Automorphisms of a rooted tree of countably infinite valency

Automorphisms of a rooted tree of infinite countable valency are studied. Two families of subgroups associated with growths of functions are introduced. This gives a classification of large sublattices of subgroups. Bibliography: 7 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 343, 2007, pp. 199–205.     

On algebras with unique essentiallyn-ary operations

In this paper we characterize the class of algebras with one fundamental operation having for every nonnegative integern exactly one essentiallyn-ary polynomial.Presented by Joel Berman.     

The Length-scale Effect in the Buckling of Thin Periodic Plates Resting on a Periodic Winkler Foundation

In this paper a new modelling method, called the tolerance averaging method, is presented and applied to analyse a buckling of thin periodic plates resting on a periodically heterogeneous Winkler foundation. The derived length-scale model makes it possible to take into account the effect of periodicity cell size (the length-scale effect) on the overall plate behaviour, on the contrary to the known homogenised models of periodic plates neglecting this effect. In order to evaluate obtained results the buckling problems of those plates are analysed using not only the proposed model but also a certain effective stiffnesses model. A comparison between obtained results leads to a conclusion that the length-scale effect could not be neglected in buckling of periodic plates resting on a Winkler foundation.     

Thermodynamical evaluation of usefulness of future hydrocarbon fuels for use in compression ignition engines

The paper discusses the issues of the influence of the fuel spray formation on the generation of self-ignition spots and the development of pre-flame processes in the cylinder of a model diesel engine. The investigations were carried out for a standard diesel fuel and two other types of fuel that were mixtures of ethanol, butanol, and diethylether in a variety of proportions. By applying optical methods of analysis, the authors determined the geometrical indexes of the injected fuel spray as well as fuel mass distribution in the longitudinal and transverse cross section of the fuel spray during the injection process. The location and number of the self-ignition spots in the combustion chamber were evaluated on the basis of a comparison under various conditions: in presence of the charge swirl and at the lack of it. Research conducted for the single-cylinder engine confirmed the possibility of the use of diesel-like fuels for compression ignition engines.

     

In Metric-measure Spaces Sobolev Embedding is Equivalent to a Lower Bound for the Measure

We study Sobolev inequalities on doubling metric measure spaces. We investigate the relation between Sobolev embeddings and lower bound for measure. In particular, we prove that if the Sobolev inequality holds, then the measure μ satisfies the lower bound, i.e. there exists b such that μ(B(x,r))≥b r ^α for r∈(0,1] and any point x from metric space.     

Automorphisms of the mapping class group of a nonorientable surface

Let \(\mathcal {X}_S\) denote the class of spaces homeomorphic to two closed orientable surfaces of genus greater than one identified to each other along an essential simple closed curve in each surface. Let \(\mathcal {C}_S\) denote the set of fundamental groups of spaces in \(\mathcal {X}_S\). In this paper, we characterize the abstract commensurability classes within \(\mathcal {C}_S\) in terms of the ratio of the Euler characteristic of the surfaces identified and the topological type of the curves identified. We prove that all groups in \(\mathcal {C}_S\) are quasi-isometric by exhibiting a bilipschitz map between the universal covers of two spaces in \(\mathcal {X}_S\). In particular, we prove that the universal covers of any two such spaces may be realized as isomorphic cell complexes with finitely many isometry types of hyperbolic polygons as cells. We analyze the abstract commensurability classes within \(\mathcal {C}_S\): we characterize which classes contain a maximal element within \(\mathcal {C}_S\); we prove each abstract commensurability class contains a right-angled Coxeter group; and, we construct a common CAT(0) cubical model geometry for each abstract commensurability class.     

The Matsumoto–Yor Property and Its Converse on Symmetric Cones

The Matsumoto–Yor (MY) property of the generalized inverse Gaussian and gamma distributions has many generalizations. As was observed in Letac and Weso?owski (Ann Probab 28:1371–1383, 2000), the natural framework for the multivariate MY property is symmetric cones; however, they prove their results for the cone of symmetric positive definite real matrices only. In this paper, we prove the converse to the symmetric cone-variate MY property, which extends some earlier results. The smoothness assumption for the densities of respective variables is reduced to continuity only. This enhancement was possible due to the new solution of a related functional equation for real functions defined on symmetric cones.     

Diffusion-Mediated Transport¶and the Flashing Ratchet

Diffusion-mediated transport is a phenomenon in which a unidirectional motion of particles is achieved as a result of two opposing tendencies: diffusion, which spreads the particles uniformly through the medium and transport, which concentrates the particles at some special sites. The flashing-ratchet version of the Brownian motor, a simple model for protein motors, where the switching between transport and diffusion is periodic, illustrates diffusion-mediated transport. In this paper we show rigorously that the flashing ratchet can be tuned in such a way that the transport of mass against the gradient of the potential takes place and the concentration of mass during the transport phase occurs at sites located at the wells of an asymmetric potential. This goal is accomplished by comparing the flashing ratchet with an approximating Markov chain. A principle achievement of this work is to establish the connection between the dynamics of the ratchet and the Markov chain in the weak^* topology.