Asymptotic Behavior of Factorization and Projection Constants

This paper is concerned with estimates of important factorization constants that appear in Banach space theory. We prove upper bounds of the Hilbertian norm of projections on finite-dimensional spaces of interpolation spaces generated by certain abstract interpolation functors and show applications to Calderón–Lozanovskii spaces. We also prove estimates of the p-factorization norm and projection constants for finite-dimensional Banach lattices. We show as a consequence of our results that in a large class of n-dimensional Banach sequence lattices \(E_n\) the projection constants \(\lambda (E_n)\) satisfy \(\lim _{n\rightarrow \infty }\lambda (E_n)/\sqrt{n} = c\), where \(c=\sqrt{2/\pi }\) in the real case and \(c= \sqrt{\pi }/2\) in the complex case. Applications are given to vector-valued sequence spaces.     

Thermal evolution of ladder-like silsesquioxanes during formation of black glasses

Heat capacity of single-crystal samples of five chalcogenides (LiInS₂, LiInSe₂, LiGaS₂, LiGaSe₂, and LiGaTe₂) was measured with DSC in a temperature range from 180 to 460 K. The data for LiInS₂ and LiInSe₂ were compared with the literature data and shown to agree with the results of adiabatic calorimetry (Gmelin and Hönle in Thermochimica Acta 269: 575–590, 1995) better than with other DSC data (Kühn et al. in Cryst Res Technol 22: 265–269, 1987). Besides, the high-temperature fitting polynomial for C _P(T) published about 30 years ago for LiInS₂ is wrong. LiGaS₂, LiGaSe₂, and LiGaTe₂ were measured for the first time.     

Improved lower bounds for the online bin stretching problem

We use game theory techniques to automatically compute improved lower bounds on the competitive ratio for the bin stretching problem. Using these techniques, we improve the best lower bound for this problem to 19/14. We explain the technique and show that it can be generalized to compute lower bounds for any online or semi-online packing or scheduling problem.     

Analysis of an elasto-piezoelectric system of hemivariational inequalities with thermal effects

In this paper we prove the existence and uniqueness of a weak solution for a dynamic electo-viscoelastic problem that describes a contact between a body and a foundation. We assume the body is made from thermoviscoelastic material and consider nonmonotone boundary conditions for the contact. We use recent results from the theory of hemivariational inequalities and the fixed point theory.     

Lévy-driven GPS queues with heavy-tailed input

In this paper, we derive exact large buffer asymptotics for a two-class generalized processor sharing (GPS) model, under the assumption that the input traffic streams generated by both classes correspond to heavy-tailed Lévy processes. Four scenarios need to be distinguished, which differ in terms of (i) the level of heavy-tailedness of the driving Lévy processes as well as (ii) the values of the corresponding mean rates relative to the GPS weights. The derived results are illustrated by two important special cases, in which the queues’ inputs are modeled by heavy-tailed compound Poisson processes and by \(\alpha \)-stable Lévy motions.     

On stationary Markov processes with polynomial conditional moments

We study a class of stationary Markov processes with marginal distributions identifiable by moments such that every conditional moment of degree say m is a polynomial of degree at most m. We show that then under some additional, natural technical assumption there exists a family of orthogonal polynomial martingales. More precisely we show that such a family of processes is completely characterized by the sequence {(α_n, p_n)}_{n ? 0} where α′_ns are some positive reals while p′_ns are some monic orthogonal polynomials. Bakry and Mazet (Séminaire de Probabilit?s, vol. 37, 2003) showed that under some additional mild technical conditions each such sequence generates some stationary Markov process with polynomial regression.

We single out two important subclasses of the considered class of Markov processes. The class of harnesses that we characterize completely. The second one constitutes of the processes that have independent regression property and are stationary. Processes with independent regression property so to say generalize ordinary Ornstein–Uhlenbeck (OU) processes or can also be understood as time scale transformations of Lévy processes. We list several properties of these processes. In particular we show that if these process are time scale transforms of Lévy processes then they are not stationary unless we deal with classical OU process. Conversely, time scale transformations of stationary processes with independent regression property are not Lévy unless we deal with classical OU process.     

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.