Energy transfer in double plate system dynamics

The study of energy transfer between coupled subsystems in a hybrid system is very important for applications. This paper presents an analytical analysis of energy transfer between plates of a visco-elastically connected double-plate system in free transversal vibrations. The analytical analysis shows that the visco-elastic connection between plates is responsible for the appearance of two-frequency regime in the time function, which corresponds to one eigen amplitude function of one mode, and also that time functions of different vibration modes are uncoupled, but energy transfer between plates in one eigen mode appears. It was shown for each shape of vibrations. Series of the two Lyapunov exponents corresponding to the one eigen amplitude mode are expressed by using the energy of the corresponding eigen amplitude time component.     

The transversal homoclinic point of a saddle-node implies horseshoe

A method of identifying the existence of horseshoe for a two-dimension diffeomorphism is introduced and utilized to generalize the Birkhoff-Smale Theorem to the saddle-node case. Project supported by the National Natural Science Foundation of China (Grant No. 19531070).     

完全单半群及完全正则半群的逆断面

指出完全单半群Ｓ的任何一个Ｆ－类是逆断面,且为Ｑ－逆断面,而Ｓ的任何一个逆断面必是一个Ｆ－类,因而所有逆断面同构。并且给出完全正则半群的逆断面存在的充要条件。     

Affine planar geodesic immersions with maximal codimension

This work gives a classification theorem for affine immersions with planar geodesics in the case where the codimension is maximal. Vrancken classified parallel affine immersions in this case and obtained, among others, generalized Veronese submanifolds. In this work it is shown that the immersions with planar geodesics are the same as the parallel ones in the considered case. A geometric interpretation of parallel immersions is also given： The affine immersions with pointwise planar normal sections （with respect to the equiaffine transversal bundle） are parallel. This result is verified for surfaces in R4 and for immersions with the maximal codimension.     

时间可逆系统的等时中心问题

若在中心附近的闭轨线都具有相同的周期,则此中心称为等时中心. 时间可逆多项式系统的等时中心问题是一类公开问题. 为了构造性地解决这一难题,讨论一类范围更广的时间可逆解析动力系统, 给出相应横截交换系统的递推公式,此公式可以用于等时中心条件的推导. 在递推公式的基础上,以吴特征集方法为工具,给出一类时间可逆三次系统具有横截交换系统的充要条件.     

Further Results on Large Sets of Resolvable Idempotent Latin Squares

An idempotent Latin square of order v is called resolvable and denoted by RILS(v) if the off‐diagonal cells can be resolved into disjoint transversals. A large set of resolvable idempotent Latin squares of order v, briefly LRILS(v), is a collection of RILS(v)s pairwise agreeing on only the main diagonal. In this paper, it is established that there exists an LRILS(v) for any positive integer , except for , and except possibly for .     

Split quasi-adequate semigroups

The so-called split IC quasi-adequate semigroups are in the class of idempotent-connected quasi-adequate semigroups. It is proved that an IC quasi-adequate semigroup is split if and only if it has an adequate transversal. The structure of such semigroup whose band of idempotents is regular will be particularly investigated. Our obtained results enrich those results given by McAlister and Blyth on split orthodox semigroups.     

Checking key integrity efficiently for high-speed quantum key distribution using combinatorial group testing

With the increasing key generation rate in practical quantum key distribution, checking key integrity efficiently becomes an important problem. Since the original method that utilizes one hash value for a key string has to discard all the key bits even if just one error bit exists, it may eventually limit the practical rate of key generation. In this paper, we propose a new scheme based on combinatorial group testing to identify the rare error bits so as to avoid dropping all the key bits. Experimental results show that the scheme can precisely locate the error bits if the number of error bits is within the maximum guaranteed number set by the scheme while the overhead is insignificant (for a 10⁶-bit key, additional bits: 0.1% of the key; hashing time: 16 ms; checking time: 22 ms) and it can still keep the majority of the correct bits (95%) even if the number of error bits is 10 times of the maximum. The results also indicate that the minimum key size for the CGT-based scheme to gain an advantage over the original method is about 2 × 10⁴ bits.