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 ${\|\sqrt{\rho_0(\cdot)}{\bf u}_0(\cdot)\|_{L^2(\Omega)} + \|\nabla{\bf u}_0(\cdot)\|_{L^2(\Omega)}}$ .     

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.     

Monte Carlo simulation of brain sensing by optical diffuse spectroscopy

We report on development of adapted Monte Carlo based algorithm and code for simulation of light propagation in turbid media with complex geometry aimed for simulation of optical diffuse spectroscopy signal in noninvasive brain sensing. Simulation will allow to determine optimal characteristics of a prototype device for optical diffuse brain sensing. The developed Monte Carlo code can be efficiently parallelized both for SMP and distributed memory systems. We show that the speed-up of the developed algorithm almost linearly depends on the number of nodes/threads in a utilized system.     

Atomistic-continuum multiscale modelling of magnetisation dynamics at non-zero temperature

In this article, a few problems related to multiscale modelling of magnetic materials at finite temperatures and possible ways of solving these problems are discussed. The discussion is mainly centred around two established multiscale concepts: the partitioned domain and the upscaling-based methodologies. The major challenge for both multiscale methods is to capture the correct value of magnetisation length accurately, which is affected by a random temperature-dependent force. Moreover, general limitations of these multiscale techniques in application to spin systems are discussed.     

Raman investigation of hydrostatic and nonhydrostatic compressions of OH‐ and F‐apophyllites up to 8 GPa

Layer silicates F‐ and OH‐apophyllites, KCa₄Si₈O₂₀(F, OH)·8H₂O, have been investigated by Raman spectroscopy at hydrostatic and nonhydrostatic pressures up to ~8 GPa in diamond anvil cells using a 4 : 1 methanol–ethanol mix as pressure‐transmitting medium. Our experiments show that at hydrostatic compression, apophyllites retain their crystalline states (i.e. no amorphization) up to 5 GPa. The wavenumbers of most bands exhibit linear dependences on pressure, except for a few ones, e.g. at 162 and 3565 cm^–1 in OH‐form (160.5 and 3558 cm^–1 in F‐form) that show nonlinear dependences. Nonhydrostatic compression with additional uniaxial loading induces amorphization of apophyllites. The majority of the bands in OH‐apophyllite decreases markedly in intensity and shows considerable broadening under nonhydrostatic compression up to 3–6 GPa. In addition, the wavenumbers of several bands at nonhydrostatic compression exhibit considerable nonlinear dependences on pressure with strong hysteresis. These bands are mainly associated with vibrations of the interlayer ions and molecules and also of stretching and bending silicate sheets, hence being highly sensitive to the interlayer distance. Finally, we have calculated the lattice dynamics of F‐apophyllite and interpreted the majority of bands, and these data are used to explain the complex baric behavior of the bands. Copyright © 2011 John Wiley & Sons, Ltd.