Backward Stochastic H2/H∞ Control with Random Jumps

This paper is concerned with H₂/H_∞ control of a new class of stochastic systems. The most distinguishing feature, compared with the existing literature, is that the systems are described by backward stochastic differential equations (BSDEs) with Brownian motion and random jumps. It is shown that the backward stochastic H₂/H_∞ control under consideration is associated with the of the corresponding uncontrolled backward stochastic perturbed system. A necessary and sufficient condition for the existence of a unique solution to the control problem under consideration is derived. The resulting solution is characterized by the solution of an uncontrolled forward backward stochastic differential equation (FBSDE) with Brownian motion and random jumps. When the coefficients are all deterministic, the equivalent linear feedback solution involves a pair of Riccati‐type equations and an uncontrolled BSDE. In addition an uncontrolled forward stochastic differential equation (SDE) is given.     

Uq(sl(2)) Satisfies a Bernstein Duality

It is well known that in some cases the functorExt_R^μ( − , R) defines a duality between module categories. In earlier papers we studied when this duality can be represented by a bimodule and have characterized when this happens. In this paper, using some computational methods of noncommutative Gröbner bases in the construction of projective resolutions of irreducible finite-dimensional representations, we show new examples of algebras satisfying this property.     

Sn1-xFexOy: a new material with high carbon monoxide sensitivity

The preparation method and the sensing properties (sensitivity and selectivity to interfering gases) towards carbon monoxide of the new ternary compound Sn_1-xFe_xO_y deposited in the form of thin films, are presented in this paper. The metal of the VIIIB group is introduced with concentrations in the range 0<x<25 at %. Thin films are sputtered using the RGTO (rhotaxial growth and thermal oxidation) technique. This technique consists of metal deposition onto a substrate maintained at a temperature higher than the metal melting point and metal oxidation by means of an annealing cycle in pure oxygen. Particular emphasis is given to the relations between some preparation parameters of the material, namely the atomic percentage ofiron or the annealing cycle, and to the sensor sensitivity towards CO and other interfering gases like C₂H₅OH, H₂ and NO_x diluted in dry air. A sensitivity S=(G_gas-G_air)/G_air=3.5 towards 10 ppm of CO has been measured: the kinetic characteristics of the sensors are also presented, together with the working mechanism.     

Manufacture and characterization of sol–gel V1−x−yWxSiyO2 films for uncooled thermal detectors

V_1−x−yW_xSi_yO₂ films for uncooled thermal detectors were coated on sodium-free glass slides with sol–gel process, followed by the calcination under a reducing atmosphere (Ar/H₂ 5%). The V_1−x−yW_xSi_yO₂ films as prepared inherit various phase transition temperatures ranging from 20 to 70 °C depending on the dopant concentrations and the fabrication conditions. Compared to the hysteresis loop of plain VO₂ films, a rather steep loop was obtained with the addition of tungsten components, while a relaxed hysteresis loop with the tight bandwidth was contributed by Si dopants. Furthermore, the films with switching temperature close to room temperature were fabricated to one-element bolometers to characterize their figures of merit. Results showed that the V_0.905W_0.02Si_0.075O₂ film presented a satisfactory responsivity of 2600 V/W and detectivity of 9 × 10⁶ cm  Hz^1/2/W with chopper frequencies ranging from 30 to 60 Hz at room temperature. It was proposed that with appropriate amount of silicon and tungsten dopants mixed in the VO₂, the film would characterize both a relaxed hysteresis loop and a fair TCR value, which effectively reduced the magnitude of noise equivalent power without compromising its performance in detectivity and responsivity.     

基于A2范数的加权低秩子空间聚类

子空间聚类在运动分割、人脸聚类上得了广泛的应用,并且取得很好的聚类效果.针对稀疏子空间聚类和最小二乘回归子空间聚类求得的表示系数存在类内过于稀疏和类间过于稠密的问题,本文利用l₂范数,提出一种基于欧氏距离的且具有组效应的加权低秩子空间聚类算法,此算法通过基于欧氏距离的加权方式,使得最终的表示系数在保证同一子空间数据点联系的同时,减小不同子空间数据点之间的联系.利用此表示系数建立相似矩阵J,将J应用到谱聚类得到聚类结果.实验结果表明,与当前流行的算法比较,本算法取得了较好的聚类效果.     

Computing Homomorphisms Between HolonomicD-modules

Let K C be a subfield of the complex numbers, and let D be the ring of K -linear differential operators on R = K [ x₁, . . . , x_n]. If M and N are holonomic left D -modules we present an algorithm that computes explicit generators for the finite dimensional vector space _D(M, N). This enables us to answer algorithmically whether two given holonomic modules are isomorphic. More generally, our algorithm can be used to get explicit generators for _Dⁱ(M, N) for any i in the sense of Yoneda.     

H∞ Estimation for Uncertain Systems With Limited Communication Capacity

This paper investigates the problem of robust H_infin estimation for uncertain systems subject to limited communication capacity. The parameter uncertainty belongs to a given convex polytope and the communication limitations include measurement quantization, signal transmission delay, and data packet dropout, which appear typically in a network environment. The problem of H_infin filter design is first solved for a nominal system subject to the aforementioned information limitations, which is then extended to the uncertain case based on the notion of quadratic stability. To further reduce the overdesign in the quadratic framework, this paper also proposes a parameter-dependent filter design procedure, which is much less conservative than the quadratic approach. The quadratic and parameter-dependent approaches provide alternatives for designing robust H_infin filters with different degrees of conservativeness and computational complexity. Two examples, including a mass-spring system, are utilized to illustrate the design procedures proposed in this paper.     

单片机系统中PS/2键盘驱动程序设计

分析PS/2协议;介绍PS/2标准键盘的第二套扫描码和命令集,并给出在单片机系统中支持 PS/2 键盘的硬件连接方式和利用Keil C51语言实现的驱动程序设计及部分代码。该驱动程序可以方便地移植到其他单片机或嵌入式系统中。     

Exact 3-satisfiability is decidable in time O(20.16254n)

Let F = C ₁ C _m be a Boolean formula in conjunctive normal form over a set V of n propositional variables, s.t. each clause C _i contains at most three literals l over V. Solving the problem exact 3-satisfiability (X3SAT) for F means to decide whether there is a truth assignment setting exactly one literal in each clause of F to true (1). As is well known X3SAT is NP-complete [6]. By exploiting a perfect matching reduction we prove that X3SAT is deterministically decidable in time O(2^0.18674n ). Thereby we improve a result in [2,3] stating X3SAT O(2^0.2072n ) and a bound of O(2^0.200002n ) for the corresponding enumeration problem #X3SAT stated in a preprint [1]. After that by a more involved deterministic case analysis we are able to show that X3SAT O(2^0.16254n ).An extended abstract of this paper was presented at the Fifth International Symposium on the Theory and Applications of Satisfiability Testing (SAT 2002).     

Jumps and logic in the law

The main stream of legal theory tends to incorporate unwritten principles into the law. Weighing of principles plays a great role in legal argumentation, inter alia in statutory interpretation. A weighing and balancing of principles and other prima facie reasons is a jump. The inference is not conclusive.To deal with defeasibility and weighing, a jurist needs both the belief-revision logic and the nonmonotonic logic. The systems of nonmonotonic logic included in the present volume provide logical tools enabling one to speak precisely about various kinds of rules about rules, dealing with such things as applicability of rules, what is assumed by rules, priority between rules and the burden of proof. Nonmonotonic logic is an example of an extension of the domain of logic. But the more far-reaching the extension is, the greater problems it meets. It seems impossible to make logical reconstruction of the totality of legal argumentation.The lawyers' search for reasons has no obvious end point. Ideally, the search for reasons may end when one arrives at a coherent totality of knowledge. In other words, coherence is the termination condition of reasoning. Both scientific knowledge and knowledge of legal and moral norms progresses by trial and error, and that one must resort to a certain convention to define what error means. The main difference is, however, that conventions of science are much more precise than those of legal scholarship.Consequently, determination of error in legal science is often holistic and circular. The reasons determining that a legal theory is erroneous are not more certain than the contested theory itself. A strict and formal logical analysis cannot give us the full grasp of legal rationality. A weaker logical theory, allowing for nonmonotonic steps, comes closer, at the expense of an inevitable loss of computational efficiency. Coherentist epistemology grasps even more of this rationality, at the expense of a loss of preciseness.     

Gas-sensing property and mechanism of CaxLa1−xFeO3 ceramics

LaFEO₃ and Ca_xLa_1−xFeO₃ ceramic powders have been prepared by the coprecipitation method from La(NO₃)₃, Fe(NO₃)₃ and Ca(NO₃)₂ aqueous solutions. The orthorhombic perovskite phases of LaFeO₃ and Ca_xLa_1−xFeO₃ are characterized by X-ray diffraction patterns. The sensors fabricated with those powders have high sensitivity to alcohol. Partial substitution of La³⁺ in LaFeO₃ with Ca²⁺ can enhance the sensitivity of the materials to reducing gases. The resistance of an LaFeO₃ sensor in air, vacuum and alcohol-containing air has been measured. Complex impedance spectroscopy has been used to try and analyse the gas-sensing mechanism. According to the experimental results, it can be deduced that the surface adsorptive and lattice oxygen govern the sensing properties of LaFeO₃ and Ca_xLa_1−xFeO₃ ceramics.     

Nanowire structured SnOx–SWNT composites: High performance sensor for NOx detection

A nanowire structured nanocomposite of tin oxide (SnO_x) and a single-walled carbon nanotube (SWNT) are fabricated using rheotaxial growth and thermal oxidation method for gas sensor application. The morphology, gas sensing properties, as well as the chemical and electrical properties are investigated. The oxidation temperature for Sn mainly determines the stoichiometry of the SnO_x nano-beads, and consequently the electrical and gas sensing properties of the nanocomposite sensors. The gas sensing to nitrogen oxide, hydrogen, oxygen, xylene, acetone, carbon monoxide, and ammonia are also examined to determine the gas selectivity of the sensor. The high sensitivity and selectivity towards NO_x of the nanocomposite sensor is realized via the porous structure of the SWNT template. The gas sensing mechanism of the nanocomposite structure is also discussed.     

模2n 加和模2加混合运算的异或分支数

研究了扩散结构为二元域上非线性变换的异或分支数.给出了扩散结构为二元域上非线性变换的异或分支数的定义及其与分组密码抗差分攻击和线性分析能力的关系,证明了以模2n加和模2加的混合运算为扩散结构的异或分支数等于将模2n加换成模2加且将各变元系数模2后所得的二元域上线性变换的异或分支数,从而简化了此类非线性扩散结构异或分支数的计算问题.     

Robust p stability and performance

In this paper we study robust stability, in the _p sense, against structured perturbations of bounded _p norm. The perturbations may be either linear time-varying, nonlinear time-varying, or nonlinear time-invariant. We develop exact tests for robust stability for each case in terms of convex optimization problems. These results are extended to solve the corresponding robust performance problems, with performance measured via the induced _p norm.     

A Polynomial with Galois GroupSL2(11)

We compute a polynomial with Galois group SL₂(11) over Q. Furthermore we prove that SL₂(11) is the Galois group of a regular extension ofQ (t).     

Codimension two bifurcation in a simple delayed neuron model

This paper reports a simple delayed neuron model. Bogdanov-Takens bifurcation is studied by using the center manifold reduction and the normal form method for retarded functional differential equation. We get the versal unfolding of the norm forms at double zero singularity and show that the model can exhibit pitchfork, Hopf, homoclinic bifurcation and saddle node bifurcation of periodic orbits. Some numerical simulations are given to support the analytic results.     

Titania NOx sensors for exhaust monitoring

Oxide semiconductors have been examined to develop NO_x sensors for exhaust monitoring. Titania doped with trivalent elements, such as Al³⁺, Sc³⁺, Ga³⁺ or In³⁺, has a good sensitivity and selectivity to NO between 450 and 550 °C, and shows rapid response. A sensor probe for monitoring exhaust NO_x has been fabricated. Many kinds of interference gases, such as C₃H₆, CO and SO₂, have been found to have only a slight influence on the sensor response to NO. The influence of O₂ and H₂O is also negligible, except for the cases of 0% H₂O and fuel-rich conditions. In accordance with these results, the sensor probe operates satisfactority in the exhaust gas of various combustion conditions without interference from the various kinds of gas species in the exhaust gases.     

Generic and Explicit Realization of Smallp-groups

We prove the existence of a generic polynomial for the Heisenberg groupH_p³ over a field of characteristic not p, where p is an odd prime.