The martingale problem for a class of nonlocal operators of diagonal type

We consider systems of stochastic differential equations of the form $$\begin{array}{c}\hfill d{X}_t^i=\sum _{j=1}^d{A}_{ij}\left(X_{t?}\right)d{Z}_t^j\end{array}$$ for $i=1,?,d$ with continuous, bounded and non‐degenerate coefficients. Here $Z_t^1,?,Z_t^d$ are independent one‐dimensional stable processes with ${\alpha }_1,?,{\alpha }_d\in (0,2)$. In this article we research on uniqueness of weak solutions to such systems by studying the corresponding martingale problem. We prove the uniqueness of weak solutions in the case of diagonal coefficient matrices.     

On uniform propagation of chaos

In this paper we obtain a time-uniform propagation estimate for a system of interacting diffusion processes. Using a well defined metric function h , our result guarantees a time-uniform estimate for the convergence of a class of interacting stochastic differential equations towards their mean field limit, under conditions that ensure that the decay associated to the internal dynamics term dominates the interaction and noise terms. Our result should have diverse applications, particularly in neuroscience, and allows for models more elaborate than the one of Wilson and Cowan. In particular, the internal dynamics need not be that of linear decay.     

Attractor solutions in f(T) cosmology

We present the results of three-dimensional simulations of quasar polarizations in the presence of pseudoscalar?Cphoton mixing in the intergalactic medium. The intergalactic magnetic field is assumed to be uncorrelated in wave vector space but correlated in real space. Such a field may be obtained if its origin is primordial. Furthermore we assume that the quasars, located at cosmological distances, have negligible initial polarization. In the presence of pseudoscalar?Cphoton mixing we show, through a direct comparison with observations, that this may explain the observed large scale alignments in quasar polarizations within the framework of big bang cosmology. We find that the simulation results give a reasonably good fit to the observed data.     

Nitrogen dissociation and its excitation/vibrational temperature with hydrogen admixture in 50 Hz DC discharge

Trace rare gas optical emission spectroscopy (TRG-OES) is carried out to determine the excitation temperature, vibrational temperature, dissociation fraction and nitrogen (N) atom density in 50?Hz active screen cage nitrogen plasma, as a function of discharge parameters (current density and fill pressure) and hydrogen concentrations. The excitation temperature is determined from Ar–I emission lines and is found to increase with hydrogen mixing. In a similar fashion, the vibrational temperature of second positive system is determined and found to have increasing trend with hydrogen addition. The dissociation fraction increases with hydrogen concentration up to 40% H₂ in the nitrogen plasma, so as the nitrogen atom density.     

Structural,morphological and mechanical properties of niobium nitride thin films grown by ion and electron beams emanated from plasma

The influence of variation in plasma deposition parameters on the structural, morphological and mechanical characteristics of the niobium nitride films grown by plasma-emanated ion and electron beams are investigated. Crystallographic investigation made by X-ray diffractometer shows that the film synthesized at 10?cm axial distance with 15 plasma focus shots (PFS) exhibits better crystallinity when compared to the other deposition conditions. Morphological analysis made by scanning electron microscope reveals a definite granular pattern composed of homogeneously distributed nano-spheroids grown as clustered particles for the film synthesized at 10?cm axial distance for 15 PFS. Roughness analysis demonstrates higher rms roughness for the films synthesized at shorter axial distance and by greater number of PFS. Maximum niobium atomic percentage (35.8) and maximum average hardness (19.4?±?0.4?GPa) characterized by energy-dispersive spectroscopy and nano-hardness analyzer respectively are observed for film synthesized at 10?cm axial distance with 15 PFS.     

One-pot synthesis of 1, 3-thiazolidin-4-one using Bi(SCH2COOH)3 as catalyst

A catalytic multi-component reaction involving aromatic amine,aromatic aldehydes,mercapto acid as substrates and Bi（SCH₂COOH）₃ as catalyst under solvent free conditions,afforded thiazolidin-4-one in good yields.The efficiency of the catalyst was proved with a variety of substrates,ranging from electrondeficient to electron-rich aldehydes.     

Enantio- and Diastereoselective Oxidation of N-Alkylimines Using Chiral α-Bromonitriles and Hydrogen Peroxide System

Chiral α-bromonitriles were prepared with good chemical and optical yields starting from natural α-amino acids by dehydrating the corresponding α-bromoamides with thionyl chloride. The combined system α-bromonitriles/hydrogen peroxide was examined for the enantio- and diastereoselective oxidation of N-alkylimines in basic media at room temperature. The oxidation of N-tertiobutylarylimines leads to optically active oxaziridines with moderate enantiomeric excess. However, the oxidation of (S)-1-phenylethylarylimines affords the corresponding oxaziridines with good diasteromeric excess up to 97/3 as proved by gaseous-phase chromatography.     

Simple and Efficient Procedure for the Synthesis of Novel 1,3-Diphenyl-2-azaphenalene Derivatives via One-Pot Multicomponent Reactions

A new, one-pot multicomponent reaction of two molecules of aromatic aldehydes with 2,7-naphthalenediol and ammonium hydrogen phosphate is described as an efficient and direct procedure for the preparation of novel 1,3-diphenyl-2-azaphenalene derivatives in a mixture of EtOH-H₂O (3:1) under reflux conditions.     

Kinetics of the Oxidation of Phenylhydrazine by [Fe(CN)6]3− in Water‐in‐Oil Microemulsions

The oxidation reaction of phenyl hydrazine (Phh) by hexacyanoferrate ([Fe(CN)₆]^3?) has been studied in water‐in‐oil (w/o) microemulsion media. The kinetic profile of the reaction was investigated as a function of [Phh], droplet size, and droplet concentration. Comparison of the kinetic profiles of the reaction in microemulsion, water‐urea, and water‐AOT‐urea media indicates that the kinetic profile of the reaction in microemulsion shows a behavior similar to that of the reaction in water‐AOT‐urea medium at 4 M urea. An initial increase and then a decrease in k_obs is observed with increasing molar ratio, W_o(=[H₂O]/[AOT]) at constant [AOT] (=0.4 M), whereas k_obs decreases upon increasing the AOT concentration at constant molar ratio.     

Oil-Water Partitioning of a Synthetic Tetracarboxylic Acid as a Function of pH

The oil-water partitioning of a synthetic tetraacid acting as a model compound for indigenous C₈₀-C₈₂ ARN acids has been studied as a function of pH, ionic strength and type of monovalent counterion. Experimental data obtained with ultraviolet-visible and HPLC/UV analyses have been fitted to thermodynamic models based on one, two or four dissociation steps to obtain o/w partition coefficients (K _wo ) of the fully protonated acid between chloroform and aqueous solutions, and its apparent acidity constant(s), pK _a. As the study is conducted above the CMC of the tetraacid, in general high apparent acidity constants were obtained in the range from 6 to 8 resulting from micellization equilibria. K _wo values were obtained in the range from 10^?3 to 10^?4, and decreasing with increasing salinity. At 50 mM K⁺, no conclusions could be made regarding the number of distinguishable dissociation steps, while at higher ionic strength (184 mM and 452 mM K⁺) and at 184 mM Na⁺ a model with two dissociation steps provided good fits to the experimental data. The first step was found to be given by a pK _a ≈ 6.6–6.8 and the second dissociation step at pK _a values ≈ 7.8–8.3. The two-step mechanism supports previous results obtained by potentiometric titrations. No significant difference in the o/w behavior was observed when changing the counterion from potassium to sodium. The main partitioning of the tetraacid in the aqueous phase occurred above pH 8, where the fully deprotonated acid was formed.