We derive expressions, in terms of ‘polar shapelets’, for the image distortion operations associated with weak gravitational lensing. Shear causes galaxy shapes to become elongated, and is sensitive to the second derivative of the projected gravitational potential along their line of sight; flexion bends galaxy shapes into arcs, and is sensitive to the third derivative. Polar shapelets provide ...

A biologically active vitamin D(3) metabolite ("peak V metabolite") more polar than 25-hydroxycholecalciferol has been isolated from chicken intestines in pure form as a mono(trimethylsilyl)ether derivative. The molecule has been identified as 1,25-dihydroxycholecalciferol by means of mass spectrometry, ultraviolet absorption spectrophotometry, and specific chemical reactions.

Anchoring a BODIPY onto Ga(III)corrole via a meso-β linkage facilitated PeT in polar solvents, which quenched the fluorescence, and is further confirmed by electrochemical studies. The triad exhibits unprecedented crystal emission, which is not known for a corrole derivative, due to unique packing. Compound 4 hosts the first example of a novel B-F∙∙∙F interaction as well.

The first examples of arylphosphonium salts containing a dicarba-closo-dodecaborane(12) (closo-carborane) are reported; in contrast to the 1,12-carborane derivative, the 1,2- and 1,7-isomers undergo a facile deboronation reaction in polar solvents to afford the corresponding nido-carborane phosphonium zwitterions.

The solid-phase synthesis of new amphiphilic compounds is reported. It is based on a newly designed 1,4-naphthoquinone derivative that contains polar and nonpolar groups and self-assembles into micelles or vesicles in water depending on the concentration. They also display redox-active properties.

We prove some results for algebraic polynomials in the complex plane that relate L-norm of polar derivative a polynomial and under conditions. The obtained include several interesting generalizations Zygmund-type integral inequalities derive analogues classical Bernsteintype sup-norms on unit disk as well.

Fat arcs form bounding boxes for planar curves. An example on approximation by fat arcs, provided by Qun and Rokne, is corrected. The third derivative of the given curve segment under the polar coordinate system is increasing only at the beginning of the curve segment, and then decreasing, rather than monotonically increasing for the whole curve segment. Some numerical data are corrected as well.

Carbocupration of alpha-heterosubstituted alkynes leads to the formation of stereodefined functionalized vinyl copper species as single isomer. Recent advances in the field show that a simple pre-association of the organometallic derivative with an additional polar functional group in the vicinity of the reaction center may completely change the stereochemical outcome of the reaction. Represent...

Two regioisomers with C3 or D3 symmetry of water-soluble carboxylic acid C60 derivatives, containing three malonic acid groups per molecule, were synthesized and found to be equipotent free radical scavengers in solution as assessed by EPR analysis. Both compounds also inhibited the excitotoxic death of cultured cortical neurons induced by exposure to N-methyl-D-aspartate (NMDA), alpha-amino-3-...