Stability of Multiplier Ideal Sheaves

Chinese Annals of Mathematics, Series B - In the present article, the authors find and establish stability of multiplier ideal sheaves, which is more general than strong openness.     

Dinuclear gold (I)-di-N-heterocyclic carbene complexes: syntheses,structure, density functional theory calculation and photoluminescence study

The synthesis and characterizations for a series of dinuclear gold (I)-di-NHC complexes, 1–8 through the trans-metalation method of their respective silver (I)-di-NHC complexes, i–viii are reported (where NHC = N-heterocyclic carbene). The successful complexation of a series of unusual non-symmetrical and symmetrical di-NHC ligands, 3,3'-(ethane-1,2-diyl)-1-alkylbenzimidazolium-1'-butylbenzimidazolium (with alkyl = methyl, ethyl, propyl, butyl, pentyl, hexyl, heptyl, benzyl) with the gold (I) ions are suggested by elemental analysis, Fourier transform-infrared, ¹H- and ¹³C-NMR data. The ¹³C-NMR spectra of 1–8 show a singlet sharp peak in the range of 190.00–192.00 ppm, indicating the presence of a carbene carbon that bonded to the gold (I) ion. From single crystal X-ray diffraction data, the structure of complex 6 with the formula of [di-NHC-Au (I)]₂·2PF₆ is obtained [where NHC = 3,3'-(ethane-1,2-diyl)-1-hexylbenzimidazolium-1'-butylbenzimidazolium]. The photophysical study in solid state of 6 displays an intense photoluminescence with a strong emission maxima, λ_em = 480 nm, upon excitation at 340 nm at room temperature. Interestingly, the emission maximum at 77 K shows a structural character with a strong peak at 410 nm, a medium at 433 nm and a weak at 387 nm, accompanied by a tail band to about 500 nm.     

Facile synthesis of graft copolymers containing rigid poly(dialkyl fumarate) branches by macromonomer method

Graft copolymers show microphase separated structure as seen in block copolymers and have lower intrinsic viscosity than block copolymers because of a branching structure. Therefore, considering molding processability, especially for polymers containing rigid segments, graft copolymers are useful architectures. In this work, graft copolymers containing rigid poly(diisopropyl fumarate) (PDiPF) branches were synthesized by full free‐radical polymerization process. First, synthesis of PDiPF macromonomers by addition‐fragmentation chain transfer (AFCT) was investigated. 2,2‐Dimethyl‐4‐methylene‐pentanedioic acid dimethyl ester was found to be an efficient AFCT agent for diisopropyl fumarate (DiPF) polymerization because of the suppression of undesired primary radical termination, which significantly took place when common AFCT agent, methyl 2‐(bromomethyl)acrylate, was used. Copolymerization of PDiPF macromonomer with ethyl acrylate accomplished the generation of the graft copolymer having flexible poly(ethyl acrylate) backbone and rigid PDiPF branches. The graft copolymer showed a microphase separated structure, high transparency, and characteristic thermal properties to PDiPF and poly(ethyl acrylate). © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 2474–2480     

NIFTy 3 – Numerical Information Field Theory: A Python Framework for Multicomponent Signal Inference on HPC Clusters

NIFTy , “Numerical Information Field Theory,” is a software framework designed to ease the development and implementation of field inference algorithms. Field equations are formulated independently of the underlying spatial geometry allowing the user to focus on the algorithmic design. Under the hood, NIFTy ensures that the discretization of the implemented equations is consistent. This enables the user to prototype an algorithm rapidly in 1D and then apply it to high‐dimensional real‐world problems. This paper introduces NIFTy  3, a major upgrade to the original NIFTy  framework. NIFTy  3 allows the user to run inference algorithms on massively parallel high performance computing clusters without changing the implementation of the field equations. It supports n‐dimensional Cartesian spaces, spherical spaces, power spaces, and product spaces as well as transforms to their harmonic counterparts. Furthermore, NIFTy  3 is able to handle non‐scalar fields, such as vector or tensor fields. The functionality and performance of the software package is demonstrated with example code, which implements a mock inference inspired by a real‐world algorithm from the realm of information field theory. NIFTy  3 is open‐source software available under the GNU General Public License v3 (GPL‐3) at https://gitlab.mpcdf.mpg.de/ift/NIFTy/tree/NIFTy_3 .     

Development and validation of an ultra‐high‐performance liquid chromatography–tandem mass spectrometry method to determine the bioavailability of warfarin and its major metabolite 7‐hydroxy warfarin in rats dosed with oral formulations containing different polymorphic forms

A simple, sensitive and rapid ultra‐high‐performance liquid chromatography–electrospray ionization–tandem mass spectrometry method was developed and validated for the quantification of warfarin and 7‐hydroxy warfarin in Sprague Dawley (SD) rats. Animals were administered a single dose of warfarin sodium formulations (crystalline and amorphous) at 12 mg/kg via oral gavage and blood was drawn over a 96‐h time course. Sample process recoveries, matrix effect and analyte stability were determined. The linearity for warfarin and 7‐hydroxy warfarin was from 5 to 2000 ng/mL in blank SD rat plasma. Correlation coefficients (r²) for standard calibration curves were >.98 and analytes quantified within ±15% of target at all calibrator concentrations. The average percent accuracy and precision for intra‐ and inter‐day were 93.7%–113.8% and ≤12.1%, respectively, for warfarin and 7‐hydroxy warfarin, across the quality control standards (5, 10, 500, 1800 and 2000 ng/mL). Acceptable analytical recovery (>55%) was achieved with process efficiencies >41.5% and matrix effects <139.9% over the analytical range. Both analytes were stable in stock solution, autosampler, benchtop and three cycles of freeze–thaw with percent accuracy ≥90.2% and precision (percent relative standard deviation) ≤14%. The validated method was successfully applied to a pre‐clinical bioavailability study of crystalline and amorphous warfarin sodium formulations in SD rats.     

DNA interaction,cytotoxicity and molecular structure of cobalt complex of 4‐amino‐N‐(6‐chloropyridazin‐3‐yl)benzene sulfonamide in the presence of secondary ligand pyridine

Novel cobalt complex of 4‐amino‐N‐(6‐chloropyridazin‐3‐yl)benzene sulfonamide (sulfachloropyridazine) has been synthesized and characterized by elemental analysis, FT‐IR spectroscopy and magnetic susceptibility (VSM). Cobalt complex of Sulfachloropyridazine (Co‐SCP) crystallized in monoclinic space group P2₁/n with Z = 4. The structure is solved by direct method and refined to R = 0.099 for 4720 reflections with I ?4σ(I). The results of FT‐IR spectra suggest the binding of cobalt atom to the sulfonamide ligand which is in agreement with the crystal structure determination. In crystal structure, molecule is linked via, C‐H … π, C‐Cl … π and π … π intermolecular interactions. The computational studies like the optimization energy and root means square deviation compare with single crystal structure, frontier molecular orbital (Homo‐Lumo energy) and binding energy of the Co‐SCP has been carried out using DFT/B3LYP level of theory in gaseous phase. Hirshfeld surfaces and the 2D‐fingerprint analysis are performed to study the nature of interactions and their measurable contributions towards crystal packing. The interaction of the complex with DNA is investigated using viscosity measurement and absorption titration studies. The result shows the complex bind to DNA with intercalative mode with high DNA‐binding constant (K_b). Also, in vivo and in vitro cytotoxic studies are performed using S. pombe cells and brine shrimp lethality bioassay. DNA‐cleavage study shows better cleaving ability of the complex.     

A dynamic free-entry oligopoly with sluggish entry and exit adjustments

We study a dynamic free-entry oligopoly with sluggish entry and exit of firms under general demand and cost functions. We show that the number of firms in a steady-state open-loop solution for a dynamic free-entry oligopoly is smaller than that at static equilibrium and that the number of firms in a steady-state memoryless closed-loop solution is larger than that in an open-loop solution.     

Unconditionally Superclose Analysis of a New Mixed Finite Element Method for Nonlinear Parabolic Equation

This paper develops a framework to deal with the unconditional superclose analysis of nonlinear parabolic equation. Taking the finite element pair $Q_{11}/Q_{01} × Q_{10}$ as an example, a new mixed finite element method (FEM) is established and the $τ$ -independent superclose results of the original variable $u$ in $H^1$-norm and the flux variable $\mathop{q} \limits ^{\rightarrow}= −a(u)∇u$ in $L^2$-norm are deduced ($τ$ is the temporal partition parameter). A key to our analysis is an error splitting technique, with which the time-discrete and the spatial-discrete systems are constructed, respectively. For the first system, the boundedness of the temporal errors is obtained. For the second system, the spatial superclose results are presented unconditionally, while the previous literature always only obtain the convergent estimates or require certain time step conditions. Finally, some numerical results are provided to confirm the theoretical analysis, and show the efficiency of the proposed method.