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With any -manifold M are associated two dglas and , whose cohomologies and are Gerstenhaber algebras. We establish a formality theorem for -manifolds: there exists an quasi-isomorphism whose first ‘Taylor coefficient’ (1) is equal to the Hochschild–Kostant–Rosenberg map twisted by the square root of the Todd cocycle of the -manifold M, and (2) induces an isomorphism of Gerstenhaber algebras on the level of cohomology. Consequently, the Hochschild–Kostant–Rosenberg map twisted by the square root of the Todd class of the -manifold M is an isomorphism of Gerstenhaber algebras from to . 相似文献
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A uniqueness criterion of limit cycles for planar polynomial systems with homogeneous nonlinearities
This paper is devoted to study the planar polynomial system: where and are homogeneous polynomials of degree . Denote . We prove that the system has at most 1 limit cycle surrounding the origin provided . Furthermore, this upper bound is sharp. This is maybe the first uniqueness criterion, which only depends on a (linear) condition of ψ, for the limit cycles of this kind of systems. We show by examples that in many cases, the criterion is applicable while the classical ones are invalid. The tool that we mainly use is a new estimate for the number of limit cycles of Abel equation with coefficients of indefinite signs. Employing this tool, we also obtain another geometric criterion which allows the system to possess at most 2 limit cycles surrounding the origin. 相似文献
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Michael Winkler 《Journal of Differential Equations》2018,264(10):6109-6151
A class of chemotaxis-Stokes systems generalizing the prototype is considered in bounded convex three-dimensional domains, where is given.The paper develops an analytical approach which consists in a combination of energy-based arguments and maximal Sobolev regularity theory, and which allows for the construction of global bounded weak solutions to an associated initial-boundary value problem under the assumption that
(0.1)
Moreover, the obtained solutions are shown to approach the spatially homogeneous steady state in the large time limit.This extends previous results which either relied on different and apparently less significant energy-type structures, or on completely alternative approaches, and thereby exclusively achieved comparable results under hypotheses stronger than (0.1). 相似文献
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We consider the Choquard equation (also known as the stationary Hartree equation or Schrödinger–Newton equation) Here stands for the Riesz potential of order , and . We prove that least energy nodal solutions have an odd symmetry with respect to a hyperplane when α is either close to 0 or close to N. 相似文献
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Let l be a prime number and let be a finite field of characteristic with elements. Let . We determine the number N of solutions in k of the Kummer equation in terms of the trace of a certain Jacobi sum. 相似文献
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Konstantin Tikhomirov 《Journal of Functional Analysis》2018,274(1):121-151
Let n be a sufficiently large natural number and let B be an origin-symmetric convex body in in the ?-position, and such that the space admits a 1-unconditional basis. Then for any , and for random -dimensional subspace E distributed according to the rotation-invariant (Haar) measure, the section is -Euclidean with probability close to one. This shows that the “worst-case” dependence on ε in the randomized Dvoretzky theorem in the ?-position is significantly better than in John's position. It is a previously unexplored feature, which has strong connections with the concept of superconcentration introduced by S. Chatterjee. In fact, our main result follows from the next theorem: Let B be as before and assume additionally that B has a smooth boundary and for a small universal constant , where is the gradient of and is the standard Gaussian measure in . Then for any the p-th power of the norm is -superconcentrated in the Gauss space. 相似文献
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Zhidong Pan 《Linear algebra and its applications》2012,436(11):4251-4260
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Iz-iddine EL-Fassi 《Journal of Mathematical Analysis and Applications》2018,457(1):322-335
Let be the set of real numbers. In this paper, we first introduce the notions of non-Archimedean -normed spaces and we will reformulate the fixed point theorem [10, Theorem 1] in this space, after it, we introduce and solve the radical quintic functional equation Also, under some weak natural assumptions on the function , we show that this theorem is a very efficient and convenient tool for proving the hyperstability results when satisfy the following radical quintic inequality with . 相似文献
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For fractional Navier–Stokes equations and critical initial spaces X, one used to establish the well-posedness in the solution space which is contained in . In this paper, for heat flow, we apply parameter Meyer wavelets to introduce Y spaces where is not contained in . Consequently, for , we establish the global well-posedness of fractional Navier–Stokes equations with small initial data in all the critical oscillation spaces. The critical oscillation spaces may be any Besov–Morrey spaces or any Triebel–Lizorkin–Morrey spaces where . These critical spaces include many known spaces. For example, Besov spaces, Sobolev spaces, Bloch spaces, Q-spaces, Morrey spaces and Triebel–Lizorkin spaces etc. 相似文献
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We study the chemotaxis effect vs. logistic damping on boundedness for the well-known minimal Keller–Segel model with logistic source: in a smooth bounded domain with , nonnegative initial data , , and homogeneous Neumann boundary data. It is well known that this model allows only for global and uniform-in-time bounded solutions for any . Here, we carefully employ a simple and new method to regain its boundedness, with particular attention to how upper bounds of solutions qualitatively depend on χ and μ. More, precisely, it is shown that there exists such that and uniformly on , where and We notice that these upper bounds are increasing in χ, decreasing in μ, and have only one singularity at , where the corresponding minimal model (removing the term in the first equation) is widely known to possess blow-ups for large initial data. 相似文献
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Dennis I. Merino 《Linear algebra and its applications》2012,436(7):1960-1968