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

In this paper, we propose and analyze a mixed formulation for the Kelvin-Voigt-Brinkman-Forchheimer equations for unsteady viscoelastic flows in porous media. Besides the velocity and pressure, our approach introduces the vorticity as a further unknown. Consequently, we obtain a three-field mixed variational formulation, where the aforementioned variables are the main unknowns of the system. We establish the existence and uniqueness of a solution for the weak formulation, and derive the corresponding stability bounds, employing a fixed-point strategy, along with monotone operators theory and Schauder theorem. Afterwards, we introduce a semidiscrete continuous-in-time approximation based on stable Stokes elements for the velocity and pressure, and continuous piecewise polynomial spaces for the vorticity. Additionally, employing backward Euler time discretization, we introduce a fully discrete finite element scheme. We prove well-posedness, derive stability bounds, and establish the corresponding error estimates for both schemes. We provide several numerical results verifying the theoretical rates of convergence and illustrating the performance and flexibility of the method for a range of domain configurations and model parameters.

In this paper, we consider an inverse space-dependent source problem for a time-fractional diffusion equation. To deal with the ill-posedness of the problem, we transform the problem into an optimal control problem with total variational (TV) regularization. In contrast to the classical Tikhonov model incorporating $L^2$ penalty terms, the inclusion of a TV term proves advantageous in reconstructing solutions that exhibit discontinuities or piecewise constancy. The control problem is approximated by a fully discrete scheme, and convergence results are provided within this framework. Furthermore, a lineraed primal-dual iterative algorithm is proposed to solve the discrete control model based on an equivalent saddle-point reformulation, and several numerical experiments are presented to demonstrate the efficiency of the algorithm.

The present work concerns the derivation of a numerical scheme to approximate weak solutions of the Euler equations with a gravitational source term. The designed scheme is proved to be fully well-balanced since it is able to exactly preserve all moving equilibrium solutions, as well as the corresponding steady solutions at rest obtained when the velocity vanishes. Moreover, the proposed scheme is entropy-preserving since it satisfies all fully discrete entropy inequalities. In addition, in order to satisfy the required admissibility of the approximate solutions, the positivity of both approximate density and pressure is established. Several numerical experiments attest the relevance of the developed numerical method.

We consider the problem of low-rank rectangular matrix completion in the regime where the matrix $M$ of size $n\times m$ is ``long", i.e., the aspect ratio $m/n$ diverges to infinity. Such matrices are of particular interest in the study of tensor completion, where they arise from the unfolding of a low-rank tensor. In the case where the sampling probability is $\frac{d}{\sqrt{mn}}$, we propose a new spectral algorithm for recovering the singular values and left singular vectors of the original matrix $M$ based on a variant of the standard non-backtracking operator of a suitably defined bipartite weighted random graph, which we call a \textit{non-backtracking wedge operator}. When $d$ is above a Kesten-Stigum-type sampling threshold, our algorithm recovers a correlated version of the singular value decomposition of $M$ with quantifiable error bounds. This is the first result in the regime of bounded $d$ for weak recovery and the first for weak consistency when $d\to\infty$ arbitrarily slowly without any polylog factors. As an application, for low-CP-rank orthogonal $k$-tensor completion, we efficiently achieve weak recovery with sample size $O(n^{k/2})$ and weak consistency with sample size $\omega(n^{k/2})$. A similar result is obtained for low-multilinear-rank tensor completion with $O(n^{k/2})$ many samples.

Let $G$ be a group with undecidable domino problem (such as $\mathbb{Z}^2$). We prove the undecidability of all nontrivial dynamical properties for sofic $G$-subshifts, that such a result fails for SFTs, and an undecidability result for dynamical properties of $G$-SFTs similar to the Adian-Rabin theorem. For $G$ amenable we prove that topological entropy is not computable from presentations of SFTs, and a more general result for dynamical invariants taking values in partially ordered sets.

Complex conjugate matrix equations (CCME) have aroused the interest of many researchers because of computations and antilinear systems. Existing research is dominated by its time-invariant solving methods, but lacks proposed theories for solving its time-variant version. Moreover, artificial neural networks are rarely studied for solving CCME. In this paper, starting with the earliest CCME, zeroing neural dynamics (ZND) is applied to solve its time-variant version. Firstly, the vectorization and Kronecker product in the complex field are defined uniformly. Secondly, Con-CZND1 model and Con-CZND2 model are proposed and theoretically prove convergence and effectiveness. Thirdly, three numerical experiments are designed to illustrate the effectiveness of the two models, compare their differences, highlight the significance of neural dynamics in the complex field, and refine the theory related to ZND.

We consider Newton's method for finding zeros of mappings from a manifold $\mathcal{X}$ into a vector bundle $\mathcal{E}$. In this setting a connection on $\mathcal{E}$ is required to render the Newton equation well defined, and a retraction on $\mathcal{X}$ is needed to compute a Newton update. We discuss local convergence in terms of suitable differentiability concepts, using a Banach space variant of a Riemannian distance. We also carry over an affine covariant damping strategy to our setting. Finally, we will discuss some applications of our approach, namely, finding fixed points of vector fields, variational problems on manifolds and finding critical points of functionals.

Two numerical schemes are proposed and investigated for the Yang--Mills equations, which can be seen as a nonlinear generalisation of the Maxwell equations set on Lie algebra-valued functions, with similarities to certain formulations of General Relativity. Both schemes are built on the Discrete de Rham (DDR) method, and inherit from its main features: an arbitrary order of accuracy, and applicability to generic polyhedral meshes. They make use of the complex property of the DDR, together with a Lagrange-multiplier approach, to preserve, at the discrete level, a nonlinear constraint associated with the Yang--Mills equations. We also show that the schemes satisfy a discrete energy dissipation (the dissipation coming solely from the implicit time stepping). Issues around the practical implementations of the schemes are discussed; in particular, the assembly of the local contributions in a way that minimises the price we pay in dealing with nonlinear terms, in conjunction with the tensorisation coming from the Lie algebra. Numerical tests are provided using a manufactured solution, and show that both schemes display a convergence in $L^2$-norm of the potential and electrical fields in $\mathcal O(h^{k+1})$ (provided that the time step is of that order), where $k$ is the polynomial degree chosen for the DDR complex. We also numerically demonstrate the preservation of the constraint.

We consider the two-pronged fork frame $F$ and the variety $\mathbf{Eq}(B_F)$ generated by its dual closure algebra $B_F$. We describe the finite projective algebras in $\mathbf{Eq}(B_F)$ and give a purely semantic proof that unification in $\mathbf{Eq}(B_F)$ is finitary and not unitary.

We show that it is undecidable whether a system of linear equations over the Laurent polynomial ring $\mathbb{Z}[X^{\pm}]$ admit solutions where a specified subset of variables take value in the set of monomials $\{X^z \mid z \in \mathbb{Z}\}$. In particular, we construct a finitely presented $\mathbb{Z}[X^{\pm}]$-module, where it is undecidable whether a linear equation $X^{z_1} \boldsymbol{f}_1 + \cdots + X^{z_n} \boldsymbol{f}_n = \boldsymbol{f}_0$ has solutions $z_1, \ldots, z_n \in \mathbb{Z}$. This contrasts the decidability of the case $n = 1$, which can be deduced from Noskov's Lemma. We apply this result to settle a number of problems in computational group theory. We show that it is undecidable whether a system of equations has solutions in the wreath product $\mathbb{Z} \wr \mathbb{Z}$, providing a negative answer to an open problem of Kharlampovich, L\'{o}pez and Miasnikov (2020). We show that there exists a finitely generated abelian-by-cyclic group in which the problem of solving a single quadratic equation is undecidable. We also construct a finitely generated abelian-by-cyclic group, different to that of Mishchenko and Treier (2017), in which the Knapsack Problem is undecidable. In contrast, we show that the problem of Coset Intersection is decidable in all finitely generated abelian-by-cyclic groups.