Optimal triangular decompositions of matrices with entries from residuated lattices

We describe optimal decompositions of an n×m matrix I into a triangular product of an n×k matrix A and a k×m matrix B. We assume that the matrix entries are elements of a residuated lattice, which leaves binary matrices or matrices which contain numbers from the unit interval [0, 1] as special cases. The entries of I, A, and B represent grades to which objects have attributes, factors apply to objects, and attributes are particular manifestations of factors, respectively. This way, the decomposition provides a model for factor analysis of graded data. We prove that fixpoints of particular operators associated with I, which are studied in formal concept analysis, are optimal factors for decomposition of I in that they provide us with decompositions with the smallest number k of factors possible. Moreover, we describe transformations between the m-dimensional space of original attributes and the k-dimensional space of factors. We provide illustrative examples and remarks on the problem of computing the optimal decompositions. Even though we present the results for matrices, i.e. for relations between finite sets in terms of relations, the arguments behind are valid for relations between infinite sets as well.     

Incorporation of Dyes into Polystyrene-block-poly(4-vinylpyridine) Nanotemplates

Summary: The present study provides some basic concepts of functionalization of diblock copolymer (BC) nanotemplates for optical applications. It is focused on the polystyrene-block-poly(4-vinylpyridine) (PS-b-P4VP) building medium which is suitable for hydrogen bonding, undergoes phase segregation, and is well-accessible. Two techniques are described and demonstrated on several dye complexes with PS-b-P4VP. Relation between optical properties and thin film structure is tentatively studied in dependence on solvent effects in thin films.     

Synthesis of novel azanorbornylpurine derivatives

Azanorbornylpurine derivatives were prepared by Mitsunobu reaction of appropriate hydroxyazanorbornane derivative with 6-chloropurine or construction of purine base at azanorbornylamines. The prepared target compounds were evaluated for antiviral activity and effect on neuronal and muscle nicotinic acetylcholine receptors.     

Fuzzy Horn logic II

The paper studies closure properties of classes of fuzzy structures defined by fuzzy implicational theories, i.e. theories whose formulas are implications between fuzzy identities. We present generalizations of results from the bivalent case. Namely, we characterize model classes of general implicational theories, finitary implicational theories, and Horn theories by means of closedness under suitable algebraic constructions.     

Fuzzy Horn logic I

The paper presents generalizations of results on so-called Horn logic, well-known in universal algebra, to the setting of fuzzy logic. The theories we consider consist of formulas which are implications between identities (equations) with premises weighted by truth degrees. We adopt Pavelka style: theories are fuzzy sets of formulas and we consider degrees of provability of formulas from theories. Our basic structure of truth degrees is a complete residuated lattice. We derive a Pavelka-style completeness theorem (degree of provability equals degree of truth) from which we get some particular cases by imposing restrictions on the formulas under consideration. As a particular case, we obtain completeness of fuzzy equational logic.     

Retention of phosphates from aqueous solutions with in sol–gel-derived amorphous CaO–MgO–Al<Subscript>2</Subscript>O<Subscript>3</Subscript>–SiO<Subscript>2</Subscript> system as a model of blast furnace slag

The article proposes new possibilities for the estimation of the maximum phosphate retention capacities (PRC) in blast furnace slags using their modeling. The amorphous blast furnace slag model (BFS–SG) and slag samples along the joining of the CaO:SiO₂ = 1 and (CaO + MgO):SiO₂ = 1 of the CaO–MgO–Al₂O₃–SiO₂ phase diagram were prepared by the sol–gel method. The surface analysis of BFS–SG was performed and the results were compared with real BFS. Batch adsorption experiments were performed to evaluate the phosphate removal of slags. SEM analysis and Raman spectroscopy were used to identify phosphate adsorbed forms. Phosphate retention is realized by the surface reactions of hydration products resulting in a nanostructured Ca-hydroxyapatite. The acid–base properties of the model samples in the selected cross-sections were characterized by the values of the optical basicity. An excellent linear relation between the phosphorus retention capacity (PRC) and the optical basicity of the model samples was found, which allows an estimation of slag retention capacities and the forms of adsorbed phosphorus.     

Synthesis of atropoisomeric pyridines via cobalt-catalyzed cocyclotrimerization of diynes with benzonitrile

Arylpyridines (precursors for potential organocatalysts) are easily accesible by cobalt-catalyzed cocyclotrimerization of ortho-substituted 1-aryl-1,7-octadiynes with benzonitrile. The scope of the reaction with respect to the ortho substituents (OMe, Me, COOMe, NHCOMe, F, etc.) was investigated. Three potentially atropoisomeric arylpyridines were prepared and one of them was converted into the corresponding N-oxide and resolved into its enantiomers. The absolute configuration of the N-oxide was established by X-ray crystal structure analysis. Preliminary results of its application in asymmetric organocatalysis are presented.     

Electrophoretic investigation of the boron cluster anion [7-(2'-pyridyl)-nido-7,8-dicarbaundecaborate]- and its protonated zwitterionic product

ACN is a better solvent than methanol for both [NMe(4)] [7-(2'-pyridyl)-nido-7,8-C(2)B(9)H(11)] and its protonated anion. The investigated laboratory preparations of the salt and of its protonated anion are electrophoretically pure solids stable for 2 months at 4 degrees C. At a longer storage, the solid salt is more stable than the solid protonated anion. In the 40:60 v/v water-methanol solvent, decomposition products of the salt anion are detectable after one-week storage of the salt solution at 4 degrees C. The protonated anion does not decompose for almost 1 year in water-organic solutions at 4 degrees C. The exchange of the proton between the protonated anion and the solution is reversible and fast at room temperature. The pH dependence of the mobility of the [7-(2(-pyridyl)-nido-7,8-C(2)B(9)H(11)](-) anion reveals that the basicity of the nitrogen atom in the pyridine ring is not significantly affected by the bonding of the pyridyl group to the nido-7,8-C(2)B(9)H(11) cluster in position 7 and that the proton from the solution is accepted by the nitrogen atom in the 2-pyridyl ring. The UV-spectra of the salt and of its protonated anion indicate that the accepted proton is probably slightly shifted to the open face of the nido-7,8-C(2)B(9)H(11) cluster. The [1](-) is chiral.     

Remote stereoselective deconjugation of α,β-unsaturated esters by simple amidation reactions

The thermodynamically disfavored isomerization of α,β-unsaturated esters to deconjugated β,γ-unsaturated analogues occurs readily when coupled to an amidation. Within the framework of macrocyclic derivatives, it is shown that 15, 16, and 18 membered macrocycles react with tBuOK and anilines to generate, in one-pot, β,γ-unsaturated amides (yields up to 88%). Importantly, single (chiral) diastereomers are isolated (d.r. > 49 : 1, ¹H NMR) irrespective of the size and nature of the rings, showing an effective transmission of remote stereochemistry during the isomerization process. CSP-chromatographic resolution and absolute configuration determination by VCD are achieved.