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An approximate statistical description of the formation and evolution of structure of the universe based on the Zel'dovich theory of gravitational instability is proposed. It is found that the evolution of DM structure shows features of…
We review a number a recent advances in the study of two-dimensional statistical models with strong geometrical constraints. These include folding problems of regular and random lattices as well as the famous meander problem of enumerating…
We consider $f(R,T)$ modified theories of gravity in the context of string theory inspired dilaton gravity. We deal with a specific model that under certain conditions describes the late time Universe in accord with observational data in…
The problem of the Nature of Time is twofold: whether or not time is a fundamental quantity of Nature, and how does clock time of metrology emerge in the experimental description of dynamics. This work strongly supports the fundamental…
In this article we introduce the {\it cylindrical construction} for graphs and investigate its basic properties. We state a main result claiming a weak tensor-like duality for this construction. Details of our motivations and applications…
The thesis deals with recognizing diffeomorphisms from fractal properties of discrete orbits, generated by iterations of such diffeomorphisms. The notion of fractal properties of a set refers to the box dimension, the Minkowski content and…
We consider in this work triangulations of $\mathbb{Z}^n$ that are periodic along $\mathbb{Z}^n$. They generalize the triangulations obtained from Delaunay tessellations of lattices. Other important property is the regularity and…
[Note to the reader: properties (C2) and (C2)* are under development, in order to form a generalization of (C3) and (C3)*]
The paper is devoted to the problem of resonances in one-dimensional disordered systems. Some of the previous results are reviewed and a number of new ones is presented. These results pertain to different models (continuous as well as…
Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts…
A new approach is proposed to the quantitative estimation of the complexity of multidimensional discrete sequences in terms of the shapes of their trajectories in the extended space of states. This approach is based on the study of the…
The singly-ionized lutetium has a number of fortuitous properties well suited for a design of an optical clock and corresponding applications. In this work, we study Lu+ properties relevant to a development of the clock using the…
We start from the two existing QCD evolution equations for structure functions, the BFKL and DGLAP equations, and discuss the theoretical hints for a unifying picture of the evolution in $x$ and $Q^2.$ The main difficulty is due to the…
According to a scenario in string cosmology, a relic background of light dilatons can be a significant component of the dark matter in the Universe. A new approach of searching for such a dilatonic background by observing Earth's surface…
A class of simplified measures is constructed to capture the key features of generic spatio-temporally chaotic systems. A combined analytical and numerical investigation allows us to extablish the scaling beahviour of the fractal dimension…
In these Lectures I review possible constraints on particle physics models, obtained by means of combining the results of collider measurements with astrophysical data. I emphasize the theoretical-model dependence of these results. I…
We review several recent developments in the theory and phenomenology of deep-inelastic scattering, with particular emphasis on precision tests of QCD and progress in the detailed perturbative treatment of structure functions and parton…
This is a survey article on the existence of locally conformally flat(LCF) and self-dual(SD) metrics on various basic 4-manifolds like simply-connected ones or product types
The purpose of this paper is to present the structure of the linear codes over a finite field with q elements that have a permutation automorphism of order m. These codes can be considered as generalized quasi-cyclic codes. Quasi-cyclic…
Delay differential equations take into account the transmission time of the information. These delayed signals may turn a predictable system into chaotic, with the usual fractalization of the phase space. In this work, we study the…