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1.
In this article, we investigate the convergence rate of the CG-DESCENT method proposed by Hager and Zhang [1 W. W. Hager and H. Zhang ( 2005 ). A new conjugate gradient method with guaranteed descent and an effcient line search . SIAM Journal of Optimization 16 : 170192 .[Crossref], [Web of Science ®] [Google Scholar]]. Under reasonable conditions, we show that the CG-DESCENT method with the Wolfe line search will be n-step superlinear and even quadratic convergence if some restart technique is used. Some numerical results are also reported to verify the theoretical results.  相似文献   

2.
We prove that there are no networks homeomorphic to the Greek “Theta” letter (a double cell) embedded in the plane with two triple junctions with angles of 120 degrees, such that under the motion by curvature they are self–similarly shrinking.

This fact completes the classification of the self–similarly shrinking networks in the plane with at most two triple junctions, see [5 Chen, X., Guo, J.-S. (2007). Self-similar solutions of a 2-D multiple-phase curvature flow. Phys. D. 229(1):2234.[Crossref], [Web of Science ®] [Google Scholar], 10 Hättenschweiler, J. (2007). Mean curvature flow of networks with triple junctions in the plane. Master’s thesis. ETH Zürich. [Google Scholar], 25 Schnürer, O. C., Azouani, A., Georgi, M., Hell, J., Nihar, J., Koeller, A., Marxen, T., Ritthaler, S., Sáez, M., Schulze, F., Smith, B. (2011). Evolution of convex lens–shaped networks under the curve shortening flow. Trans. Am. Math. Soc. 363(5):22652294.[Crossref], [Web of Science ®] [Google Scholar], 2 Baldi, P., Haus, E., Mantegazza, C. (2016). Networks self-similarly moving by curvature with two triple junctions. Networks self-similarly moving by curvature with two triple junctions. 28(2017):323338. [Google Scholar]].  相似文献   

3.
In this article, we provide a semilocal analysis for the Steffensen-type method (STTM) for solving nonlinear equations in a Banach space setting using recurrence relations. Numerical examples to validate our main results are also provided in this study to show that STTM is faster than other methods ([7 I. K. Argyros , J. Ezquerro , J. M. Gutiérrez , M. Hernández , and S. Hilout ( 2011 ). On the semilocal convergence of efficient Chebyshev-Secant-type methods . J. Comput. Appl. Math. 235 : 31953206 .[Crossref], [Web of Science ®] [Google Scholar], 13 J. A. Ezquerro and M. A. Hernández ( 2009 ). An optimization of Chebyshev's method . J. Complexity 25 : 343361 .[Crossref], [Web of Science ®] [Google Scholar]]) using similar convergence conditions.  相似文献   

4.
M. Castelli  G. Pinto 《代数通讯》2018,46(4):1622-1629
A new family of non-degenerate involutive set-theoretic solutions of the Yang–Baxter equation is constructed. Two subfamilies, consisting of irretractable square-free solutions, are new counterexamples to Gateva-Ivanova’s Strong Conjecture [7 Gateva-Ivanova, T. (2004). A combinatorial approach to the set-theoretic solutions of the Yang-Baxter equation. J. Math. Phys. 45(10):38283858.[Crossref], [Web of Science ®] [Google Scholar]]. They are in addition to those obtained by Vendramin [15 Vendramin, L. (2016). Extensions of set-theoretic solutions of the Yang-Baxter equation and a conjecture of Gateva-Ivanova. J. Pure Appl. Algebra 220:20642076.[Crossref], [Web of Science ®] [Google Scholar]] and [1 Bachiller, D., Cedó, F., Jespers, E., Okniński, J. (2017). A family of irretractable square-free solutions of the Yang-Baxter equation. Forum Math. (to appear). [Google Scholar]].  相似文献   

5.
S. Eswara Rao  V. Futorny 《代数通讯》2013,41(12):5045-5057
Local Weyl modules were originally defined for affine Lie algebras by Chari and Pressley in [5 Chari, V., Pressley, A. (2001). Weyl modules for classical and quantum affine algebras. Represent. Theory 5:191223 (electronic).[Crossref] [Google Scholar]]. In this paper we extend the notion of local Weyl modules for a Lie algebra 𝔤 ?A, where 𝔤 is any Kac–Moody algebra and A is any finitely generated commutative associative algebra with unit over ?, and prove a tensor product decomposition theorem which generalizes result in [2 Chari, V., Fourier, G., Khandai, T. (2010). A categorical approach to Weyl modules. Transform. Groups 15(3):517549.[Crossref], [Web of Science ®] [Google Scholar], 5 Chari, V., Pressley, A. (2001). Weyl modules for classical and quantum affine algebras. Represent. Theory 5:191223 (electronic).[Crossref] [Google Scholar]].  相似文献   

6.
We consider three infinite families of cyclic presentations of groups, depending on a finite set of integers and having the same polynomial. Then we prove that the corresponding groups with the same parameters are isomorphic, and that the groups are almost all infinite. Finally, we completely compute the maximal Abelian quotients of such groups, and show that their HNN extensions are high-dimensional knot groups. Our results contain as particular cases the main theorems obtained in two nice articles: Johnson et al. (1999 Johnson , D. L. , Kim , A. C. , O'Brien , E. A. ( 1999 ). Certain cyclically presented groups are isomorphic . Comm. Algebra 27 ( 7 ): 35313536 . [CSA] [Taylor &; Francis Online], [Web of Science ®] [Google Scholar]) and Havas et al. (2001 Havas , G. , Holt , D. F. , Newman , M. F. ( 2001 ). Certain cyclically presented groups are infinite . Comm. Algebra 29 ( 11 ): 51755178 . [CSA] [CROSSREF] [Taylor &; Francis Online], [Web of Science ®] [Google Scholar]).  相似文献   

7.
In this article, we propose a nonmonotone linesearch sequential quadratic programming method for general constrained optimization problems without a penalty function or a filter. The algorithm proposed here is a development of the algorithm in Xue et al. [17 W. Xue , C. Shen , and D. Pu ( 2009 ). A penalty-function-free line search SQP method for nonlinear programming . Journal of Computational and Applied Mathematics 228 ( 1 ): 313325 .[Crossref], [Web of Science ®] [Google Scholar]]. Compared with the former, the novelty of the method we propose is that the new algorithm will achieve the local convergence under weaker assumptions. In order to avoid the Maratos effect, we use the second-order correction in this method, which need not be computed at each iteration. In other words, after a certain number of iterations, there is no need to compute the second-order correction step any more. The global convergence and the locally superlinear convergence of our method are proved under some suitable conditions.  相似文献   

8.
ABSTRACT

Model theorists have made use of low-dimensional continuous cohomology of infinite permutation groups on profinite modules, see Ahlbrandt and Ziegler (1991 Ahlbrandt , G. , Ziegler , M. ( 1991 ). What's so special about (?/4?)ω? Archive for Math. Logic 31 : 115132 . [CSA] [Crossref] [Google Scholar]), Evans (1997b Evans , D. M. ( 1997b ). Computation of first cohomology groups of finite covers . J. Algebra 193 : 214238 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] [Google Scholar]), Evans et al. (1997 Evans , D. M. , Ivanov , A. A. , Macpherson , H. D. ( 1997 ). Finite covers . In: Evans , D. M. , ed. Model Theory of Groups and Automorphism Groups . London Mathematical Society Lecture Notes 244 . Cambridge : Cambridge Univ Press , pp. 172 .[Crossref] [Google Scholar]), and Hodges and Pillay (1994 Hodges , W. , Pillay , A. ( 1994 ). Cohomology of structures and some problems of Ahlbrandt and Ziegler . J. London Math. Soc. 50 ( 2 ): 116 . [CSA] [Crossref] [Google Scholar]), for example. We expand the module category in order to widen the cohomological toolkit. For an important class of groups we use these tools to establish criteria for finiteness of cohomology.  相似文献   

9.
P. N. Ánh 《代数通讯》2013,41(2):823-836
Continuing the study of divisibility theory of arithmetical rings started in [1 Ánh, P. N., Márki, L., Vámos, P. (2012). Divisibility theory in commutative rings: Bezout monoidss. Trans. Amer. Math. Soc. 364:39673992.[Crossref], [Web of Science ®] [Google Scholar]] and [2 Ánh, P. N., Siddoway, M. (2010). Divisibility theory of semi-hereditary rings. Proc. Amer. Math. Soc. 138:42314242.[Crossref], [Web of Science ®] [Google Scholar]], we show that the divisibility theory of arithmetical rings with one minimal prime ideal is axiomatizable as Bezout monoids with one minimal m-prime filter. In particular, every Bezout monoid with one minimal m-prime filter is order-isomorphic to the partially ordered monoid with respect to inverse inclusion, of principal ideals in a Bezout ring with a smallest prime ideal. Although this result can be considered as a satisfactory answer to the divisibility theory of both semihereditary domains and valuation rings, the general representation theory of Bezout monoids is still open.  相似文献   

10.
We give a correct statement for [2 Karamzadeh, O. A. S., Motamedi, M. (1994). On α-DICC modules. Commun. Algebra 22(6):19331944.[Taylor &; Francis Online], [Web of Science ®] [Google Scholar], Proposition 1.2]. However, this new form of the proposition needs no different proof from that of [2 Karamzadeh, O. A. S., Motamedi, M. (1994). On α-DICC modules. Commun. Algebra 22(6):19331944.[Taylor &; Francis Online], [Web of Science ®] [Google Scholar], Proposition 1.2].  相似文献   

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