Residuated Lattices of Size ≤ 12

We present the numbers of all non-isomorphic residuated lattices with up to 12 elements and a link to a database of these lattices. In addition, we explore various characteristics of these lattices such as the width, length, and various properties considered in the literature and provide the corresponding statistics. We also present algorithms for computing finite residuated lattices including a fast heuristic test of non-isomorphism.     

Two Simple Derivations of Universal Bounds for the C.B.S. Inequality Constant

Universal bounds for the constant in the strengthened Cauchy-Bunyakowski-Schwarz inequality for piecewise linear-linear and piecewise quadratic-linear finite element spaces in 2 space dimensions are derived. The bounds hold for arbitrary shaped triangles, or equivalently, arbitrary matrix coefficients for both the scalar diffusion problems and the elasticity theory equations.     

Displacement decomposition—incomplete factorization preconditioning techniques for linear elasticity problems

Two preconditioning techniques for the numerical solution of linear elasticity problems are described and studied. Both techniques are based on spectral equivalence approach. The first technique consists in an incomplete factorization of the separate displacement component part of the stiffness matrix. The second technique uses an incomplete factorization of the isotropic approximation to the stiffness matrix. Results concerning existence, stability and efficiency of these preconditioning techniques are presented. The efficiency and robustness of the described techniques are illustrated by numerical experiments.     

Silicon-(thio)urea Lewis acid catalysis

We present a new class of catalysts based on the combination of N,N'-diaryl(thio)ureas and weak silicon Lewis acids (e.g., SiCl(4)). Such silicon-(thio)urea catalysts effectively catalyze the stereospecific rearrangement of epoxides to quaternary carbaldehydes.     

Synthesis of novel thienonorbornylpurine derivatives

The synthesis and antiviral evaluation of 6-amino- and 6-chloro-9-(exo-bicyclo[2.2.1]hept-2yl)-9H-purine derivatives with thiophene and tetrahydrothiophenes annelated to a norbornane moiety are described. The key step in the synthesis of derivatives with the symmetrically annelated thiophene was the Mitsunobu reaction of endo-4-thiatricyclo[5.2.1.0^2,6]deca-2,5-dien-8-ol with 6-chloropurine. The key alcohol was obtained by DDQ mediated aromatization of the corresponding tetrahydro derivatives, which were used for the preparation of the target tetrahydrothieno analogs. The key intermediate for the synthesis of derivatives with the asymmetrically annelated thiophene was 8-exo-azido-3-thiatricyclo[5.2.1.0^2,6]deca-2(6),4-diene, which was prepared from 5-exo-azido[2.2.1]heptan-2-one by aldol condensation with O-ethyl S-(2-oxoethyl) carbonodithioate, deprotection and cyclization. The target compounds were obtained by the construction of the purine base on an amine, which was obtained by LAH reduction of the key azide. The synthesized compounds were evaluated for antiviral and cytostatic activity.     

The effect of the number of carbohydrate moieties on the azaphthalocyanine properties

A series of azaphthalocyanines (AzaPc) bearing one, two, four or eight isopropylidene-protected galactosyl units was prepared by azide-alkyne click reaction or by classical Pc template cyclotetramerization of the corresponding dicyanopyrazine and AzaPc properties important for photodynamic therapy were compared. All compounds absorbed at long wavelengths (above 650 nm) and belonged to strong singlet oxygen producers (Φ(Δ) = 0.58-0.64) retaining significant fluorescence emission (Φ(F) = 0.026-0.23). The only exception was the compound with four isopropyliden-protected galactosyl units where partial aggregation was observed. Removal of protecting groups increased the polar character of all AzaPc. However, only AzaPc bearing eight galactoses was found to be water-soluble (105 mg mL(-1)) but noticeably aggregated in water as well as in organic solvents (DMF, DMSO). Amphiphilic AzaPc bearing one deprotected galactose was incorporated into the lipidic bilayer of liposomes in a nonaggregated form. Liposomes may therefore be a suitable delivery system for this amphiphilic photosensitizer.     

Optimal Factorization of Three-Way Binary Data Using Triadic Concepts

We present a new approach to factor analysis of three-way binary data, i.e. data described by a 3-dimensional binary matrix I, describing a relationship between objects, attributes, and conditions. The problem consists in finding a decomposition of I into three binary matrices, an object-factor matrix A, an attribute-factor matrix B, and a condition-factor matrix C, with the number of factors as small as possible. The scenario is similar to that of decomposition-based methods of analysis of three-way data but the difference consists in the composition operator and the constraint on A, B, and C to be binary. We show that triadic concepts of I, developed within formal concept analysis, provide us with optimal decompositions. We present an example demonstrating the usefulness of the decompositions. Since finding optimal decompositions is NP-hard, we propose a greedy algorithm for computing suboptimal decompositions and evaluate its performance.     

Polypyrrole-Coated and Polysulfate-Modified CE Capillaries

Fused-silica capillaries covalently coated with polypyrrole offer some interesting properties for capillary electrophoresis. The polymeric, surface-bonded coating is chemically stable and reduces the adsorptive properties of the silica surface. At the same time, the weak positive surface charges offer the possibility of creating a strongly anionic surface when poly-sulfates are used as counter-ions. This affords an electroosmotic flow which is largely independent of pH. With sodium dodecyl sulfate in the background electrolyte, this effect is further enhanced. The potential of the approach is demonstrated with the separation of herbicides by micellar electrokinetic chromatography. Repeatability of electroosmotic mobility of less than 1% RSD is achieved.     

Some Properties of Residuated Lattices

We investigate some (universal algebraic) properties of residuated lattices--algebras which play the role of structures of truth values of various systems of fuzzy logic.     

How quantum correlations enhance prediction of complementary measurements

If there are correlations between two qubits, then the results of the measurement on one of them can help to predict measurement results on the other one. It is an interesting question as to what can be predicted about the results of two complementary projective measurements on the first qubit. To quantify these predictions the complementary knowledge excesses are used. A nontrivial constraint restricting them is derived. For any mixed state and for arbitrary measurements the knowledge excesses are bounded by a factor depending only on the maximal violation of Bell's inequalities. This result is experimentally verified on two-photon Werner states prepared by means of spontaneous parametric down-conversion.