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.     

Left dihedral codes over finite chain rings

Let R be a finite commutative chain ring, $D_{2n}$ be the dihedral group of size 2n and $R[D_{2n}]$ be the dihedral group ring. In this paper, we completely characterize left ideals of $R[D_{2n}]$ (called left $D_{2n}$-codes) when $\gcd (char(R),n)=1$. In this way, we explore the structure of some skew-cyclic codes of length 2 over R and also over $R\times S$, where S is an isomorphic copy of R. As a particular result, we give the structure of cyclic codes of length 2 over R. In the case where $R={\mathbb{F}}_{p^m}$ is a Galois field, we give a classification for left $D_{2N}$-codes over ${\mathbb{F}}_{p^m}$, for any positive integer N. In both cases we determine dual codes and identify self-dual ones.     

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.     

Shimalactone Biosynthesis Involves Spontaneous Double Bicyclo-Ring Formation with 8π-6π Electrocyclization

Shimalactones A and B are neuritogenic polyketides possessing characteristic oxabicyclo[2.2.1]heptane and bicyclo[4.2.0]octadiene ring systems that are produced by the marine fungus Emericella variecolor GF10. We identified a candidate biosynthetic gene cluster and conducted heterologous expression analysis. Expression of ShmA polyketide synthase in Aspergillus oryzae resulted in the production of preshimalactone. Aspergillus oryzae and Saccharomyces cerevisiae transformants expressing ShmA and ShmB produced shimalactones A and B, thus suggesting that the double bicyclo-ring formation reactions proceed non-enzymatically from preshimalactone epoxide. DFT calculations strongly support the idea that oxabicyclo-ring formation and 8π-6π electrocyclization proceed spontaneously after opening of the preshimalactone epoxide ring through protonation. We confirmed the formation of preshimalactone epoxide in vitro, followed by its non-enzymatic conversion to shimalactones in the dark.     

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.     

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.     

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.