Correlated Markov Quantum Walks

We consider the discrete time unitary dynamics given by a quantum walk on ${\mathbb {Z}^d}$ performed by a particle with internal degree of freedom, called coin state, according to the following iterated rule: a unitary update of the coin state takes place, followed by a shift on the lattice, conditioned on the coin state of the particle. We study the large time behavior of the quantum mechanical probability distribution of the position observable in ${\mathbb {Z}^d}$ for random updates of the coin states of the following form. The random sequences of unitary updates are given by a site-dependent function of a Markov chain in time, with the following properties: on each site, they share the same stationary Markovian distribution and, for each fixed time, they form a deterministic periodic pattern on the lattice. We prove a Feynman–Kac formula to express the characteristic function of the averaged distribution over the randomness at time n in terms of the nth power of an operator M. By analyzing the spectrum of M, we show that this distribution possesses a drift proportional to the time and its centered counterpart displays a diffusive behavior with a diffusion matrix we compute. Moderate and large deviation principles are also proven to hold for the averaged distribution and the limit of the suitably rescaled corresponding characteristic function is shown to satisfy a diffusion equation. An example of random updates for which the analysis of the distribution can be performed without averaging is worked out. The random distribution displays a deterministic drift proportional to time and its centered counterpart gives rise to a random diffusion matrix, the law of which we compute. We complete the picture by presenting an uncorrelated example.     

Geological and radioactivity studies accompanied by uranium recovery: Um Bogma Formation,southwestern Sinai,Egypt

Journal of Radioanalytical and Nuclear Chemistry - High radioactive anomalies were recorded in the variegated claystones at the middle member of Um Bogma Formation, the eU-content reaches...     

Heat pipes: progress in thermal performance enhancement for microelectronics

Journal of Thermal Analysis and Calorimetry - The aim of this study is to oversee the impact of various techniques on thermal performance of heat pipes and to comprehensively cover the progress...     

Operational rules and a generalized Hermite polynomials

In this paper, we use operational rules associated with three operators corresponding to a generalized Hermite polynomials introduced by Szegö to derive, as far as we know, new proofs of some known properties as well as new expansions formulae related to these polynomials.     

Equilibrium and kinetic studies on the reactions of alkylcobalamins with cyanide

Ligand substitution equilibria of different alkylcobalamins (RCbl, R = Me, CH(2)Br, CH(2)CF(3), CHF(2), CF(3)) with cyanide have been studied. It was found that CN(-) first substitutes the 5,6-dimethylbenzimidazole (Bzm) moiety in the alpha-position, followed by substitution of the alkyl group in the beta-position trans to Bzm. The formation constants K(CN) for the 1:1 cyanide adducts (R(CN)Cbl) were found to be 0.38 +/- 0.03, 0.43 +/- 0.03, and 123 +/- 9 M(-1) for R = Me, CH(2)Br, and CF(3), respectively. In the case of R = CH(2)CF(3), the 1:1 adduct decomposes in the dark with CN(-) to give (CN)(2)Cbl. The unfavorable formation constants for R = Me and CH(2)Br indicate the requirement of very high cyanide concentrations to produce the 1:1 complex, which cause the kinetics of the displacement of Bzm to be too fast to follow kinetically. The kinetics of the displacement of Bzm by CN(-) could be followed for R = CH(2)CF(3) and CF(3) to form CF(3)CH(2)(CN)Cbl and CF(3)(CN)Cbl, respectively, in the rate-determining step. Both reactions show saturation kinetics at high cyanide concentration, and the limiting rate constants are characterized by the activation parameters: R = CH(2)CF(3), DeltaH = 71 +/- 1 kJ mol(-1), DeltaS = -25 +/- 4 J K(-1) mol(-1), and DeltaV = +8.9 +/- 1.0 cm(3) mol(-1); R = CF(3), DeltaH = 77 +/- 3 kJ mol(-1), DeltaS = +44 +/- 11 J K(-1) mol(-1), and DeltaV = +14.8 +/- 0.8 cm(3) mol(-1), respectively. These parameters are interpreted in terms of an I(d) and D mechanism for R = CH(2)CF(3) and CF(3), respectively. The results of the study enable the formulation of a general mechanism that can account for the substitution behavior of all investigated alkylcobalamins including coenzyme B(12).     

Measurement of deuterium in water by the falling drop method

Summary The falling drop method for the isotopic analysis of water sample is fully described. The optimum parameters of the ultra thermostat, the micropipet, the drop size, and the dropping medium for maximum accuracy are discussed. The o-fluorotoluene used should be of the highest purity elsewhere non-reproducible results are obtained. The accuracy obtained is 0.001% up to 0.096 mole% D₂O and 0.01% up to 0.994 mole% D₂O, although the relative accuracy is the same ±1.4% through the whole calibration curve and is comparable with that of mass spectrometry.

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Bestimmung von Deuterium in Wasser mit Hilfe der Methode des fallenden Tropfens

Zusammenfassung Das Verfahren wird beschrieben und die optimalen Arbeitsbedingungen diskutiert. Das als Medium verwendete o-Fluortoluol muß von höchster Reinheit sein, da sonst keine reproduzierbaren Ergebnisse erhalten werden. Die Genauigkeit beträgt 0,001%–0,096 Mol-% D₂O und 0,01%–0,994 Mol-% D₂O. Die relative Genauigkeit, die im gesamten Bereich ±1,4% beträgt, ist mit der von massenspektrometrischen Bestimmungen vergleichbar.

     

Atomic decomposition of identity: General formalism for population analysis and energy decomposition

The concept of “atomic resolution of identity” has been introduced, leading to a very simple general formalism for generating different decomposition schemes of molecular quantities. Thus, different population analysis and energy partitioning schemes can be treated as special cases of a common framework. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

The mixing advantage is less than 2

Corresponding to n independent non-negative random variables X ₁,...,X _n , are values M ₁,...,M _n , where each M _i is the expected value of the maximum of n independent copies of X _i . We obtain an upper bound for the expected value of the maximum of X ₁,...,X _n in terms of M ₁,...,M _n . This inequality is sharp in the sense that the random variables can be chosen so that the bound is approached arbitrarily closely. We also present related comparison results.      

One-pot combination of the Wittig olefination with oxidation, hydrogenation, bromination, and photocyclization reactions

Co-polycondensation of tetramethoxysilane, 2-diphenyl(phosphino)ethyltri(ethoxy)silane, and N-2-(aminoethyl)-3-aminopropyltri(methoxy)silane forms a heterogenized tertiary phosphine reagent (HPR) that reacts with benzyl chlorides and aldehydes to give alkenes. This Wittig condensation can be coupled, as a one-pot process, with hydrogenation, oxidation, bromination or photocyclization.