RELATIONAL STATISTICAL SPACE-TIME FOR COSMOLOGICAL SCALES

The relational statistical approach is used in the study of phenomena of macroscopic cosmological scales. In fact, a variant of the generalized Mach’s principle is developing. Theoretical models of Dark matter as well as Dark energy without introducing additional particles and forces are discussed. Changes in the ordinary kinematic and dynamic equations for ultra-ultra-high speeds are considered. Some new effects are predicted at such energy scales.

Space-time processing of random fields of signals in radar-tracking systems using adaptive stricture of unified algorithms and elements

The efficiency of synthesized optimum algorithms of processing of random fields of signals is based on adequacy of mathematical model to the real phenomena which lay the foundation in mathematical models of useful and hindered signals. The basic and principal difference of the prospective approach to the development of new theoretical positions of the scientific – methodical means of space-time processing of random fields of signals from the known one is statistical space and time optimization with exception of mutual negative influence to each other. The advantage of the proposed approach is that synthesis becomes possible for the first time by solving statistical optimization problems at the spatial and temporal stages of processing. The use of kronecker-tensor product will make it possible to replace obsolete algorithms for processing multidimensional random received signals with better and more efficient ones, taking into account the real randomness of spatial structures and satisfying modern requirements of military science.

Some inequalities for statistical submanifolds of quaternion Kaehler-like statistical space forms

Motivated by one of the problems proposed by [Vilcu and Vilcu, Statistical manifolds with almost quaternionic structures and quaternionic Kaehler-like statistical submersions, Entropy 17 (2015) 6213–6228] in this paper, we study the statistical submanifolds of quaternion Kaehler-like statistical space forms and provide an answer to the problem. Further, we derive the statistical version of Chen inequality for totally real statistical submanifold in such ambient.

Pinching Theorems for Statistical Submanifolds in Sasaki-Like Statistical Space Forms

In this paper, we obtain the upper bounds for the normalized δ -Casorati curvatures and generalized normalized δ -Casorati curvatures for statistical submanifolds in Sasaki-like statistical manifolds with constant curvature. Further, we discuss the equality case of the inequalities. Moreover, we give the necessary and sufficient condition for a Sasaki-like statistical manifold to be η -Einstein. Finally, we provide the condition under which the metric of Sasaki-like statistical manifolds with constant curvature is a solution of vacuum Einstein field equations.