African
Journals Online
Quaestiones Mathematicae
Volume 24 Issue 1, 2001
Quaestiones Mathematicae 24(1) 2001, 1-8
© 2001 NISC Pty Ltd, www.nisc.co.za
The Lattice of Ideals of the Nearring of Coset Preserving
Functions
G Alan Cannon 1 and Lucyna Kabza
2
Department of Mathematics, Southeastern Louisiana
University, Hammond, LA 70402, USA.
* Corresponding author, e-mail: 1[email protected]
2 [email protected]
Abstract: Let G be a group and let N be a normal
subgroup of G. The lattice of ideals of the nearring $\D(N) = {f
: G \rightarrow G \mid f(0) = 0 and f(x + N) \subseteq f(x) + N
for all x \in G}$ is determined.
Mathematics Subject Classification (1991): 16Y30
Keywords: near-rings, ideals, lattice
Quaestiones Mathematicae 24(1) 2001, 9–19
© 2001 NISC Pty Ltd, www.nisc.co.za
Some Invariant Solutions for Unsaturated Flow Models with
Plant Root Extraction
VA Baikov 1 and CM Khalique
2
1 Institute for Symmetry
Analysis and Mathematical Modelling, University of North-West,
Private Bag X2046, Mmabatho 2375, South Africa
2 Department of Mathematical Sciences,
University of North-West, Private Bag x2046, Mmabatho 2735, South
Africa.
e-mail: [email protected]
Abstract: Using two parameter symmetry groups we shall
obtain exact (invariant) solutions for a class of non-linear
partial differential equations which models soil water
infiltration and redistribution in a bedded soil profile
irrigated by a drip irrigation system. Studying of such solutions
is important from the agricultural point of view because the
solution will help to determine the irrigation input while
optimizing the production returns.
Mathematics Subject Classification (1991): 35Q35, 22S76
Keywords: plant root extraction, soil, water,
infiltration, irrigation, agricultural/other equations arising in
fluid mechanics/symmetry, nonlinear, partial differential
equations, differential equations
Quaestiones Mathematicae 24(1) 2001, 21–37
© 2001 NISC Pty Ltd, www.nisc.co.za
Almost 2-Fully Normal, Pairwise Paracompact and Complete
Developable Bispaces
Salvador Romaguera
Escuela de Caminos, Deparmento de Matemática Aplicada,
Universidad Politécnica de Valencia, 46071, Valencia, Spain.
e-mail: [email protected]
Abstract: We introduce and study the notion of an
almost 2-fully normal bispace. In particular; we prove that a
bispace is quasi-pseudometrizable if and only if it is almost
2-fully normal and pairwise developable. We obtain conditions
under which an almost 2-fully normal bispace is
subquasi-metrizable and show that the fine quasi-uniformity of
any subquasi-metrizable topological space is bicomplete. We prove
that every pairwise paracompact bispace (in the sense of Romguera
and Marin, 1988) is almost 2-fully normal and that the finest
quasi-uniformity of any 2-Hausdorff pairwise paracompact bispace
is bicomplete. We also characterize pairwise paracompactness in
terms of a property of $\sigma$-Lebesgue type of the finest
quasi-uniformity. Finally, we use Salbany's compactification of
pairwise Tychonoff bispaces to characterize those bispaces that
admit a bicomplete pair development and deduce that an
interesting example of R. Fox of a non-quasi-metrizable pairwise
stratifiable pairwise developable bispace admits a bicomplete
pair development.
Mathematics Subject Classification (1991): 54E55,
54E35, 54E15, 54E30
Keywords: bispace, almost 2-fully normal, pair
development, quasi-metrizable, subquasi-metrizable, finest
quasi-uniformity, bicomplete, pairwise paracompact, s-Lebesgue,
Salbany's compactification, bitopologies, metric spaces,
metrizability, uniform structures and generalizations, Moore
spaces, study, quasi-uniformity, topological space,
compactification, Tychonoff
Quaestiones Mathematicae 24(1) 2001, 39–50
© 2001 NISC Pty Ltd, www.nisc.co.za
On the Strict Completion of a Nearness Space
HL Bentley 1 and H Herrlich 2
1 Department of
Mathematics, University of Toledo, Toledo, Ohio, USA.
e-mail: [email protected]
2 Fachbereich Mathematik und Informatik,
Universitat Bremen, Bremen, Germany.
e-mail: [email protected]
Abstract: The strict completion of a nearness space was
constructed in 1974 in Herrlich's original paper on nearness. we
present an external characterization of this completion. Among
the consequences of this result is the fact that for nearness
spaces X and Y with completions $\X^{*}$ and $\Y^{*}$, if $X
\subset Y \subset X^{*}$ then $\Y^{*}$ is isomorphic to $\X^{*}$.
Mathematics Subject Classification (1991): 54E17,
54D35, 54E15
Keywords: completeness, nearness space, completion,
initial map, strict map, dense map, nearness spaces, extensions
of spaces, uniform structures and generalizations, completions
Quaestiones Mathematicae 24(1) 2001, 51–54
© 2001 NISC Pty Ltd, www.nisc.co.za
On a Theorem of Kwapien
JC Ferrando
Departmento de Esadística y Matemática Aplicada,
Universidad Miduel Hernández, Avenida Ferrocarril, s/n. 03202
Elche (Alicante), Spain.
e-mail: [email protected]
Abstract: If $(\Omega, \Sigma, \nu)$ is the Cantor
group with its resident Haar measure, X a Banach space and
$\{x_{n}}$ a sequence in X, a classic theorem of Kwapien is used
in this note to investigate the relationship between the
convergence of the series $\sum_{n=1}^{\infty}\omega_{n}\x_{n}$
in $\L_{1}(\nu, X)$ and the existence of certain convergent
subseries of $\sum_{n=1}^{\infty}\x_{n}$ in X.
Mathematics Subject Classification (1991): 46B15, 46B09
Keywords: Unconditionally convergent series, measure
preserving transformation, summability and bases, probabilistic
methods in Banach space theory, convergence
Quaestiones Mathematicae 24(1) 2001, 55–63
© 2001 NISC Pty Ltd, www.nisc.co.za
A Note on Reconstruction of Spaces and Maps from Lattice
Data
A Pultr 1 and A Tozzi 2
1 Department of Applied
Mathematics, MFF, Charles University, Malostranské Nám. 25,
CZ-11800 Praha 1- Malá Strana, Chech Republic.
e-mail: [email protected]
2 Dipartmento Mathematica Pura ed
Applicata, Università degli Studi di L'Aquila , Via Vetoio -
Loc. Coppito, I-67100 L'Aquila, Italy.
e-mail: [email protected]
Abstract: Reconstruction of topological spaces from the
lattices $\Omega(X)$of open sets, and of continuous maps from
lattice homomorphisms satisfying additional properties
(formulated in lattice terms) is discussed. We focus on the
question when and how the filters $\lambda(x) = {U \mid x \in U
\in \Omega(X)}$ can be specified by algebraic means.
Mathematics Subject Classification (1991): 54D10, 06D99
Keywords: lattice, frame, centred filters, lower
seperation axioms, topological space, open, sets, continuous
maps, continuous map, homomorphisms
Quaestiones Mathematicae 24(1) 2001, 65–73
© 2001 NISC Pty Ltd, www.nisc.co.za
Amplitude-Shape Method for the Numerical Solution of
Ordinary Differential Equations
N Parumasur 1 and JR Mika
2
1 Department of Mathematics
and Applied Mathematics, University of Durban-Westville, Private
Bag X54001, Durban 4001, South Africa.
e-mail: [email protected]
2 Technical University, Lodz, Poland and
Institute of Atomic Energy, Swierk, Poland.
e-mail: [email protected]
Abstract: The numerical solution of large stiff systems of
ordinary differential equations is very expensive and often
impossible to be done on a PC. Even if a large mainframe computer
is used, it might be too slow to follow the evolution of a
physical system in real time and parallel computations are
needed. In this paper we propose an amplitude-shape method which
takes into account the particular structuure of some evolution
problems, especially those described by partial differental
equations. This method consists in transforming the system so
that only a few equations remain stiff, the majority of the
equations are non-stiff. The system is treated with a mixed
explicit-implicit scheme which leads to a considerable reduction
of numerical effort. We compare our approach with a classical
solver of ordinary differential equations taking as an example,
stiff systems of equations describing spatially dependent
chemical kinetics.
Keywords: amplitude-shape/ode/numerical/stiff
equations/differential equations/computer
Mathematics Subject Classification (1991): 34A65
Quaestiones Mathematicae 24(1) 2001, 75–92
© 2001 NISC Pty Ltd, www.nisc.co.za
Disconnectedness Classes
G Castellini
Department of Mathematics, University of Puerto Rico,
Mayagüez campus, PO Box 9018, Mayagüez, PR 00681-9018, USA.
e-mail: [email protected]
Abstract: Let $\cal X$ be an $(\bold E, \cal
M)$-category for sinks. A notion of disconnectedness with respect
to a closure operator C on $\cal X$ and to a class of $\cal
X$-monomorphisms $\cal N$ is introduced. This gives rise to the
notion of $\cal N$-disconnectedness class, a characterization of
which is presented in a category with a terminal object. Some
examples are provided.
Mathematics Subject Classification (1991): 18A32,
06A15, 18E40
Keywords: closure operator, disconnectedness, Galois
connection, constant morphism, torsion theories, radicals,
factorization of morphisms, substructures, quotient structures,
congruences, amalgams, Galois correspondences, closure operators,
sink, category, categories, terminal object
Quaestiones Mathematicae 24(1) 2001, 93–104
© 2001 NISC Pty Ltd, www.nisc.co.za
Heat and Mass Transfer in a Pipe with Moving Surface:
Effects of Viscosity Variation and Energy Dissipation
OD Makinde
Department of Applied Mathematics, University of the North,
Private Bag X1106, Sovenga 0727, South Africa.
e-mail: [email protected]
Abstract: In this study, we investigate the combined
effects of viscosity variation and energy dissipation on steady
flow of an incompressable fluid in a pipe with moving surface. On
the basis of certain simplifying assumptions, the fluid equations
of continuity, momentum, energy and concentration are obtained.
Analytical solutions are therefore constructed for the problem
and important properties of the overall structure of the flow are
discuseed. The model is appropriate to simulate wind tunnel tests
on lubrication phenomenon in engineering systems.
Mathematics Subject Classification (1991): 76Z05, 76E25
Keywords: pipe flow, moving surface, viscosity
variation;, heat and material flux, energy dissipation,
physiological flows, magnetohydrodynamic and electrohydrodynamic
instabilities
Quaestiones Mathematicae 24(1) 2001, 105–109
© 2001 NISC Pty Ltd, www.nisc.co.za
Rings Related to Special Atoms
Halina France-Jackson
Department of Mathematics, Vista University, Private Bag
X613, Port Elizabeth 6000, South Africa.
e-mail: [email protected]
Abstract: A ring which is an essential extension of a
prime ring without proper prime homomorphic images is called a
$\ast_{k}$-ring. $\ast_{k}$-rings are characterized and it is
shown that every non-zero prime ring whose every proper
homomorphic image is artinian on right (left, two-sided) ideals
can be homomorphically mapped onto a non-zero $\ast_{k}$-ring.
This gives a partial answer to Gardner's question (Problem 1 in
[4]).
Mathematics Subject Classification (1991): 16A21, 16A12
Keywords: ring, special atoms, atoms, *k-ring, prime
ring, *-ring, Jacobson, artinia, essential extension, homomorphic
image, ideals
Quaestiones Mathematicae 24(1) 2001, 111–122
© 2001 NISC Pty Ltd, www.nisc.co.za
An Extension of the direct Method via an Application
Qu Changzheng 1 and FM Mahomed 2
1 Department of
Mathematics, Northwest University, Xi'an, 710069 Peoples Republic
of China.
e-mail: [email protected]
2 Department of Computational and Applied
Mathematics, and Centre for Differentional Equations, Continuum
Mechanics and applications, University of the Witwatersrand, Wits
2050, Johannesburg, South Africa.
e-mail: [email protected]
Abstract: The Direct Method due to Clarkson and Kruskal
[9] for finding similarity reductions of partial differential
equations is extended to obtain similarity reductions of
nonlinear partial differential equations with arbitrary
functions. The extension is illustrated by the nonlinear
hyperbolic equation with arbitrary wave velocity. The known
results of symmetry reductions [2] for this equation are
recovered by an extension of the direct method.
Mathematics Subject Classification (1991): 35L05,
35L70, 58J90, 58J70
Keywords: similarity reductions, partial differential
equations, symmetry, direct method, wave equation, nonlinear
second-order PDE of hyperbolic type, differential equations,
nonlinear
Quaestiones Mathematicae 24(1) 2001, 123–128
© 2001 NISC Pty Ltd, www.nisc.co.za
On the Metrization Lemma for Uniform Spaces
B Windels
University of Antwerp, Groenenborgerlaan 171, 2020 Antwerp,
Belgium.
e-mail: [email protected]
Abstract: We show a numeric generalization of the
well-known metrization lemma for uniform spaces, thereby
answering a question left open in [2] to the affirmative. An
application of the new lemma in the setting of approach theory
yields the conclusion that every approach uniformity has a basis
of pseudo-metrics.
Mathematics Subject Classification (1991): 54E15, 54E35
Keywords: metrization, uniform space, approach uniform
space, metric spaces, metrizability, uniform structures and
generalizations, uniform spaces, open
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