Relaxing mixed integer optimal control problems using a time transformation

Mixed integer control systems are used to model dynamical behavior that can change instantly, for example a driving car with different gears. Changing a gear corresponds to an instant change of the differential equation what is achieved in the model by changing the value of the integer control function. The optimal control of a mixed integer control system by a discretize-then-optimize approach leads to a mixed integer optimization problem that is not differentiable with respect to the integer variables, such that gradient based optimization methods can not be applied. In this work, differentiability with respect to all optimization variables is achieved by reformulating the mixed integer optimal control problem (MIOCP). A fixed integer control function and a time transformation are introduced. The combination of both allows to change the sequence of active differential equations by partially deactivating the fixed integer control function. In contrast to other works, here different fixed integer control functions are taken into account. Advantages of so called control consistent (CC) fixed integer control functions are discussed and confirmed on a numerical example. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Contribution of Cytosine‐Containing Cyclobutane Dimers to DNA Damage Produced by Photosensitized Triplet–Triplet Energy Transfer

Mutagenic cyclobutane pyrimidine dimers (CPDs) can be induced in DNA through either direct excitation or photosensitized triplet–triplet energy transfer (TTET). In the latter pathway, thymines are expected to receive the excitation energy from the photosensitizer and react with adjacent pyrimidines. By using state‐of‐the art analytical tools, we provide herein additional information on the formation of cytosine‐containing CPDs. We thus determined the yield of all possible CPDs upon TTET in a series of natural DNAs with various base compositions. We show that the distribution of CPDs cannot be explained only by excitation of individual thymines. We propose that the mechanism for TTET involves at least dinucleotides as the minimal targets. The observation of the formation of cytosine–cytosine CPDs also suggests that additional pathways are involved in this photosensitized reaction.     

Mapping Multivalency and Differential Affinities within Large Intrinsically Disordered Protein Complexes with Segmental Motion Analysis

Intrinsically disordered proteins (IDPs) can bind to multiple interaction partners. Numerous binding regions in the IDP that act in concert through complex cooperative effects facilitate such interactions, but complicate studying IDP complexes. To address this challenge we developed a combined fluorescence correlation and time‐resolved polarization spectroscopy approach to study the binding properties of the IDP nucleoporin153 (Nup153) to nuclear transport receptors (NTRs). The detection of segmental backbone mobility of Nup153 within the unperturbed complex provided a readout of local, region‐specific binding properties that are usually masked in measurements of the whole IDP. The binding affinities of functionally and structurally diverse NTRs to distinct regions of Nup153 can differ by orders of magnitudes—a result with implications for the diversity of transport routes in nucleocytoplasmic transport.     

Molar mass determination by end group analysis - amino group determination in aliphatic and partially aromatic polyamides with 1-fluoro-2,4-dinitrobenzene in benzyl alcohol

End group analysis is the most important absolute method of obtaining number-average molar mass values for polymers of the step-growth polymerization type. A great number of methods are available which primarily differ in the detection of the end group concerned. Special chemical methods based on the formation of covalent derivatives of the end groups (e.g. introduction of UV/VIS chromophores) are important if there is a need to demonstrate, with the aid of gel permeation chromatography, that damage to the polymer (e.g. onset of cross-linking) has occurred. In the case of fibre-forming polycondensation products, the applicability of end group analysis is often restricted by the lack of suitable reagents and solvents. This is also true of the determination of amino end groups in polyamides by means of 1-fluoro-2,4-dinitrobenzene, as is already contained in the German Standards specification (DIN 54 274) - albeit only for polyamide 6 and 6,6. This contribution describes a modified version of the 1-fluoro-2,4-dinitrobenzene method. The analytical principle and practical procedure correspond to those of DIN 54 274, but the solvent used for the reaction with the reagent is benzyl alcohol, and that for the photometric evaluation is 1,1,1,3,3,3-hexafluoro-2-propanol. The scope of the method is thus increased. Examples of applications for this method are commercial products based on aliphatic polyamides (6; 11; 12; 6,6; 6, 12), partially aromatic polyamides (2,4,4-trimethylhexamethylenediamine, terephthalic acid; copolyamides with bis-(4-aminocyclohexyl)propane(2), isophthalic acid, ω-aminododecanoic acid) and multicomponent systems with the abovementioned polyamides (bicomponent fibres, blends). It is shown that large differences may arise between the value determined by titration and the actual amino end group content. In addition, the presence of secondary amino groups can be demonstrated in polyamides of the Trogamid T type.     

Torification and factorization of birational maps

Building on work of the fourth author and Morelli's work, we prove the weak factorization conjecture for birational maps in characteristic zero: a birational map between complete nonsingular varieties over an algebraically closed field of characteristic zero is a composite of blowings up and blowings down with nonsingular centers.

     

Die Verteilung von Molybdänsäure-Brenzcatechin-Komplexen zwischen wäßrigen Lösungen und organischen Lösungsmitteln

Molybdic-acid catechol complexes can be extracted from acidic aqueous solutions by organic solvents, if organic basic compounds are added. Results with tetraphenyl arsonium chloride were especially favourable.     

Direkte elektrometrische Bestimmung des Fluorid-Ions

Zusammenfassung Die Arbeitsweise einer Fluoridionen-empfindlichen Elektrode wurde geprüft und der Einfluß von Fremdsubstanzen auf die Potentiale untersucht. Die Störungen können durch Maskierung, Pufferung oder durch eine Auswertmethode vermindert werden.

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Summary The working characteristics of a fluoride-sensitive electrode and the influence of foreign substances on the fluoride potentials were tested. Changes in potential can be diminished by masking or buffering. Furthermore, a special addition technique can be applied.

     

Microcomputer interfaced stopped-flow spectrometer with interactive graphics

One problem in the use of stopped-flow rapid-mixing systems is that data can be collected much more rapidly than they can be digitized and analyzed. Microprocessor based systems can overcome this problem, but until now they have been expensive and have required experts to assemble the appropriate components.