Topological monodromy as an obstruction to Hamiltonization of nonholonomic systems: pro or contra?

The phenomenon of a topological monodromy in integrable Hamiltonian and nonholonomic systems is discussed. An efficient method for computing and visualizing the monodromy is developed. The comparative analysis of the topological monodromy is given for the rolling ellipsoid of revolution problem in two cases, namely, on a smooth and on a rough plane. The first of these systems is Hamiltonian, the second is nonholonomic. We show that, from the viewpoint of monodromy, there is no difference between the two systems, and thus disprove the conjecture by Cushman and Duistermaat stating that the topological monodromy gives a topological obstruction for Hamiltonization of the rolling ellipsoid of revolution on a rough plane.Comment: 31 pages, 11 figure

Peculiarities of the seasonal biology of ectoparasites of the Genus Spinturnix von Heyden, 1826 (Mesostigmata: Gamasina: Spinturnicidae) in the boreal zone of the Palearctic region

The most complete data on the peculiarities of seasonal biology of gamasid mites of the genus Spinturnix, which are ectoparasites of bats of the boreal zone of the Old World, are presented. Data on the dynamics of the sex and age structure of superpopulations of parasites throughout the year are presented; the infestation of various bat species is analyzed, and the factors affecting it are discussed. The main differences between the life cycles of the boreal and subboreal Spinturnicidae mites were revealed

Mixed germ cell sex cord-stromal tumors of the testis and ovary. Morphological, immunohistochemical, and molecular genetic study of seven cases

We present the morphological, immunohistochemical, and molecular genetic features of three cases of testicular and four cases of ovarian mixed germ cell sex cord-stromal tumors (MGSCT). The germ cells in the testicular MGSCTs morphologically differed from those in classical seminomas by lacking the typical square off quality of the nuclei. In contrast to the nuclei in classical seminomas, their size in testicular MGSCTs was smaller and nucleoli were inconspicuous and the cytoplasm was Periodic Acid-Schiff(PAS) negative. Quite on the contrary, the variability in the size of the nuclei of the germ cells in the testicular MGSCTs was more similar to that seen in the germ cells of spermatocytic seminomas. Immunohisto-chemically, the germ cells of MGSCTs in one case reacted positively with antibody to AE1-AE3 by paranuclear dotlike or rodlike positivity. All three testicular MGSCTs had a negative reaction with the rest of antibodies, including placental alkaline phosphatase (PLAP), OCT4, and c-kit protein. Ovarian MGSCT in our series differed from the testicular lesions in both the germ cell component and the sex cord component. The germ cells in all four ovarian cases had cytomorphological and immuno-histochemical features identical to those in classical seminomas/dysgerminomas. They possessed the typical square off quality of the nuclei, which were much more blastic, with more mitoses compared with the testicular tumors in our series, and they were PLAP (4/4), OCT4 (4/4) and c-kit protein (3/4) positive immunohisto-chemically. The cytoplasm of the germ cells in ovarian neoplasms contained PAS positive glycogen. Germ cells in one ovarian MGSCTs showed amplification of l2p. All other germ cells were negative for amplification of 12p. All five successfully analyzed cases showed no mutation in all studied exons and exon-intron junctions in c-kit and PDFGRA genes

Minimal Liouville gravity correlation numbers from Douglas string equation

We continue the study of (q, p) Minimal Liouville Gravity with the help of Douglas string equation. We generalize the results of [1,2], where Lee-Yang series (2, 2s + 1) was studied, to (3, 3s + p 0) Minimal Liouville Gravity, where p 0 = 1, 2. We demonstrate that there exist such coordinates \u3c4 m,n on the space of the perturbed Minimal Liouville Gravity theories, in which the partition function of the theory is determined by the Douglas string equation. The coordinates \u3c4 m,n are related in a non-linear fashion to the natural coupling constants \u3bb m,n of the perturbations of Minimal Lioville Gravity by the physical operators O m,n . We find this relation from the requirement that the correlation numbers in Minimal Liouville Gravity must satisfy the conformal and fusion selection rules. After fixing this relation we compute three- and four-point correlation numbers when they are not zero. The results are in agreement with the direct calculations in Minimal Liouville Gravity available in the literature [3-5]. \ua9 2014 The Author(s)

Dimensional recurrence relations: an easy way to evaluate higher orders of expansion in ϵ\epsilon

Applications of a method recently suggested by one of the authors (R.L.) are presented. This method is based on the use of dimensional recurrence relations and analytic properties of Feynman integrals as functions of the parameter of dimensional regularization, $d$. The method was used to obtain analytical expressions for two missing constants in the $\epsilon$-expansion of the most complicated master integrals contributing to the three-loop massless quark and gluon form factors and thereby present the form factors in a completely analytic form. To illustrate its power we present, at transcendentality weight seven, the next order of the $\epsilon$-expansion of one of the corresponding most complicated master integrals. As a further application, we present three previously unknown terms of the expansion in $\epsilon$ of the three-loop non-planar massless propagator diagram. Only multiple $\zeta$ values at integer points are present in our result.Comment: Talk given at the International Workshop `Loops and Legs in Quantum Field Theory' (April 25--30, 2010, W\"orlitz, Germany)

Research of the Effect of Modification on the Structure and Properties of Castings from Steel H11 Obtained by Using Electrosfining Technology

Рассмотрены методы повышения неравновесности системы за счет модифицирования отливок из легированной стали, полученных электрошлаковым кокильным литьем. Показаны микроструктуры отливок и представлены результаты испытаний по определению механических свойств образцов, полученных при различных технологических режимах электрошлаковой технологииThe methods of increasing the disequilibrium of the system due to the modification, castings of alloy steel, obtained by electroslag chill casting are considered. The microstructures of the castings are shown and the results of tests to determine the mechanical properties of the samples obtained under various technological regimes of the electroslag technology are presente

Form factors at strong coupling via a Y-system

We compute form factors in planar N=4 Super Yang-Mills at strong coupling. Namely we consider the overlap between an operator insertion and 2n gluons. Through the gauge/string duality these are given by minimal surfaces in AdS space. The surfaces end on an infinite periodic sequence of null segments at the boundary of AdS. We consider surfaces that can be embedded in AdS_3. We derive set of functional equations for the cross ratios as functions of the spectral parameter. These equations are of the form of a Y-system. The integral form of the Y-system has Thermodynamics Bethe Ansatz form. The area is given by the free energy of the TBA system or critical value of Yang-Yang functional. We consider a restricted set of operators which have small conformal dimension