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921.
Recently, Barreira and Schmeling (2000) [1] and Chen and Xiong (1999) [2] have shown, that for self-similar measures satisfying the SSC the set of divergence points typically has the same Hausdorff dimension as the support K. It is natural to ask whether we obtain a similar result for self-similar measures satisfying the OSC. However, with only the OSC satisfied, we cannot do most of the work on a symbolic space and then transfer the results to the subsets of Rd, which makes things more difficult. In this paper, by the box-counting principle we show that the set of divergence points has still the same Hausdorff dimension as the support K for self-similar measures satisfying the OSC.  相似文献   
922.
Let M1,…,Mn be right modules over a ring R. Suppose that the endomorphism ring of each module Mi has at most two maximal right ideals. Is it true that every direct summand of M1⊕?⊕Mn is a direct sum of modules whose endomorphism rings also have at most two maximal right ideals? We show that the answer is negative in general, but affirmative under further hypotheses. The endomorphism ring of uniserial modules, that is, the modules whose lattice of submodules is linearly ordered under inclusion, always has at most two maximal right ideals, and Pavel P?íhoda showed in 2004 that the answer to our question is affirmative for direct sums of finitely many uniserial modules.  相似文献   
923.
We define model structures on exact categories, which we call exact model structures. We look at the relationship between these model structures and cotorsion pairs on the exact category. In particular, when the underlying category is weakly idempotent complete, we get Hovey’s one-to-one correspondence between model structures and complete cotorsion pairs. We classify the right and the left homotopy relation in terms of the cotorsion pairs and look at examples of exact model structures. In particular, we see that given any hereditary abelian model category, the full subcategories of cofibrant, fibrant and cofibrant-fibrant subobjects each has natural exact model structures equivalent to the original model structure. These model structures each has interesting characteristics. For example, the cofibrant-fibrant subobjects form a Frobenius category, whose stable category is the same as the homotopy category of its model structure.  相似文献   
924.
Let V be a linear subspace of Mn,p(K) with codimension lesser than n, where K is an arbitrary field and n?p. In a recent work of the author, it was proven that V is always spanned by its rank p matrices unless n=p=2 and K?F2. Here, we give a sufficient condition on codim V for V to be spanned by its rank r matrices for a given r∈?1,p-1?. This involves a generalization of the Gerstenhaber theorem on linear subspaces of nilpotent matrices.  相似文献   
925.
In this note, we show that, if the Druzkowski mappings F(X)=X+(AX)∗3, i.e. F(X)=(x1+(a11x1+?+a1nxn)3,…,xn+(an1x1+?+annxn)3), satisfies TrJ((AX)∗3)=0, then where δ is the number of diagonal elements of A which are equal to zero. Furthermore, we show the Jacobian Conjecture is true for the Druzkowski mappings in dimension ?9 in the case .  相似文献   
926.
The objects of the Dranishnikov asymptotic category are proper metric spaces and the morphisms are asymptotically Lipschitz maps. In this paper we provide an example of an asymptotically zero-dimensional space (in the sense of Gromov) whose space of compact convex subsets of probability measures is not an absolute extensor in the asymptotic category in the sense of Dranishnikov.  相似文献   
927.
We study the classification of ultrametric spaces based on their small scale geometry (uniform homeomorphism), large scale geometry (coarse equivalence) and both (bi-uniform equivalences). Using a combinatoric approach we consider every ultrametric space as the end space of a chain and prove that all these equivalences can be characterized by the existence of a common zig-zag chain.  相似文献   
928.
This paper is the first part of a two-part investigation. It introduces full and balanced biframes which capture useful properties of the reals viewed as a biframe (or bitopological space). The subsequent paper will apply these concepts to the study of completions of quasi-nearness biframes.We start with the smallest dense quotient for biframes. Next we discuss the reals as a biframe and introduce the key ideas of balanced, full and stable biframes. The crucial tool here is the frame pseudocomplement. We include a discussion of the relations between the newly introduced ideas and regularity. Order topology biframes are all regular, normal and balanced but not necessarily full. We consider the plane and various examples related to zero-dimensionality. We provide methods of transferring fullness and balancedness from domain to codomain and conversely under various kinds of maps.Of particular importance to our later study of completions is the idea of a biframe map whose right adjoint preserves the first and second parts of the biframe. We give a result providing sufficient conditions for a map to have a part-preserving right adjoint. We present an example of a dense onto map (which is in fact a compactification) between normal, regular biframes whose right adjoint is not part-preserving. The paper concludes with internal properties of full and balanced biframes showing the particularly close connection between the first and second parts and ends with a final visit to the biframe of reals.  相似文献   
929.
We characterize the Lefschetz periodic point free self-continuous maps on the following connected compact manifolds: CPn the n-dimensional complex projective space, HPn the n-dimensional quaternion projective space, Sn the n-dimensional sphere and Sp×Sq the product space of the p-dimensional with the q-dimensional spheres.  相似文献   
930.
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