Modal theory for the two-frequency mutual coherence function in random media: general theory and plane wave solution: I

In this paper, the modal expansion theory is presented as a new analytical approach together with the resulting new physical parameters. In particular, the features of an arbitrary power-law structure function are investigated. The exact expression for the Gaussian spectrum is rederived. An approximate analytical expression for the two-frequency coherence function evaluated at equal positions for the Kolmogorov spectrum is presented and comparison with the numerical solution in the literature exhibits a remarkable agreement. As a result of the modal decomposition, general properties for a transversally homogeneous and isotropic medium are demonstrated, such as the exponential decay of the amplitude of the solution and the linear phase behaviour at large propagation distances.     

2-Methiopropamine, a thiophene analogue of methamphetamine: studies on its metabolism and detectability in the rat and human using GC-MS and LC-(HR)-MS techniques

2-Methiopropamine [1-(thiophen-2-yl)-2-methylaminopropane, 2-MPA], a thiophene analogue of methamphetamine, is available from online vendors selling “research chemicals.” The first samples were seized by the German police in 2011. As it is a recreational stimulant, its inclusion in routine drug screening protocols should be required. The aims of this study were to identify the phase I and II metabolites of 2-MPA in rat and human urine and to identify the human cytochrome-P450 (CYP) isoenzymes involved in its phase I metabolism. In addition, the detectability of 2-MPA in urine samples using the authors’ well-established gas chromatography–mass spectrometry (GC-MS) and liquid chromatography-linear ion trap-mass spectrometry (LC-MSⁿ) screening protocols was also evaluated. The metabolites were isolated from rat and human urine samples by solid-phase extraction without or following enzymatic cleavage of conjugates. The phase I metabolites, following acetylation, were separated and identified by GC-MS and/or liquid chromatography–high-resolution linear ion trap mass spectrometry (LC-HR-MSⁿ) and the phase II metabolites by LC-HR-MSⁿ. The following major metabolic pathways were proposed: N-demethylation, hydroxylation at the side chain and at the thiophene ring, and combination of these transformations followed by glucuronidation and/or sulfation. CYP1A2, CYP2C19, CYP2D6, and CYP3A4 were identified as the major phase I metabolizing enzymes. They were also involved in the N-demethylation of the analogue methamphetamine and CYP2C19, CYP2D6, and CYP3A4 in its ring hydroxylation. Following the administration of a typical user’s dose, 2-MPA and its metabolites were identified in rat urine using the authors’ GC-MS and the LC-MSⁿ screening approaches. Ingestion of 2-MPA could also be detected by both protocols in an authentic human urine sample.     

Modelling Photosynthesis with ZnII‐Protoporphyrin All‐DNA G‐Quadruplex/Aptamer Scaffolds

All‐DNA scaffolds act as templates for the organization of photosystem I model systems. A series of DNA templates composed of Zn^II‐protoporphyrin IX (Zn^IIPPIX)‐functionalized G‐quadruplex conjugated to the 3′‐ or 5′‐end of the tyrosinamide (TA) aptamer and Zn^IIPPIX/G‐quadruplex linked to the 3′‐ and 5′‐ends of the TA aptamer through a four‐thymidine bridge. Effective photoinduced electron transfer (ET) from Zn^IIPPIX/G‐quadruplex to bipyridinium‐functionalized tyrosinamide, TA‐MV²⁺, bound to the TA aptamer units is demonstrated. The effectiveness of the primary ET quenching of Zn^IIPPIX/G‐quadruplex by TA‐MV²⁺ controls the efficiency of the generation of TA‐MV^+.. The photosystem‐controlled formation of TA‐MV^+. by the different photosystems dictates the secondary activation of the ET cascade corresponding to the ferredoxin‐NADP⁺ reductase (FNR)‐catalysed reduction of NADP⁺ to NADPH by TA‐MV^+., and the sequestered alcohol dehydrogenase catalysed reduction of acetophenone to 1‐phenylethanol by NADPH.     

Approachability in infinite dimensional spaces

The approachability theorem of Blackwell (1956b) is extended to infinite dimensional spaces. Two players play a sequential game whose payoffs are random variables. A set C of random variables is said to be approachable by player 1 if he has a strategy that ensures that the difference between the average payoff and its closest point in C, almost surely converges to zero. Necessary conditions for a set to be approachable are presented. Received February 2002/Final version July 2002  I acknowledge Eilon Solan for his helpful comments. The author acknowledges the support of the Israel Science Foundation, grant no. 178/99.     

Pulsed beam reflection and transmission at a planar interface: exact solutions and local models

Pulsed beams (PB) are collimated space-time wavepackets that propagate along ray trajectories. Because they are localized in spacetime, they are useful in modeling applications addressing highly focused energy transfer, local (high resolution) probing of the propagation environment, etc. An important class of PB are the complex source PB (CSPB) which are modeled mathematically by a pulsed source located at a complex coordinate point. Their properties, physical realization and application have been explored extensively in recent years. A whole new class of wavepacket scattering problems can therefore be modeled by substituting complex source coordinates into the time-dependent Green's function of the environment. The response to the PB input can be evaluated exactly via the previously introduced spectral theory of transients (STT). This procedure is applied here for the canonical problem of a PB scattering at a planar interface separating two homogeneous half spaces. Exact field solutions are derived in closed form via the STT while extension to more general interface configurations is addressed by deriving approximate scattering models that depend on the local properties of the interrogation wavepacket and of the interface. Depending on the PB angle, these models involve PB reflection and refraction, evanescent wavepackets and local excitation of a head-wavepacket. Via numerical examples and parametrical studies, we emphasize both the physical phenomena and the new mathematical procedures of the full 3D solution.     

Allocation processes in cooperative games

This paper deals with a temporal aspect of cooperative games. A solution of the game is reached through an allocation process. At each stage of the allocation process of a cooperative game a budget of fixed size is distributed among the players. In the first part of this paper we study a type of process that, at any stage, endows the budget to a player whose contribution to the total welfare, according to some measurements, is maximal. It is shown that the empirical distribution of the budget induced by each process of the family converges to a least square value of the game, one such value being the Shapley value. Other allocation processes presented here converge to the core or to the least core. Received: January 2001/Revised: July 2002 I am grateful to the Associate Editor and to the two anonymous referees of International Journal of Game Theory. This research was partially supported by the Israel Science Foundation, grant no. 178/99     

Apparent stoichiometry of water in proton hydration and proton dehydration reactions in CH3CN/H2O solutions

Gradual solvation of protons by water is observed in liquids by mixing strong mineral acids with various amounts of water in acetonitrile solutions, a process which promotes rapid dissociation of the acids in these solutions. The stoichiometry of the reaction XH(+) + n(H(2)O) = X + (H(2)O)(n)H(+) was studied for strong mineral acids (negatively charged X, X = ClO(4)ˉ, Clˉ, Brˉ, Iˉ, CF(3)SO(3)ˉ) and for strong cationic acids (uncharged X, X = R*NH(2), H(2)O). We have found by direct quantitative analysis preference of n = 2 over n = 1 for both groups of proton transfer reactions at relatively low water concentrations in acetonitrile. At high water concentrations, we have found that larger water solvates must also be involved in the solvation of the proton while the spectral features already observed for n = 2, H(+)(H(2)O)(2), remain almost unchanged at large n values up to at least 10 M of water.