Ab initio calculations of magnetic structure and lattice dynamics of Fe/Pt multilayers

The magnetization distribution, its energetic characterization by the interlayer coupling constants and lattice dynamics of (001)-oriented Fe/Pt multilayers are investigated using density functional theory combined with the direct method to determine phonon frequencies. It is found that ferromagnetic order between consecutive Fe layers is favoured, with the enhanced magnetic moments at the interface. The bilinear and biquadratic coupling coefficients between Fe layers are shown to saturate fast with increasing thickness of nonmagnetic Pt layers which separate them. The phonon calculations demonstrate a rather strong dependence of partial iron phonon densities of states on the actual position of Fe monolayer in the multilayer structure.     

The Index of the Complex Eigenvalues of a Parity Progressive Population Operator

In this paper we discuss the index of the complex eigenvalue of a parity progressive population operator. Under certain conditions, we first prove that all the complex eigenvalues of this operator, except at most finitely many ones, are of index 1, and then, as an application of this result, we obtain the asymptotic expansion of the solution of the corresponding parity progressive population equation.     

Non-Uniformity and Generalised Sacks Splitting

We show that there do not exist computable functions f ₁(e, i), f ₂(e, i), g ₁(e, i), g ₂(e, i) such that for all e, i ∈ ω, (1) $ {\left( {W_{{f_{1} {\left( {e,i} \right)}}} - W_{{f_{2} {\left( {e,i} \right)}}} } \right)} \leqslant _{{\rm T}} {\left( {W_{e} - W_{i} } \right)}; $ (2) $ {\left( {W_{{g_{1} {\left( {e,i} \right)}}} - W_{{g_{2} {\left( {e,i} \right)}}} } \right)} \leqslant _{{\rm T}} {\left( {W_{e} - W_{i} } \right)}; $ (3) $ {\left( {W_{e} - W_{i} } \right)} \not\leqslant _{{\rm T}} {\left( {W_{{f_{1} {\left( {e,i} \right)}}} - W_{{f_{2} {\left( {e,i} \right)}}} } \right)} \oplus {\left( {W_{{g_{1} {\left( {e,i} \right)}}} - W_{{g_{2} {\left( {e,i} \right)}}} } \right)}; $ (4) $ {\left( {W_{e} - W_{i} } \right)} \not\leqslant _{{\rm T}} {\left( {W_{{f_{1} {\left( {e,i} \right)}}} - W_{{f_{2} {\left( {e,i} \right)}}} } \right)}{\text{unless}}{\left( {W_{e} - W_{i} } \right)} \leqslant _{{\rm T}} {\emptyset};{\text{and}} $ (5) $ {\left( {W_{e} - W_{i} } \right)} \leqslant _{{\rm T}} {\left( {W_{{g_{1} {\left( {e,i} \right)}}} - W_{{g_{2} {\left( {e,i} \right)}}} } \right)}{\text{unless}}{\left( {W_{e} - W_{i} } \right)} \leqslant _{{\rm T}} {\emptyset}. $ It follows that the splitting theorems of Sacks and Cooper cannot be combined uniformly.     

平面多项式系统及其相伴系统

引进平面多项式系统的相伴系统的概念 ,分析了多项式系统与其相伴系统之间在极限环不存在性 ,唯一性 ,中心焦点的判定等问题上的相似之处和不同之处 ,提出了几个公开问题 .     

Zur Reaktion eines Bis(amino)germylens mit Germaniumaziden: Abfangreaktionen von instabilen Germa-Iminen

Reaction of a Cyclic Bis(amino)germylene with Germaniumazides: Trapping-Reactions of Unstable Germa-Imines . The cyclic bis(amino)germylene 1 reacts with different germaniumazides of the type Me₂Si(NtBu)₂Ge(R)N₃ (R = Me ( 2 ), tBu ( 3 ), N(SiMe₃)₂ ( 4 ), R = N₃ ( 5 )). With the exception of 4 all azides lose dinitrogen when treated with 1 and the Ge^II center coordinates the α-nitrogen of the azide group. It seems to be reasonable to assume a transient germaimine (nitride) which is trapped by further reaction with the azide molecules 2 and 5 or by reaction with the solvent pyridine ( 3 ). In the case of 2 the germatetrazole [Me₂Si(NtBu)₂]GeN₄[Ge(NtBu)₂SiMe₂]₂ ( 6 ) is formed, the tetrazole nitrogens being exclusively substituted by germanium atoms (point symmetry of the molecule C_s(m)). When 1 is treated with 5 a tris(germa)amine [Me₂Si(NtBu)₂Ge(N₃)]₃N ( 8 ) is formed, which has an azide group attached to each Ge-atom. X-ray analysis reveals that the nine nitrogen atoms of the azide groups are coplanar with the trigonal planar Ge₃N moiety (crystallographic symmetry: 3/m). The reaction of 1 with 3 is very surprising: the pyridine in the product Me₂Si(NtBu)₂Ge(C₅H₄N)? N(H)Ge(tBu)(NtBu)₂SiMe₂ ( 7 ) is bonded via an α-carbon atom while the remaining hydrogen has added to the nitride-nitrogen. 6 crystallizes in the monoclinic system space group C2/m, a = 24.306(9), b = 10.933(6), c = 19.420(9) Å, β = 91.81(2)° and Z = 4. 7 crystallizes in the hexagonal system space group P6₃/m with a = b = 16.73(1), c = 11.006(8) Å, γ = 120° and Z = 2, and 8 crystallizes in the monoclinic system space group P2₁/n, a = 11.341(6), b = 26.086(9), c = 13.244(7) Å, β = 98. I2(2)° mit Z = 4.     

Microemulsions: Effect of alkyl chain length of alcohol and alkane

In microemulsions consisting of four components, i.e. detergent — water — oil — cosurfactant, the free energy of transfer from the continuous oil phase to the interfacial region for the cosurfactant is reported. From the effect of temperature on the free energy, the entropy and the enthalpy values are also reported. The effect of chain length of the alcohol (cosurfactant) is also described. It is further shown, that if the oil phase consists of hexadecane, then the free energy changes as a linear function of the number of carbon atoms in the cosurfactant. On the other hand, if the oil phase is benzene, the cosurfactant chain length has very little effect. These data are analyzed with respect to the microemulsion structure and stability.     

Charakterisierung eines schweren Kohleverflüssigungsproduktes durch kombinierte Hochleistungsflüssigkeitschromatographie/Massenspektrometrie

Zusammenfassung Ein Recycleöl wurde semipräparativ auf einer Tetrachlorphthalimidopropylsilan-modifizierten Säule hochleistungsflüssigkeitschromatographisch in 23 Fraktionen getrennt. Zur Identifizierung der Hauptkomponenten wurden die Fraktionen mit einer einfachen Präparationstechnik in das Massenspektrometer eingebracht und die Molekülionenspektren unter Benutzung der Low Voltage-Technik gemessen. Vorteilhaft für die Charakterisierung hochsiedender technischer Gemische ist die Tatsache, daß die chromatographische Trennung streng nach der Anzahl der aromatischen Ringe im Molekül erfolgt, weitgehend unabhängig von der Alkylsubstitution.

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Characterization of a heavy coal liquefaction product by combined high-performance liquid chromatography/mass spectrometry

Summary A recycle-oil was separated on a semi-preparative scale into 23 fractions by means of HPLC with a tetrachlorophthalimidopropylsilane-modified column. Mass spectrometry enabled a more or less complete identification of the main components. For this, the fractions were introduced into the mass spectrometer by a simple preparation technique, followed by measurement of the molecule ion spectra by the low voltage technique. An advantage of HPLC for the characterization of high-boiling oil mixtures is that separation takes place almost exclusively accoding to the number of aromatic rings in the molecule and is largely independent of the degree of alkylation.

     

Influence of the Brownian step size in off-lattice Monte Carlo simulations of irreversible particle aggregation

The influence of the Brownian step size in off-lattice Monte Carlo simulations of the aggregation and gelation of spheres is studied. It is found that the kinetics are strongly influenced if the step size is larger than the mean smallest distance between the sphere surfaces. The structure of the clusters and the gels is influenced, but only over length scales smaller than the step size. Using large step sizes leads to a narrower size distribution of the clusters. Implications of the present results are discussed for simulations reported in the literature in which the Brownian step size was chosen equal to the sphere diameter.     

Solving the Problem of Gravitational Compression of a Layered Sphere (by the Example of the Earth)

The problem of spherically symmetric, gravitational compression of an isotropic hyperelastic layered sphere which modeling the region of the Earth below the Mohorovii boundary is solved. The known mechanical characteristics of the Earth in the compressed state are used to find its characteristics in the unstrained state obtained by adiabatic or isothermal stress relief. The stress state differs significantly from the state of purely hydrostatic compression. The minimum bulk compression and maximum radial tension occur not on the boundary of the sphere but in depth at certain distances from the boundary.