The probability of generating a soluble subgroup of a finite group

It is proved that for finite groups G, the probability thattwo randomly chosen elements of G generate a soluble subgrouptends to zero as the index of the largest soluble normal subgroupof G tends to infinity.     

Is life improbable?

E. P. Wigner's argument that the probability of the existence of self-reproducing units, e.g., organisms, is zero according to standard quantum theory is stated and analyzed. Theorems are presented which indicate that Wigner's mathematical result in fact should not be interpreted as asserting the improbability of self-reproducing units.     

Infinite products for power series

An algorithm is introduced and shown to lead to a unique infinite product representation for a given formal power series A(z) with A(0) = 1. The infinite product is , where all b_n ≠ 0, r_n , and r_n+1 > r_n. The degree of approximation by the polynomial (1 + b₁z^r₁) · · · (1 + b_nz^r_n) is also considered.     

A C-symplectic free -manifold with contractible orbits and

An interesting question in symplectic geometry concerns whether or not a closed symplectic manifold can have a free symplectic circle action with orbits contractible in the manifold. Here we present a c-symplectic example, thus showing that the problem is truly geometric as opposed to topological. Furthermore, we see that our example is the only known example of a c-symplectic manifold having non-trivial fundamental group and Lusternik-Schnirelmann category precisely half its dimension.

     

Particle systems on flows

We start with a stochastic flow of diffeomorphisms of the space. Particles enter the space at random times and places. Each particle is carried by the flow for some random amount of time. We examine the point process formed by the particles at a fixed time, on the evolution of that point process as time varies, and on the equilibrium law of the point process.     

Characterization of supercommuting matrices

For a given n-by-n matrix A, we consider the set of matrices which commute with A and all of whose principal submatrices commute with the corresponding principal submatrices of A. The properties of this set are examined, with particular attention to its dimension.     

Fluorescence anisotropy decay study of self-association of bacterial luciferase intermediates

The fluorescence dynamics parameters of the fluorescent transient flavin-luciferase species from the typesVibrio fischeri andPhotobacterium leiognathi are presented. The fluorescence anisotropy decay is a single exponential function for both types. The correlation time is 70 ns for theP. leiognathi fluorescent transient intermediate (2°C, aqueous buffer, pH 7.0), consistent with the rotational correlation time of the luciferase macromolecule (77 kD) to which the flavin fluorophore is rigidly attached. In contrast, for theV. fischeri species the observed correlation time for the anisotropy decay function is 133 ns. This suggests that protein self-association occurs in theV. fischeri case and this is confirmed by filtration, where the fluorescent transient fromV. fischeri does not pass through a 100,000 molecular weight cutoff membrane, whereas theP. leiognathi species does. The filtration method also demonstrates self-association in the luciferase peroxyflavin and photoflavin fromV. fischeri. A monomer-dimer equilibrium also explains the previously reported high correlation times for theV. harveyi luciferase-flavin species. It is proposed that the self-association competes with the lumazine protein interaction in the bioluminescence reaction.