Constacyclic codes over finite local Frobenius non-chain rings with nilpotency index 3

The main results of this paper are in two directions. First, the family of finite local Frobenius non-chain rings of length 4 (hence of nilpotency index 3) is determined. As a by-product all finite local Frobenius non-chain rings with $p^4$ elements, (p a prime) are given. Second, the number and structure of γ-constacyclic codes over finite local Frobenius non-chain rings with nilpotency index 3, of length relatively prime to the characteristic of the residue field of the ring, are determined.     

On realization of fusion rings from generalized Cartan matrices

The Casimir element of a fusion ring (R, B) gives rise to the so called Casimir matrix C of (R, B). This enables us to construct a generalized Cartan matrix D-C in the sense of Kac for a suitable diagonal matrix D. In this paper, we study some elementary properties of the Casimir matrix C and use them to realize certain fusion rings from the generalized Cartan matrix D-C of finite (resp. affine) type. It turns out that there exists a fusion ring with D-C being of finite (resp. affine) type if and only if D-C has only the form A₂ (resp. A₁⁽¹⁾. We also realize all fusion rings with D-C being a particular generalized Cartan matrix of indefinite type.     

Solid-Phase Synthesis of an Insect Pyrokinin Analog Incorporating an Imidazoline Ring as Isosteric Replacement of a trans Peptide Bond

A facile solid-phase synthetic method for incorporating the imidazoline ring motif, a surrogate for a trans peptide bond, into bioactive peptides is reported. The example described is the synthesis of an imidazoline peptidomimetic analog of an insect pyrokinin neuropeptide via a cyclization reaction of an iminium salt generated from the preceding amino acid and 2,4-diaminopropanoic acid (Dap).     

Interplay of Hückel and Möbius Aromaticity in Metal-Metal Quintuple Bonded Complexes of Cr,Mo, and W with Amidinate Ligand: Ab initio DFT and Multireference Analysis**

The aromaticity of metal-metal quintuple bonded complexes of the type M₂L₂ (M=Cr, Mo, and W; L=amidinate) are studied employing gauge including magnetically induced ring current (GIMIC) analysis and electron density of delocalized bonds (EDDB). It is found that the complexes possess two types of aromaticity: i) Hückel aromaticity through delocalization of ligand π electrons with metal-metal δ-bond-forming 6 conjugated electrons (4π and 2δ) ring; ii) Craig-Möbius aromaticity through delocalization of π electrons of both the ligands with metal d-orbitals in Craig type orientation forming 10π electrons ring with a double twist. Extended transition state natural orbital chemical valence (ETS-NOCV) and canonical molecular orbital natural chemical shielding (CMO-NCS) analysis confirm the Craig-Möbius type arrangement of the orbitals. Furthermore, the unprecedented Hückel and Möbius type aromaticity is confirmed from the plot of the current pathways using 3D line integral convolution (3D-LIC) plots. The metal-metal bond order also increases down the group as justified from the complete active space self-consistent field (CASSCF) analysis. Due to an increase in the π and δ electron conjugation, both the Hückel and Möbius aromaticity increase down the group.     

Selective Construction of Trefoil knots and a Molecular Borromean Ring Induced by Steric Hindrance of Thioether Ligands

Two Cp*−Rh^III based trefoil knots were obtained in high yield under ambient conditions via the coordination-driven self-assembly of semi-rigid thioether dipyridyl ligand 1,4-bis[(pyridin-4-ylthio)methyl]benzene ( L₁ ), ligand chloranilic acid (H₂− CA ) and 6,11-dihydroxytetracene-5,12-dione (H₂- TtDo ) with Cp*Rh^III metal corner units, respectively. Furthermore, using the bulkier 4,4′-{[(2,5-dimethyl-1,4-phenylene)bis(methylene)]bis(sulfanediyl)}dipyridine ( L₂ ) in the place of ligand L₁ in the construction process resulted in the formation of a teranuclear metallacycle and a template-free Borromean ring in high yields thanks to significantly altered intermolecular forces between the constituent ligands induced by the sterically-hindering methyl groups of L₂ , as demonstrated via a detailed X-ray crystallographic analysis and NMR spectroscopy.     

Synthesis,chemical properties,and CO2 electroreduction of π-conjugated polymers bearing imidazolium and imidazolinium rings in the polymer backbone

π-Conjugated polymers (CPs) bearing imidazolium and imidazolinium rings in the polymer backbone were prepared from a previously reported monomer, 1,3-bis(2,3-dimethyl-4-bromophenyl)imidazolium chloride, and a newly synthesized monomer, 1,3-bis(2,3-dimethyl-4-bromophenyl)imidazolinium chloride, via Sonogashira and Suzuki–Miyaura coupling reactions. The corresponding model compounds were also synthesized via the same reactions and monomers. The absorption maxima and onset position of the UV–vis spectra of the polymers were observed at longer wavelengths than those of the model compounds, thus revealing the presence of extended π-conjugation along the polymer backbone chain. Both polymers and model compounds were photoluminescent in solution and exhibited solvatochromism. The cast films of the polymers on the Pt and Ag electrodes were demonstrated to be effective catalysts for CO₂ electroreduction.     

A Close-to-Aromatize Approach for the Late-Stage Functionalization through Ring Closing Metathesis

An efficient approach for the synthesis of monosubstituted aromatic compounds relying on a ring-closing metathesis followed by spontaneous 1,2-elimination is presented. The efficiency for late-stage functionalization is highlighted in various solvents (up to 920 TON). This approach is compatible with strained cycles and other multiple bonds in the substrate.     

C2轴手性双胍催化叶立德和不饱和吖内酯的串联反应研究

本文成功合成了4种基于联二萘酚骨架的手性双胍-酰胺类催化剂,并将其应用于邻羟基苯甲醛亚甲胺叶立德与不饱和吖内酯的1,3-偶极环加成和分子内串联反应。研究表明,在室温下以CHCl_3作为溶剂、轴手性胍(1b,10(mol)%)作为催化剂,反应12h,能以较好的收率(73%～88%)和较高的对映选择性(72%～86%)得到苯并吡喃衍生物。     

Analysis of the escape in systems with four exit channels

In this paper, we have performed a numerical investigation of the escape of a particle from two different dynamical systems with the same number of exit channels. We have chosen specific values of the parameters of the systems so that the openings of the potential well in both systems are approximately of the same size. We have found that, in the galactic system, the distribution of the times of escape follows a sequential pattern that has never been detected before. Moreover, we have proved that this pattern is directly related to the geometry of the stable manifolds to the Lyapunov orbits located at the openings of the potential. Finally, we have shown that the different nature of the two systems affects the way the escape occurs, due to the difference in the geometry of the manifolds to the Lyapunov orbits in both systems.     

On-surface synthesis of porous graphene nanoribbons containing nonplanar [14]annulene pores

The precise introduction of nonplanar pores in the backbone of graphene nanoribbon represents a great challenge. Here, we explore a synthetic strategy toward the preparation of nonplanar porous graphene nanoribbon from a predesigned dibromohexabenzotetracene monomer bearing four cove-edges. Successive thermal annealing steps of the monomers indicate that the dehalogenative aryl-aryl homocoupling yields a twisted polymer precursor on a gold surface and the subsequent cyclodehydrogenation leads to a defective porous graphene nanoribbon containing nonplanar [14]annulene pores and five-membered rings as characterized by scanning tunneling microscopy and noncontact atomic force microscopy. Although the C–C bonds producing [14]annulene pores are not achieved with high yield, our results provide new synthetic perspectives for the on-surface growth of nonplanar porous graphene nanoribbons.