Design of Hyperbolic Billiards

We formulate a general framework for the construction of hyperbolic billiards. Spherical symmetry is exploited for a simple treatment of billiards with spherical caps and soft billiards in higher dimensions. Other examples include the Papenbrock stadium. Reproduction of the entire article for non-commercial purposes is permitted without charge.     

Two 1-substituted 4-nitro­imidazoles

Crystalline 4-nitro-1-phenyl­imidazole, C₉H₇N₃O₂, (I), and 4′-­nitro-1-phenyl-4,1′-bii­imidazole, C₁₂H₉N₅O₂, (II), contain C—H⃛O and C—H⃛N hydrogen bonds, connecting the mol­ecules into infinite chains. The aromatic fragments in both compounds are nearly planar. The dihedral angles between the benzene and imidazole rings are 26.78 (5)° in (I) and 29.36 (8)° in (II).     

Synthesis of new 2-oxosparteine derivatives

For the first time, substituents to the 3-position of 2-oxosparteine have been introduced. The synthesis of 3-phenylthiolupanine, 3,3-di(phenylthio)lupanine, 3-dehydrolupanine, 3-bromodehydro-lupanine and 2-thiono-3-dehydrosparteine has been described. The stereochemistry of these compounds has been determined and by NMR spectroscopy and X-ray crystallography.     

Analysis of the normal modes of molecules with D3h symmetry: Infrared spectra of monomeric s-triazine and cyanuric acid

Normal modes of s-triazine and cyanuric acid were calculated at the DFT(B3LYP)/6-311++G(d,p) level. These modes were analyzed in terms of potential energy distribution (PED), computed using a specially designed set of symmetry coordinates. The normal-mode analysis was described in detail and the PED matrix definition used in the calculations was provided. Particular attention has been devoted to the degenerate vibrations. The experimental infrared spectra of s-triazine and cyanuric acid isolated in low-temperature Ar matrices have been recorded and interpreted by comparison with the theoretically predicted normal modes. In the spectrum of matrix-isolated s-triazine, the IR bands originating from ¹³C and ¹⁵N isotopologues with one of the ring atoms substituted by a rare isotope were detected. These bands were identified thanks to the excellent agreement between the experimentally observed and theoretically predicted isotope shifts.     

Simultaneous confidence bands for the integrated hazard function

The construction of the simultaneous confidence bands for the integrated hazard function is considered. The Nelson–Aalen estimator is used. The simultaneous confidence bands based on bootstrap methods are presented. Four methods of construction of such confidence bands are proposed. The weird and conditional bootstrap methods are used for resampling. Simulations are made to compare the actual coverage probability of the bootstrap and the asymptotic simultaneous confidence bands. It is shown that the equal-tailed bootstrap confidence band has the coverage probability closest to the nominal one. We also present application of our confidence bands to the data regarding survival after heart transplant. This research was partly supported by AGH grant No. 10.420.03.     

Investigation of thermal power of reaction of titanium slag with sulphuric acid

Enriched titanium raw materials with high titanium content called titanium slags are received by the electrothermal reduction of ilmenite. Titanium slags are most frequently used in the titanium dioxide industry. The reaction of titanium slags with sulphuric acid is strongly exothermic and creates danger of thermal explosion. Kinetics of this reaction depends on the parameters such as temperature of initiation, sulphuric acid concentration and dimension of particles of titanium slag. The reaction of titanium slag with sulphuric acid was investigated at non-isothermal conditions in a special construction calorimeter. The observed thermal power changes in the calorimeter (“calorimeter run”), are the basis for estimation of reaction kinetics. A proposed model describing the thermal power changes and taking into account the moment of initiation of reaction is presented. The calorimetric investigations showed, that reaction rate of titanium slags with sulphuric acid depends on initial temperature of reaction, size of particles of titanium raw material and sulphuric acid concentration.     

Two isomorphous azastilbene derivatives: 1‐(2‐chlorobenzyl)‐4‐[(E)‐2‐(4‐hydroxyphenyl)ethenyl]pyridinium chloride and 1‐(2‐bromobenzyl)‐4‐[(E)‐2‐(4‐hydroxyphenyl)ethenyl]pyridinium bromide

The crystal structures of the two title (E)‐stilbazolium halogenates, C₂₀H₁₇ClNO⁺·Cl⁻ and C₂₀H₁₇BrNO⁺·Br⁻, are isomorphous, with an isostructurality index of 0.985. The azastyryl fragments are almost planar, with dihedral angles between the benzene and pyridine rings of ca 4.5°. The rings of the benzyl groups are, in turn, almost perpendicular to the azastyryl planes, with dihedral angles larger than 80°. The cations and anions are connected by O—H...X⁻ (X = halogen) hydrogen bonds. The halide anions are `sandwiched' between the charged pyridinium rings of neighbouring molecules, and weak C—H...O hydrogen bonds and C—H...X and C—H...π interactions also contribute to the crystal structures.     

The Crystal Structure of Fluphenazinium Dipicrate Dimethylsulphoxide Solvate

Abstract  

The title compound, C₂₂H₂₈F₃N₃OS²⁺ × 2(C₆H₂N₃O₇ ⁻) × (CH₃)₂SO—the picrate salt of the potent antipsychotic drug, fluphenazine—crystallizes in the triclinic P-1 space group with unit cell parameters a = 10.6333(12) ?, b = 11.9696(12) ?, c = 17.7036(15) ?, α = 103.265(9)°, β = 98.414(9)°, γ = 102.702(10)°. The ionic fragments: the fluphenazinium dictation, and two picrate anions, are joined by means of strong N–H···O and weak C–H···O hydrogen bonds into the chains of alternating cations and anions, expanding along [010] direction. Within the chain, the picrates interact by means of short π···π interactions: the mean distance between the planes is 3.366 ?; additional interaction of the same type between one of the picrates and the phenyl ring of the phenothiazine ring system additionally strengthen the pattern. The phenothiazine ring exists in a typical, “butterfly-like” conformation, with two terminal rings planar and the central ring in a slightly flattened boat form. This conformation results in the dihedral angle between the terminal rings of 41.76(5)°. The aliphatic chain which substitutes phenothiazine at N-position is not in an extended conformation, the torsion angles along this chain are 75.95(14)° and −163.96(10)°. The structure contains also the solvent—dimethylsulphoxide molecules, which are connected with the cation–anion structure by means of strong O–H···O hydrogen bonds.