Automatic approximation using asymptotically optimal adaptive interpolation

Numerical Algorithms - We present an asymptotic analysis of adaptive methods for Lp approximation of functions f ∈ Cr([a, b]), where $1\le p\le +\infty $ . The methods rely on piecewise...     

Thermal properties of pressure sintered alumina–graphene composites

Journal of Thermal Analysis and Calorimetry - The work concerns the alumina–graphene materials sintered by two different pressure methods. The different particle sizes of graphene were used....     

The representation dimension of domestic weakly symmetric algebras

Auslander’s representation dimension measures how far a finite dimensional algebra is away from being of finite representation type. In [1], M. Auslander proved that a finite dimensional algebra A is of finite representation type if and only if the representation dimension of A is at most 2. Recently, R. Rouquier proved that there are finite dimensional algebras of an arbitrarily large finite representation dimension. One of the exciting open problems is to show that all finite dimensional algebras of tame representation type have representation dimension at most 3. We prove that this is true for all domestic weakly symmetric algebras over algebraically closed fields having simply connected Galois coverings.     

On characterization of Poisson and Jacobi structures

We characterize Poisson and Jacobi structures by means of complete lifts of the corresponding tensors: the lifts have to be related to canonical structures by morphisms of corresponding vector bundles. Similar results hold for generalized Poisson and Jacobi structures (canonical structures) associated with Lie algebroids and Jacobi algebroids.     

Configurational and conformational preferences in stereoselective acylations of <Emphasis Type="Italic">N</Emphasis>-methyl-1,3-diaminopropane with acyl chlorides

Evidence for a stereoinduction profile of the reaction of N-methyl-1,3-diaminopropane with acyl chlorides has been provided. A possibility to engage in intramolecular CH₂⋯HN and Cl⋯H-N interactions and the proton migration process to the methylamino group leads to the E secondary amides carrying the N⋯H⁺⋯N or N-H⋯N bridges, that show unusual spectroscopic images. Empirical relations between the Δδ _C chemical shift differences, the polarizability of the CO(S) groups and hydrogen bonding strength have been found. Both ¹H-¹⁵N-GHSQC and GHMBC experiments provide insight into the nature of hydrogen bonding and confirm the cyclic array of atoms.     

Strongly countable dimensional compacta form the Hurewicz set

The hyperspaces of strongly countable dimensional compacta of positive dimension and of strongly countable dimensional continua of dimension greater than 1 in the Hilbert cube are homeomorphic to the Hurewicz set of all nonempty countable closed subsets of the unit interval [0,1]. These facts hold true, in particular, for covering dimension dim and cohomological dimension dimG, where G is any Abelian group.     

Structure of 18-cyanoprogesterone,C22H29O2N

The crystal structure of 18-cyanoprogesterone was determined by X-ray diffraction methods:P2₁2₁2₁ a=7.436(2),b=11.322(2),c=22.642(2) Å. The structure was solved usingShelx-86. Final conventionalR=0.054.R _w =0.051 for 1841 reflections. TheA ring has an intermediate sofa-half-chair conformation with asymmetry parameters C _s ^/1 =11.0, C ₂ ^3,4 =14.9. The steroid skeleton exhibits a flattening of theA ring relative to the rest of the molecule. The progesterone side chain has a typical conformation, and the C16-C17-C20-O20 torsion angle is –19.0(6)°.     

The group of local biholomorphisms of ℂ1 and conformal field theory in the operator formalism

Motivated by the operator formulation of conformal field theory on Riemann surfaces, we study the properties of the infinite dimensional group of local biholomorphic transformations (conformal reparametrizations) of ¹ and develop elements of its representation theory.     

Synthesis of Functionalized (2-Thienylcarbonyl)thiazoles and 4-(2-Thienyl)pyridines by Reaction of (2-Thienylcarbonyl)thioacetanilides and their Enamine Derivatives

Summary. The condensation of two molecules of 2-(2-thienylcarbonyl)thioacetanilides catalyzed by piperidine yielded thiazole derivatives as confirmed by X-ray crystal structure analysis. The reaction of malononitrile with 3-morpholino-3-(2-thienyl)acrylic acid thioanilides furnished 6-amino-1-aryl-4-(2-thienyl)-1,2-dihydro-2-thioxopyridine-5-carbonitriles. A similar reaction of malononitrile with 3-morpholino-3-(2-thienyl)acrylic acid anilides provided 2-oxopyridine-5-carbonitriles.     

pH gradient high-performance liquid chromatography: theory and applications

pH gradient high-performance liquid chromatography (HPLC) is a method of reversed-phase high-performance liquid chromatography suitable for ionogenic substances. It consists in programmed increase during the chromatographic process of the eluting strength of eluent with respect to the analytes separated. On the analogy of the conventional organic modifier gradient reversed-phase HPLC, in the pH gradient approach the eluting strength of the mobile phase increases due to its changing pH: increasing in case of acids or decreasing in case of bases. At the same time the content of organic modifier remains constant. A theory of the pH gradient HPLC has been elaborated. The resulting mathematical model is easily manageable. Its ability to predict changes in retention and separation of analytes following the changes in chromatographic conditions is demonstrated. The pH gradient method is uniquely suitable to determine pKa values of analytes. An equation is presented allowing to calculate pKa values basing on appropriate retention data. The effects on pKa are discussed of the concentration of methanol in the mobile phase. The RP HPLC-derived pKa data correlate to the reference pKa values (w(w)pKa) but are not identical. That may be explained by the effects on the chromatographically determined pKa of the specific interactions of analytes with stationary phases. The proposed pH gradient RP HPLC procedure offers a fast and convenient means to get comparable acidity parameters for larger series of compounds, like drug candidates, also when the analytes are available only in minute amounts and/or as complex mixtures.