Optimal control problems with applications to the elimination of substrate diffusing and convecting through immobilized enzyme

Some optimization problems concerning a substrate in a fluid are considered. The concentration of the substrate is affected by diffusion, convection, and elimination by enzymes, and the problem is to find the optimal distribution of enzymes. In this paper, the rate of elimination and the transmission coefficient are optimized. Mathematically, these problems are optimal control problems, and they are analyzed by means of Pontryagin's maximum principle.     

Untersuchung von Textilien und Textilrohstoffen

Ohne Zusammenfassung     

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.     

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.