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51.
Shaul K. Bar-Lev Daoud Bshouty Peter Enis Gérard Letac I-Li Lu Donald Richards 《Journal of Theoretical Probability》1994,7(4):883-929
A natural exponential family (NEF)F in ? n ,n>1, is said to be diagonal if there existn functions,a 1,...,a n , on some intervals of ?, such that the covariance matrixV F (m) ofF has diagonal (a 1(m 1),...,a n (m n )), for allm=(m 1,...,m n ) in the mean domain ofF. The familyF is also said to be irreducible if it is not the product of two independent NEFs in ? k and ? n-k , for somek=1,...,n?1. This paper shows that there are only six types of irreducible diagonal NEFs in ? n , that we call normal, Poisson, multinomial, negative multinomial, gamma, and hybrid. These types, with the exception of the latter two, correspond to distributions well established in the literature. This study is motivated by the following question: IfF is an NEF in ? n , under what conditions is its projectionp(F) in ? k , underp(x 1,...,x n )∶=(x 1,...,x k ),k=1,...,n?1, still an NEF in ? k ? The answer turns out to be rather predictable. It is the case if, and only if, the principalk×k submatrix ofV F (m 1,...,m n ) does not depend on (m k+1,...,m n ). 相似文献
52.
Trigonometric wavelets for Hermite interpolation 总被引:4,自引:0,他引:4
Ewald Quak. 《Mathematics of Computation》1996,65(214):683-722
The aim of this paper is to investigate a multiresolution analysis of nested subspaces of trigonometric polynomials. The pair of scaling functions which span the sample spaces are fundamental functions for Hermite interpolation on a dyadic partition of nodes on the interval . Two wavelet functions that generate the corresponding orthogonal complementary subspaces are constructed so as to possess the same fundamental interpolatory properties as the scaling functions. Together with the corresponding dual functions, these interpolatory properties of the scaling functions and wavelets are used to formulate the specific decomposition and reconstruction sequences. Consequently, this trigonometric multiresolution analysis allows a completely explicit algorithmic treatment.
53.
Samuel S. Wagstaff Jr.. 《Mathematics of Computation》1996,65(213):383-391
We show that the minimum period modulo of the Bell exponential integers is for all primes and several larger . Our proof of this result requires the prime factorization of these periods. For some primes the factoring is aided by an algebraic formula called an Aurifeuillian factorization. We explain how the coefficients of the factors in these formulas may be computed.
54.
The distributions of two--block--factors arising from i.i.d. sequences are observed to coincide with the distributions of the superdiagonals of jointly exchangeable and dissociated arrays . An inequality for superdiagonal probabilities of the arrays is presented. It provides, together with the observation, a simple proof of the fact that a special one--dependent Markov sequence of Aaronson, Gilat and Keane (1992) is not a two--block factor.
55.
NMR spectroscopy plays an important part in the determination of the structures of organic compounds. The parameters of importance here are the chemical shifts of the 1H and 13C nuclei and the spin-spin interactions both between 1H nuclei and between 1H and 13C nuclei. Couplings between 13C nuclei were almost completely neglected until a few years ago, since they were extremely difficult to observe because of the low natural abundance of 13C. However, it is these couplings which afford information directly on the carbon-carbon connectivities in the molecule. It is now possible to use a special NMR pulse sequence to make these couplings more readily visible: the result of using this sequence is a 13C-NMR spectrum from which the carbon skeleton concerned can be directly read off. Two-dimensional spectra in particular are very easy to evaluate. The pulse sequence involved, which bears the somewhat puzzling name INADEQUATE, produces double-quantum coherences from which the NMR signals of the coupled carbon nuclei can be obtained. In this article the principle of double-quantum coherence is described and a number of examples for the application of the INADEQUATE pulse sequences to problems in synthetic organic chemistry, biosynthesis and natural products chemistry are presented; in addition, the possibility of applying the INADEQUATE method to other nuclei is considered. 相似文献
56.
Jin Chen Lin-xi Zhang A-gen Xia 《高分子科学》2006,(1):13-19
It is important to know the rate of intra-molecular contact formation in proteins in order to understand how proteins fold clearly. Here we investigate the rate of intra-molecular contact formation in short two-dimensional compact polymer chains by calculating the probability distribution p(r) of end-to-end distance r using the enumeration calculation method and HP model on two-dimensional square lattice. The probability distribution of end-to-end distance p(r) of short two-dimensional compact polymers chains may consist of two parts, i.e. p(r) = p1(r) p2(r), where p1(r) and p2(r) are different for small r. The rate of contact formation decreases monotonically with the number of bonds N, and the rate approximately conforms to the scaling relation of k(N) ∝ N-α. Here the value of α increases with the contact radius a and it also depends on the percentage of H (hydrophobic) residues in the sequences of compact chains and the energy parameters of εHH, εHP and εPP . Some comparisons of theoretical predictions with experimental results are also made. This investigation may help us to understand the protein folding. 相似文献
57.
Eric S. Key 《Journal of Theoretical Probability》1992,5(2):375-389
Suppose thatX
1,X
2,... is a sequence of iid random variables taking values inZ
+. Consider the random sequenceA(X)(X
1,X
2,...). LetY
n
be the number of integers which appear exactly once in the firstn terms ofA(X). We investigate the limit behavior ofn
–(1–)
Y
n
for [0, 1]. 相似文献
58.
关于两两NQD列的若干极限性质 总被引:32,自引:0,他引:32
本文讨论了两两NQD列的Marcinkiewicz型弱大数律及Jamison型加权和的强稳定性,指出了两两NQD列与独立列的一个本质性区别,从而提出了解决两两NQD旬几乎处处收敛和完全收敛的一种方式。 相似文献
59.
60.
The partial order on monomials that corresponds to domination when evaluated at positive Newton sequences is fully understood. Here we take up the corresponding partial order on linear combinations of monomials. In part using analysis based upon the cone structure of the exponents in p-Newton sequences, an array of conditions is given for this new partial order. It appears that a characterization in general will be difficult. Within the case in which all coefficients are 1, the situation in which, for general sequence length, there are two monomials, each of length two and nonnegative integer exponents, the partial order is fully characterized. The characterization is combinatorial, in terms of indices in the monomials, and, already here there is much more than term-wise domination. 相似文献