Beryllium (boron) clustering quest in relativistic multifragmentation (BECQUEREL Project)

A physical program of irradiation of emulsions in beams of relativistic nuclei named the BECQUEREL Project is reviewed. It is destined to study in detail the processes of relativistic fragmentation of light radioactive and stable nuclei. The expected results would make it possible to answer some topical questions concerning the cluster structure of light nuclei. Owing to the best spatial resolution, the nuclear emulsions would enable one to obtain unique and evident results. The most important irradiations will be performed in the secondary beams of He, Be, B, C, and N radioactive nuclei formed on the basis of JINR Nuclotron beams of stable nuclei. We present results on the charged state topology of relativistic fragmentation of the ¹⁰B nucleus at low energy-momentum transfers as the first step of the research.     

Universal Models For Real Submanifolds

In previous papers by the present author, a machinery for calculating automorphisms, constructing invariants, and classifying real submanifolds of a complex manifold was developed. The main step in this machinery is the construction of a “nice” model surface. The nice model surface can be treated as an analog of the osculating paraboloid in classical differential geometry. Model surfaces suggested earlier possess a complete list of the desired properties only if some upper estimate for the codimension of the submanifold is satisfied. If this estimate fails, then the surfaces lose the universality property (that is, the ability to touch any germ in an appropriate way), which restricts their applicability. In the present paper, we get rid of this restriction: for an arbitrary type (n,K) (where n is the dimension of the complex tangent plane, and K is the real codimension), we construct a nice model surface. In particular, we solve the problem of constructing a nondegenerate germ of a real analytic submanifold of a complex manifold of arbitrary given type (n,K) with the richest possible group of holomorphic automorphisms in the given class.     

Crystallographic report: A new polymorph for bis[bis(N,N‐dibenzyldithiocarbamato)cadmium(II)]

The title compound is a centrosymmetric dimer with each cadmium in a distorted CdS₅ square pyramidal geometry. The Cd–S bond distances range from 2.5626(11) to 2.8459(11) Å. Copyright © 2004 John Wiley & Sons, Ltd.     

On the equivalence of linear equations under nonlocal transformation

Linear nth order (n?3) ordinary differential equations have been shown to possess n+1, n+2 or n+4 Lie point symmetries. Each class contains equations which are equivalent under point transformation. By taking the example of third order equations, we show that all linear equations are equivalent if the class of transformation is broadened to include nonlocal transformations and hence the representative of this class of equations is y⁽ⁿ⁾=0.     

Application of MMMA method: Dispersed superconductors and magnetic nanolayers

Microwave nonresonant dissipation observed around zero field makes a powerful method in characterizing superconducting state (to determineT _C,H _C1,H _CJ parameters). This review shows several successful applications of magnetically modulated microwave absorption (MMMA). MMMA enables to study MgB₂ superconducting nanoregions embedded in the Mg host structure. Application of MMMA to study intercalation of fullerence enabled the observation of a new superconducting phase. The pressure effect dT _C/dp has been studied below the percolation threshold in YBaCuO/PST composites. The local temperature of the Josephson junction measured by the MMMA technique showed that a granular superconductor consists of two phases: host phase and Josephson junction system. MMMA has been applied lately to separate the giant magnetoresistance from the magnetization effect in differential hysteresis loops.     

Fundamentals of the direct measurement of sound intensity and practical applications

Sound intensity is a measure of the magnitude and direction of the flow of sound energy. Developments in sound intensity measurement capabilities in the last quarter century have occurred because of several reasons. The main ones include the derivation of the cross-spectral formulation for sound intensity and developments in digital signal processing. This paper begins with a brief historical introduction of sound intensity measurements. Then elementary theory for sound intensity is presented. A section on sound intensity measurements is then included. The next section of the paper discusses sources of measurement error; the major sources of error are described in some detail. The paper continues with a discussion of the main applications of sound intensity measurements: sound power determination, noise source identification, and transmission loss measurements. The paper concludes with a discussion of ISO and ANSI intensity related standards and relevant references.     

Modelling and design of a travelling-wave electro-optic modulator on InP

Based on a rigorous vectorial analysis, a fast travelling-wave Mach–Zehnder modulator is modelled and designed. The cross-section of the semiconductor layer stack and the lossy electrodes are carefully modelled using the method of lines in order to investigate propagation characteristics, velocity and losses. This yields an accurate microwave and optical field distribution to explain the behaviour of the component. In order to enhance the modulation efficiency, design curves are derived and the cross-sectional dimensions for minimum microwave loss are determined. The loss of the optimized modulator agrees very well with small-signal measurements up to 40 GHz and HFSS simulations. The layerstack of the fabricated device is suitable for integration with InP multi-wavelength lasers.     

A remark on divisibility of definable groups

We show that if G is a definably compact, definably connected definable group defined in an arbitrary o‐minimal structure, then G is divisible. Furthermore, if G is defined in an o‐minimal expansion of a field, k ∈ ? and p_k : G → G is the definable map given by p_k (x ) = x^k for all x ∈ G , then we have |(p_k )^–1(x )| ≥ k^r for all x ∈ G , where r > 0 is the maximal dimension of abelian definable subgroups of G . (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)