The double deflating technique for irreducible singular M-matrix algebraic Riccati equations in the critical case

As is known, Alternating-Directional Doubling Algorithm (ADDA) is quadratically convergent for computing the minimal nonnegative solution of an irreducible singular M-matrix algebraic Riccati equation (MARE) in the noncritical case or a nonsingular MARE, but ADDA is only linearly convergent in the critical case. The drawback can be overcome by deflating techniques for an irreducible singular MARE so that the speed of quadratic convergence is still preserved in the critical case and accelerated in the noncritical case. In this paper, we proposed an improved deflating technique to accelerate further the convergence speed – the double deflating technique for an irreducible singular MARE in the critical case. We proved that ADDA is quadratically convergent instead of linearly when it is applied to the deflated algebraic Riccati equation (ARE) obtained by a double deflating technique. We also showed that the double deflating technique is better than the deflating technique from the perspective of dimension of the deflated ARE. Numerical experiments are provided to illustrate that our double deflating technique is effective.     

Subdirectly irreducible medial quandles

We describe all subdirectly irreducible medial quandles. We show that they fall within one of four disjoint classes. In particular, in the finite case they are either connected (and therefore Alexander quandles) or reductive. Moreover, we provide a representation of all non-connected subdirectly irreducible medial quandles.     

Hybrid Battery-Capacitor System based on Li4Ti5O12Anode and PTPAn Cathode北大核心CSCD

Owing to its high safe, high rate and long life characteristics, lithium titanate (Li4Ti5O12) anode material has attracted extensive attention in recent years, and many efforts are being made to develop the Li4Ti5O12based high performance hybrid supercapacitors and Li-ion batteries. Herein, we prepared the organic cathode material polytriphenylamine (PTPAn) through chemical oxidation and polymerization of triphenylamine (TPAn), and investigated its charge storage mechanism and electrode kinetics with the typical electrochemical methods in an organic electrolyte. It was demonstrated that the PTPAn exhibited the reversible capacity of 85 mA·g-1. The charge storage depended on the reversible adsorption/desorption of anion, which is not controlled by the diffusion process, and thus, can be considered as the pseudocapacitive behavior. Then, the PTPAn cathode was coupled with the Li4Ti5O12anode to form a hybrid capacitor/battery system with high power and improved energy density. Finally, the inherent drawback and the challenge for practical application of such an organic cathode are briefly discussed. © Journal of Electrochemistry 2018.     

Topologically Irreducible Representations and Radicals in Banach Algebras

It is shown that the topologically irreducible representationsof a normed algebra define a certain topological radical inthe same way that the strictly irreducible representations definethe Jacobson radical and that this radical can be strictly smallerthan the Jacobson radical. An abstract theory of ‘topologicalradicals’ in topological algebras is developed and usedto relate this radical to the Baer radical (prime radical).The relations with topologically transitive representationsand standard representations in the sense of Meyer are alsoexplored. 1991 Mathematics Subject Classification: 46H15, 46H25,16Nxx.     

Globally Irreducible Representations of Finite Groups and Integral Lattices

The notion of globally irreducible representations of finite groups has been introduced by B. H. Gross, in order to explain new series of Euclidean lattices discovered recently by N. Elkies and T. Shioda using Mordell--Weil lattices of elliptic curves. In this paper we first give a necessary condition for global irreducibility. Then we classify all globally irreducible representations of L ₂(q) and ²B₂(q), and of the majority of the 26 sporadic finite simple groups. We also exhibit one more globally irreducible representation, which is related to the Weil representation of degree (pⁿ-1)/2 of the symplectic group Sp_2n(p) (p 1 (mod 4) is a prime). As a consequence, we get a new series of even unimodular lattices of rank 2(pⁿ–1). A summary of currently known globally irreducible representations is given.     

The geography of irreducible 4-manifolds

In this paper we investigate the existence and the uniqueness problems for simply connected irreducible -manifolds. By taking fiber sums along an embedded surface of square and by a rational blow-down procedure, we construct many new irreducible -manifolds which have infinitely many distinct smooth structures. Furthermore, we prove that all but at most finitely many lattice points lying in the non-positive signature region with are covered by these irreducible -manifolds.

     

广义Minkowski不等式的进一步改进

针对"亚正定阵理论(Ⅱ)"一文的广义Minkowski不等式不成立问题,在已有的修正结果基础上,给出一种完整的修正结果;并更正了"亚正定阵的几个开问题及一些不等式"一文中有关的错误结论;用反例说明"广义正定矩阵的进一步研究"一文中的有关结论是错误的,给出完整的修正结果.     

亚/超临界乙醇中羟基和氢自由基作用下的纤维素液化行为

以水杨酸为羟基自由基(HO·)捕捉剂、四氯化碳为氢自由基(H·)捕捉剂,采用间歇高压反应釜对玉米秸秆纤维素在亚/超临界乙醇中的液化行为进行了研究,通过考察自由基捕捉剂用量、反应温度和反应时间对纤维素液化行为的影响,研究亚/超临界乙醇产生的HO·和H·自由基对纤维素的液化作用。结果表明,随着水杨酸用量增加(0-4mL),HO·浓度升高,生物油收率由29.3%提高至47.9%,固体残渣收率从26.7%降低至24.3%;反应温度从250℃升高至320℃,HO·活性随之增强,生物油收率由35.9%升高至58.2%,固体残渣收率由51.8%降低至20.4%;随着四氯化碳用量由0增加为2mL时,H·浓度降低,生物油收率由24.7%降低至20.7%,固体残渣收率由54.1%增加至59.1%;反应时间从0到30min,液化作用不断增强,生物油收率从8.7%升高至28.5%,固体残渣收率由86.3%下降至60.9%;30min之后,四氯化碳对H·活性的抑制加强,导致液化作用减弱,生物油收率有所下降。实验结果表明,乙醇在亚/超临界状态下能够产生HO·和H·,且HO·和H·浓度和活性与反应条件相关,对纤维素液化产物的收率及其分布具有明显的影响。     

On local irreducibility of the spectrum

Let be the algebra of complex matrices, and for denote by and the spectrum and spectral radius of respectively. Let be a domain in containing 0, and let be a holomorphic map. We prove: (1) if for , then for ; (2) if for , then again for . Both results are special cases of theorems expressing the irreducibility of the spectrum near .

     

Square Integrable Representation of Groupoids

A notion of an irreducible representation, as well as of a square integrable representation on an arbitrary locally compact groupoid, is introduced. A generalization of a version of Schur＇s lemma on a locally compact groupoid is given. This is used in order to extend some well-known results from locally compact groups to the case of locally compact groupoids. Indeed, we have proved that if L is a continuous irreducible representation of a compact groupoid G defined by a continuous Hilbert bundle H = （Hu）u∈G^0, then each Hu is finite dimensional. It is also shown that if L is an irreducible representation of a principal locally compact groupoid defined by a Hilbert bundle （G^0, （Hu）,μ）, then dimHu = 1 （u ∈ G^0）. Furthermore it is proved that every square integrable representation of a locally compact groupoid is unitary equivalent to a subrepresentation of the left regular representation. Furthermore, for r-discrete groupoids, it is shown that every irreducible subrepresentation of the left regular representation is square integrable.