Coxeter Transformation and Quasiquivers

Mathematical Notes -     

Explosive decomposition of pentaerythritol tetranitrate pellets containing nickel nanoparticles with various radii

The kinetics of the explosive decomposition of pressed pentaerythritol tetranitrate pellets containing nickel nanoparticles with various radii has been investigated experimentally, with the explosion initiated by a neodymium laser pulse (wavelength, 1064 nm; pulse duration at half-height, 14 ns), and probability curves for this process have been recorded. The experimental values of critical initiation energy density corresponding to 50% explosion probability are 0.9, 0.7, and 1.4 J/cm² at a nickel particle radius of 67, 78, and 138 nm, respectively. The initial time interval in which the intensity of light emission accompanying the explosive decomposition increases begins during the action of the pulse and is described by a Gaussian function with an effective constant of k = (1.4 ± 0.1) × 10⁸ s^–1, which is independent of the nanoparticle radius. Experimental data of this study can be interpreted within the micro-hotspot model of thermal explosion.     

On commuting mappings

The cardinality of the centralizer of an element in infinite symmetric semigroups is studied.     

Reflections and Three-Dimensionality

If the dimension of a linear space is not greater than 3, then the characteristic polynomial of the Coxeter transformation associated with any symmetric matrix is invariant under the natural action of the symmetric group. If the dimensionality is greater than 3, then this statement does not hold. The set of all trees such that the spectrum of their associated Coxeter transformation contains negative one is three-dimensional.     

Study of cluster materials obtained by selective laser photochemistry

This paper presents experimental results from the study of the characteristics of cluster materials obtained by resonance laser photochemistry. The effect of the redox reagents used in the photoprocessing on the size and shape of cluster structures of gold has been studied. The minimum size of the structures, measured by electron microscopy, is 30–50 nm. When organic acids are used as redox reagents, fractal structures formed from flat scales are synthesized. Redox reagents based on alcohols form cluster structures of fractal type consisting of spherical clusters. Fiz. Tverd. Tela (St. Petersburg) 40, 2236–2238 (December 1998)     

Monoids and decay

We propose some formalization of the concept of critical decay number and describe the class of models with this number at most 4 (i.e., every object is decomposable which consists of four or more elements).     

Nonnegativity for Cartan-Tits and Kac-Moody forms

Forms generalizing Cartan-Tits and Kac-Moody forms are considered. Necessary conditions for these forms to be nonnegative are found.     

Balanced subsets of a symmetric inverse semigroup

For elements in the subsets of some symmetric inverse semigroup we study the problem of equal cardinality for the sets of commuting and noncommuting elements.     

Coxeter transformations: Construction of deltoids

The Coxeter transformations associated with deltoids (i.e., with graphs in which all simple cycles have length 3) are considered. The structure of the set of all connected deltoids whose spectra do not contain ?1 is described.     

Coxeter transformation: Density Theorems

Mathematical Notes -