MC elements in pronilpotent DG Lie algebras

Consider a pronilpotent DG (differential graded) Lie algebra over a field of characteristic 0. In the first part of the paper we introduce the reduced Deligne groupoid associated to this DG Lie algebra. We prove that a DG Lie quasi-isomorphism between two such algebras induces an equivalence between the corresponding reduced Deligne groupoids. This extends the famous result of Goldman–Millson (attributed to Deligne) to the unbounded pronilpotent case.In the second part of the paper we consider the Deligne 2-groupoid. We show it exists under more relaxed assumptions than known before (the DG Lie algebra is either nilpotent or of quasi quantum type). We prove that a DG Lie quasi-isomorphism between such DG Lie algebras induces a weak equivalence between the corresponding Deligne 2-groupoids.In the third part of the paper we prove that an L-infinity quasi-isomorphism between pronilpotent DG Lie algebras induces a bijection between the sets of gauge equivalence classes of Maurer–Cartan elements. This extends a result of Kontsevich and others to the pronilpotent case.     

On the efficiency of water soluble antioxidants

The wide use of high intensity ultrasound (HIU) in modern medicine raises the question of bio-safety. It has been shown that the effect of HIU in biological media may have similarity to the effects of ionizing radiation. Exposure of biological media to HIU field may lead to cavitation phenomenon followed by formation of free radicals such as hydroxyl radical (OH) and the super-oxide ion (O₂-). These are highly reactive species that may cause harmful effects and induce oxidative stress. In the present study we employed electron spin resonance (ESR) spectroscopy together with spin traps to quantify the dynamics of hydroxyl radical formation during exposure to HIU field in the presence of different amounts of six antioxidants. Thus, the efficiency of water-soluble antioxidants, namely Allicin, Melatonin, Deoxyribose, Trolox, Nuphlutine and Hermidin, to suppress accumulation of OH radicals was examined. The results show that among the six, Trolox and Allicin reduce hydroxyl concentration with the highest efficiency.     

Reply to the paper “comments on the theory of phase-conjugated waves”, by E. Wolf and W.H. Carter

The NH₄Br crystal is irradiated simultaneously with a modulated red light and a steady UV light in the region of the fundamental absorption band. The resulting recombination luminescence of electrons with V_K centers is phase-sensitively detected, and compared with the emission which is directly excited by UV light. From measurements of the excitation spectra for recombination luminescence, it is pointed out that the dissociation of free excitons occurs efficiently in NH₄Br.     

Four wave nonlinear optical mixing as real time holography

The phenomenon of four-wave optical mixing is an exact analog of the sequential operations of holographic recording and reconstruction. It should thus be possible to realize, in real time, holographic experiments and devices using such mixing.     

On residue complexes,dualizing sheaves and local cohomology modules

According to Grothendieck Duality Theory [RD], on each varietyV over a fieldk, there is a canonical complex of -modules, theresidue complex . These complexes satisfy (and are characterized by) functorial properties in the categoryV ofk-varieties. In [Ye] a complex is constructed explicitly (when the fieldk is perfect). The main result of this paper is that the two families of complexes, and , which carry certain additional data (such as trace maps…), are uniquely isomorphic. As a corollary we recover Lipman’s canonical dualizing sheaf of [Li], and we obtain formulas for residues of local cohomology classes of differential forms.     

Percolation,fractals, and anomalous diffusion

Both the infinite cluster and its backbone are self-similar at the percolation threshold,p _c . This self-similarity also holds at concentrationsp nearp _c , for length scalesL which are smaller than the percolation connectedness length,. ForL<, the number of bonds on the infinite cluster scales asL ^D , where the fractal dimensionalityD is equal to(d-/v). Geometrical fractal models, which imitate the backbone and on which physical models are exactly solvable, are presented. Above six dimensions, one has D=4 and an additional scaling length must be included. The effects of the geometrical structure of the backbone on magnetic spin correlations and on diffusion at percolation are also discussed.     

Elucidating dissociation activation energies in host–guest assemblies featuring fast exchange dynamics

The ability to mediate the kinetic properties and dissociation activation energies (E_a) of bound guests by controlling the characteristics of “supramolecular lids” in host–guest molecular systems is essential for both their design and performance. While the synthesis of such systems is well advanced, the experimental quantification of their kinetic parameters, particularly in systems experiencing fast association and dissociation dynamics, has been very difficult or impossible with the established methods at hand. Here, we demonstrate the utility of the NMR-based guest exchange saturation transfer (GEST) approach for quantifying the dissociation exchange rates (k_out) and activation energy (E_a,out) in host–guest systems featuring fast dissociation dynamics. Our assessment of the effect of different monovalent cations on the extracted E_a,out in cucurbit[7]uril:guest systems with very fast k_out highlights their role as “supramolecular lids” in mediating a guest''s dissociation E_a. We envision that GEST could be further extended to study kinetic parameters in other supramolecular systems characterized by fast kinetic properties and to design novel switchable host–guest assemblies.

GEST-NMR is utilized for quantifying the dissociation activation energy (E_a,out) in host-guest systems featuring fast dissociation dynamics.     

Nonperfect synchronization of reaction center rehybridization in the transition state of the hydride transfer catalyzed by dihydrofolate reductase

It has been suggested that the magnitudes of secondary kinetic isotope effects (2 degrees KIEs) of enzyme-catalyzed reactions are an indicator of the extent of reaction-center rehybridization at the transition state. A 2 degrees KIE value close to the corresponding secondary equilibrium isotope effects (2 degrees EIE) is conventionally interpreted as indicating a late transition state that resembles the final product. The reliability of using this criterion to infer the structure of the transition state is examined by carrying out a theoretical investigation of the hybridization states of the hydride donor and acceptor in the Escherichia coli dihydrofolate reductase (ecDHFR)-catalyzed reaction for which a 2 degrees KIE close to the 2 degrees EIE was reported. Our results show that the donor carbon at the hydride transfer transition state resembles the reactant state more than the product state, whereas the acceptor carbon is more productlike, which is a symptom of transition state imbalance. The conclusion that the isotopically substituted carbon is reactant-like disagrees with the conclusion that would have been derived from the criterion of 2 degrees KIEs and 2 degrees EIEs, but the breakdown of the correlation with the equilibrium isotope effect can be explained by considering the effect of tunneling.     

Retro [2 + 2 + 2] ring opening in tricyclobutabenzene derivatives. Thermochemistry and reaction barriers. A theoretical hybrid density functional study

The starting materials, transition states, and products of the concerted retro [2 + 2 + 2] ring-opening reactions of several tricyclobutabenzene derivatives substituted by double-bonded substituents were calculated at the B3LYP/6-31G theoretical level. It was found that the geometries of the products (cyclododecatriyne derivatives) are governed by the electronegativity of the substituents and hyperconjugation effects. The transition-state geometries of all the derivatives are similar. It was found that the retro [2 + 2 + 2] ring-opening reactions are endothermic (ca. 30-85 kcal mol(-1), depending on the substituents) with high barriers, ranging between ca. 95 and 115 kcal mol(-1). It is predicted that the tricyclobutabenzene derivatives under study will be stable when prepared and that they can be made by [2 + 2 + 2] intramolecular ring closure of the respective cyclododecatriyne derivative, especially with the use of transition metals as mediators or catalysts.