亚洲男人的天堂2018av,欧美草比,久久久久久免费视频精选,国色天香在线看免费,久久久久亚洲av成人片仓井空

We consider the stochastic Cahn-Hilliard equation with additive space-time white noise $\epsilon^{\gamma}\dot{W}$ in dimension $d=2,3$, where $\epsilon>0$ is an interfacial width parameter. We study numerical approximation of the equation which combines a structure preserving implicit time-discretization scheme with a discrete approximation of the space-time white noise. We derive a strong error estimate for the considered numerical approximation which is robust with respect to the inverse of the interfacial width parameter $\epsilon$. Furthermore, by a splitting approach, we show that for sufficiently large scaling parameter $\gamma$, the numerical approximation of the stochastic Cahn-Hilliard equation converges uniformly to the deterministic Hele-Shaw/Mullins-Sekerka problem in the sharp interface limit $\epsilon\rightarrow 0$.

We use a functional analogue of the quantile function for probability measures admitting a continuous Lebesgue density on $\mathbb{R}^d$ to characterise the class of non-trivial limit distributions of radially recentered and rescaled multivariate exceedances. A new class of multivariate distributions is identified, termed radially-stable generalised Pareto distributions, and is shown to admit certain stability properties that permit extrapolation to extremal sets along any direction in cones such as $\mathbb{R}^d$ and $\mathbb{R}_+^d$. Leveraging the limit Poisson point process likelihood of the point process of radially renormalised exceedances, we develop parsimonious statistical models that exploit theoretical links between structural star-bodies and are amenable to Bayesian inference. Our framework sharpens statistical inference by suitably including additional information from the angular directions of the geometric exceedances and facilitates efficient computations in dimensions $d=2$ and $d=3$. Additionally, it naturally leads to the notion of return level-set, which is a canonical quantile set expressed in terms of its average recurrence interval, and a geometric analogue of the uni-dimensional return level. We illustrate our methods with a simulation study showing superior predictive performance of probabilities of rare events, and with two case studies, one associated with river flow extremes, and the other with oceanographic extremes.

This work proposes a novel variational approximation of partial differential equations on moving geometries determined by explicit boundary representations. The benefits of the proposed formulation are the ability to handle large displacements of explicitly represented domain boundaries without generating body-fitted meshes and remeshing techniques. For the space discretization, we use a background mesh and an unfitted method that relies on integration on cut cells only. We perform this intersection by using clipping algorithms. To deal with the mesh movement, we pullback the equations to a reference configuration (the spatial mesh at the initial time slab times the time interval) that is constant in time. This way, the geometrical intersection algorithm is only required in 3D, another key property of the proposed scheme. At the end of the time slab, we compute the deformed mesh, intersect the deformed boundary with the background mesh, and consider an exact transfer operator between meshes to compute jump terms in the time discontinuous Galerkin integration. The transfer is also computed using geometrical intersection algorithms. We demonstrate the applicability of the method to fluid problems around rotating (2D and 3D) geometries described by oriented boundary meshes. We also provide a set of numerical experiments that show the optimal convergence of the method.

We design an algorithm for computing the $L$-series associated to an Anderson $t$-motives, exhibiting quasilinear complexity with respect to the target precision. Based on experiments, we conjecture that the order of vanishing at $T=1$ of the $v$-adic $L$-series of a given Anderson $t$-motive with good reduction does not depend on the finite place $v$.

We prove that the Weihrauch degree of the problem of finding a bad sequence in a non-well quasi order ($\mathsf{BS}$) is strictly above that of finding a descending sequence in an ill-founded linear order ($\mathsf{DS}$). This corrects our mistaken claim in arXiv:2010.03840, which stated that they are Weihrauch equivalent. We prove that K\"onig's lemma $\mathsf{KL}$ is not Weihrauch reducible to $\mathsf{DS}$ either, resolving the main open question raised in arXiv:2010.03840.

We give a lower bound of $\Omega(\sqrt n)$ on the unambiguous randomised parity-query complexity of the approximate majority problem -- that is, on the lowest randomised parity-query complexity of any function over $\{0,1\}^n$ whose value is "0" if the Hamming weight of the input is at most n/3, is "1" if the weight is at least 2n/3, and may be arbitrary otherwise.

The large-sample behavior of non-degenerate multivariate $U$-statistics of arbitrary degree is investigated under the assumption that their kernel depends on parameters that can be estimated consistently. Mild regularity conditions are given which guarantee that once properly normalized, such statistics are asymptotically multivariate Gaussian both under the null hypothesis and sequences of local alternatives. The work of Randles (1982, Ann. Statist.) is extended in three ways: the data and the kernel values can be multivariate rather than univariate, the limiting behavior under local alternatives is studied for the first time, and the effect of knowing some of the nuisance parameters is quantified. These results can be applied to a broad range of goodness-of-fit testing contexts, as shown in one specific example.

We prove that if $X,Y$ are positive, independent, non-Dirac random variables and if for $\alpha,\beta\ge 0$, $\alpha\neq \beta$, $$ \psi_{\alpha,\beta}(x,y)=\left(y\,\tfrac{1+\beta(x+y)}{1+\alpha x+\beta y},\;x\,\tfrac{1+\alpha(x+y)}{1+\alpha x+\beta y}\right), $$ then the random variables $U$ and $V$ defined by $(U,V)=\psi_{\alpha,\beta}(X,Y)$ are independent if and only if $X$ and $Y$ follow Kummer distributions with suitably related parameters. In other words, any invariant measure for a lattice recursion model governed by $\psi_{\alpha,\beta}$ in the scheme introduced by Croydon and Sasada in \cite{CS2020} is necessarily a product measure with Kummer marginals. The result extends earlier characterizations of Kummer and gamma laws by independence of $$ U=\tfrac{Y}{1+X}\quad\mbox{and}\quad V= X\left(1+\tfrac{Y}{1+X}\right), $$ which corresponds to the case of $\psi_{1,0}$. We also show that this independence property of Kummer laws covers, as limiting cases, several independence models known in the literature: the Lukacs, the Kummer-Gamma, the Matsumoto-Yor and the discrete Korteweg de Vries models.

The degree-diameter problem consists of finding the maximum number of vertices $n$ of a graph with diameter $d$ and maximum degree $\Delta$. This problem is well studied, and has been solved for plane graphs of low diameter in which every face is bounded by a 3-cycle (triangulations), and plane graphs in which every face is bounded by a 4-cycle (quadrangulations). In this paper, we solve the degree diameter problem for plane graphs of diameter 3 in which every face is bounded by a 5-cycle (pentagulations). We prove that if $\Delta \geq 8$, then $n \leq 3\Delta - 1$ for such graphs. This bound is sharp for $\Delta$ odd.

We introduce a single-set axiomatisation of cubical $\omega$-categories, including connections and inverses. We justify these axioms by establishing a series of equivalences between the category of single-set cubical $\omega$-categories, and their variants with connections and inverses, and the corresponding cubical $\omega$-categories. We also report on the formalisation of cubical $\omega$-categories with the Isabelle/HOL proof assistant, which has been instrumental in finding the single-set axioms.