Classical and quantum integrability for a class of potentials in two dimensions

A method for the construction of the second constant of motion in fourth order is carried out. Correspondingly the fourth order potential equation is obtained whose solutions directly provide the classical integrable systems. Second constant of motion is obtained for a large class of potentials. Quantum invariants are also obtained with second order quantum corrections of the order O(?²) to the corresponding classical invariants. The phase space diagrams for these cases are drawn using a mathematical computer software package in two dimensions.     

An evaluation of the CYP2D6 and CYP3A4 inhibition potential of metoprolol metabolites and their contribution to drug–drug and drug–herb interaction by LC‐ESI/MS/MS

The aim of the present study was to evaluate the contribution of metabolites to drug–drug interaction and drug–herb interaction using the inhibition of CYP2D6 and CYP3A4 by metoprolol (MET) and its metabolites. The peak concentrations of unbound plasma concentration of MET, α‐hydroxy metoprolol (HM), O‐desmethyl metoprolol (ODM) and N‐desisopropyl metoprolol (DIM) were 90.37 ± 2.69, 33.32 ± 1.92, 16.93 ± 1.70 and 7.96 ± 0.94 ng/mL, respectively. The metabolites identified, HM and ODM, had a ratio of metabolic area under the concentration–time curve (AUC) to parent AUC of ≥0.25 when either total or unbound concentration of metabolite was considered. In vitro CYP2D6 and CYP3A4 inhibition by MET, HM and ODM study revealed that MET, HM and ODM were not inhibitors of CYP3A4‐catalyzed midazolam metabolism and CYP2D6‐catalyzed dextromethorphan metabolism. However, DIM only met the criteria of >10% of the total drug related material and <25% of the parent using unbound concentrations. If CYP inhibition testing is solely based on metabolite exposure, DIM metabolite would probably not be considered. However, the present study has demonstrated that DIM contributes significantly to in vitro drug–drug interaction. Copyright © 2016 John Wiley & Sons, Ltd.     

Synthesis,characterization, and antiplasmodial efficacy of sulfonamide-appended [1,2,3]-triazoles

A series of benzenesulfonamide-appended [1,2,3]-triazole hybrids was synthesized by using [3 + 2] cycloaddition of primary, secondary, and tertiary sulfonamide azides with various phenoxymethylacetylenes under click reaction conditions. After structural characterization, the compounds were subjected to in-silico absorption, distribution, metabolism, excretion and toxicity (ADMET) screening to evaluate their drug-likeness and other pharmacokinetic parameters. Furthermore, their in vitro antiplasmodial potential was assessed against Plasmodium falciparum (3D7) strain, and some of the synthesized compounds displayed promising antimalarial potency. On cytotoxicity evaluation using MTT cell viability assay, the most active candidate N-(4,6-dimethylpyridin-2-yl)-4-(4-(4-nitrophenoxy)methyl)-1H-[1,2,3]-triazol-1-yl)benzenesulfonamide ( 14 ; IC₅₀ 6.2 μg/mL) demonstrated CC₅₀ 7.5 μg/mL against human hepatocarcinoma (HUH-7) cells.     

Nickel‐Catalyzed α‐Carbonylalkylarylation of Vinylarenes: Expedient Access to γ,γ‐Diarylcarbonyl and Aryltetralone Derivatives

We report a Ni‐catalyzed regioselective α‐carbonylalkylarylation of vinylarenes with α‐halocarbonyl compounds and arylzinc reagents. The reaction works with primary, secondary, and tertiary α‐halocarbonyl molecules, and electronically varied arylzinc reagents. The reaction generates γ,γ‐diarylcarbonyl derivatives with α‐secondary, tertiary, and quaternary carbon centers. The products can be readily converted to aryltetralones, including a precursor to Zoloft, an antidepressant drug.     

Efficient broadband silicon-on-insulator grating coupler with low backreflection

We design and fabricate an efficient broadband grating coupler on a 400 nm thick silicon-on-insulator wafer. The measured coupling loss is 3 dB when coupling to a single-mode fiber at 1310 nm wavelength with TE polarization. The spectral FWHM and backreflection are determined to be 58 nm and -27 dB, respectively.     

Rapid production of monodisperse cross-linked red blood corpuscle-like particles via scalable one-pot dispersion polymerization

Cross-linked polystyrene (PS) particles having red blood corpuscle (RBC)-like shape were synthesized by one-pot dispersion polymerization of styrene with ethanol/water mixture and ethylene glycol dimethacrylate (EGDMA) as the reaction medium and cross-linker, respectively. Monitoring of the reaction showed that RBC-like shape forms due to asymmetric shrinkage of a cross-linked network during the phase separation. In addition, three dimensional phase diagram was generated based on the yielded data that showed that the formation of such unique shape extremely depends on the polarity of the medium and injection time of the cross-linker. In situ synthesis of RBC-like particles, as promising biomaterials in targeted drug delivery and a model for the understanding of the cell behavior, via such fast and high solid content approach makes it to be conducive to subsequent scale up, i.e. potential commercial adoption.     

A Petrov-Galerkin method for solving the generalized equal width (GEW) equation

The generalized equal width (GEW) equation is solved numerically by the Petrov-Galerkin method using a linear hat function as the test function and a quadratic B-spline function as the trial function. Product approximation has been used in this method. A linear stability analysis of the scheme shows it to be conditionally stable. Test problems including the single soliton and the interaction of solitons are used to validate the suggested method, which is found to be accurate and efficient. Finally, the Maxwellian initial condition pulse is studied.     

On the q-ampleness of the tensor product of two line bundles

Multiple zeta values (MZVs) are generalizations of Riemann zeta values at positive integers to multiple variable setting. These values can be further generalized to level N multiple polylog values by evaluating multiple polylogs at Nth roots of unity. In this paper, we consider another level N generalization by restricting the indices in the iterated sums defining MZVs to congruence classes modulo N, which we call the MZVs at level N. The goals of this paper are twofold. First, we shall lay down the theoretical foundations of these values such as their regularizations and double shuffle relations. Second, we will generalize the bracket functions related to multiple divisor sums defined by Bachmann and Kühn to arbitrary level N and study their relations to MZVs at level N. The brackets are all q-series and similar to MZVs, they have both weight and depth filtrations. But unlike that of MZVs, the product of brackets usually has mixed weights; however, after projecting to the highest weight we can obtain an algebra homomorphism from brackets to MZVs. Moreover, the image of the derivation \({\mathfrak{D}=q\frac{d}{dq}}\) on brackets vanishes on the MZV side, which gives rise to many nontrivial \({\mathbb{Q}}\)-linear relations.