A generalization of Marshall's equivalence relation

For prime and for a field containing a root of unity of order , we generalize Marshall's equivalence relation on orderings to arbitrary subgroups of of index . The equivalence classes then correspond to free pro- factors of the maximal pro- Galois group of . We generalize to this setting results of Jacob on the maximal pro- Galois group of a Pythagorean field.

     

Inhibition of Cysteine Proteases by 6,6′-Dihydroxythiobinupharidine (DTBN) from Nuphar lutea

The specificity of inhibition by 6,6′-dihydroxythiobinupharidine (DTBN) on cysteine proteases was demonstrated in this work. There were differences in the extent of inhibition, reflecting active site structural-steric and biochemical differences. Cathepsin S (IC₅₀ = 3.2 μM) was most sensitive to inhibition by DTBN compared to Cathepsin B, L and papain (IC₅₀ = 1359.4, 13.2 and 70.4 μM respectively). DTBN is inactive for the inhibition of M^pro of SARS-CoV-2. Docking simulations suggested a mechanism of interaction that was further supported by the biochemical results. In the docking results, it was shown that the cysteine sulphur of Cathepsin S, L and B was in close proximity to the DTBN thiaspirane ring, potentially forming the necessary conditions for a nucleophilic attack to form a disulfide bond. Covalent docking and molecular dynamic simulations were performed to validate disulfide bond formation and to determine the stability of Cathepsins-DTBN complexes, respectively. The lack of reactivity of DTBN against SARS-CoV-2 M^pro was attributed to a mismatch of the binding conformation of DTBN to the catalytic binding site of M^pro. Thus, gradations in reactivity among the tested Cathepsins may be conducive for a mechanism-based search for derivatives of nupharidine against COVID-19. This could be an alternative strategy to the large-scale screening of electrophilic inhibitors.     

Undecidability of pseudop-adically closed fields

The content of this paper corresponds to a part of the author's Ph.D. thesis carried out in Tel Aviv University under the supervision of Prof. Moshe Jarden. The work was partially supported by a grant from the G.I.F., the German-Israeli Foundation for Scientific Research and Development.     

The homogeneous reaction CD4 + NH3 → CD3H + NH2D: The effect of ethane impurities

The homogeneous exchange reaction between tetradeutero methane and ammonia was studied behind reflected shocks in a single-pulse shock tube over the temperature range of 1300–1800°K. The rate of production of CD₃H at the early stages of the reaction in mixtures ranging between 1-4.5% NH₃ and 1–4.3% CD₄ in argon is given by d[CD₃H]/dt=k_b [CD₄]₀[NH₃]₀, where k_b=8 × 10¹⁶ exp (?65.3 × 10³/RT) cm³/mole·sec. This activation energy is considerably lower than the one that may be expected on the basis of a pure free radical mechanism. It is rationalized by C₂D₆ impurities in the methane. No clear answer can be obtained regarding the role of a four-center intermediate in this reaction.     

Energetics and dynamics of decaying cluster ions

The recent addition of (i) a third sector field to our two sector field mass spectrometer (resulting in a BE1E2 field configuration) and of (ii) a high performance electron gun enables us now to study in detail the time dependence of the kinetic energy release distribution (KERD) over a relatively wide range of cluster ion lifetimes. Using this newly constructed device we have studied here for the first time KERDs and deduced binding energies BEs (using finite heat bath theory) of large rare gas cluster ions (an upper size limit in earlier studies arose from the fact that different naturally occurring isotopes will contribute to a chosen metastable peak when the size exceeds a certain value) and in addition of fullerene ions smaller and larger than (here again contaminating coincidences did not allow such studies earlier). Moreover, high precision KERD measurements for the decay of rare gas dimer ions in conjunction with model calculations (using recently calculated potential energy curves for the rare gas dimer ions) also enable us to obtain information on the dynamics and the mechanisms of the underlying spontaneous decay reactions . In addition, we are also reporting here a novel method (unified breakdown graph method) to determine cluster ion binding energies using a recently constructed tandem mass spectrometer BESTOF allowing us to measure fragmentation patterns arising from the unimolecular decay of molecular cluster ions induced by surface collisions. The fragmentation and reaction patterns of protonated ethanol cluster ions investigated here clearly demonstrate in contrast to some of the earlier cluster ion studies that unimolecular dissociation kinetics determines the formation of product ions in the surface-induced decomposition.     

Synthesis and characterization of brightly photoluminescent CdTe nanocrystals

A new synthesis procedure for the preparation of spherical shaped CdTe nanocrystals (NCs) is presented, exhibiting bright luminescence with exceptionally high quantum efficiency (up to 85%). The growth of these NCs occurs in a non-coordinating solvent, octadecene, with the addition of oleic acid/tri-octylphosphine stabilizers, CdO as a precursor for the Cd monomers and additional Cd metal particles as a supplementary Cd reservoir source. The dependence of the crystalline quality and the optical properties of the CdTe NCs, on the initial Cd:Te precursors’ molar ratio, and the reaction duration were investigated. It was demonstrated that the NCs’ properties improved significantly as the initial Cd:Te molar ratios are increased. The obtained NCs’ properties were correlated with measurements of the Cd⁰ concentration in Cd metal particles, CdTe NCs and in Cd monomer solutions.     

On the stochasticity in relativistic cosmology

It was shown earlier by I. M. Lifshitz and two of us that the evolution of the relativistic cosmological models towards the singularity undergoes spontaneous stochastization.⁽¹⁾ In the present paper it is shown that the statistical parameters of this evolution can be calculated in an exact manner. From the point of view of the general ergodic theory we deal here with a specific mode of stochastization of a deterministic dynamical system with a five-dimensional phase space. The knowledge of the source of stochasticity makes it possible to develop a quantitative statistical theory with appreciable completeness.     

Signatures for a classical to quantum transition of a driven nonlinear nanomechanical resonator

We seek the first indications that a nanoelectromechanical system (NEMS) is entering the quantum domain as its mass and temperature are decreased. We find them by studying the transition from classical to quantum behavior of a driven nonlinear Duffing resonator. Numerical solutions of the equations of motion, operating in the bistable regime of the resonator, demonstrate that the quantum Wigner function gradually deviates from the corresponding classical phase-space probability density. These clear differences that develop due to nonlinearity can serve as experimental signatures, in the near future, that NEMS resonators are entering the quantum domain.     

Experimental estimates of dephasing time in molecular magnets

Muon spin relaxation measurements in isotropic molecular magnets (MM) with a spin value S ranging from 7/2 to 27/2 are used to determine the magnitude and origin of dephasing time tau(phi) of molecular magnets. It is found that tau(phi) approximately 10 nsec with no S or ligand dependence. This indicates a nuclear origin for the stochastic field. Since tau(phi) is a property of the environment, we argue that it is a number common to similar types of MM. Therefore, tau(phi) is shorter than the Zener and tunneling times of anisotropic MM such as Fe(8) or Mn(4) for standard laboratory sweep rates. Our findings call for a stochastic Landau-Zener theory in this particular case.