On the gonality of stable curves

In this paper we use admissible covers to investigate the gonality of a stable curve C over $\mathbb{C}$. If C is irreducible, we compare its gonality to that of its normalization. If C is reducible, we compare its gonality to that of its irreducible components. In both cases we obtain lower and upper bounds. Furthermore, we show that four admissible covers constructed give rise to generically injective maps between Hurwitz schemes. We show that the closures of the images of three of these maps are components of the boundary of the target Hurwitz schemes, and the closure of the image of the remaining map is a component of a certain codimension‐1 subscheme of the boundary of the target Hurwitz scheme.     

On Klein’s icosahedral solution of the quintic

We present an exposition of the icosahedral solution of the quintic equation first described in Klein’s classic work ‘Lectures on the icosahedron and the solution of equations of the fifth degree’. Although we are heavily influenced by Klein we follow a slightly different approach which enables us to arrive at the solution more directly.     

Generic linear systems for projective CR manifolds

For compact CR manifolds of hypersurface type which embed in complex projective space, we show that for all k large enough there exist linear systems of O(k) which when restricted to the CR manifold are generic in a suitable sense. These systems are constructed using approximately holomorphic geometry.     

Stochastic matrices arising from genetic inheritance

We establish a connection between two different approaches that can be used to describe the same genetic situation. We focus on the notion of coalgebra with genetic realization introduced by Tian and Li and show how their structure constants can be used to characterize different stochastic processes related to the genetic inheritance.     

Commutators of symmetries in characteristic 2

Let V be a nonsingular vector space over a field K of characteristic 2 with |K|>3. Suppose K is perfect and π is an element in the special orthogonal group SO(V)=Ω(V) with dimB(π)=2d. The length of π with respect to the symmetry commutators is d if B(π) is not totally isotropic; otherwise it is d+1.     

A generalization of the spherical inversion

In the present article, we introduce a generalization of the spherical inversion. In particular, we define an inversion with respect to an ellipsoid, and prove several properties of this new transformation. The inversion in an ellipsoid is the generalization of the elliptic inversion to the three-dimensional space. We also study the inverse images of planes, spheres, ellipsoids and other curves. We use the software Mathematica to generate these graphics. Finally, we generalize the Pappus chain theorem to ellipsoids.     

A unified method for boundedness in fully parabolic chemotaxis systems with signal-dependent sensitivity

This paper deals with the Keller–Segel system where Ω is a bounded domain in with smooth boundary , ; χ is a nonnegative function satisfying for some and . In the case that and , Fujie 2 established global existence of bounded solutions under the condition . On the other hand, when , Winkler 14 asserted global existence of bounded solutions for arbitrary . However, there is a gap in the proof. Recently, Fujie tried modifying the proof; nevertheless it also has a gap. It seems to be difficult to show global existence of bounded solutions for arbitrary . Moreover, the condition for K when cannot connect with the condition when . The purpose of the present paper is to obtain global existence and boundedness under more natural and proper condition for χ and to build a mathematical bridge between the cases and .     

单片机控制的速度发送装置的应用研究

本文介绍了一种由ＭＣＳ—５１单片机控制的速度发送装置，阐述了该速度发送装置的作用，探讨了其硬件设计特点和软件设计所依据的基本原理。最后，通过实际分析，给出程序流程图。     

Radiotracer Evaluation of Laterite and Coal-Ash Dust Discharged into Environment

Abstract

In Elbasan steel plant a large quantity of dust is discharged into the environment by laterite fluidized bed calciner and the coal boiler for steam production.

By means of radiotracers the erosion of the laterite in the fluidized bed calciner was estimated experimentally. Based on the experimental data a mathematical model has been constructed for the erosion, which permits calculation of the mass of the dust deriving from erosion when the granulometric composition of the mineral on entry to the calciner is known.

The efficiency of two types of cyclones in laterite calciner and coal boiler, for three granulometric classes of laterite dust and coal-ash was studied.

Ways for reducing the quantity of dust discharged into environment are proposed.