Conformationally controlled intramolecular heterocyclization of 2,4-diaminoperfluoro-4-methyl-2-pentenethiocyanate-3

Perfluoro-2-methyl-2-pentene-thiocyanate-3 reacts with ammonia to give 2,4-diaminoperfluoro-4-methyl-2-pentenethiocyanate-3 ( 4 ) and 2-aminoperfluoro-4, 4-dimethyl-4,5-dihydro-5-ethylidene-1,3-thiazole ( 5 ). Compound 4 is kinetically stable and at 150°C under-goes rotational isomerization to afford the cyclic isomer 2-amino-4,4-bis(trifluoromethyl)-4,5-dihydro-5-(1-aminoperfluoroethylidene) -1,3-thiazole ( 6 ). Intramolecular cyclizations, resulting in the thiazolines 5 and 6 , proceed likewise via the Thorpe reaction. For compounds 4–6 , X-ray diffraction analyses were undertaken and IR spectra in solution and in solid state were investigated. It is supposed that a high kinetic preference for formation of 4 and the fact that it does not undergo spontaneous cyclization in ammonolysis stem from the NH …︁ N intramolecular hydrogen bonding between two amino groups.     

An Efficient Parallel Reverse Conversion of Residue Code to Mixed-Radix Representation Based on the Chinese Remainder Theorem

In this paper, we deal with the critical problems in residue arithmetic. The reverse conversion from a Residue Number System (RNS) to positional notation is a main non-modular operation, and it constitutes a basis of other non-modular procedures used to implement various computational algorithms. We present a novel approach to the parallel reverse conversion from the residue code into a weighted number representation in the Mixed-Radix System (MRS). In our proposed method, the calculation of mixed-radix digits reduces to a parallel summation of the small word-length residues in the independent modular channels corresponding to the primary RNS moduli. The computational complexity of the developed method concerning both required modular addition operations and one-input lookup tables is estimated as , where k equals the number of used moduli. The time complexity is modular clock cycles. In pipeline mode, the throughput rate of the proposed algorithm is one reverse conversion in one modular clock cycle.     

Effect of nonlinear correlations on the statistics of return intervals in multifractal data sets

We study the statistics of return intervals between events above a certain threshold in multifractal data sets without linear correlations. We find that nonlinear correlations in the record lead to a power-law (i) decay of the autocorrelation function of the return intervals, (ii) increase in the conditional return period, and (iii) decay in the probability density function of the return intervals. We show explicitly that all the observed quantities depend both on the threshold value and system size, and hence there is no simple scaling observed. We also demonstrate that this type of behavior can be observed in real economic records and can be used to improve considerably risk estimation.     

Recovering the Sturm-Liouville Operator with Singular Potential Using Nodal Data

The paper deals with the Sturm-Liouville operator with singular potential. We assume that the potential is a sum of an a priori known distribution from a certain class and an unknown sufficiently smooth function. The inverse problem is to recover the operator using zeros of eigenfunctions (nodes) as an input data. For this inverse problem we obtain a procedure for constructing the solution.     

Model problem for the motion of a compressible, viscous flow with the no-slip boundary condition

We consider the Navier–Stokes equations for the motion of a compressible, viscous, pressureless fluid in the domain ${\Omega = \mathbb{R}^3_+}$ with the no-slip boundary conditions. We construct a global in time, regular weak solution, provided that initial density ρ ₀ is bounded and the magnitude of the initial velocity u ₀ is suitably restricted in the norm ${\|\sqrt{\rho_0(\cdot)}{\bf u}_0(\cdot)\|_{L^2(\Omega)} + \|\nabla{\bf u}_0(\cdot)\|_{L^2(\Omega)}}$ .     

Chaotic motion of a cylindrical body during contactless transportation from MEO to LEO by ion beam

Nonlinear Dynamics - The attitude dynamics of a cylindrical body under the action of an ion beam generated by the low-thrust engine of an active spacecraft is studied. The aim of the work is the...     

Four-component stereoselective synthesis of tetracyano-substituted piperidines

Research on Chemical Intermediates - A novel four-component stereoselective synthesis of polysubstituted piperidines is reported. The Knoevenagel–Michael–Mannich cascade of two...     

On Solution of the Integrable Initial Boundary Value Problem for KdV Equation on the Semi-axis

This paper is concerned with the Korteweg-de Vries (KdV) equation on the right semi-axis. The initial boundary value problem with inhomogeneous integrable boundary conditions is studied. We show that, under some conditions on the initial data the problem has a solution and provide the procedure for constructing this solution. The procedure is based on the inverse spectral method and consists of several steps reducing to either solving some linear problems or calculations via some explicit formulas.