Entanglement of formation and concurrence for mixed states

We review some results on analytical computations of the measures for quantum entanglement: entanglement of formation and concurrence. We introduce some estimations of the lower bounds for the entanglement of formation in bipartite mixed states, and of lower bounds for the concurrence in bipartite and tripartite systems. The results on lower bounds for the concurrence are also generalized to arbitrary multipartite systems.     

Exponential lower bounds for the pigeonhole principle

In this paper we prove an exponential lower bound on the size of bounded-depth Frege proofs for the pigeonhole principle (PHP). We also obtain an (loglogn)-depth lower bound for any polynomial-sized Frege proof of the pigeonhole principle. Our theorem nearly completes the search for the exact complexity of the PHP, as S. Buss has constructed polynomial-size, logn-depth Frege proofs for the PHP. The main lemma in our proof can be viewed as a general Håstad-style Switching Lemma for restrictions that are partial matchings. Our lower bounds for the pigeonhole principle improve on previous superpolynomial lower bounds.     

Exponential lower bounds for depth three Boolean circuits

We consider the class of unbounded fan-in depth three Boolean circuits, for which the bottom fan-in is limited by k and the top gate is an OR. It is known that the smallest such circuit computing the parity function has gates (for k = O(n ^1/2)) for some , and this was the best lower bound known for explicit (P-time computable) functions. In this paper, for k = 2, we exhibit functions in uniform NC ¹ that require size depth 3 circuits. The main tool is a theorem that shows that any circuit on n variables that accepts a inputs and has size s must be constant on a projection (subset defined by equations of the form x _i = 0, x _i = 1, x _i = x _j or x _i = ) of dimension at least log(a/s)log n. Received: April 1, 1997.     

空间少自由度并联机构瞬时螺旋运动轴线曲面的几何表示方法

对于单自由度的平面机构或单自由度空间机构来说,机构中各个点的运动都是确定的。机构在运动过程中的一系列瞬时螺旋运动轴线所形成的曲面也是唯一的,比较容易求解,可以得到其数学表达式。但对于多自由度的空间机构来说,由于在每一个位形下,机构的运动有多种可能性,瞬时运动轴线所形成的曲面也不是唯一的,很难得到其数学表达式。本文通过求解空间机构在运动过程中的一系列瞬时运动轴线,利用几何方法绘制出空间少自由度并联机构的瞬轴曲面,从而可以更直观地了解少自由度并联机构的空间运动。     

蒲石河抽水蓄能电站下库蓄水对下游的影响

为了确保蒲石河抽水蓄能电站工程按期投产发电,保证水库及电站初期蓄水和发电运行安全,就不同蓄水方案对下游各业用水部门的影响进行了分析。下游各行业用水的调查分析,为尽可能减轻水库初期蓄水影响,制定切实可行的电站初期下闸蓄水方案提供了技术支撑。     

Solution of impulsive boundary value problems on infinite intervals

In this paper, the upper and lower solution method and monotone iterative technique are employed to study the boundary value problem for a class of first-order impulsive ordinary differential equations with Carathéodory condition on infinite intervals. Several existence theorems are obtained.     

两种情形下威布尔分布置信下限的确定

采用样本空间排序法,讨论了在Ⅰ型区间删失数据情形下和定时截尾情形下的数据服从威布尔分布时的可靠度置信下限问题,其中威布尔分布的形状参数是在某有限区间内.对给定的置信水平和任意大小的样本,给出了威布尔分布下可靠度置信下限的确定方法.     

基于能量平衡的黄河下游平滩流量计算方法

根据能量平衡原理建立了平滩流量计算方法,并利用黄河下游5个主要测站的实测水沙及平滩流量资料进行了检验。结果表明:建立的平滩流量计算方法能较好地反映平滩流量随水流含沙量及来水量的变化趋势,计算值与实测值较为符合;来水量在一定范围内时,水流含沙量越大,平滩流量越小;水流含沙量在一定范围内时,来水量越大,则平滩流量越大。     

淮河流域和长江中下游流域旱涝年的划分

利用1951—2007年国家气象信息中心提供的756站逐日降水资料,通过计算6—7月降水标准差,确定淮河流域和长江中下游流域降水变率最大的站点,分别计算各站与这两个流域降水变率最大的站点相关系数,把通过显著性检验的站点分别作为淮河流域和长江中下游流域的代表站。利用两流域代表站的标准化降水指数确定了1951—2007年的旱涝年份:淮河流域的旱年为1952年、1959年、1961年等共10 a,涝年为1954年、1956年、1957年等共9 a;长江中下游流域的旱年为1952年、1958年、1961年等共11 a,涝年为1954年、1969年、1980年等共10 a。结合水文资料进行修订后,确定了1951—2007年淮河流域和长江流域因梅雨季降水而导致的洪涝年份。