von Neumann’s trace inequality for Hilbert–Schmidt operators

von Neumann’s inequality in matrix theory refers to the fact that the Frobenius scalar product of two matrices is less than or equal to the scalar product of the respective singular values. Moreover, equality can only happen if the two matrices share a joint set of singular vectors, and this latter part is hard to find in the literature. We extend these facts to the separable Hilbert space setting, and provide a self-contained proof of the “latter part”.     

PTML modeling for peptide discovery: in silico design of non-hemolytic peptides with antihypertensive activity

Molecular Diversity - Hypertension is a medical condition that affects millions of people worldwide. Despite the high efficacy of the current antihypertensive drugs, they are associated with...     

Effect of pretreatment on pyrolysis products of Pennisetum purpureum Schum. by Py-GC/MS

Journal of Thermal Analysis and Calorimetry - Elephant grass (Pennisetum purpureum Schum.) is one such resource with a great amount of carbohydrate and lignin polymers that together represent high...     

Synthesis and liquid crystalline behavior of bulky poly(methacrylamide)s

N‐(Bis(4‐(2‐ethylhexyloxy)phenyl)(phenyl)‐methyl)methacrylamide was synthesized and polymerized via reversible addition‐fragmentation chain‐transfer (RAFT) polymerization. The chain‐transfer agent (4‐cyano‐4‐(phenylcarbonothioylthio) pentanoic acid (CPADB)), combined with a chiral additive, and a radical initiator yielded polymers with dispersities between 1.2 and 1.4. At low concentrations, the polymers are soluble in hexanes and chloroform while at higher concentrations they swell in these solvents. Characterization of the polymers by wide‐angle X‐ray scattering (WAXS) revealed an interplanar distance of 19.0 Å. The WAXS data combined with polarized optical microscopy support a lamellar crystallization and lyotropic liquid crystalline behavior in hexanes and chloroform. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2563–2568     

Exploring Regioselective Bond Cleavage and Cross‐Coupling Reactions using a Low‐Valent Nickel Complex

Recently, esters have received much attention as transmetalation partners for cross‐coupling reactions. Herein, we report a systematic study of the reactivity of a series of esters and thioesters with [{(dtbpe)Ni}₂(μ‐η²:η²‐C₆H₆)] (dtbpe=1,2‐bis(di‐tert‐butyl)phosphinoethane), which is a source of (dtbpe)nickel(0). Trifluoromethylthioesters were found to form η²‐carbonyl complexes. In contrast, acetylthioesters underwent rapid C_acyl?S bond cleavage followed by decarbonylation to generate methylnickel complexes. This decarbonylation could be pushed backwards by the addition of CO, allowing for regeneration of the thioester. Most of the thioester complexes were found to undergo stoichiometric cross‐coupling with phenylboronic acid to yield sulfides. While ethyl trifluoroacetate was also found to form an η²‐carbonyl complex, phenyl esters were found to predominantly undergo C_aryl?O bond cleavage to yield arylnickel complexes. These could also undergo transmetalation to yield biaryls. Attempts to render the reactions catalytic were hindered by ligand scrambling to yield nickel bis(acetate) complexes, the formation of which was supported by independent syntheses. Finally, 2‐naphthyl acetate was also found to undergo clean C_aryl?O bond cleavage, and although stoichiometric cross‐coupling with phenylboronic acid proceeded with good yield, catalytic turnover has so far proven elusive.