THE VARIATION OF INVARIANT LINES AND LIMIT CYCLES FOR A QUADRATIC DIFFERENTIAL SYSTEM

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Sets of Type (a, b) From Subgroups of ΓL(1, pR)

In this paper k-sets of type (a, b) with respect to hyperplanes are constructed in finite projective spaces using powers of Singer cycles. These are then used to construct further examples of sets of type (a, b) using various disjoint sets. The parameters of the associated strongly regular graphs are also calculated. The construction technique is then related to work of Foulser and Kallaher classifying rank three subgroups of AL(1, p ^R). It is shown that the sets of type (a, b) arising from the Foulser and Kallaher construction in the case of projective spaces are isomorphic to some of those constructed in the present paper.     

Curvatures and Currents for Unions of Sets with Positive Reach, II

A class of subsets of ^d which can berepresented as locally finite unions of sets with positive reach isconsidered. It plays a role in PDE's on manifolds with singularities.For such a set, the unit normal cycle (determining the d – 1curvature measures) is introduced as a (d – 1)-currentsupported by the unit normal bundle and its properties are established.It is shown that, under mild additional assumptions, the unit normalcycle (and, hence, also the curvature measures) of such a set can beapproximated by that of a close parallel body or, alternatively, by themirror image of that of the closure of the complement of the parallelbody (which has positive reach). Finally, the mixed curvature measuresof two sets of this class are introduced and a translative integralgeometric formula for curvature measures is proved.     

Vertex‐disjoint cycles of length at most four each of which contains a specified vertex*

We obtain a sharp minimum degree condition δ (G) ≥ of a graph G of order n ≥ 3k guaranteeing that, for any k distinct vertices, G contains k vertex‐disjoint cycles of length at most four each of which contains one of the k prescribed vertices. © 2001 John Wiley & Sons, Inc. J Graph Theory 37: 37–47, 2001     

Mixed Partitions of Projective Geometries

Starting from a linear collineation of PG(2n–1,q) suitably constructed from a Singer cycle of GL(n,q), we prove the existence of a partition of PG(2n–1,q) consisting of two (n–1)-subspaces and caps, all having size (qⁿ–1)/(q–1) or (qⁿ–1)/(q+1) according as n is odd or even respectively. Similar partitions of quadrics or hermitian varieties into two maximal totally isotropic subspaces and caps of equal size are also obtained. We finally consider the possibility of partitioning the Segre variety of PG(8,q) into caps of size q²+q+1 which are Veronese surfaces.     

Langford系统Hopf分叉的线性反馈控制

分析Langford系统的Hopf分叉现象，并研究采用线性反馈控制方法控制该系统的Hopf分叉.从理论上推导出受控系统产生Hopf分叉的条件，给出了某些极限环的解析表达式，对该系统进行了分叉点的转移与极限环的稳定性控制.数值模拟说明本文采用的方法对Langford系统的Hopf分叉控制是有效的. 关键词： Langford系统 反馈控制 Hopf分叉 极限环     

A conceptual high flux reactor design with scope for use in ADS applications

A 100 MWt reactor design has been conceived to support flux level of the order of 10¹⁵ n/cm²/s in selected flux trap zones. The physics design considers high enriched metallic alloy fuel in the form of annular plates placed in a D₂O moderator tank in a hexagonal lattice arrangement. By choosing a tight lattice pitch in the central region and double the lattice pitch in the outer region, it is possible to have both high fast flux and thermal flux trap zones. By design the flux level in the seed fuel has been kept lower than in the high flux trap zones so that the burning rate of the seed is reduced. Another important objective of the design is to maximize the time interval of refueling. As against a typical refueling interval of a few weeks in such high flux reactor cores, it is desired to maximize this period to as much as six months or even one year. This is possible to achieve by eliminating the conventional control absorbers and replacing them with a suitable amount of fertile material loading in the reactor. Requisite number of seedless thorium-aluminum alloy plates are placed at regular lattice locations vacated by seed fuel in alternate fuel layers. It is seen that these thorium plates are capable of acquiring asymptotic fissile content of 14 g/kg in about 100 days of irradiation at a flux level of 8 × 10¹⁴ n/cm²/s. In summary, the core has a relatively higher fast flux in the central region and high thermal flux in the outer region. The present physics design envisages a flat core excess reactivity for the longest possible cycle length of 6 months to one year. It is also possible to modify the design for constant subcriticality for about the same period or longer duration by considering neutron spallation source at the centre and curtailing the power density in the inner core region by shielding it with a layer of thoria fuel loading.      

Operation of CANDU power reactor in thorium self-sufficient fuel cycle

This paper presents the results of calculations for CANDU reactor operation in thorium fuel cycle. Calculations are performed to estimate the feasibility of operation of heavy-water thermal neutron power reactor in self-sufficient thorium cycle. Parameters of active core and scheme of fuel reloading were considered to be the same as for standard operation in uranium cycle. Two modes of operations are discussed in the paper: mode of preliminary accumulation of ²³³U and mode of operation in self-sufficient cycle. For the mode of accumulation of ²³³U it was assumed for calculations that plutonium can be used as additional fissile material to provide neutrons for ²³³U production. Plutonium was placed in fuel channels, while ²³²Th was located in target channels. Maximum content of ²³³U in target channels was estimated to be ∼13 kg/t of ThO₂. This was achieved by irradiation for six years. The start of the reactor operation in the self-sufficient mode requires ²³³U content to be not less than 12 kg/t. For the mode of operation in self-sufficient cycle, it was assumed that all channels were loaded with identical fuel assemblies containing ThO₂ and certain amount of ²³³U. It is shown that nonuniform distribution of ²³³U in fuel assembly is preferable.      

The ridge waveguide fabrication with periodically poled MgO-doped lithium niobate for green laser

Ridge waveguides were fabricated using an external field, a precision lapping machine and neutron loop discharge (NLD) in magnesium-oxide-doped lithium niobate. The measured quasi-phase-matching (QPM) wavelength of the second-harmonic generation (SHG) in a 30 mm long periodically poled magnesium-doped lithium niobate (PPMgLN) ridge waveguide which has a domain period of 6.8 μm is about 532 nm. A fabricated periodically poled magnesium-doped lithium niobate ridge waveguide was duty cycle of 51.9 ± 2.83% and demonstrated second-harmonic generation. By using this periodically poled magnesium-doped lithium niobate ridge waveguide, highly effective, low-cost optical devices with high power or short wavelength can be achieved.