A class of stochastic differential equations with pathwise unique solutions

We propose a new method viz., using stochastic partial differential equations to study the pathwise uniqueness of stochastic (ordinary) differential equations. We prove the existence and pathwise uniqueness of a class of stochastic differential equations with coefficients in suitable Hermite-Sobolev class using our approach.     

Effect of annular apodization and pupil beam parameter in the focal region of high NA lens

Focusing properties of the radially polarized axisymmetric Bessel-modulated Gaussian beam with quadratic radial dependence (QBG beam) and annular aperture are investigated theoretically by vector diffraction theory. Simulation results show that the intensity distribution in the focal region of the radially polarized axisymmetric QBG beam can be adjusted considerably by small beam parameter (μ) and annular aperture (δ). When μ increases, the focal spot may change to focal hole and changes focal pattern remarkably. On introducing annular aperture, focus can split or extends along the optical axis for different μ. In this paper, we have shown the generation of the focal spot, dark focal spot, focal split and increase in focal depth in the axial direction of the incident beam propagating through the aligned optical system.     

Growth,optical, mechanical and electrical studies of nonlinear optical crystal: l-Valinium oxalate

l-Valinium oxalate (LVO) single crystal has been grown by solution growth technique at room temperature. The crystal structure and lattice parameters were determined for the grown crystal by single crystal X-ray diffraction studies. Optical constants like band gap, refractive index, reflectance, extinction coefficient and electric susceptibility were determined from UV–vis–NIR spectrum. The microhardness studies reveal the mechanical strength of the grown crystal. The dielectric constant, dielectric loss and AC conductivity of the compound were calculated at different temperatures and frequencies to analyze the electrical properties. Nonlinear optical property was discussed to confirm the SHG efficiency of the grown crystal.     

The <Emphasis Type="Italic">recombination activation gene 1</Emphasis> (<Emphasis Type="Italic">Rag1</Emphasis>) is expressed in a subset of zebrafish olfactory neurons but is not essential for axon targeting or amino acid detection

Background  

Rag1 (Recombination activation gene-1) mediates genomic rearrangement and is essential for adaptive immunity in vertebrates. This gene is also expressed in the olfactory epithelium, but its function there is unknown.     

Optimal execution with weighted impact functions: a quadratic programming approach

In this paper, we develop optimal trading strategies for a risk averse investor by minimizing the expected cost and the risk of execution. Here we consider a law of motion for price which uses a convex combination of temporary and permanent market impact. In the special case of unconstrained problem for a risk neutral investor, we obtain a closed form solution for optimal trading strategies by using dynamic programming. For a general problem, we use a quadratic programming approach to get approximate dynamic optimal trading strategies. Further, numerical examples of optimal execution strategies are provided for illustration purposes.     

Free convection effects on the oscillatory flow past a vertical porous plate in the presence of radiation for an optically thin fluid

The purpose of this work is to study the effect of transverse sinusoidal suction velocity on the flow and mass transfer on free convective oscillatory viscous and optically thin grey fluid over a porous vertical plate in the presence of radiation. The flow becomes three-dimensional due to the variation of suction velocity in the transverse direction. Analytical expressions for velocity and temperature fields are obtained using the perturbation technique. The governing equations has been transformed to ordinary differential equations. Numerical solutions are obtained for different values of radiation parameter, Grashof number and Schmidt number. It is found that non-dimensional velocity decreases with increase of radiation parameter, increases with increase of Grashof number, decreases with increase of Schmidt number and non-dimensional temperature decreases with the increase of radiation parameter.     

Enantioselective LC‐ESI‐MS/MS determination of dropropizine enantiomers in rat plasma and application to a pharmacokinetic study

We developed and validated a simple, sensitive, selective and reliable LC–ESI‐MS/MS method for direct quantitation of dropropizine enantiomers namely levodropropizine (LDP) and dextrodropropizine (DDP) in rat plasma without the need for derivatization as per regulatory guidelines. Dropropizine enantiomers and carbamazepine (internal standard) were extracted from 50 μL rat plasma using ethyl acetate. LDP and DDP resolved with good baseline separation (R_s = 4.45) on a Chiralpak IG‐3 column. The mobile phase consisted of methanol with 0.05% diethylamine pumped at a flow rate of 0.5 mL/min. Detection and quantitation were done in multiple reaction monitoring mode following the transitions m/z 237 → 160 and 237 → 194 for dropropizine enantiomers and the internal standard, respectively, in the positive ionization mode. The proposed method provided accurate and reproducible results over the linearity range of 3.23–2022 ng/mL for each enantiomer. The intra‐ and inter‐day precisions were in the ranges of 3.38–13.6 and 5.11–13.8 for LDP and 4.19–11.8 and 8.89–10.1 for DDP. Both LDP and DDP were found to be stable under different stability conditions. The method was successfully used in a stereoselective pharmacokinetic study of dropropizine enantiomers in rats following oral administration of racemate dropropizine at 100 mg/kg. The pharmacokinetic results indicate that the disposition of dropropizine enantiomers is not stereoselective and chiral inversion does not occur in rats.     

Validated HPLC method for simultaneous quantification of mutant IDH1/2 inhibitors (enasidenib,ivosidenib and vorasidenib) in mouse plasma: Application to a pharmacokinetic study

Isocitrate dehydrogenase (IDH) inhibitors comprise a novel class of anticancer drugs, which are approved to treat acute myeloid leukemia patients having mutations on IDH1/2. We report the development and validation of a high‐performance liquid chromatography (HPLC) method for the simultaneous quantitation of IDH inhibitors, namely enasidenib (EDB), ivosidenib (IDB) and vorasidenib (VDB), in mouse plasma as per the US Food and Drug Administration regulatory guidelines. The method involves extraction of EDB, IDB and VDB along with internal standard (IS; phenacetin) from mouse plasma (100 μl) using a simple protein precipitation process. The chromatographic analysis was performed on an HPLC system using a gradient mobile phase (comprising 10 mm ammonium acetate and acetonitrile in a flow‐gradient) and an X‐Terra Phenyl column. The UV detection wave length was set at λ_max 265 nm. EDB, IDB, VDB and the IS eluted at 7.36, 8.60, 9.50 and 5.12 min, respectively, with a total run time of 10 min. The calibration curve was linear over a concentration range of 0.20–12.5 μg/ml for EDB and 0.50–12.5 μg/ml for IDB and VDB (r² = ≥0.998 for all of the analytes). Validation results met the acceptance criteria. The validated HPLC method was successfully applied to a pharmacokinetic study in mice.     

Biosynthesis of zinc oxide nanoparticles using Euphorbia milii leaf constituents: Characterization and improved photocatalytic degradation of methylene blue dye under natural sunlight

A facile biosynthesis route was followed to prepare zinc oxide nanoparticles (ZnO NPs) using Euphorbia milii (E. milii) leaf constituents. The SEM images exhibited presence of spherical ZnO NPs and the corresponding TEM images disclosed monodisperse nature of the ZnO NPs with diameter ranges between 12 and 20 nm. The Brunauer–Emmett–Teller (BET) analysis revealed that the ZnO NPs have specific surface area of 20.46 m²/g with pore diameter of 2 nm–10 nm and pore volume of 0.908 cm³/g. The EDAX spectrum exemplified the existence of Zn and O elements and non-appearance of impurities that confirmed pristine nature of the ZnO NPs. The XRD pattern indicated crystalline peaks corresponding to hexagonal wurtzite structured ZnO with an average crystallite size of 16.11 nm. The FTIR spectrum displayed strong absorption bands at 512 and 534 cm^?1 related to ZnO. The photocatalytic action of ZnO NPs exhibited noteworthy degradation of methylene blue dye under natural sunlight illumination. The maximum degradation efficiency achieved was 98.17% at an illumination period of 50 min. The reusability study proved considerable photostability of the ZnO NPs during photocatalytic experiments. These findings suggest that the E. milii leaf constituents can be utilized as suitable biological source to synthesis ZnO NPs for photocatalytic applications.     

Nelumbo nucifera leaves as source of water-repellent wax: Extraction through polar and non-polar organic solvents

Nelumbo nucifera leaves are rich source of natural wax possessing super-hydrophobic properties. It provides protection to them from ecological turbulences and climatic wear and tear. In this study, various experiments have been conducted to observe the yield of extraction and the determination of various functional groups, which are present in natural wax, derived from Nelumbo nucifera leaves. The natural wax has been extracted from lotus leaves through non-polar (hexane) and polar (ethanol) solvent via different extraction methods. The superhydrophobic wax has been successfully extracted with hexane. Whereas, ethanol did not extract the water-repellent wax of lotus leaf. Considering the cumulative amount, i.e. (desired + undesired), the maceration shows the extraction of 2.9% (%w/w, through hexane) and 10.2% (%w/w, through ethanol), while it was found 2.5% (%w/w, cycle period 15 min) and 9.0% (%w/w, cycle period 26 min) respectively, in case of Soxhlet extraction technique. For this specific case of natural wax recovery from biomass (lotus leaf), the maceration (traditional method) resulted a little bit superior extraction yield in comparison to the Soxhlet extraction method for extraction of crude wax. In the case of non-polar solvent (hexane), an extraction yield of 1.97% (%w/w) through maceration method was observed while in the case of non-polar solvent (ethanol), an extraction yield of 1.62% (%w/w) through Soxhlet extraction was observed. The TLC analysis on both types of extracts was performed. For the detection of various hydrocarbon chains in the crude wax extracts, FTIR was also performed. Topography of wax surface and wax-coated waterproof fabric was compared through SEM.