A Depth Formula for Generic Singularities and Their Weak Normality

Let X be a smooth projective variety of dimension r and π:X → ?^m a generic projection with r + 1 ≤ m ≤ 2r. It is shown that, at any point on X′ = π(X) of multiplicity μ, off a closed subset of the triple locus of codimension four, the depth of the local ring is equal to r ? (μ ? 1)(m ? r ? 1). This leads to some improvements on the affirmation of a conjecture of Andreotti–Bombieri–Holm on the weak normality of X′ and a conjecture of Piene on the weak normality of Sing(X′).     

与星象函数有关的拟共形近于凸调和映射

讨论了一类解析部分为星象函数的拟共形近于凸调和映射的基本性质,得到了此类映射的系数不等式、积分表达式、增长定理、面积定理与部分和的近于凸半径.     

Strongly Even‐Cycle Decomposable Graphs

A graph is strongly even‐cycle decomposable if the edge set of every subdivision with an even number of edges can be partitioned into cycles of even length. We prove that several fundamental composition operations that preserve the property of being Eulerian also yield strongly even‐cycle decomposable graphs. As an easy application of our theorems, we give an exact characterization of the set of strongly even‐cycle decomposable cographs.     

New Triazinoindole Bearing Benzimidazole/Benzoxazole Hybrids Analogs as Potent Inhibitors of Urease: Synthesis,In Vitro Analysis and Molecular Docking Studies

Twenty-four analogs based on triazinoindole bearing benzimidazole/benzoxazole moieties (1–25) were synthesized. Utilizing a variety of spectroscopic methods, including ¹H-, ¹³C-NMR, and HREI-MS, the newly afforded compounds (1–25) were analyzed. The synthesized analogs were tested against urease enzyme (in vitro) as compared to the standard thiourea drug. All triazinoindole-based benzimidazole/benzoxazole analogs (1–25) exhibited moderate to excellent inhibition profiles, having IC₅₀ values of 0.20 ± 0.01 to 36.20 ± 0.70 μM when evaluated under the positive control of thiourea as a standard drug. To better understand the structure–activity relationship, the synthesized compounds were split into two groups, “A” and “B.” Among category “A” analogs, analogs 8 (bearing tri-hydroxy substitutions at the 2,4,6-position of aryl ring C) and 5 (bearing di-hydroxy substitutions at the 3,4-position of aryl ring C) emerged as the most potent inhibitors of urease enzyme and displayed many times more potency than a standard thiourea drug. Besides that, analog 22 (which holds di-hydroxy substitutions at the 2,3-position of the aryl ring) and analog 23 (bearing ortho-fluoro substitution) showed ten-fold-enhanced inhibitory potential compared to standard thiourea among category “B” analogs. Molecular docking studies on the active analogs of each category were performed; the results obtained revealed that the presence of hydroxy and fluoro-substitutions on different positions of aryl ring C play a pivotal role in binding interactions with the active site of the targeted urease enzyme.     

Absorptiometric determination of sulphide ion

An absorptiometric method is described for sulphide ion, based on the green colour which is formed when sulphide ions are treated in ammoniacal solution with iron(III) and an excess of nitrilotriacetic acid. The recommended procedure can be applied from 1200 down to 8 ppm of sulphide and is interfered with seriously only by selenite from amongst seventeen other anions examined. The colour system is stabilized by an excess of sulphite. Suggestions are made about the nature of the colour body and its mechanism of production.     

Mid infrared resonant cavity detectors and lasers with epitaxial lead-chalcogenides

Wavelength tunable emitters and detectors in the mid-IR wavelength region allow applications including thermal imaging and gas spectroscopy. One way to realize such tunable devices is by using a resonant cavity. By mechanically changing the cavity length with MEMS mirror techniques, the wavelengths may be tuned over a considerable range.     

A hybrid proximal point algorithm for finding minimizers and fixed points in CAT(0) spaces

We introduce a hybrid proximal point algorithm and establish its strong convergence to a common solution of a proximal point of a lower semi-continuous mapping and a fixed point of a demicontractive mapping in the framework of a CAT(0) space. As applications of our new result, we solve variational inequality problems for these mappings on a Hilbert space. Illustrative example is given to validate theoretical result obtained herein.     

Correlation between carbon nanotube microstructure and their catalytic efficiency towards the p-coumaric acid degradation

Pristine and annealed multi-walled C nanotubes are preliminarily tested as catalysts towards the degradation of p-coumaric acid with better performances than the widely used activated carbon. In order to clarify the origin of their different catalytic efficiency, the samples are analysed by means of high-resolution transmission electron microscopy, X-ray photoemission, reflection electron energy loss and micro-Raman spectroscopy. Chemical composition, mass density, bonding configurations and threefold- to fourfold-coordinated carbon bonding ratios are determined. The comparative discussion of the results obtained leads to attribute the higher catalytic activity of the pristine nanotubes to their larger sp²/sp³ carbon bonding fraction and greater amount of oxygen containing functional groups.     

Comparison of phase error sensitivities of all-optical discrete Fourier transforms for OFDM demultiplexing

The design of three different filter structures for the separation of 8 sub-channels in an optical OFDM system are compared. They are based on serial, serial-parallel and parallel filtering and can be realized as planar lightwave circuits. We investigate the tolerance towards phase errors in these structures using a Monte-Carlo simulation.