On the theorems of Drake and Lenz

A generalization and an improvement of the results of Drake and Lenz on the constructions of projective Hjelmslev planes are obtained. Using this, some new series of invariant pairs including 4 new pairs (t, 2),t 1000, for projective Hjelmslev planes are obtained.     

Numerical treatment of delay differential equations by Hermite Interpolation

Summary A class of numerical methods for the treatment of delay differential equations is developed. These methods are based on the wellknown Runge-Kutta-Fehlberg methods. The retarded argument is approximated by an appropriate multipoint Hermite Interpolation. The inherent jump discontinuities in the various derivatives of the solution are considered automatically.Problems with piecewise continuous right-hand side and initial function are treated too. Real-life problems are used for the numerical test and a comparison with other methods published in literature.     

Cellularity in polyhedra

A compact subset X of a polyhedron P is cellular in P if there is a pseudoisotropy of P shrinking precisely X to a point. A proper surjection between polyhedra f:P→Q is cellular if each point inverse of f is cellular in P. It is shown that if f:P→Q is a cellular map and either P or Q is a generalized n-manifold, n≠4, then f is approximable by homeomorphisms. Also, if P or Q is an n-manifold with boundary, n≠4, 5, then a cellular map f:P→Q is approximable by homeomorphisms. A cellularity criterion for a special class of cell-like sets in polyhedra is established.     

The rational line partitions every self-dense metrisable space

In the present note we shall prove that a metrisable space can be partitioned by the rational line if that space is self-dense. This gives an affirmative answer to a question raised by Rankston-McGovern [1].     

Valence band and chemical interactions of Zn/CdSnAs2 interfaces

X-ray photoelectron spectroscopy (XPS) together with argon ion sputtering was used to investigate the interface of the Zn/CdSnAs₂ system at various temperatures. The formation of an intermediate compound between Zn and As is proposed. The surface enrichment of Cd and Sn at 200 and 400°C is explained in terms of bond breaking and lattice strain theories.NCL Communication No. 4352     

CARS measurements of temperature and species concentrations in an IC engine

Temperature measurements alone, and also simultaneous CO₂ concentration and temperature measurements, have been performed inside a fired IC engine. To tackle the two main problems encounted when making measurements in an engine (i.e., cycle-to-cycle variations and beam steering by density gradients), the shot-by-shot referencing technique and the in situ referencing technique using N₂ to determine [CO₂] were used. The temperature is deduced from the broadband N₂ CARS signal and narrow band detection is used for CO₂. A representative example of temperature measurements is given which shows a correlation between temperature and knocking intensity in the burnt gas of a knocking engine. The first simultaneous determinations of temperature and [CO₂] are also reported; so far these are reliable only during the compression stoke.     

基于光子晶体光纤中FWM的4×10 Gbit/s全光波长转换

 多波长转换对于增强波分复用光网络的灵活性具有重要意义。基于光子晶体光纤中的多四波混频原理,实现了4×10 Gbit/s全光波长转换,深入调查了泵浦功率、光纤长度、信号光与泵浦光偏振失配对波长转换信号质量的影响。结果表明：当泵浦光功率从6 dBm到20 dBm增长的过程中,转换信号Q因子随泵浦光功率增大而增大,最大为82.01,光纤长度从50 m到120 m变化过程中,转换信号Q因子最大为57.41,而随着信号光与泵浦光偏振失配角的增大,转换信号Q因子逐渐降低,当失配角大于60°后,转换信号质量急剧下降。     

Eisenstein type series for Calabi–Yau varieties

In this article we introduce an ordinary differential equation associated to the one parameter family of Calabi–Yau varieties which is mirror dual to the universal family of smooth quintic three folds. It is satisfied by seven functions written in the q-expansion form and the Yukawa coupling turns out to be rational in these functions. We prove that these functions are algebraically independent over the field of complex numbers, and hence, the algebra generated by such functions can be interpreted as the theory of (quasi) modular forms attached to the one parameter family of Calabi–Yau varieties. Our result is a reformulation and realization of a problem of Griffiths around seventies on the existence of automorphic functions for the moduli of polarized Hodge structures. It is a generalization of the Ramanujan differential equation satisfied by three Eisenstein series.