On Free Quotients of Complete Intersection Calabi-Yau Manifolds

In order to find novel examples of non-simply connected Calabi-Yau threefolds, free quotients of complete intersections in products of projective spaces are classified by means of a computer search. More precisely, all automorphisms of the product of projective spaces that descend to a free action on the Calabi-Yau manifold are identified.Comment: 39 pages, 3 tables, LaTe

Zassenhaus conjecture for central extensions of S5

We confirm a conjecture of Zassenhaus about rational conjugacy of torsion units in integral group rings for a covering group of the symmetric group S5 and for the general linear group GLð2; 5Þ. The first result, together with others from the literature, settles the conjugacy question for units of prime-power order in the integral group ring of a finite Frobenius group

On the structure of Borel stable abelian subalgebras in infinitesimal symmetric spaces

Let g=g_0+g_1 be a Z_2-graded Lie algebra. We study the posets of abelian subalgebras of g_1 which are stable w.r.t. a Borel subalgebra of g_0. In particular, we find out a natural parametrization of maximal elements and dimension formulas for them. We recover as special cases several results of Kostant, Panyushev, Suter.Comment: Latex file, 35 pages, minor corrections, some examples added. To appear in Selecta Mathematic

Quantum tops as examples of commuting differential operators

We study the quantum analogs of tops on Lie algebras $so(4)$ and $e(3)$ represented by differential operators.Comment: 24 p

Fullerenes: prospects of using in medicine, biology and ecology

Обобщены результаты собственных исследований и данные научной литературы последнего десятилетия о свойствах фуллеренов и углеродных нанотрубок. Химическая стабильность структуры и низкая токсичность фуллеренов определяют их использование в медицинской химии, фармакологии, косметологии. Благодаря механической прочности нанотрубки стали основой экологически чистых конструкционных и защитных материалов. На основе фуллерита С60 можно получить матрицу, которая позволяет накапливать до 7,7 мас. % водорода с образованием гидрофуллерита С60Н60. Использование фуллеренов для накопления и хранения водорода расширяет перспективы развития экологически чистой водородной энергетики. Узагальнено результати власних досліджень і дані наукової літератури останнього десятиліття про властивості фулеренів і вуглецевих нанотрубок. Хімічна стабільність структури та низька токсичність фулеренів визначають їх застосування у медичній хімії, фармакології, косметології. Завдяки механічній міцності нанотрубки стали основою екологічно чистих конструкційних і захисних матеріалів. На основі фулериту С60 можна отримати матрицю, що дозволяє накопичувати до 7,7 мас. % гідрогену з утворенням гідрофулериту С60Н60. Застосування фулеренів для накопичення та збереження водню перспективне для розвитку екологічно чистої водневої енергетики. Results of our own research and academic literature data on the properties of fullerenes and carbon nanotubes are analysed and summarized. Chemical stability of the structure and low toxicity of fullerenes determine their usage in medical chemistry, pharmacology and cosmetology. Due to its mechanical strength the nanotubes have become the basis of clean construction and barrier materials. It is shown that a matrix based on fullerit C60 can be obtained. It allows to store up to 7.7 wt. % hydrogen with formation of hydrofullerit C60H60. The usage of fullerenes for accumulation and storage of hydrogen enhances the prospects of clean hydrogen energy development.

Fermionic representations for characters of M(3,t), M(4,5), M(5,6) and M(6,7) minimal models and related Rogers-Ramanujan type and dilogarithm identities

Characters and linear combinations of characters that admit a fermionic sum representation as well as a factorized form are considered for some minimal Virasoro models. As a consequence, various Rogers-Ramanujan type identities are obtained. Dilogarithm identities producing corresponding effective central charges and secondary effective central charges are derived. Several ways of constructing more general fermionic representations are discussed.Comment: 14 pages, LaTex; minor correction

Polynomial super-gl(n) algebras

We introduce a class of finite dimensional nonlinear superalgebras $L = L_{\bar{0}} + L_{\bar{1}}$ providing gradings of $L_{\bar{0}} = gl(n) \simeq sl(n) + gl(1)$. Odd generators close by anticommutation on polynomials (of degree $>1$) in the $gl(n)$ generators. Specifically, we investigate `type I' super-$gl(n)$ algebras, having odd generators transforming in a single irreducible representation of $gl(n)$ together with its contragredient. Admissible structure constants are discussed in terms of available $gl(n)$ couplings, and various special cases and candidate superalgebras are identified and exemplified via concrete oscillator constructions. For the case of the $n$-dimensional defining representation, with odd generators $Q_{a}, \bar{Q}{}^{b}$, and even generators ${E^{a}}_{b}$, $a,b = 1,...,n$, a three parameter family of quadratic super-$gl(n)$ algebras (deformations of $sl(n/1)$) is defined. In general, additional covariant Serre-type conditions are imposed, in order that the Jacobi identities be fulfilled. For these quadratic super-$gl(n)$ algebras, the construction of Kac modules, and conditions for atypicality, are briefly considered. Applications in quantum field theory, including Hamiltonian lattice QCD and space-time supersymmetry, are discussed.Comment: 31 pages, LaTeX, including minor corrections to equation (3) and reference [60

Continued Fractions and Fermionic Representations for Characters of M(p,p') minimal models

We present fermionic sum representations of the characters $\chi^{(p,p')}_{r,s}$ of the minimal $M(p,p')$ models for all relatively prime integers $p'>p$ for some allowed values of $r$ and $s$. Our starting point is binomial (q-binomial) identities derived from a truncation of the state counting equations of the XXZ spin ${1\over 2}$ chain of anisotropy $-\Delta=-\cos(\pi{p\over p'})$. We use the Takahashi-Suzuki method to express the allowed values of $r$ (and $s$) in terms of the continued fraction decomposition of $\{{p'\over p}\}$ (and ${p\over p'}$) where $\{x\}$ stands for the fractional part of $x.$ These values are, in fact, the dimensions of the hermitian irreducible representations of $SU_{q_{-}}(2)$ (and $SU_{q_{+}}(2)$) with $q_{-}=\exp (i \pi \{{p'\over p}\})$ (and $q_{+}=\exp ( i \pi {p\over p'})).$ We also establish the duality relation $M(p,p')\leftrightarrow M(p'-p,p')$ and discuss the action of the Andrews-Bailey transformation in the space of minimal models. Many new identities of the Rogers-Ramanujan type are presented.Comment: Several references, one further explicit result and several discussion remarks adde

The effects of social service contact on teenagers in England

Objective: This study investigated outcomes of social service contact during teenage years. Method: Secondary analysis was conducted of the Longitudinal Survey of Young People in England (N = 15,770), using data on reported contact with social services resulting from teenagers’ behavior. Outcomes considered were educational achievement and aspiration, mental health, and locus of control. Inverse-probability-weighted regression adjustment was used to estimate the effect of social service contact. Results: There was no significant difference between those who received social service contact and those who did not for mental health outcome or aspiration to apply to university. Those with contact had lower odds of achieving good exam results or of being confident in university acceptance if sought. Results for locus of control were mixed. Conclusions: Attention is needed to the role of social services in supporting the education of young people in difficulty. Further research is needed on the outcomes of social services contact

Multipoint Schur algorithm and orthogonal rational functions: convergence properties, I

Classical Schur analysis is intimately connected to the theory of orthogonal polynomials on the circle [Simon, 2005]. We investigate here the connection between multipoint Schur analysis and orthogonal rational functions. Specifically, we study the convergence of the Wall rational functions via the development of a rational analogue to the Szeg\H o theory, in the case where the interpolation points may accumulate on the unit circle. This leads us to generalize results from [Khrushchev,2001], [Bultheel et al., 1999], and yields asymptotics of a novel type.Comment: a preliminary version, 39 pages; some changes in the Introduction, Section 5 (Szeg\H o type asymptotics) is extende