Strongly convex functions of higher order

The notion of strongly n-convex functions with modulus c>0 is introduced and investigated. Relationships between such functions and n-convex functions in the sense of Popoviciu as well as generalized convex functions in the sense of Beckenbach are given. Characterizations by derivatives are presented. Some results on strongly Jensen n-convex functions are also given.     

Higher order variational origin of the Dixonʼs system and its relation to the quasi-classical ‘Zitterbewegung’ in General Relativity

We show how the Dixon?s system of first order equations of motion for the particle with inner dipole structure together with the side Mathisson constraint follows from rather general construction of the ‘Hamilton system’ developed by Weyssenhoff, Rund and Grässer to describe the phase space counterpart of the evolution under the ordinary Euler–Poisson differential equation of the parameter-invariant variational problem with second derivatives. One concrete expression of the ‘Hamilton function’ leads to the General Relativistic form of the fourth order equation of motion known to describe the quasi-classical ‘quiver’ particle in Special Relativity. The corresponding Lagrange function including velocity and acceleration coincides in the flat space of Special Relativity with the one considered by Bopp in an attempt to give an approximate variational formulation of the motion of self-radiating electron, when expressed in terms of geometric quantities.     

Magnetostructural D correlations in hexacoordinated cobalt(II) complexes

The magnetostructural D correlation for hexacoordinated cobalt(II) complexes is outlined. The structural and magnetic properties of a series of mononuclear cobalt(II) complexes with the general formulas [Co(II)(L)(6)]X(2), [Co(II)(L)(2)X(2)], and [Co(II)(L)(2)(H(2)O)(2)(car)(2)] have been investigated where the coordination sphere is formed by nitrogen/oxygen-donor heterocycle (L), carboxylato (car), aqua, and chlorido ligands. The chromophores of these compounds involve {CoN(6)}, {CoO(6)}, {CoO(4)O'(2)}, {CoN(2)O(2)O'(2)}, and {CoN(2)O(2)Cl(2)}. All complexes were subjected to magnetochemical investigation down to 2 K (SQUID susceptibility and magnetization measurements). Most of the studied complexes show magnetic behavior typical for zero-field-splitting systems. The magnetism of the complex [Co(H(2)O)(6)](6-OHnic)(2) reflects the presence of the magnetic angular momentum in the ground-state crystal-field term. The obtained values of the magnetic anisotropy (D or δ) have been correlated with the structural distortion of the coordination polyhedron. This correlation can be understood with the help of crystal-field theory, where the magnetic anisotropy parameters are related to the splitting of the lowest crystal-field multiplets.     

Colloidal and chemical aspects of nanosized hydrated zirconium dioxide synthesized via a sol-gel process

The processes of coagulation and gelation of sols in zirconium oxychloride aqueous solutions and the properties of hydrated zirconium dioxide sols (pH, particles size, dynamic viscosity) depending on the aging conditions of partially neutralized zirconium oxychloride feedstock solution-zirconyl hydroxychloride used for the synthesis and molar ratio of initial reagents (Zr/NaOH, Zr/CH(3)COO(-)) were first studied in the paper. The concentration and temperature limits of hydrated zirconium dioxide sols stability were determined. The coagulation constant, gelation activation energy, and gelation thermal effect values were found.     

Reversible anion-templated self-assembly of [2+2] and [3+3] metallomacrocycles containing a new dicopper(I) motif

A new dicopper(I) complex is reported that can be incorporated into extended architectures through multitopic carboxylate linkers; reversible carboxylate templation under pH control led to the formation of [2+2] and [3+3] metallomacrocycles.     

Electron ionization mass spectra of alkylated sulfabenzamides

Mono‐, di‐ and trialkyl derivatives of 'sulfabenzamide' (N‐4‐aminophenylsulfonylbenzamide) have been prepared and their electron ionization (EI) mass spectra examined. It is found that the fragmentation of N‐alkylsulfabenzamides (alkyl = CH₃ to n‐C₅H₁₁) proceeds via a very specific rearrangement process. The proposed mechanism involves an intermediate formation of distonic molecular ions, and the driving force for this process is the formation of stable N‐alkylphenylcyanide cations [R‐N⁺ ? CC₆H₅]. The findings are confirmed by exact mass measurements, tandem mass spectrometry (MS/MS) experiments and deuterium labeling. Published in 2011 by John Wiley & Sons, Ltd.