scholarly journals On One Method of Studying Spectral Properties of Non-selfadjoint Operators

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Maksim V. Kukushkin
Keyword(s):  
Spectral Properties ◽  
Root Vector ◽  
Vector System ◽  
Real Component ◽  
Von Neumann ◽  
The Real ◽  
Selfadjoint Operators ◽  
Neumann Class ◽  
Nonselfadjoint Operator

In this paper, we explore a certain class of Non-selfadjoint operators acting on a complex separable Hilbert space. We consider a perturbation of a nonselfadjoint operator by an operator that is also nonselfadjoint. Our consideration is based on known spectral properties of the real component of a nonselfadjoint compact operator. Using a technique of the sesquilinear forms theory, we establish the compactness property of the resolvent and obtain the asymptotic equivalence between the real component of the resolvent and the resolvent of the real component for some class of nonselfadjoint operators. We obtain a classification of nonselfadjoint operators in accordance with belonging their resolvent to the Schatten-von Neumann class and formulate a sufficient condition of completeness of the root vector system. Finally, we obtain an asymptotic formula for the eigenvalues.

scholarly journals Asymptotics of eigenvalues for differential operators of fractional order

2019 ◽  
Vol 22 (3) ◽  
pp. 658-680 ◽  
Author(s):  
Maksim V. Kukushkin
Keyword(s):  
Differential Operators ◽  
Asymptotics Of Eigenvalues ◽  
Real Component ◽  
Von Neumann ◽  
Root Functions ◽  
Fractional Differential Operator ◽  
Neumann Class ◽  
Novel Method ◽  
Fractional Differential

Abstract In this paper we deal with a linear combination of a second order uniformly elliptic operator and the Kipriyanov fractional differential operator. We use a novel method based on properties of a real component to study such type of operators. We conduct the classification of the operators by belonging of their resolvent to the Schatten-von Neumann class and formulate the sufficient condition for the completeness of the root functions system. Finally we obtain an asymptotic formula.

Complex seismic trace analysis

Geophysics ◽  
1979 ◽  
Vol 44 (6) ◽  
pp. 1041-1063 ◽  
Author(s):  
M. T. Taner ◽  
F. Koehler ◽  
R. E. Sheriff
Keyword(s):  
Instantaneous Frequency ◽  
Seismic Data ◽  
Trace Analysis ◽  
Color Patterns ◽  
Phase Information ◽  
Real Component ◽  
The Real ◽  
Geological Interpretation ◽  
Envelope Amplitude ◽  
Spatial Changes

The conventional seismic trace can be viewed as the real component of a complex trace which can be uniquely calculated under usual conditions. The complex trace permits the unique separation of envelope amplitude and phase information and the calculation of instantaneous frequency. These and other quantities can be displayed in a color‐encoded manner which helps an interpreter see their interrelationship and spatial changes. The significance of color patterns and their geological interpretation is illustrated by examples of seismic data from three areas.

scholarly journals Identification features of the minutes of interrogation and ways of authorship examination

2019 ◽  
Vol 17 (3) ◽  
pp. 97-108
Author(s):  
Elena E. Abramkina
Keyword(s):  
Current Paper ◽  
Authorship Attribution ◽  
Features Selection ◽  
New Classification ◽  
Semantic Type ◽  
The Real ◽  
Language Analysis ◽  
Authorship Analysis

Forensic authorship analysis is a frequently used technique to identify the real author of an arguable document. Often enough, under study are interrogation minutes. This kind of text is difficult for examination because of its stylistic and genre characteristics: formal phrases and structure as well as different author and compiler of the document. The above features restrict the use of some levels of language analysis. This issue, however, is poorly covered in specialist literature, with only a few articles related to it. The current paper describes the main discursive features of interrogation minutes used in authorship expertise. First we look at conventional techniques of authorship expertise and discuss their limitations. Special attention is given to the analysis of the interrogation minutes genre characteristics and their influence on the whole set of identifiers. The analysis of several conventional interrogation minutes techniques singled out two central tendencies in the authorship attribution: an identification features selection with new identifiers being added. The aim of the article is to propose a solution to the problem. Our technique is based on the methods of The Federal Ministry of the Interior, but it also takes into account genre charecteristics of the interrogation minutes. A new classification of identifiers has been developed. Additional features are offered to improve the attribution accuracy. These are clarifications, which are classified according to the semantic type of the object. In the article clarifications are divided into six types and a few subtypes and are also divided into low and high informative ones. The analysis of clarification is illustrated with the example of three different interrogation minutes. The concluding part of the article is concerned with the techniques of the interrogation minutes used in authorship expertise description, materials requirements and the steps of the analysis.

scholarly journals One Case of Forensic Clinical Identification of Ulnar Radius Fracture not Involving Epiphysis

2020 ◽  
Vol 1 (1) ◽  
Author(s):  
Dawei Jiang ◽  
Yujun Zhou
Keyword(s):  
Clinical Examination ◽  
Technical Specification ◽  
Epiphyseal Plate ◽  
Forensic Identification ◽  
The Real ◽  
Degree Of Disability ◽  
The Relationship ◽  
Case Data ◽  
Human Injury

In order to investigate the relationship between injury and injury of the identified person, to determine the real disability of the identified person, to determine whether the fracture of ulna and radius of the identified person is involved in the epiphysis, and to be commissioned by the court, the identified person is specially re-identified. According to the contents and methods of the Technical Specification for Forensic Identification (SF/ZJD0103003-2011) of the Ministry of Justice, the forensic clinical examination was conducted. After consulting the case data and conducting the forensic clinical examination of the identified person, this appraisal concluded that the left ulna and radius broken line of the patient disappeared, the epiphyseal plate was clear, and there was no deformity, and the disability grade was not constructed according to the provisions of the Classification of the degree of disability caused by human injury.

scholarly journals THE REAL ANATOMY OF COMPLEX LINEAR SUPERFIELDS

2012 ◽  
Vol 27 (24) ◽  
pp. 1250143 ◽  
Author(s):  
S. JAMES GATES ◽  
JARED HALLETT ◽  
TRISTAN HÜBSCH ◽  
KORY STIFFLER
Keyword(s):  
Recent Work ◽  
Vast Number ◽  
The Real ◽  
Explicit Analysis ◽  
Complex Linear

Recent work on classification of off-shell representations of N-extended worldline supersymmetry without central charges has uncovered an unexpectedly vast number — trillions of even just (chromo)topology types — of so-called adinkraic supermultiplets. Herein, we show by explicit analysis that a long-known but rarely used representation, the complex linear supermultiplet, is not adinkraic, cannot be decomposed locally, but may be reduced by means of a Wess–Zumino type gauge. This then indicates that the already unexpectedly vast number of adinkraic off-shell supersymmetry representations is but the proverbial tip of the iceberg.

Avicenna’s Interpretation of Aristotle’s Metaphysics (Ε1, 1026a13-16)

2018 ◽  
pp. 137-143
Author(s):  
Silvia Gullino
Keyword(s):  
Modern Philosophy ◽  
Middle Ages ◽  
Natural Science ◽  
Arab World ◽  
Point Of View ◽  
The Real ◽  
First Time ◽  
First Philosophy ◽  
Aristotle's Metaphysics

During the 9th century Aristotle’s Metaphysics was translated for the first time from Greek into Arabic by Ustâth, at the request of al-Kindî and, afterwards, the interest of the Arab world in this oeuvre grew with the production of several translations, comments and paraphrases of the work. Among the books which compose the Metaphysics, one of the most studied was book Epsilon. In particular Arab philosophers focused their interest on the passage of Ε1, which contains a classification of the theoretical sciences (1026a13-1026a16), founded on the degree of immateriality and of separation from the matter of their object. Aristotle states: “Natural science deals with things which are inseparable from matter but not immovable, and some parts of mathematics deal with things which are immovable, but probably not separable, but are embodied in matter; while the first science deals with things which are both separable and immovable”. According to the Arab exegetes, Aristotle introduces here the doctrine of the three degrees of abstraction, on the base of which the object of first philosophy is the most abstract among the beings, both from the conceptual point of view and from the real one. This interpretation of the Aristotelian text – already present in Avicenna – had a huge influence on the Latin Middle Ages and on modern philosophy.

The Asymptotic Ratio Set and Direct Integral Decompositions of a Von Neumann Algebra

1971 ◽  
Vol 23 (4) ◽  
pp. 598-607 ◽  
Author(s):  
Ole A. Nielsen
Keyword(s):  
Von Neumann Algebra ◽  
Von Neumann Algebras ◽  
Direct Integral ◽  
Von Neumann ◽  
Ratio Set ◽  
Almost All ◽  
Direct Integral Decomposition ◽  
Integral Decomposition ◽  
Remarkable Progress

The fact that any von Neumann algebra on a separable Hilbert space has an essentially unique direct integral decomposition into factors means that there is a global as well as a local aspect to any partial classification of von Neumann algebras. More precisely, suppose that J is a statement about von Neumann algebras which is either true or false for any given von Neumann algebra. Then a von Neumann algebra is said to satisfy J globally if it satisfies J, and to satsify J locally if almost all the factors appearing in some (and hence in any) central decomposition of it satisfy J . In a recent paper [3], H. Araki and E. J. Woods introduced the notion of the asymptotic ratio set of a factor, and by means of this they made remarkable progress in the classification of factors.

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