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关于循环子半群的结构与数量问题及拟环的特征与结构 总被引:1,自引:0,他引:1
朱平 《纯粹数学与应用数学》2002,18(3):239-243,249
彻底解决了所有循环半群及其子群的结构和数量问题,并讨论了拟群分解问题,同时,对群论基本定理作了部分推广,并给出了定理的另一部分不可推广的反例,最后,建立了一类特殊环-拟环。 相似文献
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We find topological models for the tiling dynamical systems corresponding to the chair and table rep-tiles. 相似文献
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Hermann König Vitali Milman 《Proceedings of the Steklov Institute of Mathematics》2013,280(1):191-207
We study rigidity and stability properties of the Leibniz and chain rule operator equations. We describe which non-degenerate operators V, T 1, T 2,A: C k (?) → C(?) satisfy equations of the generalized Leibniz and chain rule type for f, g ∈ C k (?), namely, V (f · g) = (T 1 f) · g + f · (T 2 g) for k = 1, V (f · g) = (T 1 f) · g + f · (T 2 g) + (Af) · (Ag) for k = 2, and V (f ○ g) = (T 1 f) ○ g · (T 2 g) for k = 1. Moreover, for multiplicative maps A, we consider a more general version of the first equation, V (f · g) = (T 1 f) · (Ag) + (Af) · (T 2 g) for k = 1. In all these cases, we completely determine all solutions. It turns out that, in any of the equations, the operators V, T 1 and T 2 must be essentially equal. We also consider perturbations of the chain and the Leibniz rule, T (f ○ g) = Tf ○ g · Tg + B(f ○ g, g) and T (f · g) = Tf · g + f · Tg + B(f, g), and show under suitable conditions on B in the first case that B = 0 and in the second case that the solution is a perturbation of the solution of the standard Leibniz rule equation. 相似文献
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The correspondence in two-dimensional elasticity between the stress fields of cavities and rigid inclusions has been obtained by Dundurs [1] and Markenscoff [3]. It was shown that if the limit of the stress of the inclusion boundary-value problem, which depends on the elastic constants, exists when the Poisson's ratio v tends to 1, then this solves the traction boundary-value problem for the cavity problem since it satisfies equilibrium and boundary conditions, and, by the uniqueness theorem, exists and is unique. In three dimensions the solution of the traction boundary-value problem of elasticity does depend on Poisson's ratio since the Beltrami-Mitchell compatability conditions for the stress depend on Poisson's ratio. So the similar argument for the correspondence between cavities and rigid inclusions cannot in principle be made. However, the Beltrami-Mitchell compatability conditions are independent of v if the dilatation is a constant or a linear function of the position. In this case we can show that the same result goes through for the correspondence. In order to investigate the behavior of the solutions in the vicinity of v = 1, we use some results obtained for the Cosserat spectrum by Mikhlin [4], Maz'ya and Mikhlin [3], see also [6]. The existence of the limit for 2D and 3D when v tends to 1 is proved on the basis of the fact that the eigenvalue ω = — 1 of the Cosserat spectrum is isolated. 相似文献
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We study the (2+1)-dimensional model proposed by Kadomtsev and Petviashvili (KP) to describe slowly varying nonlinear waves in a dispersive medium. Applying an appropriate Lie transformation and following the method introduced by Tajiri et al., the KP equation is reduced to a one-dimensional equation, that is, to a certain version of the Boussinesq equation (BqE). Then, we solve the BqE by the Hirota method, and finally we use the inverse transformation in order to obtain de KP solutions. We Analyze some remarkable properties of the solutions found in this work. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2008,13(7):1264-1271
An algebraic system is constructed from which establishes two isospectral problems. By solving the zero curvature equations, two resulting integrable couplings of the Li hierarchy and Tu hierarchy are obtained, respectively. By making use of the quadratic-form identity, the Hamiltonian structures of the above integrable couplings are generated, which are Liouville integrable. 相似文献
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Fred Richman 《Proceedings of the American Mathematical Society》2001,129(4):1189-1193
A bounded operator between Hilbert spaces has an adjoint if and only if the image of the unit ball is located.
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Randolf Arnold 《Monatshefte für Mathematik》1993,115(1-2):1-11
LetF be a closed convex hypersurface in Euclideand-space with almost constantq-th mean curvatureH
q (q=1, ...,d–1). The deviation ofF from a suitable sphere is estimated explicitely in terms of geometric quantities ofF. The proof depends on a new stability result on the Aleksandrov-Fenchel inequality, which improves a theorem of Schneider. 相似文献
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Gonzalo Fiz Pontiveros Simon Griffiths Robert Morris David Saxton Jozef Skokan 《Combinatorica》2016,36(1):71-89
The Ramsey number r(K 3,Q n ) is the smallest integer N such that every red-blue colouring of the edges of the complete graph K N contains either a red n-dimensional hypercube, or a blue triangle. Almost thirty years ago, Burr and Erd?s conjectured that r(K 3,Q n )=2 n+1?1 for every n∈?, but the first non-trivial upper bound was obtained only recently, by Conlon, Fox, Lee and Sudakov, who proved that r(K 3,Q n )?7000·2 n . Here we show that r(K 3,Q n )=(1+o(1))2 n+1 as n→∞. 相似文献
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Stevo Stevi 《Applied mathematics and computation》2009,215(6):2199-2205
Let H(X) be the class of all holomorphic functions on the set and uH(X). We calculate operator norms of the multiplication operators Mu(f)=uf, on the weighted Bergman space , as well as on the Hardy space Hp(X), where X is the unit polydisk or the unit ball in . We also calculate the norm of the weighted composition operator from the weighted Bergman space , and the Hardy space , to a weighted-type space on the unit polydisk. 相似文献
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L. A. Khan A. B. Thaheem 《International Journal of Mathematical Education in Science & Technology》2013,44(4):620-622
The equivalence of the Heine-Borel theorem and the Bolzano-Weierstrass theorem is proved. 相似文献
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Razvan Gelca 《Proceedings of the American Mathematical Society》2002,130(4):1235-1241
This paper shows that the noncommutative generalization of the A-polynomial of a knot, defined using Kauffman bracket skein modules, together with finitely many colored Jones polynomials, determines the remaining colored Jones polynomials of the knot. It also shows that under certain conditions, satisfied for example by the unknot and the trefoil knot, the noncommutative generalization of the A-polynomial determines all colored Jones polynomials of the knot.