Strongly regular family of boundary-fitted tetrahedral meshes of bounded C2 domains

We give a constructive proof that for any bounded domain of the class C² there exists a strongly regular family of boundary-fitted tetrahedral meshes. We adopt a refinement technique introduced by K?í?ek and modify it so that a refined mesh is again boundary-fitted. An alternative regularity criterion based on similarity with the Sommerville tetrahedron is used and shown to be equivalent to other standard criteria. The sequence of regularities during the refinement process is estimated from below and shown to converge to a positive number by virtue of the convergence of q-Pochhammer symbol. The final result takes the form of an implication with an assumption that can be obviously fulfilled for any bounded C² domain.     

X-ray fluorescence determination of total sulfur in fly ash

Standard addition, double dilution and standard calibration were used for x-ray fluorescence (XRF) determinations of sulfur in fly ashes. Samples were analysed as pellets prepared by mixing with acrylate copolymer or with microcrystalline cellulose (in the case of the double dilution method). Lithium sulfate was used for the standard addition method and also as standard with known sulfur content for the double dilution method. Fly ashes analysed by optical emission spectrometry with an inductively coupled plasma (ICP-OES) were used as standards for the standard calibration XRF method. Sulfur was determined in the range of ca. 10^–1–10⁰ % S. For the fly ashes from the North-Bohemian brown coals, the differences between the XRF determinations and the ICP-OES determinations ranged from ca. 1.4 to 10% rel. and precision (repeatability) was better than 10% (RSD). The standard calibration method is suitable for routine analyses of real samples of similar nature. The methods of standard addition and double dilution are rather laborious in sample preparation compared with the standard calibration. Received: 27 October 1998 / Revised: 5 March 1999 / Accepted: 11 March 1999     

Lattices of Fixed Points of Fuzzy Galois Connections

We give a characterization of the fixed points and of the lattices of fixed points of fuzzy Galois connections. It is shown that fixed points are naturally interpreted as concepts in the sense of traditional logic.     

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.     

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.     

Exploration of the electrophoretic behaviour of borane cluster anions and of the capability of capillary electrophoresis to separate them chirally

Mobilities of investigated boron cluster compounds in 3-(N-morpholino)propanesulfonic and phosphate buffers adjusted to pH 7 either with sodium hydroxide or with tris(hydroxymethyl)aminomethane depend on both buffer ions. The zone width and zone asymmetry, which are usually markedly higher than those of organic or common inorganic ions of comparable size, depend on the type of the borane cluster anion. Unusual shapes of zones of two investigated compounds have been found in tris phosphate buffer. Acetonitrile was superior to methanol as an organic additive to separation systems from the viewpoint of the zone symmetry and separation speed. Narrow trigonal zones, typical of organic ions non-interacting with the capillary wall, have been observed for some bridged sandwich cobalt complexes in run buffers with the addition of acetonitrile. The interaction of borane cluster anions with beta-cyclodextrin cavity is excessively strong in purely aqueous solutions. Methanol and acetonitrile, which generally weaken the interaction, sometimes affect the separation enantioselectivity of various compounds in different ways in addition to the weakening effect. Chiral discrimination was reached for all ten investigated anions, which belong to four different structural types of cluster boranes. Stability constants estimated for some analyte-beta-cyclodextrin complexes range between 100 and 1800 l/mol in acceptable separations. The relative difference of the constants was from 3 to 20%.     

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.