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1.
The lattice profile analyzes the intrinsic structure of pseudorandom number sequences with applications in Monte Carlo methods and cryptology. In this paper, using the discrete Fourier transform for periodic sequences and the relation between the lattice profile and the linear complexity, we give general formulas for the expected value, variance, and counting function of the lattice profile of periodic sequences with fixed period. Moreover, we determine in a more explicit form the expected value, variance, and counting function of the lattice profile of periodic sequences for special values of the period. 相似文献
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Inequalities satisfied by the zeros of the solutions of second-order hypergeometric equations are derived through a systematic use of Liouville transformations together with the application of classical Sturm theorems. This systematic study allows us to improve previously known inequalities and to extend their range of validity as well as to discover inequalities which appear to be new. Among other properties obtained, Szegő's bounds on the zeros of Jacobi polynomials for , are completed with results for the rest of parameter values, Grosjean's inequality (J. Approx. Theory 50 (1987) 84) on the zeros of Legendre polynomials is shown to be valid for Jacobi polynomials with |β|1, bounds on ratios of consecutive zeros of Gauss and confluent hypergeometric functions are derived as well as an inequality involving the geometric mean of zeros of Bessel functions. 相似文献
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The phase boundary theory and the contact rule of phase regions are compared, and some weaknesses of the latter are manifested.
The comparison between the Gupta’s method and the boundary theory method for constructing multicomponent isobaric sections
is also presented. 相似文献
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吴臻 《数学物理学报(B辑英文版)》2004,24(1):91-99
The existence and uniqueness results of fully coupled forward-backward stochastic differential equations with stopping time (unbounded) is obtained. One kind of comparison theorem for this kind of equations is also proved. 相似文献
8.
A model proposed in the literature for fish schools of relatively large size is studied for mathematical and qualitative properties. Existence, uniqueness and positivity of solutions are established and bifurcation properties relative to diffusion and alignment parameters are studied. 相似文献
9.
Automatic detection and identification of shocks in Gaussian state‐space models: a Bayesian approach
An automatic monitoring and intervention algorithm that permits the supervision of very general aspects in an univariate linear Gaussian state–space model is proposed. The algorithm makes use of a model comparison and selection approach within a Bayesian framework. In addition, this algorithm incorporates the possibility of eliminating earlier interventions when subsequent evidence against them comes to light. Finally, the procedure is illustrated with two empirical examples taken from the literature. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
10.
The asymptotic null distribution of the likelihood ratio test for two cases of ordered hypotheses in a particular genetic model is considered. A simple iterative process is proposed in order to get the restricted estimates. It is shown that both tests have asymptotically a chi-bar squared distribution and the same size. A simulation study is also conducted in order to compare the usual unrestricted test with the corresponding one of ordered hypotheses. Finally, the results are extended to some special cases. 相似文献