The index of representations associated with stabilisers

Let $Q$ be an algebraic group and $V$ a $Q$-module. The index of $V$ is the minimal codimension of the $Q$-orbits in the dual space $V^*$. There is a general inequality, due to Vinberg, relating the index of $V$ and the index of $Q_v$-module $V/q.v$ for any $v\in V$. In this article, we study conditions that guarantee us the equality. It was recently proved by Charbonnel (Bull. Soc. Math. France. v.132, 2004) that such an equality holds for the adjoint representation of a semisimple group. Another proof for the classical series was given by the second author, see math.RT/0407065. One of our goals, which is almost achieved, is to understand what is going on in the case of isotropy representations of symmetric spaces.Comment: 22 pages, some classification results added in Sections 6 and

On maximal commutative subalgebras of Poisson algebras associated with involutions of semisimple Lie algebras

For any involution $\sigma$ of a semisimple Lie algebra $\mathfrak g$, one constructs a non-reductive Lie algebra $\mathfrak k$, which is called a $\mathbb Z_2$-contraction of $\mathfrak g$. In this paper, we attack the problem of describing maximal commutative subalgebras of the Poisson algebra $S(\mathfrak k)$. This is closely related to the study of the coadjoint representation of $\mathfrak k$ and the set, $\mathfrak k^*_{reg}$, of the regular elements of $\mathfrak k^*$. By our previous results, in the context of $\mathbb Z_2$-contractions, the argument shift method provides maximal commutative subalgebras of $S(\mathfrak k)$ whenever $codim(\mathfrak k^* \setminus \mathfrak k^*_{reg})\ge 3$. Our main result here is that $codim(\mathfrak k^* \setminus \mathfrak k^*_{reg})\ge 3$ if and only if the Satake diagram of $\sigma$ has no trivial nodes. (A node is trivial, if it is white, has no arrows attached, and all adjacent nodes are also white.) The list of suitable involutions is provided. We also describe certain maximal commutative subalgebras of $S(\mathfrak k)$ if the (-1)-eigenspace of $\sigma$ in $\mathfrak g$ contains regular elements.Comment: 18 pages, to appear in Bull. Sci. Mat

Prospects for the internal state financial control development in the Russian Federation

Purpose: The presented article is aimed at assessing the modern development of internal state financial control in the Russian Federation. The most important condition for the effective functioning of public finances is the transition to a qualitatively new level required for the dynamic development of the public administration sector, improving the social status of citizens, as well as the investment climate. This predetermines the objective need to rethink and identify fundamentally new approaches to the study of theoretical, methodological and practical problems of financial management. Design/Methodology/Approach: The article is a comprehensive review of the main changes in legislation governing internal state financial control that determines the nature of this concept, the methodology of internal state financial control is presented, problems are identified, substantiated and structured and directions for their solution are proposed in order to increase its development effectiveness. The study used methods of comparative analysis, systematization, classification, analogy and comparison. Findings: The authors identified, substantiated the problems and developed recommendations for improving internal state financial control, which can improve the quality of public and municipal finance management and facilitate the transfer of public administration to a level that meets the needs of modern reform of the Russian economy. Practical Implications: The results of the study can be introduced into the practice of organizing internal state financial control in the Russian Federation in order to improve the quality of public and municipal finance management. Originality/Value: The main contribution of this study is to develop recommendations for the development of internal state financial control, which will contribute to the effective management of public finances in the executive bodies of the Russian Federation.peer-reviewe

The interaction of polymer dispersed liquid crystal sensors with ultrasound

Polymer dispersed liquid crystals (PDLCs) have been shown to be sensitive to ultrasound through the acousto-optic effect. The acousto-optic response of PDLCs was studied over a broad frequency range (0.3–10 MHz). We demonstrate that the displacements required to produce acousto-optic clearing of PDLC films can be as low as a few nanometers, which is at least 103 times smaller than the PDLC droplet size, is 105 times smaller than the PDLC layer thickness, and of the order of the molecular size of the liquid crystal constituents. This suggests that the acousto-optic effect in PDLCs is due to the microscopic effects of the LC reorientation under torques or flows rather than the LC reorientation through macroscopic droplet deformation. The displacement required for clearing is related to the frequency of operation via an exponential decay. We attribute the observed frequency response to a freezing out of the rotational motion around the short axis of the liquid crystal. The reported frequency dependence and displacements required indicate that the effects and materials described here could be used for ultrasound visualization in a non-destructive testing context

Assessing Descriptive Substance in Free-Text Collection-Level Metadata

Collection-level metadata has the potential to provide important information about the features and purpose of individual collections. This paper reports on a content analysis of collection records in an aggregation of cultural heritage collections. The findings show that the free-text Description field often provides more accurate and complete representation of subjects and object types than the specified fields. Properties such as importance, uniqueness, comprehensiveness, provenance, and creator are articulated, as well as other vital contextual information about the intentions of a collector and the value of a collection, as a whole, for scholarly users. The results demonstrate that the semantically rich free-text Description field is essential to understanding the context of collections in large aggregations and can serve as a source of data for enhancing and customizing controlled vocabulariesIMLS NLG Research and Demonstration grant LG-06-07-0020-07published or submitted for publicationis peer reviewe

Методичні рекомендації до організації навчально-дослідницької діяльності та написання наукових робіт студентів біологів

Методичні рекомендації до організації навчально-дослідницької діяльності студентів та написання наукових робіт студентів біологів відповідають вимогам до написання такого типу робіт і розраховані на студентів біологічного факультету СНУ імені Лесі Українки

The teoretical aspects of integration of students with dissabilities of higher education institution educational environment.

У статті подається теоретичний аналіз підходів учених до проблеми інтеграції студентів з обмеженими можливостями у навчально-виховне середовище вищого навчального закладу. The article presents a theoretical analysis of approaches to the problem of integrating of students with disabilities into the educational environment of higher education institution.Роботу виконано на кафедрі соціальної педагогіки ВНУ ім. Лесі УкраїнкиБартків Оксана Степанівна - кандидат педагогічних наук, доцент кафедри соціальної педагогіки інституту педагогіки Східноєвропейського національного університету імені Лесі Українки Дурманенко О. Л. - аспірантка Східноєвропейського національного університету імені Лесі Українк