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Noise-Induced Origin of the Fundamental Scalar Field

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Journal of Modern physics 2020年第4期11卷 502-508页

作者： B. I. Lev A. G. Zagorodny bogolyubov institute for theoretical physics NAS of Ukraine Kyiv Ukraine

The physical nature of the fundamental scalar field generation and hence the origination of the Universe is a matter of the discussions for many years. We propose to use the statistical approach to the description of the steady states of the quasi stationary systems with the elements of the quantum field theory methods as a basis to explain the appearance of the cosmological scalar field. Particularly, we apply two fundamental principles, i.e., the H-theorem and least-energy principle to show principal possibility of the scalar field origination. Along with the basic statement that in the presence of the fundamental scalar field, the energy of the vacuum ground state is lower than the ground state energy of the vacuum with no scalar field (primary vacuum), and with regard to the nonlinear interaction of fluctuating physical fields with the scalar field, these principles are employed to reveal probable phase transitions that may be associated with origin and further evolution of the Universe. Thus, we propose the possible physical justification of the spontaneous cosmological scalar field generation.

关键词： Cosmology Noise Fundamental Scalar Field

Description of Incomplete Financial Markets for Time Evolution of Risk Assets

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Advances in Pure Mathematics 2019年第6期9卷 567-610页

作者： Nicholas S. Gonchar bogolyubov institute for theoretical physics of nas Kiev Ukraine

In the paper, a class of discrete evolutions of risk assets having the memory is considered. For such evolutions the description of all martingale measures is presented. It is proved that every martingale measure is an integral on the set of extreme points relative to some measure on it. For such a set of evolutions of risk assets, the contraction of the set of martingale measures on the filtration is described and the representation for it is found. The inequality for the integrals from a nonnegative random value relative to the contraction of the set of martingale measure on the filtration which is dominated by one is obtained. Using these inequalities a new proof of the optional decomposition theorem for super-martingales is presented. The description of all local regular super-martingales relative to the regular set of measures is presented. The applications of the results obtained to mathematical finance are presented. In the case, as evolution of a risk asset is given by the discrete geometric Brownian motion, the financial market is incomplete and a new formula for the fair price of super-hedge is founded.

关键词： Random Process Regular Set of Measures Optional Doob Decomposition Local Regular Super-Martingale Martingale Discrete Geometric Brownian Motion

Martingales and Super-Martingales Relative to a Convex Set of Equivalent Measures

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Advances in Pure Mathematics 2018年第4期8卷 428-462页

作者： Nicholas S. Gonchar bogolyubov institute for theoretical physics of nas Kiev Ukraine

In the paper, the martingales and super-martingales relative to a convex set of equivalent measures are systematically studied. The notion of local regular super-martingale relative to a convex set of equivalent measures is introduced and the necessary and sufficient conditions of the local regularity of it in the discrete case are founded. The description of all local regular super-martingales relative to a convex set of equivalent measures is presented. The notion of the complete set of equivalent measures is introduced. We prove that every bounded in some sense super-martingale relative to the complete set of equivalent measures is local regular. A new definition of the fair price of contingent claim in an incomplete market is given and the formula for the fair price of Standard Option of European type is found. The proved Theorems are the generalization of the famous Doob decomposition for super-martingale onto the case of super-martingales relative to a convex set of equivalent measures.

关键词： Random Process Convex Set of Equivalent Measures Optional Doob Decomposition Local Regular Super-Martingale Martingale Fair Price of Contingent Claim

Assessment of Contingent Liabilities for Risk Assets Evolutions Built on Brownian Motion

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Advances in Pure Mathematics 2020年第5期10卷 259-296页

作者： Nicholas Simon Gonchar bogolyubov institute for theoretical physics of nas of ukraine Kyiv Ukraine

This paper is a generalization of the results of the previous papers. Using these results a class of evolutions of risk assets based on the geometric Brownian motion is constructed. Among these evolutions of risk assets, the important class of the random processes is the random processes with parameters built on the basis of the discrete geometric Brownian motion. For this class of random processes the interval of non-arbitrage prices are found for the wide class of contingent liabilities. In particular, for the payoff functions of standard options call and put of the European type the fair prices of super-hedge are obtained. Analogous results are obtained for the put and call of arithmetical options of Asian type. For the parameters entering in the definition of random process the description of all statistical estimates is presented. Statistical estimate for which the fair price of super-hedge for the payoff functions of standard call and put options of European type is minimal is indicated. From the formulas found it follows that the fair price of super-hedge can be less than the price of the underlying asset. In terms of estimates the simple formula for the fair price of super-hedge is found. Every estimates can be realized in the reality. This depends on the distribution function of the observed dates in the financial market.

关键词： Random Process Regular Set of Measures Optional Doob Decomposition Local Regular Super-Martingale Martingale Assessment of Derivatives

Wave Function as Geometric Entity

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Journal of Modern physics 2012年第8期3卷 709-713页

作者： Bohdan I. Lev bogolyubov institute for theoretical physics nas ukraine Metrolohichna Kyiv

A spacial approach to the geometrization the theory of the electron has been proposed. The particle wave function is represented by a geometric entity, i.e., Clifford number, with the translation rules possessing the structure of Dirac equation for any manifold. A solution of this equation is obtained in terms of geometric treatment. New experiments concerning the geometric nature wave function of electrons are proposed.

关键词： Wave Function Clifford Algebra Theory of Electron

Effect of Multiple Martensitic Transformations on Structure of Fe-Ni Alloys

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Journal of Materials Science & Technology 2013年第3期29卷 279-282页

作者： V.Danilchenko Ie.Dzevin V.Sagaradze G.V.Kurdyumov institute of Metal physics NAS of UkraineKievUkraine institute of Metal physics Ural Division of RASEkaterinburgRussia

Effect of multiple direct and reverse martensitic transformations on fragmentation of austenitic grains in Fe-Ni alloys have been studied by X-ray diffraction and scanning electron microscopy. An ultra-fine structure was formed by fragmentation inside austenitic grains due to progressing misorientation of austenitic sub-grains during multiple γ-α-γ-martensitic phase transitions. An increase in the number of γ-α-γ-transformations increases misorientation angle between austenitic sub-grains and leads to transformation of an austenitic single crystal into a textured polycrystal. It has been shown that multiple γ-α-γ-martensitic phase transitions change the mechanism of internal stress relaxation from dislocation-based to deformation twinning.

关键词： Austenite Crystal lattice Ultra-fine structure Martensitic transformation

Localized States of an Excess Electron in an Ionic Cluster

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Communications in theoretical physics 2013年第12期60卷 738-746页

作者： K.V.Grigorishin B.I.Lev Boholyubov institute for theoretical physics of the National Academy of Sciences of ukraine

A theory of an electron afnity for an ionic cluster is proposed both in a quasiclassical approach and with quantization of a polarization electric field in a nanoparticle. A critical size of the cluster regarding in formation of an electron's autolocalized state, dependencies of energy and radius of a polaron on a cluster's size are obtained by a variational method. It has been found that binding energy of the electron in the cluster depends on a cluster's radius but a radius of electron's auto-localization does not depend on the cluster's radius and it equals to the polaron radius in a corresponding infinity crystal. A bound state of the electron in a cluster is possible only if the cluster's radius is more than the polaron radius.

关键词：电子亲和势离子簇局域态小极化子经典方法极化电场临界尺寸变分方法

Simple Model of Transformation of a Crystal Structures

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Journal of Modern physics 2016年第16期7卷 2366-2373页

作者： B. I. Lev bogolyubov institute for theoretical physics of the nas of ukraine Kyiv Ukraine Department of physics Chungnam National University Daejeon Korea

A simple model of the closely packed structure for system of hard-sphere particles interacting via the long-range Newtonian type attraction is suggested. Based on density functional theory, the exact equation of state is obtained and the mutual transformations of the crystal structures in such systems are studied. The description takes into account the fact impossibility of hard-sphere particles which have the same spatial occupation place.

关键词： Density Functional Theory Transformation of Structures Close-Packing Structure

Statistical Derivation of the Fundamental Scalar Field

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Journal of Modern physics 2018年第12期9卷 2223-2232页

作者： B. I. Lev bogolyubov institute for theoretical physics of the nas of ukraine Kyiv Ukraine Department of physics Chungnam National University Daejeon Korea

Based on a nonequilibrium statistical operator, it has been shown that the fundamental scalar field provides a natural representation of the repulsive interaction that produces scattering in the system and thus motiva... 详细信息

关键词： Statistical physics Fundamental Scalar