Convergence of Distributed Optimal Controls on the Internal Energy in Mixed Elliptic Problems when the Heat Transfer Coefficient Goes to Infinity

We consider a steady-state heat conduction problem P _α with mixed boundary conditions for the Poisson equation depending on a positive parameter α , which represents the heat transfer coefficient on a portion Γ ₁ of the boundary of a given bounded domain in R ⁿ . We formulate distributed optimal control problems over the internal energy g for each α . We prove that the optimal control g_ op _α and its corresponding system u_ g_ op _α α and adjoint p_ g_ op _α α states for each α are strongly convergent to g _op , u_ g _op and p _ g _op , respectively, in adequate functional spaces. We also prove that these limit functions are respectively the optimal control, and the system and adjoint states corresponding to another distributed optimal control problem for the same Poisson equation with a different boundary condition on the portion Γ ₁ . We use the fixed point and elliptic variational inequality theories.     

Solid‐State NMR investigations of anhydrous proton‐conducting acid–base poly(acrylic acid)– poly(4‐vinyl pyridine) polymer blend system: A study of hydrogen bonding and proton conduction

NMR studies of the structure and dynamics of a system composed of the acidic polymer poly(acrylic acid) (PAA) and the basic polymer poly(4‐vinyl pyridine) (P4VP) are presented. This system aims at the application of anhydrous proton‐conducting membranes that can be used at elevated temperatures at which the proton conduction of hydrated membranes breaks down. The ¹H NMR measurements have been preformed under fast magic angle spinning (MAS) conditions to achieve sufficient resolution and the applied ¹H NMR methods vary from simple ¹H MAS to double‐quantum filtered methods and two‐dimensional ¹H double‐quantum spectroscopy. The dynamic behavior of the systems has been investigated via variable temperature ¹H MAS NMR. ¹³C cross‐polarization MAS NMR provides additional aspects of dynamic and structural features to complete the picture. Different types of acidic protons have been identified in the studied PAA‐P4VP systems that are nonhydrogen‐bonded free acidic protons, hydrogen‐bonded dicarboxylic dimers, and protons forming hydrogen bonds between carboxylic protons and ring nitrogens. The conversion of dimer structures in dried PAA to free carboxylic acid groups is accomplished at temperatures above 380 K. However, the stability of hydrogen‐bonding strongly depends on the hydration level of the polymer systems. The effect of hydration becomes less apparent in the complexes. An inverse proportionality between hydrogen‐bonding strength and proton conduction in the PAA‐P4VP acid–base polymer blend systems was established. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 138–155, 2009     

Formulation of a holistic model for the kinetics of steady state growth of porous anodic alumina films

A holistic model for the kinetics of steady state growth of porous anodic alumina films in oxalic acid, H₂C₂O₄, solution was developed not necessarily requiring the adoption of any ‘a priori’ mechanism of porous film growth. By this model the effect of anodising conditions on the transport numbers of Al³⁺ cations and O²⁻ anions across the barrier layer was revealed. The cation (anion) transport number decreased (increased) with current density, increased (decreased) with temperature and was unaffected by the concentration of electrolyte or pH. A complementary atomistic-ionic kinetic model was developed that fully justified these results and showed that the activation distances of Al³⁺ and O²⁻ transport are comparable, but the activation energy of Al³⁺ transport is lower mainly due to the much smaller size of Al³⁺. The validity of the model was tested on the basis of SEM observations, while structural features and the rate of pore wall dissolution were determined.     

MJ and collision energy dependent attenuation of Rg (3P2) by CF3Br

The total attenuation cross-section of Rg (³P₂) (Rg = Ar, Kr) by the collision with CF₃Br is measured as a function of the magnetic sub level M_J of Rg (³P₂) and the collision energy. For Ar (³P₂), the attenuation process indicates a M_J dependence, in particular, the cross-section of the M_J = 0 state is lower compared with that for other states. On the other hand, Kr (³P₂) shows no M_J dependent attenuation.     

S为1/2体系粉末或冷冻玻璃态电子自旋共振谱的模拟

本文较详细地介绍了模拟s为1/2体系粉末或冷冻玻璃态电子自旋共振谱的理论基础。给出了具体计算公式,利用这些公式完全可以在微机上进行计算机模拟电子自旋共振谱。     

Bound states of a system of two fermions on a one-dimensional lattice

We consider the Hamiltonian of a system of two fermions on a one-dimensional integer lattice. We prove that the number of bound states N(k) is a nondecreasing function of the total quasimomentum of the system k ∈ [0, π]. We describe the set of discontinuity points of N(k) and evaluate the jump N(k +0) − N(k) at the discontinuity points. We establish that the bound-state energy z _n (k) increases as the total quasimomentum k ∈ [0, π] increases. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 1, pp. 47–57, April, 2006.     

On the optimality equation for average cost Markov control processes with Feller transition probabilities

We consider Markov control processes with Borel state space and Feller transition probabilities, satisfying some generalized geometric ergodicity conditions. We provide a new theorem on the existence of a solution to the average cost optimality equation.