7,398 research outputs found
On an argument of J.--F. Cardoso dealing with perturbations of joint diagonalizers
B. Afsari has recently proposed a new approach to the matrix joint
diagonalization, introduced by J.--F. Cardoso in 1994, in order to investigate
the independent component analysis and the blind signal processing in a wider
prospective. Delicate notions of linear algebra and differential geometry are
involved in the works of B. Afsari and the present paper continues such a line
of research, focusing on a theoretical condition which has significant
consequences in the numerical applications.Comment: 9 pages; the published version contains significant revisions
(suggested by the referees
On the Connectivity of the Sylow Graph of a Finite Group
The Sylow graph of a finite group originated from recent
investigations on the so--called --closed classes of groups. The
connectivity of was proved only few years ago, involving the
classification of finite simple groups, and the structure of may be
strongly restricted, once information on are given. The first
result of the present paper deals with a condition on --closed
classes of groups. The second result deals with a computational criterion,
related to the connectivity of .Comment: 8 pp. with Appendix; Fundamental revisions have been don
Functional it{\^o} versus banach space stochastic calculus and strict solutions of semilinear path-dependent equations
Functional It\^o calculus was introduced in order to expand a functional
depending on time , past and present values of
the process . Another possibility to expand
consists in considering the path as an
element of the Banach space of continuous functions on and to use
Banach space stochastic calculus. The aim of this paper is threefold. 1) To
reformulate functional It\^o calculus, separating time and past, making use of
the regularization procedures which matches more naturally the notion of
horizontal derivative which is one of the tools of that calculus. 2) To exploit
this reformulation in order to discuss the (not obvious) relation between the
functional and the Banach space approaches. 3) To study existence and
uniqueness of smooth solutions to path-dependent partial differential equations
which naturally arise in the study of functional It\^o calculus. More
precisely, we study a path-dependent equation of Kolmogorov type which is
related to the window process of the solution to an It\^o stochastic
differential equation with path-dependent coefficients. We also study a
semilinear version of that equation.Comment: This paper is a substantial improvement with additional research
material of the first part of the unpublished paper arXiv:1401.503
About Fokker-Planck equation with measurable coefficients and applications to the fast diffusion equation
The object of this paper is the uniqueness for a -dimensional
Fokker-Planck type equation with non-homogeneous (possibly degenerated)
measurable not necessarily bounded coefficients. We provide an application to
the probabilistic representation of the so called Barenblatt solution of the
fast diffusion equation which is the partial differential equation with . Together with the mentioned
Fokker-Planck equation, we make use of small time density estimates uniformly
with respect to the initial conditio
Some extremal contractions between smooth varieties arising from projective geometry
We construct explicit examples of elementary extremal contractions, both
birational and of fiber type, from smooth projective n-dimensional varieties,
n\geq 4, onto smooth projective varieties, arising from classical projective
geometry and defined over sufficiently small fields, not necessarily
algebraically closed.
The examples considered come from particular special homaloidal and
subhomaloidal linear systems, which usually are degenerations of general
phenomena classically investigated by Bordiga, Severi, Todd, Room, Fano, Semple
and Tyrrell and more recently by Ein and Shepherd-Barron.
The first series of examples is associated to particular codimension 2
determinantal smooth subvarieties of P^m, 3\leq m\leq 5. We get another series
of examples by considering special cubic hypersurfaces through some surfaces in
P^5, or some 3-folds in P^7 having one apparent double point. The last examples
come from an intriguing birational elementary extremal contraction in dimension
6, studied by Semple and Tyrrell and fully described in the last section.Comment: 29 pages. Proc. London Math. Society, to appea
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