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• 1.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
Conditions and constraints for transferring Japanese structured problem solving to Swedish mathematics classroom2019In: Article in journal (Refereed)
• 2.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
Japanese Mathematics Teachers’ Professional Knowledge: International case studies based on praxeological analysis2019Doctoral thesis, comprehensive summary (Other academic)

The thesis describes and studies the Japanese mathematics teachers’ professional knowledge and its dissemination. This theme is investigated in several concrete situations: the knowledge of teaching practice of school mathematics taught in the teacher education, the relation between the educational goals described in the national curriculum and concrete teaching methods discussed among the Japanese lower secondary teachers in service. The thesis investigates also critical phenomena, which arise in an attempt to transfer the Japanese teaching practice in a different teaching context.

• 3.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics. University of Copenhagen, Copenhagen, Denmark.
The Didactic Notion of “Mathematical Activity” in Japanese Teachers’ Professional Scholarship: A case study of an open lesson2019In: International Journal of Mathematical Education in Science and Technology, ISSN 0020-739X, E-ISSN 1464-5211Article in journal (Refereed)
• 4.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
Japanese and Swedish Mathematics Teacher Educators’ Pedagogical Content Knowledge: An Institutional Perspective2019In: Educaçao Matemática Pesquissa, ISSN 1983-3156, Vol. 21, no 4, p. 157-170Article in journal (Refereed)

The aim of this paper is to investigate which kind of conditions and constraints affect Japanese and Swedish teacher educators’ pedagogical content knowledge (PCK). We analyse the praxeologies of the lessons in which the educators teach area determination. Our study shows that the Japanese teacher educators’ PCK are more explicitly shared by the community of the teacher educators compared to the Swedish counterpart. Also, the detailed Japanese curriculum and the structured problem solving approach promote to illustrate how to construct rich mathematical and didactical organisations for prospective teachers.

• 5.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics. Department of Science Education, University of Copenhagen, Copenhagen, Denmark.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics. Department of Science Education, University of Copenhagen, Copenhagen, Denmark.
Comparing mathematics education lessons for primary school teachers: case studies from Japan, Finland and Sweden2019In: International Journal of Mathematical Education in Science and Technology, ISSN 0020-739X, E-ISSN 1464-5211Article in journal (Refereed)

The aim of this paper is to investigate and compare lessons given in primary school teacher education in Japan, Finland and Sweden. We analyse one lesson from each country and compare them using a common framework. Chevallard’s anthropological theory of the didactic (ATD) is used to frame this analysis and in particular to model teacher educators' didactic organization of the lessons. The focus is on how the didactic organizations of the teacher educators relate to the mathematical and didactic organizations of primary school. Based on official documents and viewpoints of the teacher educators, we also discuss how the contents and descriptions of the national curricula, and the different traditions of the teaching practices in each country, influence the didactic organizations found in the lessons.

• 6.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
Se mig!: En studie om matematiskt särskilt begåvade elever2019Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis

Syftet med studien är att utforska vilka uppfattningar lågstadielärare har av matematiskt särskilt begåvade elever, samt undersöka vilka arbetssätt lärare har för att motivera och stimulera de här eleverna i matematik. Studien har en metod med kvalitativ ansats med en fenomenografisk och fenomenologisk inriktning. Datainsamlingsmetoden för studien är intervjuer. Fyra lärare intervjuades och de är alla något så när överens om att matematiskt särskilt begåvade elever skiljer sig från andra elever, samt på vilket sätt de gör det. Lärarnas uppfattningar av matematiskt särskilt begåvade elever överensstämmer även med tidigare forskning gällande ämnesområdet. Samtliga lärares arbetssätt innehåller extra anpassningar för de här eleverna och största skillnaden som kunnat urskiljas mellan arbetssätten är huruvida de även innehåller särskilt stöd. Till viss del överensstämmer dessa uppfattningar även med tidigare forskning då det även där råder oenigheter om matematiskt särskilt begåvade elever ska differentieras eller inte.

• 7.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
Vill du spela bingo med mig?: En studie med laborativt material för att utveckla elevers kunskaper om positionssystemet2019Independent thesis Advanced level (degree of Master (Two Years)), 240 HE creditsStudent thesis

Studiens syfte är att med hjälp av en learning study med förtest och eftertest undersöka elevers förkunskaper om positionssystemet samt om elever genom laborativt material kan fördjupa sina kunskaper om positionssystemet. Studiens teoretiska utgångspunkt är hämtad från variationsteorin. Att arbeta med ett laborativt material möjliggör för eleverna att utveckla en utökad förståelse för positionssystemet med basen 10. En av slutsatserna från denna studie är att ett variationsteoretiskt perspektiv på undervisningen underlättar lärandet.

• 8.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
Motivation till matematik: En kvalitativ studie om hur elever i årskurs 4–6 kan motiveras i matematikundervisningen ur ett lärarperspektiv2019Independent thesis Advanced level (degree of Master (One Year)), 20 credits / 30 HE creditsStudent thesis

Syftet med denna studie är att undersöka hur lärare arbetar med att motivera elever i årskurs 4–6 i matematik. För att undersöka detta genomfördes klassrumsobservationer och semistrukturerade intervjuer med tre verksamma lärare i årskurs 4–6. Studiens resultat visar att en hög motivation hos eleverna skapas av tydliga strukturer i klassrummet, att läraren synliggör målen för eleverna, att läraren varierar sina arbetssätt och undervisningsformer samt att eleven tar ansvar för sitt eget lärande.

• 9.
Politecnico di Torino, Torino, Italy.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics. Politecnico di Torino, Torino, Italy.
Analysis of the surface impedance of a sinusoidally modulated metasurface2019In: 2019 International Conference on Electromagnetics in Advanced Applications (ICEAA), IEEE, 2019, p. 0075-0077Conference paper (Refereed)

Metasurfaces have been extensively exploited in recent years for mantle cloaking applications. In this type of problems it is of fundamental importance to determine the connection between the metasurface geometrical parameters and the realised value of surface impedance, in order to properly design the metasurface. In this paper the surface impedance of a non homogeneous metasurface, based on a sinusoidally modulated metallic pattern is analysed.

• 10.
Swinburne University of Technology.
Loughborough University. University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics. University of Agder. University of Agder.
"I'm still making dots for them": mathematics lecturers' views on their mathematical modelling practices2019In: International Journal of Mathematical Education in Science and Technology, ISSN 0020-739X, E-ISSN 1464-5211Article in journal (Refereed)

Using Cultural-Historical Activity Theory, we analyze lecturers’ views on the aims and teaching practices of mathematical modelling (MM) education in Norway and England. We aim to expose the tensions that exist within the activity of teaching MM at university, such as those between multiple, sometimes competing, aims for teaching MM, or between the lecturers’ professional identities and the structure of university degrees. Our conceptualization of these tensions might help lecturers consider how to overcome obstacles in their own contexts.

• 11.
Technion, Israel Institute of Technology.
University of the Witwatersrand. Haifa University. Levinsky College. Tel Aviv University. Rhodes University. Rhodes University. University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
Research Forum: Rituals and explorations in mathematical teaching and learning2019In: Proceedings: 43rd Annual Meeting of the International Group for the Psychology of Mathematics Education (Vol. 1) / [ed] Mellony Graven, Hamsa Venkat, Anthony A Essien and Pamela Vale, 2019, Vol. 1, p. 137-164Conference paper (Refereed)
• 12.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics. B. Verkin Institute for Low Temperature Physics and Engineering of NASU, 47 Nauky Ave., Kharkiv, 61103, Ukraine.
Derivation of cable equation by multiscale analysis for a model of myelinated axons2020In: Discrete and continuous dynamical systems. Series B, ISSN 1531-3492, E-ISSN 1553-524X, Vol. 25, no 3, p. 815-839Article in journal (Refereed)

We derive a one-dimensional cable model for the electric potential propagation along an axon. Since the typical thickness of an axon is much smaller than its length, and the myelin sheath is distributed periodically along the neuron, we simplify the problem geometry to a thin cylinder with alternating myelinated and unmyelinated parts. Both the microstructure period and the cylinder thickness are assumed to be of order ε, a small positive parameter. Assuming a nonzero conductivity of the myelin sheath, we find a critical scaling with respect to ε which leads to the appearance of an additional potential in the homogenized nonlinear cable equation. This potential contains information about the geometry of the myelin sheath in the original three-dimensional model.

• 13.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
Uppsala University. University of Warwick, Coventry, UK.
Phase transitions in long-range Ising models and an optimal condition for factors of g-measures2019In: Ergodic Theory and Dynamical Systems, ISSN 0143-3857, E-ISSN 1469-4417, Vol. 39, no 5, p. 1317-1330Article in journal (Refereed)

We weaken the assumption of summable variations in a paper by Verbitskiy [On factors of g-measures. Indag. Math. (N.S.) 22 (2011), 315-329] to a weaker condition, Berbee's condition, in order for a one-block factor (a single-site renormalization) of the full shift space on finitely many symbols to have a g-measure with a continuous g-function. But we also prove by means of a counterexample that this condition is (within constants) optimal. The counterexample is based on the second of our main results, where we prove that there is a critical inverse temperature in a one-sided long-range Ising model which is at most eight times the critical inverse temperature for the (two-sided) Ising model with long-range interactions.

• 14.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
Chevalley-Warnings sats om nollställemängder i projektiva rum över ändliga kroppar2020Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

I detta arbete studeras de aﬃna och projektiva rummen över ändliga kroppar för att vidare analysera polynom och nollställemängderna till dessa, över just ändliga kroppar. Djupgående kommer vi bland annat undersöka vilka ändliga kroppar som ﬁnns, studera polynom över dessa, deﬁniera vektorrum och konstruera det projektiva rummet. Chevalley-Warnings sats kommer vara ett huvudresultat och bevisas grundligt. Vi kommer även fördjupa vår studie något genom att studera projektiv geometri över ändliga kroppar. De ändliga kropparnas egenskaper, konstruering av projektiva rum, homogenisering av polynom och beviset till Chevalley-Warnings sats kommer vara nyckelresultat. Vi illustrerar resultaten genom att studera nollställemängderna till några enklare polynom.

• 15.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Biology.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
The school–university intersection as a professional learning arena: evaluation of a two-year action research project2019In: Teacher Development, ISSN 1366-4530, E-ISSN 1747-5120Article in journal (Refereed)
• 16.
Ambedkar Institute of Advanced Communication Technologies and Research (AIACTR), Delhi, India.
Amity School of Engineerng and Technology, Amity University, Noida, India. Netaji Subhash Institute of Technology (NSIT), N. Delhi, India. University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics. Russian Technological University, MIREA, Moscow, Russia.
Inverse Scattering and Imaging Using Second Order Optical Nonlinearities2019In: 2019 6th International Conference on Signal Processing and Integrated Networks, SPIN 2019, IEEE, 2019, p. 1086-1089Conference paper (Refereed)

In this paper a mathematical technique is developed to find the parameters of a medium in terms of its scattered electromagnetic fields. Optical nonlinearity plays an important role in finding the scattering parameters of a medium. Using perturbation theory and nonlinear inverse scattering techniques with first order, second order and third order optical nonlinearity we find scattered electromagnetic fields. Using error minimization techniques parameters are estimated in term of permittivity and permeability up to second order. © 2019 IEEE.

• 17.
Riga Technical University.
Riga Technical University. University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
Mechanically tunable coupled resonator waveguide bandpass filter2019In: 2019 IEEE Microwave Theory and Techniques in Wireless Communications (MTTW), 2019, Vol. 1, p. 52-56Conference paper (Refereed)

This paper proposes a novel mechanically tunable waveguide filter design, based on a coupled resonator topology. The resonator geometry consists of a rectangular waveguide cavity and a dielectric cylinder. Unlike conventional cylindrical resonators which are made out of a single part, here the cylinders are cut in half. By changing the distance between these two parts, the resonating frequency of the resonator can be changed, which allows for a tunable filter design. A filter using the proposed geometry has a large tuning bandwidth as well as relatively constant passband frequencies. The performance of the proposed filter is demonstrated by evaluating the filter using 3D simulation software CST Studio Suite.

• 18.
Riga Technical University, Latvia.
Riga Technical University, Latvia. Riga Technical University, Latvia. University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
Novel High-sensitivity Non-destructive Technique for the Measurement of Permittivity of a Low-loss Dielectric Slab in Free Space2019In: 2019 PhotonIcs & Electromagnetics Research Symposium - Spring (PIERS-Spring), 2019, p. 1723-1731Conference paper (Refereed)

In the present paper, the high-sensitivity technique for reducing the uncertainty of the free-space measurements of the real part of the permittivity of dielectric slab is proposed. The real part of the permittivity is extracted from the absolute value of the reflection coefficient measured by means of horn antenna. It is shown that making measurements for the slab under test (SUT) alone (original experimental model), in many cases results in large uncertainty because of low sensitivity of the model in the range of possible values of the real part of permittivity. The total measurement uncertainty depends on the slope of the measurement curve that can be used as a measure of the sensitivity of the model; consequently, to reduce it one has to increase the slope of the measurement curve that can be achieved by varying parameters of the model, such as the operating frequency or thickness of SUT. However, when the measurements are to be made in a non-destructive manner at a given frequency (in case of highly dispersive materials), neither frequency, nor thickness can be changed thus making it impossible to increase the slope of the measurement curve in the region of interest and, therefore, reduce the uncertainty. To overcome the problem we propose to extend the original model by introducing into it one or two auxiliary slabs (extended model) with known constitutive properties thereby extending the set of model parameters affecting the shape of the curve. Alternatively, with extended models one can achieve higher sensitivity without having to vary the frequency and thickness. Optimal choice of dimensions of auxiliary slab(s) is discussed in detail herein. The validity of the proposed method is verified through numerical experiments.

• 19.
Russian Technological University (MIREA), Moscow, Russia.
Russian Technological University (MIREA), Moscow, Russia. University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
Regression Methods of Obtaining Angular Superresolution2019In: 2019 URSI Asia-Pacific Radio Science Conference (AP-RASC), New Dehli: IEEE, 2019, article id 8738539Conference paper (Refereed)

New methods of signal processing based on nonlinear regression methods are presented. They allow us to restore images of individual objects of group targets with superresolution at signal-to-noise ratios that are significantly lower than those provided by the known methods.

• 20.
National Taras Shevchenko University, Kiev, Ukraine .
National Taras Shevchenko University, Kiev, Ukraine . University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
The Minimax Estimation Method for a Class of Inverse Helmholtz Transmission Problems2019In: Minimax Theory and its Applications, ISSN 2199-1413, Vol. 4, no 2, p. 305-328Article in journal (Refereed)

We present complete mathematical statements and perform detailed investigations of the minimax estimation problems of unknown data for the Helmholtz transmission problems from indirect noisy observations of their solutions. We construct optimal, in certain sense, estimates, which are called minimax mean-square estimates, of the values of linear functionals from unknown data. It is established that when unknown data and correlation functions of errors in observations belong to special sets, the minimax mean square estimates are expressed via solutions to certain transmission problems for systems of Helmholtz equations. We prove that these systems are uniquely solvable. Several possible generalizations of the techniques and results are proposed including applications to the problems with incomplete data and pointwise observations.

• 21.
School of Education and Lifelong Learning, University of East Anglia, Norwich, UK.
School of Education, Culture and Communication, Mälardalen University, Västerås, Sweden. Department of Mathematics and Science Education, Stockholm University, Stockholm, Sweden. University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics. Department of Mathematics, Karlstad University, Karlstad, Sweden.
Commognitive analyses of the learning and teaching of mathematics at university level: The case of discursive shifts in the study of Calculus2014In: Research in Mathematics Education, ISSN 1479-4802, E-ISSN 1754-0178, Vol. 16, no 2, p. 182-198Article in journal (Refereed)

In this paper we outline the main tenets of the commognitive approach and we exemplify its application in studies that investigate the learning and teaching of mathematics at university level. Following an overview of such applications, we focus on three studies that explore fundamental discursive shifts often occurring in the early stages of studying Calculus. These shifts concern the lecturers' and students' communicative practices, routines of constructing mathematical objects and ways of resolving commognitive conflicts. We then propose that commognitive constructs such as subjectification can be deployed towards 'scaling-up' the hitherto fine-grained focus of commognitive analyses. Finally, we conclude with observing how the commognitive approach relates to constructs from other sociocultural approaches to research in university mathematics education, such as "legitimate peripheral participation" from the theory of Communities of Practice and "didactic contract" from the Theory of Didactic Situations.

• 22.
Sergo Ordzhonikidze Russian State Geological Prospecting University, Moscow.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics. Lukoil. Lukoil.
Alternative concept of monitoring and optimization water flooding of oil reservoirs in the conditions of instability of the displacement front2019In: Neftânoe hozâjstvo, ISSN 0028-2448, Vol. 2019, no 12, p. 118-123Article in journal (Refereed)

It has always been an urgent issue for the oil and gas industry to improve oil, gas, and condensate recovery at liquid and gaseous hydrocarbon fields developed with the use of artificial formation pressure maintenance techniques that involve injection of water or water combined with other displacement agents. Therefore, due to the aforesaid issues, permanent attention should still be paid to the practical problem of optimizing the non-stationary hydrodynamic pressure applied to a reservoir by regulating the operating conditions of the production and injection wells, development process optimization in general, and water flooding in particular. The theory of Buckley and Leverett, does not take into account the loss of stability of the displacement front, which provokes a stepwise change and the triple value of water saturation. Traditionally a mathematically simplified approach was proposed-a repeatedly differentiable approximation to eliminate the “jump” in water saturation. Such a simplified solution led to negative consequences well-known from the water flooding practice, recognized by experts as “viscous instability of the displacement front” and “fractal geometry of displacement front”. The core of the issue is an attempt to predict the beginning of the stability loss of the front of oil displacement by water and to prevent its negative consequences on the water flooding process under difficult conditions of interaction of hydro-thermodynamics, capillary, molecular, inertial, and gravitational forces. In this study, catastrophe theory methods applied for the analysis of nonlinear polynomial dynamical systems are used as a novel approach. Namely, a mathematical growth model is developed and an inverse problem is formulated so that the initial coefficients of the system of differential equations for a two-phase flow can be deter mined using this model. A unified control parameter has been selected, which enables one to propose and validate a discriminant criterion for oil and water growth models for monitoring and optimizing.

• 23.
Lomonosov Moscow State University,Russia.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics. Lomonosov Moscow State University,Russia.
Stability of Least Squares for the Solution of an Ill-posed Inverse Problem of Reconstructing Real Value of the Pcrrnittivity of a Dielectric Layer in a Rectangular Waveguide2019In: 2019 PhotonIcs & Electromagnetics Research Symposium - Spring (PIERS-Spring), 2019, p. 1732-1738Conference paper (Refereed)

We use the solution to Maxwell's equations in a rectangular single-mode waveguide with multi-mode boundary conditions at its flanges to determine the parameters of the inclusion. The well-posedness of the inverse problem is studied using explicit expressions for the S-parameters of the waveguide when the inclusion is a plane-parallel dielectric slab. The methods of reconstructing permittivity from the measured (experimental) data must be stable and well-conditioned. The importance of these demands is discussed taking as an example the determination of real permittivity from noisy measurement data of the transmission coefficient of the principal waveguide mode. Generally, this problem is unsolvable because the range of the function to be inverted forms a set of measure zero on the complex plane. In addition, the occurrence of self-intersections of the parametric curve leads to non-uniqueness of the solution to the inverse problem. Therefore, approximate methods of the permittivity reconstruction in the vicinity of such points may be unstable or ill-conditioned. In our study, we present several examples of such algorithms. We demonstrate that the method of least squares applied for reconstructing permittivity of the inclusion from multi-frequency measurement data is a stable algorithm for the solution to this inverse problem. This approach does not use a priori estimates for the sought parameter and information about the location of singularities of the parametric curve. We determine the interval of variation of the condition number for the method of least squares and show that this quantity decreases as one of the following parameters increases: the width of the dielectric layer, the measurement frequency band, or its distance to the lower cutoff value. Using these results, we estimate the rate of convergence of the approximate solution to the exact value of the sought parameter when the quality of the measurement data is improved and show how to choose optimal parameters of the experiment and the measurement setup.

• 24.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
A General Approach to the Analysis of Complex Waves2019In: 2019 URSI International Symposium on Electromagnetic Theory (EMTS), 2019, p. 1-2Conference paper (Refereed)

We propose a technique for the search and calculation of complex waves in open and shielded circularly symmetric metal-dielectric waveguides with piecewise homogeneous filling by proving the existence and determination of the location of roots of the corresponding dispersion equations in the complex domain. The approach develops the method employing generalized cylindrical polynomials applied earlier to the rigorous analysis and determination of real waves.

• 25.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
Justification of mathematical imaging technique for the permittivity determination of layered dielectrics in a waveguide2019In: 2019 International Conference on Electromagnetics in Advanced Applications (ICEAA), 2019, p. 0143-0146Conference paper (Refereed)

An introduction to mathematical imaging technique for solving inverse scattering problems is given. Applications are considered to inverse waveguide problems of recontructing permittivity of layered dielectric inclusions. The solution is justified of the inverse microwave imaging by establishing one-to-one correspondence between the sought quantities and the measured noisy data.

• 26.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
On a Method of Solution to Dispersion Equations in Electromagnetics2019In: 2019 URSI Asia-Pacific Radio Science Conference (AP-RASC), New Dehli, 2019, article id 8738297Conference paper (Refereed)

A possible general approach to the analysis of dispersion equations (DEs) of electromagnetics is presented. The method takes into account the known explicit forms of DEs describing eigenoscillations and normal waves in layered structures and is based on the development of the notion of generalized cylindrical polynomials. The approach enables one to complete rigorous proofs of existence and determine domains of localization of the DE roots and validate iterative numerical solution techniques.

• 27.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
RCS Resonances for Canonical Structures2019In: 2019 IEEE International Conference on Microwaves, Antennas, Communications and Electronic Systems, COMCAS 2019, IEEE, 2019Conference paper (Refereed)

A brief survey is presented on the methods aimed at rigorous validation of the occurrence of complex RCS resonances for canonical structures: dielectric and perfectly conducting cylinders covered by layered media possessing circular symmetry. It is shown that the resonances are associated with singularities of the scattered field in the complex domain. © 2019 IEEE.

• 28.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
Trigonometric and cylindrical polynomials and their applications in electromagnetics2019In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504XArticle in journal (Refereed)

Development of the theory of trigonometric polynomials (TPs) is considered that involves generalization of the notion of TP and extension of the methods and results to cylindrical polynomials (CPs). On the basis of the proposed augmentation of TPs and CPs, a general approach is presented to the analysis of guided waves and resonances in electromagnetics and beyond. The method employs the known explicit forms of dispersion equations (DEs) describing eigenoscillations and normal waves in layered structures and is based on the development of the theory of generalized TPs and CPs performed in the study. The approach enables one to complete rigorous proofs of existence and determine domains of localization of the TP and CP zeros and the DE roots and validate iterative numerical solution techniques.

• 29.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
Mathematical methods for inverse waveguide problems2019In: 2019 IEEE Microwave Theory and Techniques in Wireless Communications  (MTTW). Proceedings, 2019Conference paper (Refereed)

An introduction is given to mathematical methods for inverse waveguide  problems. Applications are considered to the solution of the inverse  waveguide problems of reconstructing permittivity of layered dielectric  inclusions. It is shown that the existence and uniqueness can be justified by  establishing one-to-one correspondence between the sought quantities and the  measured noisy data.

• 30.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
Moscow Technological University MIREA, Moscow, Russia.
On Recent Findings in the Theory of Complex Waves in Open Metal-Dielectric Waveguides2018In: 2018 2ND URSI Atlantic Radio Science Meeting (AT-RASC), IEEE, 2018Conference paper (Refereed)

Theory of complex waves (see e.g. [1] and references therein) accumulated a big volume of results. However, its biggest drawback remains which brakes significantly the development of the theory: absence of rigorous proofs of the existence of complex waves. In this respect, studies of complex waves in open metal-dielectric waveguides has been essentially enhanced when two new families of symmetric (angle-independent) complex waves have been identified [2, 3] in a dielectric rod (DR) and Goubau line (GL) with homogeneous dielectric cover: surface complex waves occurring as perturbations of real surface waves caused by the presence of lossy dielectric, and pure complex waves which have no counterpart in the set of real waves. Existence of the latter family of complex waves has been shown using a special technique and the proof [3] of the existence of an infinite set of complex roots of the dispersion equation (DE) describing waves in DR and GL.

In this work, a development of the analytical and numerical methods [2, 3] are considered for the analysis of the electromagnetic wave propagation in metal-dielectric waveguides with multi-layered dielectric filling. The first step constitutes extension of the results obtained for symmetric complex waves in DR and GLto the case of non-symmetric (angle-dependent) waves, and the second step, to multi-layered dielectric covers. Both steps are accomplished using specific forms of DEs obtained in [3]by construction analytical continuation of the functions involved in DEs to multi-sheet Riemann surfaces of the spectral parameter and applying appropriate generalization the techniques [4]forfinding complex roots of the DEs.

Calculation ofnon-symmetric complex waves employs numerical solution of the DEs with the help of parameter differentiation in the complex domain using multi-parameter setting and analysis of implicit functions of several complex variables [5] and reduction [2, 3] to numerical solution of auxiliary Cauchy problems.

1. A. S. Raevskiiand S. B. Raevskii, Complex Waves, Radiotekhnika, Moscow, 2010.

2. E. Kuzmina and Y. Shestopalov, “Waves in a lossyGoubau line,”10th European Conf. on Antennas and Propagation (EuCAP), Davos, Switzerland, 2016, doi: 10.1109/EuCAP.2016.7481368.

3. E. Kuzmina and Y. Shestopalov, “Complex waves in a dielectric rod and Goubau line,” 19th Int. Conf. on Electromagneticsin Advanced Applications (ICEAA), Verona, Italy, 2017, pp. 963-966, doi: 10.1109/ICEAA.2017.8065417.

4. Y. Shestopalov, “Resonant states in waveguide transmission problems,”PIER B,64: pp.119-143, 2015, doi: 10.2528/PIERB15083001.

5.Y. Shestopalov,“On unique solvability of multi-parameter waveguide inverse problems, ”19th Int. Conf. on Electromagnetics in Advanced Applications (ICEAA), Verona, Italy, 2017, pp. 372-376, doi: 10.1109/ICEAA.2017.8065253.

• 31.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
Russian State Geological Prospecting University, Moscow, 117997 Russia.
Qualitative Analysis of Quadratic Polynomial Dynamical Systems Associated with the Modeling and Monitoring of Oil Fields2019In: Lobachevskii Journal of Mathematics, ISSN 1995-0802, E-ISSN 1818-9962, Vol. 40, no 10, p. 1695-1710Article in journal (Refereed)

The behavior and properties of solutions of two-dimensional quadratic polynomial dynamical system on the phase plane of variables and time are considered. A complete qualitative theory is constructed which includes the analysis of all singular points and the features of solutions depending on all parameters of the problem. A main result is that, with the discriminant criteria created on the basis of the growth model constructed in the present study, it is possible to formulate practical recommendations for regulating and monitoring the process of waterflooding and the development of an oil field.

• 32.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
S. Ordzhonikidze Russian State Geological Prospecting University, Moscow, Russia. LUKOIL, PJSC, Moscow, Russia. LUKOIL, Western Siberia, Kogalym, Russia.
Alternative conception of the monitoring and optimization of water flooding of oil reservoirs  under instability of displacement front2019In: Oil industry (Neftyanoye khozyaystvo), ISSN 0028-2448, no 12, p. 118-123Article in journal (Refereed)

The theory of Buckley and Leverett does not take into account the loss of stability of the displacement front whch provokes a stepwise change and the triple value of water saturation. Traditionally a mathematically simplified approach was proposed: a differentiable approximation to eliminate the ' jump' in water saturation. Such a simplified solution led to negative consequences well-know from the water flooding practice, recognized by experts as 'viscous instability of the displacement front' and 'fractal geometry of the displacement front'.The core of the issue is to attempt to predict the beginning of the stability loss of the front of oil displacement by water and to prevent its negative effect on the water flooding process under difficult conditions of interaction of hydro-thermodynamic, capillary, molecular, inertial, and gravitational forces. In this study, catastrophe theory methods applied for the analysis of nonlinear polynomial dynamical systems are used as a novel approach. namely, a mathematical growth model is developed and an inverse problem is formulated so that the initial coefficients of the system of differential equations for a two-phase flow can be determined using this model. A unified control parameter has been selected which enables one to propose and validate a discriminant criterion for  oil and water growth models for monitoring and optimization.

• 33.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
Department of Mathematics and Supercomputing, Penza State University, Krasnaya Str. 40, Penza, 440026, Russia.
On the existence of the nonlinear leaky TE-polarized waves in a metal–dielectric cylindrical waveguide2019In: Wave motion, ISSN 0165-2125, E-ISSN 1878-433X, Vol. 91, article id 102378Article in journal (Refereed)

We consider propagation of leaky waves in the Goubau line (a perfectly conducting cylinder covered by a concentric dielectric layer) filled with nonlinear inhomogeneous medium. The problem is reduced to the analysis of a nonlinear integral equation with a kernel in the form of the Green’s function of an auxiliary boundary value problem on an interval. The existence of propagating nonlinear leaky waves for the chosen nonlinearity (Kerr law) is proved using the method of contraction. Conditions under which a finite number of waves can propagate are obtained and the intervals of localization of the corresponding propagation constants are determined. For the numerical solution, a method based on solving an auxiliary Cauchy problem (a version of the shooting method) is proposed. In numerical experiments, two types of nonlinearities are considered and compared: Kerr nonlinearity and nonlinearity with saturation. New propagation regimes are discovered.

• 34.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
Department of Mathematics and Supercomputing, Penza State University, Penza, Russia. Department of Mathematics and Supercomputing, Penza State University, Penza, Russi.
New Propagation Regimes of TE Waves in a Waveguide filled with a Nonlinear Dielectric Metamaterial2019In: 2019 URSI Asia-Pacific Radio Science Conference (AP-RASC), New Dehli: IEEE, 2019, article id 8738241Conference paper (Refereed)

We consider propagation of surface TE waves in a circular metal-dielectric waveguide filled with nonlinear (Kerr nonlinearity) metamaterial medium. Analysis is reduced to solving a nonlinear transmission eigenvalue problem for an ordinary differential equation; eigenvalues of the problem correspond to propagation constants of the waveguide. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

• 35.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
New propagation regimes of TM waves in a waveguide filled with a nonlinear dielectric metamaterial2019In: 2019 URSI International Symposium on Electromagnetic Theory, EMTS 2019, 2019Conference paper (Refereed)

We consider propagation of surface TM waves in a circular metal-dielectric waveguide filled with nonlinear (Kerr nonlinearity) metamaterial medium. Analysis is reduced to solving a nonlinear transmission eigenvalue problem for an ordinary differential equation; eigenvalues of the problem correspond to propagation constants of the surface waves. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

• 36.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
Penɀa State University, Penza, Russia. Penɀa State University, Penza, Russia.
Numerical study of nonlinear metamaterial rod2019In: 2019 International Conference on Electromagnetics in Advanced Applications (ICEAA), 2019, p. 0162-0164Conference paper (Refereed)

We consider propagation of leaky and surface TE waves in the rod filled with nonlinear metamaterial medium. The physical setting is reduced to a transmission eigenvalue problem for an ordinary differential equation. The eigenvalues of the problem are the wave propagation constants. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

• 37.
Department of Mathematics and Supercomputing, Penza State University, Russian Federation.
Department of Mathematics and Supercomputing, Penza State University, Russian Federation. University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
Diffraction of a TE-Polarized Wave by a Nonlinear Goubau Line2019In: Radio Science, ISSN 0048-6604, E-ISSN 1944-799X, Vol. 54, no 1, p. 151-157Article in journal (Refereed)

The diffraction of a cylindrical wave by a nonlinear metal-dielectric waveguide filled with nonlinear medium is considered. Two widely used types of nonlinearities (Kerr nonlinearity and nonlinearity with saturation) are considered. The problem is to find amplitudes of the reflected and the transmitted fields when the amplitude of the incident field is known. The analytical and numerical solution techniques are developed. Numerical results are presented. ©2019. American Geophysical Union. All Rights Reserved.

• 38.
Macquarie University, Sydney, Australia.
Macquarie University, Sydney, Australia. University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
Accurate cutoff wavenumbers of a waveguide perturbed by axially aligned inner conductors2019In: 2019 International Conference on Electromagnetics in Advanced Applications (ICEAA), 2019, p. 1049-1049Conference paper (Refereed)

Time-harmonic propagating modes in a perfectly electrically conducting waveguide with constant cross-section $\partial \mathrm{D}$ and axis aligned with the z-axis have the form $\mathrm{u}(\mathrm{x},\mathrm{y})\mathrm{e}^{-\mathrm{i}\omega \mathrm{t}-\mathrm{i}\gamma\mathrm{z}}$ where the cross-sectional function u satisfies the two-dimensional Helmholtz equation $(\Delta+\lambda)\mathrm{u}=0$; here $k$ denotes the wavenumber and $\lambda=\mathrm{k}^{2}-\gamma^{2}$. Propagating modes occur at values $\lambda_{1}\leq\lambda_{2}\leq\lambda_{3}\leq\cdots$ of $\lambda$ generating non-trivial solutions of the Helmholtz equation; the cutoff wavenumbers correspond to setting $\gamma$ to zero. Now suppose that axially aligned PEC structures of cross-section $\Gamma$ are inserted in the waveguide. The propagation constants are perturbed to values that may be denoted $\lambda_{1}+\Delta\lambda_{1},\lambda_{2}+\Delta\lambda_{2},\ldots$; the cutoff wavenumbers of the empty waveguide are correspondingly perturbed. In this paper we present a reliable, effective and efficient method to obtain the perturbed propagation constants. It allows us to examine the inclusion of multiple strips aligned with the z-axis, with the potential for characterizing propagation in structures with a number of small strip inserts, metamaterial-filled waveguides and so on.

• 39.
Penza State University, Russia.
Penza State University, Russia. University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
Hybrid Waves in a Cylindrical Anisotropic Inhomogeneous Metal-dielectric Waveguide2019In: 2019 PhotonIcs & Electromagnetics Research Symposium - Spring (PIERS-Spring), 2019, p. 1757-1764Conference paper (Refereed)

The propagation of hybrid waves in a cylindrical anisotropic inhomogeneous nonlinear metal-dielectric waveguide is considered. The physical setting is reduced to a transmission eigenvalue problem for a system of ordinary differential equations which is new type of nonlinear eigenvalue problem where spectral parameters are the wave propagation constants. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

• 40.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics. MatRIC, University of Agder, Kristiansand, Norway.
School of Education, University of East Anglia, Norwich, UK.
Negotiating different disciplinary discourses: Biology students’ ritualized and exploratory participation in mathematical modelling activities2019In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 101, no 2, p. 233-252Article in journal (Refereed)

Non-mathematics specialists’ competence and confidence in mathematics in their disciplines have been highlighted as in need of improvement. We report from a collaborative, developmental research project which explores the conjecture that greater integration of mathematics and biology in biology study programs, for example through engaging students with Mathematical Modeling (MM) activities, is one way to achieve this improvement. We examine the evolution of 12 first-semester biology students’ mathematical discourse as they engage with such activities in four sessions which ran concurrently with their mandatory mathematics course and were taught by a mathematician with extensive experience with MM. The sessions involved brief introductions to different aspects of MM, followed by small-group work on tasks set in biological contexts. Our analyses use the theory of commognition to investigate the tensions between ritualized and exploratory participation in the students’ MM activity. We focus particularly on a quintessential routine in MM, assumption building: we trace attempts which start from ritualized engagement in the shape of “guesswork” and evolve into more productively exploratory formulations. We also identify signs of persistent commognitive conflict in the students’ activity, both intra-mathematical (concerning what is meant by a “math task”) and extra-mathematical (concerning what constitutes a plausible solution to the tasks in a biological sense). Our analyses show evidence of the fluid interplay between ritualized and exploratory engagement in the students’ discursive activity and contribute towards what we see as a much needed distancing from operationalization of the commognitive constructs of ritual and exploration as an unhelpfully dichotomous binary.

• 41.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics. MatRIC, University of Agder, Norway.
University of East Anglia.
Ritualised and exploratory graphing routines in mathematical modelling: The Digoxin task2018In: Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education (Vol. 1) / [ed] Ewa Bergqvist, Magnus Österholm, Carina Granberg, and Lovisa Sumpter, 2018, Vol. 4, p. 363-370Conference paper (Refereed)

The project we report from in this paper explores whether and how, biology students’ competence and confidence in – as well as appreciation for – mathematics in their discipline can be improved through greater integration of mathematics and biology in their study programme. Here, we examine biology students’ mathematical discourse as they engage with a biology-related Mathematical Modelling (MM) activity, the Digoxin task. We report commognitive analyses of data collected during sessions in which biology-related MM activities were introduced to undergraduate biology students (four sessions with 12 first-semester students).We focus on the interplay between students’ ritualised and exploratory engagement with the activity, particularly concerning graphing routines, and consider pedagogical implications.

• 42.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
What to do when there is no formula? Navigating between less and more familiar routines for determining velocity in a calculus task for engineering students.2019In: Calculus in upper secondary and beginning university mathematics – Conference proceedings. Kristiansand, Norway: MatRIC / [ed] J. Monaghan, E. Nardi and T. Dreyfus, 2019, p. 167-170Conference paper (Refereed)
• 43.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics. University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics. University of Gävle, Faculty of Engineering and Sustainable Development, Department of Industrial Development, IT and Land Management, Computer science.
Programming in mathematics teacher education: A collaborative teaching approach2018Conference paper (Refereed)
• 44.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm, Sweden.
New g-formula for the sequential causal effect and blip effect of treatment in sequential causal inference2020In: Annals of Statistics, ISSN 0090-5364, E-ISSN 2168-8966, Vol. 48, no 1, p. 138-160Article in journal (Refereed)

In sequential causal inference, two types of causal effects are of practical interest, namely, the causal effect of the treatment regime (called the sequential causal effect) and the blip effect of treatmenton on the potential outcome after the last treatment. The well-known G-formula expresses these causal effects in terms of the standard paramaters. In this article, we obtain a new G-formula that expresses these causal effects in terms of the point observable effects of treatments similar to treatment in the framework of single-point causal inference. Based on the new G-formula, we estimate these causal effects by maximum likelihood via point observable effects with methods extended from single-point causal inference. We are able to increase precision of the estimation without introducing biases by an unsaturated model imposing constraints on the point observable effects. We are also able to reduce the number of point observable effects in the estimation by treatment assignment conditions.

• 45.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
Det behövs ett nytt verktyg för att reparera bristande baskunskaper i matematik: En studie om Elevate My Math´s effekter hos svensla gymnasieelever2019Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis

Mätningar av kunskaperna inom matematik hos svenska elever har under en längre tid visat på en nedåtgående trend. Samtidigt läser vi dagligen om den svenska lärarkårens höga arbetsbelastning. Syftet med det här examensarbetet är att undersöka en hållbar lösning, som både vänder den nedåtgående kunskapstrenden hos eleverna och dessutom underlättar lärarnas arbete. I Examensarbetet undersöks elevernas upplevelser samt kunskapsutveckling då de  arbetar med det digitala verktyget Elevate My Math.

Undersökningen, som är både kvantitativ och kvalitativ görs i en ekonomiklass där halva klassen får arbeta med Elevate My Math och den andra halvan får jobba med ett material som vanligtvis används inom undervisningen. Resultaten visar att eleverna upplevelse av att arbeta med Elevate My Math är mycket positiv. Samtidigt visar resultatet att vidare forskning behövs för att säkerställa elevernas kunskapsutveckling vid användandet av Elevate My Math.

• 46.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics. 19881121-1542.
Lärares syn och attityd på användandet av digitala verktyg inom matematikämnet2019Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
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