Fundamental Groups of Graphs of Cyclic Subgroup Separable and Weakly Potent Groups

We give a characterization of the cyclic subgroup separability and weak potency of the fundamental group of a graph of polycyclic-by-finite groups and free-by-finite groups amalgamating edge subgroups of the form × D,where h has infinite order and D is finite.     

Additive Hermitian idempotent preservers between operator algebras

Let L be an additive map between (real or complex) matrix algebras sending $n\times n$ Hermitian idempotent matrices to $m\times m$ Hermitian idempotent matrices. We show that there are nonnegative integers $p,q$ with $n(p+q)=r\le m$ and an $m\times m$ unitary matrix U such that$L(A)=U[(I_p?A)\oplus (I_q?A^t)\oplus 0_{m?r}]U^{?},\text{for any}n\times n\text{Hermitian}A\text{with rational trace}.$ We also extend this result to the (complex) von Neumann algebra setting, and provide a supplement to the Dye-Bunce-Wright Theorem asserting that every additive map of Hermitian idempotents extends to a Jordan ?-homomorphism.     

An analysis of overlapping Schwarz method for a weakly coupled system of singularly perturbed convection-diffusion equations

In this article, we have developed an overlapping Schwarz method for a weakly coupled system of convection-diffusion equations. The method splits the original domain into two overlapping subdomains. A hybrid difference scheme is proposed in which on the boundary layer region, we use the central finite difference scheme on a uniform mesh, whereas on the nonlayer region, we use the mid-point difference scheme on a uniform mesh. It is shown that the numerical approximations converge in the maximum norm to the exact solution. We have proved that, when appropriate subdomains are used, the method produces almost second-order convergence. Furthermore, it is shown that two iterations are sufficient to achieve the expected accuracy. Numerical examples are presented to support the theoretical results. The main advantage of this method used with the proposed scheme is that it reduces iteration counts very much and easily identifies in which iteration the Schwarz iterate terminates.     

Synthesis and Reactivity of the First Isolated Hydrogen‐Bridged Silanol–Silanolate Anions

We report on the first examples of isolated silanol–silanolate anions, obtained by utilizing weakly coordinating phosphazenium counterions. The silanolate anions were synthesized from the recently published phosphazenium hydroxide hydrate salt with siloxanes. The silanol–silanolate anions are postulated intermediates in the hydroxide‐mediated polymerization of aryl and alkyl siloxanes. The silanolate anions are strong nucleophiles because of the weakly coordinating character of the phosphazenium cation, which is perceptible in their activity in polysiloxane depolymerization.     

OCS经由F 31Π里德堡态生成CO(X1Σ+)+S(1D2)产物的波长相关性光解离

本文利用时间切片离子速度成像技术在134∽140 nm波段研究了OCS分子经由F 3¹Π里德堡态的真空紫外光解离动力学. 在选取的5个分别对应OCS(F 3¹Π, v₁=0∽4)的伸缩振动激发的光解波长，实验测得了来自CO(X¹Σ⁺)+S(¹D₂)产物通道的SS(¹D₂))实验影像，并获得了总平动能谱和CO(X¹Σ⁺, v)共生产物的振动布居及角分布. 结果分析表明OCS分子解离生成CO(X¹Σ⁺)+S(¹D₂)产物的过程经历了上态F 3¹Π 与C_?v和C_s构型的下电子态间非绝热耦合过程. 实验结果显示了很强的波长相关性：OCS (F 3¹Π, v₁)的较低转动激发态(v₁=0∽2)和较高转动激发态(v₁=3, 4)的CO(X¹Σ⁺)产物的振动布居和角分布具有显著差异，表明该解离过程中具有不同的解离机理. 本结果提供了振动耦合可能对真空紫外光解离动力学产生关键作用的相关证据.     

Synthesis of Elusive Chloropnictenium Ions

This work describes the synthesis and full characterization of elusive chloropnictenium ion salts of the type [^RAr*N(SiMe)ECl][A] (^RAr*=2,6‐(CHPh₂)‐4‐R‐C₆H₂, R=Me, tBu; E=Sb, Bi; A^?=GaCl₄, Al(OCH(CF₃)₂)₄). In these species the cation is significantly stabilized by weak arene interactions to flanking phenyl groups of the ^RAr* moiety. In this context the bonding situation has been studied by computational means and the reactivity towards the Lewis base 4‐dimethylaminopyridine (dmap) was investigated.     

Quantum effects on the stability of the He5I2 van der Waals conformers

We present 15-dimensional quantum multiconfiguration time-dependent Hartree calculations of the vibrational levels of the He₅I₂ van der Waals (vdW) complex employing an ab initio-based potential energy surface (PES). The energies and spatial features of such bound structures are analyzed, providing predictions on the structures and relative stabilities of its three lowest isomers. We found that the most stable isomer corresponds to all five He atoms encircling the I₂ molecule, indicating that in this case the anharmonic quantum effects do not stabilize the isomers involving a He atom in a linear configuration as reported previously for the smaller He_NI₂ systems. Such finding provides information on the overall structuring of the finite-size-solvent systems, highlighting the intriguing interplay between weak intermolecular interactions and quantum effects. © 2019 Wiley Periodicals, Inc.     

Polymorphism of the dinuclear CoIII–Schiff base complex [Co2(o‐van‐en)3]·4CH3CN (o‐van‐en is a salen‐type ligand)

Reactions of Co(OH)₂ with the Schiff base bis(2‐hydroxy‐3‐methoxybenzylidene)ethylenediamine, denoted H₂(o‐van‐en), under different conditions yielded the previously reported complex aqua[bis(3‐methoxy‐2‐oxidobenzylidene)ethylenediamine]cobalt(II), [Co(C₁₈H₁₈N₂O₄)(H₂O)], 1 , under anaerobic conditions and two polymorphs of [μ‐bis(3‐methoxy‐2‐oxidobenzylidene)ethylenediamine]bis{[bis(3‐methoxy‐2‐oxidobenzylidene)ethylenediamine]cobalt(III)} acetonitrile tetrasolvate, [Co₂(C₁₈H₁₈N₂O₄)₃]·4CH₃CN, i.e. monoclinic 2 and triclinic 3 , in the presence of air. Both novel polymorphs were chemically and spectroscopically characterized. Their crystal structures are built up of centrosymmetric dinuclear [Co₂(o‐van‐en)₃] complex molecules, in which each Co^III atom is coordinated by one tetradentate dianionic o‐van‐en ligand in an uncommon bent fashion. The pseudo‐octahedral coordination of the Co^III atom is completed by one phenolate O and one amidic N atom of the same arm of the bridging o‐van‐en ligand. In addition, the asymmetric units of both polymorphs contain two acetonitrile solvent molecules. The polymorphs differ in the packing orders of the dinuclear [Co₂(o‐van‐en)₃] complex molecules, i.e. alternating ABABAB in 2 and AAA in 3 . In addition, differences in the conformations, the positions of the acetonitrile solvent molecules and the pattern of intermolecular interactions were observed. Hirshfeld surface analysis permits a qualitative inspection of the differences in the intermolecular space in the two polymorphs. A knowledge‐based study employing Full Interaction Maps was used to elucidate possible reasons for the polymorphism.     

Charged pion condensation in anti-parallel electromagnetic fields and nonzero isospin density

The formation of charged pion condensate in anti-parallel electromagnetic fields and in the presence of the isospin chemical potential is studied in the two-flavor Nambu-Jona-Lasinio model.The method of Schwinger proper time is extended to explore the quantities in the off-diagonal flavor space,i.e.the charged pion.In this framework,π^± are treated as bound states of quarks and not as point-like charged particles.The isospin chemical potential plays the role of a trigger for charged pion condensation.We obtain the associated effective potential as a function of the strength of the electromagnetic fields and find that it contains a sextic term which possibly induces a weak first order phase transition.The dependence of pion condensation on model parameters is investigated.