Connecting and Integrating Theoretical Frames: The TELMA Contribution

This paper presents the methodology developed within TELMA for connecting and integrating the theoretical frames used by the different teams for studying the design and use of interactive learning environments in mathematics education. Two case studies are then analysed and compared in order to illustrate the methodology and the results it can lead to. The papers ends by a more general discussion about the outcomes of the experimental work developed within TELMA and the perspectives it offers for approaching theoretical fragmentation.     

Barbituric acid as a substituent at aryl methylium ions

Activation of different benzophenone derivatives with triflic anhydride for electrophilic aromatic substitution of 5-phenylbarbituric acids leads to regioselective formation of the ortho-substituted product. The resulting triphenylmethylium salt can be isolated when the Michlers ketone is used. More electrophilic cations form cyclic enol ethers such as 1-n-butyl-9,9-diaryl-1,9-dihydro-10-oxa-1,3-diazaphenanthrene-2,4-diones. Alternatively, supramolecular complex formation with 2,6-diacetamido pyridine as well as carbenium ion generation have been studied. Although in dilute acid only protonation of one of the carbonyl oxygens occurs, ring opening of the cyclic enol ether toward the carbenium ion is observed in 96% sulfuric acid.     

On integral graphs which belong to the class\overline {\alpha K_{a,a} \cup \beta {\rm K}_{b,b} }

LetG be a simple graph and letG denote its complement. We say thatG is integral if its spectrum consists of integral values. In this work we establish a characterization of integral graphs which belong to the class $\overline {\alpha K_{a,a} \cup \beta {\rm K}_{b,b} } $ wheremG denotes them-fold union of the graphG.     

Another step towards proving a conjecture by Plummer and Toft

A cyclic colouring of a graph G embedded in a surface is a vertex colouring of G in which any two distinct vertices sharing a face receive distinct colours. The cyclic chromatic number of G is the smallest number of colours in a cyclic colouring of G. Plummer and Toft in 1987 [M.D. Plummer, B. Toft, Cyclic coloration of 3-polytopes, J. Graph Theory 11 (1987) 507-515] conjectured that for any 3-connected plane graph G with maximum face degree Δ^∗. It is known that the conjecture holds true for Δ^∗≤4 and Δ^∗≥24. The validity of the conjecture is proved in the paper for Δ^∗≥18.     

A fuzzy system for municipalities classification

A knowledge-based fuzzy system for the purpose of municipalities classification is presented in this paper. It illustrates how fuzzy systems can be used for municipalities classification and ranking tasks. The application of the system is explained by the example of classification in one region in the Slovak Republic. The original problem of estimating and rough planning of road maintenance requirements in winter was examined. The suggested methodology is supported by GIS technology for visualization of the ranked municipalities to offer a better view on the territorial distribution of the obtained solution. A disadvantage of fuzzy systems for the end user is in their complexity. This disadvantage has been analysed and a solution is suggested to overcome it. The proposal deals with the integration of information system and self developed fuzzy system. This integration enables creating the model, importing input data, processing rules and presenting results in tables and maps in one integrated tool.     

Chromophoric Barbituric Acid Derivatives with Adjustable Hydrogen-Bonding Patterns as Component for Supramolecular Structures

Summary: The barbituric acid moiety of the presented dyes shows multifunctional properties like acidochromism, solvatochromism, and adjustable hydrogen-bonding pattern for molecular recognition. Hydrogen-bonding ability, acidity and solvatochromic effects are studied for a series of N-alkyl substituted 5-(4-nitrophenyl)-barbiturates. Solvatochromism and metal ion complexation are also investigated using chromophoric thiobarbituric acid derivatives.     

Parahoric Restriction for GSp(4)

Parahoric restriction is the parahoric analogue of Jacquet’s functor. The group GSp(4, F) of symplectic similitudes of genus two over a local number field F/? _p has five conjugacy classes of parahoric subgroups. For each we determine the parahoric restriction of the non-cuspidal irreducible smooth representations of GSp(4, F) in terms of explicit character values.     

An unusual oxidative ring transformation of purine to imidazo[1,5-c]imidazole

[reaction: see text] Reevaluation of products derived from 3,9-dimethyluric acid in a chlorination-reductive dechlorinaton sequence has demonstrated unequivocally that they are not purines. Spectroscopic and degradative evidence, in conjunction with position-labeling NMR studies, revealed an unprecedented oxidative ring transformation pathway involving the key purine-to-imidazo[1,5-c]imidazole rearrangement.