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101.
Dr. Rudolf J. Taschner 《Monatshefte für Mathematik》1978,86(3):221-237
It is the aim of this paper to introduce two new notions of discrepancy. They are defined by the formulas $$\begin{gathered} \Delta _N^r \left( {\omega ;f} \right) = \mathop {\sup }\limits_{\left| z \right| = r} \left| {\left( {{1 \mathord{\left/ {\vphantom {1 N}} \right. \kern-\nulldelimiterspace} N}} \right)\sum\limits_{n = 1}^N {f\left( {z e^2 \pi i\omega \left( n \right)} \right)} - f\left( 0 \right)} \right|, and \hfill \\ \delta _N^r \left( {\omega ;f} \right) = \mathop {\sup }\limits_{\left| z \right| = r} \left| {\left( {{1 \mathord{\left/ {\vphantom {1 N}} \right. \kern-\nulldelimiterspace} N}} \right)\sum\limits_{n = 1}^N {f\left( {z \omega \left( n \right)} \right)} \cdot z - \int\limits_0^z {f\left( \zeta \right)d\zeta } } \right|, \hfill \\ \end{gathered} $$ wheref is a holomorphic function defined in the unit disc withf (k) (0)≠0 for allk∈?,r<1 is a positive number, and ω is a sequence in [0, 1]. The first of these discrepancies can be generalized for multidimensional sequences. ω is uniform distributed if and only if lim N→∞ Δ N r (ω;f)=0 resp. lim N→∞δ N r (ω;f)=0. These results are proved in a quantitative way by estimating the classical discrepancyD N (ω) by means ofΔ N r (ω;f) and δ N r (ω;f): $$\begin{gathered} \Delta _N^r \left( {\omega ;f} \right) \ll D_N \left( \omega \right) \ll \Phi \left( {\Delta _N^r \left( {\omega ;f} \right)} \right), \hfill \\ \delta _N^r \left( {\omega ;f} \right) \ll D_N \left( \omega \right) \ll \Psi \left( {\delta _N^r \left( {\omega ;f} \right)} \right). \hfill \\ \end{gathered} $$ The functions Φ and Ψ only depend onf andr. These estimations are based on the inequalities ofKoksma-Hlawka andErdös-Turán. 相似文献
102.
The importance of the rheological behaviour of solutions of macromolecules is briefly evaluated. The viscosity of the solutions depends on concentration, shear rate and time of shear, this relation being determined by the structure of the dissolved molecules. In dilute solutions shear dependence of viscosity is very frequently caused by the preferential orientation of anisotropic molecules. In such a case the particle dimensions can be calculated from the true limiting viscosity number, an anisotropy factor, the rotational diffusion constant and the effective particle density. These numbers can be derived from the flow curve, which has been extrapolated to zero concentration. It is necessary to measure the flow curve at shear gradients, which are sufficiently low to allow for an extrapolation to vanishing shear rate. By comparing the experimental flow curve with a choice of theoretical ones, the rotational diffusion constant and the anisotropy factor (axial ratio) can be found. From the limiting viscosity number and the axial ratio, the particle density can be calculated. 相似文献
103.
L. Ramakrishnan Prof. Dr. S. Soundararajan 《Monatshefte für Chemie / Chemical Monthly》1977,108(1):225-231
Complexes of 2,6-dimethylpyridine 1-oxide with lanthanide iodides of the formulaeLn(2,6-LTNO)5I3 whereLn=La, Tb and Yb,Ln(2,6-LTNO)4I3 whereLn=Pr and Nd and Er(2,6-LTNO)4.5I3 have been prepared and characterised by chemical analysis, infrared and conductance studies. Infrared and conductance data have been interpreted in terms of dimeric (or polymeric) structures involving bridging amine oxide groups.
Mit 2 Abbildungen 相似文献
Mit 2 Abbildungen 相似文献
104.
Prof. Dr. O. Hromatka D. Binder K. Eichinger 《Monatshefte für Chemie / Chemical Monthly》1974,105(1):123-126
The synthesis of 5-(o-trifluoromethylphenyl)-1H-thieno-[3,4-e]1,4-diazepin-2(3H)-one (7) and its nitration and chlorination in pos. 8 are described. 相似文献
105.
G. Bruno P. Capezzuto G. Cicala F. Cramarossa 《Plasma Chemistry and Plasma Processing》1986,6(2):109-125
Plasma-chemical reduction of SiCl4 in mixtures with H2 and Ar has been studied by optical emission spectroscopy (OES) and laser interferometry techniques. It has been found that the Ar:H2 ratio strongly affects the plasma composition as well as the deposition (r
D) and etch (r
E) rates of Si: H, Cl films and that the electron impact dissociation is the most important channel for the production of SiClx species, which are the precursors of the film growth. Chemisorption of SiClx and the reactive surface reaction SiClx+H–SiCl(x–1)0+HCl are important steps in the deposition process. The suggested deposition model givesr
D [SiClx][H], in agreement with the experimental data. Etching of Si: H, Cl films occurs at high Ar: H2 ratio when Cl atoms in the gas phase become appreciable and increases with increasing Cl concentration. The etch rate is controlled by the Cl atom chemisorption step. 相似文献
106.
Prof. Dr. Enrique J. Baran 《Monatshefte für Chemie / Chemical Monthly》1975,106(1):121-126
Mean amplitudes of vibration of a series of tetrahedralXY 4 molecules and ions (hydrides, halides, oxides and oxoanions) have been calculated using the “Method of the Characteristic Vibrations” ofA. Müller. The results indicate that this method leads to very good values for most of the investigated species, and especially in the cases of highM X/MY mass ratio. 相似文献
107.
Doz. Dr. Friedrich Höfler Ernst Brandstätter 《Monatshefte für Chemie / Chemical Monthly》1975,106(4):893-904
The reactions of Ge2(C6H5)6 with HCl and HBr lead in nearly quantitative yields to the 1,1,2,2-tetrahalo derivatives Cl2(C6H5)GeGe(C6H5)Cl2 (I) and Br2(C6H5)GeGe(C6H5)Br2 (II), resp. The Si?Ge bond of (C6H5)3SiGe(C6H5)3 is cleaved under the conditions of hydrohalogenation. The vibrational spectra of Ge2Br6, Ge2(C6H5)6, I, and II are reported. The influence of vibrational coupling on ν GeGe in these compounds is discussed in detail, including vibrational calculations. 相似文献
108.
Two sufficient criteria for the convergence of the Rayleigh-Ritz Method (RRM) with respect to the eigenvalues (E-convergence) of non-relativistic electronic Hamiltonians of molecules are discussed and compared. Moreover, a necessary and sufficient criterion is given. By example (Sect. 9) it is shown that the L
2-completeness of the basis is not sufficient to guarantee E-convergence. The convergence of the wave functions in different norms (-convergence) is also investigated. In particular, sufficient conditions for the one-particle basis functions (orbitals) are given, such that a CI calculation in this basis is both E- and -convergent. 相似文献
109.
Prof. Dr. Edmund Hlawka 《Monatshefte für Mathematik》1980,89(1):19-44
A new proof of a theorem of W. Neiss is given that the rays of the Quadratwurzelschnecke are uniformly distributed mod 2 . The exact order of the discrepancy of the sequence is determined. Multidimensional generalizations of this sequence are also considered. It is shown that the Quadratwurzelschnecke is something like a roulette.
Mit 2 Abbildungen
Herrn Prof. R. M. Redheffer in Freundschaft zum 60. Geburtstag gewidmet 相似文献
Mit 2 Abbildungen
Herrn Prof. R. M. Redheffer in Freundschaft zum 60. Geburtstag gewidmet 相似文献
110.
Dr. Lisa Hefendehl-Hebeker 《Monatshefte für Mathematik》1980,90(3):219-228
Motivated by an investigation ofKuz'min [2], in this note we introduce a topology on the set
of nonassociative algebras of a fixed dimensionr< over a local fieldF. We obtain a space, which is notT
1. If the trivial algebra
is removed, the remaining subspace is quasicompact. The space is homeomoprhic to the group of square classes ofF
*; forr3 the space is notT
1. The set of division algebras is open in. 相似文献