The thorium cycle for fast breeder reactors

The role that could be played by liquid metal-cooled fast breeder reactors (LMFBRs) in the utilization of India’s considerable thorium resources is reviewed in this article. Distinct advantages of thorium-based fuels over plutonium-uranium fuels in LMFBRs pertain to a more favourable coolant voiding reactivity coefficient and better fuel element irradiation stability. The poorer breeding capability of thorium-fuelled fast reactors can in principle be overcome by improved core design and development of advanced fuel concepts. The technical feasibility of such advanced thorium fuels and core designs must be established by sustained research and development. It is also necessary to efficiently close the thorium fuel cycle of fast breeder reactors by appropriate development of the fuel reprocessing and refabrication stages. The Fast Breeder Test Reactor (FBTR) at Kalpakkam is expected to be an important tool for development of thorium fuel and fuel cycle technology. A quick look at the economics of the thorium cycle for fast reactors, vis-a-vis the more conventional uranium cycle indicates only a small and acceptable cost disadvantage on account of the need for remote fabrication of recycled thorium fuel. The authors felicitate Prof. D S Kothari on his eightieth birthday and dedicate this paper to him on this occasion.     

On large sets of almost Hamilton cycle decompositions

A large set of CS(v, k, λ), k‐cycle system of order v with index λ, is a partition of all k‐cycles of K_v into CS(v, k, λ)s, denoted by LCS(v, k, λ). A (v ? 1)‐cycle is called almost Hamilton. The completion of the existence spectrum for LCS(v, v ? 1, λ) only depends on one case: all v ≥ 4 for λ = 2. In this article, it is shown that there exists an LCS(v, v ? 1,2) for any v ≡ 0,1 (mod 4) except v = 5, and for v = 6,7,10,11. © 2006 Wiley Periodicals, Inc. J Combin Designs 16: 53–69, 2008     

THE UNIQUENESS OF LIMIT CYCLE AND THE STRUCTURE OF CRITICAL POINT AT INFINITY FOR A CLASS OF CUBIC SYSTEM

A class of cubic system, which is an accompany system of a quadratic differential one, is studied. It is proved that the system has at most one limit cycle, and the critical point at infinity is a higher order one. The structure and algebraic character of the critical point at infinity are obtained.     

Molecular and crystal structure of N-[2H-1,4-benzoxazin-3(4H)-ylidene]-cyclohexane aminium chloride

X-ray diffraction investigation showed that protonation of 4H-benzo-[1,4]-oxazin-3-ylidene-cyclohexylamine occurs at the exocyclic nitrogen atom. In crystal, the cation has a structure with a distinct exocyclic C=N bond.     

Two types of limit cycles of a resonant converter modelled by a three-dimensional system

In this paper, the long-run dynamics of a resonant converter is studied. The modelling of the resonant converter can be done using various approximations and the long-run dynamics of the two dimensional cases were earlier analysed. In this paper, we discuss results that can be extended to the three dimensional case. It seems that limit cycles describe the long-run dynamics in important situations in the three dimensional case, too. Our objective is to relate the limit cycles found previously in the two-dimensional case to those found now in the three dimensional approximation.     

Hamilton非二部图的弱泛圈性

图G称为弱泛圈图是指G包含了每个长为t(g(V)≤l≤c(G))的圈,其中g(G),c(v)分别是G的围长与周长.1997年Brandt提出以下猜想:边数大于[n2/4]-n 5的n阶非二部图为弱泛圈图.1999年Bollobas和Thomason证明了边数不小于[n2/4]-n 59的n阶非二部图为弱泛圈图.作者证明了如下结论:设G是n阶Hamilton非二部图,若G的边数不小于[n2/4]-n 12,则G为弱泛圈图.     

On a cycle partition problem

Let G be any graph and let c(G) denote the circumference of G. We conjecture that for every pair c₁,c₂ of positive integers satisfying c₁+c₂=c(G), the vertex set of G admits a partition into two sets V₁ and V₂, such that V_i induces a graph of circumference at most c_i, i=1,2. We establish various results in support of the conjecture; e.g. it is observed that planar graphs, claw-free graphs, certain important classes of perfect graphs, and graphs without too many intersecting long cycles, satisfy the conjecture.This work is inspired by a well-known, long-standing, analogous conjecture involving paths.     

Geometric criteria for the nonexistence of cycles in Gause-type predator-prey systems

The global stability of a multi-species interacting system has apparently important biological implications. In this paper we study the global stability of Gause-type predator-prey models by providing new criteria for the nonexistence of cycles and limit cycles. Our criteria have clear geometrical interpretations and are easier to apply than other methods employed in recent studies. Using these criteria and related techniques we are able to develop new results on the existence and uniqueness of cycles in Gause-type models with various growth and response functions.

     

一类可积非哈密顿系统的极限环数目的上界

研究了一类可积非哈密顿系统的极限环的上界,利用Abel积分证明其在一类2n+1次多项式扰动下至多可以产生n+1个极限环,并且是可以实现的.