The paper deals with homogenization of Lévy-type operators with rapidly oscillating coefficients. We consider cases of periodic and random statistically homogeneous micro-structures and show that in the limit we obtain a Lévy-operator. In the periodic case we study both symmetric and non-symmetric kernels whereas in the random case we only investigate symmetric kernels. We also address a nonlinear ...

The development of the C++ programming language and its standard library has undergone a renaissance since the introduction of the C++11 standard, making the language more relevant than ever, through modern features, simplification and expansion of the standard library. Comparing past and future feature sets (C++17, C++20, ...) similar to comparing different programming languages. In this article ...

We study embeddings of weighted local and consequently global generalized Morrey spaces defined on a quasi-metric measure set (X, d, μ) of general nature which may be unbounded, into Lebesgue spaces Ls(X), 1 ≤ s ≤ p < ∞. The main motivation for obtaining such an embedding is to have an embedding of non-separable Morrey space into a separable space. In the general setting of quasi-metric measure ...

In this paper we solve an eigenvalue problem on a circular membrane with fixed outer boundary by using a finite element method, where an element is represented as an expo-rational blending triangle. ERBS triangles combine properties of B-spline finite elements and standard polynomial triangular elements. The overlapping of local triangles allows us to provide a flexible handling of the surface while ...

This paper documents research conducted in the Norwegian FLEXNETT project.<br>It describes a new tool that was developed to study the future impact of prosumers with PV panels on the grid in Norway and the potential energy flexibility that lies with residential prosumers. Systematic use of energy flexibility can be an important instrument for managing peak loads and voltage problems in weak power ...

A number of classical inequalities and convergence results related to Fourier coefficients with respect to unbounded orthogonal systems are generalized and complemented. All results are given in the case of Lorentz–Zygmund spaces.

In this article, we describe an approach to give automatic formative evaluation by atomizing the feedback. The mechanics in this approach is a large number of multiple-choice tests. The multiplechoice tests are used as voluntary assignments and gives controlled progression by releasing the tests in an order. Instruction is in the spirit of flipped classroom with short video lectures accompanied by ...

In the homogenization theory, there are many examples where the effective conductivities of composite structures are power means of the local conductivities. The main aim of this paper is to initiate research concerning geometric construction of some power means of three or more variables. We contribute by giving methods for the geometric construction of the harmonic mean $ P_{-1} $ and the arithmetic ...

The paper deals with jump generators with a convolution kernel. Assuming that the kernel decays either exponentially or polynomially, we prove a number of lower and upper bounds for the resolvent of such operators. In particular we focus on sharp estimates of the resolvent kernel for small values of the spectral parameter. We consider two applications of these results. First we obtain pointwise ...

We consider randomly distributed mixtures of bonds of ferromagnetic and antiferromagnetic type in a two-dimensional square lattice with probability 1−p 1−p and p, respectively, according to an i.i.d. random variable. We study minimizers of the corresponding nearest-neighbour spin energy on large domains in Z 2 Z2 . We prove that there exists p 0 p0 such that for p≤ p 0 p≤p0 such ...