Combinatorial invariance of Stanley-Reisner rings

In this short note we show that Stanley—Reisner rings of simplicial complexes, which have had a dramatic application in combinatorics [2, p. 41], possess a rigidity property in the sense that they determine their underlying simplicial complexes.     

Exact solutions for Belousov-Zhabotinskii reaction-diffusion system

Abstract. We consider the following simplified model for the Belousou-Zhabotinskii(B-Z)reaction:     

Zero cycles on conic fibrations and a conjecture of Bloch

Let X be a smooth projective surface over a number field k. Let (CH₀(X)) denote the Chow group of zero-cyles modulo rational equivalence on X. Let CH₀(X) be the subgroup of CH ₀(X) consisting of classes which vanish when going over to an arbitrary completion of k. Bloch put forward a conjecture asserting that this group is isomorphic to the Tate-Shafarevich group of a certain Galois module atttached to X. In this paper, we disprove this general conjecture. We produce a conic bundle X over an elliptic curve, for which the group (CH₀(X) is not zero, but the Galois-theoretic Tate-Shafarevich group vanishes.     

Essential spectrum and -solutions of one-dimensional Schrödinger operators

In 1949, Hartman and Wintner showed that if the eigenvalue equations of a one-dimensional Schrödinger operator possess square integrable solutions, then the essential spectrum is nowhere dense. Furthermore, they conjectured that this statement could be improved and that under this condition the essential spectrum might always be void. This is shown to be false. It is proved that, on the contrary, every closed, nowhere dense set does occur as the essential spectrum of Schrödinger operators which satisfy the condition of existence of -solutions. The proof of this theorem is based on inverse spectral theory.

     

On Segal-Wilson's construction for the τ-functions of the constrained KP hierarchies

In this Letter, we study the constrained KP hierarchies by employing Segal-Wilson's theory on the -functions of the KP hierarchy. We first describe the elements of the Grassmannian which correspond to solutions of the constrained KP hierarchy, and then we show how to construct its rational and soliton solutions from these elements of the Grassmannian.     

Theq-harmonic oscillator and the Al-Salam and Carlitz polynomials

One more model of aq-harmonic oscillator based on theq-orthogonal polynomials of Al-Salam and Carlitz is discussed. The explicit form ofq-creation andq-annihilation operators,q-coherent states and an analog of the Fourier transformation are established. A connection of the kernel of this transform with a family of self-dual biorthogonal rational functions is observed.     

Perturbation analysis of the orthogonal procrustes problem

Given two arbitrary real matricesA andB of the same size, the orthogonal Procrustes problem is to find an orthogonal matrixM such that the Frobenius norm MA – B is minimized. This paper treats the common case when the orthogonal matrixM is required to have a positive determinant. The stability of the problem is studied and supremum results for the perturbation bounds are derived.     

Functional connectedness and Darboux property of multivalued functions

To 80^th birthday of Paul Erds     

Banach algebras of singular integral operators with piecewise continuous coefficients. General contour and weight

The Banach algebra generated by one-dimensional linear singular integral operators with matrix valued piecewise continuous coefficients in the spaceL _p (,) with an arbitrary weight is studied. The contour consists of a finite number of closed curves and open arcs with satisfy the Carleson condition. The contour may have a finite number of points of selfintersection. The symbol calculus in this algebra is the main result of the paper.     

Enzymatic hydrolysis reaction of phospholipids in monolayers

The hydrolysis reaction of , and , -dipalmitoylphosphatidylcholine (DPPC) catalized by bee venom phospholipase A₂ was studied in spreading monolayer at the water/air interface. DPPC and the hydrolysis products, palmitic acid and -lysophosphatidylcholine, palmitoyl were characterized at the interface by means of surface pressure, surface potential and ellipsometric measurements. Furthermore, mixed monolayers of reagents and products were investigated to ascertain their miscibility. The results show that the hydrolysis reaction can be followed by the decrease of surface pressure with time on subphases containing β-cyclodextrin, a well-known complexing agent of many amphiphilic compounds. The order of the reaction, the kinetic constant and other kinetic parameters are deduced.