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1.
Let (\gnm)n,m ? \Zst(\gnm)_{n,m\in\Zst} be a Gabor frame for \LtR\LtR for given window gg. We show that the window \ho = \SQI g\ho=\SQI g that generates the canonically associated tight Gabor frame minimizes ||g-h||\|g-h\| among all windows hh generating a normalized tight Gabor frame. We present and prove versions of this result in the time domain, the frequency domain, the time-frequency domain, and the Zak transform domain, where in each domain the canonical \ho\ho is expressed using functional calculus for Gabor frame operators. Furthermore, we derive a Wiener--Levy type theorem for rationally oversampled Gabor frames. Finally, a Newton-type method for a fast numerical calculation of \ho\ho is presented. We analyze the convergence behavior of this method and demonstrate the efficiency of the proposed algorithm by some numerical examples. 相似文献
2.
We show that functions which are invariant for suitable product semigroups (one of which is a quasi-Poisson semigroup on a general state space) decompose into a singular eigen-function and a mixture of products of minimal eigen-functions. 相似文献
3.
P. Janssen H. Vanderstraeten 《International Journal of Infrared and Millimeter Waves》1987,8(4):415-429
Data on the influence of the Stark Effect on an optically pumped FIR laser with CH3Cl or CH3Br as active medium are given for various wavelengths. A very simple method for an effective FIR power stabilisation based on the Stark Effect is described. Its working is illustrated with the EPR signal of a 10% diluted DAG sphere. 相似文献
4.
M. M. J. F. Janssen 《Zeitschrift fur Physik C Particles and Fields》1991,52(1):165-174
For theep collider at HERA, we study processes with neutrinos in the final state. Furthermore, we discuss the production ofW andZ bosons. Because of the very small lifetimes of theW andZ, we consider the production of their leptonic decay products rather than the bosons themselves. All the results are based on exact calculations of the matrix element at the tree level. Total cross sections and various kinematical distributions are presented. 相似文献
5.
T. Janssen 《Zeitschrift für Physik B Condensed Matter》1992,86(2):277-283
A discussion is given of the relation between different models for systems with incommensurate phases. Moreover, a generalisation of such models is introduced, which shows an alternative explanation for similar phase diagrams. To get this one may vary the range of the interactions and the numbers of degrees of freedom per site.Another generalization involves coupling to elastic degrees of freedom. Such a coupling may change the type of the incommensurate phase transition. 相似文献
6.
A. J. E. M. Janssen 《Journal of Fourier Analysis and Applications》1998,4(6):723-726
In this note we prove that the Wigner distribution of an f ∈ L2(ℝn) cannot be supported by a set of finite measure in ℝ2n unless f=0. We prove a corresponding statement for cross-ambiguity functions. As a strengthening of the conjecture we show
that for an f ∈ L2(ℝn) its Wigner distribution has a support of measure 0 or ∞ in any half-space of ℝ2n. 相似文献
7.
8.
9.
Hans-Gerd Janssen Henri M. J. Snijders Jacques A. Rijks Carel A. Crarners Peter J. Schoenmakers 《Journal of separation science》1991,14(7):438-445
The effects of the pressure drop across the column on retention and efficiency in SFC have been studied. Numerical methods are described which enable the prediction of hold-up time and pressure drop in both packed and open tubular columns. Predictions of both hold-up time and pressure drop are in good agreement with experimental data. The density gradient along the column can be calculated using the numerical methods and a procedure is described which enables the calculation of the overall capacity factors of the solutes from the density profile in the column. Significant variations of the capacity factor are observed along the column. The effect of the density gradient along the column on local diffusivity and dispersion is studied. The column efficiency in systems with significant pressure drops is affected by changes in: the linear velocity of the mobile phase; the diffusion coefficients; and the capacity factors of the solutes along the column. The overall efficiency of the chromatographic system can be calculated if, as is the case for open tubular columns, adequate plate height equations are available. 相似文献
10.
The equilibrium of the heterogeneous reaction between dissolved sodium sulfide and biologically produced sulfur particles has been studied. Biologically produced sulfur was obtained from a bioreactor of a hydrogen sulfide removal process in which the dominating organism is Thiobacillus sp. W5. Detailed knowledge of this reaction is essential to understand its effect on the process. The results were compared with the equilibrium of the reaction of sulfide with ‘inorganic’ elemental sulfur. The equilibrium between dissolved sodium sulfide and biologically produced sulfur particles can be described by an equilibrium constant, Kx, which consists of a weighted sum of constants for polysulfide ions of different chain length, rather than a true single equilibrium constant. For biologically produced sulfur pKx = 9.10 ± 0.08 (21 °C) and 9.17 ± 0.09 (35 °C) with an average polysulfide chain length x = 4.91 ± 0.32 (21 °C) and 4.59 ± 0.31 (35 °C). The pKx value for biologically produced sulfur is significantly higher than for reaction of dissolved sodium sulfide with inorganic sulfur (pKx = 8.82; 21 °C). This difference is probably caused by the negatively charged polymeric organic layer, which is present on biologically produced sulfur but absent with “inorganic” sulfur. Specific binding of polysulfide ions to the organic layer results in a higher polysulfide concentration at the reaction site compared to the bulk concentration. This results in an apparent decrease of the measured equilibrium constant, Kx. 相似文献