Thermal and mechanical properties of chitosan nanocomposites with cellulose modified in ionic liquids

In this paper, ionic liquid treatment was applied to produce nanometric cellulose particles of two polymorphic forms. A complex characterization of nanofillers including wide-angle X-ray scattering, Fourier transform infrared spectroscopy, and particle size determination was performed. The evaluated ionic liquid treatment was effective in terms of nanocrystalline cellulose production, leaving chemical and supermolecular structure of the materials intact. However, nanocrystalline cellulose II was found to be more prone to ionic liquid hydrolysis leading to formation larger amount of small particles. Each nanocrystalline cellulose was subsequently mixed with a solution of chitosan, so that composite films containing 1, 3, and 5% mass/mass of nanometric filler were obtained. Reference samples of chitosan and chitosan with micrometric celluloses were also solvent casted. Thermal, mechanical, and morphological properties of films were tested and correlated with properties of filler used. The results of both, tensile tests and thermogravimetric analysis showed a significant discrepancy between composites filled with nanocrystalline cellulose I and nanocrystalline cellulose II.     

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.     

New characterizations of the Takagi function via functional equations

We provide two new characterizations of the Takagi function as the unique bounded solution of some systems of two functional equations. The results are independent of those obtained by Kairies (Wy? Szko? Ped Krakow Rocznik Nauk Dydakt Prace Mat 196:73–82, 1998), Kairies (Aequ Math 53:207–241, 1997), Kairies (Aequ Math 58:183–191, 1999) and Kairies et al. (Rad Mat 4:361–374, 1989; Errata, Rad Mat 5:179–180, 1989).     

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.     

SDEs with constraints driven by semimartingales and processes with bounded p-variation

We study the existence, uniqueness and stability of solutions of general stochastic differential equations with constraints driven by semimartingales and processes with bounded $p$-variation. Applications to SDEs with constraints driven by fractional Brownian motion and standard Brownian motion are given.     

The 1‐2‐3‐Conjecture for Hypergraphs

A weighting of the edges of a hypergraph is called vertex‐coloring if the weighted degrees of the vertices yield a proper coloring of the graph, i.e. every edge contains at least two vertices with different weighted degrees. In this article, we show that such a weighting is possible from the weight set for all hypergraphs with maximum edge size and not containing edges solely consisting of identical vertices. The number is best possible for this statement.     

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.