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Yuya Mizuno 《代数通讯》2013,41(4):1654-1667
Inspired by τ-tilting theory [3], we introduce the notion of ν-stable support τ-tilting modules. For any finite dimensional selfinjective algebra Λ, we give bijections between two-term tilting complexes in K b (proj Λ), ν-stable support τ-tilting Λ-modules, and ν-stable functorially finite torsion classes in modΛ. Moreover, these objects correspond bijectively to selfinjective cluster tilting objects in 𝒞 if Λ is a 2-CY tilted algebra associated with a Hom-finite 2-CY triangulated category 𝒞. We also study some properties of support τ-tilting modules over 2-CY tilted algebras, and we give a necessary condition such that algebras are 2-CY tilted in terms of support τ-tilting modules. 相似文献
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Let M R be a right R-module over a ring R with S = End(M R ). We study the coherence of the left S-module S M relative to a hereditary torsion theory for the category of right R-modules. Various results are developed, many extending known results. 相似文献
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《Optimization》2012,61(7):823-854
In this article, a new mechanism to spread the solutions generated by a multi-objective evolutionary algorithm is proposed. This approach is based on the use of stripes that are applied in objective function space and is independent of the search engine adopted. Additionally, it overcomes some of the drawbacks of other previous proposals such as the ?-dominance method. In order to validate the proposed approach, it is coupled to a multi-objective particle swarm optimizer and its performance is assessed with respect to that of state-of-the-art algorithms, using standard test problems and performance measures taken from the specialized literature. The results indicate that the proposed approach is a viable diversity maintenance mechanism that can be incorporated to any multi-objective metaheuristic used for multi-objective optimization. 相似文献
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Stavros Iliadis 《Topology and its Applications》2010,157(17):2646-2658
In this paper by a spectrum of mappings we mean a morphism of spectra of spaces. However, using the notion of a mapping of mappings, we give the definition of a spectrum of mappings similar to that of a spectrum of spaces. In this case, the formulations of the given results are also similar to the formulations of the corresponding results concerning the spectra of spaces.For the spectra of mappings we define the notion of a τ-spectrum of mappings factorizing in a special sense and prove a version of the Spectral Theorem for such spectra. Furthermore, to a given indexed collection F of mapping we associate a τ-spectrum factorizing in the above special sense whose mappings are Containing Mappings for F constructed in Iliadis (2005) [4]. These associated τ-spectra and the corresponding version of the Spectral Theorem imply that for a given indexed collection F of mappings any so-called “natural” τ-spectrum for F factorizing in the special sense contains a cofinal and τ-closed subspectrum whose mappings are Containing Mapping for F. Thus, Containing Mappigs for F appear here without any concrete construction. The associated τ-spectra are used also in order to define and characterize the so-called second-type saturated classes of mappings (which are “saturated” by universal elements). 相似文献
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Exact solutions for KdV system equations hierarchy are obtained by using the inverse scattering transform. Exact solutions of isospectral KdV hierarchy, nonisospectral KdV hierarchies and τ-equations related to the KdV spectral problem are obtained by reduction. The interaction of two solitons is investigated. 相似文献
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We consider the symmetric schemes in Boundary Value Methods (BVMs) applied to delay differential equations y′(t)=ay(t)+by(t-τ) with real coefficients a and b. If the numerical solution tends to zero whenever the exact solution does, the symmetric scheme with (k1+m,k2)-boundary conditions is called τk1,k2(0)-stable. Three families of symmetric schemes, namely the Extended Trapezoidal Rules of first (ETRs) and second (ETR2s) kind, and the Top Order Methods (TOMs), are considered in this paper.By using the boundary locus technology, the delay-dependent stability region of the symmetric schemes are analyzed and their boundaries are found. Then by using a necessary and sufficient condition, the considered symmetric schemes are proved to be τν,ν-1(0)-stable. 相似文献
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Yuqin Yao Juhui Zhang Runliang Lin Xiaojun Liu Yehui Huang 《Journal of Nonlinear Mathematical Physics》2018,25(2):309-323
In this paper, we discuss how to construct the bilinear identities for the wave functions of the (γn, σk)-KP hierarchy and its Hirota’s bilinear forms. First, based on the corresponding squared eigenfunction symmetry of the KP hierarchy, we prove that the wave functions of the (γn, σk)-KP hierarchy are equal to the bilinear identities given in Sec.3 by introducing N auxiliary parameters zi, i = 1, 2,?…?, N. Next, we derived the bilinear equations for the tau-function of the (γn, σk)-KP hierarchy. Then, we obtain the bilinear equations for the taufunction of the mixed type of KP equation with self-consistent sources (KPESCS), which includes both the first and the second type of KPESCS as special cases by setting n = 2 and k = 3. Finally, using the relation between the Hirota bilinear derivatives and the usual partial derivatives, we show the procedure of translating the Hirota’s bilinear equations into the mixed type of KPESCS. 相似文献