Contribution to application of energy measure of fuzzy sets

The works of De Luca & Termini continued by, for example, Knopfmacher, Loo and Gottwald, are the most important on the topic of determination of measures of fuzzy sets. The matter is to evaluate how fuzzy a fuzzy set is. There are two general concepts of measures of fuzzy set, i.e. entropy and energy measures.We show that the special kind of energy measure is better suited than the entropy kind of measure in many practical situations.Applications of the use of energy measure discussed in detail include decision making, fuzzy process control and prediction in fuzzy systems.     

Fuzzy points and local properties of fuzzy topological spaces

We prove that three theorems of C.K. Wong on local properties of fuzzy topology are wrong, thereby we discuss his notions of fuzzy point, C₁, separability, and local compactness.     

The infinitesimal cone of a totally positive semigroup

Given a complex reductive linear algebraic group split over with a fixed pinning, it is shown that all elements of the Lie algebra infinitesimal to the totally positive subsemigroup of lie in the totally positive cone .

     

Flexible fluidic microchips based on thermoformed and locally modified thin polymer films

This paper presents a fundamentally new approach for the manufacturing and the possible applications of lab on a chip devices, mainly in the form of disposable fluidic microchips for life sciences applications. The new technology approach is based on a novel microscale thermoforming of thin polymer films as core process. The flexibility not only of the semi-finished but partly also of the finished products in the form of film chips could enable future reel to reel processes in production but also in application. The central so-called 'microthermoforming' process can be surrounded by pairs of associated pre- and postprocesses for micro- and nanopatterned surface and bulk modification or functionalisation of the formed films. This new approach of microscale thermoforming of thin polymer film substrates overlaid with a split local modification of the films is called 'SMART', which stands for 'substrate modification and replication by thermoforming'. In the process, still on the unformed, plane film, the material modifications of the preprocess define the locations where later, then on the spatially formed film, the postprocess generates the final local modifications. So, one can obtain highly resolved modification patterns also on hardly accessible side walls and even behind undercuts. As a first application of the new technology, we present a flexible chip-sized scaffold for three dimensional cell cultivation in the form of a microcontainer array. The spatially warped container walls have been provided with micropores, cell adhesion micropatterns and thin film microelectrodes.     

Semisynthetic murine prion protein equipped with a GPI anchor mimic incorporates into cellular membranes

Conversion of cellular prion protein (PrP(C)) into the pathological conformer (PrP(Sc)) has been studied extensively by using recombinantly expressed PrP (rPrP). However, due to inherent difficulties of expressing and purifying posttranslationally modified rPrP variants, only a limited amount of data is available for membrane-associated PrP and its behavior in vitro and in vivo. Here, we present an alternative route to access lipidated mouse rPrP (rPrP(Palm)) via two semisynthetic strategies. These rPrP variants studied by a variety of in vitro methods exhibited a high affinity for liposomes and a lower tendency for aggregation than rPrP. In vivo studies demonstrated that double-lipidated rPrP is efficiently taken up into the membranes of mouse neuronal and human epithelial kidney cells. These latter results enable experiments on the cellular level to elucidate the mechanism and site of PrP-PrP(Sc) conversion.     

Efficiency of alkoxyl radical product formation from 5-substituted 3-alkoxy-4-methylthiazole-2(3H)-thiones

In a comparative study, reactions between 5-(p-methoxyphenyl)-substituted 3-alkoxy-4-methylthiazole-2(3H)-thiones and appropriate mediators (BrCCl₃, Bu₃SnH) provided higher yields of alkoxyl radical products (δ-bromohydrins, cyclic ethers, carbonyl compounds) than respective transformations of 5-phenyl- and 5-methyl-substituted derivatives. The unusual selectivity of applied thiohydroxamates to furnish products of O-alkylation, even upon treatment with soft carbon electrophiles, and the marked propensity of 3-alkoxy-5-(p-methoxyphenyl)-4-methylthiazole-2(3H)-thiones to crystallize, facilitated preparation and purification of the new family of alkoxyl radical precursors in a noteworthy manner.     

Tertiary alkoxyl radicals from 3-alkoxythiazole-2(3H)-thiones

This study deals with the synthesis of tert-O-alkyl thiohydroxamates and their use as tert-alkoxyl radical precursors. tert-Alkoxyl radicals were applied in mechanistic studies to determine rate constants of (i) p-chlorocumyloxyl radical addition to bicyclo[2.2.1]heptene (k=1×10⁷ M⁻¹ s⁻¹), (ii) 2-phenylhex-5-en-2-oxyl radical 5-exo-trig-cyclization (k^cis=3×10⁹ s⁻¹, k^trans=1×10⁹ s⁻¹), and (iii) 2-methyl-5-phenylpent-2-oxyl to 2-hydroxy-2-methyl-5-phenylpent-5-yl radical isomerization (1,5-H-atom shift; k=0.4-1.5×10⁸ s⁻¹). The reactions pose key steps in synthesis of 2,2,5-substituted tetrahydrofurans and 2-bromo-3-alkoxybicyclo[2.2.1]heptanes. Stereoselectivity in 5-exo-trig cyclization (2,5-cis) and intermolecular addition (exo/endo>99:1), originates from torsional strain in transition structures of alkoxyl radical reactions.