On the KAM - Theory Conditions for the Kirchhoff Top

* Partially supported by Grant MM523/95 with Ministry of Science and Technologies.

Symplectic Representation of a Braid Group on 3-Sheeted Covers of the Riemann Sphere

We define Picard cycles on each smooth three-sheeted Galois cover C of the Riemann sphere. The moduli space of all these algebraic curves is a nice Shimura surface, namely a symmetric quotient of the projective plane uniformized by the complex two-dimensional unit ball. We show that all Picard cycles on C form a simple orbit of the Picard modular group of Eisenstein numbers. The proof uses a special surface classification in connection with the uniformization of a classical Picard-Fuchs system. It yields an explicit symplectic representation of the braid groups (coloured or not) of four strings.

Isomorphism of Commutative Modular Group Algebras

∗ The work was supported by the National Fund “Scientific researches” and by the Ministry of Education and Science in Bulgaria under contract MM 70/91.

Generalizations of Cole's Systems

There are four resolvable Steiner triple systems on fifteen elements. Some generalizations of these systems are presented here.

Limit Cycles of Perturbations of a Class of Quadratic Hamiltonian Vector Fields

We prove that in quadratic perturbations of generic Hamiltonian vector fields with two saddle points and one center there can appear at most two limit cycles. This bound is exact.

Perturbations of Systems Describing the Motion of a Particle in Central Fields

The present paper deals with the KAM-theory conditions for systems describing the motion of a particle in central field.

Multiplicative Systems on Ultra-Metric Spaces

AMS Subj. Classification: MSC2010: 42C10, 43A50, 43A75

Fundamental Investigations on the Unit Groups of Commutative Group Algebras in Bulgaria

In this paper we give the first investigations and also some basic results on the unit groups of commutative group algebras in Bulgaria. These investigations continue some classical results. Namely, it is supposed that the cardinality of the starting group is arbitrary.

The Variety of Leibniz Algebras Defined by the Identity x(y(zt)) ≡ 0

2000 Mathematics Subject Classification: Primary: 17A32; Secondary: 16R10, 16P99, 17B01, 17B30, 20C30

Henselian Discrete Valued Fields Admitting One-Dimensional Local Class Field Theory

2000 Mathematics Subject Classification: 11S31 12E15 12F10 12J20.

Factorizations of some Groups of Lie Type of Lie Rank 4

Еленка Генчева, Цанко Генчев В настоящата работа се разглеждат крайни прости групи G , които могат да се представят като произведение на две свои собствени неабелеви прости подгрупи A и B. Всяко такова представяне G = AB е прието да се нарича факторизация на G, а тъй като множителите A и B са избрани да бъдат прости подгрупи на G, то разглежданите факторизации са известни още като прости факторизации на G. Тук се предполага, че G е проста група от лиев тип и лиев ранг 4 над крайно поле GF (q). Ключови думи: крайни прости групи, групи от лиев тип, факторизации на групи.

On some Finite-Dimensional Representations of Artin Braid Group

Валентин В. Илиев - Авторът изучава някои хомоморфни образи G на групата на Артин на плитките върху n нишки в крайни симетрични групи. Получените пермутационни групи G са разширения на симетричната група върху n букви чрез подходяща абелева група. Разширенията G зависят от един целочислен параметър q ≥ 1 и се разцепват тогава и само тогава, когато 4 не дели q. В случая на нечетно q са намерени всички крайномерни неприводими представяния на G, а те от своя страна генерират безкрайна редица от неприводими представяния на групата на плитките.

Moduli stacks of polarized K3 surfaces in mixed characteristic

2000 Mathematics Subject Classification: 14J28, 14D22.

On Groups whose Contranormal Subgroups are Normally Complemented

2000 Mathematics Subject Classification: 20F16, 20E15.

Enjoying the third age! Discourse, identity and liminality in extra-care communities

Extra-care housing has been an important and growing element of housing and care for older people in the United Kingdom since the 1990s. Previous studies have examined specific features and programmes within extra-care locations, but few have studied how residents negotiate social life and identity. Those that have, have noted that while extra care brings many health-related and social benefits, extra-care communities can also be difficult affective terrain. Given that many residents are now ‘ageing in place’ in extra care, it is timely to revisit these questions of identity and affect. Here we draw on the qualitative element of a three-year, mixed-method study of 14 extra-care villages and schemes run by the ExtraCare Charitable Trust. We follow Alemàn in regarding residents' ambivalent accounts of life in ExtraCare as important windows on the way in which liminal residents negotiate the dialectics of dependence and independence. However, we suggest that the dialectic of interest here is that of the third and fourth age, as described by Gilleard and Higgs. We set that dialectic within a post-structuralist/Lacanian framework in order to examine the different modes of enjoyment that liminal residents procure in ExtraCare's third age public spaces and ideals, and suggest that their complaints can be read in three ways: as statements about altered material conditions; as inter-subjective bolstering of group identity; and as fantasmatic support for liminal identities. Finally, we examine the implications that this latter psycho-social reading of residents' complaints has for enhancing and supporting residents' wellbeing.