A New Two-Dimensional Pulse Sequence for T2* Measurements of Protons in C Isotopomers

A new two-dimensional pulse sequence for T₂* measurement of protons directly coupled to ¹³C spins is proposed. The sequence measures the tranverse relaxation time of heteronuclear proton single-quantum coherence under conditions of free precession and is therefore well suited to evaluate relaxation losses of proton magnetization during preparation delays of heteronuclear pulse experiments in analytical NMR. The relevant part of the pulse sequence can be inserted as a “building block” into any direct or inverse detecting H,C correlation pulse sequence if proton spin–spin relaxation is to be investigated. In this contribution, the building block is inserted into a HETCOR as well as into a HMQC pulse sequence. Experimental results for the HETCOR-based sequence are given.     

Relaxation and thermal vibrations at the NaF(100) surface

The relaxation and the thermal vibrations of the NaF(100) surface are investigated in the temperature range between 25 K and 230 K by means of low-energy electron diffraction (LEED) and a subsequent I(V) structure analysis based on the tensor LEED approach (TLEED). According to the experiments, the NaF(100) surface is not significantly relaxed and has the ideal truncated bulk structure. The thermal vibrational amplitudes of the ions in the topmost layer are significantly enhanced compared to the bulk by a factor of 1.35 ± 0.15 and are equal within the error-bars for Na⁺ and F^? ions. Moreover, the relaxation and the dynamics of the NaF(100) surface are investigated using periodic density functional theory (DFT) calculations using pseudopotentials. In agreement with the experimental findings, the calculated relaxation of the NaF(100) surface is weak with static shifts of the ions of 0.01 Å to 0.02 Å. In the topmost layer, the Na⁺ ions are predicted to be slightly inward shifted, whereas the F^? ions are outward shifted, in accordance to predictions of previous shell-model calculations. A Born Oppenheimer molecular dynamics (BO-MD) simulation of the dynamics at the NaF(100) surface leads to a smaller enhancement of thermal motions of the ions at the surface compared to the experiment.     

Spanning tree formulas and chebyshev polynomials

The Kirchhoff Matrix Tree Theorem provides an efficient algorithm for determiningt(G), the number of spanning trees of any graphG, in terms of a determinant. However for many special classes of graphs, one can avoid the evaluation of a determinant, as there are simple, explicit formulas that give the value oft(G). In this work we show that many of these formulas can be simply derived from known properties of Chebyshev polynomials. This is demonstrated for wheels, fans, ladders, Moebius ladders, and squares of cycles. The method is then used to derive a new spanning tree formula for the complete prismR _n (m) =K _m ×C _n . It is shown that $$2^{\left( {\begin{array}{*{20}c} n \\ 2 \\ \end{array} } \right)\left( {1 - \frac{1}{{r - 1}} + o\left( 1 \right)} \right)} $$ whereT _n (x) is then ^th order Chebyshev polynomial of the first kind.     

Über die numerische Behandlung von Integralgleichungen nach der Quadraturformelmethode

Ohne Zusammenfassung     

Synthesis and application of inorganic/organic composite materials

A new type of inorganic-organic composite has been developed using organic monomeric or polymerizable silanes (with appropriate organic groupings like double bonds or epoxides) as monomers or in situ prepared or separately added nano-scale ceramic or metal particles. Due to the small size of the particulate phase, these composites are still highly transparent but show properties at least partially to be attributed to the inorganic phase. The introduction of special functions into these materials has been used for the fabrication of interesting functions like non-linear optical properties, low surface free energy coatings, controlled release properties or special mechanical properties (scratch resistance).