共查询到20条相似文献,搜索用时 15 毫秒
1.
Philip R. Heath 《Topology and its Applications》2008,156(2):186-204
In this paper, we present and make computations of two equivariant Nielsen type numbers NG(f(H),k(H)) and NG(f(H),k(H)). The second one is new, while the first one extends and clarifies one given earlier by the author and Jianhan Guo. Both numbers were defined here in terms of Nielsen theory of M-ads introduced in the prequel to this work. The theory of M-ads is also used to give both upper and lower bounds on our numbers, and to make specific computations. Our numbers moreover, fit together in the same way that the two Nielsen type periodic point numbers NPn(f) and NΦn(f) fit together. In particular, we show that NG(f(H),k(H)) is greater than or equal to a sum of numbers of the form NG(f(K),k(K)), and give conditions for equality and Möbius inversion. The periodic point theory results are then seen to follow from what are actually generalizations of them.We work with both fixed point, and coincidence point classes, in the context of a category with essentiality which we introduced in the prequel on M-ads. It is intended that this paper be read in tandem with said prequel. 相似文献
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Seung Won Kim 《Journal of Pure and Applied Algebra》2007,208(2):467-479
In this paper we study the Nielsen number of a self-map f:M→M of a compact connected surface with boundary. Let G=π1(M) be the fundamental group of M which is a finitely generated free group. We introduce a new algebraic condition called “bounded solution length” on the induced endomorphism φ:G→G of f and show that many maps which have no remnant satisfy this condition. For a map f that has bounded solution length, we describe an algorithm for computing the Nielsen number N(f). 相似文献
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Consider (L,*,1) be a commutative, strictly two-sided quantale with the underlying lattice L being meet-continuous. Two adjunctions, one is between limit spaces and stratified L-limit spaces and the other is between stratified L-limit spaces and stratified L-topological spaces, are established. The first adjunction can be viewed as an extension of Lowen's adjunction between the category of topological spaces and stratified [0,1]-topological spaces. The second is an extension of an adjunction between limit spaces and (stratified) L-topological spaces established in U. Höhle and T. Kubiak (Höhle-Kubiak, Semigroup Forum (2007)). 相似文献
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For a Heyting algebra V which, as a category, is monoidal closed, we obtain characterizations of exponentiable objects and morphisms in the category of V-categories and apply them to some well-known examples. In the case these characterizations of exponentiable morphisms and objects in the categories (P)Met of (pre)metric spaces and non-expansive maps show in particular that exponentiable metric spaces are exactly the almost convex metric spaces, while exponentiable complete metric spaces are the complete totally convex ones. 相似文献
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A particular version of the singular value decomposition is exploited for an extensive analysis of two orthogonal projectors, namely FF† and F†F, determined by a complex square matrix F and its Moore-Penrose inverse F†. Various functions of the projectors are considered from the point of view of their nonsingularity, idempotency, nilpotency, or their relation to the known classes of matrices, such as EP, bi-EP, GP, DR, or SR. This part of the paper was inspired by Benítez and Rako?evi? [J. Benítez, V. Rako?evi?, Matrices A such that AA† − A†A are nonsingular, Appl. Math. Comput. 217 (2010) 3493-3503]. Further characteristics of FF† and F†F, with a particular attention paid on the results dealing with column and null spaces of the functions and their eigenvalues, are derived as well. Besides establishing selected exemplary results dealing with FF† and F†F, the paper develops a general approach whose applicability extends far beyond the characteristics provided therein. 相似文献
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Evelyn L. Hart 《Topology and its Applications》2006,153(9):1399-1420
Let denote a periodic self map of minimal period m on the orientable surface of genus g with g>1. We study the calculation of the Nielsen periodic numbers NPn(f) and NΦn(f). Unlike the general situation of arbitrary maps on such surfaces, strong geometric results of Jiang and Guo allow for straightforward calculations when n≠m. However, determining NPm(f) involves some surprises. Because fm=idFg, fm has one Nielsen class Em. This class is essential because L(idFg)=χ(Fg)=2−2g≠0. If there exists k<m with L(fk)≠0 then Em reduces to the essential fixed points of fk. There are maps g (we call them minLef maps) for which L(gk)=0 for all k<m. We show that the period of any minLef map must always divide 2g−2. We prove that for such maps Em reduces algebraically iff it reduces geometrically. This result eliminates one of the most difficult problems in calculating the Nielsen periodic point numbers and gives a complete trichotomy (non-minLef, reducible minLef, and irreducible minLef) for periodic maps on Fg.We prove that reducible minLef maps must have even period. For each of the three types of periodic maps we exhibit an example f and calculate both NPn(f) and NΦn(f) for all n. The example of an irreducible minLef map is on F4 and is of maximal period 6. The example of a non-minLef map is on F2 and has maximal period 12 on F2. It is defined geometrically by Wang, and we provide the induced homomorphism and analyze it. The example of an irreducible minLef map is a map of period 6 on F4 defined by Yang. No algebraic analysis is necessary to prove that this last example is an irreducible minLef map. We explore the algebra involved because it is intriguing in its own right. The examples of reducible minLef maps are simple inversions, which can be applied to any Fg. Using these examples we disprove the conjecture from the conclusion of our previous paper. 相似文献
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Matthew Fayers 《Advances in Mathematics》2005,193(2):438-452
Let F be a field, n a non-negative integer, λ a partition of n and Sλ the corresponding Specht module for the Iwahori-Hecke algebra HF,q(Sn). James and Mathas conjecture a necessary and sufficient condition on λ for Sλ to be irreducible. We prove the sufficiency of this condition in the case where F has infinite characteristic and also in the case where q=1. 相似文献
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Fida Moh'D 《Topology and its Applications》2010,157(2):417-438
Let be maps between closed smooth manifolds of the same dimension, and let and be finite regular covering maps. If the manifolds are nonorientable, using semi-index, we introduce two new Nielsen numbers. The first one is the Linear Nielsen number NL(f,g), which is a linear combination of the Nielsen numbers of the lifts of f and g. The second one is the Nonlinear Nielsen number NED(f,g). It is the number of certain essential classes whose inverse images by p are inessential Nielsen classes. In fact, N(f,g)=NL(f,g)+NED(f,g), where by abuse of notation, N(f,g) denotes the coincidence Nielsen number defined using semi-index. 相似文献
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In ZF, i.e., Zermelo-Fraenkel set theory without the axiom of choice, the category Top of topological spaces and continuous maps is well-behaved. In particular, Top has sums (=coproducts) and products. However, it may happen that for families (Xi)i∈I and (Yi)i∈I with the property that each Xi is homeomorphic to the corresponding Yi neither their sums ⊕i∈IXi and ⊕i∈IYi nor their products ∏i∈IXi and ∏i∈IYi are homeomorphic. It will be shown that the axiom of choice is not only sufficient but also necessary to rectify this defect. 相似文献
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This paper develops a gradient based and a least squares based iterative algorithms for solving matrix equation AXB + CXTD = F. The basic idea is to decompose the matrix equation (system) under consideration into two subsystems by applying the hierarchical identification principle and to derive the iterative algorithms by extending the iterative methods for solving Ax = b and AXB = F. The analysis shows that when the matrix equation has a unique solution (under the sense of least squares), the iterative solution converges to the exact solution for any initial values. A numerical example verifies the proposed theorems. 相似文献
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Jorge Almeida 《Journal of Pure and Applied Algebra》2008,212(3):486-499
We present an algorithm to compute the pointlike subsets of a finite semigroup with respect to the pseudovariety of all finite R-trivial semigroups. The algorithm is inspired by Henckell’s algorithm for computing the pointlike subsets with respect to the pseudovariety of all finite aperiodic semigroups. We also give an algorithm to compute -pointlike sets, where denotes the pseudovariety of all finite J-trivial semigroups. We finally show that, in contrast with the situation for , the natural adaptation of Henckell’s algorithm to computes pointlike sets, but not all of them. 相似文献
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Horst Herrlich 《Topology and its Applications》2011,158(17):2279-2286
Within the framework of Zermelo-Fraenkel set theory ZF, we investigate the set-theoretical strength of the following statements:
- (1)
- For every family(Ai)i∈Iof sets there exists a family(Ti)i∈Isuch that for everyi∈I(Ai,Ti)is a compactT2space.
- (2)
- For every family(Ai)i∈Iof sets there exists a family(Ti)i∈Isuch that for everyi∈I(Ai,Ti)is a compact, scattered, T2space.
- (3)
- For every set X, every compactR1topology (itsT0-reflection isT2) on X can be enlarged to a compactT2topology.
- (a)
- (1) implies every infinite set can be split into two infinite sets.
- (b)
- (2) iff AC.
- (c)
- (3) and “there exists a free ultrafilter” iff AC.
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Jan Andres 《Topology and its Applications》2006,153(12):1961-1974
In this note, we generalize the various existing local and relative Nielsen type numbers to the setting of maps of noncompact ANR-pairs. Then we introduce general classes of admissible maps for which these numbers are well-defined. An application of these relative Nielsen numbers to differential equations is also given. 相似文献
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In this paper, we introduce a new algebraic concept, which we call squarefree P-modules. This concept is inspired from Karu's proof of the non-negativity of the cd-indices of Gorenstein* posets, and supplies a way to study cd-indices from the viewpoint of commutative algebra. Indeed, by using the theory of squarefree P-modules, we give several new algebraic and combinatorial results on CW-posets. First, we define an analogue of the cd-index for any CW-poset and prove its non-negativity when a CW-poset is Cohen–Macaulay. This result proves that the h-vector of the barycentric subdivision of a Cohen–Macaulay regular CW-complex is unimodal. Second, we prove that the Stanley–Reisner ring of the barycentric subdivision of an odd dimensional Cohen–Macaulay polyhedral complex has the weak Lefschetz property. Third, we obtain sharp upper bounds of the cd-indices of Gorenstein* posets for a fixed rank generating function. 相似文献
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Sheldon Joyner 《Journal of Number Theory》2010,130(2):254-288