ON THE PROBLEM OF THE RIGHT HAMILTONIAN UNDER SINGULAR FORM-SUM PERTURBATIONS

2000 ◽  
Vol 12 (01) ◽  
pp. 1-24 ◽  
Author(s):  
SERGIO ALBEVERIO ◽  
VOLODYMYR KOSHMANENKO
Keyword(s):  
Quadratic Forms ◽  
Symmetric Operator ◽  
Adjoint Operator ◽  
Deficiency Indices ◽  
Singular Form ◽  
Approximating Sequence ◽  
Sum Formula ◽  
Definition Of ◽  
The Right ◽  
Adjoint Operators

Let a perturbation of the self-adjoint operator H0>0 in the Hilbert space ℋ be given by an operator V (or by a quadratic form ν) which is possibly singular and in general nonpositive, so H0+V on [Formula: see text] is only a symmetric operator with nontrivial deficiency indices. The definition of the sum [Formula: see text] in the sense of quadratic forms is extended to cases which are not covered by the well-known KLMN-theorem and conditions are found which ensure the unique self-adjoint realization of H in ℋ. It is also shown that ℋ coincides with the strong resolvent limit of the approximating sequence Hn = H0+Vn, where Vn are bounded self-adjoint operators such that Vn → V in a suitable sense. Essentially that operator V might be strongly singular and acts in the H0-scale of spaces, V:ℋ+→ℋ-.

On the Right Hamiltonian for Singular Perturbations: General Theory

1997 ◽  
Vol 09 (05) ◽  
pp. 609-633 ◽  
Author(s):  
Hagen Neidhardt ◽  
Valentin Zagrebnov
Keyword(s):  
General Theory ◽  
Symmetric Operator ◽  
Stability Domain ◽  
Bounded Operators ◽  
Friedrichs Extension ◽  
Abstract Problem ◽  
Dense Domain ◽  
Adjoint Extension ◽  
The Right ◽  
Adjoint Operators

Let the pair of self-adjoint operators {A≥0,W≤0} be such that: (a) there is a dense domain [Formula: see text] such that [Formula: see text] is semibounded from below (stability domain), (b) the symmetric operator [Formula: see text] is not essentially self-adjoint (singularity of the perturbation), (c) the Friedrichs extension [Formula: see text] of [Formula: see text] is maximal with respect to W, i.e., [Formula: see text]. [Formula: see text]. Let [Formula: see text] be a regularizing sequence of bounded operators which tends in the strong resolvent sense to W. The abstract problem of the right Hamiltonian is: (i) to give conditions such that the limit H of self-adjoint regularized Hamiltonians [Formula: see text] exists and is unique for any self-adjoint extension [Formula: see text] of [Formula: see text], (ii) to describe the limit H. We show that under the conditions (a)–(c) there is a regularizing sequence [Formula: see text] such that [Formula: see text] tends in the strong resolvent sense to unique (right Hamiltonian) [Formula: see text], otherwise the limit is not unique.

Examples of degenerate symmetric differential operators with infinite deficiency indices in L2(ℝm)

1999 ◽  
Vol 129 (1) ◽  
pp. 165-179
Author(s):  
Yurii B. Orochko
Keyword(s):  
Hilbert Space ◽  
Differential Operator ◽  
Differential Expression ◽  
Symmetric Operator ◽  
Differential Operators ◽  
Separable Hilbert Space ◽  
Adjoint Operator ◽  
Deficiency Indices ◽  
Image Position ◽  
Symmetric Differential Operators

For an unbounded self-adjoint operator A in a separable Hilbert space ℌ and scalar real-valued functions a(t), q(t), r(t), t ∊ ℝ, consider the differential expressionacting on ℌ-valued functions f(t), t ∊ ℝ, and degenerating at t = 0. Let Sp denotethe corresponding minimal symmetric operator in the Hilbert space (ℝ) of ℌ-valued functions f(t) with ℌ-norm ∥f(t)∥ square integrable on the line. The infiniteness of the deficiency indices of Sp, 1/2 < p < 3/2, is proved under natural restrictions on a(t), r(t), q(t). The conditions implying their equality to 0 for p ≥ 3/2 are given. In the case of a self-adjoint differential operator A acting in ℌ = L2(ℝn), the first of these results implies examples of symmetric degenerate differential operators with infinite deficiency indices in L2(ℝm), m = n + 1.

scholarly journals On uniqueness and structure of renormalized solutions to integro-differential equations with general measure data

2020 ◽  
Vol 27 (5) ◽  
Author(s):  
Tomasz Klimsiak
Keyword(s):  
Borel Measure ◽  
Adjoint Operator ◽  
Uniqueness Result ◽  
Measure Data ◽  
Markov Semigroup ◽  
Structure Of Solutions ◽  
General Measure ◽  
Renormalized Solution ◽  
Definition Of ◽  
The Right

Abstract We propose a new definition of renormalized solution to linear equation with self-adjoint operator generating a Markov semigroup and bounded Borel measure on the right-hand side. We give a uniqueness result and study the structure of solutions to truncated equations.

scholarly journals Singularly perturbed rank one linear operators

2021 ◽  
Vol 56 (2) ◽  
pp. 162-175
Author(s):  
M.E. Dudkin ◽  
O. Yu. Dyuzhenkova
Keyword(s):  
Adjoint Operator ◽  
Linear Operators ◽  
Singularly Perturbed ◽  
Basic Principles ◽  
Dirac Delta ◽  
Symmetric Perturbation ◽  
Rank One ◽  
Definition Of ◽  
Adjoint Operators ◽  
Symmetric Operators

The basic principles of the theory of singularly perturbed self-adjoint operatorsare generalized to the case of closed linear operators with non-symmetric perturbation of rank one.Namely, firstly linear closed operators are considered that coincide with each other on a dense set in a Hilbert space.The theory of singularly perturbed self-adjoint operators arose from the need to consider differential expressions in such terms as the Dirac $\delta$-function.Since it is important to consider expressions given not only by symmetric operators, the generalization (transfer) of the basic principles of the theory of singularly perturbed self-adjoint operators in the case of non-symmetric ones is important problem. The main facts of the theory include the definition of a singularly perturbed linear operator and the resolvent formula in the cases of ${\mathcal H}_{-1}$-class and ${\mathcal H}_{-2}$-class.The paper additionally describes the possibility of the appearance a point of the point spectrum and the construction of a perturbation with a predetermined point.In comparison with self-adjoint perturbations, the description of perturbations by non-symmetric terms is unexpected.Namely, in some cases, when the perturbed by a vectors from ${\mathcal H}_{-2}$ operator can be conveniently described by methods of class ${\mathcal H}_{-1}$, that is impossible in the case of symmetric perturbations of a self-adjoint operator. The perturbation of self-adjoint operators in a non-symmetric manner fully fits into the proposed studies.Such operators, for example, generalize models with nonlocal interactions, perturbations of the harmonic oscillator by the $\delta$-potentials, and can be used to study perturbations generated by a delay or an anticipation.

THE CONCEPT OF CONSTITUTIONAL AND LEGAL GUARANTEES OF ELECTORAL RIGHTS

2020 ◽  
Vol 10 (4) ◽  
pp. 85-90
Author(s):  
VLADIMIR TROYAN ◽  
Keyword(s):  
Scientific Research ◽  
Formal Aspect ◽  
Universal Approach ◽  
Right To Vote ◽  
Definition Of ◽  
The Right

The relevance of the interpretation of constitutional and legal guarantees of the right to vote is mediated by isolated scientific research in this area, as well as the lack of a universal approach to legal guarantees. In this regard, the purpose of the article is to argue and disclose the author’s definitive aspect of the claimed guarantees. In the work, the author named and characterized the normative (based exclusively on legal means) with the perspective of a branch of legal and technical; regulatory and institutional (combines the formal aspect with the activities of authorized entities) and associated legal (including a set of legal and other aspects) approaches to the definition of legal guarantees. Based on the second approach, as well as combining the guarantees of the right to vote directly guarantees of the subjective right itself and guarantees of its implementation, the author offers a definition of constitutional and legal guarantees of the right to vote.

administrasi ketatausahaan sekolah

2020 ◽  
Author(s):  
Isra Revenia
Keyword(s):  
Information Needs ◽  
Control Functions ◽  
Definition Of ◽  
The Right ◽  
And Control

This article is made to know the destinantion and the administrasi functions of the school in order to assist the leader of an organazation in making decisions and doing the right thing, recording of such statements in addition to the information needs also pertains to the function of accountabilitty and control functions. Administrative administration is the activity of recording for everything that happens in the organization to be used as information for leaders. While the definition of administration is all processing activities that start from collecting (receiving), recording, processing, duplicating, minimizing and storing all the information of correspondence needed by the organization. Administration is as an activity to determine everything that happens in the organization, to be used as material for information by the leadership, which includes all activities ranging from manufacturing, managing, structuring to all the preparation of information needed by the organization.

SELF ASSESSMENT TO KNOW UNDERSTANDING MATHEMATIC CONCEPT

2018 ◽  
Vol 3 (1) ◽  
pp. 14-21
Author(s):  
Deni Iriyadi
Keyword(s):  
Qualitative Study ◽  
Qualitative Analysis ◽  
Resolution Limit ◽  
Self Assessment ◽  
Limit Concept ◽  
Research Instrument ◽  
Definition Of ◽  
The Right

This research is a qualitative study aimed to determine the students' understanding of the concept of matter limit. The subjects were students of class XI IPA 1 SMA Negeri 1 Watampone. The concept includes the definition of the limit. Data obtained using a research instrument in the form of self-assessment and then proceed with the interview subjects were selected based on the results of self-assessment has been done before. Analysis using qualitative analysis of students' understanding of the concept of the limit concept. The results of this study indicate that students' understanding of concepts some of which are not / do not understand especially regarding definitions limit. In addition students are also wrong about the resolution limit. Students who understand the concept of limit dinyakatakan them restate concepts, including examples and classify the sample to non-completion of function and limit the right results.

DIRECTIONS FOR PROVISION OF PUBLIC BODIES’ TRANSPARENCY AND ACCOUNTABILITY IN CONDITIONS OF PARTICIPATORY DEMOCRACY DEVELOPMENT

2018 ◽  
Vol 1 (11) ◽  
pp. 144-154
Author(s):  
Olga Mykhailоvna Ivanitskaya
Keyword(s):  
Public Administration ◽  
Participatory Democracy ◽  
Main Task ◽  
The Public ◽  
State Governance ◽  
Legislative Initiative ◽  
The Government ◽  
Definition Of ◽  
The Right ◽  
Transparency And Accountability

The article is devoted to issues of ensuring transparency and ac- countability of authorities in the conditions of participatory democracy (democ- racy of participation). It is argued that the public should be guaranteed not only the right for access to information but also the prerequisites for expanding its par- ticipation in state governance. These prerequisites include: the adoption of clearly measurable macroeconomic and social goals and the provision of control of the processes of their compliance with the government by citizens of the country; ex- tension of the circle of subjects of legislative initiative due to realization of such rights by citizens and their groups; legislative definition of the forms of citizens’ participation in making publicly significant decisions, design of relevant orders and procedures, in particular participation in local referendum; outlining methods and procedures for taking into account social thought when making socially im- portant decisions. The need to disclose information about resources that are used by authorities to realize the goals is proved as well as key performance indicators that can be monitored by every citizen; the efforts made by governments of coun- tries to achieve these goals. It was noted that transparency in the conditions of representative democracy in its worst forms in a society where ignorance of the thought of society and its individual members is ignored does not in fact fulfill its main task — to establish an effective dialogue between the authorities and so- ciety. There is a distortion of the essence of transparency: instead of being heard, society is being asked to be informed — and passively accept the facts presented as due. In fact, transparency and accountability in this case are not instruments for the achievement of democracy in public administration, but by the form of a tacit agreement between the subjects of power and people, where the latter passes the participation of an “informed observer”.

scholarly journals Lying, speech acts, and commitment

Synthese ◽  
2020 ◽  
Author(s):  
Neri Marsili
Keyword(s):  
Speech Acts ◽  
Speech Act ◽  
Good Definition ◽  
Definition Of ◽  
The Right ◽  
Adequate Analysis

AbstractNot every speech act can be a lie. A good definition of lying should be able to draw the right distinctions between speech acts (like promises, assertions, and oaths) that can be lies and speech acts (like commands, suggestions, or assumptions) that under no circumstances are lies. This paper shows that no extant account of lying is able to draw the required distinctions. It argues that a definition of lying based on the notion of ‘assertoric commitment’ can succeed where other accounts have failed. Assertoric commitment is analysed in terms of two normative components: ‘accountability’ and ‘discursive responsibility’. The resulting definition of lying draws all the desired distinctions, providing an intensionally adequate analysis of the concept of lying.

scholarly journals Learning Curves: A Novel Approach for Robustness Improvement of Load Forecasting

2021 ◽  
Vol 5 (1) ◽  
pp. 38
Author(s):  
Chiara Giola ◽  
Piero Danti ◽  
Sandro Magnani
Keyword(s):  
Load Forecasting ◽  
Learning Curves ◽  
Machine Learning Techniques ◽  
Essential Information ◽  
Set Size ◽  
Novel Approach ◽  
Learning Techniques ◽  
Energy Plant ◽  
Definition Of ◽  
The Right

In the age of AI, companies strive to extract benefits from data. In the first steps of data analysis, an arduous dilemma scientists have to cope with is the definition of the ’right’ quantity of data needed for a certain task. In particular, when dealing with energy management, one of the most thriving application of AI is the consumption’s optimization of energy plant generators. When designing a strategy to improve the generators’ schedule, a piece of essential information is the future energy load requested by the plant. This topic, in the literature it is referred to as load forecasting, has lately gained great popularity; in this paper authors underline the problem of estimating the correct size of data to train prediction algorithms and propose a suitable methodology. The main characters of this methodology are the Learning Curves, a powerful tool to track algorithms performance whilst data training-set size varies. At first, a brief review of the state of the art and a shallow analysis of eligible machine learning techniques are offered. Furthermore, the hypothesis and constraints of the work are explained, presenting the dataset and the goal of the analysis. Finally, the methodology is elucidated and the results are discussed.

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