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On Some Power Means and Their Geometric Constructions
(Journal article; Peer reviewed, 2018)The main aim of this paper is to further develop the recently initiatedresearch concerning geometric construction of some power means wherethe variables are appearing as line segments. It will be demonstratedthat the arithmetic mean, the harmonic mean and the quadratic meancan be constructed for any number of variables and that all power meanswhere the number of variables are n = 2m, m 1 2 N for all ... 
Local Flexibility Market Design for Aggregators Providing Multiple Flexibility Services at Distribution Network Level
(Journal article; Tidsskriftartikkel; Peer reviewed, 20180402)This paper presents a general description of local flexibility markets as a marketbased management mechanism for aggregators. The high penetration of distributed energy resources introduces new flexibility services like prosumer or community selfbalancing, congestion management and timeofuse optimization. This work is focused on the flexibility framework to enable multiple participants to compete ... 
Distributed Management of Resources in a Smart City using MultiAgent Systems (MAS)
(Master thesis; Mastergradsoppgave, 20180817)This document describes study of distributed management of resources in the context of Smart City with support of multiagent systems. The investigated points include theoretical concepts of Smart City and application of multiagent systems, decentralized and centralized designs for agentbased solutions and aspects of interactions between different selfinterested agents. The document explores ... 
Detection and prediction of falls among elderly people using walkers
(Master thesis; Mastergradsoppgave, 20180817)Falls of elderly people are big health burden, especially for longterm consequence. Yet we already have research, describing how exactly elderly fall and reasons of falls. We aimed to develop means that could not only detect falls and send alerts to relatives and doctors to conquer one of the biggest fears of elderly to fall and do not have the ability to call for help, but also tried to implement ... 
Wire Gear for Small Rotary Actuator intended for Low Earth Orbit Applications.
(Master thesis; Mastergradsoppgave, 20180816)In this master thesis, a small rotary actuator with wire driveline intendent for space solutions is developed and tested. The replication of the environment with focus on surface friction, surface roughness, and more dynamical related features are considered. Features like temperature, vibration, radiation and more are excluded to limit the size. This because the field of interest in this iteration ... 
Refinements of some limit hardyType Inequalities via Superquadracity
(Journal article; Tidsskriftartikkel; Peer reviewed, 20171103)Refinements of some limit Hardytype inequalities are derived and discussed using the concept of superquadracity. We also proved that all three constants appearing in the refined inequalities obtained are sharp. The natural turning point of our refined Hardy inequality is p=2 and for this case we have even equality. 
Potential type operators in PDEs and their applications
(Journal article; Peer reviewed, 201701)We prove the boundedness of Potential operator in weighted generalized Morrey space in terms of MatuszewskaOrlicz indices of weights and apply this result to the Hemholtz equation in ℝ3 with a free term in such a space. We also give a short overview of some typical situations when Potential type operators arise when solving PDEs. 
Some new TwoSided Inequalities concerning the Fourier Transform
(Journal article; Peer reviewed, 2017)The classical HausdorffYoung and HardyLittlewoodStein inequalities do not hold for p > 2. In this paper we prove that if we restrict to net spaces we can even derive a twosided estimate for all p > 1. In particular, this result generalizes a recent result by Liflyand E. and Tikhonov S. [7] (MR 2464253). 
Predicting Bedside Falls using Current Context
(Peer reviewed; Chapter, 20180205)Each year about a third of the elderly aged 65 or older experience a fall. Many of these falls could be avoided if fall risk assessment and prevention tools where available in the daily living situation. Such tools would need to use the current context as input to predict an imminent fall. This paper presents an approach predicting imminent falls using data from a roofmounted infrared array combined ... 
Fejér and HermiteHadamard Type Inequalities for NQuasiconvex Functions
(Journal article; Peer reviewed, 20171228)Some new extensions and re finements of Hermite – Hadamard and Fejer type inequalities for functions which are N quasiconvex are derived and discussed. 
Economic evaluation of the Power grid tariff for households With solar Power installed
(Journal article; Peer reviewed, 2017)This paper focuses on alternative grid tariffs for household customers with roof top PVpanels ("prosumers"), and evaluates how alternative grid tariffs might affect the benefit from investing in a roof top PVpanel. The paper further shows how different orientations of the PVpanels can affect the benefits for the prosumers subjected to different grid tariffs (for example a power grid tariff), where ... 
Periodic homogenization of nonlocal operators with a convolutiontype kernel
(Journal article; Peer reviewed, 2017)The paper deals with a homogenization problem for a nonlocal linear operator with a kernel of convolution type in a medium with a periodic structure. We consider the natural diﬀusive scaling of this operator and study the limit behavior of the rescaled operators as the scaling parameter tends to 0. More precisely we show that in the topology of resolvent convergence the family of rescaled operators ... 
Homogenization of biomechanical models for plant tissues
(Journal article; Peer reviewed, 2017)In this paper homogenization of a mathematical model for plant tissue biomechanics is presented. The microscopic model constitutes a strongly coupled system of reactiondiffusionconvection equations for chemical processes in plant cells, the equations of poroelasticity for elastic deformations of plant cell walls and middle lamella, and Stokes equations for fluid flow inside the cells. The chemical ... 
Stationary convectiondiffusion equation in an infinite cylinder
(Journal article; Peer reviewed, 20171221)We study the existence and uniqueness of a solution to a linear stationary convection–diffusion equation stated in an infinite cylinder, Neumann boundary condition being imposed on the boundary. We assume that the cylinder is a junction of two semiinfinite cylinders with two different periodic regimes. Depending on the direction of the effective convection in the two semiinfinite cylinders, we ... 
Preevaluation and interactive editing of Bspline and GERBS curves and surfaces
(Peer reviewed; Conference object; Chapter, 201712)Interactive computer based geometry editing is very useful for designers and artists. Our goal has been to develop useful tools for geometry editing in a way that increases the ability for creative design. When we interactively editing geometry, we want to see the change happening gradually and smoothly on the screen. Preevaluation is a tool for increasing the speed of the graphics when doing ... 
Twoscale convergence in thin domains with locally periodic rapidly oscillating boundary
(Journal article; Peer reviewed, 2017)The aim of this paper is to adapt the notion of twoscale convergence in Lp to the case of a measure converging to a singular one. We present a speciﬁc case when a thin cylinder with locally periodic rapidly oscillating boundary shrinks to a segment, and the corresponding measure charging the cylinder converges to a onedimensional Lebegues measure of an interval. Themethod is then applied to the ... 
A new look at classical inequalities involving Banach lattice norms
(Journal article; Peer reviewed, 20171208)Some classical inequalities are known also in a more general form of Banach lattice norms and/or in continuous forms (i.e., for ‘continuous’ many functions are involved instead of finite many as in the classical situation). The main aim of this paper is to initiate a more consequent study of classical inequalities in this more general frame. We already here contribute by discussing some results of ... 
Matrix factorization of multivariate Bernstein polynomials
(Journal article; Peer reviewed, 2015)Ordinary univariate Bernstein polynomials can be represented in matrix form using factor matrices. In this paper we present the deﬁnition and basic properties of such factor matrices extended from the univariate case to the general case of arbitrary number of variables by using barycentric coordinates in the hypersimplices of respective dimension. The main results in the paper are related to the ... 
Multisource data collection for stateoftheart data analysis from groundproximate images in sea ice classification
(Peer reviewed; Conference object; Book, 20170808)In modern data analysis it is imperative to use well maintained data sources with curated content. This publication gives an approach for research areas, where there is no such central facility. The specific area used here is sea ice classification from images. The publication is split into two parts. The first part describes the integration of discontinuous sources for different aspects of data ... 
Additive weighted Lp estimates of some classes of integral operators involving generalized Oinarov kernels
(Journal article; Peer reviewed, 2017)