3,356 research outputs found
On The Geometric Monodromy Of The Milnor Fibre
In this paper we show that the geometric monodromy of the Milnor
fibre, has finite order q if and only if the operator acts trivially
on the homology. The proof is based on the classical methods of surgery.Comment: Milnor fibres bounded by rational homology spheres only should be
considered her
Pseudo-isotopy classes of diffeomorphisms of the unknotted pairs and
We consider two pairs: the standard unknotted -sphere in , and
the product of two -spheres trivially embedded in , and study
orientation preserving diffeomorphisms of these pairs. Pseudo-isotopy classes
of such diffeomorphisms form subgroups of the mapping class groups of and
respectively and we determine the algebraic structure of such
subgroups when and
Relative mapping class group of
Algebraic structure of the group of pseudo-isotopy classes of diffeomorphisms
of the trivial disk bundle over the standard sphere which restrict to the
identity map on the boundary is determined.Comment: 9 page
A basis of the group of primitive almost pythagorean triples
Let be a fixed square-free positive integer, then equivalence classes of
solutions of Diophantine equation form an infinitely
generated abelian group under the operation induced by the complex
multiplication. A basis of this group is constructed here using prime ideals
and the ideal class group of the field .Comment: 10 pages, continuation of arXiv:1107.286
Permutations with a distinct divisor property
A finite group of order is said to have the distinct divisor property
(DDP) if there exists a permutation of its elements such that
for all . We show that an
abelian group is DDP if and only if it has a unique element of order 2. We also
describe a construction of DDP groups via group extensions by abelian groups
and show that there exist infinitely many non abelian DDP groups
A congruence property of irreducible Laguerre polynomials in two variables
In this paper we introduce a version of irreducible Laguerre polynomials in
two variables and prove for it a congruence property, which is similar to the
one obtained by Carlitz for the classical Laguerre polynomials in one variable.Comment: 10 page
Stochastic Soliton Lattices
We introduce a new concept, Stochastic Soliton Lattice, as a random process
generated by a finite-gap potential of the Shroedinger operator. We study the
basic properties of this stochastic process and consider its KdV evolutionComment: 11 pages. To be published in Proceedings of the International
Conference `Solitons, Geometry and Topology: on the Crossroads', Moscow, 199
Angle contraction between geodesics
We consider here a generalization of a well known discrete dynamical system
produced by the bisection of reflection angles that are constructed recursively
between two lines in the Euclidean plane. It is shown that similar properties
of such systems are observed when the plane is replaced by a regular surface in
and lines are replaced by geodesics. An application of our
results to the classification of points on the surface as elliptic, hyperbolic
or parabolic is also presented.Comment: 10 pages, 2 figure
Cosmological phase transition, baryon asymmetry and dark matter Q-balls
We consider a mechanism of dark matter production in the course of first
order phase transition. We assume that there is an asymmetry between X- and
anti-X-particles of dark sector. In particular, it may be related to the baryon
asymmetry. We also assume that the phase transition is so strongly first order,
that X-particles do not permeate into the new phase. In this case, as the
bubbles of old phase collapse, X-particles are packed into Q-balls with huge
mass defect. These Q-balls compose the present dark matter. We find that the
required present dark matter density is obtained for the energy scale of the
theory in the ballpark of 1-10 TeV. As an example we consider a theory with
effective potential of one-loop motivated form.Comment: 17 pages, 3 figure
Harmonic Networks with Limited Training Samples
Convolutional neural networks (CNNs) are very popular nowadays for image
processing. CNNs allow one to learn optimal filters in a (mostly) supervised
machine learning context. However this typically requires abundant labelled
training data to estimate the filter parameters. Alternative strategies have
been deployed for reducing the number of parameters and / or filters to be
learned and thus decrease overfitting. In the context of reverting to preset
filters, we propose here a computationally efficient harmonic block that uses
Discrete Cosine Transform (DCT) filters in CNNs. In this work we examine the
performance of harmonic networks in limited training data scenario. We validate
experimentally that its performance compares well against scattering networks
that use wavelets as preset filters
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