On then-th order iterative ordinary linear differential equations

Summary It is shown that a change of the basis in the solution space of a second order linear differential equation induces a covariant change in the solution space of the corresponding iterative equation. Also studied is the problem to what extent a solution of an iterative equation determines the equation.Dedicated to the memory of Alexander M. Ostrowski on the occasion of the 100th anniversary of his birth.     

Polarized Raman scattering in single crystals of Nd0.7Sr0.3MnO3

We report polarized Raman scattering in single crystals of Nd_0.7Sr_0.3MnO₃. The temperature dependence of the MnO₆ octahedral bending and stretching modes observed in the XX spectra points to the existence of local lattice distortions, possibly polarons. The XY spectra have been analyzed using a collision-dominated model, which allows the extraction of the carrier scattering rate.     

Some properties of the generalized Jacobian elliptic functions II

Generalized Jacobian elliptic functions play an important role in some bifurcation problems involving one-dimensional p-Laplacian. One of the goals of this paper is to investigate various kinds of concavity of these functions. Also, inequalities involving functions under discussion, and in particular Slater inequality is established. Transformations changing the variable and modulus are obtained.     

Measurement of sodium ion concentration in undiluted urine with cation-selective polymeric membrane electrodes after the removal of interfering compounds

The measurement of sodium ion concentration in urine can provide diagnostic information and guide therapy. Unfortunately, neutral-carrier-based ion-selective electrodes show a large positive drift and loss in selectivity in undiluted urine. The extraction of electrically neutral lipids from the urine into the sensing membrane was suggested as the main source of the drift, loss of selectivity and the consequent incorrect concentration readings.In this work, (i) solvent-solvent extraction, (ii) membrane-immobilized solvent extraction and (iii) solid phase extraction were used to remove interfering compounds from urine samples. The “cleaned” urine samples were subsequently analyzed using a calixarene (sodium ionophore X)-based, solid-contact, sodium-selective electrode in a flow-through manifold. The solid-contact sodium sensors had excellent stability in cleaned urine and an acceptable bias compared to commercial clinical analyzers.     

1,3‐dipolar cycloadditions. Part XII ‐ selective cycloaddition route to 4‐nitroisoxazolidine ring systems

Cycloadditions of C,N‐diarylnitrones to β‐nitrostyrenes occurred to yield two diastereoisomeric cycloadducts, the 3,4‐trans‐4,5‐trans substituted isoxazolidine derivatives being formed selectively as the major products. These were characterised by spectroscopic and X‐ray data. Conformational studies were carried out by X‐ray crystallography and Molecular Modelling.     

CAAC-Based Thiele and Schlenk Hydrocarbons

Diradicals have been of tremendous interest for over a century ever since the first reports of p- and m-phenylene-bridged diphenylmethylradicals in 1904 by Thiele and 1915 by Schlenk. Reported here are the first examples of cyclic(alkyl)(amino)carbene (CAAC) analogues of Thiele's hydrocarbon, a Kekulé diradical, and Schlenk's hydrocarbon, a non-Kekulé diradical, without using CAAC as a precursor. The CAAC analogue of Thiele's hydrocarbon has a singlet ground state, whereas the CAAC analogue of Schlenk's hydrocarbon contains two unpaired electrons. The latter forms a dimer, by an intermolecular double head-to-tail dimerization. This straightforward synthetic methodology is modular and can be extended for the generation of redox-active organic compounds.     

Implementations of range restricted iterative methods for linear discrete ill-posed problems

This paper is concerned with iterative solution methods for large linear systems of equations with a matrix of ill-determined rank and an error-contaminated right-hand side. The numerical solution is delicate, because the matrix is very ill-conditioned and may be singular. It is natural to require that the computed iterates live in the range of the matrix when the latter is symmetric, because then the iterates are orthogonal to the null space. Computational experience indicates that it can be beneficial to require that the iterates live in the range of the matrix also when the latter is nonsymmetric. We discuss the design and implementation of iterative methods that determine iterates with this property. New implementations that are particularly well suited for use with the discrepancy principle are described.