Improving chaos-based pseudo-random generators in finite-precision arithmetic

Nonlinear Dynamics - One of the widely-used ways in chaos-based cryptography to generate pseudo-random sequences is to use the least significant bits or digits of finite-precision numbers defined...     

The Daugavet Property of C*-Algebras and Non-commutative Lp-Spaces

We prove that a C ^*-algebra A or a predual N _* of a von Neumann algebra N has the Daugavet property if and only if A (or N) is non-atomic. We also prove a similar (although somewhat weaker) result for non-commutative L _p-spaces corresponding to non-atomic von Neumann algebras.     

The non-commutative Gurarii space

We construct a “universal space” for 1-exact finite dimensional operator spaces (an analogue of the Gurarii space). Received: 20 June 2005     

Temporal boundary value problems in interfacial fluid dynamics

We study problems in interfacial fluid dynamics which do not have well-posed initial value problems. We prove existence of solutions for these problems by considering instead boundary value problems, where boundary data is specified at two different times. We develop a general framework, for problems on the real line and for problems which are spatially periodic. A variety of boundary conditions are considered, including Dirichlet, Neumann and mixed conditions. The framework is applied to two specific problems from interfacial fluid dynamics: a family of generalizations of the Boussinesq equations developed by Bona, Chen and Saut, and the vortex sheet.     

Groups of Units of Finite Commutative Group Rings*

Let R be a finite commutative ring with identity and ? _{p ^d} be the cyclic group of prime power order. Define R? _{p ^d} to mean the group ring of ? _{p ^d} over R. We determine the structure of the group of units of R? _{p ^d} in the case when R is generated by an element whose order is not divisible by p.     

Controlling the generation of high frequency electromagnetic pulses with relativistic flying mirrors using an inhomogeneous plasma

A method for the controlled generation of intense high frequency electromagnetic fields by a breaking Langmuir wave (relativistic flying mirrors) in a gradually inhomogeneous plasma is proposed. The wave breaking threshold depends on the local plasma density gradient. Compression, chirping and frequency multiplication of an electromagnetic wave reflected from relativistic mirrors is demonstrated using Particle-In-Cell simulations. Adjusting the shape of the density profile enables control of the reflected light properties.     

Evaluation of Ionic Liquids Based on Amino Acid Anions for Use in Liquid‐junction Free Reference Electrodes

In this paper we report on the novel polymeric membranes for the liquid junction‐free reference electrodes. The membranes contain the ionic liquids (ILs) based on the amino acid anions, namely valine‐, leucine‐, lysine‐ and histidine‐anions, and 1‐butyl‐3‐methylimidazolium cation. Addition of the ILs, and especially of the valine‐based one, to the polymeric plasticized membranes allows significant stabilization of the electrode potential and makes it insensitive to the solution composition. A simple criterion based on the calculated lipophilicities of the cation and anion of the IL is proposed for a priori estimation of its applicability for potential stabilization. The addition of the IL as a microcomponent is found to be advantageous over plasticizing the membrane with the IL due to better potential stability, higher dissociation degree and mobility of the species. The resistance of the novel reference membranes can be tuned by addition of the lipophilic membrane electrolytes, e. g. ETH500. The applicability of the developed reference electrodes is verified in the potentiometric calibration of the indicator K⁺‐ and Ca²⁺‐selective electrodes. Implementation of the amino acid‐based ionic liquids with low environmental toxicity can make a significant contribution to the development of nature‐friendly potentiometry.     

Novel approach to 6-alkenyl-substituted pyridoxine derivatives based on the Heck reaction

A new synthetic approach to 6-alkenyl-substituted pyridoxine derivatives was developed based on the Heck reaction. The reaction, which was catalyzed using a mixture of Pd(OAc)₂, (o-Tol)₃P and Bu₃N as a base, led to seven new 6-alkenyl pyridoxine derivatives. When acrylic acid was used the products of decarboxylation and dimerization were formed.