Investigation of the homogeneity of solids with a linear regression model

Testing of the hemogeneity of solids is usually based on the comparison of the variance of measurements at several sample points with the variance of repeated measurements. In the case of destructive analytical methods, empirical mathematical models are needed because repetitions at the same subsample are impossible. Successful application of such models depends on the adequacy of the mathematical model and the type of distribution observed. Gradients and textures with low or medium local frequency require other tests than stochastic distributions with high local frequency. A simple regression model base on a 2² factorial allows conclusions about the type of distribution without great mathematical effort.     

Synthesis of β-cyclodextrin-lysozyme conjugates and their physicochemical and biochemical properties

Recently a great interest in the field of protein engineering and the design of innovative drug delivery systems employing specific ligands such as cyclodextrins is observed. The paper reports the solid state, thermal method for protein coupling with β-cyclodextrin and the physicochemical and biological properties of the obtained conjugates. The structure of the obtained conjugates was investigated via liquid chromatography-mass spectrometry, dynamic light scattering and circular dichroism analysis. The presented conjugates were biologically active and covalently bound β-cyclodextrin preserved the ability to form inclusion complexes with the model compound. This report demonstrates the great potential of cyclodextrin as a modifying unit that can be used to modulate the properties of therapeutic proteins, additionally giving such conjugates the possibility to transport many therapeutic substances in the form of inclusion complexes. In addition, the paper presents the potential of protein-cyclodextrin conjugates to construct innovative bioactive molecules for biological and medical applications.     

Splitless injection of up to hundreds of microliters of liquid samples in capillary GC: Part II,experimental results

Sample evaporation in splitless injection of large volumes is rapid: depending on the experiment, results indicate that 200 μl of hexane, for instance, evaporates in 2–10 s, producing vapor at a rate of many hundreds of milliliters per minute. A 60 × 4 mm packed bed of 20–35 mesh Tenax TA enabled injection of 200 μl volumes of all solvents tested, and even 1 ml injections were possible provided they were performed over a period of 30 s. Retention of volatile sample components depends on the sample solvent, the injection volume, and the injection speed, but only little on the injector temperature. Losses of n-tridecane varied from hardly 15 % (when dissolved in pentane) to ca 60 % (ethyl acetate); losses of n-heptadecane were usually below 20 %. The column temperature during injection should be at least ca 20–30°C above the standard solvent boiling point.     

Die Reaktion von Tellurhexafluorid mit Trimethylamin,Strukturen der TeF5−- und SeF5−-Anionen

Reaction of Telluriumhexafluoride and Trimethylamine, Structures of the TeF₅^? and SeF₅^? Anions The reaction of TeF₆ and (CH₃)₃N is of the redox kind, resulting in reduction of tellurium: X-ray single crystal analysis reveals the compounds (CH₃)₂N? CH₂? N(CH₃)₂⁺TeF₅^? and [(CH₃)₃NH⁺]₅(TeF₅^?)₃(HF₂^?)₂. By comparison with published data it can be shown that this mixture is identical to previously published [(CH₃)₃N]₂TeF₆. The latter was supposed to be one of the few examples of tellurium in a coordination state of eight. (CH₃)₄N⁺TeF₅^? and (CH₃)₄N⁴SeF₅^? are obtained and their structure is investigated by single crystal x-ray methods also. The anions SF₅^?, SeF₅^? and TeF₅^? are discussed in terms of weak interactions.     

Approximate Euclidean Steiner Trees

An approximate Steiner tree is a Steiner tree on a given set of terminals in Euclidean space such that the angles at the Steiner points are within a specified error from \(120^{\circ }\). This notion arises in numerical approximations of minimum Steiner trees. We investigate the worst-case relative error of the length of an approximate Steiner tree compared to the shortest tree with the same topology. It has been conjectured that this relative error is at most linear in the maximum error at the angles, independent of the number of terminals. We verify this conjecture for the two-dimensional case as long as the maximum angle error is sufficiently small in terms of the number of terminals. In the two-dimensional case we derive a lower bound for the relative error in length. This bound is linear in terms of the maximum angle error when the angle error is sufficiently small in terms of the number of terminals. We find improved estimates of the relative error in length for larger values of the maximum angle error and calculate exact values in the plane for three and four terminals.     

On Super-KMS functionals and entire cyclic cohomology

We formulate the super-KMS condition suggested by Connes and Kastler, in the context of entire cyclic cohomology of quantum algebras. We show that the Chern character of Jaffe, Lesniewski, and Osterwalder — associated by Kastler to a super-KMS functional — satisfies the entire growth condition. Hence, a super-KMS functional defines a cocycle for the entire cyclic cohomology of quantum algebras.Supported in part by the National Science Foundation.     

Local boundedness of weak solutions to the Diffusive Wave Approximation of the Shallow Water equations

In this paper we prove that weak solutions to the Diffusive Wave Approximation of the Shallow Water equations

${?}_{t}u?\mathrm{?}?({(u?z)}^{\alpha }|\mathrm{?}u{|}^{\gamma ?1}\mathrm{?}u)=f$

are locally bounded. Here, u describes the height of the water, z is a given function that represents the land elevation and f is a source term accounting for evaporation, infiltration or rainfall.     

Fleet configuration subject to stochastic demand: an application in the distribution of liquefied petroleum gas

We study the problem of configuring a fleet, in which vehicles receive information on-line about the demand that they should fulfil while they are on the road. In each district it must be decided the number of vehicles and their capacity. The objective function is to minimise the operational cost subject to constraints for the minimum delivery capacity, the maximum vehicle size and the average waiting time for customers. The last constraint is modelled as a queuing system that is adjusted according to the simulation of the delivery process of a Chilean company that distributes liquefied petroleum gas in portable cylinders. We provide the analytical form of all the components of the model, so it can be solved using a standard non-linear programming package. We show that the fleet may increase its sales by 3% and reduce the waiting time of customers 10% by allowing a set of vehicles to share the buffer of orders rather than having vehicles to exclusively serve smaller sectors.     

Residues and telescopers for bivariate rational functions

We give necessary and sufficient conditions for the existence of telescopers for rational functions of two variables in the continuous, discrete and q-discrete settings and characterize which operators can occur as telescopers. Using this latter characterization, we reprove results of Furstenberg and Zeilberger concerning diagonals of power series representing rational functions. The key concept behind these considerations is a generalization of the notion of residue in the continuous case to an analogous concept in the discrete and q-discrete cases.     

Temperature effects in thin droplets

Thin droplets spreading on a solid substrate are investigated, with a special focus on temperature effects. The aim is to manipulate the fingering instability which may occur in the spreading in a spin coating process. The analysis bases on lubrication approximation, valid for flat thin droplets, which usually is the case. The dynamic of the wetting is implemented by using a generalized law of Tanner, coupling the contact angle (CA) of the droplet at the (apparent) contact line (CL) with its speed. A one-way coupling is used to investigate, whether viscous heating has to be taken into account. It can be derived that its role is negligible in the spreading process of a thin droplet, even for a relatively large viscous influence (large capillary number). Analyzing the results of a linear stability analysis of the fingering instability and taking Marangoni-stresses (MS) into account reveals, that the instability may be suppressed by cooling the ambient gas or heating the substrate during the spreading. Unfortunately an comparison with experiments for spreading droplets in a heated gas shows deviations for larger spreading radii. The influence of temperature on density is investigated and on the way a criteria, from which it may be obtained whether a simple Boussinesq-approximation (BA) is appropriate or not. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)