Integral Manifolds and Perturbations of the Nonlinear Part of Systems of Autonomous Differential Equations with Impulses at Fixed Moments

* This investigation was supported by the Bulgarian Ministry of Science and Education under Grant MM-7.

Deformation Lemma, Ljusternik-Schnirellmann Theory and Mountain Pass Theorem on C1-Finsler Manifolds

∗Partially supported by Grant MM409/94 Of the Ministy of Science and Education, Bulgaria. ∗∗Partially supported by Grant MM442/94 of the Ministy of Science and Education, Bulgaria.

Practical, Computation Efficient High-Order Neural Network for Rotation and Shift Invariant Pattern Recognition

In this paper, a modification for the high-order neural network (HONN) is presented. Third order networks are considered for achieving translation, rotation and scale invariant pattern recognition. They require however much storage and computation power for the task. The proposed modified HONN takes into account a priori knowledge of the binary patterns that have to be learned, achieving significant gain in computation time and memory requirements. This modification enables the efficient computation of HONNs for image fields of greater that 100 × 100 pixels without any loss of pattern information.

Proposal and design of airy-based rocket pulses for invariant propagation in lossy dispersive media

A novel kind of Airy-based pulse with an invariant propagation in lossy dispersive media is proposed. The basic principle is based on an optical energy trade-off between different parts of the pulse caused by the chromatic dispersion, which is used to compensate the attenuation losses of the propagation medium. Although the ideal concept of the proposed pulses implies infinite pulse energy, the numerical simulations show that practical finite energy pulses can be designed to obtain a partially invariant propagation over a finite distance of propagation.

On a Class Almost Contact Manifolds with Norden Metric

Certain curvature properties and scalar invariants of the mani- folds belonging to one of the main classes almost contact manifolds with Norden metric are considered. An example illustrating the obtained results is given and studied.

Linear Connections on Normal Almost Contact Manifolds with Norden Metric

Families of linear connections are constructed on almost con- tact manifolds with Norden metric. An analogous connection to the symmetric Yano connection is obtained on a normal almost contact manifold with Norden metric and closed structural 1-form. The curvature properties of this connec- tion are studied on two basic classes of normal almost contact manifolds with Norden metric.

Almost Conformal Transformation in a Class of Riemannian Manifolds

We consider a 3-dimensional Riemannian manifold V with a metric g and an a±nor structure q. The local coordinates of these tensors are circulant matrices. In V we define an almost conformal transformation. Using that definition we construct an infinite series of circulant metrics which are successively almost conformaly related. In this case we get some properties.

Natural Connections with Totally Skew-Symmetric Torsion on Manifolds with Norden-Type Metrics

This paper is a survey of results obtained by the authors on the geometry of connections with totally skew-symmetric torsion on the following manifolds: almost complex manifolds with Norden metric, almost contact manifolds with B-metric and almost hypercomplex manifolds with Hermitian and anti-Hermitian metric.

Lie Groups as Four-Dimensional Special Complex Manifolds with Norden Metric

Марта Теофилова - Конструиран е пример на четиримерно специално комплексно многообразие с норденова метрика и постоянна холоморфна секционна кривина чрез двупара-метрично семейство от разрешими алгебри на Ли. Изследвани са кривинните свойства на полученото многообразие. Дадени са необходими и достатъчни усло-вия за разглежданото многообразие да бъде изотропно келерово.

An Invariant Theory of Surfaces in the Four-Dimensional Euclidean or Minkowski Space

2010 Mathematics Subject Classification: 53A07, 53A35, 53A10.

The gauge invariant currents of the Maxwellian field

We show that a conserved current for the Maxwellian field, which is invariant under the gauge group of that field, is the sum of two currents Ф+T, where Ф corresponds to a Poincare symmetry of the field, and T is a topological form that is conserved under every dynamics.

Invariant Functions on Neil Parabola in Cn

2000 Mathematics Subject Classification: Primary 32F45.

Hermitian Manifolds of Pointwise Constant Antiholomorphic Sectional Curvatures

2000 Mathematics Subject Classification: Primary 53B35, Secondary 53C50.

Denoising Manifolds for Dimension

2000 Mathematics Subject Classification: 68T01, 62H30, 32C09.

Geometry of Warped Product Semi-Invariant Submanifolds of a Locally Riemannian Product Manifold

2000 Mathematics Subject Classification: 53C42, 53C15.