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• 1.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
Department of Mathematics, University of Bristol, Bristol, United Kingdom. Department of Mathematics, Uppsala Universitet, Uppsala, Sweden. Mathematics Institute, University of Warwick, Coventry, United Kingdom.
Multifractal analysis of non-uniformly hyperbolic systems2010In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 177, no 1, p. 125-144Article in journal (Refereed)

We prove a multifractal formalism for Birkhoff averages of continuous functions in the case of some non-uniformly hyperbolic maps, which includes interval examples such as the Manneville-Pomeau map.

• 2.
University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik.
Square summability of variations of g-functions and uniqueness of g-measures2003In: Mathematical Research Letters, ISSN 1073-2780, E-ISSN 1945-001X, Vol. 10, no 5, p. 587-601Article in journal (Refereed)

We prove uniqueness of $g$-measures for $g$-functions satisfying quadratic summability of variations. Our result is in contrast to the situation of, \eg, the one-dimensional Ising model with long-range interactions, since $\ell_1$-summability of variations is required for general potentials. We illustrate this difference with some examples. To prove our main result we use a product martingale argument. We also give conditions for uniqueness of general $G$-measures, \ie, the case for general potentials, based on our investigation of the probabilistic case involving $g$-functions.

• 3.
University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik.
Department of Mathematics, Uppsala University, Uppsala, Sweden. Mathematics Institute, University of Warwick, Coventry, United Kingdom.
Countable state shifts and uniqueness of g-measures2007In: American Journal of Mathematics, ISSN 0002-9327, E-ISSN 1080-6377, Vol. 129, no 6, p. 1501-1511Article in journal (Refereed)

In this paper we present a new approach to studying $g$-measures which is based upon local absolute continuity. We extend an earlier result that square summability of variations of $g$ ensures uniqueness of $g$-measures. The first extension is to the case of countably many symbols. The second extension is to some cases where $g \geq 0$, relaxing the earlier requirement that $\inf g>0$.

• 4.
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.

• 5.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics. Uppsala University, Department of Mathematics.
Uppsala University, Department of Mathematics. University of Warwick, Mathematics Institute.
Unique Bernoulli g-measures2012In: Journal of the European Mathematical Society (Print), ISSN 1435-9855, E-ISSN 1435-9863, Vol. 14, no 5, p. 1599-1615Article in journal (Refereed)

We improve and subsume the conditions of Johansson and Öberg and Berbee for uniqueness of a g-measure, i.e., a stationary distribution for chains with complete connections. In addition, we prove that these unique g-measures have Bernoulli natural extensions. We also conclude that we have convergence in the Wasserstein metric of the iterates of the adjoint transfer operator to the g-measure.

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• 6.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Industrial Development, IT and Land Management, Industrial economics.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Industrial Development, IT and Land Management, Industrial economics.
Faktorer kring äldres måltidssituation och deras påverkan på lönsamhet: Innovativa lösningar genom offentlig upphandling2016Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

The purpose of this study was to examine how innovative solutions within public procurement concerning the elderly with aid decisions affect well-being and economic performance. Many decisions concerning human resources are taken without consideration for its economic effect. This means that measures to achieve improvement in this area are only seen as economic costs for organizations instead of investments since the positive effects on profitability is not calculated. To be able to predict the profitability of measures concerning human resources, there is a need to be able to measure the economic impact of these actions and then get a picture of the total costs of their implementation. In Söderhamns municipality, the distribution of food supplies to the elderly living at home in Trönö/Norrala was transferred to a private company. To measure the impact of this action empirical was data gathered from the municipality concerning current expenses and the nutritional status of the elderly. Interviews and own calculations were made in order to estimate costs that the municipality did not have in its own calculations. The results of this study showed a trend towards increased well-being of the elderly, which could mean a cost reduction in medical costs in the future. The private company that now handles the food distribution also hired more staff, which leads to increased tax revenue for the municipality. Even with these factors, the total cost of the new system is still higher than the old system. However, these factors do mean a lower total cost compared to previous cost estimates of the municipality for the new system. To get a more accurate picture of the total costs off this action more extensive calculations is required. However, this study is a step forward in how these kinds of actions can be measured financially in a way that sees more to how they affect society as a whole instead of just its affect in certain areas.

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• 7.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science.
Ramification points of parameterized second-order polynomials and determination of zeros of generalized trigonometric and cylindrical polynomials2020Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

We consider the parameter dependence of zeros of polynomials and particularly the properties of the ramication points of second-order (quadratic) polynomials. The results are applied to the analysis of real and complex zeros of a particular set of generalized cylindrical polynomials in order to study resonance scattering of electromagnetic waves by a circular dielectric cylinder.

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• 8.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences.
The Dirichlet Series To The Riemann Hypothesis2018Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

This paper examines the Riemann zeta-function and its relation to the prime distribution. In this work, I present the journey from the Dirichlet series to the Riemann hypothesis. Furthermore, I discuss the prime counting function, the Riemann prime counting function and the Riemann explicit function for distribution of primes. This paper explains that the non-trivial zeros of the zeta-function are the key to understand the prime distribution.

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• 9.
T. Shevchenko Kyiv National University, Kyiv, Ukraine.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
Mixed variational approach to finding guaranteed estimates from solutions and right-hand sides of the second-order linear elliptic equations under incomplete data2016In: Minimax Theory and its Applications, ISSN 2199-1413, Vol. 1, no 2, p. 197-244Article in journal (Refereed)

We investigate the problem of guaranteed estimation of values of linear continuous functionals defined on solutions to mixed variational equations generated by linear elliptic problems from indirect noisy observations of these solutions. We assume that right-hand sides of the equations, as well as the second moments of noises in observations are not known; the only available information is that they belong to given bounded sets in the appropriate functional spaces. We are looking for linear with respect to observations optimal estimates of solutions of aforementioned equations called minimax or guaranteed estimates. We develop constructive methods for finding these estimates and estimation errors which are expressed in terms ofsolutions to special mixed variational equations and prove that Galerkin approximations of the obtained variational equations converge to their exact solutions. We study also the problem of guaranteed estimation of right-hand sides of mixed variational equations.

• 10.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
On a spectrum of complex waves in open metal-dielectric waveguides [О спектре комплексных волн в открытых металлических диэлектрических волноводах]2018In: Современные методы теории краевых задач: материалы международной конференции, посвящённой 90-летию Владимира Александровича Ильина (2-6 мая 2018 г., Москва): Понтрягинские чтения - XXIX / [ed] Budak Alexander Borisovich [Будак Александр Борисович], Moscow: Moscow State University Press , 2018, p. 243-244Conference paper (Refereed)
• 11.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
Resonant states in forward and inverse waveguide scattering problems2015In: Proceedings of the 2015 International Conference on Electromagnetics in Advanced Applications: ICEAA 2015, IEEE Press, 2015, p. 31-34Conference paper (Refereed)

It is shown that the transmission coefficient of parallel-plane multi-sectional dielectric diaphragms in a waveguide of rectangular cross section has singularities in the complex plane of the longitudinal wavenumber of each section and the singularities are associated with resonant states of the transmission problem.

• 12.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
Penza State University, Penza, Ryssland.
Advanced mathematical techniques  for the analysis of inverse scattering  in waveguides2014In: Proceedings of the 7th International Conference Inverse Problems: Modeling and Simulation (IPMS 2014): Ölüdeniz, Fethiye, Turkey, May 22–30,2014 / [ed] A. Hasanov, 2014, p. 32-Conference paper (Refereed)
• 13.
Penza State University, Penza, Ryssland.
Eigenwaves in Waveguides with Dielectric Inclusions : Spectrum2014In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 93, no 2, p. 408-427Article in journal (Refereed)

We consider fundamental issues of the mathematical theory of the wave propagation in waveguides with inclusions. Analysis is performed in terms of a boundary eigenvalue problem for the Maxwell equations which is reduced to an eigenvalue problem for an operator pencil. We formulate the definition of eigenwaves and associated waves using the system of eigenvectors and associated vectors of the pencil and prove that the spectrum of normal waves forms a non-empty set of isolated points localized in a strip with at most finitely many real points.

• 14.
Penza State University, Penza, Ryssland.
Eigenwaves in waveguides with dielectric inclusions: completeness2014In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 93, no 9, p. 1824-1845Article in journal (Refereed)

We formulate the definition of eigenwaves and associated waves in a nonhomogeneously filled waveguide using the system of eigenvectors and associated vectors of a pencil and prove its double completeness with a finite defect or without a defect. Then, we prove the completeness of the system of transversal components of eigenwaves and associated waves as well as the ‘mnimality’ of this system and show that this system is generally not a Schauder basis. This work is a continuation of the paper Eigenwaves in waveguides with dielectric inclusions: spectrum. Appl. Anal. 2013. doi:10.1080/00036811.2013.778980 by Y. Smirnov and Y. Shestopalov. Therefore, we omit the problem statements and all necessary basic definitions given in the previous paper.

• 15.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
Macquarie University, Sydney, Australia. Macquarie University, Sydney, Australia.
The effect of inserts upon propagation modes in a waveguide2018In: Proceedings of 2018 International Conference on Electromagnetics in Advanced Application (ICEAA), Piscataway, New Jersey, USA: IEEE, 2018, p. 315-318, article id 8520404Conference paper (Refereed)

When a perfectly electrically conducting (PEC) waveguide is perturbed by the insertion of a PEC structure aligned with its axis, its propagation constants are perturbed. The underlying boundary value problem may be converted to a homogeneous Fredholm matrix equation in which the propagation constants are found from the roots of the determinant of the matrix; stable and numerically efficient processes may be employed to find the propagation constants. There is no constraint on the size or shape of the inserts. As well as determining the empty waveguide parameters, this approach provides an estimate of the perturbation to the propagation constants of the empty waveguide.

• 16.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
Resonant states in waveguide transmission problems2015In: Progress in Electromagnetics Research B, ISSN 1937-6472, E-ISSN 1937-6472, Vol. 64, no 1, p. 119-143Article in journal (Refereed)

We prove the existence of complex eigenfrequencies of open waveguide resonators in the form of parallel-plate waveguides and waveguides of rectangular crosssection containing layered dielectric inclusions. It is shown that complex eigenfrequencies are finite-multiplicity poles of the analytical continuation of the operator of the initial diffraction problem and its Green's function to a multi-sheet Riemann surface, and also of the transmission coefficient extended to the complex plane of some of the problem parameters. The eigenfrequencies are associated with resonant states (RSs) and eigenvalues of distinct families of Sturm-Liouville problems on the line; they form countable sets of points in the complex plane with the only accumulation point at infinity and depend continuously on the problem parameters. The set of complex eigenfrequencies is similar in its structure to the set of eigenvalues of a Laplacian in a rectangle. The presence of a resonance domain in the form of a parallel-plane layered dielectric insert removes the continuous frequency spectrum and gives rise to a discrete set of points shifted to (upper half of) the complex plane.

• 17.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
Resonant states in waveguide transmission problems2015In: 2015 1st URSI Atlantic Radio Science Conference (URSI AT-RASC), New York: Institute of Electrical and Electronics Engineers (IEEE), 2015Conference paper (Refereed)

We prove the existence of complex eigenfrequencies of open waveguide resonators in the form of parallel-plate waveguides and waveguides of rectangular crosssection containing layered dielectric inclusions. It is shown that complex eigenfrequencies are finite-multiplicity poles of the analytical continuation of the operator of the initial diffraction problem and its Green's function to a multi-sheet Riemann surface, and also of the transmission coefficient extended to the complex plane of some of the problem parameters. The eigenfrequencies are associated with resonant states (RSs) and eigenvalues of distinct families of Sturm-Liouville problems on the line; they form countable sets of points in the complex plane with the only accumulation point at infinity and depend continuously on the problem parameters. The set of complex eigenfrequencies is similar in its structure to the set of eigenvalues of a Laplacian in a rectangle. The presence of a resonance domain in the form of a parallel-plane layered dielectric insert removes the continuous frequency spectrum and gives rise to a discrete set of points shifted to (upper half of) the complex plane.

• 18.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
T. Shevchenko Kyiv National University, Kyiv, Ukraine. T. Shevchenko Kyiv National University, Kyiv, Ukraine.
Estimation of Parameters of Boundary Value Problems for Linear Ordinary Differential Equations with Uncertain Data2014In: Advances in Pure Mathematics, ISSN 2160-0368, E-ISSN 2160-0384, Vol. 4, no 4, p. 118-146Article in journal (Refereed)

In this paper we construct optimal, in certain sense, estimates of values of linear functionals on solutions to two-point boundary value problems (BVPs) for systems of linear first-order ordinary differential equations from observations which are linear transformations of the same solutions perturbed by additive random noises. It is assumed here that right-hand sides of equations and boundary data as well as statistical characteristics of random noises in observations are not known and belong to certain given sets in corresponding functional spaces. This leads to the necessity of introducing minimax statement of an estimation problem when optimal estimates are defined as linear, with respect to observations, estimates for which the maximum of mean square error of estimation taken over the above-mentioned sets attains minimal value. Such estimates are called minimax mean square or guaranteed estimates. We establish that the minimax mean square estimates are expressed via solutions of some systems of differential equations of special type and determine estimation errors.

• 19.
Lomonosov Moscow State University, Russia.
Lomonosov Moscow State University, Russia. Lomonosov Moscow State University, Russia. University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
Absorbing boundary conditions for FDTD analysis of rectangular waveguide with non-uniform dielectric inclusions2015In: 2015 1st URSI Atlantic Radio Science Conference (URSI AT-RASC), New York: Institute of Electrical and Electronics Engineers (IEEE), 2015Conference paper (Refereed)

When the finite-difference time-domain method is used for analysis of waveguide structures, incident waves are needed for calculating electromagnetic parameters and effective absorbing boundary conditions are required for terminating open waveguide structures.

• 20.
Lomonosov Moscow State University, Russian Federation .
Lomonosov Moscow State University, Russian Federation . University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics. Lomonosov Moscow State University, Russian Federation .
Numerical simulation of a nonuniform dielectric inclusion in a waveguide aimed at reconstructing its permittivity2015In: Proceedings of the 2015 International Conference on Electromagnetics in Advanced Applications: ICEAA 2015, IEEE Press, 2015, p. 419-421Conference paper (Refereed)

We consider numerical determination of the dielectric media parameters of inclusions in a waveguide of rectangular cross-section from the transmission coefficient. We develop and apply computer codes implementing the FDTD algorithm for nonstationary Maxwell’s equations with perfectly matched layer (PML) absorbing boundary conditions using the Berenger layout and estimate parameter ranges providing the prescribed accuracy for solving forward and inverse scattering problems for waveguides with inclusions.

• 21.
Penza State University, Penza, Ryssland.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics. Penza State University, Penza, Russia.
Solution to the Inverse Problem of Reconstructing Permittivity of an n-Sectional Diaphragm in a Rectangular Waveguide2014In: Algebra, Geometry and Mathematical Physics: AGMP, Mulhouse, France, October 2011, Springer Berlin/Heidelberg, 2014, Vol 85, p. 555-566Conference paper (Refereed)

We have developed a numerical-analytical method of solution to the inverse problem of reconstructing permittivities ofn-sectional diaphragms in a waveguide of rectangular cross section. For a one-sectional diaphragm, a solution in the closed form is obtained and the uniqueness is proved.

• 22.
Tomas Bata University in Zlin, Zlin, Czech Republic .
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics. Tomas Bata University in Zlin, Zlin, Czech Republic .
Comparison of selected evolutionary techniques used in reconstruction of permittivity2015In: Proceedings of the 2015 International Conference on Electromagnetics in Advanced Applications: ICEAA 2015, IEEE conference proceedings, 2015, p. 614-617, article id 7297189Conference paper (Refereed)

This work aims at comparison of some traditional evolutionary algorithms (GA, DE, PSO) used in the computation and optimization of transmission coefficients of waveguide filters and in the estimation of the permittivity formed by multi-sectional diaphragms in a waveguide of rectangular cross-section.

• 23.
Tomas Bata University in Zlin, Zlin, Czech Republic .
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics. Tomas Bata University in Zlin, Zlin, Czech Republic .
Reconstruction of permittivity of multiple layers in free space2015In: Proceedings of the 2015 International Conference on Electromagnetics in Advanced Applications: ICEAA 2015, IEEE conference proceedings, 2015, p. 610-613Conference paper (Refereed)

The goal of this theoretical study is the improvement of the techniques of determining electromagnetic permittivity. However, it may be developed and applied for the reconstruction of other parameters. The work is aimed at the preliminary design and implementation of a system solving inverse problem of reconstruction permittivities of materials consisting of several dielectric layers based on real measurements of the transmission and reflection coefficients in free space.

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