On 321-Avoiding Permutations in Affine Weyl Groups

We introduce the notion of 321-avoiding permutations in the affine Weyl group W of type A _{n – 1} by considering the group as a George group (in the sense of Eriksson and Eriksson). This enables us to generalize a result of Billey, Jockusch and Stanley to show that the 321-avoiding permutations in W coincide with the set of fully commutative elements; in other words, any two reduced expressions for a 321-avoiding element of W (considered as a Coxeter group) may be obtained from each other by repeated applications of short braid relations.Using Shi's characterization of the Kazhdan–Lusztig cells in the group W, we use our main result to show that the fully commutative elements of W form a union of Kazhdan–Lusztig cells. This phenomenon has been studied by the author and J. Losonczy for finite Coxeter groups, and is interesting partly because it allows certain structure constants for the Kazhdan–Lusztig basis of the associated Hecke algebra to be computed combinatorially.We also show how some of our results can be generalized to a larger group of permutations, the extended affine Weyl group associated to GL _n ()     

电动自行车用无刷直流电动机辅助功能控制系统研究

研究电动自行车用无刷直流电动机辅助功能控制系统,提出如何利用脉宽调制PWM和综合译码控制来实现电动自行车无刷直流电动机的电子刹车、欠压保护、过加速防抖动、堵转保护、巡航及1∶1助力等辅助功能。实车试验表明该系统能有效地改善电动自行车的舒适性、安全性。     

带有天线转换开关的车用毫米波雷达

车用雷达作为汽车防碰撞系统以及自适应巡航控制系统的关键组成部件之一,拥有广阔的市场前景。但由于造价高昂,体积偏大而一直没有得到广泛的应用。带有天线转换开关的毫米波雷达,通过两个模拟开关分别控制3个发射天线和3个接收天线,在获得了超过20°的水平方位探测角以及小于2°的方位分辨率的同时,有效地降低了雷达的造价,减小了雷达的体积。     

多波束前视声呐在潜器避障中的应用研究

介绍了多波束前视声呐特性及其PC104处理机的功能;描述了避障系统的数据采集和传输方法;提出了用基于栅格图标的方法来完整描述声呐探测信息,从而构建出水下局部环境模型;采用带有增长率算子的运动映射直方图算法作为声呐传感器数据后处理算法,合理地表达了声呐数据的不确定性,克服了探测数据中混带的噪声;设计了基于声呐传感器的反应式避障算法,确保潜器能够及时、有效、安全地避开障碍物;最后通过湖上试验,验证了所作研究的正确性及可行性.     

Pattern avoidance for alternating permutations and Young tableaux

We define a class Ln,k of permutations that generalizes alternating (up-down) permutations and give bijective proofs of certain pattern-avoidance results for this class. As a special case of our results, we give bijections between the set A2n(1234) of alternating permutations of length 2n with no four-term increasing subsequence and standard Young tableaux of shape 〈n³〉, and between the set A2n+1(1234) and standard Young tableaux of shape 〈³n−1,2,1〉. This represents the first enumeration of alternating permutations avoiding a pattern of length four. We also extend previous work on doubly-alternating permutations (alternating permutations whose inverses are alternating) to our more general context.The set Ln,k may be viewed as the set of reading words of the standard Young tableaux of a certain skew shape. In the last section of the paper, we expand our study to consider pattern avoidance in the reading words of standard Young tableaux of any skew shape. We show bijectively that the number of standard Young tableaux of shape λ/μ whose reading words avoid 213 is a natural μ-analogue of the Catalan numbers (and in particular does not depend on λ, up to a simple technical condition), and that there are similar results for the patterns 132, 231 and 312.     

DSC Calibration During Cooling. A survey of possible compounds

A number of compounds is investigated for DSC calibration during cooling. Adamantane and Zn show fast reversible transitions and can be applied both for temperature and for heat calibrations. A third compound, namely 4,4’-azoxyanisole, has a liquid crystal to isotropic liquid transition at 409K. This compound can be used for temperature calibration. Heat calibration with this compound is more problematic because of the small heat effect and the construction of the baseline. Other compounds like NaNO₃, In, Hg and Pb, show a slight supercooling. Nevertheless they can be used for heat calibration. The use of large samples of NaNO₃ and In gives the possibility to construct the equilibrium onset temperatures of the cooling peaks, so these two compounds are also appropriate for temperature calibration on cooling. This revised version was published online in July 2006 with corrections to the Cover Date.     

Optimal Trajectories and Guidance Schemes for Ship Collision Avoidance

The best strategy for collision avoidance under emergency conditions is to maximize wrt the controls the timewise minimum distance between the host ship and the intruder ship. In a restricted waterway area, two main constraints must be satisfied: the lateral deviation of the host ship from the original course is to be contained within certain limits; the longitudinal distance covered by the host ship is to be subject to a prescribed bound. At the maximin point of the encounter, the time derivative of the relative distance vanishes; this yields an inner boundary condition (orthogonality between the relative position vector and the relative velocity vector) separating the main phases of the maneuver: the avoidance and recovery phases. In this way, the optimal trajectory problem (a Chebyshev problem) can be converted into a Bolza problem with an inner boundary condition. Numerical solutions are obtained via the multiple-subarc sequential gradient-restoration algorithm (SGRA). Because the optimal trajectory is not suitable for real-time implementation, a guidance scheme approximating the optimal trajectory in real time is to be developed. For ship collision avoidance, the optimal trajectory results show that the rudder angle time history has a bang-bang form characterized by the alternation of saturated control subarcs of opposite signs joined by rapid transitions. Just as the optimal trajectory can be partitioned into three phases (avoidance phase, recovery phase, steady phase), a guidance trajectory can be constructed in the same way. For the avoidance and recovery phases, use of decomposition techniques leads to an algorithm computing the time lengths of these phases in real time. For the steady phase, a feedback control scheme is used to maneuver the ship steadily. Numerical results are presented. Portions of this paper were presented by the senior author at the 13th International Workshop on Dynamics and Control, Wiesensteig, Germany, 22-26 May 2005, in honor of George Leitmann. This research was supported by NSF Grant CMS-02-18878.     

Optimal Control of the Obstacle for an Elliptic Variational Inequality

An optimal control problem for an elliptic obstacle variational inequality is considered. The obstacle is taken to be the control and the solution to the obstacle problem is taken to be the state. The goal is to find the optimal obstacle from H ¹ ₀ (Ω) so that the state is close to the desired profile while the H ¹ (Ω) norm of the obstacle is not too large. Existence, uniqueness, and regularity as well as some characterizations of the optimal pairs are established. Accepted 11 September 1996     

Convexity estimates for nonlinear elliptic equations and application to free boundary problems

We prove the convexity of the set which is delimited by the free boundary corresponding to a quasi-linear elliptic equation in a 2-dimensional convex domain. The method relies on the study of the curvature of the level lines at the points which realize the maximum of the normal derivative at a given level, for analytic solutions of fully nonlinear elliptic equations. The method also provides an estimate of the gradient in terms of the minimum of the (signed) curvature of the boundary of the domain, which is not necessarily assumed to be convex.