This paper concerns with the finite volume scheme for nonlinear tensor diffusion in image processing. First we provide some basic information on this type of diffusion including a construction of its diffusion tensor. Then we derive a semi-implicit scheme with the help of so-called diamond-cell method (see \cite{Coirier1} and \cite{Coirier2}). Further, we prove existence and uniqueness of a discrete solution given by our scheme. The proof is based on a gradient bound in the tangential direction by a gradient in normal direction. Moreover, the proofs of L2(Ω) - a priori estimates for our discrete solution are given. Finally we present our computational results.
This paper is devoted to studying the effects of a vanishing structural damping on the controllability properties of the one dimensional linear beam equation. The vanishing term depends on a small parameter $\varepsilon \in (0,1)$. We study the boundary controllability properties of this perturbed equation and the behavior of its boundary controls $v_{\varepsilon }$ as $\varepsilon $ goes to zero. It is shown that for any time $T$ sufficiently large but independent of $\varepsilon $ and for each initial data in a suitable space there exists a uniformly bounded family of controls $(v_\varepsilon )_\varepsilon $ in $L^2(0, T)$ acting on the extremity $x = \pi $. Any weak limit of this family is a control for the beam equation. This analysis is based on Fourier expansion and explicit construction and evaluation of biorthogonal sequences. This method allows us to measure the magnitude of the control needed for each eigenfrequency and to show their uniform boundedness when the structural damping tends to zero.
It is a classical problem in Fourier analysis to give conditions for a single sine or cosine series to be uniformly convergent. Several authors gave conditions for this problem supposing that the coefficients are monotone, non-negative or more recently, general monotone. There are also results for the regular convergence of double sine series to be uniform in case the coefficients are monotone or general monotone double sequences. In this paper we give new sufficient conditions for the uniformity of the regular convergence of sine-cosine and double cosine series, which are necessary as well in case the coefficients are non-negative. The new results also bring necessary and sufficient conditions for the uniform regular convergence of double trigonometric series in complex form.
Let $C$ be the extended complex plane; $G\subset C$ a finite Jordan with $ 0\in G$; $w=\varphi (z)$ the conformal mapping of $G$ onto the disk $ B\left( {0;\rho _{0}}\right):={\left\rbrace {w\:{\left| {w}\right| }<\rho _{0}} \right\lbrace }$ normalized by $\varphi (0)=0$ and ${\varphi }^{\prime }(0)=1$. Let us set $\varphi _{p}(z):=\int _{0}^{z}{{\left[ {{\varphi } ^{\prime }(\zeta )}\right] }^{{2}/{p}}}\mathrm{d}\zeta $, and let $\pi _{n,p}(z)$ be the generalized Bieberbach polynomial of degree $n$ for the pair $(G,0)$, which minimizes the integral $ \iint \limits _{G}{{\left| {{\varphi }_{p}^{\prime }(z)-{P}_{n}^{\prime }(z)}\right| }}^{p}\mathrm{d}\sigma _{z}$ in the class of all polynomials of degree not exceeding $\le n$ with $P_{n}(0)=0$, ${P}_{n}^{\prime }(0)=1$. In this paper we study the uniform convergence of the generalized Bieberbach polynomials $\pi _{n,p}(z)$ to $\varphi _{p}(z)$ on $\overline{G}$ with interior and exterior zero angles and determine its dependence on the properties of boundary arcs and the degree of their tangency.
We prove the existence and uniform decay rates of global solutions for a hyperbolic system with a discontinuous and nonlinear multi-valued term and a nonlinear memory source term on the boundary.
We study ergodic properties of stochastic dissipative systems with additive noise. We show that the system is uniformly exponentially ergodic provided the growth of nonlinearity at infinity is faster than linear. The abstract result is applied to the stochastic reaction diffusion equation in $\mathbb{R}^d$ with $d\le 3$.
The goal of the Uniform Meaning Representation (UMR) project is to design a meaning representation that can be used to annotate the semantic content of a text. UMR is primarily based on Abstract Meaning Representation (AMR), an annotation framework initially designed for English, but also draws from other meaning representations. UMR extends AMR to other languages, particularly morphologically complex, low-resource languages. UMR also adds features to AMR that are critical to semantic interpretation and enhances AMR by proposing a companion document-level representation that captures linguistic phenomena such as coreference as well as temporal and modal dependencies that potentially go beyond sentence boundaries. UMR is intended to be scalable, learnable, and cross-linguistically plausible. It is designed to support both lexical and logical inference.
An algebra A is uniform if for each ∅ ∈ Con A, every two classes of ∅ have the same cardinality. It was shown by W. Taylor that coherent varieties need not be uniform (and vice versa). We show that every coherent variety having transferable congruences is uniform.
The notion of a metric bead space was introduced in the preceding paper (L. Pasicki: Bead spaces and fixed point theorems, Topology Appl., vol. 156 (2009), 1811–1816) and it was proved there that every bounded set in such a space (provided the space is complete) has a unique central point. The bead spaces themselves can be considered in particular as natural extensions of convex sets in uniformly convex spaces. It appears that normed bead spaces are identical with uniformly convex spaces. On the other hand the "metric" approach leads to new elementary conditions equivalent to the uniform convexity. The initial part of the paper contains the proof that discus spaces (they seem to have a richer structure) are identical with bead spaces.
The paper examines similarities between observer design as introduced in Automatic Control Theory and filter design as established in Signal Processing. It is shown in the paper that there are obvious connections between them in spite of different aims for their design. Therefore, it is prospective to make them be compatible from the structural point of view. Introduced error invariance and error convergence properties of both of them are unifying tools for their design. Lyapunov's stability theory, signal power, system energy and a power balance relation are other basic terms used in the paper.