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...     

On Non-Continuous Dirichlet Processes

We introduce here some Itô calculus for non-continuous Dirichlet processes. Such calculus extends what was known for continuous Dirichlet processes or for semimartingales. In particular we prove that non-continuous Dirichlet processes are stable under C ¹ transformation.     

Nontrivial Solutions for Resonant Hemivariational Inequalities

We study a resonant semilinear elliptic hemivariational inequality. Under some assumptions of strong resonance on the Clarke subdifferential of the superpotential, and using nonsmooth critical point theory, the existence of a nontrivial solution of the problem is shown. This paper has been partially supported by the State Committee for Scientific Research of Poland (KBN) under research grants no. 2 P03A 003 25 and no. 4 T07A 027 26.     

Activity of TiO2 deposited by the CVD method on ammoxidized surface of a carbonaceous material in hydrogenation of styrene

Hydrogenation of styrene has been applied as a test reaction to study the catalytic activity of TiO₂ deposited by the CVD (chemical vapour deposition) method on the surface of a carbonaceous material enriched in nitrogen (C_N).     

Mechanical properties of metallic ribbons investigated by depth sensing indentation technique

The paper presents mechanical properties of two kinds of Co-based and one Fe-based metallic ribbons by the depth sensing indentation (DSI) technique. Investigations were carried out on two kinds ternary alloy Co₇₇Si_11,5B_11,5 and Fe₇₈Si₁₃B₉ and multicomponent Co₆₈Fe₄Mo₁Si_13,5B_13,5, which are so-called “zero-magnetostriction” materials. Metallic ribbons were investigated in amorphous state and partially crystallized state after annealing in 400°C in argon atmosphere. Heating of ribbons obtained by melt spinning technique was performed to check its effect on changes of mechanical properties.     

The synthesis of 1-alkyl-4a-(4-chlorophenyl)- 4,4a-dihydropyrimido[6,1-a]isoindol-9(3H)-one

The primary amino group of 3-(2-aminoethyl)-3-(4-chlorophenyl)-2,3-dihydro-1H-isoindol-1-one ( 1 ) was acylated with acetyl chloride, benzoyl chloride and phenyl acetyl chloride to form the amides 2a -c, respectively. These were cyclized in phosphorus oxychloride to give the 1-substituted-4a-(4-chlorophenyl)-4,4a-dihydropyrimido [6,1-a]isoindol-9(3H)-ones 3a-c . Heating of 1 in formic acid lead to the formation of 4a-(4-chlorophenyl)-4,4a-dihydropyrimido[6,1-a]isoindol-9(3H) -one (3d) . Heating of 1 in the presence of phosgene lead to the formation of 4a-(4-chlorophenyl)-2,3,4,4a-tetrahydropyrimido[6,1-a]isoindole-1, 9-dione (4).     

Electron impact mass spectra of some tertiary aliphatic nitro compounds. Nitrocarbonyl compounds and some analogues

The mass spectra of some tertiary aliphatic nitroaldehydes, nitroketones, nitroesters, nitronitriles and related nitrocarbonyl compounds are discussed and compared with those of some analogous nitro compounds lacking the carbonyl function. The M⁺˙ ? NO₂˙ and in several cases M⁺˙ ? HNO₂ fragmentation seem to be the most characteristic features of all tertiary aliphatic nitro compounds. In the presence of the primary nitro group, the loss of NHO₂ is always observed.     

The correlation of the intensities of the M+˙ and [M − H]+ ions in electron impact mass spectra of cyclic acetals and thioacetals containing a phenylalkoxyester group

The correlation between the intensities of the M^+˙ and [M ? H]⁺ ions of 47 cyclic acetals and thioacetals of alkyl formylphenoxyacetates and propionates as well as the fragmentation patterns in the vicinity of the molecular ion are discussed. The characteristic differences between the spectra of 1,3-dioxolanes, 1,3-oxathiolanes, 1,3-dithiolanes and 1,3-dioxanes are presented.     

Compact multipolar representation of the electrostatic potential for flexible molecules

A new method for generating a compact multipolar representation of the electrostatic potential (EP) for flexible molecules is presented. The method is based on a constrained minimization of the difference between the quantum mechanical and the classical EP. The fitting procedure used adopts the least absolute shrinkage and selection operator technique [R. Tibshirani, J. Roy. Stat. Soc. B 58, 267 (1996)] which can be seen as penalized ordinary least squares. The penalty function optimized for the particular molecule of interest effectively removes redundant multipoles. It is shown that the use of multiple conformations is crucial for the predictive ability of the EP model for flexible molecules. The multipole local coordinate systems are chosen in a way that best reflects the key conformational changes. It was demonstrated that such an approach improves the predictive ability of EP models. It also allows to exploit equivalence of atoms in the calculation of multipoles components. In the case of polar flexible molecules, the augmentation of the EP model based on charges by higher multipoles decreases the relative root mean square error by a factor of 1.5-5. The corresponding effect of enlargement of the set of multipoles was significantly reduced.