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Institute
- Institut für Biochemie und Biologie (178)
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The dimension of a variety V of algebras of a given type was introduced by E. Graczynska and D. Schweigert in [7] as the cardinality of the set of all derived varieties of V which are properly contained in V. In this paper, we characterize all solid varieties of dimensions 0, 1, and 2; prove that the dimension of a variety of finite type is at most N-0; give an example of a variety which has infinite dimension; and show that for every n is an element of N there is a variety with dimension n. Finally, we show that the dimension of a variety is related to the concept of the semantical kernel of a hypersubstitution and apply this connection to calculate the dimension of the class of all algebras of type tau = (n).
An n-ary cooperation is a mapping from a nonempty set A to the nth copower of A. A clone of cooperations is a set of cooperations which is closed under superposition and contains all injections. Coalgebras are pairs consisting of a set and a set of cooperations defined on this set. We define terms for coalgebras, coidentities and cohyperidentities. These concepts will be applied to give a new solution of the completeness problem for clones of cooperations defined on a two-element set and to separate clones of cooperations by coidentities.
Arenes with various alkyl side-chains were synthesized in high yields and excellent regioselectivities. Starting from toluic and naphthoic acids, the carboxylate group was conveniently substituted by alkyl halides by Birch reduction and subsequent decarbonylation. The method is characterized by inexpensive starting materials and reagents, and methylation of arenes was realized. Besides simple alkyl substituents, the scope of arene functionalization was extended by benzyl, fluoro, amino, and ester groups. We were able to control the alkylation of 1-naphthoic acid during Birch reduction by the addition of tert-butanol. This allowed the regioselective synthesis of mono and bis-substituted naphthalenes from the same starting material.
We discuss the relaxation of a class of nonlinear elliptic Cauchy problems with data on a piece S of the boundary surface by means of a variational approach known in the optimal control literature as "equation error method". By the Cauchy problem is meant any boundary value problem for an unknown function y in a domain X with the property that the data on S, if combined with the differential equations in X, allow one to determine all derivatives of y on S by means of functional equations. In the case of real analytic data of the Cauchy problem, the existence of a local solution near S is guaranteed by the Cauchy-Kovalevskaya theorem. We also admit overdetermined elliptic systems, in which case the set of those Cauchy data on S for which the Cauchy problem is solvable is very "thin". For this reason we discuss a variational setting of the Cauchy problem which always possesses a generalised solution.
An efficient electrocatalytic biosensor for sulfite detection was developed by co-immobilizing sulfite oxidase and cytochrome c with polyaniline sulfonic acid in a layer-by-layer assembly. QCM, UV-Vis spectroscopy and cyclic voltammetry revealed increasing loading of electrochemically active protein with the formation of multilayers. The sensor operates reagentless at low working potential. A catalytic oxidation current was detected in the presence of sulfite at the modified gold electrode, polarized at +0.1 V ( vs. Ag/AgCl 1 M KCl). The stability of the biosensor performance was characterized and optimized. A 17-bilayer electrode has a linear range between 1 and 60 mu M sulfite with a sensitivity of 2.19 mA M-1 sulfite and a response time of 2 min. The electrode retained a stable response for 3 days with a serial reproducibility of 3.8% and lost 20% of sensitivity after 5 days of operation. It is possible to store the sensor in a dry state for more than 2 months. The multilayer electrode was used for determination of sulfite in unspiked and spiked samples of red and white wine. The recovery and the specificity of the signals were evaluated for each sample.