We calculate the unpolarized cross sections for dissociation reactions of charmonia in collisions with π,ρ and K in a potential that is derived from QCD.The reactions are governed by the quark-interchange processes.The mesonic quark-antiquark relative-motion wave functions are determined by the central spinindependent terms of the potential.The numerical wave functions and cross sections are parametrized.The difference of transition amplitudes in the prior form and in the post form is explored by deriving and examining the transition amplitudes of the one-gluon-exchange spin-spin term of the potential in the two forms.We find that the post-prior discrepancy in meson-meson elastic scattering that is governed by quark-interchange processes depends on the difierence of quark or antiquark masses and of quark-antiquark spatial distributions ofthe two mesons. 相似文献
We prove that for the space of functions with mixed first derivatives bounded in norm, the weighted integration problem over bounded or unbounded regions is equivalent to the corresponding classical integration problem over the unit cube, provided that the integration domain and weight have product forms. This correspondence yields tractability of the general weighted integration problem.
We prove that for every dimension and every number of points, there exists a point-set whose -weighted unanchored discrepancy is bounded from above by independently of provided that the sequence has for some (even arbitrarily large) . Here is a positive number that could be chosen arbitrarily close to zero and depends on but not on or . This result yields strong tractability of the corresponding integration problems including approximation of weighted integrals over unbounded domains such as . It also supplements the results that provide an upper bound of the form when .
The concept of weighted discrepancy of sequences was introduced by Sloan and Woniakowski when they proved a general form of a Koksma–Hlawka inequality for the numerical integration of functions. This version takes imbalances in the importance of the projections of the integrand into account.In this paper we give estimates for the weighted discrepancy of several important point sets. Further we carry out various (high-dimensional) numerical integration experiments and we compare the results with the error bounds provided by the generalized Koksma–Hlawka inequality and by the estimates for the weighted discrepancy. Finally we discuss various consequences. 相似文献
We study quasi-Monte Carlo algorithms based on low discrepancy sequences for multivariate integration. We consider the problem of how the minimal number of function evaluations needed to reduce the worst-case error from its initial error by a factor of depends on and the dimension . Strong tractability means that it does not depend on and is bounded by a polynomial in . The least possible value of the power of is called the -exponent of strong tractability. Sloan and Wozniakowski established a necessary and sufficient condition of strong tractability in weighted Sobolev spaces, and showed that the -exponent of strong tractability is between 1 and 2. However, their proof is not constructive.
In this paper we prove in a constructive way that multivariate integration in some weighted Sobolev spaces is strongly tractable with -exponent equal to 1, which is the best possible value under a stronger assumption than Sloan and Wozniakowski's assumption. We show that quasi-Monte Carlo algorithms using Niederreiter's -sequences and Sobol sequences achieve the optimal convergence order for any 0$"> independent of the dimension with a worst case deterministic guarantee (where is the number of function evaluations). This implies that strong tractability with the best -exponent can be achieved in appropriate weighted Sobolev spaces by using Niederreiter's -sequences and Sobol sequences.
Some new statistics are proposed to test the uniformity of random samples in the multidimensional unit cube These statistics are derived from number-theoretic or quasi-Monte Carlo methods for measuring the discrepancy of points in . Under the null hypothesis that the samples are independent and identically distributed with a uniform distribution in , we obtain some asymptotic properties of the new statistics. By Monte Carlo simulation, it is found that the finite-sample distributions of the new statistics are well approximated by the standard normal distribution, , or the chi-squared distribution, . A power study is performed, and possible applications of the new statistics to testing general multivariate goodness-of-fit problems are discussed.
The use of Fourier transform mid-infrared spectroscopy with attenuated total reflection for characterizing entomopathogenic nematodes is evaluated for the first time. The resulting spectra of Steinernema glaseri and Heterorhabditis indica were compared with the spectrum of Caenorhabditis elegans. In the absorption spectra generated by the nematodes samples, the absorption bands were assigned to the molecular species and some important components were identified including triglycerides, trehalose, glycogen and collagen. Also, the use of star diagrams for the fingerprint section of nematode spectra for separating genera is discussed. 相似文献
The n-dimensional star graph Sn is an attractive alternative to the hypercube graph and is a bipartite graph with two partite sets of equal size. Let Fv and Fe be the sets of faulty vertices and faulty edges of Sn, respectively. We prove that Sn − Fv − Fe contains a fault-free cycle of every even length from 6 to n! − 2∣Fv∣ with ∣Fv∣ + ∣Fe∣ ? n − 3 for every n ? 4. We also show that Sn − Fv − Fe contains a fault-free path of length n! − 2∣Fv∣ − 1 (respectively, n! − 2∣Fv∣ − 2) between two arbitrary vertices of Sn in different partite sets (respectively, the same partite set) with ∣Fv∣ + ∣Fe∣ ? n − 3 for every n ? 4. 相似文献
Tikhonov regularization with the regularization parameter determined by the discrepancy principle requires the computation
of a zero of a rational function. We describe a cubically convergent zero-finder for this purpose.
AMS subject classification (2000) 65F22, 65H05, 65R32 相似文献
A series of well-defined core cross-linked star (CCS) polymeric ionic liquids (PILs) were synthesized via a three-step approach. First, the styrenic imidazole-based CCS polymer (S-PVBnIm) was prepared by the RAFT-mediated heterogeneous polymerization in a water/ethanol solution, followed by the quaternization of S-PVBnIm with bromoalkanes and anion exchange. The CCS polymers were characterized by gel permeation chromatography (GPC), nuclear magnetic resonance (NMR) spectroscopy, Fourier transform infrared spectroscopy (FTIR), thermal gravimetric analysis (TGA), and differential scanning calorimetry (DSC). The obtained CCS polymers were used as the effective emulsifiers for oil-in-water high internal phase emulsions (HIPEs). Multiple oils with different polarity including n-dodecane, undecanol, toluene and octanol were emulsified using 0.5 wt% S-PVBnIm aqueous solution under the acidic condition to form HIPEs with long-term stabilities. The excellent emulsification properties of CCS PILs were demonstrated by HIPE formation for a variety of oils. The properties of HIPEs in terms of emulsion type and oil droplet size were characterized by the confocal laser scanning microscopy (CLSM). The intriguing capability of CCS PILs to stabilize HIPEs of various oils holds great potentials for the practical applications. 相似文献