Gated polling with stationary ergodic walking times, Markovian routing and random feedback

We investigate a gated polling system with semi-linear feedback and Markovian routing. We thereby relax the classical independence assumption on the walking times; the walking times constitute a sequence of stationary ergodic random variables. It is shown that the dynamics of this polling system can be described by semi-linear stochastic recursive equations in a Markovian environment. We obtain expressions for the first and second order moments of the workload and queue content at polling instants and for the mean queue content and workload at random instants.     

Oxygen‐Atom Transfer Chemistry and Thermolytic Properties of a Di‐tert‐Butylphosphate‐Ligated Mn4O4 Cubane

[Mn₄O₄{O₂P(OtBu)₂}₆] ( 1 ), an Mn₄O₄ cubane complex combining the structural inspiration of the photosystem II oxygen‐evolving complex with thermolytic precursor ligands, was synthesized and fully characterized. Core oxygen atoms within complex 1 are transferred upon reaction with an oxygen‐atom acceptor (PEt₃), to give the butterfly complex [Mn₄O₂{O₂P(OtBu)₂}₆(OPEt₃)₂]. The cubane structure is restored by reaction of the latter complex with the O‐atom donor PhIO. Complex 1 was investigated as a precursor to inorganic Mn metaphosphate/pyrophosphate materials, which were studied by X‐ray absorption spectroscopy to determine the fate of the Mn₄O₄ unit. Under the conditions employed, thermolyses of 1 result in reduction of the manganese to Mn^II species. Finally, the related butterfly complex [Mn₄O₂{O₂P(pin)}₆(bpy)₂] (pin=pinacolate) is described.     

Sensitivity of constrained Markov decision processes

We consider the optimization of finite-state, finite-action Markov decision processes under constraints. Costs and constraints are of the discounted or average type, and possibly finite-horizon. We investigate the sensitivity of the optimal cost and optimal policy to changes in various parameters. We relate several optimization problems to a generic linear program, through which we investigate sensitivity issues. We establish conditions for the continuity of the optimal value in the discount factor. In particular, the optimal value and optimal policy for the expected average cost are obtained as limits of the dicounted case, as the discount factor goes to one. This generalizes a well-known result for the unconstrained case. We also establish the continuity in the discount factor for certain non-stationary policies. We then discuss the sensitivity of optimal policies and optimal values to small changes in the transition matrix and in the instantaneous cost functions. The importance of the last two results is related to the performance of adaptive policies for constrained MDP under various cost criteria [3,5]. Finally, we establish the convergence of the optimal value for the discounted constrained finite horizon problem to the optimal value of the corresponding infinite horizon problem.     

On complete Tchebycheff-systems

It is shown under what condition a Tchebycheff-space on a real set containing at most one end point, has a Tchebycheff subspace of codimension 1. It is also shown when a complete Tchebycheff-system on a real set M, is also a complete Tchebycheff-system on .     

Channel-length measurement technique based on a floating-gatedevice

By measuring the threshold voltage of the structure for several drawn channel lengths, ΔL is extracted. This technique is the translation of a capacitance measurement into a threshold measurement and as such is accurate and simple to perform. Since the technique does not involve a current flow through the transistor under test, it is especially advantageous for L_eff measurements on lightly-doped drain (LDD) and double-diffused drain (DDD) short-channel devices     

A comparison between different semiclassical approximations for optical response functions in nonpolar liquid solutions

The temporal behavior of optical response functions (ORFs) reflects the quantum dynamics of an electronic superposition state, and as such lacks a well-defined classical limit. In this paper, we consider the importance of accounting for the quantum nature of the dynamics when calculating ORFs of different types. To this end, we calculated the ORFs associated with the linear absorption spectrum and the nonlinear two-pulse photon-echo experiment, via the following approaches: (1) the semiclassical forward-backward approach; (2) an approach based on linearizing the path-integral forward-backward action in terms of the difference between the forward and backward paths; (3) an approach based on ground state nuclear dynamics. The calculations were performed on a model that consists of a two-state chromophore solvated in a nonpolar liquid. The different methods were found to yield very similar results for the absorption spectrum and "diagonal" two-pulse photon echo (i.e., the homodyne-detected signal at time t=t(0) after the second pulse, where t(0) is the time interval between the two pulses). The different approximations yielded somewhat different results in the case of the time-integrated photon-echo signal. The reasons for the similarity between the predictions of different approximations are also discussed.     

Vibrational energy relaxation rates via the linearized semiclassical approximation: applications to neat diatomic liquids and atomic-diatomic liquid mixtures

We report the results obtained from the application of our previously proposed linearized semiclassical method for computing vibrational energy relaxation (VER) rates (J. Phys. Chem. A 2003, 107, 9059, 9070) to neat liquid oxygen, neat liquid nitrogen, and liquid mixtures of oxygen and argon. Our calculations are based on a semiclassical approximation for the quantum-mechanical force-force correlation function, which puts it in terms of the Wigner transforms of the force and the product of the Boltzmann operator and the force. The calculation of the multidimensional Wigner integrals is made feasible by the introduction of a local harmonic approximation. A systematic analysis has been performed of the temperature and mole-fraction dependences of the VER rate constant, as well as the relative contributions of centrifugal and potential forces, and of different types of quantum effects. The results were found to be in very good quantitative agreement with experiment, and they suggest that this semiclassical approximation can capture the quantum enhancement, by many orders of magnitude, of the experimentally observed VER rate constants over the corresponding classical predictions.     

Hierarchical Construction of Bounded Solutions in Critical Regularity Spaces

We construct uniformly bounded solutions for the equations div U = f and U = f in the critical cases and , respectively. Criticality in this context manifests itself by the lack of a linear solution operator mapping . Thus, the intriguing aspect here is that although the problems are linear, construction of their solutions is not. Our constructions are special cases of a general framework for solving linear equations of the form , where is a linear operator densely defined in Banach space with a closed range in a (proper subspace) of Lebesgue space , and with an injective dual . The solutions are realized in terms of a multiscale hierarchical representation, , interesting for its own sake. Here, u _j's are constructed recursively as minimizers of where the residuals are resolved in terms of a dyadic sequence of scales with large enough . The nonlinear aspect of this construction is a counterpart of the fact that one cannot linearly solve in critical regularity spaces.© 2016 Wiley Periodicals, Inc.