NMR Detection of Phase Transition in a ZSM-5 Silicalite Caused by the Adsorbed Hexane and Decane Molecules

Times of longitudinal T _1b and transverse T _2b magnetic relaxation of hexane and decane molecules in micropores of ZSM-5 silicalite were measured as functions of the content of these liquid n-alkanes in zeolite and of temperature. The stepwise changes in the T _1b and T _2b times were revealed in the region of 8% content of hydrocarbons. The observed changes in the concentration and temperature dependences of T _1b and T _2b times are explained by the rearrangement of silicalite crystal lattice under the action of adsorbed molecules.     

Linear Independence of q-Analogues of Certain Classical Constants

Let K be ? or an imaginary quadratic number field, and q ∈ K an integer with ¦q¦ > 1. We give a quantitative version of Σ_n≥1 a_n/(qⁿ ? 1) ? K for non-zero periodic sequences (a_n) in K of period length ≤ 2. As a corollary, we get a quantitative version of the linear independence over K of 1, the q-harmonic series, and a q-analogue of log 2. A similar result on 1, the q-harmonic series, and a q-analogue of ζ(2) is also proved. Mathematics Subject Classification (2000): 11J72, 11J82     

Strangeness saturation: Dependence on system-size, centrality and energy

The dependence of the strangeness saturation factor on the system size, centrality and energy is studied in relativistic heavy-ion collisions.     

Stress relaxation and viscosity of a bulk Pd<Subscript>40</Subscript>Cu<Subscript>30</Subscript>Ni<Subscript>10</Subscript>P<Subscript>20</Subscript> metallic glass under isochronous heating conditions

Isochronous relaxation of tensile stresses is measured in a bulk Pd₄₀Cu₃₀Ni₁₀P₂₀ metallic glass in the initial state and after certain thermal treatments. The results of measurements are used to find the energy spectrum of irreversible structural relaxation, from which the temperature dependence of shear viscosity is then calculated. This dependence is also found independently from measurements of creep in the same glass. The calculated viscosity is shown to agree well with the experimental data.     

Piecewise Deterministic Markov Control Processes with Feedback Controls and Unbounded Costs

The control of piecewise-deterministic processes is studied where only local boundedness of the data is assumed. Moreover the discount rate may be zero. The value function is shown to be solution to the Bellman equation in a weak sense; however the solution concept is strong enough to generate optimal policies. Continuity and compactness conditions are given for the existence of nonrelaxed optimal feedback controls.