The derived category of an algebra with radical square zero

Koszul duality and covering theory are combined to realize the bounded derived category 𝒟 of an algebra with radical square zero as a certain orbit category of the bounded derived category of finitely presented representations of an associated infinite quiver. As a consequence, the possible shapes of the connected components of the Auslander–Reiten quiver of 𝒟 are described.     

TL-subrings and TL-ideals,Part3:Maximal TL-ideals and ireducible TL-ideals

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Powers of matrices over an extremal algebra with applications to periodic graphs

Consider the extremal algebra=({},min,+), using + and min instead of addition and multiplication. This extremal algebra has been successfully applied to a lot of scheduling problems. In this paper the behavior of the powers of a matrix over is studied. The main result is a representation of the complete sequence (A ^m ) _m which can be computed within polynomial time complexity. In the second part we apply this result to compute a minimum cost path in a 1-dimensional periodic graph.     

Asymptotic Ideals (Ideals in the Ring of Colombeau Generalized Constants with Continuous Parametrization)

We study the asymptotics at zero of continuous functions on (0, 1] by means of their asymptotic ideals, i.e., ideals in the ring of continuous functions on (0, 1] satisfying a polynomial growth condition at 0 modulo rapidly decreasing functions at 0. As our main result, we characterize maximal and prime ideals in terms of maximal and prime filters.     

ON THE ZEROS OF POLYNOMIALS OVER QUATERNIONS

ABSTRACT

We review and expand some results on the number of zeros of polynomials over Hamilton's quaternions, with particular emphasis on those polynomials with coefficients in a degree two subfield.     

任意域上的代数中两个幂等元线性组合的Drazin可逆性（英文）

对域上的代数中两个幂等元P和q,满足一定的条件PqP=s,其中s∈{O,P,q,Pq,qP,qPq},本文得到了它们的线性组合ip＋jq均是Drazin可逆的,并给出了其Drazin逆的表示.     

Some explicit formulas for the polynomial decomposition of the matrix exponential and applications

This paper is devoted to the study of some formulas for polynomial decomposition of the exponential of a square matrix A. More precisely, we suppose that the minimal polynomial M_A(X) of A is known and has degree m. Therefore, e^tA is given in terms of P₀(A),…,P_m−1(A), where the P_j(A) are polynomials in A of degree less than m, and some explicit analytic functions. Examples and applications are given. In particular, the two cases m=5 and m=6 are considered.     

Living copolymerization of ethylene/1‐octene with fluorinated FI‐Ti catalyst

Living copolymerization of ethylene and 1‐octene was carried out at room temperature using the fluorinated FI‐Ti catalyst system, bis[N‐(3‐methylsalicylidene)‐2,3,4,5,6‐pentafluoroanilinato] TiCl₂/dried methylaluminoxane, with various 1‐octene concentrations. The comonomer incorporation up to 32.7 mol % was achieved at the 1‐octene feeding ratio of 0.953. The living feature still retained at such a high comonomer level. The copolymer composition drifting was minor in this living copolymerization system despite of a batch process. It was found that the polymerization heterogeneity had a severe effect on the copolymerization kinetics, with the apparent reactivity ratios in slurry significantly different from those in solution. The reactivity ratios were nearly independent of polymerization temperature in the range of 0–35 °C. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

MgCl2/R'nAl(OR)3-n: an excellent activator/support for transition-metal complexes for olefin polymerization

A new and effective method for the activation, and simultaneously, immobilization of bis(phenoxyimine) early-transition-metal complexes for olefin polymerization (known as FI catalysts), which makes use of MgCl(2)/R'(n)Al(OR)(3-n) as an activator/support, has been developed. Ti-, Zr-, and V-FI catalysts combined with this MgCl(2)-based compound can form highly active MgCl(2)-supported single-site catalysts capable of demonstrating superior catalytic properties, compared to the corresponding homogeneous methylaluminoxane- (Ti- and Zr-FI catalysts) or alkylaluminum-activation systems (V-FI catalysts), in terms of their catalytic activity, molecular weight, stereoselectivity, and comonomer incorporation. Additionally, these new catalysts can produce polymers of significant morphology with high efficiency. Notably, the MgCl(2)-based compounds can also effectively activate and immobilize the early-to-late transition-metal complexes that have emerged recently. Thus, the application of MgCl(2)-based compounds as activators/supports for transition-metal complexes for olefin polymerization provides a conceptually new strategy for the development of methylaluminoxane- and borate-free, high-performance, single-site catalysts capable of controlling polymer morphology.     

烯烃聚合高性能FI催化剂的进展

FI催化剂系一近几年发展起来的烯烃聚合高性能催化剂。以它的极高的活性、聚合物分子结构的可控性、多重活性聚合等特性而引人注目。本评述首先进行该催化剂的化学描述,然后分别介绍该催化剂的主要特征、活性中心结构、聚合机理和应用,重点介绍该催化剂的五大特征。