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991.
We study power expansions of the characteristic function of a linear operator A in a p|q-dimensional superspace V. We show that traces of exterior powers of A satisfy universal recurrence relations of period q. ‘Underlying’ recurrence relations hold in the Grothendieck ring of representations of GL(V). They are expressed by vanishing of certain Hankel determinants of order q+1 in this ring, which generalizes the vanishing of sufficiently high exterior powers of an ordinary vector space. In particular,
this allows to express the Berezinian of an operator as a ratio of two polynomial invariants. We analyze the Cayley–Hamilton
identity in a superspace. Using the geometric meaning of the Berezinian we also give a simple formulation of the analog of
Cramer’s rule
Mathematics Subject Classification (2000): 15A15, 58A50, 81R99
To the memory of Felix Alexandrovich Berezin 相似文献
992.
N. Guillotin-Plantard 《Journal of Theoretical Probability》2001,14(1):241-260
In this paper, we study a
d
-random walk
on nearest neighbours with transition probabilities generated by a dynamical system
. We prove, at first, that under some hypotheses,
verifies a local limit theorem. Then, we study these walks in a random scenery
, a sequence of independent, identically distributed and centred random variables and show that for certain dynamic random walks,
satisfies a strong law of large numbers. 相似文献
993.
Clustering and long-range correlations in the nucleotide sequences of different categories of organisms are discussed. Clustering, mostly observed in higher eucaryotes, can be found at different length scales in DNA and Central Limit Theorems are used as links between these length scales. Several dynamical, statistical, mean-field models are proposed based on biologically motivated dynamical mechanisms and they successfully reproduce both the short range behavior observed in coding DNA and the long range, out-of-equilibrium features of non-coding DNA. Such dynamical mechanisms include aggregation of oligonucleotides, influx and DNA length reduction schemes, transpositions, and fusions of large DNA macromolecules. Fractality can be inferred from the short and long range correlations observed in the sequence structure of higher eucaryotes, where the non-coding part is relatively extended. In these organisms the DNA coding/non-coding alternation has the characteristics of finite size, fractal, random sets. 相似文献
994.
In the asymptotic analysis of the minimization problem for a nonsmooth convex function on a closed convex set X in n, one can consider the corresponding problem of minimizing a smooth convex function F on n, where F denotes the Moreau–Yosida regularization of f. We study the interrelationship between the minimizing/stationary sequence for f and that for F. An algorithm is given to generate iteratively a possibly unbounded sequence, which is shown to be a minimizing sequence of f under certain regularity and uniform continuity assumptions. 相似文献
995.
A. Papageorgiou. 《Mathematics of Computation》2001,70(233):297-306
We consider the approximation of -dimensional weighted integrals of certain isotropic functions. We are mainly interested in cases where is large. We show that the convergence rate of quasi-Monte Carlo for the approximation of these integrals is . Since this is a worst case result, compared to the expected convergence rate of Monte Carlo, it shows the superiority of quasi-Monte Carlo for this type of integral. This is much faster than the worst case convergence, , of quasi-Monte Carlo.
996.
997.
The Welch lower bound on the total-squared-correlation (TSC) of binary signature sets is loose for binary signature sets whose length L is not a multiple of 4. Recently Karystinos and Pados [6,7] developed new bounds that are better than the Welch bound in those cases, and showed how to achieve the bounds with modified Hadamard matrices except in a couple of cases. In this paper, we study the open cases. 相似文献
998.
Enkelejd Hashorva Jürg Hüsler 《Annals of the Institute of Statistical Mathematics》2003,55(3):507-522
Let {X
n, n
≥1} be a sequence of standard Gaussian random vectors in ℝ
d
,d ≥ 2. In this paper we derive lower and upper bounds for the tail probabilityP{X
n
>t
n
} witht
n ∈ ℝ
d
some threshold. We improve for instance bounds on Mills ratio obtained by Savage (1962,J. Res. Nat. Bur. Standards Sect. B,66, 93–96). Furthermore, we prove exact asymptotics under fairly general conditions on bothX
n
andt
n
, as ‖t
n
‖→∞ where the correlation matrix Σ
n
ofX
n
may also depend onn. 相似文献
999.
Eiichi Isogai 《Annals of the Institute of Statistical Mathematics》1990,42(4):699-708
A somewhat more general class of nonparametric estimators for estimating an unknown regression functiong from noisy data is proposed. The regressor is assumed to be defined on the closed interval [0, 1]. This class of estimators
is shown to be pointwisely consistent in the mean square sense and with probability one. Further, it turns out that these
estimators can be applied to a wide class of noises. 相似文献
1000.
Chain sequences are positive sequences {cn} of the form cn=gn(1−gn−1) for a nonnegative sequence {gn}. They are very useful in estimating the norms of Jacobi matrices and for localizing the interval of orthogonality for orthogonal polynomials. We give optimal estimates for the chain sequences which are more precise than the ones obtained in the paper (Constructive Approx. 6 (1990) 363) and in our earlier paper (J. Approx. Theory 118 (2002) 94). 相似文献