Students’ Interest in Physical Education and Sports.

У статті зазначено, що в процесі навчання у вищому навчальному закладі простежено тенденцію до зниження рівня інтересу студентів до фізичного виховання й спорту. The tendency of decline of students’ interest in physical education and sports during studying at higher education institution is indicated in the article

Cohomology of groups of diffeomorphims related to the modules of differential operators on a smooth manifold

Let $M$ be a manifold and $T^*M$ be the cotangent bundle. We introduce a 1-cocycle on the group of diffeomorphisms of $M$ with values in the space of linear differential operators acting on $C^{\infty} (T^*M).$ When $M$ is the $n$-dimensional sphere, $S^n$, we use this 1-cocycle to compute the first-cohomology group of the group of diffeomorphisms of $S^n$, with coefficients in the space of linear differential operators acting on contravariant tensor fields.Comment: arxiv version is already officia

Quantum differential forms

Formalism of differential forms is developed for a variety of Quantum and noncommutative situations

Cellular automaton rules conserving the number of active sites

This paper shows how to determine all the unidimensional two-state cellular automaton rules of a given number of inputs which conserve the number of active sites. These rules have to satisfy a necessary and sufficient condition. If the active sites are viewed as cells occupied by identical particles, these cellular automaton rules represent evolution operators of systems of identical interacting particles whose total number is conserved. Some of these rules, which allow motion in both directions, mimic ensembles of one-dimensional pseudo-random walkers. Numerical evidence indicates that the corresponding stochastic processes might be non-Gaussian.Comment: 14 pages, 5 figure

Simulating spin-3/2 particles at colliders

Support for interactions of spin-3/2 particles is implemented in the FeynRules and ALOHA packages and tested with the MadGraph 5 and CalcHEP event generators in the context of three phenomenological applications. In the first, we implement a spin-3/2 Majorana gravitino field, as in local supersymmetric models, and study gravitino and gluino pair-production. In the second, a spin-3/2 Dirac top-quark excitation, inspired from compositness models, is implemented. We then investigate both top-quark excitation and top-quark pair-production. In the third, a general effective operator for a spin-3/2 Dirac quark excitation is implemented, followed by a calculation of the angular distribution of the s-channel production mechanism.Comment: 20 pages, 7 figure

Cyclic Statistics In Three Dimensions

While 2-dimensional quantum systems are known to exhibit non-permutation, braid group statistics, it is widely expected that quantum statistics in 3-dimensions is solely determined by representations of the permutation group. This expectation is false for certain 3-dimensional systems, as was shown by the authors of ref. [1,2,3]. In this work we demonstrate the existence of ``cyclic'', or $Z_n$, {\it non-permutation group} statistics for a system of n > 2 identical, unknotted rings embedded in $R^3$. We make crucial use of a theorem due to Goldsmith in conjunction with the so called Fuchs-Rabinovitch relations for the automorphisms of the free product group on n elements.Comment: 13 pages, 1 figure, LaTex, minor page reformattin

Differential operators on supercircle: conformally equivariant quantization and symbol calculus

We consider the supercircle $S^{1|1}$ equipped with the standard contact structure. The conformal Lie superalgebra K(1) acts on $S^{1|1}$ as the Lie superalgebra of contact vector fields; it contains the M\"obius superalgebra $osp(1|2)$. We study the space of linear differential operators on weighted densities as a module over $osp(1|2)$. We introduce the canonical isomorphism between this space and the corresponding space of symbols and find interesting resonant cases where such an isomorphism does not exist

All Stable Characteristic Classes of Homological Vector Fields

An odd vector field $Q$ on a supermanifold $M$ is called homological, if $Q^2=0$. The operator of Lie derivative $L_Q$ makes the algebra of smooth tensor fields on $M$ into a differential tensor algebra. In this paper, we give a complete classification of certain invariants of homological vector fields called characteristic classes. These take values in the cohomology of the operator $L_Q$ and are represented by $Q$-invariant tensors made up of the homological vector field and a symmetric connection on $M$ by means of tensor operations.Comment: 17 pages, references and comments adde

Cross-over behaviour in a communication network

We address the problem of message transfer in a communication network. The network consists of nodes and links, with the nodes lying on a two dimensional lattice. Each node has connections with its nearest neighbours, whereas some special nodes, which are designated as hubs, have connections to all the sites within a certain area of influence. The degree distribution for this network is bimodal in nature and has finite variance. The distribution of travel times between two sites situated at a fixed distance on this lattice shows fat fractal behaviour as a function of hub-density. If extra assortative connections are now introduced between the hubs so that each hub is connected to two or three other hubs, the distribution crosses over to power-law behaviour. Cross-over behaviour is also seen if end-to-end short cuts are introduced between hubs whose areas of influence overlap, but this is much milder in nature. In yet another information transmission process, namely, the spread of infection on the network with assortative connections, we again observed cross-over behaviour of another type, viz. from one power-law to another for the threshold values of disease transmission probability. Our results are relevant for the understanding of the role of network topology in information spread processes.Comment: 12 figure

Gaugino production in proton-proton collisions at a center-of-mass energy of 8 TeV

Motivated by hints for a light Standard Model-like Higgs boson and a shift in experimental attention towards electroweak supersymmetry particle production at the CERN LHC, we update in this paper our precision predictions at next-to-leading order of perturbative QCD matched to resummation at the next-to-leading logarithmic accuracy for direct gaugino pair production in proton-proton collisions with a center-of-mass energy of 8 TeV. Tables of total cross sections are presented together with the corresponding scale and parton density uncertainties for benchmark points adopted recently by the experimental collaborations, and figures are presented for up-to-date model lines attached to them. Since the experimental analyses are currently obtained with parton showers matched to multi-parton matrix elements, we also analyze the precision of this procedure by comparing invariant-mass and transverse-momentum distributions obtained in this way to those obtained with threshold and transverse-momentum resummation.Comment: 28 pages, 7 figures, 9 tables; version to appear in JHE