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.     

Investigation of clustering in light nuclei by means of relativistic-multifragmentation processes

New results concerning the topology of the fragmentation of relativistic nuclei ⁷Li and ¹⁰B are presented. A program is proposed for studying the cluster structure of stable and radioactive nuclei. The use of emulsions in the investigation of nuclear clustering in the fragmentation of light nuclei at energies are in excess of 1 GeV per nucleon is discussed.     

On testing the divisibility of lacunary polynomials by cyclotomic polynomials

An algorithm is described that determines whether a given polynomial with integer coefficients has a cyclotomic factor. The algorithm is intended to be used for sparse polynomials given as a sequence of coefficient-exponent pairs. A running analysis shows that, for a fixed number of nonzero terms, the algorithm runs in polynomial time.

     

Standardization of Methods for Characterizing the Surface Geometry of Solids

Since a comprehensive survey published in 1999 [1] much work was done in standardizing measuring methods to characterize the surface geometry of dispersed and/or porous solids and to certify reference materials. The present paper is an extension of a short communication [2]. It gives a survey on existing standards and reports on new drafts and proposals.     

The representation dimension of domestic weakly symmetric algebras

Auslander’s representation dimension measures how far a finite dimensional algebra is away from being of finite representation type. In [1], M. Auslander proved that a finite dimensional algebra A is of finite representation type if and only if the representation dimension of A is at most 2. Recently, R. Rouquier proved that there are finite dimensional algebras of an arbitrarily large finite representation dimension. One of the exciting open problems is to show that all finite dimensional algebras of tame representation type have representation dimension at most 3. We prove that this is true for all domestic weakly symmetric algebras over algebraically closed fields having simply connected Galois coverings.     

Neocompact Sets and the Fixed Point Property

We use a newly introduced concept of neocompactness to study problems from metric fixed point theory. In particular, we give a sufficient condition for a superreflexive Banach space X to have the fixed point property and obtain shorter proofs of some well-known results in that theory.     

Deactivation reactions in the modeled 2,2,6,6‐tetramethyl‐1‐piperidinyloxy‐mediated free‐radical polymerization of styrene: A comparative study with the 2,2,6,6‐tetramethyl‐1‐piperidinyloxy/acrylonitrile system

The competitiveness of the combination and disproportionation reactions between a 1‐phenylpropyl radical, standing for a growing polystyryl macroradical, and a 2,2,6,6‐tetramethyl‐1‐piperidinyloxy (TEMPO) radical in the nitroxide‐mediated free‐radical polymerization of styrene was quantitatively evaluated by the study of the transition geometry and the potential energy profiles for the competing reactions with the use of quantum‐mechanical calculations at the density functional theory (DFT) UB3‐LYP/6‐311+G(3df, 2p)//(unrestricted) Austin Model 1 level of theory. The search for transition geometries resulted in six and two transition structures for the radical combination and disproportionation reactions, respectively. The former transition structures, mainly differing in the out‐of‐plane angle of the N? O bond in the transition structure TEMPO molecule, were correlated with the activation energy, which was determined to be in the range of 8.4–19.4 kcal mol^?1 from a single‐point calculation at the DFT UB3‐LYP/6‐311+G(3df, 2p)//unrestricted Austin Model 1 level. The calculated activation energy for the disproportionation reaction was less favorable by a value of more than 30 kcal mol^?1 in comparison with that for the combination reaction. The approximate barrier difference for the TEMPO addition and disproportionation reaction was slightly smaller for the styrene polymerization system than for the acrylonitrile polymerization system, thus indicating that a β‐proton abstraction through a TEMPO radical from the polymer backbone could diminish control over the radical polymerization of styrene with the nitroxide even more than in the latter system. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 232–241, 2007     

On invariability of self-injective algebras of tilted type under stable equivalences

We prove that a large class of self-injective algebras of tilted type is invariant under stable equivalences of module categories.

     

PARTIAL VERSUS GENERAL STORAGE POLICY: COMMODITIES AND RESOURCES

This paper examines joint storage considerations when both commodities and resources can be stored, e.g., grain and water for irrigation. Results suggest that when separate agencies control public resource and commodity storage, suboptimal storage rules occur unless (i) each agency is sensitive to the policies of the other, (ii) commodity inventories are adjusted in response to prices, and (iii) resource inventories are adjusted in response to both commodity demand and resource supply conditions. For example, the common case where water storage depends on weather and reservoir conditions alone is not sufficiently general. The results imply that water management agencies that tend to be dominated by engineers and hydrological considerations need to incorporate economic considerations into decision processes.