The Intertwining Lemma

2019 ◽  
pp. 199-210
Author(s):  
Richard Evan Schwartz
Keyword(s):  
Single Point ◽  
Inductive Step ◽  
Induction Step ◽  
Definition Of

This chapter gives a proof of the Intertwining Lemma. Section 20.2 lists out the formulas for all the maps involved. Section 20.3 recalls the definition of Z* and proves Statement 3 of the Intertwining Lemma. Section 20.4 proves statements 1 and 2 of the Intertwining Lemma for a single point. Section 20.5 decomposes Z* into two smaller pieces as a prelude to giving the inductive step in the proof. Section 20.6 proves the following induction step: If the Intertwining Lemma is true for g ɛ GA then it is also true for g + dTA (0, 1). Section 20.7 explains what needs to be done to finish the proof of the Intertwining Lemma. Section 20.8 proves the Intertwining Theorem for points in Π‎A corresponding to the points gn = (n + 1/2)(1 + A, 1 − A) for n = 0, 1, 2, ... which all belong to GA. This result combines with the induction step to finish the proof, as explained in Section 20.7.

UNCERTAINTY BASED ROBUST OPTIMIZATION IN AERODYNAMICS

2009 ◽  
Vol 23 (03) ◽  
pp. 477-480 ◽  
Author(s):  
ZHILI TANG
Keyword(s):  
Nash Equilibrium ◽  
Robust Design ◽  
Single Point ◽  
Optimization Method ◽  
Equilibrium Solutions ◽  
Design Problems ◽  
Nash Equilibrium Solutions ◽  
Definition Of ◽  
Taguchi Robust Design ◽  
Statistical Definition

The Taguchi robust design concept is combined with the multi-objective deterministic optimization method to overcome single point design problems in Aerodynamics. Starting from a statistical definition of stability, the method finds, Nash equilibrium solutions for performance and its stability simultaneously.

scholarly journals ANALYSIS OF DISTANCE LEARNING SYSTEMS ON THE EXAMPLE OF STATE UNIVERSITIES IN THE CHUVASH REPUBLIC

2021 ◽  
pp. 156-166
Author(s):  
Татьяна Ароновна Лавина ◽  
Николай Игоревич Степанов
Keyword(s):  
Distance Learning ◽  
Single Point ◽  
Educational Environment ◽  
Learning Systems ◽  
State Universities ◽  
Access To Information ◽  
Chuvash Republic ◽  
Definition Of ◽  
Electronic Support ◽  
The University

Данная статья посвящена исследованию систем дистанционного обучения в вузах Чувашской Республики, определению основных функций систем управления дистанционным обучением. Проведен анализ систем дистанционного взаимодействия со студентами в федеральных вузах Чувашской Республики. С целью формирования требований к функциям современной единой универсальной платформы дистанционного взаимодействия в университете проведен анализ корпоративной платформы, объединяющей в рабочем пространстве чат, встречи, заметки и вложения MS Teams, позволяющей организовывать дистанционное обучение. На примере веб-ресурсов для поддержки организации дистанционного обучения государственных университетов Чувашской Республики, таких как система управления курсами, использующая лицензию GNU GPL Moodle, системы видеоконференций Big Blue Button, рассматриваются их функциональные возможности и недостатки, выявляются ключевые особенности построения единого информационного пространства вуза на основе идеи использования инструментов образовательных платформ в обеспечении электронной поддержки дистанционного обучения. Представлены преимущества интеграции систем LMS Moodle и MS Teams для построения интерактивного формата обучения на примере построения единой образовательной среды в ЧГПУ им. И. Я. Яковлева. Рассмотрено внедрение единой учетной записи для организации принципа единой точки доступа к информационным системам дистанционного обучения для построения единой электронной образовательной среды университета на базе технологии OpenID Connect. This article is devoted to the study of distance learning systems in universities of the Chuvash Republic, the definition of the main functions of distance learning systems. It presents the analysis of systems of distance learning interaction with students in federal universities of the Chuvash Republic. In order to form the requirements for the functions of a modern unified universal platform for distance learning interaction at the university, the authors analysed the corporate platform that combines chat, meetings, notes and attachments of MS Teams in the workspace. Using the example of web resources to support the organization of distance learning of state universities of the Chuvash Republic, such as the course management system using the GNU GPL Moodle license, the Big Blue Button video conferencing systems, their functionality and shortcomings are considered, the key features of building a unified information space of the university based on the idea of using the tools of educational platforms in providing electronic support for distance learning are identified. The advantages of integrating the LMS Moodle and MS Teams systems for building an interactive learning format are presented on the example of building a unified educational environment at I. Yakovlev CHSPU. The introduction of a single account for the organization of a single point of access to information systems of distance learning for the construction of a single electronic educational environment of the university based on OpenID Connect technology is considered.

scholarly journals Points at Issue With the Definition of Forgery (the Case Study of Article 326 of the Criminal Code of the Russian Federation)

2019 ◽  
pp. 1-17
Author(s):  
Evgeniy Mikhailovich Trubin ◽  
Stanislav Igorevich Golubev
Keyword(s):  
Russian Federation ◽  
Single Point ◽  
Criminal Code ◽  
Point Of View ◽  
Legal Provisions ◽  
Analysis And Synthesis ◽  
The Russian Federation ◽  
Analysis System ◽  
Definition Of ◽  
State Registration

The object of the research is the definition of forgery as it is used by the legislation, in particular, in Article 326 of the Criminal Code of the Russian Federation. The authors see the following problems: no legal definition, no single point of view in the doctrine of criminal law and incoordinations with other terms used in law. The wording 'forgery or counterfeiting state registration sign' used in Article 326 of the Criminal Code of the Russian Federation makes the situation even more complicated. Thus, the subject of this research is different doctrinal interpretations of the term 'forgery' and judicial practice. The methodological framework of the research covers such methods as analysis and synthesis, comparative law analysis, system-structured and formal law approaches, theoretical prognistic method and interpretation of legal provisions. The novelty of the research is caused by the fact that the author offer their own definition of the term 'forgery' and concludes that forgery and forgery documents/items are compatible and intersecting terms. The authors also conclude what criteria of truth and authenticity can be used to describe items/documents as forgery-counterfeiting, forgery but not counterfeiting and counterfeiting but not forgery. They also make recommendations on what amendments should be made in the applicable law. 

Failure Prediction for Textile Composites Via Micromechanics

Materials ◽  
2003 ◽  
Author(s):  
Brian Cox ◽  
Qingda Yang
Keyword(s):  
Single Point ◽  
Failure Mechanisms ◽  
Material Constant ◽  
Local Stress ◽  
Failure Criteria ◽  
Textile Composites ◽  
Local Damage ◽  
Stress Components ◽  
Definition Of ◽  
2D And 3D

The question of failure criteria for textile composites is taken up, with reference to the micormechanics of known failure mechanisms in broad classes of 2D and 3D textile composites. Of primary importance is the definition of the measure of local stress or strain that should be compared against a putative material constant to predict local damage. In most prior work, some combination of strain or stress components evaluated at a single point has been used. Due to the complexity and inevitahle irregularity of textile composites, this approach is not favoured. Instead, micromechanical considreations recommend using strains averaged over gauge volumes whose dimensions are greater than or equal to approximately half the width dimensions of a single tow. Engineering tests that can be used for calibration are suggested but remain to be proven repeatable and consistent.

scholarly journals Markov processes with spatial delay: Path space characterization, occupation time and properties

2017 ◽  
Vol 17 (06) ◽  
pp. 1750042 ◽  
Author(s):  
Michael Salins ◽  
Konstantinos Spiliopoulos
Keyword(s):  
Local Time ◽  
Markov Processes ◽  
Single Point ◽  
Occupation Time ◽  
One Dimensional ◽  
Stochastic Dynamical System ◽  
Second Derivatives ◽  
Continuous Markov Process ◽  
Positive Time ◽  
Definition Of

In this paper, we study one-dimensional Markov processes with spatial delay. Since the seminal work of Feller, we know that virtually any one-dimensional, strong, homogeneous, continuous Markov process can be uniquely characterized via its infinitesimal generator and the generator’s domain of definition. Unlike standard diffusions like Brownian motion, processes with spatial delay spend positive time at a single point of space. Interestingly, the set of times that a delay process spends at its delay point is nowhere dense and forms a positive measure Cantor set. The domain of definition of the generator has restrictions involving second derivatives. In this paper we provide a pathwise characterization for processes with delay in terms of an SDE and an occupation time formula involving the symmetric local time. This characterization provides an explicit Doob–Meyer decomposition, demonstrating that such processes are semi-martingales and that all of stochastic calculus including Itô formula and Girsanov formula applies. We also establish an occupation time formula linking the time that the process spends at a delay point with its symmetric local time there. A physical example of a stochastic dynamical system with delay is lastly presented and analyzed.

scholarly journals On Weak Super Ricci Flow through Neckpinch

2021 ◽  
Vol 9 (1) ◽  
pp. 120-159
Author(s):  
Sajjad Lakzian ◽  
Michael Munn
Keyword(s):  
Ricci Flow ◽  
Single Point ◽  
Cost Functions ◽  
Final Time ◽  
Convex Cost ◽  
Measure Spaces ◽  
Totally Geodesic Hypersurfaces ◽  
Flow Through ◽  
Definition Of ◽  
Singular Time

Abstract In this article, we study the Ricci flow neckpinch in the context of metric measure spaces. We introduce the notion of a Ricci flow metric measure spacetime and of a weak (refined) super Ricci flow associated to convex cost functions (cost functions which are increasing convex functions of the distance function). Our definition of a weak super Ricci flow is based on the coupled contraction property for suitably defined diffusions on maximal diffusion subspaces. In our main theorem, we show that if a non-degenerate spherical neckpinch can be continued beyond the singular time by a smooth forward evolution then the corresponding Ricci flow metric measure spacetime through the singularity is a weak super Ricci flow for a (and therefore for all) convex cost functions if and only if the single point pinching phenomenon holds at singular times; i.e., if singularities form on a finite number of totally geodesic hypersurfaces of the form {x} × 𝕊 n . We also show the spacetime is a refined weak super Ricci flow if and only if the flow is a smooth Ricci flow with possibly singular final time.

scholarly journals PROSPECTS OF DEOFFSHORIZATION IN UKRAINE

2020 ◽  
Vol 11 (87) ◽  
Author(s):  
Alina Steblianko ◽  
◽  
Yarina Vereshchaka ◽  
Keyword(s):  
Tax Evasion ◽  
Single Point ◽  
Point Of View ◽  
Effective Control ◽  
Tax Havens ◽  
Tax Legislation ◽  
Stage Of Development ◽  
Definition Of ◽  
National Economies ◽  
Relationship Of

The article is devoted to the analysis of the process of deoffshorization at the present stage of development of the Ukrainian statehood and prospects of its further development. The urgency of the problem described in the article is due to significant losses from offshoring for the economy of Ukraine, which, in turn, requires the development of effective tools to regulate the relationship of residents with «tax havens». It is noted that despite significant scientific works and current research, today there is no single point of view on the effectiveness of the existing mechanism of deoffshorization of national economies by international regulators, tools to combat tax erosion and tax evasion. The article considers the definition of «deoffshorization», describes the mechanism of deoffshorization of the national economy. It has been established that one of the most important goals of global deoffshorization is to create equal conditions for the movement of capital between countries, without giving preference to countries that have more attractive tax conditions. Emphasis is placed on the fact that the harmonization of anti-offshore and tax policies is one of the key processes, as deoffshorization cannot be effective without increasing the responsibility for non-compliance with tax legislation. International experience on deoffshorization processes is analyzed. Attempts by the Ukrainian legislature to resolve issues related to deoffshorization are considered. It is emphasized that despite the fact that some mechanisms of counteraction to cross-border tax evasion schemes are fragmented in Ukraine, such mechanisms need further clarification and implementation of tools that will allow effective control over the relevant areas and ensure effective functioning of the domestic counteraction system. tax minimization. It is concluded that there is an objective need to bring the degree of responsibility for violations of tax legislation as much as possible in line with international practice and to ensure the transition to a qualitatively new level of international cooperation in the exchange of tax information.

scholarly journals TURNOVER OF LAND PLOTS AS OBJECTS OF CIVIL RIGHTS

2021 ◽  
pp. 30-35
Author(s):  
O.A. Rozhkova ◽  
S.V. Voronina
Keyword(s):  
Civil Rights ◽  
Single Point ◽  
Civil Code ◽  
Point Of View ◽  
Scientific Discussion ◽  
The Subject ◽  
Federal Laws ◽  
Definition Of ◽  
Land Code

The definition of the concept of turnover is absent in the provisions of the civil code and other normativelegal acts. The scientific discussion is based on the content of the concepts of turnover, civil turnover and legalregime, and their relationship. In civil turnover, most of the objects of civil rights are freely used, which ispredetermined by their inherent legal property of turnover. The civil code defines turnover as the ability ofan object of civil rights to be freely alienated and transferred from one person to another. Turnover is oftenidentified with the ability of an object to be an object of civil rights in General. The doctrine also does nothave a single point of view regarding the understanding of turnover and its relationship to the legal regime.Land plots are objects of civil turnover, participate in land legal relations as objects of civil turnover.The turnover of land plots is carried out to the extent that it is allowed by the legislation. The question ofthe correlation between land and civil legislation in regulating the turnover of land plots is relevant. Thecivil code refers the determination of the degree of turnover of land plots to the subject of regulation of landlegislation. In accordance with the land code, the turnover of land plots is carried out in accordance withcivil legislation and the code, while the content of restrictions on the turnover of land plots is establishedby the land code and Federal laws.

A Single-Point Base Definition of the Xiejian Age as an Exemplar for Refining Chinese Land Mammal Ages

2013 ◽  
pp. 124-141 ◽  
Author(s):  
Jin Meng ◽  
Jie Ye ◽  
Wen-Yu Wu ◽  
Xi-Jun Ni ◽  
Shun-Dong Bi
Keyword(s):  
Single Point ◽  
Definition Of ◽  
Land Mammal

NONPARAMETRIC DETECTION OF DEPENDENCES IN STOCHASTIC POINT PROCESSES

2004 ◽  
Vol 14 (06) ◽  
pp. 1987-1993 ◽  
Author(s):  
ANDREAS KAISER ◽  
THOMAS SCHREIBER
Keyword(s):  
Point Process ◽  
Point Processes ◽  
Single Point ◽  
Crucial Point ◽  
Process Dynamics ◽  
Time Index ◽  
Common Time ◽  
Nonparametric Detection ◽  
Definition Of ◽  
Stochastic Point Processes

A new, parameter-free approach based on information theoretical tools is presented which allows the detection of dependences in the dynamics between two point processes. The crucial point is the definition of sequences of inter-event intervals between the events of two stochastic point processes where these sequences are ordered to only one common time index. This is an enhancement of the concept of event intervals of a single point process and makes the analysis of the process dynamics of more than one point processes possible. An application of this method is also illustrated using a model consisting of two synaptically coupled Hindmarsh–Rose neurons.

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