A solid-state 39K and 13C NMR study of polymeric potassium metallocenes

The quadrupolar Carr-Purcell Meiboom-Gill (QCPMG) and double frequency sweep (DFS)/QCPMG pulse sequences are applied in order to acquire the first solid-state 39K NMR spectra of organometallic complexes, the polymeric main group metallocenes cyclopentadienyl potassium (CpK) and pentamethylcyclopentadienyl potassium (Cp*K). Piecewise QCPMG NMR techniques are used to acquire a high S/N 39K spectrum of the broad central transition of Cp*K, which is ca. 200 kHz in breadth. Analytical and numerical simulations indicate that there is a significant quadrupolar interaction present at both potassium nuclei (C(Q)(39K) = 2.55(6)/2.67(8) MHz and 4.69(8) MHz for CpK (static/MAS) and Cp*K, respectively). Experimental quadrupolar asymmetry parameters suggest that both structures are bent about the potassium atoms (eta(Q)(39K) = 0.28(3)/0.29(3) for CpK (static/MAS) and eta(Q)(39K) = 0.30(3) for Cp*K). Variable-temperature (VT) 39K NMR experiments on CpK elucidate temperature-dependent changes in quadrupolar parameters which can be rationalized in terms of alterations of bond distances and angles with temperature. 13C CP/MAS NMR experiments are conducted upon both samples to quantify the carbon chemical shielding anisotropy (CSA) at the Cp' ring carbon atoms. Ab initio carbon CSA and 39K electric-field gradient (EFG) and CSA calculations are conducted and discussed for the CpK complex, in order to correlate the experimental NMR parameters with molecular structure in CpK and Cp*K. 39K DFS/QCPMG and 13C CP/MAS experiments prove invaluable for probing molecular structure, temperature-dependent structural changes, and the presence of impurities in these systems.     

Rapid high-pressure liquid chromatographic analysis of verapamil in blood and plasma

A high-pressure liquid chromatographic assay procedure has been developed for verapamil in blood or plasma. A paired-ion solvent system with a reversed-phase column is employed. The procedure is specific for verapamil and the retention times of the major metabolites are identified. This procedure is sensitive to a lower blood concentration of 1 ng/ml and standard curves were found to be linear up to the highest concentration tested, 500 ng/ml. Several drugs were tested for interference with the assay, but none were found to cause any problems. The procedure is simple, rapid and permits the analysis of up to 25 samples per day.     

van der Waals corrections to density functional theory calculations: Methane,ethane, ethylene,benzene, formaldehyde,ammonia, water,PBE, and CPMD

Parameters are developed for a practical application of the empirical van der Waals (vdW) correction infrastructure available in the CPMD density functional theory (DFT) code. The binding energy, geometry, and potential energy surface (PES) are examined for methane, ethane, ethylene, formaldehyde, ammonia, three benzene dimer geometries, and three benzene–water geometries. The vdW corrected results compare favorably with MP2 and CCSD(T) calculations near the complete basis set limits, and with experimental results where they are available.     

An asymptotic definition of K-groups of automorphisms and a non-Bernoullian counter-example

Summary Let GZⁿ be a group of measure preserving transformations of a Lebesgue space. J. P. Conze [1] has developed an entropy theory for such groups and described a class of groups obeying a form of the Kolmogorov zero-one law called K-groups. A Bernoulli group is a group isomorphic to the group of translates (shifts) of elements of the space with product measure where X _g =X is a probability space. Bernoulli groups are also K-groups. Katznelson and Weiss [3] have shown entropy is a complete invariant for isomorphism classes of Bernoulli groups. We give an asymptotic definition of K-groups in terms of finite -algebras and justify this definition in terms of entropy and Conze's formulation. This definition s used to help us construct a K-group GZ ⁿ that is completely non-Bernoulli, that is one that contains no Bernoulli subgroup.     

Energy and momentum conserving methods of arbitrary order for the numerical integration of equations of motion

Summary Conventional numerical methods, when applied to the ordinary differential equations of motion of classical mechanics, conserve the total energy and angular momentum only to the order of the truncation error. Since these constants of the motion play a central role in mechanics, it is a great advantage to be able to conserve them exactly. A new numerical method is developed, which is a generalization to arbitrary order of the discrete mechanics described in earlier work, and which conserves the energy and angular momentum to all orders. This new method can be applied much like a corrector as a modification to conventional numerical approximations, such as those obtained via Taylor series, Runge-Kutta, or predictor-corrector formulae. The theory is extended to a system of particles in Part II of this work.     

Zur Minimalität trigonometrischer Polynomoperatoren

Cheney and others [2] have shown that, with respect to the norm of uniform convergence, the Fourier operator F_n:C₂p_n is the only minimal projection. For a more detailed study of operators A:C₂P_n we investigate the evaluation functionals respectively the mean of their norms . We give a complete characterization of polynomial operators which minimize this quantity. As an application we can simplify the proof in [2]. Moreover, we show that the trigonometric interpolation operators, having the above minimal-property,are exactly those with equidistant nodes.

---

---

Diese Arbeit enthält die wesentlichen Resultate einer Diplomarbeit, die der Verfasser an der Eberhard-Karls-Universität Tübingen unter der Anleitung von A.Schönhage angefertigt hat.     

über die Striktionslinien von einparametrigen Scharen linearer Räume

A generalisation of a ruled surface in n-dimensional euclidean space may be generated by euclidean motion of a s-plane A_s. For this one-parametric family {A_s} the curve of striction is defined and the following theorems are proved:

1. The generators A_s are parallel along the curve of striction, i.e. the multivectors representing A_s form a parallel vector field along the curve of striction.
2. If the curve of striction is geodesic on {A_s}, it is also an isogonal trajectory of the family of generators {A_s}.

     

Meromorphic Traveling Wave Solutions of the Complex Cubic-Quintic Ginzburg-Landau Equation

We look for singlevalued solutions of the squared modulus M of the traveling wave reduction of the complex cubic-quintic Ginzburg-Landau equation. Using Clunie??s lemma, we first prove that any meromorphic solution M is necessarily elliptic or degenerate elliptic. We then give the two canonical decompositions of the new elliptic solution recently obtained by the subequation method.     

Separable geodesic action slicing in stationary spacetimes

A simple observation about the action for geodesics in a stationary spacetime with separable geodesic equations leads to a natural class of slicings of that spacetime whose orthogonal geodesic trajectories represent the world lines of freely falling fiducial observers. The time coordinate function can then be taken to be the observer proper time, leading to a unit lapse function, although the time coordinate lines still follow Killing trajectories to retain the explicitly stationary nature of the coordinate grid. This explains some of the properties of the original Painlevé-Gullstrand coordinates on the Schwarzschild spacetime and their generalization to the Kerr-Newman family of spacetimes, reproducible also locally for the Gödel spacetime. For the static spherically symmetric case the slicing can be chosen to be intrinsically flat with spherically symmetric geodesic observers, leaving all the gravitational field information in the shift vector field.