186 research outputs found
Canonical almost pseudo-K\"{a}hler structures on six-dimensional nilpotent Lie groups
It is known that there are 34 classes of isomorphic connected simply
connected six-dimensional nilpotent Lie groups. Of these, only 26 classes
suppose left-invariant symplectic structures \cite{Goze-Khakim-Med}. In
\cite{CFU2} it is shown that 14 classes of symplectic six-dimensional nilpotent
Lie groups suppose compatible complex structures and, therefore, define
pseudo-K\"{a}hler metrics. In this paper we show that on the remaining 12
classes of six-dimensional nilpotent symplectic Lie groups there are
left-invariant almost pseudo-K\"{a}hler metrics, and we study their geometrical
properties.Comment: 26 pages. arXiv admin note: text overlap with arXiv:1310.539
Bi-invariant metric on symplectic diffeomorphisms group
We show the existence of a weak bi-invariant symmetric nondegenerate 2-form
on the symplectic diffeomorphisms group of a symplectic
Riemannian manifold and study its properties. We describe the
Euler's equation on a Lie algebra of group and calculate
the sectional curvature of .Comment: 12 page
Canonical pseudo-K\"{a}hler structures on six-dimensional nilpotent Lie groups
In this paper we consider left-invariant pseudo-K\"{a}hler structures on
six-dimensional nilpotent Lie algebras. The explicit expressions of the
canonical complex structures are calculated, and the curvature properties of
the associated pseudo-K\"{a}hler metrics are investigated. It is proved that
the associated pseudo-K\"{a}hler metric is Ricci-flat, that the curvature
tensor has zero pseudo-Riemannian norm, and that the curvature tensor has some
non-zero components that depend only on two or, at most, three parameters. The
pseudo-K\"{a}hler structures obtained give basic models of pseudo-K\"{a}hler
six-dimensional nilmanifolds.Comment: 21 page
Almost complex and almost para-complex Cayley structures on six-dimensional pseudo-Riemannian spheres
In this paper we study almost complex and almost para-complex Cayley
structures on six-dimensional pseudo-Riemannian spheres in the space of purely
imaginary octaves of the split Cayley algebra . It is shown that
the Cayley structures are non-integrable, their basic geometric characteristics
are calculated. In contrast to the usual Riemann sphere , there
exist (integrable) complex structures and para-complex structures on the
pseudospheres under consideration.Comment: 17 pages, 1 figur
On the space of almost complex structures
The space of almost complex structures on a closed manifold
is studied. A natural parametrization of the space is
defined. It is shown, that is a infinite dimensional complex
weak Pseudo-Riemannian manifold. A curvature of the space is
found. The space of associated almost complex structures
on a symplectic manifold and space of orthogonal
almost complex structures on a Riemannian manifold are considered in
more detail.Comment: LaTeX, 8 page
About construction of orthogonal wavelets with compact support and with scaling coefficient N
In this paper a simple method of construction of scaling function
and orthogonal wavelets with the compact support for any natural coefficient of
scaling is given. Examples of construction of wavelets for
coefficients of scaling N=2 and N=3 are produced.Comment: LaTeX2e, 15 page
Construction of some types wavelets with coefficient of scaling N
In this paper it is shown, that B-splines are scaling functions for any
natural N. For any natural N construction of Haar wavelets, Kotelnikov-Shannon
wavelets, nonorthogonal wavelets based on B-splines is given. Examples of
construction of filters of N-channel decomposition of signal and filters of
reconstruction based on B-splines are givenComment: LaTeX2e, 19 page
The space of associated metrics on a symplectic manifold
The spaces of Riemannian metrics on a closed manifold are studied. On the
space of all Riemannian metrics on the various weak
Riemannian structures are defined and the corresponding connections are
studied. The space of associated metrics on a symplectic
manifold is considered in more detail. A natural parametrization of
the space is defined. It is shown, that is a
complex manifold. A curvature of the space and quotient space
is found. The finite dimensionality of
the space of associated metrics of a constant scalar curvature with Hermitian
Ricci tensor is shown.Comment: LaTeX, 83 page
Bi-invariant metric on contact diffeomorphisms group
We show the existence of a weak bi-invariant symmetric nondegenerate 2-form
on the contact diffeomorphisms group of a contact
Riemannian manifold and study its properties. We describe the
Euler's equation on a Lie algebra of group and calculate
the sectional curvature of . In a case
connection between the bi-invariant metric on and the
bi-invariant metric on volume-preserving diffeomorphisms group
of is discover.Comment: 12 page
Wavelet analysis in problems of classification of ECG signals
In this paper, the wavelet analysis is used to study the ECG signal. We show
that the high-frequency wavelet components of the ECG signal contain
information on the functioning of the heart and can be used in diagnosis. We
describe the automated classification system that separates the ECG of sick and
healthy persons using only a high-frequency ECG component.Comment: 15 pages, 5 figure
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