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81.
This paper describes several combinatorial models for Laguerre, Charlier, and Hermite polynomials, and uses them to prove combinatorially some classical formulas. The so-called “Italian limit formula” (from Laguerre to Hermite), the Appel identity for Hermite polynomials, and the two Sheffer identities for Laguerre and Charlier polynomials are proved. We also give bijective proofs of the three-term recurrences. These three families form the bottom triangle in R. Askey's chart classifying hypergeometric orthogonal polynomials. 相似文献
82.
In this paper, a bivariate generating function CF(x, y) =f(x)-yf(xy)1-yis investigated, where f(x)= n 0fnxnis a generating function satisfying the functional equation f(x) = 1 + r j=1 m i=j-1aij xif(x)j.In particular, we study lattice paths in which their end points are on the line y = 1. Rooted lattice paths are defined. It is proved that the function CF(x, y) is a generating function defined on some rooted lattice paths with end point on y = 1. So, by a simple and unified method, from the view of lattice paths, we obtain two combinatorial interpretations of this bivariate function and derive two uniform partitions on these rooted lattice paths. 相似文献
83.
This paper investigates the optimal threshold values of age to perform preventive maintenance (PM) actions for leased equipment
within the lease period. In this paper, we use age reduction method to describe the degree of PM and construct the maintenance
cost function. For repairable leased equipment, two maintenance models are proposed: (i) maintenance policy of single-phase
and (ii) maintenance policy of two-phase. During the lease period, PM actions are carried out when the age of equipment reaches
a certain threshold value. Any failure of the leased equipment is rectified by a minimal repair within the lease period. Under
these maintenance schemes, the mathematical models of the expected total cost for maintenance policies of single-phase and
two-phase are established, and the optimal maintenance policies are derived such that the expected total cost is minimized.
Finally, the features of the optimal maintenance policy are illustrated through numerical examples. 相似文献
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This paper analyzes, and thus reveals the structure of the stable invariant subspace of the related Hamiltonian matrix arising from the measurement feedback H
-control problem. Using this, it presents another method for the verification of the admissibility of the controller derived by Doyle et al. in 1989. The method not only eliminates unnecessary assumptions on stabilizability and detectability, but also gives deeper insight into the relationship among the stable parts of the associated matrices. 相似文献
90.
Li-Ming Yeh 《Journal of Differential Equations》2011,250(4):1828-1849
A priori estimate for non-uniform elliptic equations with periodic boundary conditions is concerned. The domain considered consists of two sub-regions, a connected high permeability region and a disconnected matrix block region with low permeability. Let ? denote the size ratio of one matrix block to the whole domain. It is shown that in the connected high permeability sub-region, the Hölder and the Lipschitz estimates of the non-uniform elliptic solutions are bounded uniformly in ?. But Hölder gradient estimate and Lp estimate of the second order derivatives of the solutions in general are not bounded uniformly in ?. 相似文献