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.     

New evidence on the structure of potassium salts of 12-tungstophosphoric acid, KxH3-xPW12O40

Physicochemical properties and compositions of KxH(3-x)PW12O40 salts, where 2 < or = x < or = 3, have been investigated. It has been found that freshly prepared K2HPW12O40 salt (drying at 313 K) contains particles of heteropolyacid and particles of the neutral potassium salt, the sample being in 78.6% amorphous. On aging at room temperature, the heteropolyacid spreads to form a surface layer covering the neutral potassium salt particles K3PW12O40. Heat treatment of KxH(3-x)PW12O40 salts, where 2 < or = x < 3, from 313 K to higher temperatures induces the transformation of the heteropolyacid-covering K(3) core into a well-dispersed, amorphous surface layer. On further heating of the acidic potassium salts, the surface layer decomposes between 855 and 915 K with the formation of a PW8O26-type bronze as a new phase, the K3PW12O40 salt remaining unchanged. The latter starts to decompose at 1093 K, and in the case of all samples, the process is completed at about 1183 K. Rietveld structure refinement, XPS, and 31P NMR measurements of acidic potassium salts indicate that the core of these salts is always formed by the K3PW12O40 salt, which is covered by a heteropolyacid. Comparison of lattice parameters of the K3 salt and HPW leads to the conclusion that the layer is composed of partially or completely dehydrated heteropolyacid molecules. The coverage of the core by HPW in the K2 sample was estimated to be equal to one monolayer.     

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.