2p − 1 is prime, is a perfect number; (2) every even perfect number is a triangular number; (3) τ(n) = 2p, where τ(n) is the number of positive divisors of n; (4) the product of the positive divisors of n is np; and (5) the sum of the reciprocals of the positive divisors of n is 2. Values of p for which 30 even perfect numbers have been found so far are also given.

Corrigendum: Thirty-nine perfect numbers and their divisorsdx.doi.org/10.1155/S0161171286001047
Sequences in power residue classes
Authors: Buell Duncan A. , Hudson Richard H.
Published: September 2002

Using A. Well′s estimates the authors have given bounds for the largest prime P0 such that all primes p > P0 have sequences of quadratic residues of length m. For m ≤ 8 the smallest prime having m consecutive quadratic residues is ≡3(mod4) and P0 ≡ 1(mod4). The reason for this phenomenon is investigated in this paper and the theory developed is used to successfully uncover analogous phenomena for rth power residues, r ≥ 2, r even.
Irregular amalgams
Authors: Stewart James , Watson Saleem
Published: September 2002

The amalgam of Lp and ℓq consists of those functions for which the sequence of Lp‐norms over the intervals [n, n + 1) is in ℓq. These spaces (Lp, ℓq) have been studied in several recent papers. Here we replace the intervals [n, n + 1) by a cover α = {In; n ∈ Z} of the real line consisting of disjoint half‐open intervals In each of the form [a, b), and investigate which properties of (Lp, ℓq) carry over to these irregular amalgams . In particular, we study how varies as p, q, and α vary and determine conditions under which translation is continuous.
The maximum term of a power series
Authors: Srivastava G. S. , Juneja O. P.
Published: September 2002

Let be a power series, representing an analytic function f(z) in the disc |z| < R. A characterization for the type of such functions was obtained by the authors [J. Math. Anal. Appl. 81(1981), 1‐7] in terms of the maximum term and rank. It is proved in this paper by means of an example, that a similar relation does not hold in general for lower type and sufficient conditions have been obtained for the validity of the corresponding result for lower type. Alternative coefficient characterization for type and lower type have been given and a necessary and sufficient condition for the analytic function f(z) to be of perfectly regular growth has been obtained.
k‐component disconjugacy for systems of ordinary differential equations
Authors: Henderson Johnny
Published: September 2002

Disconjugacy of the kth component of the mth order system of nth order differenttal equations Y(n) = f(x, Y, Y′, …, Y(n−1)), (1.1), is defined, where f(x, Y1, …, Yn), are continuous. Given a solution Y0(x) of (1.1), k‐component disconjugacy of the variational equation , (1.2), is also studied. Conditions are given for continuous dependence and differentiability of solutions of (1.1) with respect to boundary conditions, and then intervals on which (1.1) is k‐component disconjugate are characterized in terms of intervals on which (1.2) is k‐component disconjugate.
Fine topology on function spaces
Authors: McCoy R. A.
Published: September 2002

This paper studies the topological properties of two kinds of “fine topologies” on the space C(X, Y) of all continuous functions from X into Y.
Characterizations of some near‐continuous functions andnear‐open functions
Authors: Baker C. W.
Published: September 2002

A subset N of a topological space is defined to be a θ‐neighborhood of x if there exists an open set U such that x ∈ U⫅C1   U⫅N. This concept is used to characterize the following types of functions: weakly continuous, θ‐continuous, strongly θ‐continuous, almost strongly θ‐continuous, weakly δ‐continuous, weakly open and almost open functions. Additional characterizations are given for weakly δ‐continuous functions. The concept of θ‐neighborhood is also used to define the following types of open maps: θ‐open, strongly θ‐open, almost strongly θ‐open, and weakly δ‐open functions.
On the cardinality of solutions of multilinear differential equations and applications
Authors: Argyros Ioannis K.
Published: September 2002

We study the existnece and cardinality of solutions of multilinear differential equations giving upper bounds on the number of solutions.
Fast complete locally convex linear topological spaces
Authors: Bosch Carlos , Kucera Jan , McKennon Kelly
Published: September 2002

This is a study of relationship between the concepts of Mackey, ultrabornological,
bornological, barrelled, and infrabarrelled spaces and the concept of fast completeness. An example of a fast complete but not sequentially complete space is presented.
On powerful numbers
Authors: Mollin R. A. , Walsh P. G.
Published: September 2002

A powerful number is a positive integer n satisfying the property that p2 divides n whenever the prime p divides n; i.e., in the canonical prime decomposition of n, no prime appears with exponent 1. In [1], S.W. Golomb introduced and studied such numbers. In particular, he asked whether (25, 27) is the only pair of consecutive odd powerful numbers. This question was settled in [2] by W.A. Sentance who gave necessary and sufficient conditions for the existence of such pairs. The first result of this paper is to provide a generalization of Sentance′s result by giving necessary and sufficient conditions for the existence of pairs of powerful numbers spaced evenly apart. This result leads us naturally to consider integers which are representable as a proper difference of two powerful numbers, i.e. n = p1 − p2 where p1 and p2 are powerful numbers with g.c.d. (p1, p2) = 1. Golomb (op.cit.) conjectured that 6 is not a proper difference of two powerful numbers, and that there are infinitely many numbers which cannot be represented as a proper difference of two powerful numbers. The antithesis of this conjecture was proved by W.L. McDaniel [3] who verified that every non‐zero integer is in fact a proper difference of two powerful numbers in infinitely many ways. McDaniel′s proof is essentially an existence proof. The second result of this paper is a simpler proof of McDaniel′s result as well as an effective algorithm (in the proof) for explicitly determining infinitely many such representations. However, in both our proof and McDaniel′s proof one of the powerful numbers is almost always a perfect square (namely one is always a perfect square when n≢2(mod4)). We provide in §2 a proof that all even integers are representable in infinitely many ways as a proper nonsquare difference; i.e., proper difference of two powerful numbers neither of which is a perfect square. This, in conjunction with the odd case in [4], shows that every integer is representable in infinitely many ways as a proper nonsquare difference. Moreover, in §2 we present some miscellaneous results and conclude with a discussion of some open questions.
Reflexive algebras and sigma algebras
Authors: Przymusinski T. C. , Srinivasan V. K.
Published: September 2002

The concept of a reflexive algebra (σ‐algebra) β of subsets of a set X is defined in this paper. Various characterizations are given for an algebra (σ‐algebra) β to be reflexive. If V is a real vector lattice of functions on a set X which is closed for pointwise limits of functions and if β = {A|A⫅X   and   CA(x) ∈ V} is the σ‐algebra induced by V then necessary and sufficient conditions are given for β to be reflexive (where CA(x) is the indicator function).
On the boundedness and oscillation of solutions to
Authors: Kroopnick Allan J.
Published: September 2002

In this paper, we discuss under what conditions the solutions to are bounded, oscillatory, and stable. Furthermore, some applications of these results are given during the discussion and proofs of the theorems.

Corrigendum: On the boundness and oscillation of solutions to dx.doi.org/10.1155/S0161171287000759
On nth‐order differential operators with Bohr‐Neugebauer type property
Authors: Rao Aribindi Satyanarayan
Published: September 2002

Suppose B is a bounded linear operator in a Banach space. If the differential operator has a Bohr‐Neugebauer type property for Bochner almost periodic functions, then, for any Stepanov almost periodic continuous function g(t) and any Stepanov‐bounded solution of the differential equation , u(n−1), …, u′, u are all almost periodic.
Analytic approach to systems in potential models
Authors: Chatterjee Lali , Bhattacharyya S.
Published: September 2002

Analytic solutions for systems obtained from a cut‐off type approximation to the funnel potential are applied to and systems. Perturbative corrections to oscillator energy levels due to inclusion of short range
a/r effect are also obtained.
A note on quasi‐monotone operators
Authors: Chow S. S.
Published: September 2002

The treatment of nonlinear problems using a general framework is often a delicate issue. This is illustrated by the fact that the quasi‐monotone operators of M. A. Noor are constant operators.
Differentiable structures on a generalized product of spheres
Authors: Ajala Samuel Omoloye
Published: September 2002

In this paper, we give a complete classification of smooth structures on a generalized product of spheres. Ihe result generalizes our result in [1] and R. de Sapio′s result in [2].
λ‐similar bases
Authors: Gupta Manjul , Kamthan P. K.
Published: September 2002

Corresponding to an arbitrary sequence space λ, a sequence {xn} in a locally convex space (l.c.s.) (X, T) is said to be λ‐similar to a sequence {yn} in another l.c.s. (Y, S) if for an arbitrary sequence {αn} of scalars, {αn p(xn)} ϵ λ for all p ϵ DT⇔{αn q(yn)} ϵ λ, for all q ϵ DS, where DT and DS are respectively the family of all T and S continuous seminorms generating T and S.

In this note we investigate conditions on λ and the spaces (X, T) and (Y, S) which ultimately help to characterize λ similarity between two Schauder bases. We also determine relationship of this concept with λ‐bases.
Fourier coefficients and growth of harmonic functions
Authors: fryant A. , Shankar H.
Published: September 2002

We consider Harmonic Functions, H of several variables. We obtain necessary and sufficient conditions on its Fourier coefficients so that H is an entire harmonic (that is, has no finite singularities) function; the radius of harmonicity
in terms of its Fourier coefficients in case H is not entire. Further, we obtain, in terms of its Fourier coefficients, the Order and Type growth measures, both in case H is entire or non‐entire.
Weakly α‐continuous functions
Authors: Noiri Takashi
Published: September 2002

In this paper, we introduce the notion of weakly α‐continuous functions in topological spaces. Weak α‐continuity and subweak continuity due to Rose [1] are independent of each other and are implied by weak continuity due to Levine [2]. It is shown that weakly α‐continuous surjections preserve connected spaces and that weakly α‐continuous functions into regular spaces are continuous. Corollary 1 of [3] and Corollary 2 of [4] are improved as follows: If f1 : X → Y is a semi continuous function into a Hausdorff space Y, f2 : X → Y is either weakly α‐continuous or subweakly continuous, and f1 = f2 on a dense subset of X, then f1 = f2 on X.
Some general classes of comatching graphs
Authors: Farrell E. J. , Wahid S. A.
Published: September 2002

Some sufficient conditions are given for two graphs to have the same matching polynomial (comatching graphs). Several general classes of comatching graphs are given. Also, techniques are discussed for extending certain pairs of comatching graphs to larger pairs of comatching graphs.
On permutation polynomials over finite fields
Authors: Mollin R. A. , Small C.
Published: September 2002

A polynomial f over a finite field F is called a permutation polynomial if the mapping F → F defined by f is one‐to‐one. In this paper we consider the problem of characterizing permutation polynomials; that is, we seek conditions on the coefficients of a polynomial which are necessary and sufficient for it to represent a permutation. We also give some results bearing on a conjecture of Carlitz which says essentially that for any even integer m, the cardinality of finite fields admitting permutation polynomials of degree m is bounded.
Totally umbilical CR‐submanifolds of Semi‐Riemannian Kaehler manifolds
Authors: Duggal K. L. , Sharma R.
Published: September 2002

We study totally umbilical CR‐submanifolds of a Kaehler manifold carrying a semi‐Riemannian metric. It is shown that for dimension of the totally real distribution greater than one, these submanifolds are locally decomposable into a complex and a totally real submanifold of the Kaehler manifold. For dimension equal to one, we show, in particular, that they are endowed with a normal contact metric structure if and only if the second fundamental form is parallel.
The shallow water equations: conservation laws and symplectic geometry
Authors: Akyildiz Yilmaz
Published: September 2002

We consider the system of nonlinear differential equations governing shallow
water waves over a uniform or sloping bottom. By using the hodograph method we construct solutions, conservation laws, and Böcklund transformations for these equations. We show that these constructions are canonical relative to a symplectic form introduced by Manin.
Multifacility location problems on a sphere
Authors: Aykin Turgut , Babu A. J. G.
Published: September 2002

A unified approach to multisource location problems on a sphere is presented. Euclidean, squared Euclidean and the great circle distances are considered. An algorithm is formulated and its convergence properties are investigated.
On a class of p‐valent starlike functions of order α
Authors: Aouf M. K.
Published: September 2002

Let Ω denote the class of functions w(z), w(0) = 0, |w(z)| < 1 analytic in the unit disc ⋃ = {z : |z| < 1}. For arbitrary fixed numbers A, B, −1 < A ≤ 1, −1 ≤ B < 1 and 0 ≤ α < p, denote by P(A, B, p, α) the class of functions analytic in ⋃ such that P(z) ϵ P(A, B, p, α) if and only if , w ϵ Ω, z ϵ ⋃. Moreover, let S(A, B, p, α) denote the class of functions analytic in ⋃ and satisfying the condition that f(z) ϵ S(A, B, p, α) if and only if for some P(z) ϵ P(A, B, p, α) and all z in ⋃.

In this paper we determine the bounds for |f(z)| and in S(A, B, p, α), we investigate the coefficient estimates for functions of the class S(A, B, p, α) and we study some properties of the class S(A, B, p, α).
Unstable periodic wave solutions of Nerve Axion diffusion equations
Authors: Ling Rina
Published: September 2002

Unstable periodic solutions of systems of parabolic equations are
studied. Special attention is given to the existence and stability of solutions.
An inverse problem for Helmholtz′s equation
Authors: Ramm A. G.
Published: September 2002

The refraction coefficient in Helmholtz′s equation is found from the
knowledge of a family of the solutions to this equation on two lines.
Homomorphisms and related contractions of graphs
Authors: Girse Robert D. , Gillman Richard A.
Published: September 2002

For every homomorphism ϕ of a graph G there exists a contraction θϕ on , the complement of G. Here we study the graph equation . In the course of our work we show that Hadwiger′s Conjecture is true for every self‐complementary graph.
On solvability of boundary value problem for elliptic equations with Bitsadze‐Samarskiĭ condition
Authors: Chabrowski J. H.
Published: September 2002

In this paper we investigate the solvability of a non‐local problem for a linear elliptic equation, which is also known as the boundary value problem with the Bitsadze‐Samarskiĭ condition. We prove the existence and uniqueness of a classical solution to this problem. In the final part of this paper we propose an L2‐approach which gives a rise to weak solutions in a weighted Sobolev space. The crucial point in proving the existence of weak solutions is a suitable modification of the Bitsadze‐Samarskiĭ condition.
On asymptotic normality for m‐dependent U‐statistics
Authors: Rhee Wansoo T.
Published: September 2002

Let (Xn) be a sequence of m‐dependent random variables, not necessarily equally distributed. We give a Berry‐Esseen estimate of the convergence to normality of a suitable normalization of a U‐statistic of the (Xn). This bound holds under moment assumptions quite weaker than the existence of third moments for the kernel. Since we obtain the sharpest bound, the order of the bound can not be improved.
Analysis of straightening formula
Authors: Kulkarni Devadatta M.
Published: September 2002

The straightening formula has been an essential part of a proof showing that the set of
standard bitableaux (or the set of standard monomials in minors) gives a free basis for a polynomial ring in a matrix of indeterminates over a field. The straightening formula expresses a nonstandard bitableau as an integral linear cobmbination of standard bitableaux. In this paper we analyse the exchanges in the process of straightening a nonstandard pure tableau of depth two. We give precisely the number of steps required to straighten a given violation of a nonstandard tableau. We also characterise the violation which is eliminated in a single step.
On a class of p‐valent close‐to‐convex functions of order β and type α
Authors: Aouf M. K.
Published: September 2002

Let S(A, B, p, α) denote the class of functions analytic in the unit disc U = {z : |z| < 1} and satisfying the condition

urn:x-wiley:01611712:media:ijmm294247:ijmm294247-math-0002

Let C(A, B, p, β, α) denote the class of functions analytic in U, and satisfying the condition

urn:x-wiley:01611712:media:ijmm294247:ijmm294247-math-0004

In this paper we determine the coefficient estimates and distortion theorems for the class C(A, B, p, β, α).
A variational principle for complex boundary value problems
Authors: Hajj Adnan Atef
Published: September 2002

This paper provides a variational formalism for boundary value problems which arise in certain feilds of research such as that of electricity, where the associated boundary conditions contain complex periodic conditions. A functional is provided which embodies the boundary conditions of the problem and hence the expansion (trial) functions need not satisfy any of them.
A convex operator function
Authors: Wang Derming
Published: September 2002

It is shown that inversion is a convex function on the set of strictly positive elements of a C*‐algebra.
On the dual space of a weighted Bergman space on the unit ball of Cn
Authors: Choa J. S. , Kim H. O.
Published: September 2002

The weighted Bergman space , of the holomorphic functions on the unit ball Bn of Cn forms an F‐space. We find the dual space of by determining its Mackey topology.
A maximal chain approach to topology and order
Authors: Vainio R.
Published: September 2002

On ordered sets (posets, lattices) we regard topologies (or, more general convergence
structures) which on any maximal chain of the ordered set induce its own interval topology. This construction generalizes several well‐known intrinsic structures, and still contains enough to produce interesting results on for instance compactness and connectedness.
The maximal chain compatibility between topology (convergence structure) and order is preserved by formation of arbitrary products, at least in case the involved order structures are conditionally complete lattices.
Mixed foliate CR‐submanifolds in a complex hyperbolic space are non‐proper
Authors: Chen Bang-Yen , Wu Bao-Qiang
Published: September 2002

It was conjectured in [1 II] (also in [2]) that mixed foliate CR‐submanifolds in a complex hyperbolic space are either complex submanifolds or totally real submanifolds. In this paper we give an affirmative solution to this conjecture.
On the numerical solution of the multidimensional singular integrals and integral equations, used in the theory of linear viscoelasticity
Authors: Ladopoulos E. G.
Published: September 2002

In the present report, we investigate the formulation, for the numerical evaluation of the multidimensional singular integrals and integral equations, used in the theory of linear viscoelasticity. Some simple formulas are given for the numerical solution of the general case of the multidimensional singular integrals. Moreover a numerical technique is also established for the numerical solution of some special cases of the multidimensional singular integrals like the two ‐ and three ‐ dimensional singular integrals. An application is given to the determination of the fracture behaviour of a thick, hollow circular cylinder of viscoelastic material restrained by an enclosing thin elastic ring and subjected to a uniform pressure.
Studies on the differential equations of enzyme kinetics. II. bimolecular reaction: the fitting of experimental data to the simplified model
Authors: Marmasse Claude , Wiener Joseph
Published: September 2002

Efficient and unbiased estimates of the parameters of the differential system, as well as simultaneous fiducial limits, are obtained through an (eventually weighted) least‐squares fitting to a Taylor expansion of the concentration of the products of the reaction.
A note on equivalent interval covering systems for Hausdorff dimension on ℝ
Authors: Cutler C. D.
Published: September 2002

The Hausdorff dimension of a set in ℝ is usually defined by considering countable coverings of the set by general intervals. In this note we establish sufficient conditions under which coverings whose members are restricted to a particular family g of intervals will produce the same value for dimension. A result of Billingsley is then employed to obtain a general technique for computing the dimensions of sets defined by certain types of generalized expansions. A specific example is included.
Another note on Kempisty′s generalized continuity
Authors: Lee J. P. , Piotrowski Z.
Published: September 2002

Under a fairly mild completeness condition on spaces Y and Z we show that every x‐continuous function f : X × Y × Z → M has a substantial set C(f) of points of continuity. Some odds and ends concerning a related earlier result shown by the authors are presented. Further, a generalization of S. Kempisty′s ideas of generalized continuity on products of finitely many spaces is offered. As a corollary from the above results, a partial answer to M. Talagrand′s problem is provided.
A note on the vertex‐switching reconstruction
Authors: Krasikov I.
Published: September 2002

Bounds on the maximum and minimum degree of a graph establishing its reconstructibility from the vertex switching are given. It is also shown that any disconnected graph with at least five vertices is reconstructible.
On weaker forms of compactness Lindelöfness and countable compactness
Authors: Baboolal D. , Backhouse J. , Ori R. G.
Published: September 2002

A theory of e‐countable compactness and e‐Lindelöfness which are weaker than the concepts of countable compactness and Lindelöfness respectively is developed. Amongst other results we show that an e‐countably compact space is pseudocompact, and an example of a space which is pseudocompact but not e‐countably compact with respect to any dense set is presented. We also show that every e‐Lindelöf metric space is separable.
Some spectral inclusions on D‐commuting systems
Authors: Verma R. U. , Jou S. S.
Published: September 2002

Some spectral inclusions for the Taylor joint Browder spectra of D‐commuting systems are estabished. The obtained results are applied in generalizing the spectral mapping theorems.
Iterative solution of negative exponent Emden‐Fowler problems
Authors: Luning C. D. , Perry W. L.
Published: September 2002

A monotone iterative technique for proving existence of a positive solution pair (λ, y) of y″(x) + λa(x)yμ(x) = 0, 0 < x < 1, y(0+) = y(1−) = 0, μ ≤ −1 is shown. The method is computationally effective and an example is given.
On the symmetry axiom for values of nonatomic games
Authors: Monderer Dov , Ruckle William H.
Published: September 2002

In this paper, a weaker version of the Symmetry Axiom on BV, and values on subspaces of BV are discussed. Included are several theorems and examples.
On the nature of time
Authors: Muraskin M.
Published: September 2002

We study how the notion of time can affect the motion of particles within the No Integrability Aesthetic Field Theory. We show that the Minkowski hypothesis of treating x4 as pure imaginary as well as the fourth component of vectors as pure imaginary, does not lead to different solutions provided we alter the sign of dx4 and certain origin point field components. We next show that it is possible to introduce time in the situation where all fields are real so that: (1) The field equations treat all coordinates the same way; (2) The flow concept is associated with time but not with space; (3) Data is prescribed at a single point rather than on a hypersurface as in hyperbolic theories. We study the lattice solution in the approximation that ignores zig‐zag paths. This enables us to investigate the effect of a non‐trivial superposition principle in the simplest way. We find that such a system, combined with our new approach to time, gives rise to an apparent infinite particle system in which particles can be looked at as not having well defined trajectories. This result is similar to what we obtained when we treated time in the same manner as the space variables in our previous work.
Invariants of number fields related to central embedding problems
Authors: Opolka H.
Published: September 2002

Every central embedding problem over a number field becomes solvable after enlarging its kernel in a certain way. We show that these enlargements can be arranged in a universal way.
Location of approximations of a Markoff theorem
Authors: Prasad K. C. , Lari M. , Singh P.
Published: September 2002

Relative to the first two theorems of the well known Markoff Chain (J.W.S. Cassels, An introduction to diophantine approximation approximations are well located. Literature is silent on the question of location of approximations in reference to the other theorems of the Chain. Here we settle it for the third theorem of the Chain.
A note on the k‐domination number of a graph
Authors: Caro Y. , Roditty Y.
Published: September 2002

The k‐domination number of a graph G = G(V, E), γk(G), is the least cardinality of a set X ⊂ V such that any vertex in VX is adjacent to at least k vertices of X.

Extending a result of Cockayne, Gamble and Shepherd [4], we prove that if , n ≥ 1, k ≥ 1 then, , where p is the order of G.
Separation properties of the Wallman ordered compactification
Authors: Kent D. C. , Richmond T. A.
Published: September 2002

The Wallman ordered compactification ω0X of a topological ordered space X is T2‐ordered (and hence equivalent to the Stone‐Čech ordered compactification) iff X is a T4‐ordered c‐space. In particular, these two ordered compactifications are equivalent when X is n dimensional Euclidean space iff n ≤ 2. When X is a c‐space, ω0X is T1‐ordered; we give conditions on X under which the converse statement is also true. We also find conditions on X which are necessary and sufficient for ω0X to be T2. Several examples provide further insight into the separation properties of ω0X.
On α‐convex functions of order β with m‐fold symmetry
Authors: Ma Wancang
Published: September 2002

This note is a continuation of the previous work [1,2,3]. First we get a new subordination for α‐convex functions of order β when α = 1 − 2β, which implies the rotation theorem for (1 − 2β)/m‐convex functions of order β with m‐fold symmetry. Then we extend the known results on α‐convex functions of order β to the functions with m‐fold symmetry. In particular, we give the sharp order of convexity of α‐convex functions of order β with m‐fold symmetry for α ≥ 1, which is analogous in sharpness to a result given by Miller, Mocanu and Reade [1].
Permutation binomials
Authors: Small Charles
Published: September 2002

A polynomial f over a finite feld F is a permutation polynomial if the mapping F → F defined by f is one‐to‐one. We are concerned here with binomials, that is, polynomials of the shape f = aXi + bXj + c, i > j ≥ 1. Even in this restricted setting, it is impossible to give general necessary and sufficient conditions on a, b, c for f to be a permutation polynomial. We review, and systematize, what is known.
Tau numbers, natural density, and Hardy and Wright′s theorem 437
Authors: Kennedy Robert E. , Cooper Curtis N.
Published: September 2002

An element of the set T = {n : τ(n) is a factor of n} is called a Tau number, where τ(n) denotes the number of divisors of the integer n. We determine the natural density of this set by use of Hardy and Wright′s Theorem 437 (4th ed.).
Limit cycles in a Kolmogorov‐type model
Authors: Huang Xun-Cheng
Published: September 2002

In this paper, a Kolmogorov‐type model, which includes the Gause‐type model (Kuang and Freedman, 1988), the general predator‐prey model (Huang 1988, Huang and Merrill 1989), and many other specialized models, is studied. The stability of equilibrium points, the existence and uniqueness of limit cycles in the model are proved.
Order‐theoretical connectivity
Authors: Richmond T. A. , Vainio R.
Published: September 2002

Order‐theoretically connected posets are introduced and applied to create the notion of T‐connectivity in ordered topological spaces. As special cases T‐connectivity contains classical connectivity, order‐connectivity, and link‐connectivity.
A theorem for Fourier coefficients of a function of class Lp
Authors: Gaur A. K.
Published: September 2002

This paper deals with the Fourier coefficients of a function of class Lp. We give a necessary and sufficient condition for function to be of class Lp for p greater than one.
A note on quasi R*‐invariant measures on semigroups
Authors: Tserpes N. A.
Published: September 2002

A characterization of quasi r*‐invariant measures on metric topological semigroups is obtained by showing that their support has a left group structure thus generalizing previously known results for relatively r*‐invariant measures and the topo‐algebraic structure of their support.
Almost none of the sequences of 0′s and 1′s are almost convergent
Authors: Connor Jeff
Published: September 2002

We establish that, in the sense of the Law of Large Numbers, almost none of the sequences of 0’s and 1’s are assigned the same value by every Banach limit.
Norms in finite galois extensions of the rationals
Authors: Opolka Hans
Published: September 2002

We show that under certain conditions a rational number is a norm in a given finite Galois extension of the rationals if and only if this number is a local norm at a certain finite number of places in a certain finite abelian extension of the rationals.
On the discrepancy of coloring finite sets
Authors: Hajela D.
Published: September 2002

Given a subset S of {1, …, n} and a map X : {1, …, n} → {−1, 1}, (i.e. a coloring of {1, …, n} with two colors, say red and blue) define the discrepancy of S with respect to X to be (the difference between the reds and blues on S). Given n subsets of {1, …, n}, a question of Erdos was to find a coloring of {1, …, n} which simultaneously minimized the discrepancy of the n subsets. We give new and simple proofs of some of the results obtained previously on this problem via an inequality for vectors.

Corrigendum to
“On the discrepancy of coloring finite sets”dx.doi.org/10.1155/S0161171291000534
Some functionals for copulas
Authors: Alsina C. , Damas A. , Quesada J. J.
Published: September 2002

In this paper we study some functionals operating on the set of the n‐copulas defined
on [0, 1] n. Conditions under which such functionals are well defined are determined and some
counterexamples are described. The study of the fixed points (n‐copulas) for these functionals is also
considered, and, finally, some open problems are presented.
A remark on weighted averages for superadditive processes
Authors: Cömez Dogan
Published: September 2002

A decompostion of a superadditive process into a difference of an additive
and a positive purely superadditive process is obtained. This result is used to prove
an ergodic theorem for weighted averages of superadditive processes.
Factorization of k‐quasihyponormal operators
Authors: Arora S. C. , Thukral J. K.
Published: September 2002

Let A be the class of all operators T on a Hilbert space H such that
R(T*kT), the range space of T*KT, is contained in R(T*k+1), for a positive integer k.
It has been shown that if T ϵ A, there exists a unique operator CT
on H such that

urn:x-wiley:01611712:media:ijmm367931:ijmm367931-math-0001

The main objective of this paper is to characterize k‐quasihyponormal; normal, and
self‐adjoint operators T in A in terms of CT. Throughout the paper, unless stated
otherwise, H will denote a complex Hilbert space and T an operator on H, i.e., a
bounded linear transformation from H into H itself. For an operator T, we write R(T)
and N(T) to denote the range space and the null space of T.
Functions starlike with respect to other points
Authors: Abdul Halim S.
Published: September 2002

In [7], Sakaguchi introduce the class of functions starlike with respect
to symmetric points. We extend this class. For p ≤ β < 1, let be the
class of normalised analytic functions f defined in the open unit disc D such
that Rezf′(z)/(f(z) − f(−z)) > β, for some z ϵ D. In this paper, we introduce 2
other similar classes , as well as give sharp results for the real
part of some function for , and The behaviour of certain
integral operators are also considered.
Partitioning the positive integers with higher order recurrences
Authors: Kimberling Clark
Published: September 2002

Associated with any irrational number α > 1 and the function is an
array {s(i, j)} of positive integers defined inductively as follows: s(1, 1) = 1, s(1, j) = g(s(1, j − 1))
for all j ≥ 2, s(i, 1) = the least positive integer not among s(h, j) for h ≤ i − 1 for i ≥ 2, and
s(i, j) = g(s(i, j − 1)) for j ≥ 2. This work considers algebraic integers α of degree ≥3 for which
the rows of the array s(i, j) partition the set of positive integers. Such an array is called a Stolarsky
array. A typical result is the following (Corollary 2): if α is the positive root of xk − xk−1 − …−x − 1
for k ≥ 3, then s(i, j) is a Stolarsky array.
Polynomials with minimal value set over Galois rings
Authors: Acosta-De-Orozco Maria T. , Gomez-Calderon Javier
Published: September 2002

Let GR(pn, m) denote the Galois ring of order pn,m, where p is a prime. In this
paper we define and characterize minimal value set polynomials over GR(pn, m).
Functional differential equations with infinite delay in Banach spaces
Authors: Liang Jin , Xiao Tijun
Published: September 2002

In this paper, a definition of the fundamental operator for the linear autonomous functional
differential equation with infinite delay in a Banach space is given, and some sufficient and necessary
conditions of the fundamental operator being exponentially stable in abstract phase spaces which satisfy
some suitable hypotheses are obtained. Moreover, we discuss the relation between the exponential
asymptotic stability of the zero solution of nonlinear functional differential equation with infinite delay in
a Banach space and the exponential stability of the solution semigroup of the corresponding linear equation,
and find that the exponential stability problem of the zero solution for the nonlinear equation can be discussed
only in the exponentially fading memory phase space.
A Parseval‐Goldstein type theorem on the widder potential transform and its applications
Authors: Yürekli O. , Sadek I.
Published: September 2002

In this paper a Parseval‐Goldstein type theorem involving the Widder potential
transform and a Laplace type integral transform is given. The theorem is then shown
to yield a relationship between the 𝒦‐transform and the Laplace type integral transform.
The theorem yields some simple algorithms for evaluating infinite integrals. Using the theorem
and its results, a number of new infinite integrals of elementary and special functions
are presented. Some illustrative examples are also given.