Microwave spectrum and structure of cyanamide: Semirigid bender treatment

An extensive study of the microwave spectrum of cyanamide has been undertaken, the analysis being based in part on semirigidbender calculations by the methods of Bunker and Szalay. Inversion lines of NH₂CN, $\text{K}{}_{\mathrm{?1}}\text{= 2}{}^{\mathrm{a}}\text{Q}$ branches and a number of vibrational satellites of the J = 2?1 transition were observed. A two-vibrational-state Hamiltonian was used to fit simultaneously the 0⁺ and 0^? microwave data and yielded rotational constants X, Y, Z, D_J, D_JK, d₁, H_JK as well as the inversion splitting and the μ_yz-connecting matrix element. Vibrational satellite data of seven isotopic species and infrared frequencies of NH₂CN were included in the semirigid bender calculations: The NCN spine is nonlinear by ca. 5° in the equilibrium structure of the molecule. Also, $\text{r}{}_{\mathrm{<mtext>NH</mtext>}}\text{A}\text{?}\text{= 0.9994 + 0.0144?}{}^2$; <HNH/2 = 60.39° ? 0.1134?²; $\text{r}{}_{\mathrm{<mtext>NC</mtext>}}\text{A}\text{?}\text{= 1.3301 + 0.0327?}{}^2$ (? is the inversion angle in rad); $\text{r}{}_{\mathrm{<mtext>CN</mtext>}}\text{= 1.1645}\text{A}\text{?}$ fixed. The inclusion of the NC bond flexing was necessary in order to reproduce the observed vibrational satellite patterns of NH₂CN, NHDCN, and ND₂CN. The barrier to inversion of the amino group is 510 ± 6 cm^?1 with minima at ±45.0 ±0.2°. The inversion dipole moment is 0.91 ± 0.02 Debye.     

Über Anzahl und Verteilung der Scheitel ebener Bogen

Zusammenfassung Seit der Entdeckung des 4-Scheitel-Satzes durch S. Mukhopadhaya (1909) und A. Kneser (1912) hat sich eine umfangreiche Literatur über Scheitel- und verwandte Sätze entwickelt. Unter anderem wurden ebene Bogen auf Scheitel hin untersucht bzgl. Charakteristiken, welche von k 1 Parametern stetig abhängen. Wir legen für die wichtigsten Sätze aus diesem Teil der Theorie überarbeitete Definitionen und Beweise unter vereinfachten Voraussetzungen vor.

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Bargaining over the division of a shrinking pie: An axiomatic approach

The Bargaining Problem paradigm is extended to time-consuming conflict situations. Such a situation can be represented by a chain of bargaining domains, each representing the conflict at a different point in time. The solution function selects a point in the union of all these domains. We characterize a solution function which satisfies several requirements and explore its properties. One of the results is that an extension of the Adding requirement (Thomson-Myerson 1980) is enough, under some conditions, to yield a solution point, so there is no need to extend the stronger requirements of Independence of Irrelevant Alternatives (Nash 1950) or Monotonicity (Kalai-Smorodinsky 1975).     

On regular polyhedra with hidden symmetries

We consider polyhedral realizations of oriented regular maps with or without self-intersections in E³ whose symmetry group is a subsgroup of small index in their. automorphism group. The four classical kepler-poinsot polyhedra are the only ones of index 1. There are exactly five of Index 2, all with icosahedral symmetry group [W2] as the Kepler-poinsot polyhedra. In this paper we show that there are no such polyhedral realizations with octahedral (tetrahedral) symmetry group and index 2 or 3 (2,3,4,5), which is best possible in the octahedral case.     

On switching paths polyhedra

A class of integer polyhedra with totally dual integral (tdi) systems is proposed, which generalizes and unifies the “Switching Paths Polyhedra” of Hoffman (introduced in his generalization of Max Flow-Min Cut) and such polyhedra as the convex hull of (the incidence vectors of) all “path-closed sets” of an acyclic digraph, or the convex hull of all sets partitionable intok path-closed sets. As an application, new min-max theorems concerning the mentioned sets are given. A general lemma on when a tdi system of inequalities is box tdi is also given and used.     

Atmospheric chemistry of diazomethane – an experimental and theoretical study

The kinetics of the O₃, OH and NO₃ radical reactions with diazomethane were studied in smog chamber experiments employing long-path FTIR and PTR-ToF-MS detection. The rate coefficients were determined to be k _CH2NN+O3?=?(3.2?±?0.4)?×?10^?17 and k _CH2NN+OH?=?(1.68?±?0.12)?×?10^?10 cm³ molecule^?1 s^?1 at 295?±?3?K and 1013?±?30 hPa, whereas the CH₂NN?+?NO₃ reaction was too fast to be determined in the static smog chamber experiments. Formaldehyde was the sole product observed in all the reactions. The experimental results are supported by CCSD(T*)-F12a/aug-cc-pVTZ//M062X/aug-cc-pVTZ calculations showing the reactions to proceed exclusively via addition to the carbon atom. The atmospheric fate of diazomethane is discussed.     

Geometric dynamic recrystallization of austenitic stainless steel through linear plane-strain machining

ABSTRACT

Type 316L austenitic stainless steel was severely plastically deformed at room temperature using linear plane-strain machining in a single pass that imparted shear strains up to 2.2 at strain rates up to 2?×?10³ s^?1. The resulting microstructures exhibited significant grain size refinement and improved mechanical strength where geometric dynamic recrystallization was identified as the primary microstructural recrystallization mechanism active at high strain rates. This mechanism is rarely observed in low to medium stacking fault energy materials. The critical stress required for twin initiation is raised by the combined effects of refined grain size and the increase in stacking fault energy due to the adiabatic heating of the chip, thus permitting geometric dynamic recrystallization. The suppression of martensite formation was observed and is correlated to the significant adiabatic heating and mechanical stabilisation of the austenitic stainless steel. A gradient of the amount of strain induced martensite formed from the surface towards the interior of the chip. As the strain rate is increased from 4?×?10² s^?1–2?×?10³ s^?1, a grain morphology change was observed from a population of grains with a high fraction of irregular shaped grains to one dominated by elongated grain shapes with a microstructure characterised by an enhanced density of intragranular sub-cell structure, serrated grain boundaries, and no observable twins. As strain rates were increased, the combination of reduction in strain induced martensite and non-uniform intragranular strain led to grain softening where a Hall-Petch relationship was observed with a negative strengthening coefficient of ?0.08?MPa m^1/2.     

Steady state photoisomer accumulation in the absorber jet of the passively mode-locked femtosecond dye laser

In continuous were passively mode-locked dye lasers a steady state distribution of two isomers of the saturable absorber dye can be established. We report the first intracavity transmission measurement and estimation of the amount of the photoisomer of DODCI in the femtosecond CPM ring laser. Comparison with a simple model based on rate equations allows to estimate the quantum yield of a photo-back reaction. The obtained dependence of the photoisomer concentration on the laser wavelength and pulse energy can be used in theories describing the generation process for adequate estimation of its part in the modelocking regime.     

Bosonization,topological solitons and fractional charges in two-dimensional quantum field theory

We further develop the quantization of topological solitons in two-dimensional quantum field theory in terms of Euclidean region functional integrals. Our approach is nonperturbative and mathematically rigorous. We apply it to construct physical states with fractional fermion number in models of interacting bosons and fermions without recurring to a semiclassical approximation. A related issue discussed in this paper is two-dimensional chiral bosonization.