On the equivalence of ball conditions for simplicial finite elements in Rd

We prove that the inscribed and circumscribed ball conditions, commonly used in finite element analysis, are equivalent in any dimension.     

Scale Invariant Boundary Harnack Principle at Infinity for Feller Processes

In this paper we prove a uniform and scale invariant boundary Harnack principle at infinity for a large class of purely discontinuous Feller processes in metric measurespaces.     

1,2,4‐Triazole‐based N‐heterocyclic carbene complexes of gold(I): synthesis,characterization and biological activity

Two gold(I) complexes of the (NHC)AuX type bearing a triazole‐based N‐heterocyclic carbene (NHC) ligand (1‐tert‐butyl‐4‐(4‐methylphenyl)‐3‐phenyl‐1H‐1,2,4‐triazol‐4‐ium‐5‐ylidene) and various halide ligands (X = Br, I) were synthesized and characterized in solution using NMR spectroscopy as well as in the solid state using X‐ray diffraction techniques. The cytotoxic properties of both compounds and the precursor, (NHC)AuCl, were screened against a panel of human tumour cell lines including liver cancer (HepG2), cervical cancer (HeLa S3) and leukaemia (CCRF‐CEM, HL‐60) and compared to cisplatin and auranofin. It was found that the activities of the chloro and bromo derivatives were generally superior to that of cisplatin and slightly less effective compared to auranofin, except for HepG2 cells where auranofin was not as effective. In addition, the ability to induce membrane phosphatidyl serine externalization as a hallmark of apoptosis in CCRF‐CEM leukaemic cells was investigated. Copyright © 2016 John Wiley & Sons, Ltd.     

Palladium(II) complexes of Y,C,Y‐chelated phosphines: synthesis,structure, and catalytic activity in Suzuki–Miyaura reaction

The phosphines L¹PPh₂ (1) and L²PPh₂ (2) containing different Y,C,Y‐chelating ligands, L¹ = 2,6‐(^tBuOCH₂)₂C₆H₃^? and L² = 2,6‐(Me₂NCH₂)₂C₆H₃^?, were treated with PdCl₂ and di‐µ‐chloro‐bis[2‐[(N,N‐dimethylamino)methyl]phenyl‐C,N]‐dipalladium(II) and yielded complexes trans‐{[2,6‐(^tBuOCH₂)₂C₆H₃]PPh₂}₂PdCl₂ (3), {[2,6‐(Me₂NCH₂)₂C₆H₃]PPh₂} PdCl₂ (4), {[2,6‐(^tBuOCH₂)₂C₆H₃]PPh₂}Pd(Cl)[2‐(Me₂NCH₂)C₆H₄] (5) and {[2,6‐(Me₂NCH₂)₂C₆H₃]PPh₂}Pd(Cl)[2‐(Me₂NCH₂)C₆H₄] (6) as the result of different ability of starting phosphines 1 and 2 to complex PdCl₂. Compounds 3–6 were characterized by ¹H, ¹³C, ³¹P NMR spectroscopy and ESI‐MS. The molecular structures of 3,4 and 6 were also determined by X‐ray diffraction analysis. The catalytic activity of complexes 3–6 was evaluated in the Suzuki‐Miyaura cross‐coupling reaction. Copyright © 2010 John Wiley & Sons, Ltd.     

A generalization of the original Jordan–von Neumann theorem

The problem of representability of quadratic functionals (acting on modules over unital complex ∗-algebras), by sesquilinear forms, is generalized by weakening the homogeneity equation. The corresponding representation theorem can be considered as a generalization of (the original form of) the classical Jordan–von Neumann characterization of complex inner product spaces.