Synthesis of chromeno[3,4-c][1,2]oxazine-N-oxides via formal [4+2] cycloaddition of 3-nitro-2-trihalomethyl-2H-chromenes with cyclohexanone and pinacolone enamines

3-Nitro-2-trichloro(trifluoro)methyl-2H-chromenes undergo a formal [4+2] cycloaddition reaction to cyclohexanone and pinacolone enamines, producing chromeno[3,4-c][1,2]benzoxazin-6-oxides with high diastereoselectivity and in good yields. In addition, some novel 2,3,4-trisubstituted chromanes were obtained. The stereochemistry of the products was established based on a 2D NOESY experiment and an X-ray diffraction study.     

Novel design of 3,8-diazabicyclo[3.2.1]octane framework in oxidative sulfonamidation of 1,5-hexadiene

1,5-Hexadiene reacts with trifluoromethanesulfonamide in the oxidative system (t-BuOCl+NaI) to give trans-2,5-bis(iodomethyl)-1-(trifluoromethylsulfonyl)pyrrolidine 5 and 3,8-bis(trifluoromethylsulfonyl)-3,8-diazabicyclo[3.2.1]octane 6. With arenesulfonamides ArSO₂NH₂ (Ar=Ph, Tol), the reaction stops at the formation of the trans and cis isomers of 2,5-bis(iodomethyl)-1-(arenesulfonyl)pyrrolidine 7 and 8 (1:1). The cis isomers of 7 and 8 do not undergo cyclization to the corresponding 3,8-disubstituted 3,8-diazabicyclo[3.2.1]octanes. The reaction with triflamide represents the first example of one-pot two-step route to 3,8-diazabicyclo[3.2.1]octane system.     

Assembling of 3,6-diazabicyclo[3.1.0]hexane framework in oxidative triflamidation of substituted buta-1,3-dienes

Reaction of trifluoromethanesulfonamide (triflamide) CF₃SO₂NH₂ with 2,3-dimethylbuta-1,3-diene (2) and 2,5-dimethylhexa-2,4-diene (3) in the oxidative system (t-BuOCl+NaI) results in the formation of 2,4-dimethyl- or 2,2,4,4-tetramethyl-3,6-bis(triflyl)diazabicyclo[3.1.0]hexane through two successive heterocyclizations. Reaction of diene (3) with arenesulfonamides ArSO₂NH₂ (Ar=Ph, Tol), stops at the formation of the product of oxidative 1,4-addition, N,N′-(2,3-dimethylbut-2-ene-1,4-diyl)diarenesulfonamides, providing evidence of the essential difference between the reactivity of triflamide and arenesulfonamides.     

A New Method of Preparing Copper Oxide from Dinitrourea Copper Salt

A new approach for the preparation of copper nanooxide by solvothermal decomposition of N, N′‐dinitrourea copper(II) salt in an aprotic solvent was developed. The resulting particles were studied by transmission electron microscopy, X‐ray photoelectron spectroscopy, and small‐angle X‐ray scattering. The effects of different solvents on shapes of the agglomerates formed are shown.     

Wasserstein convergence rates for random bit approximations of continuous Markov processes

We determine the convergence speed of a numerical scheme for approximating one-dimensional continuous strong Markov processes. The scheme is based on the construction of certain Markov chains whose laws can be embedded into the process with a sequence of stopping times. Under a mild condition on the process' speed measure we prove that the approximating Markov chains converge at fixed times at the rate of 1/4 with respect to every p-th Wasserstein distance. For the convergence of paths, we prove any rate strictly smaller than 1/4. Our results apply, in particular, to processes with irregular behavior such as solutions of SDEs with irregular coefficients and processes with sticky points.     

Limiting case of modified electroweak model for contracted gauge group

The modification of the Electroweak Model with 3-dimensional spherical geometry in the matter fields space is suggested. The Lagrangian of this model is given by the sum of the free (without any potential term) matter fields Lagrangian and the standard gauge fields Lagrangian. The vector boson masses are generated by transformation of this Lagrangian from Cartesian coordinates to coordinates on the sphere S ³. The limiting case of the bosonic part of the modified model, which corresponds to the contracted gauge group SU(2; j) × U(1) is discussed. Within framework of the limit model Z boson and electromagnetic fields can be regarded as external ones with respect to W-boson fields in the sence that W-boson fields do not effect on these external fields. The masses of all particles of the Electroweak Model remain the same, but field interactions in contracted model are more simple as compared with the standard Electroweak Model.     

Some aspects of <Emphasis Type="Italic">m</Emphasis>-adic analysis and its applications to <Emphasis Type="Italic">m</Emphasis>-adic stochastic processes

In this paper we consider a generalization of analysis on p-adic numbers field to the m case of m-adic numbers ring. The basic statements, theorems and formulas of p-adic analysis can be used for the case of m-adic analysis without changing. We discuss basic properties of m-adic numbers and consider some properties of m-adic integration and m-adic Fourier analysis. The class of infinitely divisible m-adic distributions and the class of m-adic stochastic Levi processes were introduced. The special class of m-adic CTRW process and fractional-time m-adic random walk as the diffusive limit of it is considered. We found the asymptotic behavior of the probability measure of initial distribution support for fractional-time m-adic random walk.     

Nonlinear and diffraction effects in propagation of N-waves in randomly inhomogeneous moving media

Finite amplitude acoustic wave propagation through atmospheric turbulence is modeled using a Khokhlov-Zabolotskaya-Kuznetsov (KZK)-type equation. The equation accounts for the combined effects of nonlinearity, diffraction, absorption, and vectorial inhomogeneities of the medium. A numerical algorithm is developed which uses a shock capturing scheme to reduce the number of temporal grid points. The inhomogeneous medium is modeled using random Fourier modes technique. Propagation of N-waves through the medium produces regions of focusing and defocusing that is consistent with geometrical ray theory. However, differences up to ten wavelengths are observed in the locations of fist foci. Nonlinear effects are shown to enhance local focusing, increase the maximum peak pressure (up to 60%), and decrease the shock rise time (about 30 times). Although the peak pressure increases and the rise time decreases in focal regions, statistical analysis across the entire wavefront at a distance 120 wavelengths from the source indicates that turbulence: decreases the mean time-of-flight by 15% of a pulse duration, decreases the mean peak pressure by 6%, and increases the mean rise time by almost 100%. The peak pressure and the arrival time are primarily governed by large scale inhomogeneities, while the rise time is also sensitive to small scales.     

Ambipolar diffusion and drift in computational weakly-ionized plasmadynamics

Modeling of ambipolar diffusion and drift taking place within a weakly-ionized fluid can lead to some convergence difficulties when the ion conservation equation and the electric field potential equation are solved consecutively. A novel formulation of the ion flow rate is proposed here that reduces the computing effort to reach convergence by a factor of 10 or more. It is shown that by recasting the ion flow rate in terms of drift and ambipolar diffusion components, the sensitivity to the electric field is reduced hence alleviating the stiffness of the system of equations and permitting significantly faster convergence. What makes the method particularly appealing is that (i) it yields faster convergence without affecting the accuracy of the converged solution and (ii) it is not restricted to specific discretization or relaxation schemes and can hence be readily implemented in existing flow solvers. Because it is developed in general form (i.e. applicable to a multicomponent plasma in the simultaneous presence of electric current and magnetic and electric fields), the method is notably well-suited to simulate ambipolar diffusion within ionized multi-species flow solvers and is recommended for all flowfields as long as the plasma remains weakly-ionized and quasi-neutral.