Sample paths of white noise in spaces with dominating mixed smoothness

The sample paths of white noise are proved to be elements of certain Besov spaces with dominating mixed smoothness. Unlike in isotropic spaces, here the regularity does not get worse with increasing space dimension. Consequently, white noise is actually much smoother than the known sharp regularity results in isotropic spaces suggest. An application of our techniques yields new results for the regularity of solutions of Poisson and heat equation on the half space with boundary noise. The main novelty is the flexible treatment of the interplay between the singularity at the boundary and the smoothness in tangential, normal and time direction.

Analysis of Noise Environment and Noise Reduction Measures in Urban 110kV Indoor Substations

With the rapid development of society and economy, the public awareness of environmental protection has gradually increased, and urban substation noise has become an environmental issue of concern to residents. In order to study the current status of the noise environment of urban substations, to guide the management of substation noise and the construction of transmission and transformation projects, this article selects 50 110kV indoor substations as objects, and measures their boundary noise. By analyzing the characteristics of the noise source of the substation with excessive noise and various noise reduction measures, the noise reduction methods suitable for urban indoor substations are summarized.

Absolute continuity of the law for solutions of stochastic differential equations with boundary noise

We study the existence and regularity of the density for the solution [Formula: see text] (with fixed [Formula: see text] and [Formula: see text]) of the heat equation in a bounded domain [Formula: see text] driven by a stochastic inhomogeneous Neumann boundary condition with stochastic term. The stochastic perturbation is given by a fractional Brownian motion process. Under suitable regularity assumptions on the coefficients, by means of tools from the Malliavin calculus, we prove that the law of the solution has a smooth density with respect to the Lebesgue measure in [Formula: see text].

Existence and regularity of the density for solutions of stochastic differential equations with boundary noise

We study the existence and regularity of densities for the solution of a nonlinear heat diffusion with stochastic perturbation of Brownian and fractional Brownian motion type: we use the Malliavin calculus in order to prove that, if the nonlinear term is suitably regular, then the law of the solution has a smooth density with respect to the Lebesgue measure.

MAT-Based Thinning for Line Patterns

Reducing branching effect and increasing boundary noise immunity are of great importance for thinning patterns. An approach based on medial axis transform (MAT) to obtain a connected 1-pixel wide skeleton with few redundant branches is presented in this paper. Though the obtained skeleton by MAT is isotropic with few redundant branches, however, the skeleton points are usually disconnected. In order to rend the merits of the MAT and avoid its disadvantages, the proposed approach is composed of distance-map generation, grouping, ridge-path linking, and refining to obtain the connected 1-pixel wide thin line. The ridge-path linking strategy can guarantee the skeletons connected, whereas the refining process can be readily performed by a conventional thinning process to obtain the 1-pixel wide thinned pattern. The performances investigated by branching effect, signal-to-noise ratio (SNR), and measurement of skeleton deviation (MSD) confirm the feasibility of the proposed MAT-based thinning for line patterns.