bluuebunny/crossref_metadata_2025 huggingface dataset:
Method of replacing the variables for generalized symmetry of the D′Alembert equation
Authors: Kotel′nikov Gennadii A.
Published: September 2002

We show that by the generalized understanding of symmetry, the
D′Alembert equation for one component field is invariant with
respect to arbitrary reversible coordinate transformations.
Intermediate values and inverse functions on non‐Archimedean fields
Authors: Shamseddine Khodr , Berz Martin
Published: September 2002

Continuity or even differentiability of a function on a closed
interval of a non‐Archimedean field are not sufficient for the
function to assume all the intermediate values, a maximum, a
minimum, or a unique primitive function on the interval. These
problems are due to the total disconnectedness of the field in
the order topology. In this paper, we show that differentiability
(in the topological sense), together with some additional mild
conditions, is indeed sufficient to guarantee that the function
assumes all intermediate values and has a differentiable inverse
function.
Optimal bound for the number of (−1)‐curves on extremal rational surfaces
Authors: Lahyane Mustapha
Published: September 2002

We give an optimal bound for the number of (−1)‐curves on an extremal rational surface X under the assumption that −KX is numerically effective and having self‐intersection zero. We also prove that a nonelliptic extremal rational surface has at most nine (−1)‐curves.
A geometrical analysis of the field equations in field theory
Authors: Echeverría-Enríquez A. , Muñoz-Lecanda M. C. , Román-Roy N.
Published: September 2002

We give a geometric formulation of the field equations in the
Lagrangian and Hamiltonian formalisms of classical field theories
(of first order) in terms of multivector fields. This formulation
enables us to discuss the existence and nonuniqueness of
solutions of these equations, as well as their integrability.
Ar (λ)‐weighted Caccioppoli‐type and Poincaré‐type inequalities for A‐harmonic tensors
Authors: Liu Bing
Published: September 2002

We prove a local version of weighted Caccioppoli‐type inequality,
then we prove a version of weighted Poincaré‐type inequality
for A‐harmonic tensors both locally and globally.

Ar(λ)-weighted Caccioppoli-type and Poincaré-type inequalities
for A-harmonic tensors (erratum)dx.doi.org/10.1155/S0161171203305320
Application of uniform asymptotics to the fifth Painlevé transcendant
Authors: Lu Youmin , Shao Zhoude
Published: September 2002

We apply the uniform asymptotics method to the fifth Painlevé transcendants, find its asymptotics of the form y = −1 + t−1/2A(t) as t → ∞ along the positive t‐axis, and obtain the corresponding monodromy data.
On Matlis dualizing modules
Authors: Enochs Edgar E. , López-Ramos J. A. , Torrecillas B.
Published: September 2002

We consider rings admitting a Matlis dualizing module E. We argue that if R admits two such dualizing modules, then a module is reflexive with respect to one if and only if it is reflexive with respect to the other. Using this fact we argue that
the number (whether finite or infinite) of distinct dualizing modules equals the number of distinct invertible
(R, R)‐bimodules. We show by example that this number can be greater than one.
Controllability of semilinear stochastic delay evolution equations in Hilbert spaces
Authors: Balasubramaniam P. , Dauer J. P.
Published: September 2002

The controllability of semilinear stochastic delay evolution equations is studied by using a stochastic version of the well‐known Banach fixed point theorem and semigroup theory. An
application to stochastic partial differential equations is given.
Explicit L2 inequalities for parabolic and pseudoparabolic equations with Neumann boundary conditions
Authors: Kuttler J. R. , Sigillito V. G.
Published: September 2002

Explicit L2 inequalities are derived for second and third order diffusion equations with Neumann boundary conditions. Such inequalities are useful in approximating solutions to partial differential equations by the method of a priori inequalities.
A note on strictly cyclic Shifts on ℓp
Authors: Fricke Gerd H.
Published: September 2002

In this paper the author shows that a well known sufficient condition for strict cycliclty of a weighted shift on ℓp is not a necessary condition for any p with 1 < p < ∞.
On the range of completely bounded maps
Authors: Loebl Richard I.
Published: September 2002

It is shown that if every bounded linear map from a C*‐algebra α to a von Neumann algebra β is completely bounded, then either α is finite‐dimensional or β⫅𝒞 ⊗ Mn, where 𝒞 is a commutative von Neumann algebra and Mn is the algebra of n × n complex matrices.
A Stone‐Weierstrass theorem for group representations
Authors: Repka Joe
Published: September 2002

It is well known that if G is a compact group and π a faithful (unitary) representation, then each irreducible representation of G occurs in the tensor product of some number of copies of π and its contragredient. We generalize this result to a separable type I locally compact group G as follows: let π be a faithful unitary representation whose matrix coefficient functions vanish at infinity and satisfy an appropriate integrabillty condition. Then, up to isomorphism, the regular representation of G is contained in the direct sum of all tensor products of finitely many copies of π and its contragredient.

We apply this result to a symplectic group and the Weil representation associated to a quadratic form. As the tensor products of such a representation are also Weil representations (associated to different forms), we see that any discrete series representation can be realized as a subrepresentation of a Weil representation.
On separable extensions of group rings and quaternion rings
Authors: Szeto George
Published: September 2002

The purposes of the present paper are (1) to give a necessary and sufficient condition for the uniqueness of the separable idempotent for a separable group ring extension RG(R may be a non‐commutative ring), and (2) to give a full description of the set of separable idempotents for a quaternion ring extension RQ over a ring R, where Q are the usual quaternions i, j, k and multiplication and addition are defined as quaternion algebras over a field. We shall show that RG has a unique separable idempotent if and only if G is abelian, that there are more than one separable idempotents for a separable quaternion ring RQ, and that RQ is separable if and only if 2 is invertible in R.
Gaussian integers with small prime factors
Authors: Hazlewood D. G.
Published: September 2002

Let ψG(xt, x) denote the number of Gaussian integers with norm not exceeding x2t whose Gaussian prime factors have norm not exceeding x2. Previous estimates have required restrictions on the parameter t with respect to x. The purpose of this note is to present asymptotic estimates for ψG(xt, x) for all ranges of the parameter t with respect to x.
Sign changes in linear combinations of derivatives and convolutions of Polya frequency functions
Authors: Nahmias Steven , Proschan Frank
Published: September 2002

We obtain upper bounds on the number of sign changes of linear
combinations of derivatives and convolutions of Polya frequency functions using the variation diminishing properties of totally positive functions. These constitute extensions of earlier results of Karlin and Proschan.
Rings with a finite set of nonnilpotents
Authors: Putcha Mohan S. , Yaqub Adil
Published: September 2002

Let R be a ring and let N denote the set of nilpotent elements of R. Let n be a nonnegative integer. The ring R is called a θn‐ring if the number of elements in R which are not in N is at most n. The following theorem is proved: If R is a θn‐ring, then R is nil or R is finite. Conversely, if R is a nil ring or a finite ring, then R is a θn‐ring for some n. The proof of this theorem uses the structure theory of rings, beginning with the division ring case, followed by the primitive ring case, and then the semisimple ring case. Finally, the general case is considered.
Alternative integration procedure for scale‐invariant ordinary differential equations
Authors: Rosen Gerald
Published: September 2002

For an ordinary differential equation invariant under a one‐parameter group of scale transformations x → λx, y → λαy, y′ → λα−1y′, y″ → λα−2y″, etc., it is shown by example that an explicit analytical general solution may be obtainable in parametric form in terms of the scale‐invariant variable . This alternative integration may go through, as it does for the example equation y″ = kxy−2y′, in cases for which the customary dependent and independent variables (x−αy) and (ℓnx) do not yield an analytically integrable transformed equation.
Equation of the fixed membrane in the n‐dimensional space: some remarks on the maxima of the eigenfunctions subjected to various norms
Authors: Biollay Yves
Published: September 2002

We show in this paper that the sequence {max|uk|}, where the uk are the eigenfunctions of the problem Δu + λu = 0 in D ⊂ Rn and u = 0 on ∂D, is not bounded generally if one imposes the norm ∫Du2p(x)dx = 1, p = (1), 2, 3, …. The same holds with the norm ∫D|gradu|2pdx = 1 when n > 4p − 1. On the other hand, if D ⊂ R2, resp. R3 the norm ∫D|gradu|2dx = 1 implies , resp. max|uk| = 0(1).
Prestarlike functions with negative coefficients
Authors: Silverman H. , Silvia E. M.
Published: September 2002

The extreme points for prestarlike functions having negative coefficients are determined. Coefficient, distortion and radii of univalence, starlikeness, and convexity theorems are also obtained.
Equivalence classes of matrices over a finite field
Authors: Mullen Gary L.
Published: September 2002

Let Fq = GF(q) denote the finite field of order q and F(m, q) the ring of m × m matrices over Fq. Let Ω be a group of permutations of Fq. If A, BϵF(m, q) then A is equivalent to B relative to Ω if there exists ϕϵΩ such that ϕ(A) = B where ϕ(A) is computed by substitution. Formulas are given for the number of equivalence classes of a given order and for the total number of classes induced by a cyclic group of permutations.
On slow oscillation and nonoscillation in retarded equations
Authors: Singh Bhagat
Published: September 2002

Sufficient conditions have been found to ensure that all oscillatory solutions of

urn:x-wiley:01611712:media:ijmm153934:ijmm153934-math-0001

are slowly oscillating. This behaviour is further linked to nonoscillation.
An elementary inequality
Authors: Haber Seymour
Published: September 2002

An elementary inequality is proved in this note.
A note on local asymptotic behaviour for Brownian motion in Banach spaces
Authors: Chang Mou-Hsiung
Published: September 2002

In this paper we obtain an integral characterization of a two‐sided upper function for Brownian motion in a real separable Banach space. This characterization generalizes that of Jain and Taylor [2] where B = ℝn. The integral test obtained involves the index of a mean zero Gaussian measure on the Banach space, which is due to Kuelbs [3]. The special case that when B is itself a real separable Hilbert space is also illustrated.
Arithmatical consequences of two identities of B. Gordon
Authors: Ewell John A.
Published: September 2002

From two partition identities of Basil Gordon the author derives two recursive formulas for the sum‐of‐divisors function. A third application yields an alternate proof of Rmanujan′s theorem on the divisibility of certain values of the partition function by the modulus 5.
On osculatory interpolation by trigonometric polynomials
Authors: Newman D. J. , Rubel L. A.
Published: September 2002

A short and simple proof is given that osculatory interpolation by
trigonometric polynomials is always possible.
The continous Legendre transform, its inverse transform, and applications
Authors: Butzer P. L. , Stens R. L. , Wehrens M.
Published: September 2002

This paper is concerned with the continuous Legendre transform, derived from the classical discrete Legendre transform by replacing the Legendre polynomial Pk(x) by the function Pλ(x) with λ real. Another approach to T.M. MacRobert′s inversion formula is found; for this purpose an inverse Legendre transform, mapping L1(ℝ+) into L2(−1, 1), is defined. Its inversion in turn is naturally achieved by the continuous Legendre transform. One application is devoted to the Shannon sampling theorem in the Legendre frame together with a new type of error estimate. The other deals with a new representation of Legendre functions giving information about their behaviour near the point x = −1.
On the initial value problem for a partial differential equation with operator coefficients
Authors: El-Borai Mahmoud M.
Published: September 2002

In the present work it is studied the initial value problem for an equation of the form

urn:x-wiley:01611712:media:ijmm267936:ijmm267936-math-0001

where L is an elliptic partial differential operator and (Lj : j = 1, …, k) is a family of partial differential operators with bounded operator coefficients in a suitable function space. It is found a suitable formula for solution. The correct formulation of the Cauchy problem for this equation is also studied.
Contributions to the theory of Hermitian series III. Meanvalues
Authors: Hille Einar
Published: September 2002

Let f(z) be holomorphic in the strip −σ < y < σ < ∞ and satisfy the conditions for having an expansion in an Hermitian series

urn:x-wiley:01611712:media:ijmm869379:ijmm869379-math-0001

absolutely convergent in the strip. Two meanvalues

urn:x-wiley:01611712:media:ijmm869379:ijmm869379-math-0002

are discussed, directly using the condition on f(z) or via the Hermitian series. Integrals involving products hm(x + iy)hn(x − iy) are discussed. They lead to expansions of the mean squared in terms of Laguerre functions of y2 when k = 0 and in terms of Hermite functions when k = 1. The sumfunctions are holomorphic in y. They are strictly increasing when |y| increases.
Shear flow past a flat plate in hydromagnetics
Authors: Sastry S. R. N.
Published: September 2002

The problem of simple shear flow past a flat plate has been extended to the hydromagnetic case in which a viscous, electrically conducting, incompressible fluid flows past an electrically insulated flat plate with a magnetic field parallel to the plate. For simplicity all physical parameters are assumed constant. A series solution for the velocity field has been developed for small values of a magnetic parameter. The equations governing this flow field were integrated numerically It is found that the effect of the magnetic field is to diminish and increase respectively, the first and second order contributions for the skin friction.
Steady state response of a nonlinear system
Authors: Karmakar Sudhangshu B.
Published: September 2002

This paper presents a method of the determination of the steady state response for a class of nonlinear systems. The response of a nonlinear system to a given input is first obtained in the form of a series solution in the multidimensional frequency domain. Conditions are then determined for which this series solution will converge. The conversion from multidimensions to a single dimension is then made by the method of association of variables, and thus an equivalent linear model of the nonlinear system is obtained. The steady state response is then found by any technique employed with linear system.
Representation theory of finite abelian groups applied to a linear diatomic crystal
Authors: Boyd J. N. , Raychowdhury P. N.
Published: September 2002

After a brief review of matrix representations of finite abelian groups, projection operators are defined and used to compute symmetry coordinates for systems of coupled harmonic oscillators. The Lagrangian for such systems is discussed in the event that the displacements along the symmetry coordinates are complex. Lastly, the natural frequencies of a linear, diatomic crystal are determined through application of the Born cyclic condition and the determination of the symmetry coordinates.
The Heegaard genus of manifolds obtained by surgery on links and knots
Authors: Clark Bradd
Published: September 2002

Let L ⊂ S3 be a fixed link. It is shown that there exists an upper bound on the Heegaard genus of any manifold obtained by surgery on L. The tunnel number of L, T(L), is defined and used as an upper bound. If K′ is a double of the knot K, it is shown that T(K′) ≤ T(K) + 1. If M is a manifold obtained by surgery on a cable link about K which has n components, it is shown that the Heegaard genus of M is at most T(K) + n + 1.
On the foundations of a new approach to statistical mechanics of classical systems
Authors: Bagghi S. N.
Published: September 2002

It has been known for a long time that the fundamental approaches to equilibrium and nonequillbrium statistical mechanics available at present lead to physical and mathematical inconsistencies for dense systems. A new approach, whose foundation lies in the more powerful statistical method of counting complexions, had been formulated which not only overcomes all these difficulties but also yields satisfactory physical results for dense ′hard sphere′ systems as well as for systerns containing charged particles for which a mathematically consistent theory cannot even be formulated if we follow the available formalisms. The specific computational techniques rely on the following four recipes which also are justified theoretically.

(i) The phase space (μ‐space) is separated into configuration space and momentum
space.

(ii) The configuration space is partitioned into cells of size b, the exclusion volume of Boltzmann.

(iii) The partition function (pf) due to the kinetic energy is obtained directly from Planck′s “Zustandssumme” pertaining to the kinetic energies of the individual particles.

(iv) Instead of calculating Gibbs′ configuration integral, one obtains the average potential of the system from a suitable nonlinear partial differential equatlon (pde) and finally the “excess” free energy of the system due to the potential field alone by utilizing Debye‐Hueckel′s concept of ion‐atmosphere and their technique for calculating the free energy.

Even in the linear approximation of the ion‐atmosphere potential this method gives reliable results for both equilibrium and transport properties of fused alkali halides.

In order to emphasize that this new approach has a secure theoretical foundation and has also considerable advantages over all other existing methods, this review offers a few brief critical remarks about the limitations and inadequacies of the concepts used in the conventional treatments of classical statistical mechanics. Further, in view of the fact that the literature on the subject of Debye‐Hueckel (DH) theory of strong electrolytes is replete with many assertions, already disproved in the past, a brief review of the controversial aspects of this theory is also presented. The next paper will show that this new approach as well as the
modified DH theory yields physical results for actual dense systems much more satisfactorily
than those which could be obtained by any other available method.
k‐space function spaces
Authors: McCoy R. A.
Published: September 2002

A study is made of the properties on X which characterize when Cπ(X) is a k‐space, where Cπ(X) is the space of real‐valued continuous functions on X having the topology of pointwise convergence. Other properties related to the k‐space property are also considered.
A numerical method for the solution of plane crack problems in finite media
Authors: Theocaris P. S. , Ioakimidis N.
Published: September 2002

A general method for the solution of plane isotropic elasticity crack problems inside a finite medium of arbitrary shape or an infinite medium with holes of arbitrary shape is presented. This method is based on the complex potential approach of plane elasticity problems due to Kolosov and Muskhelishvili [1] and makes no assumption on the way of loading of the cracks and of the other boundaries of the medium.

The whole problem is reduced to a complex singular integral equation along the cracks and the other boundaries and the values of the stress intensity factors at the crack tips may be evaluated directly and accurately from the numerical solution of this equation. An application of the method to a circular medium with a straight crack is also made.
Probabilistic derivation of a bilinear summation formula for the Meixner‐Pollaczek polynominals
Authors: Lee P. A.
Published: September 2002

Using the technique of canonical expansion in probability theory, a bilinear summation formula is derived for the special case of the Meixner‐Pollaczek polynomials which are defined by the generating function

urn:x-wiley:01611712:media:ijmm239895:ijmm239895-math-0002

These polynomials satisfy the orthogonality condition

urn:x-wiley:01611712:media:ijmm239895:ijmm239895-math-0003

with respect to the weight function

urn:x-wiley:01611712:media:ijmm239895:ijmm239895-math-0004

urn:x-wiley:01611712:media:ijmm239895:ijmm239895-math-0005
Rings and groups with commuting powers
Authors: Abu-Khuzam Hazar , Yaqub Adil
Published: September 2002

Let n be a fixed positive integer. Let R be a ring with identity which satisfies (i) xnyn = ynxn for all x, y in R, and (ii) for x, y in R, there exists a positive integer k = k(x, y) depending on x and y such that xkyk = ykxkand (n, k) = 1. Then R is commutative. This result also holds for a group G. It is further shown that R and G need not be commutative if any of the above conditions is dropped.
The effect of couple‐stresses on the stress concentration around a moving crack
Authors: Itou S.
Published: September 2002

The problem of a uniformly propagating finite crack in an infinite medium is solved within the linearized couple‐stress theory. The self‐equilibrated system of pressure is applied to the crack surfaces. The problem is reduced to dual integral equations and solved by a series‐expansion method. The dynamic stress‐intensity factor is computed numerically.
Permutation matrices and matrix equivalence over a finite field
Authors: Mullen Gary L.
Published: September 2002

Let F = GF(q) denote the finite field of order q and Fm×n the ring of m × n matrices over F. Let 𝒫n be the set of all permutation matrices of order n over F so that 𝒫n is ismorphic to Sn. If Ω is a subgroup of 𝒫n and A, BϵFm×n then A is equivalent to B relative to Ω if there exists Pϵ𝒫n such that AP = B. In sections 3 and 4, if Ω = 𝒫n formulas are given for the number of equivalence classes of a given order and for the total number of classes. In sections 5 and 6 we study two generalizations of the above definition.
Error estimates for the finite element solutions of variational inequalities
Authors: Noor M. Aslam
Published: September 2002

For piecewise linear approximation of variational inequalities associated
with the mildly nonlinear elliptic boundary value problems having auxiliary constraint conditions, we prove that the error estimate for u − uh in the W1,2‐norm is of order h.
A note on sufficiency in coherent models
Authors: Basu D. , Cheng S. C.
Published: September 2002

Partly of an expository nature, this article brings together a number of notions related to sufficiency in an abstract measure theoretic setting. The notion of a coherent statistical model, as introduced by Hasegawa and Perlman [6], is studied in some details. A few results are generalized and their earlier proofs simplified. Among other things, it is shown that a coherent model can be connected in the sense of Basu [2] if and only if no splitting set (Koehn and Thomas, [7])
exists.
Effect of vacuum polarization on the excitation of hydrogen atom by electron impact
Authors: Bhattacharyya Sujata , Chatterjee Lali , Roy T.
Published: September 2002

The vacuum polarization potential is included in the interaction Hamiltonian
for 1S − 2S excitation of the hydrogen atom by electron impact. The excitation amplitude calculated field theoretically is found to be lowered by

urn:x-wiley:01611712:media:ijmm467403:ijmm467403-math-0001

where t2 = 4|P−Q|2, P and Q being the momenta of the incident and scattered electrons respectively.
On holomorphic functions with certain extremal properties of its absolute values
Authors: Schmersau Dieter
Published: September 2002

This paper is concerned with a special class of holomorphic functions with extremal properties of its absolute values on arbitrary closed line segments in the complex plane. The main result is a geometrical characterization of the functions z → eaz+b, z → (az + b) n and z → (az + b) α+iβ with a, b, ∈ℂ, α, β ∈ ℝ, n ∈ ℤ.
On linear algebraic semigroups III
Authors: Putcha Mohan S.
Published: September 2002

Using some results on linear algebraic groups, we show that every connected
linear algebraic semigroup S contains a closed, connected diagonalizable subsemigroup T with zero such that E(T) intersects each regular J‐class of S. It is also shown that the lattice (E(T), ≤) is isomorphic to the lattice of faces of a rational polytope in some ℝn. Using these results, it is shown that if S is any connected semigroup with lattice of regular J‐classes U(S), then all maximal chains in U(S) have the same length.
Qualitative properties of solutions of certain fourth order linear differential equations
Authors: Taylor W. E.
Published: September 2002

This work considers differential equations of the form

urn:x-wiley:01611712:media:ijmm136247:ijmm136247-math-0001

where p, q and r are positive continuous functions defined on [0, ∞). The main concentration is on the oscillatory and asymptotic behavior of the solutions. Such an investigation is important because the above equation often arises in the study of mechanical vibrations.
Almost‐continuous path connected spaces
Authors: Herrington Larry L. , Long Paul E.
Published: September 2002

M. K. Singal and Asha Rani Singal have defined an almost‐continuous
function f : X → Y to be one in which for each x ∈ X and each regular‐open set V containing f(x), there exists an open U containing x such that f(U) ⊂ V. A space Y may now be defined to be almost‐continuous path connected if for each y0, y1 ∈ Y there exists an almost‐continuous f : I → Y such that f(0) = y0 and f(1) = y1 An investigation of these spaces is made culminating in a theorem showing when the
almost‐continuous path connected components coincide with the usual components of Y.
Combined effect of free and forced convection on MHD flow in a rotating porous channel
Authors: Rao D. R. V. Prasada , Krishna D. V. , Debnath Lokenath
Published: September 2002

This paper gives a steady linear theory of the combined effect of the free and forced convection in rotating hydromagnetic viscous fluid flows in a porous channel under the action of a uniform magnetic field. The flow is governed by the Grashof number G, the Hartmann number H, the Ekman number E, and the suction Reynolds number S. The solutions for the velocity field, temperature distribution, magnetic field, mass rate of flow and the shear stresses on the channel boundaries are obtained using a perturbation method with the small parameter S. The nature of the associated boundary layers is investigated for various values of the governing flow parameters. The velocity, the temperature, and the shear stresses are discussed numerically by drawing profiles with reference to the variations in the flow parameters.
The power mean and the logarithmic mean
Authors: Imoru Christopher Olutunde
Published: September 2002

In a very interesting and recent note, Tung‐Po Lin [1] obtained the least value q and the greatest value p such that

urn:x-wiley:01611712:media:ijmm718951:ijmm718951-math-0001

is valid for all distinct positive numbers x and y where

urn:x-wiley:01611712:media:ijmm718951:ijmm718951-math-0002

The object of this paper is to give a simpler proof than Lin′s of a more general result. More precisely, the author obtained the classes of functions fα and hα, α ∈ R such that

urn:x-wiley:01611712:media:ijmm718951:ijmm718951-math-0003
On integral transforms
Authors: Gupta K. C.
Published: September 2002

A number of interesting theorems have recently been added to the existing ones in the field of integral transforms. The new arrivals can be broadly classified under two categories. The first expresses relationship between images and originals of related functions in the transforms concerned while the second reveals interconnections existing between images of related functions in the respective transforms. An attempt has been made in this paper to unify and extend all such results by establishing two most general theorems, embracing each of the two types mentioned above, and of elucidate their basic underlying principle. Certain special cases of these theorems which are of interest in themselves and
do not seem to be recorded in the literature have also been given. Exact reference to twenty four theorems which follow as simple special cases of our theorems has also been given.
The dual of the multiplier algebra of Pedersen′s ideal
Authors: McKennon Kelly
Published: September 2002

It is shown that the dual of the multiplier algebra of Pederson′s ideal is not always spanned by its positive elements.
Inversion of the Poisson‐Hankel transform
Authors: Nasim C.
Published: September 2002

The Poisson‐Hankel transform is defined as an integral transform of the initial temperature function, with the kernel as the source solution of the generalized heat equation. In this paper a technique involving integral and differential operators has been used to effect the inversion of the Poisson‐Hankel transform.
A new formulation of the law of octic reciprocity for primes ≡±3(mod8) and its consequences
Authors: Hudson Richard H. , Williams Kenneth S.
Published: September 2002

Let p and q be odd primes with q ≡ ±3(mod8), p ≡ 1(mod8) = a2 + b2 = c2 + d2 and with the signs of a and c chosen so that a ≡ c ≡ 1(mod4). In this paper we show step‐by‐step how to easily obtain for large q necessary and sufficient criteria to have for j = 1, …, 8 (the cases with j odd have been treated only recently [3] in connection with the sign ambiguity in Jacobsthal sums of order 4. This is accomplished by breaking the formula of A.E. Western into three distinct parts involving two polynomials and a Legendre symbol; the latter condition restricts the validity of the method presented in section 2 to primes q ≡ 3(mod8) and significant modification is needed to obtain similar results for q ≡ ±1(mod8). Only recently the author has completely resolved the case q ≡ 5(mod8), j = 1, …, 8 and a sketch of the method appears in the closing section of this paper.

Our formulation of the law of octic reciprocity makes possible a considerable extension of the results for q ≡ ±3(mod8) of earlier authors. In particular, the largest prime ≡3(mod8) treated to date is q = 19, by von Lienen [6] when j = 4 or 8 and by Hudson and Williams [3] when j = 1, 2, 3, 5, 6, or 7. For q = 19 there are 200 distinct choices relating a, b, c, d which are equivalent to (−q)(p−1)/8 ≡ ((a−b)d/ac)j(modp) for one of j = 1, …, 8. We give explicit results in this paper for primes as large as q = 83 where there are 3528 distinct choices.

This paper makes several other minor contributions including a computationally efficient version of Gosset′s [2] formulation of Gauss′ law of quartic reciprocity, observations on sums ∑γi,j where the γi,j′s are the defining parameters for the distinct choices mentioned above, and proof that the results of von Lienen [6] may not only be appreciably abbreviated, but may be put into a form remarkably similar to the case in which q is a quadratic residue but a quartic non‐residue of p.

An important contribution of the paper consists in showing how to use Theorems
1 and 3 of [3], in conjunction with Theorem 4 of this paper, to reduce from (q + 1/4)2 to (q − 1)/2 the number of cases which must be considered to obtain the criteria in Theorems 2 and 3.
Square variation of Brownian paths in Banach spaces
Authors: Chang Mou-Hsiung
Published: September 2002

It is known that if {W(t),    0 ≤ t ≤ 1} is a standard Brownian motion in ℝ then almost surely. We generalize this celebrated theorem of Levy to Brownian motion in real separable Banach spaces.
On whitehead′s second lemma for Lie algebras
Authors: Fletcher William T.
Published: September 2002

A proof of Whitehead′s second lemma which is independent of the first Whitehead lemma is given.
Recent developments in the theory of Walsh series
Authors: Wade William R.
Published: September 2002

We survey research done on the theory of Walsh series during the decade 1971‐1981. Particular attention is given to convergence of Walsh‐Fourier series, gap Walsh series, growth of Walsh‐Fourier coefficients, dyadic differentiation, and uniqueness of Walsh series.
Forest decompositions of graphs with cyclomatic number 2
Authors: Farrell E. J.
Published: September 2002

The tree polynomials [1] of the basic graphs with cyclomatic number 2 are
derived. From these polynomials, results about forest decompositions are deduced. Explicit formulae are given for the number of decompositions of the basic graphs into forest with specified finite cardinalities.
The continuous Jacobi transform
Authors: Deeba E. Y. , Koh E. L.
Published: September 2002

The purpose of this paper is to define the continuous Jacobi transform as an extension of the discrete Jacobi transform. The basic properties including the inversion theorem for the continuous Jacobi transform are studied. We also derive an inversion formula for the transform which maps L1(R+) into where w(x) = (1 − x) α(1 + x) β.
Generalized function treatment of the Alfvén‐gravity wave problem
Authors: Debnath L. , Vajravelu K.
Published: September 2002

A study is made of the steady‐state Alfvén‐gravity waves in an inviscid
incompressible electrically conducting fluid with an interface due to a harmonically oscillating pressure distribution acting on the interface. The generalized function method is employed to solve the problem in the fluid of infinite, finite and shallow depth. A unique solution of physical interest is derived by imposing the Sommerfeld radiation condition at infinity. Several limiting cases of physical interest are obtained from the present analysis. The physical significance of the solutions and
their limiting cases are discussed.
Dot product rearrangements
Authors: Erdos Paul , Weiss Gary
Published: September 2002

Let a = (an), x = (xn) denote nonnegative sequences; x = (xπ(n)) denotes the rearranged sequence determined by the permutation π, a · x denotes the dot product ∑anxn; and S(a, x) denotes {a · xπ : π is a permuation of the positive integers}. We examine S(a, x) as a subset of the nonnegative real line in certain special circumstances. The main result is that if an↑∞, then S(a, x) = [a · x, ∞] for every if and only if an+1/an is uniformly bounded.
Local expansions and accretive mappings
Authors: Kirk W. A.
Published: September 2002

Let X and Y be complete metric spaces with Y metrically convex, let D ⊂ X be open, fix u0 ∈ X, and let d(u) = d(u0, u) for all u ∈ D. Let f : X → 2Y be a closed mapping which maps open subsets of D onto open sets in Y, and suppose f is locally expansive on D in the sense that there exists a continuous nonincreasing function c : R+ → R+ with ∫+∞c(s)ds = +∞ such that each point x ∈ D has a neighborhood N for which dist(f(u), f(v)) ≥ c(max{d(u), d(v)})d(u, v) for all u, v ∈ N. Then, given y ∈ Y, it is shown that y ∈ f(D) iff there exists x0 ∈ D such that for x ∈ X\D, dist(y, f(x0)) ≤ dist(u, f(x)). This result is then applied to the study of existence of zeros of (set‐valued) locally strongly accretive and ϕ‐accretive mappings in Banach spaces
Some remarks on the space R2(E)
Authors: Fernström Claes
Published: September 2002

Let E be a compact subset of the complex plane. We denote by R(E) the algebra consisting of the rational functions with poles off E. The closure of R(E) in Lp(E), 1 ≤ p < ∞, is denoted by Rp(E). In this paper we consider the case p = 2. In section 2 we introduce the notion of weak bounded point evaluation of order β and identify the existence of a weak bounded point evaluation of order β, β > 1, as a necessary and sufficient condition for R2(E) ≠ L2(E). We also construct a compact set E such that R2(E) has an isolated bounded point evaluation. In section 3 we examine the smoothness properties of functions in R2(E) at those points which admit bounded point evaluations.
Knots with proprety R+
Authors: Clark Bradd Evans
Published: September 2002

If we consider the set of manifolds that can be obtained by surgery on
a fixed knot K, then we have an associated set of numbers corresponding to the Heegaard genus of these manifolds. It is known that there is an upper bound to this set of numbers. A knot K is said to have Property R+ if longitudinal surgery yields a manifold of highest possible Heegaard genus among those obtainable by surgery on K. In this paper we show that torus knots, 2‐bridge knots, and knots which are the connected sum of arbitrarily many (2, m)‐torus knots have Property R+ It is shown that if K is constructed from the tangles (B1, t1), (B2, t2), …, (Bn, tn) then where T(K) is the tunnel of K and T(Bi, ti) is the tunnel number of the tangle (Bi, ti). We show that there exist prime knots of arbitrarily high tunnel number that have Property R+ and that manifolds of arbitrarily high Heegaard genus can be obtained by surgery on prime knots.
Fibonacci polynominals of order k, multinomial expansions and probability
Authors: Philippou Andreas N. , Georghiou Costas , Philippou George N.
Published: September 2002

The Fibonacci polynomials of order k are introduced and two expansions of them are obtained, in terms of the multinomial and binomial coefficients, respectively. A relation between them and probability is also established. The present work generalizes results of [2] ‐ [4] and [5].
A note on solutions of Schiffer′s differential equation
Authors: Leach Ronald J.
Published: September 2002

We consider Schiffer′s differential equation for functions in the class of
normalized univalent functions which maximize the coefficient. By considering a class of functionals converging to the coefficient functional, we determine some additttional symmetries that extremal functions possess.
Singularities in a two‐fluid medium
Authors: Chakrabarti Rathindra Nath , Mandal Birendranath
Published: September 2002

We compute the irrotational motion of two fluids with a horizontal plane surface of separation, under gravity. The fluids are nonviscous and incompressible, the upper one of finite depth with a free surface; they contain a line singularity or a point singularity. We obtain the velocity potentials for each singularity located in the upper or the lower fluid; if the upper depth tends to infinity, known results are recovered.
Weak openness and almost openness
Authors: Rose David A.
Published: September 2002

Weak openness and almost openness for arbitrary functions between topological spaces are defined as duals to the weak continuity of Levine and the almost continuity of Husain respectively. Independence of these two openness conditions is noted and comparison is made between these and the almost openness of Singal and Singal. Some results dual to those known for weak continuity and almost continuity are obtained. Nearly almost openness is defined and used to obtain an improved link from weak continuity to almost continuity.
Common fixed points for family of mappings
Authors: Anderson D. E. , Singh K. L. , Whitfield J. H. M.
Published: September 2002

The main aim of the present paper is to prove the existence of common fixed points for mappings which are not necessarily continuous. Our results, which are primarly motivated by investigation of Husain and Sehgal (Bull. Austral. Math. Soc. 13 (1975), 261‐267), generalize the results of Husain and Sehgal, Sehgal, Kannan, Reich, Hardy and Rogers, and others.
On automorphism group of free quadratic extensions over a ring
Authors: Szeto George
Published: September 2002

Let R be a ring with 1, ρ an automorphism of R of order 2. Then a normal extension of the free quadratic extension R[x, ρ] with a basis {1, x} over R with an R‐automorphism group G is characterized in terms of the element (x − (x)α) for α in G. It is also shown by a different method from the one given by Nagahara that the order of G of a Galois extension R[x, ρ] over R with Galois group G is a unit in R. When 2 is not a zero divisor, more properties of R[x, ρ] are derived.
A temperature control problem
Authors: Athanasopoulos Ioannis
Published: September 2002

In an open bounded region of n‐space occupied by a homogeneous and isotropic medium, we control the temperature through the boundary. The normal derivative of the temperature (which measures the appropriate heat flux) is restricted to be nonnegative. This gives rise to a free boundary in space‐time separating the areas of positive and zero heat flux. Under a natural monotonicity condition, the free boundary is the graph of a function of space. This function is shown to be locally Lipschitz. Moreover for n = 2 the time derivative of the temperature is proven to be continuous across the free boundary.
Lie transforms and motion of a charged particle in a periodic magnetic field
Authors: Bhattacharyya Sikha , Choudhury R. K. Roy
Published: September 2002

We use the Lie series averaging method to obtain a complete second order solution for motion of a charged particle in a spatially periodic magnetic field. A comparison is made with the first order solution obtained previously by Coffey.
Quasifields with irreducible nuclei
Authors: Kallaher Michael J.
Published: September 2002

This article considers finite quasifields having a subgroup N of either the right or middle nucleus of Q which acts irreducibly as a group of linear transformations on Q as a vector space over its kernel. It is shown that Q is a generalized André system, an irregular nearfield, a Lüneburg exceptional quasifield of type R∗p or type F∗p, or one of four other possibilities having order 52, 52, 72, or 112, respectively. This result generalizes earlier work of Lüneburg and Ostrom characterizing generalized André systems, and it demonstrates the close similarity of the Lüneburg exceptional quasifields to the generalized André system.
Bridge and cycle degrees of vertices of graphs
Authors: Chartrand Gary , Saba Farrokh , Wormald Nicholas C.
Published: September 2002

The bridge degree bdeg v and cycle degree cdeg v of a vertex v in a graph G are, respectively, the number of bridges and number of cycle edges incident with v in G. A characterization of finite nonempty sets S of nonnegative integers is given for which S is the set of bridge degrees (cycle degrees) of the vertices of some graph. The bridge‐cycle degree of a vertex v in a graph G is the ordered pair (b, c), where bdeg v = b and cdeg v = c. Those finite sets S of ordered pairs of nonnegative integers for which S is the set of bridge‐cycle degrees of the vertices of some graph are also characterized.
The extrapolated successive overrelaxation (ESOR) method for consistently ordered matrices
Authors: Missirlis N. M. , Evans D. J.
Published: September 2002

This paper develops the theory of the Extrapolated Successive Overrelaxation (ESOR) method as introduced by Sisler in [1], [2], [3] for the numerical solution of large sparse linear systems of the form Au = b, when A is a consistently ordered 2‐cyclic matrix with non‐vanishing diagonal elements and the Jacobi iteration matrix B possesses only real eigenvalues. The region of convergence for the ESOR method is described and the optimum values of the involved parameters are also determined. It is shown that if the minimum of the moduli of the eigenvalues of B, does not vanish, then ESOR attains faster rate of convergence than SOR when , where denotes the spectral radius of B.
On the existence of equations of evolution
Authors: Lubliner J.
Published: September 2002

A time‐independent, non‐autonomous non‐linear system governed by a principle of determinism (the state at a given time is determined by the initial state and by the control history during the intervening closed interval) is shown to obey a generalized evolution equation (1.2), where n is such that the state is continuously differentiabie with respect to time whenever the control is of class Cn.
a*‐families of analytic functions
Authors: Kapoor G. P. , Mishra A. K.
Published: September 2002

Using convolutions, a new family of analytic functions is introduced. This family, called a*‐family, serves in certain situations to unify the study of many previously well known classes of analytic functions like multivalent convex, starlike, close‐to‐convex or prestarlike functions, functions starlike with respect to symmetric points and other such classes related to the class of univalent or multivalent functions. A necessary and sufficient condition on the Taylor series coefficients so that an analytic function with negative coefficients is in an a*‐family is obtained and sharp coefficents bound for functions in such a family is deduced. The extreme points of an a*‐family of functions with negative coefficients are completely determined. Finally, it is shown that Zmorvic conjecture is true if the concerned families consist of functions with negative coefficients.
A unified approach to radius of convexity problems for certain classes of univalent analytic functions
Authors: Mogra M. L. , Juneja O. P.
Published: September 2002

We consider functions f analytic in the unit disc and assume the power series representation of the form

urn:x-wiley:01611712:media:ijmm357921:ijmm357921-math-0001

where an+1 is fixed throughout. We provide a unified approach to radius convexity problems for different subclasses of univalent analytic functions. Numerous earlier estimates concerning the radius of convexity such as those involving fixed second coefficient, n initial gaps, n + 1 symmetric gaps, etc. are discussed. It is shown that several known results, follow as special cases of those presented in this paper.
Doubly stochastic right multipliers
Authors: Kim Choo-Whan
Published: September 2002

Let P(G) be the set of normalized regular Borel measures on a compact group G. Let Dr be the set of doubly stochastic (d.s.) measures λ on G × G such that λ(As × Bs) = λ(A × B), where s ∈ G, and A and B are Borel subsets of G. We show that there exists a bijection μ↔λ between P(G) and Dr such that ϕ−1 = m ⊗ μ, where m is normalized Haar measure on G, and ϕ(x, y) = (x, xy−1) for x, y ∈ G. Further, we show that there exists a bijection between Dr and Mr, the set of d.s. right multipliers of L1(G). It follows from these results that the mapping μ → Tμ defined by Tμf = μ∗f is a topological isomorphism of the compact convex semigroups P(G) and Mr. It is shown that Mr is the closed convex hull of left translation operators in the strong operator topology of B[L2(G)].
A property of L − L integral transformations
Authors: Wei Yu Chuen
Published: September 2002

The main result of this paper is the result that the collection of all integral transformations of the form for all x ≥ 0, where f(y) is defined on [0, ∞) and G(x, y) defined on D = {(x, y) : x ≥ 0,    y ≥ 0} has no identity transformation on L, where L is the space of functions that are Lebesgue integrable on [0, ∞) with norm . That is to say, there is no G(x, y) defined on D such that for every f ∈ L, for almost all x ≥ 0. In addition, this paper gives a theorem that is an improvement of a theorem that is proved by J. B. Tatchell (1953) and Sunonchi and Tsuchikura (1952).
The quasi‐stationary approximation for the Stefan problem with a convective boundary condition
Authors: Solomon A. D. , Wilson D. G. , Alexiades V.
Published: September 2002

We show that the solution to the Stefan problem with a convective boundary condition tends to the quasi‐stationary approximation as the specific heat tends to zero. Additional properties of the approximation are given, and some examples are presented.
The largest proper congruence on S(X)
Authors: Magill K. D.
Published: September 2002

S(X) denotes the semigroup of all continuous selfmaps of the topological space X. In this paper, we find, for many spaces X, necessary and sufficient conditions for a certain type of congruence to be the largest proper congruence on S(X).