bluuebunny/crossref_metadata_2025 huggingface dataset:
The basic properties of Bloch functions
Authors: Cima Joseph A.
Published: September 2002

A Bloch function f(z) is an analytic function on the unit disc 𝔻 whose derivative grows no faster than a constant times the reciprocal of the distance from z to ∂𝔻. We reprove here the basic analytic facts concerning Bloch functions. We establish the Banach space structure and collect facts concerning the geometry of the space. We indicate duality relationships, and known isomorphic correspondences are given. We give a rather complete list of references for further study in the case of several variables.
A class of rings which are algebric over the integers
Authors: Rall Douglas F.
Published: September 2002

A well‐known theorem of N. Jacobson states that any periodic associative ring is commutative. Several authors (most notably Kaplansky and Herstein) generalized the “periodic polynomial” condition and were still able to conclude that the rings under consideration were commutative. (See [3]) In this paper we develop a structure theory for a class of rings which properly contains the periodic rings. In particular, an associative ring R is said to be a quasi‐anti‐integral (QAI) ring if for every a ≠ 0 in R there exist a positive integer k and integers n1, n2, …, nk (all depending on a), so that 0 ≠ n1a = n2a2 + …+nkak. In the main theorems of this paper, we show that any QAl‐ring is a subdirect sum of prime QAl‐rings, which in turn are shown to be left and right orders in division algebras which are algebraic over their prime fields.
A graph and its complement with specified properties III: girth and circumference
Authors: Akiyama Jin , Harary Frank
Published: September 2002

In this series, we investigate the conditions under which both a graph G and its complement possess certain specified properties. We now characterize all the graphs G such that both G and have the same girth. We also determine all G such that both G and have circumference 3 or 4.
Existence theorem for the difference equation Yn+1 − 2Yn + Yn−1 = h2f(yn)
Authors: Weil F.
Published: September 2002

For the difference equation sufficient conditions are shown such that for a given Y0 there is either a unique value of Y1 for which the sequence Yn strictly monotonically approaches a constant as n approaches infinity or a continuum interval of such values. It has been shown previously that the first alternative is related to the existence of a Peierls barrier energy in the dislocation model of Frenkel and Kontorova.
Limit theorems for solutions of stochastic differential equation problems
Authors: Scheidt J. Vom , Purkert W.
Published: September 2002

In this paper linear differential equations with random processes as coefficients and as inhomogeneous term are regarded. Limit theorems are proved for the solutions of these equations if the random processes are weakly correlated processes.

Limit theorems are proved for the eigenvalues and the eigenfunctions of eigenvalue problems and for the solutions of boundary value problems and initial value problems.
Spline solutions for nonlinear two point boundary value problems
Authors: Usmani Riaz A.
Published: September 2002

Necessary formulas are developed for obtaining cubic, quartic, quintic, and sextic spline solutions of nonlinear boundary value problems. These methods enable us to approximate the solution of the boundary value problems, as well as their successive derivatives smoothly. Numerical evidence is included to demonstrate the relative performance of these four techniques.
Properties of complements in the lattice of convergence structures
Authors: Riecke C. V.
Published: September 2002

Relative complements and differences are investigated for several convergence structure lattices, especially the lattices of Kent convergence structures and the lattice of pretopologies. Convergence space properties preserved by relative complementation are studied. Mappings of some convergence structure lattices into related lattices of lattice homomorphisms are considered.
Representation of certain classes of distributive lattices by sections of sheaves
Authors: Swamy U. Maddana , Manikyamba P.
Published: September 2002

Epstein and Horn ([6]) proved that a Post algebra is always a P‐algebra and in a P‐algebra, prime ideals lie in disjoint maximal chains. In this paper it is shown that a P‐algebra L is a Post algebra of order n ≥ 2, if the prime ideals of L lie in disjoint maximal chains each with n − 1 elements. The main tool used in this paper is that every bounded distributive lattice is isomorphic with the lattice of all global sections of a sheaf of bounded distributive lattices over a Boolean space. Also some properties of P‐algebras are characterized in terms of the stalks.
On certain groups of functions
Authors: Yang J. S.
Published: September 2002

Let C(X, G) denote the group of continuous functions from a topological space X into a topological group G with the pointwise multiplication and the compact‐open topology. We show that there is a natural topology on the collection of normal subgroups Δ(X) of C(X, G) of the Mp = {f ∈ C(X, G) : f(p) = e} which is analogous to the hull‐kernel topology on the commutative Banach algegra C(X) of all continuous real or complex‐valued functions on X. We also investigate homomorphisms between groups C(X, G) and C(Y, G).
A pointwise growth estimate for analytic functions in tubes
Authors: Carmichael Richard D. , Hayashi Elmer K.
Published: September 2002

A class of analytic functions in tube domains TC = ℝn + iC in n‐dimensional complex space, where C is an open connected cone in ℝn, which has been defined by V. S. Vladimirov is studied. We show that a previously obtained L2 growth estimate concerning these functions can be replaced by a pointwise growth estimate, and we obtain further new properties of these functions. Our analysis shows that these functions of Vladimirov are exactly the Hardy H2 class of functions corresponding to the tube TC.
Reflection and transmission of seismic waves under initial stress at the earth′s core‐mantle boundary
Authors: Dey Sukhendu , Addy Sushil Kumar
Published: September 2002

In the present paper the influence of the initial stress is shown on the reflection and transmission of P waves at the core‐mantle boundary. Taking a particular value of the inherent initial stress, the variations of reflection and transmission coefficients with respect to the angle of emergence are represented by graphs. These graphs when compared with those having no initial stress show that the effect of the initial stress is to produce a reflected P and S waves with numerically higher amplitudes but a transmitted P wave with smaller amplitude. A method is also indicated in this paper to calculate the actual value of the initial stress near the core‐mantle boundary by measuring the amplitudes of incident and reflected P waves.
Translation planes of even order in which the dimension has only one odd factor
Authors: Ostrom T. G.
Published: September 2002

Let G be an irreducible subgroup of the linear translation complement of a finite translation plane of order qd where q is a power of 2. GF(q) is in the kernel and d = 2sr where r is an odd prime. A prime factor of |G| must divide .

One possibility (there are no known examples) is that G has a normal subgroup W which is a W‐group for some prime W.

The maximal normal subgroup 0(G) satisfies one of the following:

1. Cyclic. 2. Normal cyclic subgroup of index r and the nonfixed‐point‐free elements in 0(G) have order r. 3. 0(G) contains a group W as above.
Some Tauberian theorems for Euler and Borel summability
Authors: Fridy J. A. , Roberts K. L.
Published: September 2002

The well‐known summability methods of Euler and Borel are studied as mappings from ℓ1 into ℓ1. In this ℓ − ℓ setting, the following Tauberian results are proved: if x is a sequence that is mapped into ℓ1 by the Euler‐Knopp method Er with r > 0 (or the Borel matrix method) and x satisfies , then x itself is in ℓ1.
Expansions of distributions in terms of generalized heat polynominals and their Appell transforms
Authors: Pathak R. S. , Debnath Lokenath
Published: September 2002

This paper is concerned with expansions of distributions in terms of the generalized heat polynomials and of their Appell transforms. Two different techniques are used to prove theorems concerning expansions of distributions. A theorem which provides an orthogonal series expansion of generalized functions is also established. It is shown that this theorem gives an inversion formula for a certain generalized integral transformation.
The order topology for function lattices and realcompactness
Authors: Feldman W. A. , Porter J. F.
Published: September 2002

A lattice K(X, Y) of continuous functions on space X is associated to each compactification Y of X. It is shown for K(X, Y) that the order topology is the topology of compact convergence on X if and only if X is realcompact in Y. This result is used to provide a representation of a class of vector lattices with the order topology as lattices of continuous functions with the topology of compact convergence. This class includes every C(X) and all countably universally complete function lattices with 1. It is shown that a choice of K(X, Y) endowed with a natural convergence structure serves as the convergence space completion of V with the relative uniform convergence.
Growth of HP functions in tubes
Authors: Carmichael Richard D. , Richters Stephen P.
Published: September 2002

Let C be an open convex cone in n dimensional real space Rn such that does not contain any entire straight line. We obtain a growth condition on functions in the Hardy spaces HP(TC), 1 ≤ p ≤ ∞, corresponding to the tube TC = Rn + iC in n dimensional complex space ℂn.
On related vector fields of capillary surfaces
Authors: Özok Afet K.
Published: September 2002

In this paper, some necessary and sufficient conditions are given for the related vector fields of capillary surfaces to be Killing, conformal Killing, and homothetic conformal Killing vectors in the n‐dimensional domain Ω, and a construction of capillary surfaces is also given by means of the related vector fields.
LNC points for m‐convex sets
Authors: Breen Marilyn
Published: September 2002

Let S be closed, m‐convex subset of Rd, S locally a full d‐dimensional, with Q the corresponding set of lnc points of S. If q is an essential lnc point of order k then for some neighborhood U of q, Q ⋂ U is expressible as a union of k or fewer (d − 2)‐dimensional manifolds, each containing q For S compact, if to every q ∈ Q there corresponds a k > 0 such that q is an essential lnc point of order k then Q may be written as a finite union of (d − 2)‐manifolds.

For q any lnc point of S and N a convex neighborhood of q, N ⋂ bdry  S⊈Q That is, Q is nowhere dense in bdry S. Moreover, if conv(Q ⋂ N)⫅S then Q ⋂ N is not homeomorphic to a (d − 1)‐dimensional manifold.
Symmetrized solutions for nonlinear stochastic differential equations
Authors: Adomian G. , Sibul L. H.
Published: September 2002

Solutions of nonlinear stochastic differential equations in series form can be put into convenient symmetrized forms which are easily calculable. This paper investigates such forms for polynomial nonlinearities, i.e., equations of the form Ly + ym = x where x is a stochastic process and L is a linear stochastic operator.
On uniform convergence for (μ, ν)‐type rational approximants in ℂn‐II
Authors: Lutterodt Clement H.
Published: September 2002

This paper shows that if f(z) is analytic in some neighborhood of the origin, but meromorphic in ℂn otherwise, with a denumerable non‐accumulating pole sections in ℂn and if for each fixed ν the pole set of each (μ, ν) unisolvent rational approximant πμν(z) tends to infinity as , then f(z) must be entire in ℂn. This paper also shows a monotonicity property for the “error sequence” on compact subsets K of  ℂn.
On the almost sure convergence of weighted sums of random elements in D[0, 1]
Authors: Taylor R. L. , Calhoun C. A.
Published: September 2002

Let {wn} be a sequence of positive constants and Wn = w1 + …+wn where Wn → ∞ and wn/Wn → ∞. Let {Wn} be a sequence of independent random elements in D[0, 1]. The almost sure convergence of is established under certain integral conditions and growth conditions on the weights {wn}. The results are shown to be substantially stronger than the weighted sums convergence results of Taylor and Daffer (1980) and the strong laws of large numbers of Ranga Rao (1963) and Daffer and Taylor (1979).
On the differentiability of T(r, f)
Authors: Townsed Douglas W.
Published: September 2002

It is well known that T(r, f) is differentiable at least for r > r0. We show that, in fact, T(r, f) is differentiable for all but at most one value of r, and if T(r, f) fails to have a derivative for some value of r, then f is a constant times a quotient of finite Blaschke products.
Univalence of normalized solutions of W″(z) + p(z)W(z) = 0
Authors: Brown R. K.
Published: September 2002

Denote solutions of W″(z) + p(z)W(z) = 0 by and , where 0 < ℛ(β) ≤ 1/2 ≤ ℛ(α) and z2p(z) is holomorphic in |z| < 1. We determine sufficient conditions on p(z) so that and are univalent in |z| < 1.
A singular functional‐differential equation
Authors: Siafarikas P. D.
Published: September 2002

The representation of the Hardy‐Lebesque space by means of the shift operator is used to prove an existence theorem for a singular functional‐differential equation which yields, as a corollary, the well known theory of Frobenius for second order differential equations.
Short proofs of theorems of Lekkerkerker and Ballieu
Authors: Riederle Max
Published: September 2002

For any irrational number ξ let A(ξ) denote the set of all accumulation points of {z : z = q(qξ − p),    p ∈ ℤ,    q ∈ ℤ − {0},    p   and   q   relatively prime}. In this paper the following theorem of Lekkerkerker is proved in a short and elementary way: The set A(ξ) is discrete and does not contain zero if and only if ξ is a quadratic irrational. The procedure used for this proof simultaneously takes care of a theorem of Ballieu.
Solutions of type rm for a class of singular equations
Authors: Altin Abdullah
Published: September 2002

We obtain all solutions of radial type for a class of singular partial differential equations of even order. The essential operators here are elliptic or ultrahyperbolic.
Introductory remarks on complex multiplication
Authors: Cohn Harvey
Published: September 2002

Complex multiplication in its simplest form is a geometric tiling property. In its advanced form it is a unifying motivation of classical mathematics from elliptic integrals to number theory; and it is still of active interest. This interrelation is explored in an introductory expository fashion with emphasis on a central historical problem, the modular equation between j(z) and j(2z).
On the spectrum of a distribution function and on unique factorization
Authors: Pham-Gia T.
Published: September 2002

The spectrum of a distribution function is related to the quasi‐analyticity of a class of functions {CM(j)}, where M(j) is a multisequence of positive numbers. For a regular multisequence, a result on the uniqueness of characteristic function decomposition is given.
On the acyclic point‐connectivity of the n‐cube
Authors: Banks John , Mitchem John
Published: September 2002

The acyclic point‐connectivity of a graph G, denoted α(G), is the minimum number of points whose removal from G results in an acyclic graph. In a 1975 paper, Harary stated erroneously that α(Qn) = 2n−1 − 1 where Qn denotes the n‐cube. We prove that for n > 4, 7 · 2n−4 ≤ α(Qn) ≤ 2n−1 − 2n−y−2, where y = [log2(n − 1)]. We show that the upper bound is obtained for n ≤ 8 and conjecture that it is obtained for all n.
Equivalence classes of functions on finite sets
Authors: Chao Chong-Yun , Deisher Caroline I.
Published: September 2002

By using Pólya′s theorem of enumeration and de Bruijn′s generalization of Pólya′s theorem, we obtain the numbers of various weak equivalence classes of functions in RD relative to permutation groups G and H where RD is the set of all functions from a finite set D to a finite set R, G acts on D and H acts on R. We present an algorithm for obtaining the equivalence classes of functions counted in de Bruijn′s theorem, i.e., to determine which functions belong to the same equivalence class. We also use our algorithm to construct the family of non‐isomorphic fm‐graphs relative to a given group.
Identities involving iterated integral transforms
Authors: Nasim Cyril
Published: September 2002

A number of identities involving iterated integral transforms are established,
making use of the fact that a function which is a linear combination of the Macdonald′s function Kν(z), where z is a complex variable, is a Fourier kernel.
A note on selecting the better binominal population
Authors: Chitgopekar S. S.
Published: September 2002

An inverse sampling procedure is proposed for the problem of selecting the better of two treatments when the responses are dichotomous. This procedure is particularly useful when it is desired to limit the number of failures during the decision making stage. The regret function of the procedure is derived and it is shown that this procedure has a minimax regret property when compared to a fixed sample procedure studied by Pradhan and Sathe [2]. Numerical evidence indicates that this procedure dominates the fixed sample procedure of Pradhan and Sathe over the entire parameter space.
Dual characterization of the Dieudonne‐Schwartz theorem on bounded sets
Authors: Bosch C. , Kucera J. , McKennon K.
Published: September 2002

The Dieudonné‐Schwartz Theorem on bounded sets in a strict inductive limit is investigated for non‐strict inductive limits. Its validity is shown to be closely connected with the problem of whether the projective limit of the strong duals is a strong dual itself. A counter‐example is given to show that the Dieudonné‐Schwartz Theorem is not in general valid for an inductive limit of a sequence of reflexive, Fréchet spaces.
Distributional and entire solutions of ordinary differential and functional differential equations
Authors: Shah S. M. , Wiener Joseph
Published: September 2002

A brief survey of recent results on distributional and entire solutions of
ordinary differential equations (ODE) and functional differential equations (FDE) is given. Emphasis is made on linear equations with polynomial coefficients. Some work on generalized‐function solutions of integral equations is also mentioned.
On the radius of univalence of convex combinations of analytic functions
Authors: Noor Khalida I. , Aloboudi Fatima M. , Aldihan Naeela
Published: September 2002

We consider for α > 0, the convex combinations f(z) = (1 − α)F(z) + αzF′(z), where F belongs to different subclasses of univalent functions and find the radius for which f is in the same class.
On solving the plateau problem in parametric form
Authors: cahlon Baruch , Solomon Alan D. , Nachman Louis J.
Published: September 2002

This paper presents a numerical method for finding the solution of Plateau′s problem in parametric form. Using the properties of minimal surfaces we succeded in transferring the problem of finding the minimal surface to a problem of minimizing a functional over a class of scalar functions. A numerical method of minimizing a functional using the first variation is presented and convergence is proven. A numerical example is given.
Functions in the space R2(E) at boundary points of the interior
Authors: Wolf Edwin
Published: September 2002

Let E be a compact subset of the complex plane ℂ. We denote by R(E) the algebra consisting of (the restrictions to E of) rational functions with poles off E. Let m denote 2‐dimensional Lebesgue measure. For p ≥ 1, let Rp(E) be the closure of R(E) in Lp(E, dm).

In this paper we consider the case p = 2. Let x ϵ ∂E be a bounded point evaluation for R2(E). Suppose there is a C > 0 such that x is a limit point of the set s = {y | y ϵ Int E, Dist(y, ∂E) ≥ C|y − x|}. For those y ϵ S sufficiently near x we prove statements about |f(y) − f(x)| for all f ϵ R(E).
Forest decompositions of graphs with cyclomatic number 3
Authors: Farrell E. J.
Published: September 2002

The simple tree polynomials of the basic graphs with cyclomatic number 3
are derived. From these results, explicit formulae for the number of decompositions of the graphs into forests with specified cardinalities are extracted. Explicit expressions are also given for the number of spanning forests and spanning trees in the graphs. These results complement the results given in [1].
Oscillation criteria for certain nonlinear fourth order equations
Authors: Taylor W. E.
Published: September 2002

This work investigates the behavior of solutions of certain nonlinear fourth
order differential equations. An example is given showing that these equations can have both oscillatory and nonoscillatory solutions simultaneously. Finally, several criteria for the existence of oscillator solutions are established.
Asymptotic relationships between two higher order ordinary differential equations
Authors: Kusano Takasi
Published: September 2002

Some asymptotic relationships between the two ordinary differential equations

urn:x-wiley:01611712:media:ijmm527124:ijmm527124-math-0001

,

urn:x-wiley:01611712:media:ijmm527124:ijmm527124-math-0002

,
are studied. Conditions are given that lead to an asymptotic equivalence between certain of the solutions of (1) and certain of the solutions of (2). The case where the perturbation f(t, y) depends on a functional argument is also discussed.
Modified Gauss‐Legendre, Lobatto and Radau cubature formulas for the numerical evaluation of 2‐D singular integrals
Authors: Theocaris P. S.
Published: September 2002

A numerical technique, first reported in 1979 in refs.[1] and [2], for the numerical evaluation of two‐dimensional Cauchy-type principal‐value integrals, is
extended in this paper to include several cubature formlas of the Radau and Lobatto types. For the construction of such a cubature formula the 2‐D singular integral is considered as an iterated one, and the second‐order pole involved in this integral analyzed into a pair of complex poles. Based on this procedure, the methods of numerical integration, valid for one‐dimensional singular integrals, are extanded to the case of two‐dimensional singular integrals. The cubature formulas of the Lobatto‐ and Radau‐type are now formulated to include the cases where some of the desired abscissas may be chosen accordins to any appropriate criterion.

Moreover, the theory developed is enlarged to include the case of a 2‐D principal‐value integral, containing a logarithmic singularity. The validity of the results is illustrated by considering certain numerical examples. Furthermore, a complete analysis of the convergence and the construction of error estimates is also presented.
A scalar geodesic deviation equation and a phase theorem
Authors: Choudhury P. , Dolan P. , Swaminarayan N. S.
Published: September 2002

A scalar equation is derived for η, the distance between two structureless test particles falling freely in a gravitational field:

urn:x-wiley:01611712:media:ijmm427949:ijmm427949-math-0001

.
An amplitude, frequency and a phase are defined for the relative motion. The phases are classed as elliptic, hyperbolic and parabolic according as

urn:x-wiley:01611712:media:ijmm427949:ijmm427949-math-0002

In elliptic phases we deduce a positive definite relative energy E and a phase‐shift theorem. The relevance of the phase‐shift theorem to gravitational plane waves is discussed.
An analytical solution of Bohr′s collective hamiltonian
Authors: El-Adawi M. K. , Ismail H. A. , Shalaby S. A. , Sayed E. M.
Published: September 2002

The collective states of  126Xe,  128Xe,  130Xe, and  130Be, 52 < z, N ≤ 116 are studied using Bohr′s Collective Hamiltonian and a simple analytic form for the potential. The energy levels are calculated for this model and the results are compared with previously published experimental and calculated values.
Some isometrical identities in the wave equation
Authors: Saitoh Saburou
Published: September 2002

We consider the usual wave equation utt(x, t) = c2uxx(x, t) on the real line with some typical initial and boundary conditions. In each case, we establish a natural isometrical identity and inverse formula between the sourse function and the response function.
Quasiconformal extensions for some geometric subclasses of univalent functions
Authors: Brown Johnny E.
Published: September 2002

Let S denote the set of all functions f which are analytic and univalent in the unit disk D normalized so that f(z) = z + a2z2 + …. Let S∗ and C be those functions f in S for which f(D) is starlike and convex, respectively. For 0 ≤ k < 1, let Sk denote the subclass of functions in S which admit (1 + k)/(1 − k)‐quasiconformal extensions to the extended complex plane. Sufficient conditions are given so that a function f belongs to Sk ⋂ S∗ or Sk ⋂ C. Functions whose derivatives lie in a half‐plane are also considered and a Noshiro‐Warschawski‐Wolff type sufficiency condition is given to determine which of these functions belong to Sk. From the main results several other sufficient conditions are deduced which include a generalization of a recent result of Fait, Krzyz and Zygmunt.
Dual integral equations with Fox′s H‐function kernel
Authors: Kalia R. N.
Published: September 2002

The dual integral equations involving Bessel function kernels were first considered by Weber in 1873. The problem comprised of finding potential of an electrified disc which belongs to a general category of mixed boundary value problems. Titchmarsh gave the formal solution using Wiener‐Hopf procedure. We use this direct method as improvised by Busbridge to solve a class of dual integral equations which can be reduced to other known kernels by particularizing the parameters in the Fox′s H‐function.
Fixed points and self‐reference
Authors: Smullyan Raymond M.
Published: September 2002

It is shown how Gödel′s famous diagonal argument and a generalization of the recursion theorem are derivable from a common construation. The abstract fixed point theorem of this article is independent of both metamathematics and recursion theory and is perfectly comprehensible to the non‐specialist.
Preconvergence compactness and P‐closed spaces
Authors: Herrmann Robert A.
Published: September 2002

In this article the major result characterizes preconvergence compactness in terms of the preconvergence closedness of second projections. Applying this result to a topological space (X, T) yields similar characterizations for H‐closed, nearly compact, completely Hausdorff‐closed, extremely disconnected Hausdorff‐closed, Urysohn‐closed, S‐closed and R‐closed spaces, among others. Moreover, it is established that the s‐convergence of Thompson (i.e. rc‐convergence) is equivalent to topological convergence where the topology has as a subbase the set of all regular‐closed elements of T.
On a method for inverse theorems for (C, 1) and gap (C, 1) summability
Authors: Maric Vojislav , Tomić Miodrag
Published: September 2002

A simple method for proving several theorems of Tauberian and Mercerian type for (C, 1) and gap (C, 1) summability is presented.
Almost‐periodicity in linear topological spaces and applications to abstract differential equations
Authors: N′Guerekata Gaston Mandata
Published: September 2002

Let E be a complete locally convex space (l.c.s.) and f : R → E a continuous function; then f is said to be almost‐periodic (a.p.) if, for every neighbourhood (of the origin in E) U, there exists ℓ = ℓ(U) > 0 such that every interval [a, a + ℓ] of the real line contains at least one τ point such that f(t + τ) − f(t) ∈ U for every t ∈ R. We prove in this paper many useful properties of a.p. functions in l.c.s, and give Bochner′s criteria in Fréchet spaces.
A fundamental special‐relativistic theory valid for all real‐valued speeds
Authors: Sewjathan Vedprakash
Published: September 2002

This paper constitutes a fundamental rederivation of special relativity based on the c‐invariance postulate but independent of the assumption (Einstein [1], Kittel et al [2], Recami [3]), the equivalence principle, homogeneity of space‐time, isotropy of space, group properties and linearity of space‐time transformations or the coincidence of the origins of inertial space‐time frames. The mathematical formalism is simpler than Einstein′s [4] and Recami′s [3]. Whilst Einstein′s subluminal and Recami′s superluminal theories are rederived in this paper by further assuming the equivalence principle and “mathematical inverses” [4,3], this paper derives (independent of these assumptions) with physico‐mathematical motivation an alternate singularity‐free special‐relativistic theory which replaces Einstein′s factor and Recami′s extended‐relativistic factor by , where n equals the value of as |V| → c. In this theory both Newton′s and Einstein′s subluminal theories are experimentally valid on account of negligible terms. This theory implies that non‐zero rest mass luxons will not be detected as ordinary non‐zero rest mass bradyons because of spatial collapse, and non‐zero rest mass tachyons are undetectable because they exist in another cosmos, resulting in a supercosmos of matter, with the possibility of infinitely many such supercosmoses, all moving forward in time. Furthermore this theory is not based on any assumption giving rise to the twin paradox controversy. The paper concludes with a discussion of the implications of this theory for general relativity.
Some radius of convexity problems for certain classes of analytic functions
Authors: Noor Khalida I. , Al-Madifer Hailah
Published: September 2002

In this paper we consider some radius of convexity problems for certain classes of analytic functions. These classes, in general, are related with functions of bounded boundary rotation.
Longitudinal dispersion of tracer particles in a channel bounded by Porous media using slip condition
Authors: Pal Dulal , Veerabhadraiah R. , Shivakumar P. N. , Rudraiah N.
Published: September 2002

Longitudinal dispersion of solute in a channel bounded by porous layers is studied using the analysis of Taylor [4] with BJ slip condition. The results of the present analysis are compared with those of Fung and Tang [2] obtained from using the no‐slip condition. It is found that the effect of slip is significant only in the case when the membrane is permeable to solvent but not to the tracer. However, in the case when the membrane is permeable to both the tracer and the solvent, we find that our results coincide with those of Fung and Tang [2].
Asymptotic solution of the low Reynolds‐number flow between two co‐axial cones of common apex
Authors: Serag-Eldin M. A. , Gayed Y. K.
Published: September 2002

The paper is concerned with the axi‐symmetrlc, incompressible, steady, laminar and Newtonian flow between two, stationary, conical‐boundaries, which exhibit a common apex but may include arbitrary angles. The flow pattern and pressure field are obtained by solving the pertinent Navier‐Stokes′ equations in the spherical coordinate system. The solution is presented in the form of an asymptotic series, which converges towards the creeping flow solution as a cross‐sectional Reynolds‐number tends to zero. The first term in the series, namely the creeping flow solution, is given in closed form; whereas, higher order terms contain functions which generally could only be expressed in infinite series form, or else evaluated numerically. Some of the results obtained for converging and diverging flows are displayed and they are demonstrated to be plausible and informative.
Dynamical properties of maps derived from maps with strong negative Schwarzian derivative
Authors: Boyarsky Abraham
Published: September 2002

A strong Schwarzian derivative is defined, and it is shown that the convolution of a function with a map from an interval into itself having negative strong Schwarzian derivative is a function with negative Schwarzian derivative. Such convolutions have 0 as a stable periodic point and at most one other stable periodic orbit in the interior of the domain.
scattering of surface waves by a half immersed circular cylinder in fluid of finite depth
Authors: Mandel Birendranath , Goswami Sudip Kumar
Published: September 2002

A train of surface waves is normally incident on a half immersed circular cylinder in a fluid of finite depth. Assuming the linearized theory of fluid under gravity an integral equation for the scattered velocity potential on the half immersed surface of the cylinder is obtained. It has not been found possible to solve this in closed form even for infinite depth of fluid. Our purpose is to obtain the asymptotic effect of finite depth “h” on the transmission and reflection coefficients when the depth is large. It is shown that the corrections to be added to the infinite depth results of these coefficients can be expressed as algebraic series in powers of a/h starting with (a/h) 2 where “a” is the radius of the circular cylinder. It is also shown that the coefficients of (a/h) 2 in these corrections do not vanish identically.
Uniform distribution of Hasse invariants
Authors: Mollin R. A.
Published: September 2002

I. Schur′s study of simple algebras around the turn of the century, and
subsequent investigations by R. Brauer, E. Witt and others, were later reformulated in terms of what is now called the Schur subgroup of the Brauer group. During the last twenty years this group has generated substantial interest and numerous palatable results have ensued. Among these is the discovery that elements of the Schur group satisfy uniform distribution of Hasse invariants. It is the purpose of this paper to continue an investigation of the latter concept and to highlight certain applications of these results, not only to the Schur group, but also to embeddings of simple
algebras and extensions of automorphisms, among others.
Laplace transform pairs of N‐dimensions
Authors: Dahiya R. S.
Published: September 2002

In this paper I prove a theorem to obtain new n‐dimensional Laplace transform pairs.
A note on exponentially bounded stopping times of certain one‐sample sequential rank order tests
Authors: Govindarajulu Z.
Published: September 2002

A simple proof of the exponential boundedness of the stopping time of the one‐sample sequential probability ratio tests (SPRT′s) is obtained.
Weak gardens of Eden for 1‐dimensional tessellation automata
Authors: Taylor Michael D.
Published: September 2002

If T is the parallel map associated with a 1‐dimensional tessellation automaton, then we say a configuration f is a weak Garden of Eden for T if f has no pre‐image under T other than a shift of itself. Let WG(T) = the set of weak Gardens of Eden for T and G(T) = the set of Gardens of Eden (i.e., the set of configurations not in the range of T). Typically members of WG(T) − G(T) satisfy an equation of the form Tf = Smf where Sm is the shift defined by (Smf)(j) = f(j + m). Subject to a mild restriction on m, the equation Tf = Smf always has a solution f, and all such solutions are periodic. We present a few other properties of weak Gardens of Eden and a characterization of WG(T) for a class of parallel maps we call (0, 1)‐characteristic transformations in the case where there are at least three cell states.
Gallilei covariant quantum mechanics in electromagnetic fields
Authors: Wilhelm H. E.
Published: September 2002

A formulation of the quantum mechanics of charged particles in time‐dependent electromagnetic fields is presented, in which both the Schroedinger equation and wave equations for the electromagnetic potentials are Galilei covariant, it is shown that the Galilean relativity principle leads to the introduction of the electromagnetic substratum in which the matter and electromagnetic waves propagate. The electromagnetic substratum effects are quantitatively significant for quantum mechanics in reference frames, in which the substratum velocity w is in magnitude comparable with the velocity of light c. The electromagnetic substratum velocity w occurs explicitly in the wave equations for the electromagnetic potentials but not in the Schroedinger equation.
Convex curves of bounded type
Authors: Goodman A. W.
Published: September 2002

Let C be a simple closed convex curve in the plane for which the radius of curvature ρ is a continuous function of the arc length. Such a curve is called a convex curve of bounded type, if ρ lies between two fixed positive bounds. Here we give a new and simpler proof of Blaschke′s Rolling Theorem. We prove one new theorem and suggest a number of open problems.
On convergence of (μ, ν)‐sequences of unisolvent rational approximants to meromorphic functions in Cn
Authors: Lutterodt C. H.
Published: September 2002

A generalization of the classical Montessus de Ballore theorem in ℂn and some related theorems are discussed. Non‐Montessus type of convergence in ℝ2n dimensional Lebesgue measure is presented linking it to a result of Gonĉar.
On two new characterizations of Steiltjes transforms for distributions
Authors: Sinha Sunil Kumar
Published: September 2002

Two new characterizations of the Stieltjes transform for distribution are
developed, using two transformations on the space of distributions viz., dilation Un and exponential shifts T−p. The standard theorem on analyticity, uniqueness and invertibility of the Stieltjes transform are proved, using the new characterization as the definition of the Stieltjes transform.
Categorical constructions in graph theory
Authors: Bumby Richard T. , Latch Dana May
Published: September 2002

This paper presents some graph‐theoretic questions from the viewpoint of the portion of category theory which has become common knowledge. In particular, the reader is encouraged to consider whether there is only one natural category of graphs and how theories of directed graphs and undirected graphs are related.
Relative integral basis for algebraic number fields
Authors: Haghighi Mohmood
Published: September 2002

At first conditions are given for existence of a relative integral basis for with [K; k] = n. Then the constrtiction of the ideal I in is given for proof of existence of a relative integral basis for . Finally existence and construction of the relative integral basis for for some values of n are given.
Basic singularities in the theory of internal waves with surface tension
Authors: Gorgui M. A. , Faltas M. S.
Published: September 2002

The study of linearized interface wave problems for two superposed fluids often involves the consideration of different types of singularities in one of the two fluids. In this paper the line and point singularities are investigated for the case when each fluid is of finite constant depth. The effect of surface tension at the surface of separation is included.
The rational canonical form of a matrix
Authors: Devitt J. S. , Mollin R. A.
Published: September 2002

The purpose of this paper is to provide an efficient algorithmic means of determining the rational canonical form of a matrix using computational symbolic algebraic manipulation packages, and is in fact the practical implementation of a classical mathematical method.
Recurrent and weakly recurrent points in βG
Authors: Nassar Mostafa
Published: September 2002

It is shown in this paper that if βG is the Stone‐Čech compactification of a group G, and G satisfying a certain condition, then there is a weakly recurrent point in βG which is not almost periodic, and if another condition will be added, then there is a recurrent point in βG which is not almost periodic point.
On the characteristic function of a sum of M‐dependent random variables
Authors: Rhee Wansoo T.
Published: September 2002

Let S = f1 + f2 + …+fn be a sum of 1‐dependent random variables of zero mean. Let σ2 = ES2, . There is a universal constant a such that for a|t|L < 1, we have

urn:x-wiley:01611712:media:ijmm781385:ijmm781385-math-0002

This bound is a very useful tool in proving Berry‐Esseen theorems.
The GCD property and irreduciable quadratic polynomials
Authors: Malik Saroj , Mott Joe L. , Zafrullah Muhammad
Published: September 2002

The proof of the following theorem is presented: If D is, respectively, a Krull domain, a Dedekind domain, or a Prüfer domain, then D is correspondingly a UFD, a PID, or a Bezout domain if and only if every irreducible quadratic polynomial in D[X] is a prime element.
On the non‐existence of some interpolatory polynomials
Authors: Anderson C. H. , Prasad J.
Published: September 2002

Here we prove that if xk, k = 1, 2, …, n + 2 are the zeros of (1 − x2)Tn(x) where Tn(x) is the Tchebycheff polynomial of first kind of degree n, αj, βj, j = 1, 2, …, n + 2 and γj, j = 1, 2, …, n + 1 are any real numbers there does not exist a unique polynomial Q3n+3(x) of degree ≤3n + 3 satisfying the conditions: Q3n+3(xj) = αj, Q3n+3(xj) = βj, j = 1, 2, …, n + 2 and , j = 2, 3, …, n + 1. Similar result is also obtained by choosing the roots of (1 − x2)Pn(x) as the nodes of interpolation where Pn(x) is the Legendre polynomial of degree n.
On the computation of the class numbers of some cubic fields
Authors: Scarowsky Manny , Boyarsky Abraham
Published: September 2002

Class numbers are calculated for cubic fields of the form x3 + 12Ax − 12 = 0, A > 0, for 1 ≤ a ≤ 17, and for some other values of A. These fields have a known unit, which under certain conditions is the fundamental unit, and are important in studying the Diophantine Equation x3 + y3 + z3 = 3.
Functional differential equations—a reciprocity principle
Authors: Williams Lloyd K.
Published: September 2002

The functional differential equations proposed for solution here are mainly ordinary differential equations with fairly general argument deviations. Included among them are equations with involutions and some with reflections of the argument. Solutions will be obtained by quadratures in terms of implicitly defined functions. They have a wide range of applicability from the stability theory of differential‐difference equations to electrodynamics and biological models.
Oscillation theorems for second order nonlinear differential equations with deviating arguments
Authors: Grace S. R. , Lalli B. S.
Published: September 2002

New oscillation criteria for the oscillatory behaviour of the differential

urn:x-wiley:01611712:media:ijmm148051:ijmm148051-math-0001

and

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are established
Blumberg property versus almost continuity
Authors: Piotrowski Z.
Published: September 2002

Some relations between the Blumberg property and almost continuity are
established. A problem of S.‐Y. Lin and Y.‐F. Lin is completely resolved.
Finite p′‐nilpotent groups. I
Authors: Srinivasan S.
Published: September 2002

In this paper we consider finite p′‐nilpotent groups which is a generalization of finite p‐nilpotent groups. This generalization leads us to consider the various special subgroups such as the Frattini subgroup, Fitting subgroup, and the hypercenter in this generalized setting. The paper also considers the conditions under which product of p′‐nilpotent groups will be a p′‐nilpotent group.
On the reconstraction of the matching polynomial and the reconstruction conjecture
Authors: Farrell E. J. , Wahid S. A.
Published: September 2002

Two results are proved. (i) It is shown that the matching polynomial is both node and edge reconstructable. Moreover a practical method of reconstruction is given. (ii) A technique is given for reconstructing a graph from its node‐deleted and edge‐deleted subgraphs. This settles one part of the Reconstruction Conjecture.
A new proof of a theorem of Toeplitz in summability theory
Authors: Antosik P. , Srinivasan V. K.
Published: September 2002

The object of this paper is to give a new proof of a Theorem in Summability, as an application of a result of Antosik.
An H1‐Galerkin method for a Stefan problem with a quasilinear parabolic equation in non‐divergence form
Authors: Pani A. K. , Das P. C.
Published: September 2002

Optimal error estimates in L2, H1 and H2‐norm are established for a single phase Stefan problem with quasilinear parabolic equation in non‐divergence form by an H1‐Galerkin procedure.
On the q‐Konhauser biorthogonal polynomials
Authors: Madhekar H. C. , Chamle V. T.
Published: September 2002

Recently Al‐Salam and Verma discussed two polynomial sets and which are biorthogonal on (0, ∞) with respect to a continuous or discrete distribution function. For the polynomials the operational formula is derived.
A new class of composition operators
Authors: Pattanayak S. , Mohapatra C. K. , Mishra A. K.
Published: September 2002

A new class of composition operators Pϕ : H2(T) → H2(T), with is introduced. Sufficient conditions on ϕ for Pϕ to be bounded and Hilbert‐Schmidt are obtained. Properties of Pϕ with ϕ(eit) = aeit + be−it for different values of the parameters a and b have been investigated. This paper concludes with a discussion on the compactness of Pϕ.
Typically real functions and typically real derivatives
Authors: Trimble S. Y.
Published: September 2002

Sufficient conditions, in terms of typically real derivatives, are given which force functions to be univalent.
Nonseparated manifolds and completely unstable flows
Authors: Goel Sudhir K.
Published: September 2002

We define an order structure on a nonseparated n‐manifold. Here, a nonseparated manifold denotes any topological space that is locally Euclidean and has a countable basis; the usual Hausdorff separation property is not required. Our
result is that an ordered nonseparated n‐manifold X can be realized as an ordered orbit space of a completely unstable continuous flow ϕ on a Hausdorff (n + 1)‐manifold E.
A note on rings which are multiplicatively generated by idempotents and nilpotents
Authors: Abu-Khuzam Hazar
Published: September 2002

We give the structure of certain rings which are multiplicatively generated by nilpotents or multiplicatively generated by idempotents and nilpotents.
Two properties of the power series ring
Authors: Al-Ezeh H.
Published: September 2002

For a commutative ring with unity, A, it is proved that the power series ring A〚X〛 is a PF‐ring if and only if for any two countable subsets S and T of A such that , there exists such that bc = b for all b ∈ S. Also it is proved that a power series ring A〚X〛 is a PP‐ring if and only if A is a PP‐ring in which every increasing chain of idempotents in A has a supremum which is an idempotent.
Coefficient estimates for some classes of p‐valent functions
Authors: Aouf M. K.
Published: September 2002

Let Ap, where p is a positive integer, denote the class of functions which are analytic in U = {z : |z| < 1}.

For 0 < λ ≤ 1, , 0 ≤ β < p, let Fλ(α, β, p) denote the class of functions f(z) ∈ Ap which satisfy the condition

urn:x-wiley:01611712:media:ijmm136791:ijmm136791-math-0003

where .

Also let Cλ(b, p), where p is a positive integer, 0 < λ < 1, and b ≠ 0 is any complex number, denote the class of functions g(z) ∈ Ap which satisfy the condition

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urn:x-wiley:01611712:media:ijmm136791:ijmm136791-math-0006

In this paper we obtain sharp coefficient estimates for the above mentioned classes.
On a class of functions unifying the classes of Paatero, Robertson and others
Authors: Bhargava S. , Rao S. Nanjunda
Published: September 2002

We study a class of analytic functions which unifies a number of classes studied previously by Paatero, Robertson, Pinchuk, Moulis, Mocanu and others. Thus our class includes convex and starlike functions of order β, spirallike functions of order β and functions for which zf′ is spirallike of order β, functions of boundary rotation utmost kπ, α‐convex functions etc. An integral representation of Paatero and a variational principle of Robertson for the class Vk of functions of bounded boundary rotation, yield some representation theorems and a variational principle for our class. A consequence of these basic theorems is a theorem for this class which unifies some earlier results concerning the radii of convexity of functions in the class of Moulis and those concerning the radii of starlikeness of functions in the classes Uk of Pinchuk and U2(β) of Robertson etc. By applying an estimate of Moulis concerning functions in , we obtain an inequality in the class which will contain an estimate for the Schwarzian derivative of functions in the class and in particular the estimate of Moulis for the Schwarzian of functions in .