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.     

Minimal Projections onto Subspaces with Codimension 2

In this article, the relationship between absolute projection constants with dimension n and with codimension n is given. In particular, bounds from below are found for absolute projection constants with codimension 2. Also, exact formulas for minimal projections in this case are given. It is shown that these minimal projections are not unique.     

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.     

Relations Between Relaxation Modulus and Creep Compliance in Anisotropic Linear Viscoelasticity

The results obtained previously for scalar and class P completely monotone relaxation moduli are extended to arbitrary anisotropy. It is shown for general anisotropic viscoelastic media that, if the relaxation modulus is a locally integrable completely monotone function, then the creep compliance is a Bernstein function and conversely. The elastic and equilibrium limits of the two material functions are related to each other. The relaxation modulus or its derivative can be singular at 0. A rigorous general formulation of the relaxation spectrum in an anisotropic viscoelastic medium is given. The effect of Newtonian viscosity on creep compliance is examined. Put some makeup on him and lay him to rest. Anonymous     

Non-linear Heat and Mass Transfer During Convective Drying of Kaolin Cylinder Under Non-steady Conditions

The self-consistent model of heat and mass transfer during convective drying of capillary porous media describing both the first and the second periods of drying is presented in Musielak (Wydawnictwo Politechniki Poznańskiej, seria Rozprawy, nr 386 (2004a); Chem. Process Eng. 25, 393–409 (2004b)). The results of simulations of processes in steady conditions are shown (Musielak Wydawnictwo Politechniki Poznańskiej, seria Rozprawy, nr 386 (2004a); Chem. Process Eng. 25, 393–409 (2004b)). The main aim of the present work is to compare experimental results with those from numerical simulations. Three convective drying processes have been performed experimentally. The first and the second periods of drying are considered, during which the humidity of air in the dryer changes due to evaporation. The first process is used to establish drying parameters, whereafter the two remaining processes are simulated. Good agreement between experimental and simulation results is found, both qualitative and quantitative.     

On-line measurements of the rheological properties of fermentation broth

The paper is concerned with measurements of rheological properties of fermentation broth. An on-line rheometer, Rheohelix-1, based on the application of a helical screw impeller rotating in a draught tube has been constructed. The instrument was used for measurements of the rheological parameters of fermentation broth of Aspergillus niger in a submerged fermentation process. The results of rheological and some standard measurements have been compared and proved the applicability of the instrument.Presented at the Golden Jubilee Conference of the British Society of Rheology and Third European Rheology Conference, Edinburgh, 3–7 September, 1990.     

A Unified Approach to Dynamic Contact Problems in Viscoelasticity

In this paper we consider mathematical models describing dynamic viscoelastic contact problems with the Kelvin–Voigt constitutive law and subdifferential boundary conditions. We treat evolution hemivariational inequalities which are weak formulations of contact problems. We establish the existence of solutions to hemivariational inequalities with different types of non-monotone multivalued boundary relations. These results are consequences of an existence theorem for second order evolution inclusions. In a particular case we deliver sufficient conditions under which the solution to a hemivariational inequality is unique. Finally, applications to several unilateral and bilateral problems in contact mechanics are provided.*Research supported in part by the State Committee for Scientific Research of the Republic of Poland (KBN) under Grants no. 2 P03A 003 25 and 4 T07A 027 26.