Eine Schwefelbestimmungsmethode von allgemeiner Anwendbarkeit

Ohne Zusammenfassung     

Regularity of multiwavelets

The motivation for this paper is an interesting observation made by Plonka concerning the factorization of the matrix symbol associated with the refinement equation for B-splines with equally spaced multiple knots at integers and subsequent developments which relate this factorization to regularity of refinable vector fields over the real line. Our intention is to contribute to this train of ideas which is partially driven by the importance of refinable vector fields in the construction of multiwavelets. The use of subdivision methods will allow us to consider the problem almost entirely in the spatial domain and leads to exact characterizations of differentiability and Hölder regularity in arbitrary L _p spaces. We first study the close relationship between vector subdivision schemes and a generalized notion of scalar subdivision schemes based on bi-infinite matrices with certain periodicity properties. For the latter type of subdivision scheme we will derive criteria for convergence and Hölder regularity of the limit function, which mainly depend on the spectral radius of a bi-infinite matrix induced by the subdivision operator, and we will show that differentiability of the limit functions can be characterized by factorization properties of the subdivision operator. By switching back to vector subdivision we will transfer these results to refinable vectors fields and obtain characterizations of regularity by factorization and spectral radius properties of the symbol associated to the refinable vector field. Finally, we point out how multiwavelets can be generated from orthonormal refinable bi-infinite vector fields.     

Correlated polarization propagator calculations of static polarizabilities

We present a systematic comparison of the correlation contribution at the level of the second-order polarization propagator approximation (SOPPA ) and MP 2 to the static dipole polarizability of (1) Be, BeH^?, BH, CH⁺, MgH^?, AIH, SiH⁺, and GeH⁺; (2) BH₃, CH₄, NH₃, H₂O, HF, BF, and F₂; and (3) N₂, CO, CN^?, HCN, C₂H₂, and HCHO . Fairly extended basis sets were used in the calculations. We find that the agreement with experimental values is improved in SOPPA and MP .2 over the results at the SCF level. The signs and magnitudes of the correlation contribution in SOPPA are similar to those obtained in analytical derivative MP 2 calculations. However, it is not possible to say, in general, which method gives the largest correlation contribution or the best agreement with experiment, nor is it possible to make a priori prediction of the sign of the correlation contribution. For the first group of molecules, which have a quasi-degenerate ground state, additional CCDPPA and CCSDPPA calculations were performed and compared with polarizabilities obtained as analytical/numerical derivatives of the CCD and CCSD energies. The CCSDPPA results were found to be in better agreement with other calculations than were the SOPPA results, demonstrating the necessity of using methods based on infinite-order perturbation theory for these systems. © 1994 John Wiley & Sons, Inc.     

Preemptive scheduling of interval orders is polynomial

In 1979, Papadimitriou and Yannakakis gave a polynomial time algorithm for the scheduling of jobs requiring unit completion times when the precedence constraints form an interval order. The authors solve here the corresponding problem, for preemptive scheduling (a job can be interrupted to work on more important tasks, and completed at a later time, subject to the usual scheduling constraints.) The m-machine preemptive scheduling problem is shown to have a polynomial algorithm, for both unit time and variable execution times as well, when the precedence constraints are given by an interval order.     

Ab initio predictions of zeolite structures and Si NMR chemical shifts

A recent shell-model potential parameterized on ab initio data is used for predicting the all-silica structures of zeolites MFI, MEI, MTW, TON, FAU and of α-quartz. Cluster models are defined around each site and the ²⁹Si NMR shielding constants are calculated by ab initio techniques (GIAO-HF). Good agreement with observed ²⁹Si NMR chemical shifts is found. Comparison is made with shifts calculated for observed structures. The structures predicted by the ab initio shell-model potential prove as accurate as the observed ones when judged on the quality of the calculated ²⁹Si NMR spectra.     

Thermally stimulated current and DSC studies of the broadened glass transition in liquid crystalline polymers

The high sensitivity of the thermally stimulated current, thermal sampling (TS) method is emphasized in a study of the breadth of the glass transition in several liquid-crystalline polymers (LCPs). Differential scanning calorimetry (DSC) was performed on all samples to further quantify the glass transition regions. For “random” copolyester LCPs with widely varying degrees of crystallinity, including highly amorphous samples, very broad glass tran-sition regions were observed. One semicrystalline alternating copolyester and a series of semicrystalline azomethine LCPs were studied as examples of structurally regular polymers. These exhibited relatively sharp glass transitions more comparable to ordinary isotropic amorphous or semicrystalline polymers. The broad glass transitions in the random copolyesters are attributed to structural heterogeneity of the chains. In one example of a moderate-crystallinity random copolyester LCP (Vectra), glass transitions ranging up to ca. 150°C in breadth were determined by the thermal sampling (TS) method and DSC. In other lower crystallinity copolyester LCPs, the main glass transition temperature as determined by DSC was comparable to that determined by TSC although cooperative relaxations of a minor fraction of the overall relaxing species were detected well below the main T_g, by the TS method and not by DSC. Rapid quenches from the isotropic melt to an isotropic glass were possible with one LCP. The anisotropic and isotropic glassy states for this LCP were found to have the same breadth of the glass transition as was determined by the TS method, although TSC and DSC show that T_g is shifted downward by ca. 15°C in the anisotropic glass as compared to the isotropic glass. © 1993 John Wiley & Sons, Inc.