Quantum collisional thermostats

Collisional reservoirs are becoming a major tool for modelling open quantum systems. In their simplest implementation, an external agent switches on, for a given time, the interaction between the system and a specimen from the reservoir. Generically, in this operation the external agent performs work onto the system, preventing thermalization when the reservoir is at equilibrium. One can recover thermalization by considering an autonomous global setup where the reservoir particles colliding with the system possess a kinetic degree of freedom. The drawback is that the corresponding scattering problem is rather involved. Here, we present a formal solution of the problem in one dimension and for flat interaction potentials. The solution is based on the transfer matrix formalism and allows one to explore the symmetries of the resulting scattering map. One of these symmetries is micro-reversibility, which is a condition for thermalization. We then introduce two approximations of the scattering map that preserve these symmetries and, consequently, thermalize the system. These relatively simple approximate solutions constitute models of quantum thermostats and are useful tools to study quantum systems in contact with thermal baths. We illustrate their accuracy in a specific example, showing that both are good approximations of the exact scattering problem even in situations far from equilibrium. Moreover, one of the models consists of the removal of certain coherences plus a very specific randomization of the interaction time. These two features allow one to identify as heat the energy transfer due to switching on and off the interaction. Our results prompt the fundamental question of how to distinguish between heat and work from the statistical properties of the exchange of energy between a system and its surroundings.

From Bachelier to Dupire via optimal transport

Famously, mathematical finance was started by Bachelier in his 1900 PhD thesis where – among many other achievements – he also provided a formal derivation of the Kolmogorov forward equation. This also forms the basis for Dupire’s (again formal) solution to the problem of finding an arbitrage-free model calibrated to a given volatility surface. The latter result has rigorous counterparts in the theorems of Kellerer and Lowther. In this survey article, we revisit these hallmarks of stochastic finance, highlighting the role played by some optimal transport results in this context.

Excitation of the Round Infinite Impedance Cylinder by Internal Extrinsic Current: Far-Field Radiation

The paper considers the method of solving the problem of excitation a circular infinite impedance cylinder by means of extrinsic current with an arbitrary spatial orientation. The formal solution of the problem is based on the method of expanding the fields in a complete system of eigenfunctions. Arbitrary distribution of extrinsic currents is taken into account factors excitation. An approximate solution of the problem in the far field is presented. The effect of a dielectric cylinder on the directional diagram of an axial electric dipole is studied.

Monumental painting in stone Catholic churches of Eastern Galicia in the second half of XVIII century. Topography, compositional types and techniques of illusionistic monumental art

The purpose of the article is to analyze compositional types, topography, methods, and techniques used in the formal solution of mural compositions in the Catholic churches of Eastern Galicia in the second half of the XVIII century. The methodology lies in the usage of art historical methods of stylistic analysis and generally scientific methods of analysis, synthesis, induction, deduction. The scientific novelty of the research is in the analysis of methods and techniques used by Galician masters in the second half of XVII century for implementation of mural compositions that were interpreted, adapted to local artistic traditions. The research can be used in the attribution of saved samples of the monumental art. Conclusions. The monumental painting in the Polish-Lithuanian Commonwealth, in particular in Galicia, developed in the context of artistic trends in West and Central European countries. Chronologically, the development of monumental painting in Galicia ranged from the thirties until the late XVIII century. As for the formal characteristics of monumental art, in the territory of the Commonwealth, the most common were three compositional types of polychrome: local variation of Italian «quadro riportato», illusionistic and panoramic. The basis of the first is the method of placing of the image on the vault area, framed with imitated or sculpted frame, the second is based on the quadrature and other methods and techniques of illusionistic monumental art, the third includes a panoramic image on the vault. In Galicia, the third type of vault decoration has not become widespread. Visiting masters were the bearers of these trends. They implemented the polychrome in local cathedrals, using a wide variety of methods and techniques for the formal solutions of mural compositions, typical for European art schools. Later, local artists adopted this experience, creating polychromes with certain interpretations of compositional types.

A Novel Exact Plate Theory for Bending Vibrations Based on the Partial Differential Operator Theory

Thick wall structures are usually applied at a highly reduced frequency. It is crucial to study the refined dynamic modeling of a thick plate, as it is directly related to the dynamic mechanical characteristics of an engineering structure or device, elastic wave scattering and dynamic stress concentration, and motion stability and dynamic control of a distributed parameter system. In this paper, based on the partial differential operator theory, an exact elasto-dynamics theory without assumptions for bending vibrations is presented by using the formal solution proposed by Boussinesq–Galerkin, and its dynamic equations are obtained under appropriate gauge conditions. The exact plate theory is then compared with other theories of plates. Since the derivation of the dynamic equation is conducted without any prior assumption, the proposed dynamic equation of plates is more exact and can be applied to a wider frequency range and greater thickness.

Світобудова Михайла Гуйди

Purpose of the article is to show the particular features of the model of the universe in the genre portrait-paintings and compositions of the modern Ukrainian artist M. E. Guyda are investigated. Historico-culturalogical, comparative, iconographic and iconological methods are applied. The ideological content and the particular features of the formal solution of figurative compositions are considered in the context of the heritage of world art. The national character of the images and symbols of the house, the clan and the native land are revealed; as is the nature of the manifestation of the relationship of the earthly and the heavenly. It was found that in the center of creation in compositions of M. E. Guyda is a spiritually inspired person from the folk. The depiction of people of different ages in interaction with nature helps to convey a natural course of time. It was clarified that the European aristocratic ceremonial portrait is foundational for the Ukrainian master. Artistic-stylistic analysis revealed that in the portrait-paintings "At the Well" (2013) and "Baba Kilyna" (2016), canonical composition was transformed by the artist through the expansion of space filled with individual symbolic content. The components of the ritual ceremonial portrait (columns, draperies, table-altar) are transformed into the image of a Cossack courtyard with a hedge, a tree of life, a well, a rainbow path. In the painting "Green Festivities" (2004), the house is shown as a temple. In the composition "Chumatsky Way" (2014), the world is presented as a universe – a model of the universe-house, with the architectonics of earth and sky. Scientific novelty is that the transformation of the canonical composition of the ceremonial portrait in the work of the contemporary artist M. E. Guyda is shown. The cultural and historical content of the master’s compositions was studied in connection with the problems of national self-identification and polystylism of the art of the twentieth century.is that the appeal to archetypes and symbols allowed the artist to expand the chamber space of his native Cossack house-yard to the "Model of Guyda’s Universe". The persuasiveness of individual pictorial images and symbols is based on the unity of personal, emotional perception of life with supra-individual mythological thinking. Practical significance. The presented materials, their artistic and stylistic analysis and generalization can be used in scientific research devoted to the art of portrait painting in Ukraine and in the world.

Card Index of Former Latvian SSR KGB Agents: Trauma and the Path to Public Reconciliation

In August 1991, the Republic of Latvia took over the documents of the former Latvian SSR KGB, including the card index of KGB agents. At that time, by postponing the card index publication, the political authorities made the issue of former KGB agents a hostage of their political interests. Discussion on the fate of the card index continued in Latvian public sphere over the next 27 years. The stance of the political elite, which found support in some groups of society, was opposed to the publication of the card index, being concerned about a possible witch-hunt and psychological trauma of the people mentioned in the card index as well as their relatives. However, as a result of public pressure, after lengthy indecision, the card index was made public in December 2018. Unfortunately, the publication of the card index has offered only a formal solution to the issue of the former KGB agents, and the expected results have been achieved from the aspect of neither historical truth nor public reconciliation. Only a small number of people mentioned in the card index have admitted the fact of their cooperation and just a few have expressed public regret. In turn, after 27 years of political elite’s hesitancy, most of the KGB persecution victims accepted the publication of the card index in silence. However, it is clear that denial and silence are not the way to public reconciliation and comprehension of trauma. Those few attempts to make one’s experience public show that in today’s situation people can seek reconciliation only with themselves and within themselves.

Mathematical Modelling for Semiconductor and Piezoelectric Media

In this analysis the importance of mathematical modelling of the physical systems has been outlined. The constitutive relations and basic governing equations of motion for homogeneous isotropic elastic semiconductor (n-type) and homogeneous transversely isotropic ( class) piezoelectric elastic media, in the absence of body forces and electric sources are made non-dimensional in order to reduce the mathematical complexity. All the obtained equations are rewritten in matrix form. Then considering the harmonic wave solution the eigen values and eigen vectors are calculated to obtained the formal solution of the problem.

APPLICATION OF THE MATRIX FACTOR ANALYSIS METHOD FOR DETERMINING PARAMETERS OF THE OBJECTIVE FUNCTION FOR TRANSPORT RISK MINIMIZATION

The paper regards a common transport problem with a non-classic optimization criterion to minimize transportation risks. It demonstrates that the risk parameters of the function could be found through the factor analysis method. Besides, considering that the problem contains several points of sending and delivering loads, the method is dealt with as a matrix. The research also regards the algorithm of matrix factor analysis application for determining parameters of the objective function for the problem to be solved. The survey results in a new method to construct the objective function for the optimization problem with probability parameters. It generally assists in suggesting a formal solution to such problems, foremost due to particular software.