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We state and discuss a number of fundamental asymptotic properties of solutions to one-dimensional advection–diffusion equations of the form , , , assuming initial values for some . To cite this article: P. Braz e Silva, P.R. Zingano, C. R. Acad. Sci. Paris, Ser. I 342 (2006). 相似文献
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A well-known cancellation problem of Zariski asks when, for two given domains (fields) and over a field k, a k-isomorphism of () and () implies a k-isomorphism of and . The main results of this article give affirmative answer to the two low-dimensional cases of this problem:1. Let K be an affine field over an algebraically closed field k of any characteristic. Suppose , then .2. Let M be a 3-dimensional affine algebraic variety over an algebraically closed field k of any characteristic. Let be the coordinate ring of M. Suppose , then , where is the field of fractions of A.In the case of zero characteristic these results were obtained by Kang in [Ming-chang Kang, A note on the birational cancellation problem, J. Pure Appl. Algebra 77 (1992) 141–154; Ming-chang Kang, The cancellation problem, J. Pure Appl. Algebra 47 (1987) 165–171]. However, the case of finite characteristic is first settled in this article, that answered the questions proposed by Kang in [Ming-chang Kang, A note on the birational cancellation problem, J. Pure Appl. Algebra 77 (1992) 141–154; Ming-chang Kang, The cancellation problem, J. Pure Appl. Algebra 47 (1987) 165–171]. 相似文献
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Saïd Asserda 《Comptes Rendus Mathematique》2006,342(6):393-398
Let be a complete Riemannian manifold without boundary of dimension n and V be a vector field on M such that is bounded. Suppose that outside a compact set of M, where denotes the upper eigenvalue of ?V and are non-negative decreasing functions such that . There exists positive numbers and which depend only on n and such that if h is a function defined on M with and , where , where is a sequence of M such that , then the equation has no positive solution on M. To cite this article: S. Asserda, C. R. Acad. Sci. Paris, Ser. I 342 (2006). 相似文献
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We study the limit, when , of the solutions of (E) in , , with , . If where satisfies to , the limit function is a solution of (E) with a single singularity at , while if , is the maximal solution of (E). We examine similar questions for equations such as with and . To cite this article: A. Shishkov, L. Véron, C. R. Acad. Sci. Paris, Ser. I 342 (2006). 相似文献
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In this Note, we give sufficient conditions for the regularity of Leray–Hopf weak solutions to the Navier–Stokes equation. We prove that, if one of three conditions (i) where and , (ii) where and , or (iii) where and , is satisfied, then the solution is regular. These conditions improve earlier results on the conditional regularity of the Navier–Stokes equations. To cite this article: I. Kukavica, M. Ziane, C. R. Acad. Sci. Paris, Ser. I 343 (2006). 相似文献
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Donghi Lee 《Journal of Algebra》2009,321(1):167-193
Let be a free group of rank n generated by . In this paper we discuss three algorithmic problems related to automorphisms of .A word of is called positive if no negative exponents of occur in u. A word u in is called potentially positive if is positive for some automorphism ? of . We prove that there is an algorithm to decide whether or not a given word in is potentially positive, which gives an affirmative solution to problem F34a in [G. Baumslag, A.G. Myasnikov, V. Shpilrain, Open problems in combinatorial group theory, second ed., in: Contemp. Math., vol. 296, 2002, pp. 1–38, online version: http://www.grouptheory.info] for the case of .Two elements u and v in are said to be boundedly translation equivalent if the ratio of the cyclic lengths of and is bounded away from 0 and from ∞ for every automorphism ? of . We provide an algorithm to determine whether or not two given elements of are boundedly translation equivalent, thus answering question F38c in the online version of [G. Baumslag, A.G. Myasnikov, V. Shpilrain, Open problems in combinatorial group theory, second ed., in: Contemp. Math., vol. 296, 2002, pp. 1–38, online version: http://www.grouptheory.info] for the case of .We also provide an algorithm to decide whether or not a given finitely generated subgroup of is the fixed point group of some automorphism of , which settles problem F1b in [G. Baumslag, A.G. Myasnikov, V. Shpilrain, Open problems in combinatorial group theory, second ed., in: Contemp. Math., vol. 296, 2002, pp. 1–38, online version: http://www.grouptheory.info] in the affirmative for the case of . 相似文献
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Maria Carmela Lombardo Marco Sammartino Vincenzo Sciacca 《Comptes Rendus Mathematique》2005,341(11):659-664
In this Note we are concerned with the well-posedness of the Camassa–Holm equation in analytic function spaces. Using the Abstract Cauchy–Kowalewski Theorem we prove that the Camassa–Holm equation admits, locally in time, a unique analytic solution. Moreover, if the initial data is real analytic, belongs to with , and does not change sign, we prove that the solution stays analytic globally in time. To cite this article: M.C. Lombardo et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005). 相似文献
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On normal families of meromorphic functions 总被引:1,自引:0,他引:1
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