An optimal theorem for the spherical maximal operator on the Heisenberg group

Let be the Heisenberg group and μ _r be the normalized surface measure on the sphere of radiusr in ℂ ⁿ . Let . We prove an optimalL ^p-boundedness result for the spherical maximal functionMf, namely we prove thatM is bounded onL ^p(I ⁿ ) if and only ifp>2n/2n−1.     

Probabilistic representations of solutions to the heat equation

In this paper we provide a new (probabilistic) proof of a classical result in partial differential equations, viz. if ϕ is a tempered distribution, then the solution of the heat equation for the Laplacian, with initial condition ϕ, is given by the convolution of ϕ with the heat kernel (Gaussian density). Our results also extend the probabilistic representation of solutions of the heat equation to initial conditions that are arbitrary tempered distributions.     

Enantiocomplementary Epoxidation Reactions Catalyzed by an Engineered Cofactor‐Independent Non‐natural Peroxygenase

Peroxygenases are heme‐dependent enzymes that use peroxide‐borne oxygen to catalyze a wide range of oxyfunctionalization reactions. Herein, we report the engineering of an unusual cofactor‐independent peroxygenase based on a promiscuous tautomerase that accepts different hydroperoxides (t‐BuOOH and H₂O₂) to accomplish enantiocomplementary epoxidations of various α,β‐unsaturated aldehydes (citral and substituted cinnamaldehydes), providing access to both enantiomers of the corresponding α,β‐epoxy‐aldehydes. High conversions (up to 98 %), high enantioselectivity (up to 98 % ee), and good product yields (50–80 %) were achieved. The reactions likely proceed via a reactive enzyme‐bound iminium ion intermediate, allowing tweaking of the enzyme's activity and selectivity by protein engineering. Our results underscore the potential of catalytic promiscuity for the engineering of new cofactor‐independent oxidative enzymes.     

Facile construction of non-precious iron nitride-doped carbon nanofibers as cathode electrocatalysts for proton exchange membrane fuel cells

We demonstrate a facile construction of iron nitride-doped carbon nanofiber by effectively utilizing the existing slit pores and rough edges along the inner wall of the substrate as originated by virtue of its cup-stack structure for effectively increasing the number of active sites and consequently the oxygen reduction activity.     

Optimization of Factors Influencing Microinjection Method for Agrobacterium tumefaciens-Mediated Transformation of Tomato

A simple and efficient protocol for Agrobacterium-mediated genetic transformation of tomato was developed using combination of non-tissue culture and micropropagation systems. Initially, ESAM region of 1-day-old germinated tomato seeds were microinjected for one to five times with Agrobacterium inoculums (OD₆₀₀?=?0.2–1.0). The germinated seeds were cocultivated in the MS medium fortified with (0–200 mM) acetosyringone and minimal concentrations of (0–20 mg?L^?1) kanamycin, and the antibiotic concentration was doubled during the second round of selection. Bacterial concentration of OD₆₀₀?=?0.6 served as an optimal concentration for infection and the transformation efficiency was significantly higher of about 46.28 %. In another set of experiment, an improved and stable regeneration system was adapted for the explants from the selection medium. Four-day-old double cotyledonary nodal explants were excised from the microinjected seedlings and cultured onto the MS medium supplemented with 1.5 mg?L^?1 thidiazuron, 1.5 mg?L^?1 indole-3-butyric acid, 30 mg?L^?1 kanamycin, and 0–1.5 mg?L^?1 adenine sulphate. Maximum of 9 out of 13 micropropagated shoots were shown positive to GUS assay. By this technique, the transformation efficiency was increased from 46.28 to 65.90 %. Thus, this paper reports the successful protocol for the mass production of transformants using microinjection and micropropagation techniques.     

In Silico Molecular Docking Analysis of Karanjin against Alzheimer’s and Parkinson’s Diseases as a Potential Natural Lead Molecule for New Drug Design,Development and Therapy

Parkinson’s disease (PD) and Alzheimer’s disease (AD) are neurodegenerative disorders that have emerged as among the serious health problems of the 21st century. The medications currently available to treat AD and PD have limited efficacy and are associated with side effects. Natural products are one of the most vital and conservative sources of medicines for treating neurological problems. Karanjin is a furanoflavonoid, isolated mainly from Pongamia pinnata with several medicinal plants, and has been reported for numerous health benefits. However, the effect of karanjin on AD and PD has not yet been systematically investigated. To evaluate the neuroprotective effect of karanjin, extensive in silico studies starting with molecular docking against five putative targets for AD and four targets for PD were conducted. The findings were compared with three standard drugs using Auto Dock 4.1 and Molegro Virtual Docker software. Additionally, the physiochemical properties (Lipinski rule of five), drug-likeness and parameters including absorption, distribution, metabolism, elimination and toxicity (ADMET) profiles of karanjin were also studied. The molecular dynamics (MD) simulations were performed with two selective karanjin docking complexes to analyze the dynamic behaviors and binding free energy at 100 ns time scale. In addition, frontier molecular orbitals (FMOs) and density-functional theory (DFT) were also investigated from computational quantum mechanism perspectives using the Avogadro-ORCA 1.2.0 platform. Karanjin complies with all five of Lipinski’s drug-likeness rules with suitable ADMET profiles for therapeutic use. The docking scores (kcal/mol) showed comparatively higher potency against AD and PD associated targets than currently used standard drugs. Overall, the potential binding affinity from molecular docking, static thermodynamics feature from MD-simulation and other multiparametric drug-ability profiles suggest that karanjin could be considered as a suitable therapeutic lead for AD and PD treatment. Furthermore, the present results were strongly correlated with the earlier study on karanjin in an Alzheimer’s animal model. However, necessary in vivo studies, clinical trials, bioavailability, permeability and safe dose administration, etc. must be required to use karanjin as a potential drug against AD and PD treatment, where the in silico results are more helpful to accelerate the drug development.