A new class of long-tailed pausing time densities for the CTRW

We present some asymptotic results for the family of pausing time densities having the asymptotic (t) property(t) [t ln¹⁺(t/T)]^–1. In particular, we show that for this class of pausing time densities the mean-squared displacement r ²(t) is asymptotically proportional to ln(t/T), and the asymptotic distribution of the displacement has a negative exponential form.     

Linear AAD potentials and the consistency of two conservation law approaches

For the linear action-at-a-distance (AAD) potentials, generated from the function Lagrangian, the equivalence of the direct-interaction and field-mediated energies is proved. It is next shown that in dynamics built on these potentials the virial theorem acquires the same form as in dynamics of the Liénard-Wiechert potentials.The author is grateful to Prof. H. C. von Baeyer for his proposal to explore the virial theorem by the designated manner and for other valuable remarks.     

Properties of noninteger moments in a first passage time problem

We calculate the moments t ^q , whereq is not necessarily an integer, of the first passage time to trapping for a simple diffusion problem in one dimension. If a characteristic length of the system isL and t _q ~L (q) asL, then we show that there is a phase transition atq=q _c such that whenq<q _c ,(g)=0, and forq>q _c , (q) is a linear function ofq. These analytical results can be used to explain results for large moments for diffusion on a hierarchic structure. We also show how to calculate noninteger moments in terms of characteristic functions.     

Polarization Fourier transform infrared spectroscopy on ionic single crystal surfaces: Davydov splittings, adsorbated structures and 2D-phase transitions on NaCl(100) and MgO(100)

Polarized infrared spectra of adsorbates on NaCl(100) and MgO(100) single crystal cleavage planes reveal Davydov splittings, structures with adsorbate orientations and/or 2D-phase transitions, in concert with diffraction studies. CO₂ on NaCl shows the sharpest adsorbate spectra known ( ).     

35Cl Nqr spectroscopy of the [PO2Cl2]− and POCl3 groups in Me(PO2Cl2)2·2D (Me = Mg,Ca, Mn; D = POCl3,CH3COOC2H5,CH3COCH3)

³⁵Cl NQR spectra of dichlorophosphates Me(PO₂Cl₂)₂ · 2D (Me = Mg, Ca, Mn; D = CH₃COOC₂H₅, CH₃COCH₃, POCl₃) are studied in the temperature range 77 ? T (K) ? 305. It is shown that the three compounds with CH₃COOC₂H₅ as donor are isomorphic at 77 K, the crystal structure of Mn(PO₂Cl₂)₂· 2CH₃COOC₂H₅. The structure of Mg(PO₂Cl₂)_2^?· 2CH₃COCH₃ and of Mg(PO₂Cl₂)₂ · 2POCl₃ probably consists of infinite chains as found for Mn(PO₂Cl₂)₂· 2CH₃COOC₂H₅. Mg(PO₂Cl₂)₂· 2CH₃COOC₂H₅ shows phase transformations and a complicated dynamical behaviour leading to strong deviations from a Bayertype NQR function v = f(T). The donor capacity of POCl₃ in Mg(PO₂Cl₂)₂· 2POCl₃ is comparable with the donor strength in AsCl₃ · POCl₃ · A d_π-p_π overlap of the P-O bond influences the P-Cl bond.     

Hydroxylamido(1-)-O,N-Komplexe des Molybdäns(VI) mit terminalen Oxo-, Sulfido- und Selenido-Liganden Die Kristallstrukturen von [MoO2(C5H10NO)2] und von [MoS2(C5H10NO)2]

Hydroxylamido(1-)-O,N Complexes of Molybdenum(VI) Containing Terminal Oxo, Sulfido, and Selenido Ligands. Crystal Structures of [MoO₂(C₅H₁₀NO)₂] and of [MoS₂(C₅H₁₀NO)₂] Molecular complexes of cis-dioxo-bis(hydroxylamido(1-)-O,N)molybdenum(VI) containing O,N-coordinated, N,N-substituted hydroxylamine ligands react with H₂S in toluene substituting one or both terminal oxo groups yielding cis-oxosulfido- and cis-disulfido-bis (hydroxylamido(1-)-O,N) molybdenum complexes, respectively. With H₂Se the corresponding cis-oxoselenido complexes are formed. The crystal structures of the two title compounds containing piperidine-N-oxide as ligands are described: The cis-disulfido complex crystallizes tetragonal in the space group D—I 4 2 m with four formula units per unit cell; the corresponding cis-dioxo complex crystallizes orthorhombic (D—P 2₁2₁2₁; Z = 4). The ¹H—nmr spectra and the UV-visible absorption spectra are reported.