De Schepper, H.
Some computational aspects of the consistent mass finite element
method for a (semi-)periodic eigenvalue problem
(pp. 177-184)
A B S T R A C T S
THE PERTURBED GENERALIZED TIKHONOV'S ALGORITHM
P. Alexandre
P.Alexandre@ulg.ac.be
1991 Mathematics Subject Classification: 65J15, 65K10.
Key words:
Tikhonov's regularization,
perturbation, variable metric, relaxation, variational convergence.
We work on the research of a zero of a maximal monotone operator on
a real Hilbert space. Following the recent progress made in the context
of the proximal point algorithm devoted to this problem, we introduce
simultaneously a variable metric and a kind of relaxation in the perturbed
Tikhonov's algorithm studied by P. Tossings. So, we are led to work
in the context of the variational convergence theory.
PARACOMPACT SPACES AND RADON SPACES
Baltasar Rodriguez-Salinas
1991 Mathematics Subject Classification: 46A50, 46G12.
Key words:
Radon spaces, paracompact, weak topology.
We prove that if E is a subset of a Banach space
whose density is of measure zero and such that (E,weak) is a
paracompact space, then (E,weak) is a Radon space of type
(F) under very general
conditions.
RELATIVE COMPACTNESS FOR HYPERSPACES
ON THE BRILL--NOETHER THEORY OF
SPANNED VECTOR BUNDLES ON SMOOTH CURVES
E. Ballico
ballico@science.unitn.it
1991 Mathematics Subject Classification: 14H60.
Key words:
stable vector bundle, spanned
vector bundle, vector bundles on curves, gonality, curves with
general moduli.
Here we study
the integers (d,g,r) such that on a smooth projective curve of
genus g there exists a rank $r$ stable vector bundle with degree
d and spanned by its global sections.
AN EXAMPLE CONCERNING VALDIVIA COMPACT SPACES
Ondrej Kalenda
kalenda@karlin.mff.cuni.cz
1991 Mathematics Subject Classification:
46B04, 54D30.
Key words:
Valdivia compact space, Fréchet-Urysohn space,
countably compact space, countably 1-norming Markusevic basis.
We prove that the dual unit ball of the space
C_{0}
[0,w_{1})
endowed with the weak* topology is not a
Valdivia compact. This answers a question posed to the author by
V. Zizler and has several consequences. Namely, it yields an example of an
affine continuous image of a convex Valdivia compact (in the
weak* topology of a dual Banach space) which is not
Valdivia, and shows that the property of the dual unit ball being
Valdivia is not an isomorphic property. Another consequence is
that the space
C_{0}
[0,w_{1}) has no countably 1-norming
Markusevic basis.
ON THE MAXIMUM OF A BRANCHING PROCESS CONDITIONED
ON THE TOTAL PROGENY
Tzvetozar B. Kerbashev
tkerbashev@yahoo.com
1991 Mathematics Subject Classification:
Primary 60J80. Secondary 60J15, 05C05.
Key words:
Bienaymé-Galton-Watson branching process, maximum,
total progeny, left-continuous random walk, random rooted labeled trees.
The maximum M of a critical Bienaymé-Galton-Watson process
conditioned on the total progeny N is studied.
Imbedding of the process in a random walk is used.
A limit theorem for the distribution of M as N
® ¥
is proved.
The result is trasferred to the non-critical processes.
A corollary for the maximal strata of a random rooted labeled tree
is obtained.
SOME COMPUTATIONAL ASPECTS OF THE CONSISTENT MASS FINITE ELEMENT
METHOD FOR A (SEMI-)PERIODIC EIGENVALUE PROBLEM
H. De Schepper
hds@cage.rug.ac.be
1991 Mathematics Subject Classification:
65N25, 65N30, 15A18.
Key words:
eigenvalue problems, periodic boundary conditions,
circulant matrices.
We consider a model eigenvalue problem (EVP) in 1D, with periodic or
semi-periodic boundary conditions (BCs). The discretization of this
type of EVP by consistent mass finite element methods (FEMs) leads to
the generalized matrix EVP Kc = l Mc,
where K and M are
real, symmetric matrices, with a certain (skew-)circulant structure.
In this paper we fix our attention to the use of a quadratic
FE-mesh. Explicit expressions for the eigenvalues of the resulting
algebraic EVP are established. This leads to an explicit form for
the approximation error in terms of the mesh parameter, which confirms
the theoretical error estimates, obtained in [2].
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