A theoretical overview of hypernuclear weak decay

The physics of the weak decay of hypernuclei is briefly reviewed from a theoretical point of view. Special regard is devoted to the recent progress concerning the determination of the non-mesonic decay widths and the asymmetry parameters. Convincing evidence has been achieved for a solution of the long-standing puzzle on the ratio Γ_n/Γ_p. Very recently, it has been shown that the exchange of a ππ pair in the weak mechanism plays a crucial role in explaining the discrepancies between theory and experiment on the decay asymmetries.     

A periodic isoperimetric problem related to the unique games conjecture

We prove the endpoint case of a conjecture of Khot and Moshkovitz related to the unique games conjecture, less a small error. Let n ≥ 2. Suppose a subset Ω of n‐dimensional Euclidean space satisfies ?Ω = Ω^c and Ω + v = Ω^c (up to measure zero sets) for every standard basis vector . For any and for any q ≥ 1, let and let . For any x ∈ ?Ω, let N(x) denote the exterior normal vector at x such that ‖N(x)‖₂ = 1. Let . Our main result shows that B has the smallest Gaussian surface area among all such subsets Ω, less a small error: In particular, Standard arguments extend these results to a corresponding weak inequality for noise stability. Removing the factor 6 × 10^?9 would prove the endpoint case of the Khot‐Moshkovitz conjecture. Lastly, we prove a Euclidean analogue of the Khot and Moshkovitz conjecture. The full conjecture of Khot and Moshkovitz provides strong evidence for the truth of the unique games conjecture, a central conjecture in theoretical computer science that is closely related to the P versus NP problem. So, our results also provide evidence for the truth of the unique games conjecture. Nevertheless, this paper does not prove any case of the unique games conjecture.     

Normal phase HPLC-based activity profiling of non-polar crude plant extracts – acetylcholinesterase inhibiting guttiferones from Montrouziera cauliflora as a case study

The study describes bioactive compounds as inhibitors of acetylcholinesterase (AChE), from the stem bark extract of Montrouziera cauliflora, selected among 19 dichloromethane extracts from Clusiaceae species. Our work focused on the development of an original normal phase HPLC microfractionation strategy to rapidly assess highly active zones from this crude active non-polar plant extract. Two different microfraction collection methods were evaluated for the assessment of the AChE inhibition. Two guttiferones and a tocotrienol were directly isolated among five compounds identified off-line by NMR after upscaling the fractionation and their AChE inhibition was evaluated. The strengths and weaknesses of the two microfractionation collection methods for HPLC-AChE activity-based profiling are discussed.     

矩形区域不等圆形随机堆放的数值模拟

将若干待堆放的圆形堆放到一个给定矩形区域,是一类特殊的Packing问题。针对这一具有NP难度的困难问题,提出一种快速的数值模拟方法以及模拟力学检验的方法。该方法将圆形堆放的力学平衡规律化为几何形体相互接触的几何条件,把大量的圆形按级配及分布律等约束条件,随机堆放形成空间区域。按此方法得到的圆形堆体,在不加外力的情形下即可保持自身的稳定。使用该方法,在边长为15cm的正方形区域内,取圆形的直径范围为0.5cm~4cm,模拟了孔隙率小于25%(面积比)的圆形堆体。最后,将所模拟的圆形堆体试件进行了有限元网格划分及力学加载试算,结果表明该堆体是稳定的。为进一步在细观层次研究圆形堆体提供了一个快速的数值模拟方法。     

带多重选择的最短路问题:复杂性和算法

本文提出了带出重选择的是短路问题,建立了该问题的数学模型,利用背包问题的一个变形问题－带限制选择的背包问题,证明了该问题是ＮＰ－Ｃ的,最后利用动态规则给出了一个伪多项式算法,其时间复杂性Ｏ（Ｃｈｍｎ）,其中ｈ是最大的选择重数。     

一类带核的平行机排序问题

研究了一类工件具有相似加工时间的带核的平行机排序问题,运用ＬＰＴ算法求解,得到ＬＰＴ算法界的精确估计并对问题的某些情形,给出了界紧的例子。     

基于遗传算法的TSP问题研究

TSP是一个典型的组合优化问题，并且是一个NP难题，其可能的路径总数与城市数目n是成指数型增长的，所以一般很难精确地求出其最优解，因而寻找出有效的近似求解算法就具有重要的意义。现就提出的一种求解TSP问题比较有效的改进的遗传算法进行了研究，从遗传算子、评估函数、种群多样性等方面对算法进行了分析，并对实例CHN144进行了测试，实验结果表明文中提出的算法在求解TSP问题上是有效的。     

How to construct constant-round zero-knowledge proof systems for NP

Constant-round zero-knowledge proof systems for every language in are presented, assuming the existence of a collection of claw-free functions. In particular, it follows that such proof systems exist assuming the intractability of either the Discrete Logarithm Problem or the Factoring Problem for Blum integers.     

Graph‐based optimal asynchronous scheduling in large propagation delay underwater acoustic sensor networks

Optimal scheduling is essential to minimize the time wastage and maximize throughput in high propagation delay networks such as in underwater and satellite communication. Understanding the drawbacks of synchronous scheduling, this paper addresses an asynchronous optimal scheduling problem to minimize the time wastage during the transmission. The proposed scheduling problem is analyzed in both broadcast and non‐broadcast networks, which is highly applicable in high propagation delay networks. In broadcast networks, the proposed scheduling method reduces to a graph‐theoretic model that is shown to be equivalent to the classic algorithmic asymmetric traveling salesman problem (TSP) which is NP‐Hard. Although it is NP‐Hard, the TSP is well‐investigated with many available methods to find the best solution for up to tens of thousands of nodes. In non‐broadcast networks, the optimal solution to the scheduling problem considers the possibility of parallel transmission, which is optimized using graph coloring algorithm. The groups obtained through graph coloring are solved using Asymmetric Traveling Salesman algorithm to obtain the optimal schedule. The proposed method efficiently solves the scheduling problem for networks of practical size.