Triangular halogen trimers. A DFT study of the structure, cooperativity, and vibrational properties

Triangular halogen trimers (RX)3, where X = Br, I and R represents H, H3C, H2FC, HF2C, F3C, CH2=CH, CH[triple bond]C, and Ph, have been investigated using the density functional theory in the Perdew, Burke, and Ernzerhof method. We report herein the optimized geometries of the stable structures, their vibrational frequencies, and binding energies with the two- and three-body terms. All trimer structures possess a cyclic array of halogen atoms in the type II approach by virtue of the nonspherical atomic charge distribution around the halogens. The Br...Br interactions in trimers are very weak, whereas the I...I interactions in trimers are relatively stronger. While all bromine trimers and most of iodine trimers are predicted to be noncooperative, three of iodine trimers show weak cooperativity. The analysis of vibration modes reveals that all halogen trimers exhibit no especially remarkable frequency shifts. It is also shown that the electrostatic contribution plays a major role in the halogen...halogen interactions in halogen trimers. In contrast to bromine trimers, the relative contribution of charge-transfer component to the halogen...halogen interactions becomes more important for iodine trimers.     

Classification of homomorphisms and dynamical systems

Let be a unital simple -algebra, with tracial rank zero and let be a compact metric space. Suppose that are two unital monomorphisms. We show that and are approximately unitarily equivalent if and only if

for every and every trace of Inspired by a theorem of Tomiyama, we introduce a notion of approximate conjugacy for minimal dynamical systems. Let be a compact metric space and let be two minimal homeomorphisms. Using the above-mentioned result, we show that two dynamical systems are approximately conjugate in that sense if and only if a -theoretical condition is satisfied. In the case that is the Cantor set, this notion coincides with the strong orbit equivalence of Giordano, Putnam and Skau, and the -theoretical condition is equivalent to saying that the associate crossed product -algebras are isomorphic.

Another application of the above-mentioned result is given for -dynamical systems related to a problem of Kishimoto. Let be a unital simple AH-algebra with no dimension growth and with real rank zero, and let We prove that if fixes a large subgroup of and has the tracial Rokhlin property, then is again a unital simple AH-algebra with no dimension growth and with real rank zero.

     

Classification of Homomorphisms from C (X) to Simple C*-Algebras of Real Rank Zero

Abstract Let A be a unital simple C*-algebra of real zero, stable rank one, with weakly unperforated K ₀₍ A) and unique normalized quasi-trace τ, and let X be a compact metric space. We show that two monomorphisms φ, ψ : C(X)→A are approximately unitarily equivalent if and only if φ and ψ induce the same element in KL(C(X), A) and the two lineal functionals τ∘φ and τ∘ψ are equal. We also show that, with an injectivity condition, an almost multiplicative morphism from C(X) into A with vanishing KK-obstacle is close to a homomorphism. Research partially supported by NSF Grants DMS 93-01082 (H.L) and DMS-9401515(G.G). This work was reported by the first named author at West Coast Operator Algebras Seminar (Sept. 1995, Eugene, Oregon)     

When almost multiplicative morphisms are close to homomorphisms

It is shown that approximately multiplicative contractive positive morphisms from (with dim ) into a simple -algebra of real rank zero and of stable rank one are close to homomorphisms, provided that certain -theoretical obstacles vanish. As a corollary we show that a homomorphism is approximated by homomorphisms with finite dimensional range, if gives no -theoretical obstacle.

     

The Tracial Topological Rank of C*-Algebras

We introduce the notion of tracial topological rank for C*-algebras.In the commutative case, this notion coincides with the coveringdimension. Inductive limits of C*-algebrasof the form PM_n(C(X))P,where X is a compact metric space with dim X k, and P is aprojection in M_n(C(X)), have tracial topological rank no morethan k. Non-nuclear C*-algebras can have small tracial topologicalrank. It is shown that if A is a simple unital C*-algebra withtracial topological rank k (< ), then

(i) A is quasidiagonal,

(ii) A has stable rank 1,

(iii) A has weakly unperforatedK₀(A),

(iv) A has the following Fundamental Comparabilityof Blackadar:if p, q A are two projections with (p) < (q)for all tracialstates on A, then p q

. 2000 MathematicsSubject Classification: 46L05, 46L35.     

结合傅里叶变换合成法设计均匀薄膜

基于傅里叶变换合成法的基本原理,合成了一个K9基底上的负滤光片,合成的渐变折射率薄膜具有期望光学特性,但实际制备难度很大,因此将其细分为足够多层离散折射率的均匀薄膜,由于实际薄膜材料种类有限,不能获得任意折射率膜层,鉴于两层高低折射率薄层可近似为一层中间折射率膜层的思想,将膜系转化成一个可实际制备的膜系结构:膜系采用ZrO2和SiO2两种膜料,膜层总数为183层,经单纯形调法优化后,膜层总厚度为7.09 μm,通带和截止带内平均透射比分别为97.56%和3.13%,其结果优于直接采用傅里叶方法合成的非均匀膜系,与期望透射比曲线吻合更好.说明通过这种思想设计任意光谱特性的膜系是可行的,也使傅里叶变换合成法设计的薄膜实际制备成为可能.     

An asymmetric full velocity difference car-following model

This paper presents a car-following model that considers the asymmetric characteristic of the velocity differences of the vehicles in a traffic stream. The problems of the prevalent general force (GF) model and the full velocity difference (FVD) model were solved. Furthermore, the optimal velocity (OV) model, the GF model, and the FVD model are proved to be the special cases of the proposed asymmetric full velocity difference (AFVD) model. The mathematical model is presented, followed by simulation analysis which demonstrates the properties of the AFVD model.     

Investigating interactions between chloroquine/hydroxychloroquine and their single enantiomers and angiotensin-converting enzyme 2 by a cell membrane chromatography method

Chloroquine and hydroxychloroquine have been studied since the early clinical treatment of SARS-CoV-2 outbreak. Considering these two chiral drugs are currently in use as the racemate, high-expression angiotensin-converting enzyme 2 cell membrane chromatography was established for investigating the differences of two paired enantiomers binding to angiotensin-converting enzyme 2 receptor. Molecular docking assay and detection of SARS-CoV-2 spike pseudotyped virus entry into angiotensin-converting enzyme 2-HEK293T cells were also conducted for further investigation. Results showed that each single enantiomer could bind well to angiotensin-converting enzyme 2, but there were differences between the paired enantiomers and corresponding racemate in frontal analysis. R-Chloroquine showed better angiotensin-converting enzyme 2 receptor binding ability compared to S-chloroquine/chloroquine (racemate). S-Hydroxychloroquine showed better angiotensin-converting enzyme 2 receptor binding ability than R-hydroxychloroquine/hydroxychloroquine. Moreover, each single enantiomer was proved effective compared with the control group; compared with S-chloroquine or the racemate, R-chloroquine showed better inhibitory effects at the same concentration. As for hydroxychloroquine, R-hydroxychloroquine showed better inhibitory effects than S-hydroxychloroquine, but it slightly worse than the racemate. In conclusion, R-chloroquine showed better angiotensin-converting enzyme 2 receptor binding ability and inhibitory effects compared to S-chloroquine/chloroquine (racemate). S-Hydroxychloroquine showed better angiotensin-converting enzyme 2 receptor binding ability than R-hydroxychloroquine/hydroxychloroquine (racemate), while the effect of preventing SARS-CoV-2 pseudovirus from entering cells was weaker than R-hydroxychloroquine/hydroxychloroquine (racemate).     

The generalized Berg theorem and BDF-theorem

Let be a separable simple -algebra with finitely many extreme traces. We give a necessary and sufficient condition for an essentially normal element , i.e., is normal ( is the quotient map), having the form for some normal element and We also show that a normal element can be quasi-diagonalized if and only if the Fredholm index for all In the case that is a simple -algebra of real rank zero, with stable rank one and with continuous scale, and has countable rank, we show that a normal element with zero Fredholm index can be written as

where is an (increasing) approximate identity for consisting of projections, is a bounded sequence of numbers and with for any given

     

熔融碳酸盐燃料电池研究

以烧结Ｎｉ作电极，以ＬｉＡｌＯ２无机膜作电池隔膜，组装成了电极而积２８ｃｍ＾２的小型熔融碳酸盐燃料电池，试验了各种工作条件对电池性能的影响，电池经多次启动性能无衰减，放电电流密度１００ｍＡ／ｃｍ＾２，电池电压０．９５Ｖ，放电电流密度１２５ｍＡ／ｃｍ＾２，电池输出功率１１４ｍＷ／ｃｍ＾２，燃料气利用率８０％，电池能量效率３１％。