Algorithms for non-linear huber estimation

The Huber criterion for data fitting is a combination of thel ₁ and thel ₂ criteria which is robust in the sense that the influence of wild data points can be reduced. We present a trust region and a Marquardt algorithm for Huber estimation in the case where the functions used in the fit are non-linear. It is demonstrated that the algorithms converge under the usual conditions.     

Periodic solutions of some infinite-dimensional Hamiltonian systems associated with non-linear partial difference equations. II

This is our second paper devoted to the study of some non-linear Schrödinger equations with random potential. We study the non-linear eigenvalue problems corresponding to these equations. We exhibit a countable family of eigenfunctions corresponding to simple eigenvalues densely embedded in the band tails. Contrary to our results in the first paper, the results established in the present paper hold for an arbitrary strength of the non-linear (cubic) term in the non-linear Schrödinger equation.     

The magnetic moment of the 10+ isomer in140Ce andE1 transitions inN=82 isotones caused by outer subshell configurations

Using the reaction¹³⁸Ba(α,2n)¹⁴⁰Ce the magnetic moment of the 10 ₁ ⁺ isomer atE _x =3714.7 keV in theN=82 nucleus¹⁴⁰Ce has been determined by means of the TDPAD method toμ=+10.3(4)μ _N . Measuredg-factors in¹⁴⁰Ce are compared to calculations within the shell model with configuration mixing. For the 10 ₁ ⁺ isomer in¹⁴⁰Ce the four proton configuration π(1g ₇ ^2/2 ,2d ₅ ^2/2 ) has been found to be dominant. From theg-factor measurement strong contributions of multiparticle excitations to thegp2d _3/2,π3s ₁ ² or π1h ₁₁ ² shells and admixtures of neutron excitations to the wave function of the 10 ₁ ⁺ state could be excluded. The strongE1γ-branch of the deexcitation of the 10 ₁ ⁺ isomer in¹⁴⁰Ce can be explained by means of small admixtures of configurations which contain the outer subshell excitationsπ2f _7/2 andπ1h _9/2. On this basisE1 transitions experimentally observed in theN=82 nuclei¹⁴⁰Ce,¹⁴¹Pr and¹⁴⁵Eu may be understood.     

Surface composition of spray-dried milk protein-stabilised emulsions in relation to pre-heat treatment of proteins

Several important technical properties of spray-dried food powders depend on particle-liquid interactions (e.g. wettability, dispersability) and particle-particle interactions (e.g. flowability). It can be assumed that the chemical composition of the surface layer of the particles to a large extent determine these properties. The present study has been aimed to investigate the relation between the surface composition of spray-dried milk protein-stabilised emulsions and pre-heat treatment of the proteins. Solutions of WPC were heat-treated at low (60-90 degrees C) and high (140 degrees C) temperature and the degree of denaturation was determined, prior to the preparation of emulsions with rapeseed oil. The surface composition of the dry powders were established by using ESCA (electron spectroscopy of chemical analysis). The emulsions were characterised by droplet size distribution before spray drying and after dissolution of the powders. Also free fat extractions and estimations of wettability (dissolution rates) were performed. The powder surface coverage of protein decreased with increasing degree of protein denaturation before the emulsification, whereas the emulsion droplet size increased both before spray drying and after reconstitution of powders. The free fat extraction as well as the dissolution rate, whereof the latter decreased with increasing surface fat coverage, correlated well with the fat coverage of the powder surface.     

Dicopper(I) oxalate complexes as molecular precursors for the deposition of copper compounds

The synthesis, characterization, and thermal decomposition behavior of dicopper(I) oxalato complexes L₄Cu₂(C₂O₄) (L = CNtBu (2a), CNCMe₂CH₂tBu (2b), CNC₆H₃Me₂-2,6 (2c)) is reported. 2c can be prepared in a straightforward manner by the reaction of stoichiometric amounts of Cu₂O and oxalic acid with four equivalents of CNC₆H₃Me₂-2,6, while those complexes with aliphatic isocyanides are better prepared from a copper(I) oxalato complex with alkine capping ligands (Me₃SiCCSiMe₃)₂Cu₂(C₂O₄) (1) via ligand exchange. Crystallographic and spectroscopic evidence for 2a-c confirms the anticipated dinuclear structure with the oxalate in a μ-1,2,3,4 bridging mode and an essentially σ-character of the terminal isocyanides. In solid form the complexes are stable at room temperature and can be handled in air for some time. Their decomposition was studied by thermal gravimetric analysis coupled with mass spectrometry, and the degradation pathway was shown to depend on the type of isocyanide capping ligand. Decomposition of 2a,b takes place between 150 and 200 °C to give CuCN in a clean process that involves isobutene elimination from the terminal ligands, with elimination of (CN)₂ and conversion to elemental copper at higher temperatures. Heating of 2c leads to CuO (and then to Cu₂O) via release of the intact isocyanide, CO₂, and CO in a well-behaved thermal process around 200-280 °C.     

Chemical analysis of acidic silicon etch solutions: I. Titrimetric determination of HNO3, HF, and H2SiF6

The chemical etching of silicon using HF-HNO₃ mixtures is a widely used process in the processing of silicon wafers for microelectronic or photovoltaic applications. The control of the etch bath composition is the necessary condition for an effective bath utilization, for the replenishment of the consumed acids, and to maintain a certain etch rate. The present paper describes two methods for the total analysis of the individual etch bath constituents HF, HNO₃, and H₂SiF₆. Both methods start with an aqueous acid-base titration determining the total acid concentration and the concentration of H₂SiF₆. The first method is an acid-base titration using a 0.1 mol L⁻¹ methanolic solution of cyclohexylamine (CHA) as non-aqueous titrant to determine the content of nitric acid. Then, the amount of hydrofluoric acid is calculated from the difference between the total acid and nitric acid content. The second method is based on the determination of the total fluoride concentration using a fluoride ion-selective electrode (F-ISE). The content of hydrofluoric acid is obtained from the difference between the total fluoride content and the amount of fluoride bound as H₂SiF₆. The amount of nitric acid results finally calculated as difference to the total acid content.