Statistics and characterization of matrices by determinant and trace

The Ramanujan Journal - Answering a question of Erdös, Komlós proved in 1968 that almost all $$n\times n$$ Bernoulli matrices are nonsingular as $$n\rightarrow \infty $$ . In this paper,...     

Orthogonal polynomials and continued fractions arising from contiguous relations and generalizations of Kummer and q-Kummer identities

The Ramanujan Journal - In this paper, we show formally how can we generate continued fractions starting from three-term contiguous relations. Then as examples, starting from certain contiguous...     

Self-similar asymptotic behavior for the solutions of a linear coagulation equation

In this paper we consider the long-time asymptotics of a linear version of the Smoluchowski equation which describes the evolution of a tagged particle moving in a random distribution of fixed particles. The volumes v of these particles are independently distributed according to a probability distribution which decays asymptotically as a power law $v^{?\sigma }$. The validity of the equation has been rigorously proved in [22] taking as a starting point a particle model and for values of the exponent $\sigma >3$, but the model can be expected to be valid, on heuristic grounds, for $\sigma >\frac{5}{3}$. The resulting equation is a non-local linear degenerate parabolic equation. The solutions of this equation display a rich structure of different asymptotic behaviors according to the different values of the exponent σ. Here we show that for $\frac{5}{3}<\sigma <2$ the linear Smoluchowski equation is well-posed and that there exists a unique self-similar profile which is asymptotically stable.     

Asymmetric Reactions involving Lewis Base Catalyst Tethered Dearomatized Intermediates

Numerous protocols have been developed for the functionalization of aromatic substances. Among them, the strategy by which aromatic substrates are activated in situ to generate dearomatized intermediates is highly efficient but challenging, especially in the field of asymmetric catalysis. In this Concept article, the application of some well-established chiral Lewis base catalysis, including primary/secondary amines and N-heterocyclic carbenes, that can covalently form catalyst-tethered dearomatized ortho/para-quinodimethane species with diverse heteroaryl and aryl carbonyl substrates is summarized in a number of asymmetric cycloaddition and addition reactions with diverse reagents generally having electrophilic properties. As a result, a variety of enantioenriched aromatic products with higher molecular complexity are constructed effectively through a rearomatization process.     

Imide-Functionalized Polymer Semiconductors

Imide-functionalized π-conjugated polymer semiconductors have received a great deal of interest owing to their unique physicochemical properties and optoelectronic characteristics, including excellent solubility, highly planar backbones, widely tunable band gaps and energy levels of frontier molecular orbitals, and good film morphology. The organic electronics community has witnessed rapid expansion of the materials library and remarkable improvement in device performance recently. This review summarizes the development of imide-functionalized polymer semiconductors as well as their device performance in organic thin-film transistors and polymer solar cells, mainly achieved in the past three years. The materials mainly cover naphthalene diimide, perylene diimide, and bithiophene imide, and other imide-based polymer semiconductors are also discussed. The perspective offers our insights for developing new imide-functionalized building blocks and polymer semiconductors with optimized optoelectronic properties. We hope that this review will generate more research interest in the community to realize further improved device performance by developing new imide-functionalized polymer semiconductors.     

Cytotoxicity of Shear Exfoliated Pnictogen (As,Sb, Bi) Nanosheets

The experimental achievement of phosphorene, which exhibits superior electronic, physical, and optical properties has spurred recent interest in other Group 15 elemental 2D nanomaterials such as arsenene, antimonene, and bismuthene. These unique and superior properties of the pnictogen nanosheets have spurred intensive research efforts and led to the discovery of their diversified potential applications; for instance, optical Kerr material, photonic devices, pnictogen-decorated microfibers, high-speed transistors, and flexible 2D electronics. Previous studies have mainly been dedicated to study the synthesis, properties, and applications of the heavy pnictogens nanosheets; however, the toxicological behaviour of these nanosheets has yet to be established. Herein, the cytotoxicity study of pnictogen nanosheets (As, Sb, and Bi) was conducted over 24 h of incubation with various concentrations of test materials and adenocarcinoma human lung epithelial A549 cells. After the treatment period, the remaining cell viabilities were obtained through absorbance measurements with WST-8 and MTT assays. These findings demonstrate that the toxicity of pnictogen nanosheets decreases down Group 15, whereby arsenic nanosheets are considered to be the most toxic, whereas bismuth nanosheets induce low cytotoxicity. The findings of this study constitute an important initial step towards enhancing our understanding of the toxicological effects of pnictogen nanosheets in light of their prospective commercial applications.