具有逆断面的局部逆半群

Let S be a locally inverse semigroup with an inverse transversal S°. In this paper, we construct an amenable partial order on S by an R-cone. Conversely, every amenable partial order on S can be constructed in this way. We give some properties of a locally inverse semigroup with a Clifford transversal. In particular, if S is a locally inverse semigroup with a Clifford transversal, then there is an order-preserving bijection from the set of all amenable partial orders on S to the set of all R-cones of S.     

具有逆断面的正则半群的同余的表示

具有道断面S°的正则半群可表示为有Saito's结构的半群W（I，S°，Λ，*，α，β）.我们利用由I，S°和Λ上的同余构成的所谓同余聚抽象地表示这类半群上的同余，进而给出了这类半群的同态象的构造法．     

Permanents and Determinants of Latin Squares

Let L be a latin square of indeterminates. We explore the determinant and permanent of L and show that a number of properties of L can be recovered from the polynomials and per(L). For example, it is possible to tell how many transversals L has from per(L), and the number of 2 × 2 latin subsquares in L can be determined from both and per(L). More generally, we can diagnose from or per(L) the lengths of all symbol cycles. These cycle lengths provide a formula for the coefficient of each monomial in and per(L) that involves only two different indeterminates. Latin squares A and B are trisotopic if B can be obtained from A by permuting rows, permuting columns, permuting symbols, and/or transposing. We show that nontrisotopic latin squares with equal permanents and equal determinants exist for all orders that are divisible by 3. We also show that the permanent, together with knowledge of the identity element, distinguishes Cayley tables of finite groups from each other. A similar result for determinants was already known.     

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.     

The Existence of Mixed Orthogonal Arrays with Four and Five Factors of Strength Two

Symmetric orthogonal arrays and mixed orthogonal arrays are useful in the design of various experiments. They are also a fundamental tool in the construction of various combinatorial configurations. In this paper, we investigated the mixed orthogonal arrays with four and five factors of strength two, and proved that the necessary conditions of such mixed orthogonal arrays are also sufficient with several exceptions and one possible exception.     

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.     

TiNi相变悬臂梁的横向冲击特性实验研究

利用改装的霍普金森压杆装置对TiNi形状记忆合金圆截面悬臂梁进行了横向冲击实验研究,并与45#钢悬臂梁的实验结果进行了对比,目的是探索相变对结构动态响应的影响。结果表明:在同样冲击条件下,TiNi悬臂梁的吸能效率优于钢悬臂梁;发现冲击过程中,TiNi试件根部内侧可能形成局部相变铰,使阻力曲线的斜率发生变化;卸载后相变铰消失,TiNi悬臂梁试件基本回复原状,钢试件则留下显著的残余变形。TiNi悬臂梁的冲击特性受热弹性马氏体相变和逆相变的支配,不同于传统的弹塑性机制。     

具有逆断面的纯正群的构造

本文用具有半格断面的带和Clifford半群给出具有逆断面的纯正群的一个构造定理.     

On the number of minimal transversals in 3-uniform hypergraphs

We prove that the number of minimal transversals (and also the number of maximal independent sets) in a 3-uniform hypergraph with n vertices is at most cⁿ, where c≈1.6702. The best known lower bound for this number, due to Tomescu, is adⁿ, where d=10^1/5≈1.5849 and a is a constant.