On new iterative method for solving systems of nonlinear equations

Solving systems of nonlinear equations is a relatively complicated problem for which a number of different approaches have been proposed. In this paper, we employ the Homotopy Analysis Method (HAM) to derive a family of iterative methods for solving systems of nonlinear algebraic equations. Our approach yields second and third order iterative methods which are more efficient than their classical counterparts such as Newton’s, Chebychev’s and Halley’s methods.     

Mixed Variational Principles and Robust Finite Element Design of Gradient Plasticity at Finite Strains

The modeling of size effects in elastic-plastic solids, such as the width of shear bands or the grain size dependence in polycrystals, must be based on non-standard theories which incorporate length-scales. This is achieved by models of strain gradient plasticity, incorporating spatial gradients of selected micro-structural fields which describe the evolving dissipative mechanisms. The key aspect of this work is to provide a rigorous incremental variational formulation and mixed finite element design of additive finite gradient plasticity in the logarithmic strain space. We start from a mixed saddle point principle for metric-type plasticity, which is specified for the important model problem of isochoric plasticity with gradient-extended hardening/softening response. To this end, we propose a novel finite element design of the coupled problem incorporating a local-global solution strategy of short- and long-range fields. This includes several new aspects, such as extended Q1P0-type and MINI-type finite elements for gradient plasticity [4]. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hyperpolarising Pyruvate through Signal Amplification by Reversible Exchange (SABRE)

Hyperpolarisation methods that premagnetise agents such as pyruvate are currently receiving significant attention because they produce sensitivity gains that allow disease tracking and interrogation of cellular metabolism by magnetic resonance. Here, we communicate how signal amplification by reversible exchange (SABRE) can provide strong ¹³C pyruvate signal enhancements in seconds through the formation of the novel polarisation transfer catalyst [Ir(H)₂(η²‐pyruvate)(DMSO)(IMes)]. By harnessing SABRE, strong signals for [1‐¹³C]‐ and [2‐¹³C]pyruvate in addition to a long‐lived singlet state in the [1,2‐¹³C₂] form are readily created; the latter can be observed five minutes after the initial hyperpolarisation step. We also demonstrate how this development may help with future studies of chemical reactivity.     

An approach to account for interfering parametric resonances and anti-resonances applied to examples from rotor dynamics

Nonlinear Dynamics - An initially unstable equilibrium position of a system can be stabilized by introducing a parametric excitation. This is especially of interest for suppressing self-excited...     

Chitosan-Based Materials for the Removal of Nickel Ions from Aqueous Solutions

Russian Journal of Physical Chemistry A - Sorption of Ni(II) ions from liquid effluents utilizing chemically modified chitosan; (vanillin, polymer I) and (ortho-vanillin, polymer II) is studied...     

New Perspectives for Old Clusters: Anderson–Evans Anions as Building Blocks of Large Polyoxometalate Frameworks in a Series of Heterometallic 3 d–4 f Species

A series of nine [Sb₇W₃₆O₁₃₃Ln₃M₂(OAc)(H₂O)₈]^17? heterometallic anions ( Ln₃M₂ ; Ln=La–Gd, M=Co; Ln=Ce, M=Ni and Zn) have been obtained by reacting 3 d metal disubstituted Krebs‐type tungstoantimonates(III) with early lanthanides. Their unique tetrameric structure contains a novel {MW₉O₃₃} capping unit formed by a planar {MW₆O₂₄} fragment to which three {WO₂} groups are condensed to form a tungstate skeleton identical to that of a hypothetical trilacunary derivative of the ?‐Keggin cluster. It is shown, for the first time, that classical Anderson–Evans {MW₆O₂₄} anions can act as building blocks to construct purely inorganic large frameworks. Unprecedented reactivity in the outer ring of these disk‐shaped species is also revealed. The Ln₃M₂ anions possess chirality owing to a {Sb₄O₄} cluster being encapsulated in left‐ or right‐handed orientations. Their ability to self‐associate in blackberry‐type vesicles in solution has been assessed for the Ce₃Co₂ derivative.     

Titania-based stationary phase in separation of ondansetron and its related compounds

Improvements in stationary phase stability have been and remain a great task for research of new stationary phases. Metal oxide-based stationary phases appear as one of perspective alternatives to classical silica based stationary phases regarding to their similar effectiveness, different selectivity, different retention mechanism and mainly better chemical and thermal stability. In this study, the retention behaviour of ondansetron and its five pharmacopoeial impurities on TiO(2)-based reversed phase was investigated. The influence of buffer type, pH and concentration on retention was studied. Different types and amount of organic solvent in mobile phase were tested. The effect of temperature and flow rate on separation was investigated. The separation conditions were optimized and developed method validated. The retention parameters - retention time (t(R)), retention factor (k'), theoretical plate number (N), resolution between peaks due to nearby peaks (R(s)) and symmetry factor (A(s)) have been compared to parameters achieved on polybutadiene-coated zirconia column. The thermodynamic parameters of retention of analysed compounds - enthalpy, entropy and Gibbs free energy - were calculated and compared to those achieved on polybutadiene-coated zirconia column. This work proves similarity of retention behaviour of ondansetron and its five related compounds on zirconia-based and titania-based stationary phases and potential utilisation of polyethylene covered TiO(2)-based reversed stationary phase as an alternative to polybutadiene-coated ZrO(2) stationary phase in pharmaceutical analysis of ondansetron.