An IC100 cyclotron based facility for producing nuclear filters and for scientific and applied research

The cyclotron IC-100 station, based on the Laboratory of Nuclear Reactions (JINR, Dubna, Russia), provides the industrial construction of nuclear filters. During modernization, the cyclotron was equipped with a superconducting ECR-ion source and an axial injection system. The specialized beam channel with a two coordinate scanning system and equipment for irradiating polymer films was installed in the implantation part of the station. High intensity heavy ion beams of Ne, Ar, Fe, Kr, Xe, I, and W have been accelerated to 1 MeV/nucleon energy. The investigation into irradiated crystals features and irradiation of different polymer films is provided. Also, a few thousands square meters of track films with holes in the wide range of densities were produced. The cyclotron-based station is capable of solving different kinds of scientific and applied problems as well. The text was submitted by the authors in English.     

Investigations of electron beam characteristics using an accelerator based on a magnetron gun with a secondary-emission cathode

The reliability and service life of accelerating installations are substantially determined by the lifetime of electron sources. The accelerator under consideration has a magnetron gun with a channel-free cold secondary-emission cathode in crossed fields as an electron source [1, 2]. In the present work, the data of the electron beam parameters obtained in the accelerator based on the magnetron gun with a secondary-emission cathode are given, and possible secondary uses are suggested. The text was submitted by the authors in English.     

Enhanced spontaneous emission factor for microcavity lasers

The microcavity and the influence of nonradiative recombination can control spontaneous emission. An analytic resolution of rate equation is studied for microcavity lasers. The relationship between output prop- erties and structural parameters of multi-quantum wells (MQWs) is obtained. One of the most important consequences of the incrcased spontaneous emission factor is the reduction of laser threshold. It is found that the characteristic curve of a "thresholdless" laser is strongly nonradiative depopulation-dependent. The light output is increased by the enhanced well number and the reduced width. In particular, there is an optimal well number corresponding to the lowest threshold current density for MQW structure in the microcavity lasers.     

Varieties of Complete Pairs of Zero-Dimensional Subschemes of Lengths ≥2 and ≥4 in Algebraic Surfaces

We prove that the varieties of complete pairs of zero-dimensional subschemes of lengths d ₁ 2, d ₂ 4 on a smooth irreducible projective algebraic surface are singular.     

The geometrical interpretation of uncertainty relation in Minkowski space

Clifford algebraic geometry corresponds to Minkowski space. Using the discrete structure of Minkowski space, we can abstract a class n-dimensional hyperbolic Hilbert phase space. To discussing the causality of physical event in Minkowski space, we can obtain the geometrical interpretation of uncertainty relation.     

Consistent Initialization for Nonlinear Index-2 Differential–Algebraic Equation: Large Sparse Systems in MATLAB

An important component of any initial-value solver for higher-index differential–algebraic equations consists in the computation of consistent initial values. In a recent paper [5], an algorithm is proposed which is applicable to a very general class of index-2 systems. Unfortunately, the computational expense is rather high. We present a modification of this approach, which gives rise to a MATLAB implementation capable of handling systems of moderate dimension (several thousands of unknowns). The algorithm is illustrated by examples.     

Algebraic Operations and Generic Effects

Given a complete and cocomplete symmetric monoidal closed category V and a symmetric monoidal V-category C with cotensors and a strong V-monad T on C, we investigate axioms under which an Ob C-indexed family of operations of the form _x :(Tx) ^v (Tx) ^w provides semantics for algebraic operations on the computational -calculus. We recall a definition for which we have elsewhere given adequacy results, and we show that an enrichment of it is equivalent to a range of other possible natural definitions of algebraic operation. In particular, we define the notion of generic effect and show that to give a generic effect is equivalent to giving an algebraic operation. We further show how the usual monadic semantics of the computational -calculus extends uniformly to incorporate generic effects. We outline examples and non-examples and we show that our definition also enriches one for call-by-name languages with effects.     

On the number of distinct prime factors of an odd perfect number

It is not known whether or not there exists an odd perfect number. We describe an algorithmic approach for showing that if there is an odd perfect number then it has t distinct prime factors, and we discuss its application towards showing that t9.     

Classification of two-orbit varieties

We obtain the classification of two-orbit varieties, i.e. the normal complete complex algebraic varieties on which a reductive complex algebraic group acts with two orbits. We prove also Luna's conjecture saying that these varieties are spherical, i.e. admit a dense orbit of a Borel subgroup. Received: September 1, 2000