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In this paper, we study the explicit expansion of the first order Melnikov function near a double homoclinic loop passing through a nilpotent saddle of order m in a near-Hamiltonian system. For any positive integer , we derive the formulas of the coefficients in the expansion, which can be used to study the limit cycle bifurcations for near-Hamiltonian systems. In particular, for , we use the coefficients to consider the limit cycle bifurcations of general near-Hamiltonian systems and give the existence conditions for 10, 11, 13, 15 and 16 (11, 13 and 16, respectively) limit cycles in the case that the homoclinic loop is of cuspidal type (smooth type, respectively) and their distributions. As an application, we consider a near-Hamiltonian system with a nilpotent saddle of order 2 and obtain the lower bounds of the maximal number of limit cycles. 相似文献
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A milestone in probability theory is the law of the iterated logarithm (LIL), proved by Khinchin and independently by Kolmogorov in the 1920s, which asserts that for iid random variables with mean 0 and variance 1 In this paper we prove that LIL holds for various functionals of random graphs and hypergraphs models. We first prove LIL for the number of copies of a fixed subgraph H. Two harder results concern the number of global objects: perfect matchings and Hamiltonian cycles. The main new ingredient in these results is a large deviation bound, which may be of independent interest. For random k‐uniform hypergraphs, we obtain the Central Limit Theorem and LIL for the number of Hamilton cycles. 相似文献
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Ivan Bazhov 《Journal of Pure and Applied Algebra》2019,223(6):2530-2542
We study the similarities between the Fano varieties of lines on a cubic fourfold, a hyper-Kähler fourfold studied by Beauville and Donagi, and the hyper-Kähler fourfold constructed by Debarre and Voisin in [3]. We exhibit an analog of the notion of “triangle” for these varieties and prove that the 6-dimensional variety of “triangles” is a Lagrangian subvariety in the cube of the constructed hyper-Kähler fourfold. 相似文献
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《Discrete Mathematics》2020,343(12):112127
Let be a positive integer. The Bermond–Thomassen conjecture states that, a digraph of minimum out-degree at least contains vertex-disjoint directed cycles. A digraph is called a local tournament if for every vertex of , both the out-neighbours and the in-neighbours of induce tournaments. Note that tournaments form the subclass of local tournaments. In this paper, we verify that the Bermond–Thomassen conjecture holds for local tournaments. In particular, we prove that every local tournament with contains disjoint cycles , satisfying that either has the length at most 4 or is a shortest cycle of the original digraph of for . 相似文献
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《Comptes Rendus Chimie》2015,18(1):45-55
The aim of this work is to investigate the contribution of the binder (NiAl2O4) on the performances of the oxygen carrier NiO/NiAl2O4. To this purpose, oxidation/reduction cycles have been performed in a fixed bed reactor using CO as a fuel. The results reveal that the binder can react with the fuel to form CO2, and that its total reduction capacity increases with temperature. XRD characterizations performed on the binder (on the fresh and after several cycles) show a shift of the diffraction peaks of NiAl2O4 toward the ones of γ-alumina, which can be attributed to a progressive decomposition of NiAl2O4 to alumina and NiO. 相似文献
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Nonlinear effects such as friction and freeplay on the control surfaces can affect aeroelastic dynamics during flight. In particular, these nonlinearities can induce limit cycle oscillations (LCO), changing the system stability, and because of this it is essential to employ computational methods to predict this type of motion during the aircraft development cycle. In this context, the present article presents a matrix notation for describing the Hénon’s method used to reduce errors when considering piecewise linear nonlinearities in the numerical integration process. In addition, a new coordinate system is used to write the aeroelastic system of equations. The proposal defines a displacement vector with generalized and physical variables to simplify the computational implementation of the Hénon’s technique. Additionally, the article discusses the influence of asymmetric freeplay and friction on the LCO of an airfoil with control surface. The results show that the extended Hénon’s technique provides more accurate LCO predictions, that friction can change the frequency and amplitude of these motions, and the asymmetry of freeplay is important to determine the LCO behavior. 相似文献
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