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Gotowa bibliografia na temat „Ε-Regularity”

Autor: Grafiati

Data publikacji: 21 grudnia 2024

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Artykuły w czasopismach na temat "Ε-Regularity"

1

FOX, JACOB, LÁSZLÓ MIKLÓS LOVÁSZ, and YUFEI ZHAO. "On Regularity Lemmas and their Algorithmic Applications." Combinatorics, Probability and Computing 26, no. 4 (2017): 481–505. http://dx.doi.org/10.1017/s0963548317000049.

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Szemerédi's regularity lemma and its variants are some of the most powerful tools in combinatorics. In this paper, we establish several results around the regularity lemma. First, we prove that whether or not we include the condition that the desired vertex partition in the regularity lemma is equitable has a minimal effect on the number of parts of the partition. Second, we use an algorithmic version of the (weak) Frieze–Kannan regularity lemma to give a substantially faster deterministic approximation algorithm for counting subgraphs in a graph. Previously, only an exponential dependence for the running time on the error parameter was known, and we improve it to a polynomial dependence. Third, we revisit the problem of finding an algorithmic regularity lemma, giving approximation algorithms for several co-NP-complete problems. We show how to use the weak Frieze–Kannan regularity lemma to approximate the regularity of a pair of vertex subsets. We also show how to quickly find, for each ε′>ε, an ε′-regular partition withkparts if there exists an ε-regular partition withkparts. Finally, we give a simple proof of the permutation regularity lemma which improves the tower-type bound on the number of parts in the previous proofs to a single exponential bound.

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2

CONLON, DAVID, JACOB FOX, and BENNY SUDAKOV. "Hereditary quasirandomness without regularity." Mathematical Proceedings of the Cambridge Philosophical Society 164, no. 3 (2017): 385–99. http://dx.doi.org/10.1017/s0305004116001055.

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AbstractA result of Simonovits and Sós states that for any fixed graph H and any ε > 0 there exists δ > 0 such that if G is an n-vertex graph with the property that every S ⊆ V(G) contains pe(H) |S|v(H) ± δ nv(H) labelled copies of H, then G is quasirandom in the sense that every S ⊆ V(G) contains $\frac{1}{2}$p|S|2± ε n2 edges. The original proof of this result makes heavy use of the regularity lemma, resulting in a bound on δ−1 which is a tower of twos of height polynomial in ε−1. We give an alternative proof of this theorem which avoids the regularity lemma and shows that δ may be taken to be linear in ε when H is a clique and polynomial in ε for general H. This answers a problem raised by Simonovits and Sós.

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3

Chen, Shibing, та Alessio Figalli. "Boundary ε-regularity in optimal transportation". Advances in Mathematics 273 (березень 2015): 540–67. http://dx.doi.org/10.1016/j.aim.2014.12.032.

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4

Gerke, Stefanie, Yoshiharu Kohayakawa, Vojtěch Rödl та Angelika Steger. "Small subsets inherit sparse ε-regularity". Journal of Combinatorial Theory, Series B 97, № 1 (2007): 34–56. http://dx.doi.org/10.1016/j.jctb.2006.03.004.

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5

Zhang, Yanjun, and Qiaozhen Ma. "Asymptotic Behavior for a Class of Nonclassical Parabolic Equations." ISRN Applied Mathematics 2013 (September 1, 2013): 1–14. http://dx.doi.org/10.1155/2013/204270.

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This paper is devoted to the qualitative analysis of a class of nonclassical parabolic equations ut-εΔut-ωΔu+f(u)=g(x) with critical nonlinearity, where ε∈[0,1] and ω>0 are two parameters. Firstly, we establish some uniform decay estimates for the solutions of the problem for g(x)∈H-1(Ω), which are independent of the parameter ε. Secondly, some uniformly (with respect to ε∈[0,1]) asymptotic regularity about the solutions has been established for g(x)∈L2(Ω), which shows that the solutions are exponentially approaching a more regular, fixed subset uniformly (with respect to ε∈[0,1]). Finally, as an application of this regularity result, a family {ℰε}ε∈[0,1] of finite dimensional exponential attractors has been constructed. Moreover, to characterize the relation with the reaction diffusion equation (ε=0), the upper semicontinuity, at ε=0, of the global attractors has been proved.

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6

Hasselblatt, Boris. "Regularity of the Anosov splitting and of horospheric foliations." Ergodic Theory and Dynamical Systems 14, no. 4 (1994): 645–66. http://dx.doi.org/10.1017/s0143385700008105.

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Abstract‘Bunching’ conditions on an Anosov system guarantee the regularity of the Anosov splitting up toC2−ε. Open dense sets of symplectic Anosov systems and geodesic flows do not have Anosov splitting exceeding the asserted regularity. This is the first local construction of low-regularity examples.

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7

HOSSEINI, KAAVE, SHACHAR LOVETT, GUY MOSHKOVITZ, and ASAF SHAPIRA. "An improved lower bound for arithmetic regularity." Mathematical Proceedings of the Cambridge Philosophical Society 161, no. 2 (2016): 193–97. http://dx.doi.org/10.1017/s030500411600013x.

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AbstractThe arithmetic regularity lemma due to Green [GAFA 2005] is an analogue of the famous Szemerédi regularity lemma in graph theory. It shows that for any abelian group G and any bounded function f : G → [0, 1], there exists a subgroup H ⩽ G of bounded index such that, when restricted to most cosets of H, the function f is pseudorandom in the sense that all its nontrivial Fourier coefficients are small. Quantitatively, if one wishes to obtain that for 1 − ε fraction of the cosets, the nontrivial Fourier coefficients are bounded by ε, then Green shows that |G/H| is bounded by a tower of twos of height 1/ε3. He also gives an example showing that a tower of height Ω(log 1/ε) is necessary. Here, we give an improved example, showing that a tower of height Ω(1/ε) is necessary.

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8

Chen, Jianyi, Zhitao Zhang, Guijuan Chang, and Jing Zhao. "Periodic Solutions to Klein–Gordon Systems with Linear Couplings." Advanced Nonlinear Studies 21, no. 3 (2021): 633–60. http://dx.doi.org/10.1515/ans-2021-2138.

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Abstract In this paper, we study the nonlinear Klein–Gordon systems arising from relativistic physics and quantum field theories { u t ⁢ t - u x ⁢ x + b ⁢ u + ε ⁢ v + f ⁢ ( t , x , u ) = 0 , v t ⁢ t - v x ⁢ x + b ⁢ v + ε ⁢ u + g ⁢ ( t , x , v ) = 0 , \left\{\begin{aligned} \displaystyle{}u_{tt}-u_{xx}+bu+\varepsilon v+f(t,x,u)&\displaystyle=0,\\ \displaystyle v_{tt}-v_{xx}+bv+\varepsilon u+g(t,x,v)&\displaystyle=0,\end{aligned}\right. where u , v u,v satisfy the Dirichlet boundary conditions on spatial interval [ 0 , π ] [0,\pi] , b > 0 b>0 and f , g f,g are 2 ⁢ π 2\pi -periodic in 𝑡. We are concerned with the existence, regularity and asymptotic behavior of time-periodic solutions to the linearly coupled problem as 𝜀 goes to 0. Firstly, under some superlinear growth and monotonicity assumptions on 𝑓 and 𝑔, we obtain the solutions ( u ε , v ε ) (u_{\varepsilon},v_{\varepsilon}) with time period 2 ⁢ π 2\pi for the problem as the linear coupling constant 𝜀 is sufficiently small, by constructing critical points of an indefinite functional via variational methods. Secondly, we give a precise characterization for the asymptotic behavior of these solutions, and show that, as ε → 0 \varepsilon\to 0 , ( u ε , v ε ) (u_{\varepsilon},v_{\varepsilon}) converge to the solutions of the wave equations without the coupling terms. Finally, by careful analysis which is quite different from the elliptic regularity theory, we obtain some interesting results concerning the higher regularity of the periodic solutions.

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9

Miura, Tatsuya, та Felix Otto. "Sharp boundary ε-regularity of optimal transport maps". Advances in Mathematics 381 (квітень 2021): 107603. http://dx.doi.org/10.1016/j.aim.2021.107603.

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10

Han, Xiaoli, та Jun Sun. "An ε-regularity theorem for the mean curvature flow". Journal of Geometry and Physics 62, № 12 (2012): 2329–36. http://dx.doi.org/10.1016/j.geomphys.2012.07.009.

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