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Old and new on the Peetre K-functional and its relations to real interpolation theory, quasi-monotone functions and wavelets
(Journal article; Tidsskriftartikkel; Peer reviewed, 2024-12-10)The Peetre K-functional is a key object in the development of the real method of interpolation. In this paper we point out a less known relation to wavelet theory and its applications to approximation theory and engineering applications. As a new basis for further development of these studies we present some known properties in the form appropriate for further applications and then derive new ... -
Augmented reality projections as a tool to enrich simulations in health care education: Combining AR projector technology with manikins
(Journal article; Tidsskriftartikkel; Peer reviewed, 2024-11-24)The advancement of augmented reality in recent years has increased the interest and potential of using the technology in various fields. In health care education augmented reality is becoming a popular tool, together with manikins, to enhance realism of patient interaction for students in a learning environment. The purpose of this research was to study an augmented reality projector and its ability ... -
Homogenization of nonlocal spectral problems
(Journal article; Tidsskriftartikkel; Peer reviewed, 2024-11-11)We consider a spectral problem for convolution-type operators in environments with locally periodic microstructure and study the asymptotic behavior of the bottom of the spectrum. We show that the bottom point of the spectrum converges as the microstructure period tends to zero, and identify the limit in terms of an additive eigenvalue problem for effective Hamilton–Jacobi equation. In the periodic ... -
Research on wavelets and artificial intelligence algorithms for structural health monitoring of concrete bridges
(Journal article; Tidsskriftartikkel; Peer reviewed, 2024-02-23)In this paper, we present a comprehensive study of wavelet theory with a focus on structural damage detection. A new example of the application of operational modal analysis (OMA) techniques to a concrete railway arch bridge located over the Kalix river in L{\aa}ngforsen, Sweden is presented. Results from the OMA techniques are used for finite element model (FEM) updating of this concrete railway ... -
ON HARDY-TYPE INEQUALITIES AS AN INTELLECTUAL ADVENTURE FOR 100 YEARS
(Journal article; Tidsskriftartikkel; Peer reviewed, 2024-02-02)We describe some chosen ideas and results for more than 100 years prehistory and history of the remarkable development concerning Hardy-type inequalities. In particular, we present a newer convexity approach, which we believe could partly have changed this development if Hardy had discovered it. In order to emphasize the current very active interest in this subject, we fnalize by presenting some ... -
Oscillatory and spectral properties of a class of fourth-order differential operators via a new Hardy-type inequality
(Journal article; Tidsskriftartikkel; Peer reviewed, 2024)In this paper, we study oscillatory properties of a fourth-order differential equation and spectral properties of a corresponding differential operator. These properties are established by f irst proving a new second-order Hardy-type inequality, where the weights are the coefficients of the equation and the operator. This new inequality, in its turn, is established for functions satisfying certain ... -
Weighted estimates of commutators of singular operators in generalized Morrey spaces beyond Muckenhoupt range and applications
(Journal article; Tidsskriftartikkel; Peer reviewed, 2024-05-30)For a certain class of radial weights, we prove weighted norm estimates for commutators with BMO coefficients of singular operators in local generalized Morrey spaces. As a consequence of these estimates, we obtain norm inequalities for such commutators in the generalized Stummel-Morrey spaces. We also discuss a.e. well-posedness of singular operators and their commutators on weighted generalized ... -
Crafting Creative Melodies: A User-Centric Approach for Symbolic Music Generation
(Journal article; Tidsskriftartikkel; Peer reviewed, 2024-03-18)Composing coherent and structured music is one of the main challenges in symbolic music generation. Our research aims to propose a user-centric framework design that promotes a collaborative environment between users and knowledge agents. The primary objective is to improve the music creation process by actively involving users who provide qualitative feedback and emotional assessments. The ... -
Computer-Aided Optimisation in Additive Manufacturing Processes A State of the Art Survey
(Journal article; Tidsskriftartikkel; Peer reviewed, 2024-04-15)Additive manufacturing (AM) is a field with both industrial and academic significance. Computer-aided optimisation has brought advances to this field over the years, but challenges and areas of improvement still remain. Design to execution inaccuracies, void formation, material anisotropy, and surface quality are examples of remaining challenges. These challenges can be improved via some of the ... -
Multi-agent Reinforcement Learning for Structured Symbolic Music Generation
(Chapter; Bokkapittel, 2023-07-12)Generating structured music using deep learning methods with symbolic representation is challenging due to the complex relationships between musical elements that define a musical composition. Symbolic representation of music, such as MIDI or sheet music, can help overcome some of these challenges by encoding the music in a format that allows manipulation and analysis. However, the symbolic ... -
Some New weak-(Hp-Lp) Type Inequalities For Weighted Maximal Operators Of Fejér Means Of Walsh–Fourier Series
(Journal article; Tidsskriftartikkel; Peer reviewed, 2023-12-13)We introduce some new weighted maximal operators of the Fejér means of the Walsh–Fourier series. We prove that for some "optimal" weights these new operators are bounded from the martingale Hardy space H<sub>p</sub>(G) to the space weak-L<sub>p</sub>(G), for 0 <p<1/2. Moreover, we also prove sharpness of this result. As a consequence we obtain some new and well-known results. -
Analysis of civil engineering infrastructure in Norway with solutions based on structural health monitoring and artificial intelligence
(Journal article; Tidsskriftartikkel; Peer reviewed, 2023-05-19)Ageing civil infrastructures such as bridges and building causes many consequences from practical and economical point of view. Especially in northern Norway, the impact of extreme arctic conditions is intense on civil engineering infrastructures (see \cite{Singh:2022:hologaland_Bridge}). With the increased loading due to the prosperous seafood industry and increased cargo activity is putting ... -
Irregular luggage classification experiments using data from Tromsø airport
(Chapter; Bokkapittel, 2023-09-22)This paper examines the current state-of-the-art in object tracking and detection in the context of baggage handling systems using a variety of technologies, with special interest in image classification. Data collection at Tromsø Airport using simple and inexpensive equipment in order to capture images of different types of luggage will be described. Furthermore, a selection of three relevant ... -
Predicting Peak Prices in the Current Day-Ahead Market
(Chapter; Bokkapittel, 2023-06)The work presented has studied price developments in the day-ahead market. The statistical properties inherent in the time series constituting the day-to-day prices have been investigated. It is shown that these properties are radically different in 2022 than former years and resemble more chance like properties for which make predicting future peak prices especially hard. To overcome this, a space ... -
Using Light Weight Electric Vehicles for V2G services in the Arctic
(Chapter; Bokkapittel, 2023-06)The proposed paper documents research carried out in the Smart Charge project. This project has investigated the use of electric snowmobiles for V2G purposes. Electric snowmobiles and ATVs have been introduced in remote areas in the Arctic to replace the fossil fuelled vehicles that dominate today. Electric versions of these can add extra loads to the local electricity grid. But they can also be ... -
Wavelet neural networks versus wavelet-based naural networks
(Journal article; Tidsskriftartikkel; Peer reviewed, 2023)This is the first paper in a sequence of studies including also [#!llhm2022!#] and [#!llhm2022_1!#] in which we introduce a new type of neural networks (NNs) – wavelet-based neural networks (WBNNs) – and study their properties and potential for applications. We begin this study with a comparison to the currently existing type of wavelet neural networks (WNNs) and show that WBNNs vastly outperform ... -
Properties of sequence of linear functionals on BV with applications
(Journal article; Tidsskriftartikkel; Peer reviewed, 2023-11-24)This paper is devoted to investigating the sequence of some linear functionals in the space BV of finite variation functions. We prove that under certain conditions this sequence is bounded. We also prove that this result is sharp. In particular, the obtained results can be used to study convergence of some general Fourier series. Moreover, the obtained conditions seem to be new and useful also for ... -
Sharpness of some Hardy-type inequalities
(Journal article; Tidsskriftartikkel; Peer reviewed, 2023-12-04)The current status concerning Hardy-type inequalities with sharp constants is presented and described in a unified convexity way. In particular, it is then natural to replace the Lebesgue measure dx with the Haar measure . There are also derived some new two-sided Hardy-type inequalities for monotone functions, where not only the two constants are sharp but also the involved function spaces are ... -
Homogenization of Non-Autonomous Operators of Convolution Type in Periodic Media<sup>∗</sup>
(Journal article; Tidsskriftartikkel; Peer reviewed, 2023-02-23)The paper deals with periodic homogenization problem for a para\-bo\-lic equation whose elliptic part is a convolution type operator with rapidly oscillating coefficients. It is assumed that the coefficients are rapidly oscillating periodic functions both in spatial and temporal variables and that the scaling is diffusive that is the scaling factor of the temporal variable is equal to the square of ... -
Well-posedness of heat and wave equations generated by Rubin’s q-difference operator in Sobolev spaces
(Journal article; Tidsskriftartikkel; Peer reviewed, 2023)In this paper, we investigate difference-differential operators of parabolic and hyperbolic types. Namely, we considern on-homogenous heat and wave equations for Rubin’s difference operator. Wellposedness results are obtained in appropriate Sobolev type spaces. In particular, we prove that the heat and wave equations generated by Rubin’s difference operator have unique solutions. We even show that ...
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