Precise bounds for the petersen time-varying real parameter uncertainty system stabilized via linear static controllers

Using a class of linear static controllers, we stabilize the Petersen open-loop two-dimensional linear system (Ref. 1), which consists of one time-varying uncertainty in the state matrixA and one timevarying uncertainty in the input matrixB. We show that the worst-case uncertainty strategy for the closed-loop system is a piecewise constant strategy of the angular state with three switches on the half-turn, –/2/2; it is unique with respect to a set of measure zero. Formulas are derived for the worst-case half-turn radius gainr _HT as a function of the parameters of the class of stabilizing linear static controllers. Using the class of scalar-quadratic Lyapunov functions, we show that a necessary and sufficient condition for the closed-loop system to be robustly stable against all time-varying admissible uncertainties is thatr _HT be less than unity. The bound on the time-varying real parameter uncertainties for the closed-loop system to be robustly stable is derived for the class of linear static feedback controllers. We obtain stabilizing linear static controllers such that the bound is as close to infinity as desired. The derived results are compared with numerical results obtained using commerical robust-control software.     

Reliability bounds in DFRA class with known mean and variance

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Two new bounds on the size of binary codes with a minimum distance of three

We prove two new upper bounds on the size of binary codes with a minimum distance of three, namelyA(10, 3)76 andA(11, 3)152.     

A new heuristic algorithm solving the linear ordering problem

The linear ordering problem is an NP-hard combinatorial problem with a large number of applications. Contrary to another very popular problem from the same category, the traveling salesman problem, relatively little space in the literature has been devoted to the linear ordering problem so far. This is particularly true for the question of developing good heuristic algorithms solving this problem.In the paper we propose a new heuristic algorithm solving the linear ordering problem. In this algorithm we made use of the sorting through insertion pattern as well as of the operation of permutation reversal. The surprisingly positive effect of the reversal operation, justified in part theoretically and confirmed in computational examples, seems to be the result of a unique property of the problem, called in the paper the symmetry of the linear ordering problem. This property consists in the fact that if a given permutation is an optimal solution of the problem with the criterion function being maximized, then the reversed permutation is a solution of the problem with the same criterion function being minimized.     

A characterization of discrete unimodality with applications to variance upper bounds

Bertin and Theodorescu (1984,Statist. Probab. Lett.,2, 23–30) developed a characterization of discrete unimodality based on convexity properties of a discretization of distribution functions. We offer a new characterization of discrete unimodality based on convexity properties of a piecewise linear extension of distribution functions. This reliance on functional convexity, as in Khintchine's classic definition, leads to variance dilations and upper bounds on variance for a large class of discrete unimodal distributions. These bounds are compared to existing inequalities due to Muilwijk (1966,Sankhy, Ser. B,28, p. 183), Moors and Muilwijk (1971,Sankhy, Ser. B,33, 385–388), and Rayner (1975,Sankhy, Ser. B,37, 135–138), and are found to be generally tighter, thus illustrating the power of unimodality assumptions.     

Parallel synthesis of multi-branched oligosaccharides related to elicitor active pentasaccharide in rice cell based on orthogonal deprotection and glycosylation strategy

We describe a parallel and efficient synthesis of multi-branched oligosaccharides 3a-g based upon the structure of the phytoalexin elicitor active branched pentasaccharide 2. One-pot sequential orthogonal deprotection of tetrasaccharide 5 with three different protecting groups provided each of seven glycosyl acceptors 4a-g. Glycosylation of the acceptors 4a-g, followed by deprotection provided branched oligosaccharides 3a-g. All the reaction processes from scaffold 5 to 3a-g except for final hydrogenolysis were achieved utilizing an automated synthesizer in a parallel fashion.     

Exact rotamer optimization for protein design

Computational methods play a central role in the rational design of novel proteins. The present work describes a new hybrid exact rotamer optimization (HERO) method that builds on previous dead-end elimination algorithms to yield dramatic performance enhancements. Measured on experimentally validated physical models, these improvements make it possible to perform previously intractable designs of entire protein core, surface, or boundary regions. Computational demonstrations include a full core design of the variable domains of the light and heavy chains of catalytic antibody 48G7 FAB with 74 residues and 10(128) conformations, a full core/boundary design of the beta1 domain of protein G with 25 residues and 10(53) conformations, and a full surface design of the beta1 domain of protein G with 27 residues and 10(60) conformations. In addition, a full sequence design of the beta1 domain of protein G is used to demonstrate the strong dependence of algorithm performance on the exact form of the potential function and the fidelity of the rotamer library. These results emphasize that search algorithm performance for protein design can only be meaningfully evaluated on physical models that have been subjected to experimental scrutiny. The new algorithm greatly facilitates ongoing efforts to engineer increasingly complex protein features.     

液相组合合成的纯化方法

综述了近8年来液相平行合成和组合合成中应用的不同技术, 包括可溶性载体、氟合成技术、离子液体、固相试剂树脂以及低聚乙烯二醇(OEG)衍生物的应用等几方面内容. 论述了它们的基本原理以及相关的应用实例, 并着重强调了目标化合物的分离纯化方法.     

化合物库的组合技巧和组合合成

从化合物库的组合技巧和组合合成方法两个方面探讨了组合化学及其在药物开发中的应用。     

Asymptotic Behavior of the t Expansion

The asymptotic behavior of a system's ground-state energy from the t expansion of Horn and Weinstein has been suggested to have the form E ₁(t)=E ₁+exp(–a _n t+b _n ). In the limit of very large t, this becomes E ₁(t)=E ₁+exp(–a ₁ t+b ₁). A simple analysis shows that the parameters are a ₁=E ₂–E ₁ and b ₁=ln[(E ₂–E ₁)|c ₂|²/|c ₁|²]. Functions are introduced which allow determination of a ₁, b ₁ and lower bounds to E ₁.