Dynamic mechanism of photochemical induction of turing superlattices in the chlorine dioxide-iodine-malonic acid reaction-diffusion system

We study the mechanism of development of superlattice Turing structures from photochemically generated hexagonal patterns of spots with wavelengths several times larger than the characteristic wavelength of the Turing patterns that spontaneously develop in the nonilluminated system. Comparison of the experiment with numerical simulations shows that interaction of the photochemical periodic forcing with the Turing instability results in generation of multiple resonant triplets of wave vectors, which are harmonics of the external forcing. Some of these harmonics are situated within the Turing instability band and are therefore able to maintain their amplitude as the system evolves and after illumination ceases, while photochemically generated harmonics outside the Turing band tend to decay.     

Bifunctional activation of amine-boranes by the W/Pd bimetallic analogs of “frustrated Lewis pairs”

The reaction between basic [(PCP)Pd(H)] (PCP = 2,6-(CH₂P(t-C₄H₉)₂)₂C₆H₄) and acidic [LWH(CO)₃] (L = Cp (1a), Tp (1b); Cp = η⁵-cyclopentadienyl, Tp = κ³-hydridotris(pyrazolyl)borate) leads to the formation of bimolecular complexes [LW(CO)₂(μ-CO)⋯Pd(PCP)] (4a, 4b), which catalyze amine-borane (Me₂NHBH₃, ^tBuNH₂BH₃) dehydrogenation. The combination of variable-temperature (¹H, ³¹P{¹H}, ¹¹B NMR and IR) spectroscopies and computational (ωB97XD/def2-TZVP) studies reveal the formation of an η¹-borane complex [(PCP)Pd(Me₂NHBH₃)]⁺[LW(CO₃)]⁻ (5) in the first step, where a BH bond strongly binds palladium and an amine group is hydrogen-bonded to tungsten. The subsequent intracomplex proton transfer is the rate-determining step, followed by an almost barrierless hydride transfer. Bimetallic species 4 are easily regenerated through hydrogen evolution in the reaction between two hydrides.

Bimetallic complexes [LW(CO)₂(μ-CO)⋯Pd(PCP)] cooperatively activate amine-boranes for their dehydrogenation via N–H proton tunneling at RDS and H₂ evolution from two neutral hydrides.     

Strong Krull primes and flat modules

There are several theorems describing the intricate relationship between flatness and associated primes over commutative Noetherian rings. However, associated primes are known to act badly over non-Noetherian rings, so one needs a suitable replacement. In this paper, we show that the behavior of strong Krull primes most closely resembles that of associated primes over a Noetherian ring. We prove an analogue of a theorem of Epstein and Yao characterizing flat modules in terms of associated primes by replacing them with strong Krull primes. Also, we partly generalize a classical equational theorem regarding flat base change and associated primes in Noetherian rings. That is, when associated primes are replaced by strong Krull primes, we show containment in general and equality in many special cases. One application is of interest over any Noetherian ring of prime characteristic. We also give numerous examples to show that our results fail if other popular generalizations of associated primes are used in place of strong Krull primes.     

Conditioned Diffusions which are Brownian Bridges

Let X _t be a one-dimensional diffusion of the form dX _t=dB _t+(X _t)dt. Let Tbe a fixed positive number and let be the diffusion process which is X _t conditioned so that X ₀=X _T=x. If the drift is constant, i.e., , then the conditioned diffusion process is a Brownian bridge. In this paper, we show the converse is false. There is a two parameter family of nonlinear drifts with this property.     

Particle Decays and Stability on the de Sitter Universe

We study particle decay in de Sitter space–time as given by first-order perturbation theory in a Lagrangian interacting quantum field theory. We study in detail the adiabatic limit of the perturbative amplitude and compute the “phase space” coefficient exactly in the case of two equal particles produced in the disintegration. We show that for fields with masses above a critical mass m _c there is no such thing as particle stability, so that decays forbidden in flat space–time do occur here. The lifetime of such a particle also turns out to be independent of its velocity when that lifetime is comparable with de Sitter radius. Particles with mass lower than critical have a completely different behavior: the masses of their decay products must obey quantification rules, and their lifetime is zero.