Unitary interpolants and factorization indices of matrix functions

For an $n\times n$ bounded matrix function $\Phi$ we study unitary interpolants $U$, i.e., unitary-valued functions $U$ such that $\hat U(j)=\hat\Phi(j)$, $j<0$. We are looking for unitary interpolants $U$ for which the Toeplitz operator $T_U$ is Fredholm. We give a new approach based on superoptimal singular values and thematic factorizations. We describe Wiener--Hopf factorization indices of $U$ in terms of superoptimal singular values of $\Phi$ and thematic indices of $\Phi-F$, where $F$ is a superoptimal approximation of $\Phi$ by bounded analytic matrix functions. The approach essentially relies on the notion of a monotone thematic factorization introduced in [AP]. In the last section we discuss hereditary properties of unitary interpolants. In particular, for matrix functions $\Phi$ of class H^\be+C we study unitary interpolants $U$ of class $QC$.Comment: 20 page

Sensitivity to sentiment: News vs social media

© 2019 We explore the rapidly changing social and news media landscape that is responsible for the dissemination of information vital to the efficient functioning of the financial markets. Using the sheer volume of social and news media activity, commonly known as buzz, we document three distinct regimes. We find that between 2011 and 2013 the news media coverage stimulates activity in social media. This is followed by a transition period of two-way causality. From 2016, however, changes in levels of social media activity seem to lead and generate news coverage volumes. We uncover similar evolution of lead-lag pattern between sentiment measures constructed from the tonality contained in textual data from social and news media posts. We discover that market variables exert stronger impact on investor sentiment than the other way around. We also find that return responses to social media sentiment almost doubled after the transition period, while return responses to news-based sentiment almost halved to its pre-transition level. The linkage between volatility and sentiment is much more persistent than that between returns and sentiment. Overall, our results suggest that social media is becoming the dominant media source

Солитоны в обобщенной квантовой гидродинамике и теория шаровой молнии

Quantum solitons are discovered with the help of generalized quantum hydrodynamics. The solitons have the character of the stable quantum objects in the self consistent electric field. The theory of quantum solitons lead to explanation of the existence of stable atom structures on the microscopic level and lightning balls on the macroscopic level of description of physical systems. The delivered theory demonstrates the great possibilities of the generalized quantum hydrodynamics in investigation of the quantum solitons. The paper can be considered also as comments and prolongation of the materials published in the known author`s monograph (Boris V. Alexeev, Generalized Boltzmann Physical Kinetics. Elsevier. 2004). The theory leads to solitons as typical formations in the generalized quantum hydrodynamics.Квантовые солитоны открыты с помощью обобщенной квантовой гидродинамики. Солитоны имеют характер стабильных квантовых объектов в самосогласованном электрическом поле. Теория квантовых солитонов приводит к объяснению существования стабильных атомов на микроскопическом уровне и шаровых молний на макроскопическом уровне описания физических систем. Разработанная теория демонстрирует большие возможности обобщенной квантовой гидродинамики в исследовании квантовых солитонов как типичных образований в обобщенной квантовой теории. Статья может также рассматриваться как продолжение исследований, изложенных в известной монографии автора (Boris V. Alexeev, Generalized Boltzmann Physical Kinetics. – Elsevier, 2004)

Обобщенная квантовая гидродинамика

This paper addresses the fundamental principles of generalized Boltzmann physical kinetics, as a part of non-local physics. It is shown that the theory of transport processes (including quantum mechanics) can be considered in the frame of unified theory based on the non-local physical description. The paper can be considered also as comments and prolongation of the materials published in the known author’s monograph (Boris V. Alexeev, Generalized Boltzmann Physical Kinetics. Elsevier. 2004).В статье рассматриваются фундаментальные принципы обобщенной Больцмановской физической кинетики как составной части нелокальной физики. Установлено, что теория процессов переноса (включая квантовую механику) может быть рассмотрена в рамках универсальной теории, основанной на нелокальном физическом описании. Статья может рассматриваться как продолжение исследований, опубликованных в известной монографии автора (Boris V. Alexeev, Generalized Boltzmann Physical Kinetics. Elsevier. 2004)

Применение нелокальной физической кинетики в теории плазмоидов. Версия гибели Гагарина

The existence of solitary plasma objects in a bounded region is established by the methods of non-local physics. The unified generalized non-local theory is applied for mathematical modeling of quantum solitons. Ball lightings are quantum solitons – plasmoids which reach stability as a result of equalizing of corresponding quantum pressures of the non-local origin and the solitary electric forces. The delivered theory demonstrates the great possibilities of the generalized quantum hydrodynamics in the investigation of quantum solitons. The theory leads to solitons as typical formations in the generalized quantum hydrodynamics. The explanation of Gagarin catastrophe is explained as the result of the interaction of MIG 15 UTI with a plasmoid.Методами нелокальной физической кинетики установлена возможность существования стационарных уединенных плазменных объектов. Создана нелокальная теория плазмоидов и проведено математическое моделирование. Предложено объяснение катастрофы УТИ МИГ-15 и гибели Ю.А. Гагарина и В.С. Серегина как результат встречи самолета с плазмоидом

К нелокальной теории высоко-температурной сверхпроводимости

The possibility of the non-local physics application in the theory of superconductivity was investigated. It is shown that under the superconducting conditions the relay motion of the soliton system («lattice ion - electron») is realized when chemical bonds are absent. In terms of quantum hydrodynamics the problem of creation of high temperature superconductors is reduced to finding materials, the lattices of which could realize the soliton motion without destruction. These materials should be created using the technology of quantum dots.Исследована возможность применения нелокальной физики в теории сверхпроводимости и, прежде всего, высокотемпературной сверхпроводимости. Показано, что в условиях сверхпроводимости при отсутствии образования химической связи происходит эстафетное движение солитонной системы «ион решетки - электрон». С позиции квантовой гидро-динамики солитонов проблема поиска высокотемпературных сверхпроводящих материалов сводится к поиску материалов, решетки которых обеспечивают движение неразрушающихся солитонов. Такие материалы нужно специально создавать (конструировать), используя технологию создания материалов со специальным упорядоченным введением квантовых точек на основе предлагаемой теории

Del Pezzo surfaces with 1/3(1,1) points

We classify del Pezzo surfaces with 1/3(1,1) points in 29 qG-deformation families grouped into six unprojection cascades (this overlaps with work of Fujita and Yasutake), we tabulate their biregular invariants, we give good model constructions for surfaces in all families as degeneracy loci in rep quotient varieties and we prove that precisely 26 families admit qG-degenerations to toric surfaces. This work is part of a program to study mirror symmetry for orbifold del Pezzo surfaces.Comment: 42 pages. v2: model construction added of last remaining surface, minor corrections, minor changes to presentation, references adde

Analysis of the thermomechanical inconsistency of some extended hydrodynamic models at high Knudsen number

There are some hydrodynamic equations that, while their parent kinetic equation satisfies fundamental mechanical properties, appear themselves to violate mechanical or thermodynamic properties. This article aims to shed some light on the source of this problem. Starting with diffusive volume hydrodynamic models, the microscopic temporal and spatial scales are first separated at the kinetic level from the macroscopic scales at the hydrodynamic level. Then we consider Klimontovich’s spatial stochastic version of the Boltzmann kinetic equation, and show that, for small local Knudsen numbers, the stochastic term vanishes and the kinetic equation becomes the Boltzmann equation. The collision integral dominates in the small local Knudsen number regime, which is associated with the exact traditional continuum limit. We find a sub-domain of the continuum range which the conventional Knudsen number classification does not account for appropriately. In this sub-domain, it is possible to obtain a fully mechanically-consistent volume (or mass) diffusion model that satisfies the second law of thermodynamics on the grounds of extended non-local-equilibrium thermodynamics

APSIS - an Artificial Planetary System in Space to probe extra-dimensional gravity and MOND

A proposal is made to test Newton's inverse-square law using the perihelion shift of test masses (planets) in free fall within a spacecraft located at the Earth-Sun L2 point. Such an Artificial Planetary System In Space (APSIS) will operate in a drag-free environment with controlled experimental conditions and minimal interference from terrestrial sources of contamination. We demonstrate that such a space experiment can probe the presence of a "hidden" fifth dimension on the scale of a micron, if the perihelion shift of a "planet" can be measured to sub-arc-second accuracy. Some suggestions for spacecraft design are made.Comment: 17 pages, revtex, references added. To appear in Special issue of IJMP