Call for 2010 Nomimations Sixth Vasil A. Popov Prize
A B S T R A C T S
UNIFORM G-CONVEXITY FOR VECTOR-VALUED L_{p} SPACES
Nataliia Boyko
maletska.nata@gmail.com,
Vladimir Kadets
vova1kadets@yahoo.com
2000 Mathematics Subject Classification:
46B20.
Key words:
Uniform convexity, complex uniform convexity, uniform
G-convexity.
Uniform G-convexity of Banach spaces is a recently introduced
natural generalization of uniform convexity and of complex uniform
convexity. We study conditions under which uniform G-convexity of
X passes to the space of X-valued functions L_{p} (m,X).
STRUCTURE OF THE UNIT GROUP OF FD_{10}
Manju Khan
manjukhan.iitd@gmail.com
2000 Mathematics Subject Classification:
16U60, 20C05.
Key words:
Unit Group, Group algebra.
The structure of the unit group of the group algebra FD_{10} of
the dihedral group D_{10} of order 10 over a finite field F
has been obtained.
DISPERSION PHENOMENA IN DUNKL-SCHRÖDINGER
EQUATION AND APPLICATIONS
H. Mejjaoli
hatem.mejjaoli@ipest.rnu.tn
2000 Mathematics Subject Classification:
35Q55,42B10.
Key words:
Dunkl-Schrödinger equation, Strichartz
estimates.
In this paper, we study the Schrödinger equation associated with
the Dunkl operators, we study the dispersive phenomena and we prove
the Strichartz estimates for this equation. Some applications are
discussed.
THE LEGENDRE FORMULA IN CLIFFORD ANALYSIS
Guy Laville
glaville@math.unicaen.fr,
Ivan Ramadanoff
rama@math.unicaen.fr
2000 Mathematics Subject Classification:
30A05, 33E05, 30G30, 30G35, 33E20.
Key words:
Clifford analysis,
monogenic functions, holomorphic Cliffordian functions, elliptic
functions, Weierstrass zeta function, Legendre formula.
Let R_{0,2m+1} be the Clifford algebra of the
antieuclidean 2m+1 dimensional space. The elliptic Cliffordian
functions may be generated by the z_{2m+2} function, analogous
to the well-known Weierstrass z-function. The latter
satisfies a Legendre equality. We prove a corresponding formula at
the level of the monogenic function D^{m} z_{2m+2}.
A NEW HEREDITARILY l^{2} BANACH SPACE
Giorgos Petsoulas
gpetsoulas@yahoo.gr
2000 Mathematics Subject Classification:
46B20, 46B26.
Key words:
l^{2}-saturated spaces, quasi-reflexive spaces.
We construct a non-reflexive, l^{2} saturated Banach space such
that every non-reflexive subspace has non-separable dual.
DENOISING MANIFOLDS FOR DIMENSION REDUCTION
Arvind K. Jammalamadaka
ajamma@mit.edu
2000 Mathematics Subject Classification:
68T01, 62H30, 32C09.
Key words:
Nonlinear dimension reduction, locally linear embedding,
noise reduction, smoothing, nearest neighbors, clustering.
Locally Linear Embedding (LLE) has gained prominence as a tool in
unsupervised non-linear dimensional reduction. While the algorithm
aims to preserve certain proximity relations between the observed
points, this may not always be desirable if the shape in higher
dimensions that we are trying to capture is observed with noise.
This note suggests that a desirable first step is to remove or at
least reduce the noise in the observations before applying the LLE
algorithm. While careful denoising involves knowledge of (i) the
level of noise (ii) the local sampling density and (iii) the local
curvature at the point in question, in most practical situations
such information is not easily available. Under the model we
discuss, a simple averaging of the neighboring points does reduce
the noise and is easy to implement. We consider the Swiss
roll example to illustrate how well this procedure works. Finally we
apply these ideas on biological data and perform
clustering after such a 2-step procedure of denoising and dimension
reduction.
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