共查询到20条相似文献,搜索用时 46 毫秒
1.
Li-feng XI~ 《中国科学A辑(英文版)》2007,50(11):1537-1551
This paper investigates the Lipschitz equivalence of generalized {1,3,5}-{1,4,5} self-similar sets D=(r_1D)∪(r_2D (1 r_1-r_2-r_3)/2)∪(r_3D 1 r_3) and E=(r_1E)∪(r_2E 1-r_2- r_3)∪(r_3E 1-r_3),and proves that D and E are Lipschitz equivalent if and only if there are positive integers m and n such that r_1~m=r_3~n. 相似文献
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Abstract In the present paper, some basic properties of MP filters of Ro algebra M are investigated. It is proved that(FMP(M),包含,′∧^-∨^-,{1},M)is a bounded distributive lattice by introducing the negation operator ′, the meet operator ∧^-, the join operator ∨^- and the implicati on operator → on the set FMP(M) of all MP filters of M. Moreover, some conditions under which (FMP(M),包含,′∨^-,→{1},M)is an Ro algebra are given. And the relationship between prime elements of FMP (M) and prime filters of M is studied. Finally, some equivalent characterizations of prime elements of .FMP (M) are obtained. 相似文献
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M. El Maghri 《Optimization Letters》2012,6(4):763-781
The paper is centered around a sum rule for the efficient (Pareto) ${\epsilon}$ -subdifferential of two convex vector mappings, having the property to be exact under a qualification condition. Such a formula has not been explored previously. Our formula which holds under the Attouch?CBrézis as well as Moreau?CRockafellar conditions, reveals strangely a primordial presence of the convex (Fenchel) ${\epsilon}$ -subdifferential. This appearance turns out to be rather favorable. This effectively permits to derive approximate efficiency conditions in terms of Pareto subgradient and vectorial normal cone, which completely characterizes an ${\epsilon}$ -efficient solution in constrained convex vector optimization in (partially) ordered spaces. Our sum rule also allows a fundamental deduction of relation between Pareto and Fenchel ${\epsilon}$ -subdifferentials, which, in reality, brings out a certain gap linking ${\epsilon}$ -efficiency with ${\epsilon}$ -optimality. Scalarization approaches in connection with ${\epsilon}$ -subdifferentials are first established by simple proofs. This principle has contributed for a large part, not only for discovering the sum formula, but also for establishing some punctual necessary and/or sufficient conditions for Pareto ${\epsilon}$ -subdifferentiability. 相似文献
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本文探讨模同态广义逆在环模理论中的应用.利用模同态的{1}-逆与{2}-逆,分别给出了一类环及一类重要模的特征刻画. 相似文献
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Joshua A. Cole 《Archive for Mathematical Logic》2008,46(7-8):649-664
Let be the lattice of degrees of non-empty subsets of 2
ω
under Medvedev reducibility. Binns and Simpson proved that FD(ω), the free distributive lattice on countably many generators, is lattice-embeddable below any non-zero element in . Cenzer and Hinman proved that is dense, by adapting the Sacks Preservation and Sacks Coding Strategies used in the proof of the density of the c.e. Turing
degrees. With a construction that is a modification of the one by Cenzer and Hinman, we improve on the result of Binns and
Simpson by showing that for any , we can lattice embed FD(ω) into strictly between and . We also note that, in contrast to the infinite injury in the proof of the Sacks Density Theorem, in our proof all injury
is finite, and that this is also true for the proof of Cenzer and Hinman, if a straightforward simplification is made.
Thanks to my adviser Peter Cholak for his guidance in my research. I also wish to thank the anonymous referee for helpful
comments and suggestions. My research was partially supported by NSF grants DMS-0245167 and RTG-0353748 and a Schmitt Fellowship
at the University of Notre Dame. 相似文献
7.
Matt Bainbridge Philipp Habegger Martin Möller 《Publications Mathématiques de L'IHéS》2016,123(1):1-67
We prove that the moduli space of compact genus three Riemann surfaces contains only finitely many algebraically primitive Teichmüller curves. For the stratum \(\Omega\mathcal{M}_{3}(4)\), consisting of holomorphic one-forms with a single zero, our approach to finiteness uses the Harder-Narasimhan filtration of the Hodge bundle over a Teichmüller curve to obtain new information on the locations of the zeros of eigenforms. By passing to the boundary of moduli space, this gives explicit constraints on the cusps of Teichmüller curves in terms of cross-ratios of six points on \(\mathbf{P}^{1}\).These constraints are akin to those that appear in Zilber and Pink’s conjectures on unlikely intersections in diophantine geometry. However, in our case one is lead naturally to the intersection of a surface with a family of codimension two algebraic subgroups of \(\mathbf{G}_{m}^{n}\times\mathbf{G}_{a}^{n}\) (rather than the more standard \(\mathbf{G}_{m}^{n}\)). The ambient algebraic group lies outside the scope of Zilber’s Conjecture but we are nonetheless able to prove a sufficiently strong height bound.For the generic stratum \(\Omega\mathcal{M}_{3}(1,1,1,1)\), we obtain global torsion order bounds through a computer search for subtori of a codimension-two subvariety of \(\mathbf{G}_{m}^{9}\). These torsion bounds together with new bounds for the moduli of horizontal cylinders in terms of torsion orders yields finiteness in this stratum. The intermediate strata are handled with a mix of these techniques. 相似文献
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In this paper we determine the method of multi-parameter interpolation and the scales of Lebesgue spaces $B_{\vec p} \left[ {0,2\pi } \right)$ and Besov spaces $B_{\vec p}^{\vec \alpha } \left[ {0,2\pi } \right)$ , which are generalizations of the Lorentz spacesL pq [0, 2π) and Besov spacesB pq α [0, 2π). We also prove imbedding theorems. 相似文献
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M. C. Crabb D. L. Gonçalves A. K. M. Libardi P. L. Q. Pergher 《manuscripta mathematica》2016,150(3-4):371-381
The purpose of this work is to classify, for given integers \({m,\, n\geq 1}\), the bordism class of a closed smooth \({m}\)-manifold \({X^m}\) with a free smooth involution \({\tau}\) with respect to the validity of the Borsuk–Ulam property that for every continuous map \({\phi : X^m \to \mathbb{R}^n}\) there exists a point \({x\in X^m}\) such that \({\phi (x)=\phi (\tau (x))}\). We will classify a given free \({\mathbb{Z}_2}\)-bordism class \({\alpha}\) according to the three possible cases that (a) all representatives \({(X^m, \tau)}\) of \({\alpha}\) satisfy the Borsuk–Ulam property; (b) there are representatives \({({X_{1}^{m}}, \tau_1)}\) and \({({X_{2}^{m}}, \tau_2)}\) of \({\alpha}\) such that \({({X_{1}^{m}}, \tau_1)}\) satisfies the Borsuk–Ulam property but \({({X_{2}^{m}}, \tau_2)}\) does not; (c) no representative \({(X^m, \tau)}\) of \({\alpha}\) satisfies the Borsuk–Ulam property. 相似文献
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令$k,\ell \geq 2$是正整数.令$A$是无限非负整数的集合.对$n\in \mathbb{N}$, 令$r_{1,k,\ldots,k^{\ell-1}}(A, n)$表示方程$n=a_0+ka_1+\cdots +k^{\ell-1}a_{\ell-1}$, $a_0, \ldots, a_{\ell-1}\in A$解的个数. 在本文中, 我们证明了对所有$n\geq 0$, $r_{1,k,\ldots,k^{\ell-1}}(A, n)=1$当且仅当$A$是$k^\ell$进制展开中数位小于$k$的所有非负整数的集合. 这个结果部分回答了S\''{a}rk\"{o}zy and S\''{o}s关于多维线性型表示的一个问题. 相似文献
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Margherita Lelli–Chiesa 《Geometriae Dedicata》2012,158(1):149-165
The Gieseker-Petri locus GP g is defined as the locus inside ${\mathcal{M}_g}$ consisting of curves which violate the Gieseker-Petri Theorem. It is known that GP g has always some divisorial components and it has been conjectured that it is of pure codimension 1 inside ${\mathcal{M}_g}$ . We prove that this holds true for genus up to 13. 相似文献
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设$h(G; x) =h(G)$和$[G]_h$分别表示图$G$的伴随多项式和伴随等价类. 文中给出了$[G]_h$的一个新应用. 利用$[G]_h$, 给出了图$H{\;}(H \cong G)$伴随唯一的充要条件, 其中$H=(\bigcup_{i{\in}A}P_i){\bigcup}(\bigcup_{j{\in}B}U_j)$, $A \subseteq A^{'}=\{1,2,3,5\} \bigcup \{2n|n \in N, n \geq 3\}$, $B \subseteq B^{'} 相似文献
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For any open orientable surface M and convex domain ${\Omega\subset \mathbb{C}^3,}$ there exist a Riemann surface N homeomorphic to M and a complete proper null curve F : N → Ω. This result follows from a general existence theorem with many applications. Among them, the followings: For any convex domain Ω in ${\mathbb{C}^2}$ there exist a Riemann surface N homeomorphic to M and a complete proper holomorphic immersion F : N → Ω. Furthermore, if ${D \subset \mathbb{R}^2}$ is a convex domain and Ω is the solid right cylinder ${\{x \in \mathbb{C}^2 \,|\, \mbox{Re}(x) \in D\},}$ then F can be chosen so that Re(F) : N → D is proper. There exist a Riemann surface N homeomorphic to M and a complete bounded holomorphic null immersion ${F:N \to {\rm SL}(2, \mathbb{C}).}$ There exists a complete bounded CMC-1 immersion ${X:M \to \mathbb{H}^3.}$ For any convex domain ${\Omega \subset \mathbb{R}^3}$ there exists a complete proper minimal immersion (X j ) j=1,2,3 : M → Ω with vanishing flux. Furthermore, if ${D \subset \mathbb{R}^2}$ is a convex domain and ${\Omega=\{(x_j)_{j=1,2,3} \in \mathbb{R}^3 \,|\, (x_1,x_2) \in D\},}$ then X can be chosen so that (X 1, X 2) : M → D is proper. Any of the above surfaces can be chosen with hyperbolic conformal structure. 相似文献
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We prove that the moduli space ${\mathcal{M}_g}$ of smooth curves of genus g is the union of g?1 affine open subsets for every g with 2 ?? g ?? 5, as predicted by an intriguing conjecture of Eduard Looijenga. 相似文献
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Consider the stationary Navier–Stokes equations in a bounded domain whose boundary consists of L + 1 smooth (n − 1)-dimensional closed hypersurfaces Γ0, Γ1, . . . , Γ L , where Γ1, . . . , Γ L lie inside of Γ0 and outside of one another. The Leray inequality of the given boundary data β on plays an important role for the existence of solutions. It is known that if the flux on Γ i (ν: the unit outer normal to Γ i ) is zero for each i = 0, 1, . . . , L, then the Leray inequality holds. We prove that if there exists a sphere S in Ω separating in such a way that Γ1, . . . , Γ k (1 ≦ k ≦ L) are contained inside of S and that the others Γ k+1, . . . , Γ L are outside of S, then the Leray inequality necessarily implies that γ 1 + · · · + γ k = 0. In particular, suppose that there are L spheres S 1, . . . , S L in Ω lying outside of one another such that Γ i lies inside of S i for all i = 1, . . . , L. Then the Leray inequality holds if and only if γ 0 = γ 1 = · · · = γ L = 0. 相似文献