In a bounded domain with a thin periodically punctured interface we study the limit behavior of the bottom of spectrum for a Steklov type spectral problem, the Steklov boundary condition being imposed on the perforation surface. For a certain range of parameters we construct the effective spectral problem and justify the convergence of eigenpairs.

The paper deals with the Neumann spectral problem for a singularly perturbed second-order elliptic operator with bounded lower order terms. The main goal is to provide a refined description of the limit behaviour of the principal eigenvalue and eigenfunction. Using the logarithmic transformation, we reduce the studied problem to an additive eigenvalue problem for a singularly perturbed Hamilton–Jacobi ...

In [14] we investigated some Vilenkin—Nörlund means with non-increasing coefficients. In particular, it was proved that under some special conditions the maximal operators of such summabily methods are bounded from the Hardy space H1/(1+α) to the space weak-L1/(1+α), (0 < α ≦ 1). In this paper we construct a martingale in the space H1/(1+α), which satisfies the conditions considered in [14], and so ...

One goal of this paper is to show that a big number of inequalities for functions in Lp(R+), p ≥ 1, proved from time to time in journal publications are particular cases of some known general results for integral operators with homogeneous kernels including, in particular, the statements on sharp constants. Some new results are also included, e.g. the similar general equivalence result is proved and ...

We prove and discuss some new Hp-Lp type inequalities of weighted maximal operators of Vilenkin-Nörlund means with monotone coefficients. It is also proved that these inequalities are the best possible in a special sense. We also apply these results to prove strong summability for such Vilenkin-Nörlund means. As applications, both some well-known and new results are pointed out.

Denne rapporten er utarbeidet i WP1 og WP2 i prosjektet "Fleksibilitet i fremtidens smarte distribusjonsnett - FlexNett" (2015-2017). FlexNett-prosjektet har som målsetting å bidra til økt fleksibilitet i fremtidens smarte distribusjonsnett gjennom å demonstrere og verifisere tekniske og markedsmessige løsninger for fleksibilitet på ulike nivå i nettet til nytte for ulike aktører. <br> Målsettingen ...

This study proposes to determine the thermal conductivity of SK One Component Polyurethane (SKOCP) developed by China Institute of Water Resources & Hydropower Research Beijing IWHR-KHL Co. Ltd. SKOCP provides excellent proof of aging and chemical resistance of this material. It is non-toxic, acts as a good anti-seepage, offers anti-abrasion and good anti-freezing performance. In addition, it has ...

Ice adhesion causes many serious problems such as aircraft accidents, navigational issues on ships, and power loss on wind turbines. These challenges are mainly associated with the acute behavior of ice adhesion. The ice adheres when water seeps into the microscopic pores of the material substrate and freezes, thereby, forming an interlocking mechanism. Therefore, surface roughness has a significant ...

One of the cornerstones of the steady operation of microgrids and virtual power plants as building blocks for smart grid is the communication system, which is the main objective for evaluation and research in this thesis. The given project investigates the most widespread communication protocols along with IEC 61850 standard for substations automation applied in smart grids. Based on the presented ...

In this thesis a mathematical quadrotor model based on cascade modeling theory, using a passivity-based control solution is derived and presented. The rotation and translation cascades are rst decoupled, modeled mathematically and simulated separately to test individual control solutions and stability, followed by total system modeling and simulations to verify the control solutions and stability ...