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In Olsen and Winter (J Lond Math Soc 67(2):103–122, 2003) and Baek et?al. (Advan Math 214:267–287, 2007) the authors have introduced the notion of “normal” and “non-normal” points of a self-similar set as a main tool for studying the Hausdorff and the packing dimensions of a set of divergence points of self-similar measures. In this paper we will extend the results about the Hausdorff and the packing dimensions of “non-normal” points of a self-similar set in a point of view of Bisbas (Bulletin des Sciences Mathématiques 129(1):25–37, 2005). Namely, we will prove that both the Hausdorff and packing dimensions remain the same if we consider subsets determined by the normality to some bases. This will be proved using the techniques from Bisbas (Bulletin des Sciences Mathématiques 129(1):25–37, 2005) and the construction of suitable measures. Simultaneously this will also give simpler proofs of some of the results from Olsen and Winter (J Lond Math Soc 67(2):103–122, 2003) and Baek et?al. (Advan Math 214:267–287, 2007).  相似文献   

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For the eigenvalues λi of an n × n matrix A the inequality
ii|2(6A64 ? 126D62)12
is proved, where D ? AA1 ? A1A and 6 ● 6; denotes the euclidean norm. Conditions for equality are stated.  相似文献   

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For an element w in the Weyl algebra generated by D and U with relation DU=UD+1, the normally ordered form is w=∑ci,jUiDj. We demonstrate that the normal order coefficients ci,j of a word w are rook numbers on a Ferrers board. We use this interpretation to give a new proof of the rook factorization theorem, which we use to provide an explicit formula for the coefficients ci,j. We calculate the Weyl binomial coefficients: normal order coefficients of the element (D+U)n in the Weyl algebra. We extend these results to the q-analogue of the Weyl algebra. We discuss further generalizations using i-rook numbers.  相似文献   

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The question if there exist nonnormal bent functions was an open question for several years. A Boolean function in n variables is called normal if there exists an affine subspace of dimension n/2 on which the function is constant. In this paper we give the first nonnormal bent function and even an example for a nonweakly normal bent function. These examples belong to a class of bent functions found in [J.F. Dillon, H. Dobbertin, New cyclic difference sets with Singer parameters, in: Finite Fields and Applications, to appear], namely the Kasami functions. We furthermore give a construction which extends these examples to higher dimensions. Additionally, we present a very efficient algorithm that was used to verify the nonnormality of these functions.  相似文献   

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Existence of a topological joining between two subshiftsX andX′ defines a relation between points of the two. SupposexX is generic for an invariant measureμ onX; when is a relatedx′X′ also generic for some corresponding measureμ′ onX′? We prove this property holds in several situations for bounded-to-one joinings: whenμ andμ′ are the measures with maximal entropy on intrinsically ergodicX andX′, and also whenμ has a unique preimage on the joining, a property for which several sufficient conditions are given. In the latter case it is also possible to prove that the nearer a point is to genericity with respect toμ, the nearer to genericity with respect toμ′ a related point is. Bounded-to-one joinings may be defined by nonambiguous rational transductions. This provides several applications, most of them in Number Theory. It is proven that transducers performing multiplication by integers have the suitable properties: this implies multiplication by a rational preserves near normality; so does addition of a rational. An application to Markov measures, and sufficient conditions for a transducer to map normality to the basep to normality to the basep′, p′p, are given.  相似文献   

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I would like to express my thanks to Professor Iekata Shiokawa for his valuable advices concerning the paper.  相似文献   

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A sequence of independent, identically distributed random vectors X1, X2, X3,… is said to belong to the domain of attraction of a random vector Y is there exist linear operators An and constant vectors bn such that An(X1,…, Xn)+bn converges in distribution to Y. We present a simple, necessary, and sufficient condition for the existence of such An, Bn in the case where Y has no normal component.  相似文献   

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By testing quotient rings, we give another viewpoint concerning the relationship between PI and Goldie properties, etc., and f-radical extensions of rings. The main result proved here is as follows: Let R be a prime algebra without nonzero nil right ideals. Suppose that R is f-radical over a subalgebra A, where f(X 1,…, X t ) is a multilinear polynomial, not an identity for p × p matrices in case char R = p > 0. Suppose that f is not power-central valued in R. Then the maximal ring of right (left) quotients of A coincides with that of R. Moreover, R is right Goldie if and only if A is.  相似文献   

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The set L of essentially non-normal numbers of the unit interval (i.e., the set of real numbers having no asymptotic frequencies of all digits in their nonterminating s-adic expansion) is studied in details. It is proven that the set L is generic in the topological sense (it is of the second Baire category) as well as in the sense of fractal geometry (L is a superfractal set, i.e., the Hausdorff-Besicovitch dimension of the set L is equal 1). These results are substantial generalizations of the previous results of the two latter authors [M. Pratsiovytyi, G. Torbin, Ukrainian Math. J. 47 (7) (1995) 971-975].The Q-representation of real numbers (which is a generalization of the s-adic expansion) is also studied. This representation is determined by the stochastic matrix Q. We prove the existence of such a Q-representation that almost all (in the sense of Lebesgue measure) real numbers have no asymptotic frequency of all digits. In the case where the matrix Q has additional asymptotic properties, the Hausdorff-Besicovitch dimension of the set of numbers with prescribed asymptotic properties of their digits is determined (this is a generalization of the Eggleston-Besicovitch theorem). The connections between the notions of “normality of numbers” respectively of “asymptotic frequencies” of their digits is also studied.  相似文献   

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In this paper, we shall discuss the conditions for a right SC right CS ring to be a QF ring. In particular, we prove that if R is a right SI right CS ring satisfying the reflexive orthogonal condition (*) and if every CS right R-module is -CS, then R is a QF ring.AMS Subject Classification (1991): 16L30 16L60  相似文献   

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This paper deals with the bias reduction of Akaike information criterion (AIC) for selecting variables in multivariate normal linear regression models when the true distribution of observation is an unknown nonnormal distribution. We propose a corrected version of AIC which is partially constructed by the jackknife method and is adjusted to the exact unbiased estimator of the risk when the candidate model includes the true model. It is pointed out that the influence of nonnormality in the bias of our criterion is smaller than the ones in AIC and TIC. We verify that our criterion is better than the AIC, TIC and EIC by conducting numerical experiments.  相似文献   

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In this paper we estimate the difference between the spectrum of A (which is supposed to be known completely) and A+E, in terms of the norms of E and AA1 ? A1A. Also we find a special upper triangular form K = Q-1AQ which separates the distinct eigenvalues of A, and we estimate the 6Q-1626Q62 from the above.  相似文献   

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We say that is a ring with duality for simple modules, or simply a DSM-ring, if, for every simple right (left) -module U, the dual module U* is a simple left (right) -module. We prove that a semiperfect ring is a DSM-ring if and only if it admits a Nakayama permutation. We introduce the notion of a monomial ideal of a semiperfect ring and study the structure of hereditary semiperfect rings with monomial ideals. We consider perfect rings with monomial socles.  相似文献   

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