Unprecedented Double aza‐Michael Addition within a Sapphyrin Core

A benzodipyrrole-derived sapphyrin.

Evaluation of planarity and aromaticity in sapphyrin and inverted sapphyrin using a bidirectional NICS (Nucleus-Independent Chemical Shift) scan method?

Using the bidirectional NICS scan method in conjunction with two-photon absorption (TPA) measurements, it has proved possible to determine the relationship between pi-conjugation and aromaticity in two structurally related expanded porphyrin systems, sapphyrin and inverted sapphyrin, and establish that differences in these defining factors depend on the presence or absence of a key sp3 hybrid m...

Double Sequence Core Theorems

In 1900, Pringsheim gave a definition of the convergence of double sequences. In this paper, that notion is extended by presenting definitions for the limit inferior and limit superior of double sequences. Also the core of a double sequence is defined. By using these definitions and the notion of regularity for 4-dimensional matrices, extensions, and variations of the Knopp Core theorem are pro...

A ricle Unprecedented Heterogeneity in the Synonymous Substitution Rate within a Plant Genome

The synonymous substitution rate varies widely among species, but it is generally quite stable within a genome due to the absence of strong selective pressures. In plants, plastid genes tend to evolve faster than mitochondrial genes, rate variation among species generally correlates between the mitochondrial and plastid genomes, and few examples of intragenomic rate heterogeneity exist. To stud...

Double Core Photonic Crystal Fiber

In this study, coupling between two cores in a specific photonic crystal fiber (PCF) structure is investigated via Localized Basis Function (LBF) method. The PCF structure considered here consists of an unbounded periodic cladding and two high index core regions. In the LBF method, a guided mode localized in the core regions and periodic variation of the refractive index in the transverse domai...