bluuebunny/crossref_metadata_2025 huggingface dataset:
Effects of Poiseuille flow on peristaltic transport
Authors: El Shehawey El Sayed F. , El Sebaei Wahed A. F.
Published: September 2002

The effects of Poiseuille flow on peristaltic transport in a cylindrical tube has been investigated. A perturbation solution is obtained, which satisfies the momentum equation for the case in which the amplitude ratio (wave amplitude/tube radius) is chosen as a small parameter. The results show that the fluid phase mean axial velocity increases with increasing the Poiseuille parameter k. The phenomena of reflux is discussed. Numerical results are reported for various values of k.
Coincidence and fixed point theorems in metric and Banach spaces
Authors: Liu Zeqing , Ume Jeong Sheok , Khan Mohammad S.
Published: September 2002

We prove some coincidence and fixed point theorems for generalized (ϕ, f)‐contractive type and f‐nonexpansive type multivalued and singlevalued mappings in metric and Banach spaces, respectively. Our results extend, improve, and unify a few known results due to Browder, Browder and Petryshyn, Chang, Huang, and Cho, Husain and Latif, Husain and Tarafdar, and Karlovitz.
Generalizations of Hölder′s inequality
Authors: Cheung Wing-Sum
Published: September 2002

Some generalized Hölder′s inequalities for positive as well as negative exponents are obtained.
On a family of dendrites
Authors: Charatonik Janusz J.
Published: September 2002

We study the open images of members of a countable family ℱ of dendrites. We show that only two members of ℱ are minimal and only one of them is unique minimal with respect to open
mappings.
Some properties of Banach‐valued sequence spaces ℓp[X]
Authors: Bu Qingying
Published: September 2002

We discuss some properties of the Banach‐valued sequence space ℓp[X](1 ≤ p < ∞), the space of weakly p‐summable sequences on a Banach space X. For example, we characterize the reflexivity of ℓp[X], convergent sequences on ℓp[X], and compact subsets of ℓp[X].
Transient probabilities for a simple birth‐death‐immigration process under the influence of total catastrophes
Authors: Swift Randall J.
Published: September 2002

The transient probabilities for a simple birth‐death‐immigration
process are considered. Catastrophes occur at a constant rate, and
when they occur, reduce the population to size zero.
Stable rings generated by their units
Authors: Chen Huanyin
Published: September 2002

We introduce the class of rings satisfying (m, 1)‐stable range and investigate equivalent characterizations of such rings. These give generalizations of the corresponding results by Badawi (1994), Ehrlich (1976), and Fisher and Snider (1976).
Fredholm‐Volterra integral equation with potential kernel
Authors: Abdou M. A. , El-Bary A. A.
Published: September 2002

A method is used to solve the Fredholm‐Volterra integral equation of the first kind in the space L2(Ω) × C(0, T), , z = 0, and T < ∞. The kernel of the Fredholm integral term considered in the generalized potential form belongs to the class C([Ω] × [Ω]), while the kernel of Volterra integral term is a positive and continuous function that belongs to the class C[0, T]. Also in this work the solution of Fredholm integral equation of the second and first kind with a potential kernel is discussed. Many interesting cases are derived and established in the paper.
Asymptotic behavior of orthogonal polynomials corresponding to a measure with infinite discrete part off an arc
Authors: Khaldi R. , Benzine R.
Published: September 2002

We study the asymptotic behavior of orthogonal polynomials. The measure is concentrated on a complex rectifiable arc and has an infinity of masses in the region exterior to the arc.
A new inequality for a polynomial
Authors: Dewan K. K. , Singh Harish , Yadav R. S.
Published: September 2002

Let be a polynomial of degree n, having no zeros in |z| < k, k ≥ 1 then it has been shown that for R > 1 and |z| = 1, |p(Rz) − p(z)| ≤ (Rn − 1)(1 + AtBtKt+1)/(1 + kt+1 + AtBt(kt+1 + k2t))max|z|=1|p(z)|−{1 − (1 + AtBtkt+1)/(1 + kt+1 + AtBt(kt+1 + k2t))}((Rn − 1)m/kn), where m = min|z|=k|p(z)|, 1 ≤ t < n, At = (Rt − 1)/(Rn − 1), and Bt = |at/a0|. Our result generalizes and improves some
well‐known results.
Arithmetic progressions that consist only of reduced residues
Authors: Tanner Paul A.
Published: September 2002

This paper contains an elementary derivation of formulas for multiplicative functions of m which exactly yield the following numbers: the number of distinct arithmetic
progressions of w reduced residues modulo m; the number of the same with first term n; the number of the same with mean n; the number of the same with common difference n. With m and odd w fixed, the values of the first two of the last three functions are fixed and equal for all n relatively prime to m; other similar relations exist among these three functions.
Quasi‐pseudometrizability of the point open ordered spaces and the compact open ordered spaces
Authors: Nailana Koena Rufus
Published: September 2002

We determine conditions for quasi‐pseudometrizability of the point open ordered spaces and the compact open ordered spaces. This generalizes the results on metrizability of the point open topology and the compact open topology for function spaces. We also study conditions for complete quasi‐pseudometrizability.
On some hyperbolic planes from finite projective planes
Authors: Celik Basri
Published: September 2002

Let Π = (P, L, I) be a finite projective plane of order n, and let Π′ = (P′, L′, I′) be a subplane of Π with
order m which is not a Baer subplane (i.e., n ≥ m2 + m). Consider the substructure Π0 = (P0, L0, I0) with P0 = P\{X ∈ P | XIl,   l ∈ L′}, L0 = L\L′ where I0 stands for the restriction of I to P0 × L0. It is shown that every Π0 is a hyperbolic plane, in
the sense of Graves, if . Also we give some combinatorial properties of the line
classes in Π0 hyperbolic planes, and some
relations between its points and lines.
Ergodic type solutions of differential equations with piecewise constant arguments
Authors: Alonso Ana Isabel , Hong Jialin
Published: September 2002

We summarize the conditions discovered for the existence of new
ergodic type solutions (asymptotically almost periodic, pseudo
almost periodic, …) of differential equations with
piecewise constant arguments. Their existence is characterized by
introducing a new tool, the ergodic sequences.
On a theorem of Schur
Authors: Hilton Peter
Published: September 2002

We study the ramifications of Schur′s theorem that, if G is a group such that G/ZG is finite, then G′ is finite, if we restrict attention to
nilpotent group. Here ZG is the center of G, and G′ is the commutator subgroup. We use localization methods and obtain relativized versions of the main theorems.
Existence of limit cycles in a predator‐prey system with a functional response
Authors: Attili Basem S.
Published: September 2002

We consider the existence of limit cycles for a predator‐prey
system with a functional response. The system has two or more
parameters that represent the intrinsic rate of the predator
population. A necessary and sufficient condition for the
uniqueness of limit cycles in this system is presented. Such
result will usually lead to a bifurcation curve.
Modified Wiener equations
Authors: Watkins Will
Published: September 2002

This paper is concerned with a class of functional differential
equations whose argument transforms are involutions. In contrast
to the earlier works in this area, which have used only
involutions with a fixed point, we also admit involutions without
a fixed point. In the first case, an initial value problem for a
differential equation with involution is reduced to an initial
value problem for a higher order ordinary differential equation.
In our case, either two initial conditions or two boundary
conditions are necessary for a solution; the equation is then
reduced to a boundary value problem for a higher order ODE.
Slightly β‐continuous functions
Authors: Noiri Takashi
Published: September 2002

We define a function f : X → Y to be slightly β‐continuous if for every clopen set V of Y, f−1(V) ⊂ Cl(Int(Cl(f−1(V)))). We obtain
several properties of such a function. Especially, we define the
notion of ultra‐regularizations of a topology and obtain
interesting characterizations of slightly
β‐continuous functions by using it.
A mathematical analysis of thermal explosions
Authors: Taira Kazuaki
Published: September 2002

This paper is devoted to the study of semilinear degenerate elliptic boundary value problems arising in
combustion theory which obey the simple Arrhenius rate law and a
general Newton law of heat exchange. We prove that ignition and
extinction phenomena occur in the stable steady temperature
profile at some critical values of a dimensionless rate of heat
production.
Precompactness and total boundedness in products of metric spaces
Authors: Windels Bart
Published: September 2002

We show that the canonical quantifications of uniform properties
such as precompactness and total boundedness, which were already
studied by Kuratowski and Hausdorff in the setting of complete
metric spaces, can be generalized in the setting of products of
metric spaces in an intuitively appealing way.
Discretization and Moyal brackets
Authors: Carroll Robert
Published: September 2002

We give a q‐analysis version of a discretization procedure of Kemmoku and Saito leading to an apparently new q‐Moyal type bracket.
On the extension of linear operators
Authors: Saccoman John J.
Published: September 2002

It is well known that the Hahn‐Banach theorem, that is, the
extension theorem for bounded linear functionals, is not true in
general for bounded linear operators. A characterization of
spaces for which it is true was published by Kakutani in 1940. We
summarize Kakutani′s work and we give an example which
demonstrates that his characterization is not valid for
two‐dimensional spaces.
On moment inequalities and stochastic ordering for weighted reliability measures
Authors: Oluyede Broderick O. , Terbeche Mekki
Published: September 2002

We obtain stochastic inequalities, error bounds, and
classification probability for a general class of distributions.
We introduce the notion of variability ordering via the
probability functional and comparisons made for the weighted and the
original distributions. We present moment inequalities,
comparisons, and applications.
Convergence theorems of the sequence of iterates for a finite family asymptotically nonexpansive mappings
Authors: Huang Jui-Chi
Published: September 2002

Let E be a uniformly convex Banach space, C a nonempty closed convex subset of E. In this paper, we introduce an iteration scheme with errors in the sense of Xu (1998) generated by as follows: , j = 1, 2, …, r, x1 ∈ C, , n ≥ 1, where Un(0) : = I, I the identity map; and {un(j)} are bounded sequences in C; and {an(j)}, {bn(j)}, and {cn(j)} are suitable sequences in [0, 1]. We first consider the behaviour of iteration scheme above
for a finite family of asymptotically nonexpansive mappings.
Then we generalize theorems of Schu and Rhoades.
Normal characterizations of lattices
Authors: Vlad Carmen D.
Published: September 2002

Let X be an arbitrary nonempty set and ℒ a lattice of subsets of X such that ∅, X ∈ ℒ. Let 𝒜(ℒ) denote the algebra generated by ℒ and I(ℒ) denote those nontrivial, zero‐one valued, finitely additive
measures on 𝒜(ℒ). In this paper, we discuss some of the normal characterizations of lattices in terms of the associated lattice regular measures, filters and outer measures. We consider
the interplay between normal lattices, regularity or σ‐smoothness properties of measures, lattice topological properties and filter correspondence. Finally, we start a study of slightly, mildly and strongly normal lattices and express then some of these results in terms of the generalized Wallman spaces.
Stress waves in a microperiodic layered elastic solid revisited
Authors: Ignaczak Józef , Mrówka-Matejewska Elżbieta
Published: September 2002

A one‐dimensional pure stress initial boundary value problem of
linear elastodynamics for a microperiodic layered semi‐space in
which a microstructural length is taken into account is
revisited. Also, the plane stress harmonic waves propagating in a
microperiodic layered infinite elastic space are discussed. It is
shown that (i) for a particular system of the length and time
units the transient stress waves in the microperiodic layered
semi‐space are independent of the microstructural length, and
(ii) there are two dispersive plane stress harmonic waves
propagating in a microperiodic layered infinite elastic space.
The graphs illustrating the transient stress waves in the
semi‐space and the dispersion of harmonic waves in the infinite
space are included.
Radiation effects on unsteady MHD free convection with Hall current near an infinite vertical porous plate
Authors: Seddeek Mohamed A. , Aboeldahab Emad M.
Published: September 2002

Radiation effect on unsteady free convection flow of an electrically conducting, gray gas near equilibrium in the optically thin limit along an infinite vertical porous plate are
investigated in the presence of strong transverse magnetic field imposed perpendicularly to the plate, taking Hall currents into account. A similarly parameter length scale (h), as a function of time and the suction velocity are considered to be inversely proportional to this parameter. Similarity equations are then derived and solved numerically using the shooting method. The numerical values of skin friction and the rate of heat transfer are represented in a table. The effects of radiation parameter, Hall parameter, and magnetic field parameters are discussed and shown graphically.
L∞‐error estimates for a class of semilinear elliptic variational inequalities and quasi‐variational inequalities
Authors: Boulbrachene M. , Cortey-Dumont P. , Miellou J. C.
Published: September 2002

This paper deals with the finite element approximation
of a class of variational inequalities (VI) and quasi‐variational inequalities (QVI) with the right‐hand
side depending upon the solution. We prove that the approximation is optimally accurate in L∞ combining the Banach fixed point theorem with the standard
uniform error estimates in linear VIs and QVIs. We also
prove that this approach extends successfully to the
corresponding noncoercive problems.
Some fixed point theorems in metric and 2‐metric spaces
Authors: Naidu S. Venkata Ratnam
Published: September 2002

We introduce the notion of compatibility for a pair of self‐maps
on a 2‐metric space and we have fixed point theorems for pairs
as well as quadruples of self‐maps on a 2‐metric space satisfying certain generalised contraction conditions. Further
metric space versions of the same have also been obtained.
Loops embedded in generalized Cayley algebras of dimension 2r, r ≥ 2
Authors: Cawagas Raoul E.
Published: September 2002

Every Cayley algebra of dimension 2r, r ≥ 2, contains an embedded invertible loop of order 2r+1 generated by its basis. Such a loop belongs to a class of non‐abelian invertible
loops that are flexible and power‐associative.
Intuitionistic fuzzy interior ideals of semigroups
Authors: Kim Kyung Ho , Jun Young Bae
Published: September 2002

We consider the intuitionistic fuzzification of the concept of interior ideals in a semigroup S, and investigate some properties of such ideals. For any homomorphism f from a semigroup S to a semigroup T, if B = (μB, γB) is an intuitionistic fuzzy interior ideal of T, then the preimage f−1(B) = (f−1(μB), f−1(γB)) of B under f is an intuitionistic fuzzy interior ideal of S.
Numerical methods of computation of singular and hypersingular integrals
Authors: Boikov I. V.
Published: September 2002

In solving numerous problems in mathematics, mechanics, physics,
and technology one is faced with necessity of calculating different singular integrals. In analytical form calculation of singular integrals is possible only in unusual cases. Therefore approximate methods of singular integrals calculation are an active developing direction of computing in mathematics. This review is devoted to the optimal with respect to accuracy algorithms of the calculation of singular integrals with fixed singularity, Cauchy and Hilbert kernels, polysingular and many‐dimensional singular integrals. The isolated section is devoted to the optimal with respect to accuracy algorithms of the calculation of the hypersingular integrals.
Relationship between ideals of BCI‐algebras and order ideals of its adjoint semigroup
Authors: Kondo Michiro
Published: September 2002

We consider the relationship between ideals of a BCI‐algebra and
order ideals of its adjoint semigroup. We show that (1) if I is an ideal, then I = M−1(M(I)), (2) M(M−1(J)) is the order ideal generated by J∩R(X), (3) if X is a BCK‐algebra, then J = M(M−1(J)) for any order ideal J of X, thus, for each BCK‐algebra X there is a one‐to‐one correspondence between the set ℐ(X) of all ideals of X and the set 𝒪(X) of all order ideals of it, and (4) the order M(M−1(J)) is an order ideal if and only if M−1(J) is an ideal. These results are the generalization of those denoted by Huang
and Wang (1995) and Li (1999). We can answer the open problem of
Li affirmatively.
On the constructions of Tits and Faulkner: an isomorphism theorem
Authors: Nath Sudhir R.
Published: September 2002

Classification theory guarantees the existence of an isomorphism
between any two E8′s, at least over an algebraically closed field of characteristic 0. The purpose of this paper is to construct for any Jordan algebra J of degree 3 over a field Φ of characteristic ≠2, 3 an explicit isomorphism between the algebra obtained from J by Faulkner′s construction and the algebra obtained from the split octonions and J by Tits construction.
Dimensions of Prym varieties
Authors: Ksir Amy E.
Published: September 2002

Given a tame Galois branched cover of curves π : X → Y with any finite Galois group G whose representations are rational, we compute the dimension of the (generalized) Prym variety Prymρ(X) corresponding to any irreducible representation ρ of G. This formula can be applied to the study of algebraic integrable systems using Lax pairs, in particular systems associated with Seiberg‐Witten theory. However, the formula is much more general and its computation and proof are entirely algebraic.
Some remarks on the invariant subspace problem for hyponormal operators
Authors: Lauric Vasile
Published: September 2002

We make some remarks concerning the
invariant subspace problem for hyponormal operators. In
particular, we bring together various hypotheses that
must hold for a hyponormal operator without nontrivial
invariant subspaces, and we discuss the existence of
such operators.
Multivariable q‐Hahn polynomials as coupling coefficients for quantum algebra representations
Authors: Rosengren Hjalmar
Published: September 2002

We study coupling coefficients for a multiple tensor
product of highest weight representations of the SU(1, 1) quantum group. These are multivariable generalizations of the q‐Hahn polynomials.
Orbifolds and finite group representations
Authors: Chiang Li , Roan Shi-Shyr
Published: September 2002

We present our recent understanding on resolutions of Gorenstein orbifolds, which involves the finite group representation theory. We concern only the quotient singularity of hypersurface type. The abelian group Ar(n) for A‐type hypersurface quotient singularity of dimension n is introduced. For n = 4, the structure of Hilbert scheme of group orbits and crepant resolutions of Ar(4)‐singularity are obtained. The flop procedure of 4‐folds is explicitly constructed through the process.
Some remarks on the Severi varieties of surfaces in ℙ3
Authors: Chen Xi
Published: September 2002

Continuing the work of Chiantini and Ciliberto (1999) on the Severi varieties of curves on surfaces in ℙ3, we complete the proof of the existence of regular components for such varieties.
On the oscillation of first‐order neutral delay differential equations with real coefficients
Authors: Al-Amri Ibrahim R.
Published: September 2002

We prove sufficient conditions for the oscillation of all
solutions of a scalar first‐order neutral delay differential
equation for all 0 < c < 1, τ, σi > 0, and
pi ∈ ℝ, i = 1, 2, …, n.
On the solvability of a class of singular parabolic equations with nonlocal boundary conditions in nonclassical function spaces
Authors: Bouziani Abdelfatah
Published: September 2002

The aim of this paper is to prove the existence, uniqueness, and continuous dependence upon the data of a generalized solution for
certain singular parabolic equations with initial and nonlocal boundary conditions. The proof is based on an a priori estimate established in nonclassical function spaces, and on the density of the range of the operator corresponding to the abstract formulation of the considered problem.
On the equation x2 + 2a · 3b = yn
Authors: Luca Florian
Published: September 2002

We find all positive integer solutions (x, y, a, b, n) of
x2 + 2a · 3b = yn with n ≥ 3 and coprime x and y.
Remarks on certain selected fixed point theorems
Authors: Imdad M.
Published: September 2002

Fixed point theorems due to Lal et al. (1996) and Jungck
(1988) are used to derive two common fixed point
theorems involving six mappings in complete and compact
metric spaces, respectively.
On unified theory for continuities
Authors: Küçük Mahide , Küçük Yalçin
Published: September 2002

The purpose of this study is to give a unified theory for some
weak and strong continuous functions using operations.
Non‐unicité du problème de Cauchypour des opérateurs différentiels quasi‐homogènes
Authors: Hella Khalgui-Ounaïes
Published: September 2002

Nous démontrons que si P est un opérateur différentiel quasi‐homogène d′ordre m sur une partie ouverte Ω de ℝ n, à coefficients de classe C ∞, tel que la m‐partie principale est à coefficients réels; et que
x 0 ∈ Ω, S = {x ∈ Ω : Φ(x) = Φ(x 0)} est une hypersurface non caractéristique en x 0 et strictement non pseudoconvexe avec {{p m, Φ}, Φ}(x 0, ξ 0) ≠ 0 et d q p m(x 0, ξ 0) ≠ 0, alors P n′a pas l′unicité de Cauchy par rapport à S.
A Galerkin method of O(h2) for singular boundary value problems
Authors: Beg G. K. , El-Gebeily M. A.
Published: September 2002

We describe a Galerkin method with special basis functions for a
class of singular two‐point boundary value problems. The
convergence is shown which is of O(h2)
for a certain subclass
of the problems.
On the solvability of parabolic and hyperbolicproblems with a boundary integral condition
Authors: Bouziani Abdelfatah
Published: September 2002

We prove the existence, uniqueness, and the continuous dependence
of a generalized solution upon the data of certain parabolic and
hyperbolic equations with a boundary integral condition. The proof
uses a functional analysis method based on a priori estimates
established in nonclassical function spaces, and on the
density of the range of the linear operator associated to the
abstract formulation of the studied problem.
Relationships of convolution products, generalizedtransforms, and the first variation on function space
Authors: Chang Seung Jun , Choi Jae Gil
Published: September 2002

We use a generalized Brownian motion process to define the
generalized Fourier‐Feynman transform, the convolution product,
and the first variation. We then examine the various
relationships that exist among the first variation, the generalized
Fourier‐Feynman transform, and the convolution product for
functionals on function space that belong to a Banach algebra
S(Lab[0, T]). These results subsume similar known results obtained by
Park, Skoug, and Storvick (1998) for the standard Wiener process.
Super parallel immersions in Euclidean space
Authors: Mersal Tarek Fathy , Basher Mohamed Esmail
Published: September 2002

Two submanifolds of Euclidean n‐space En are called super
parallel if the affine normal spaces are homothetic at
the corresponding points. Characterizations are given for the action
of conformal transformation on super parallel mates. Our notion
is generalized to super transnormal submanifolds and its relation
with super self‐parallel submanifolds and convex super
self‐parallel submanifolds.
A note on Ruscheweyh type of integral operators for uniformly α‐convex functions
Authors: Durai M. Anbu , Parvatham R.
Published: September 2002

We prove that the class of uniformly α‐convex
functions introduced by Kanas is closed under the
generalized Ruscheweyh integral operator for 0 < α ≤ 1.
An n × n matrix of linear functionals of C∗‐algebras
Authors: Sulaiman W. T.
Published: September 2002

We show that any bounded matrix of linear functionals
[fij] : Mn(A) → Mn(ℂ) has a representation
fij(a) = 〈Tπ(a)xj, xi〉, a ∈ A, i, j = 1, 2, …, n, for some representation π on a Hilbert space K and an n vectors x1, x2, …, xn in K.
Schrödinger operators with a singular potential
Authors: Diagana Toka
Published: September 2002

This note is devoted to the study of some Schrödinger
operators with a singular real potential Q. The potential Q is chosen so that the algebraic sum L = −Δ + Q is not defined. Next, we define the sum form operator which will be well defined and we show that this operator verifies the well‐known Kato′s square root problem.
Sobolev cohomology for locally polycylindrical domains
Authors: Darko Patrick W.
Published: September 2002

The Cauchy‐Riemann equation is solved with LP‐Sobolev space estimates and the result is used to obtain vanishing theorems on locally polycylindrical domains.
Radius of strongly starlikeness for certain analytic functions
Authors: Kwon Oh Sang , Owa Shigeyoshi
Published: September 2002

For analytic functions f(z) = zp + ap+1zp+1 + ⋯ in the open unit disk and a polynomial Q(z) of degree n > 0, the function F(z) = f(z)[Q(z)]β/n is introduced. The object of the present paper is to determine the radius of p‐valently strongly starlikeness of order γ for F(z).
Coincidences and fixed points of reciprocally continuous and compatible hybrid maps
Authors: Singh S. L. , Mishra S. N.
Published: September 2002

It is proved that a pair of reciprocally continuous and nonvacuously compatible single‐valued and multivalued maps on a metric space possesses a coincidence. Besides addressing two historical problems in fixed point theory, this result is applied to obtain new general coincidence and fixed point theorems for single‐valued and multivalued maps on metric spaces under tight minimal conditions.
On the roots of the substitution Dickson polynomials
Authors: Gomez-Calderon Javier
Published: September 2002

We show that under the composition of multivalued functions, the
set of the y‐radical roots of the Dickson substitution
polynomial gd(x, a) − gd(y, a) is generated by one of the roots. Hence, we show an expected generalization of the fact that, under the composition of the functions, the y‐radical
roots of xd − yd are generated by ζdy.
The union problem on complex manifolds
Authors: Darko Patrick W.
Published: September 2002

Let Ω be a relatively compact subdomain of a complex manifold, exhaustable by Stein open sets. We give a necessary and sufficient condition for Ω to be Stein, in terms of L2
‐estimates for the ‐operator, equivalent to the condition of Markoe (1977) and Silva (1978).
Asymptotic expansion of small analytic solutions to the quadratic nonlinear Schrödinger equations in two‐dimensional spaces
Authors: Hayashi Nakao , Naumkin Pavel I.
Published: September 2002

We study asymptotic behavior in time of global small solutions to
the quadratic nonlinear Schrödinger equation in
two‐dimensional spaces i∂tu + (1/2)Δu = 𝒩(u), (t, x) ∈ ℝ × ℝ2; u(0, x) = φ(x), x ∈ ℝ2, where , where
λjk, μjk ∈ ℂ. We prove that if the initial data
φ satisfy some analyticity and smallness conditions in a
suitable norm, then the solution of the above Cauchy problem has
the asymptotic representation in the neighborhood of the
scattering states.
An application to Kato′s square root problem
Authors: Diagana Toka
Published: September 2002

We find all complex potentials Q such that the
general Schrödinger operator on ℝn, given by L = −Δ + Q, where Δ is the Laplace differential operator, verifies the well‐known Kato′s square problem. As an application, we will consider the case where
.
On some trigonometric power sums
Authors: Chen Hongwei
Published: September 2002

Using the generating function method, the closed formulas for
various power sums of trigonometric functions are established.
The computer algebra system Maple is used to carry out the complex
calculations.
On the sine integral and the convolution
Authors: Fisher Brian , Al-Sirehy Fatma
Published: September 2002

The sine integral Si(λx) and the cosine integral Ci(λx) and their associated functions Si+(λx), Si−(λx), Ci+(λx), Ci−(λx) are defined as locally summable functions on the real line. Some convolutions of these functions and sin(μx), sin+(μx), and sin−(μx) are found.
The Cayley transform of Banach algebras
Authors: Pan Zhidong
Published: September 2002

The main result of Haynes (1991) is that a square matrix is convergent (limn→∞Dn = 0) if and only if it is the Cayley transform CA = (I−A)−1(I + A) of a stable matrix A. In this note, we show, with a simple proof, that the above is true in a much more general setting of complex Banach algebras.
Doubt fuzzy BCI‐algebras
Authors: Jianming Zhan , Zhisong Tan
Published: September 2002

The aim of this note is to introduce the notion of doubt fuzzy
p‐ideals in BCI‐algebras and to study their properties. We also solve the problem of classifying doubt fuzzy p‐ideals and study fuzzy relations on BCI‐algebras.
Steady vortex flows obtained from a constrained variational problem
Authors: Emamizadeh B. , Mehrabi M. H.
Published: September 2002

We prove the existence of steady two‐dimensional ideal vortex flows occupying the first quadrant and containing a bounded vortex; this is done by solving a constrained variational problem. Kinetic energy is maximized subject to the vorticity, being a rearrangement of a prescribed function and subject to a linear constraint.
Introduction of the speaking rate in the model of speech recognition
Authors: Yousfi Abdellah , Meziane Abdelouafi
Published: September 2002

We propose an improvement to the centisecond TLHMM model
(Meziane, 1999) applied to the sound duration. Indeed, the
distribution of the sound duration depends on the speaking rate.
An adaptation in a post‐processing step is needed. This
adaptation is studied by proposing a model of the speaking rate
based on average syllabic duration. The experiments elaborated on
a set of BDSONS show the interest of this approach.
This work is a continuation of those by Meziane (1999) and
Suaudeau (1994).
On the existence of bounded solutions of nonlinear elliptic systems
Authors: Ahammou Abdelaziz
Published: September 2002

We study the existence of bounded solutions to the elliptic system −Δpu = f(u, v) + h1 in Ω, −Δqv = g(u, v) + h2 in Ω, u = v = 0 on ∂Ω,
non‐necessarily potential systems. The method used is a shooting
technique. We are concerned with the existence of a negative
subsolution and a nonnegative supersolution in the sense of
Hernandez; then we construct some compact operator T and some
invariant set K where we can use the Leray Schauder′s theorem.
Dynamics of Newton′s functions of Barna′s polynomials
Authors: Niamsup Piyapong
Published: September 2002

We define Barna′s polynomials as real polynomials with all real
roots of which at least four are distinct. In this paper, we
study the dynamics of Newton′s functions of such polynomials. We
also give the upper and lower bounds of the Hausdorff dimension
of exceptional sets of these Newton′s functions.
On the structure of ionizing shock waves in magnetofluiddynamics
Authors: Aghajani A. , Hesaaraki M.
Published: September 2002

Ionizing shock waves in magnetofluiddynamics occur when the
coefficient of electrical conductivity is very small ahead of the
shock and very large behind it. For planner motion of plasma, the
structure of such shock waves are stated in terms of a system of
four‐dimensional equations. In this paper, we show that for the
above electrical conductivity as well as for limiting cases, that
is, when this coefficient is zero ahead of the shock and/or is
infinity behind it, ionizing fast, slow, switch‐on and switch‐off
shocks admit structure. This means that physically these shocks
occur.
On the Lyapunov equation in Banach spaces and applications to control problems
Authors: Phat Vu Ngoc , Kiet Tran Tin
Published: September 2002

By extending the Lyapunov equation A*Q + QA = −P to an arbitrary infinite‐dimensional Banach space, we give stability
conditions for a class of linear differential systems.
Relationship between stabilizability and exact
null‐controllability is established. The result is applied to
obtain new sufficient conditions for the stabilizability of a
class of nonlinear control systems in Banach spaces.
Fixed point and coincidence point theorems for a pair of single‐valued and multi‐valued maps on a metric space
Authors: Naidu S. Venkata Ratnam
Published: September 2002

We obtain fixed point and coincidence point theorems for a pair of
single‐valued and multi‐valued maps on a metric space satisfying a
generalized nonexpansive type condition.
The geometry of autonomous metrical multi‐timeLagrange space of electrodynamics
Authors: Neagu Mircea
Published: September 2002

The aim of this paper is to create a large geometrical background
for the study of important branch of physics: electrodynamics,
bosonic strings theory, magneto‐hydrodynamics, and so forth. The
geometrical construction is realized on the 1‐jet fibre bundle J1(T, M)
and is produced by a given quadratic multi‐time
Lagrangian function L. The Riemann‐Lagrange geometry of the
space , in the sense of
d‐connections, torsion and curvature d‐tensors, allows the
construction of a natural generalized multi‐time field theory on
, in the sense of generalized Maxwell and Einstein
equations.
Fixed‐width confidence interval for a lognormal mean
Authors: Aoshima Makoto , Govindarajulu Zakkula
Published: September 2002

We consider the problem of constructing a fixed‐width confidence
interval for a lognormal mean. We give a Birnbaum and Healy
type two‐stage procedure to construct such a confidence
interval. We discuss some asymptotic properties of the procedure.
A three‐stage procedure and an accelerated sequential procedure
are also given for the comparison of efficiency among these three
multistage methodologies.
Critical point theorems
Authors: Boukhrisse H. , Moussaoui M.
Published: September 2002

Let H be a Hilbert space such that H = V ⊕ W, where V
and W are two closed subspaces of H. We generalize an abstract theorem due to Lazer et al. (1975) and a theorem given by Moussaoui (1990‐1991) to the case where V and
W are not necessarily finite dimensional. We give two mini‐max theorems where the functional Φ : H → ℝ is of class 𝒞2 and 𝒞1, respectively.
Global asymptotic stability of inhomogeneous iterates
Authors: Chen Yong-Zhuo
Published: September 2002

Let (M, d) be a finite‐dimensional complete metric space, and {Tn} a sequence of uniformly convergent operators on
M. We study the non‐autonomous discrete dynamical system
xn+1 = Tnxn and the globally asymptotic stability of the
inhomogeneous iterates of {Tn}. Then we apply the results
to investigate the stability of equilibrium of T when it
satisfies certain type of sublinear conditions with respect to the
partial order defined by a closed convex cone. The examples of
application to nonlinear difference equations are also given.
Compact‐calibres of regular and monotonically normal spaces
Authors: Mcintyre David W.
Published: September 2002

A topological space has calibre ω1 (resp., calibre (ω1, ω)) if every point‐countable (resp.,
point‐finite) collection of nonempty open sets is countable. It
has compact‐calibre ω1 (resp., compact‐calibre (ω1, ω)) if, for every family of uncountably many nonempty open sets, there is some compact set which meets uncountably many (resp., infinitely many) of them. It has CCC (resp., DCCC) if every disjoint (resp., discrete) collection of
nonempty open sets is countable. The relative strengths of these six conditions are determined for Moore spaces, regular first countable spaces, linearly‐ordered spaces, and arbitrary regular spaces. It is shown that the relative strengths for spaces with point‐countable bases are the same as those for Moore spaces, and the relative strengths for linearly‐ordered spaces are the same
as those for arbitrary monotonically normal spaces.
On the function TreH+itK
Authors: Fannes Mark , Petz Dénes
Published: September 2002

We prove, for two free semicircularly distributed selfadjoint elements a and b in a type II1 von Neumann algebra with faithful trace τ, that the function t ∈ ℝ ↦ τ(exp(a + itb)) is positive definite. This shows that the Bessis‐Moussa‐Vilani conjecture holds for large random matrices in an asymptotic sense.
On generalized fuzzy strongly semiclosed sets in fuzzy topological spaces
Authors: Ozbakir Oya Bedre
Published: September 2002

We introduce the concept of generalized fuzzy strongly
semiclosed, generalized fuzzy almost‐strongly semiclosed, generalized fuzzy strongly closed, and generalized fuzzy almost‐strongly closed sets. In the light of these definitions, we also define some generalizations of fuzzy continuous functions and discuss the relations between these new classes of functions and other fuzzy continuous functions.
On the geometry of free loop spaces
Authors: Manoharan P.
Published: September 2002

We verify the following three basic results on the free loop space
LM. (1) We show that the set of all points, where the
fundamental form on LM is nondegenerate, is an open subset. (2)
The connections of a Fréchet bundle over LM can be extended
to S1‐central extensions and, in particular, there exist
natural connections on the string structures. (3) The notion of
Christoffel symbols and the curvature are introduced on LM and
they are described in terms of Christoffel symbols of M.
The generalized method of exhaustion
Authors: Ruffa Anthony A.
Published: September 2002

The method of exhaustion is generalized to a simple integration
formula that is valid for the Riemann integrable functions. Both
a geometric approach (following the usual procedure for the
method of exhaustion) and an independent algebraic generalization
approach are provided. Applications provided as examples include
use of the formula to generate new series for common functions as
well as computing the group velocity distribution resulting from
waves diffracted from an aperture.
On ideals and homology in additive categories
Authors: Ionescu Lucian M.
Published: September 2002

Ideals are used to define homological functors in additive
categories. In abelian categories the ideals corresponding to the
usual universal objects are principal, and the construction
reduces, in a choice dependent way, to homology groups.
The applications considered in this paper are: derived
categories and functors.
Monotone‐iterative technique of Lakshmikantham for the initial value problem for a differential equation with a step function
Authors: Hristova S. G. , Rangelova M. A.
Published: September 2002

The initial value problem for a special kind of differential
equations with a step function is studied. The monotone‐iterative
technique of Lakshmikantham for approximate finding of the
solutions of the given problem is well grounded.
Noncomplete affine structures on Lie algebras of maximal class
Authors: Remm E. , Goze Michel
Published: September 2002

Every affine structure on Lie algebra 𝔤 defines a
representation of 𝔤 in aff(ℝn). If 𝔤 is a nilpotent Lie algebra provided with a
complete affine structure then the corresponding representation
is nilpotent. We describe noncomplete affine
structures on the filiform Lie algebra Ln. As a consequence we give a nonnilpotent faithful linear representation of the 3‐dimensional Heisenberg algebra.
Fuzzy implicative hyper BCK‐ideals of hyper BCK‐algebras
Authors: Jun Young Bae , Shim Wook Hwan
Published: September 2002

We consider the fuzzification of the notion of implicative hyper
BCK‐ideals, and then investigate several properties.
Using the concept of level subsets, we give a
characterization of a fuzzy implicative hyper BCK‐ideal. We state
a relation between a fuzzy hyper BCK‐ideal and a fuzzy implicative
hyper BCK‐ideal. We establish a condition for a fuzzy hyper
BCK‐ideal to be a fuzzy implicative hyper BCK‐ideal. Finally, we
introduce the notion of hyper homomorphisms of hyper
BCK‐algebras, and discuss related properties.
Characterizing symmetric diametrical graphs of order 12 and diameter 4
Authors: Al-Addasi S. , Al-Ezeh H.
Published: September 2002

A diametrical graph G is said to be symmetric if for all u, v ∈ V(G), where is the buddy of u. If moreover, G is bipartite, then it is
called an S‐graph. It would be shown that the Cartesian product
K2 × C6 is not only the unique S‐graph of order 12 and diameter 4, but also the unique symmetric diametrical
graph of order 12 and diameter 4.
The equivalence between the Hamiltonian and Lagrangian formulations for the parametrization‐invariant theories
Authors: Muslih S. I.
Published: September 2002

The link between the treatment of singular Lagrangians as field
systems and the canonical Hamiltonian approach is studied. It
is shown that the singular Lagrangians as field systems are
always in exact agreement with the canonical approach for the
parametrization invariant theories.
A measure of graph vulnerability: scattering number
Authors: Kirlangiç Alpay
Published: September 2002

The scattering number of a graph G, denoted sc(G), is defined by sc(G) = max{c(G − S) − |S| : S⫅V(G)    and   c(G − S) ≠ 1} where c(G − S) denotes the
number of components in G − S. It is one measure of graph
vulnerability. In this paper, general results on the
scattering number of a graph are considered. Firstly,
some bounds on the scattering number are given. Further,
scattering number of a binomial tree is calculated. Also
several results are given about binomial trees and
graph operations.
On the finite Fourier transforms of functions with infinite discontinuities
Authors: Saric Branko
Published: September 2002

The introductory part of the paper is provided to give a brief review of the stability theory of a matrix pencil for discrete linear time‐invariant singular control systems, based on the causal relationship between Jordan′s theorem from the theory of Fourier series and Laurent′s theorem from the calculus of residues. The main part is concerned with the theory of the integral transforms, which has proved to be a powerful tool in the control systems theory. On the basis of a newly defined notion of the total value of improper integrals, throughout the main part of the paper, an attempt has been made to present the global theory of the integral transforms, which are slightly more general with respect to the Laplace and Fourier transforms. The paper ends with examples by which the results of the theory are verified.
Separable functors in corings
Authors: Gómez-Torrecillas J.
Published: September 2002

We develop some basic functorial techniques for the study of the
categories of comodules over corings. In particular, we prove that
the induction functor stemming from every morphism of corings has
a left adjoint, called ad‐induction functor. This construction
generalizes the known adjunctions for the categories of Doi‐Hopf
modules and entwined modules. The separability of the induction
and ad‐induction functors are characterized, extending earlier
results for coalgebra and ring homomorphisms, as well as for
entwining structures.
Ricci curvature of submanifolds in Kenmotsu space forms
Authors: Arslan Kadri , Ezentas Ridvan , Mihai Ion , Murathan Cengizhan , Özgür Cihan
Published: September 2002

In 1999, Chen established a sharp relationship between the Ricci
curvature and the squared mean curvature for a submanifold in a
Riemannian space form with arbitrary codimension. Similar problems
for submanifolds in complex space forms were studied
by Matsumoto et al. In this paper, we obtain sharp
relationships between the Ricci curvature and the squared mean
curvature for submanifolds in Kenmotsu space forms.
Integrability and L1‐convergence of Rees‐Stanojević sums with generalized semiconvex coefficients
Authors: Kaur Kulwinder , Bhatia S. S.
Published: September 2002

Integrability and L1‐convergence of modified cosine sums introduced by Rees and Stanojević (1973) under a class of generalized semiconvex null coefficients are studied, using Cesaro means of integral order.
Aspects of complete uniform spreads in frames
Authors: Siweya Hlengani James
Published: September 2002

We give a new notion of a complete uniform spread in terms of a
relative kind of uniform local connectedness. Properties of this
type of (uniform) connectedness are discussed. It is also
shown that our concept of complete spread is equivalent to that
of Hunt (1982).
Singularly perturbed Volterra integral equations with weakly singular kernels
Authors: Bijura Angelina
Published: September 2002

We consider finding asymptotic solutions of the singularly
perturbed linear Volterra integral equations with weakly singular
kernels. An interesting aspect of these problems is that the
discontinuity of the kernel causes layer solutions to decay
algebraically rather than exponentially within the initial
(boundary) layer. To analyse this phenomenon, the paper
demonstrates the similarity that these solutions have to a special
function called the Mittag‐Leffler function.
A generalised hopf algebra for solitons
Authors: Al-Solamy Falleh R. , Beggs Edwin J.
Published: September 2002

This paper considers a generalisation of the idea of a Hopf
algebra in which a commutative ring replaces the field in the
unit and counit. It is motivated by an example from the inverse
scattering formalism for solitons. We begin with the
corresponding idea for groups, where the concept of the identity
is altered.
A quantum field theoretical representation of Euler‐Zagier sums
Authors: Müller Uwe , Schubert Christian
Published: September 2002

We establish a novel representation of arbitrary Euler‐Zagier
sums in terms of weighted vacuum graphs. This representation uses
a toy quantum field theory with infinitely many propagators and
interaction vertices. The propagators involve Bernoulli
polynomials and Clausen functions to arbitrary orders. The
Feynman integrals of this model can be decomposed in terms of a
vertex algebra whose structure we investigate. We derive a large
class of relations between multiple zeta values, of arbitrary
lengths and weights, using only a certain set of graphical
manipulations on Feynman diagrams. Further uses and possible
generalisations of the model are pointed out.
Born‐infeld electrodynamics: Clifford number and spinor representations
Authors: Chernitskii Alexander A.
Published: September 2002

The Clifford number formalism for Maxwell equations is considered. The Clifford imaginary unit for space‐time is introduced as coordinate independent form of fully antisymmetric fourth‐rank tensor. The representation of Maxwell equations in massless Dirac equation form is considered; we also consider two approaches to the invariance of Dirac equation with respect to the Lorentz transformations. According to the first approach, the unknown column is invariant and according to the second approach it has the transformation properties known as spinorial ones. The Clifford number representation for nonlinear electrodynamics equations is obtained. From this representation, we obtain the nonlinear like Dirac equation which is the form of nonlinear electrodynamics equations. As a special case we have the appropriate representations for Born‐Infeld nonlinear electrodynamics.
Fixed point theorems for nonexpansive mappingson nonconvex sets in UCED Banach spaces
Authors: Du Wei-Shih , Huang Young-Ye , Yen Chi-Lin
Published: September 2002

It is shown that every asymptotically regular or λ‐firmly
nonexpansive mapping T : C → C has a fixed point
whenever C is a finite union of nonempty weakly compact convex
subsets of a Banach space X which is uniformly convex in every
direction. Furthermore, if is any compatible family of strongly nonexpansive self‐mappings on such a C and the graphs of T i, i ∈ I, have a nonempty intersection, then T i, i ∈ I, have a common fixed point in C.