共变完全多正线性映射的共变投射表示

研究了C*-代数中的共变完全多正线性映射,证明了共变完全多正线性映射可以诱导Hilbert C*-模上的共变投射表示,并且给出了共变完全多正线性映射的KS- GNS(Kasparov,Stinespring,Gel’fand,Naimark,Segal)构造.     

Magnetic-Flux-Induced Tunable Completely Flat Band and Topological Nearly Flat Band in Square Kagome Lattice

The flat bands in a square kagome lattice containing square and triangle plaquettes, are respectively investigated, and the origin of the doubly degenerated completely flat bands and the corresponding compact localized states are elucidated. It is found that the introduction of external magnetic flux enriches the modulation parameters, making the system present many interesting results. In the case that the magnetic flux penetrates through each square plaquette, the tunable completely flat band has one more tunable parameter. And when the external magnetic flux penetrates through each triangle plaquette, excepting a completely flat band, the band dispersions of the system present the topological nearly flat band, which is very useful to realize the interesting fractional quantum Hall physics. The average density of states is also calculated to corroborate the completely FB generated by the highly localized eigenstates. Furthermore, the implementation of the square kagome lattice system based on the current photonic waveguide network technology is demonstrated. The scheme opens up a way to generate the tunable completely flat band and topological nearly flat band in square kagome lattice under multi-parameter variable conditions.     

幂等元生成子半群为完全正则半群的拟完全正则半群

论文主要刻画了幂等元生成子半群为完全正则半群的拟完全正则半群. 并讨论了满足该类半群的一些子类.     

Benchmarking the completely renormalised equation-of-motion coupled-cluster approaches for vertical excitation energies

The vertical excitation energies for a comprehensive test set of about 150 singlet excited states of 28 medium-sized organic molecules computed using two variants of the completely renormalised (CR) equation-of-motion (EOM) coupled-cluster (CC) method with singles, doubles, and non-iterative triples, abbreviated as δ-CR-EOMCCSD(T), and the analogous two variants of the newer, left-eigenstate δ-CR-EOMCC(2,3) approach are benchmarked against the previously published CASPT2, CC3, and EOMCCSDT-3 results, as well as the suggested theoretical best estimate (TBE) values. The δ-CR-EOMCC approaches are also used to identify and characterise about 50 additional excited states, including several states having substantial two-electron excitation components, which have not been found in the previous work and which can be used in future benchmark studies. It is demonstrated that the non-iterative triples corrections to the EOMCCSD excitation energies defining the relatively inexpensive, single-reference, black-box δ-CR-EOMCC approaches provide significant improvements in the EOMCCSD data, while closely matching the results of the iterative and considerably more expensive CC3 and EOMCCSDT-3 calculations and their CASPT2 and TBE counterparts. It is also shown that the δ-CR-EOMCC methods, especially δ-CR-EOMCC(2,3), are capable of bringing the results of the CC3 and EOMCCSDT-3 calculations to a closer agreement with the CASPT2 and TBE data, demonstrating the utility of the cost-effective δ-CR-EOMCC methods in applications involving molecular electronic spectra. We show that there may exist a relationship between the magnitude of the triples corrections defining δ-CR-EOMCC approaches and the reduced excitation level diagnostic resulting from EOMCCSD.     

Hypercontinuous Posets

The concepts of hypercontinuous posets and generalized completely continuous posets are introduced. It is proved that for a poset P the following three conditions are equivalent:(1) P is hypercontinuous;(2) the dual of P is generalized completely continuous;(3) the normal completion of P is a hypercontinuous lattice. In addition, the relational representation and the intrinsic characterization of hypercontinuous posets are obtained.     

Harmonic Distributions for Equitable Partitions of a Hypercube

We provide general criteria for orthogonal arrays and t‐designs on equitable partitions of a hypercube by exploring harmonic distributions. Generalized harmonic weight enumerators for real‐valued functions of are introduced and applied to eigenfunctions of the adjacency matrix of . Using this, expressions for harmonic distributions are established for every cell of an equitable partition π of . Moreover, for any given cell in the partition π, the strength of the cell as an orthogonal array is explicitly expressed, and also a characterization of a t‐design of that cell is established. We also compute strengths of cells and find t‐designs from cells based on constructions of Krotov, Borges, Rifa, and Zinoviev.     

正规密码H~#-富足半群的结构

证明了H~#-富足半群S是正规密码H~#-富足半群当且仅当它是完全J~#-单半群的强半格.该结果也是正规密码超富足半群和正规密码群并半群分别在超富足半群和完全正则半群上的相应结构定理的推广.     

Poisson geometry of differential invariants of curves in some nonsemisimple homogeneous spaces

In this paper we describe a family of compatible Poisson structures defined on the space of coframes (or differential invariants) of curves in flat homogeneous spaces of the form where is semisimple. This includes Euclidean, affine, special affine, Lorentz, and symplectic geometries. We also give conditions on geometric evolutions of curves in the manifold so that the induced evolution on their differential invariants is Hamiltonian with respect to our main Hamiltonian bracket.

     

Cuntz-Pimnser algebras, completely positive maps and Morita equivalence

Let be a completely positive map on and let be the associated GNS--correspondence. We prove a result that implies, in particular, that the Cuntz-Pimsner algebra of , , is strongly Morita equivalent to the Cuntz algebra , where is the index of .

     

On some criteria for completely regular growth of entire functions of exponential type

This paper sharpens the author’s previous results concerning the completely regular growth of an entire function of exponential type all of whose zeros are simple, forming a sequence Λ = {λ_k} _k=1 ^∞ . For a function with real zeros, we write the growth regularity conditions (on the real axis and on the entire plane) in terms of lower bounds only for the absolute value of the derivative at the points λ_k. We also obtain an analog of Krein’s theorem concerning the functions whose inverse can be expanded in the corresponding series of simple fractions.