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• 51.
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
Thin Sheet Modeling Using Shell Elements in the Finite-Element Time-Domain Method2006Inngår i: IEEE Transactions on Antennas and Propagation, ISSN 0018-926X, E-ISSN 1558-2221, Vol. 54, s. 28-34Artikkel i tidsskrift (Fagfellevurdert)
• 52.
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
Waveguide Truncation Using UPML in the Finite-Element Time-Domain Method2005Rapport (Annet vitenskapelig)
• 53.
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
A General Approach for Time-Domain Simulation of Waveguides in 3D2004Inngår i: Proc. EMB 04, Computational Electromagnetics: Methods and Applications, Göteborg, Sweden: Department of Electromagnetics, Chalmers University of Technology , 2004, s. 220-226Konferansepaper (Annet vitenskapelig)
• 54.
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
Modeling of inhomogeneous waveguides using hybrid methods2005Manuskript (preprint) (Annet vitenskapelig)
• 55.
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
Solving inverse electromagnetic problems using FDTD and gradient-based minimization2006Inngår i: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 68, s. 650-673Artikkel i tidsskrift (Fagfellevurdert)
• 56. Abenius, Erik
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
Inverse Electromagnetic Scattering Using the Finite-Difference Time-Domain Method2000Inngår i: Proc. Millennium Conference on Antennas and Propagation, Noordwijk, The Netherlands: ESA Publications , 2000, s. 4-Konferansepaper (Fagfellevurdert)
• 57.
Högskolan i Gävle, Institutionen för matematik, natur- och datavetenskap.
Outdoor Education in Mathematics: Can it be implemented?2008Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave

This study examines outdoor education in mathematics at an international school under the IB PYP curriculum. Students spend most of their time indoors with the exception of lunch recess. Outdoor education provides a new and different way for both teachers and students to get fresh air. Research indicates that children who spend more time outdoors suffer less from allergies and other health problems. In the study, teachers and parents were given questionnaires, and three mathematics lessons were conducted outdoors.  Students were later interviewed in groups. Most parents and teachers were positive to the idea of academic outdoor lessons in any subject. Teachers saw some difficulties implementing it because of time, weather and behavioural problems with students outside. Furthermore, they agreed that children should spend more time outside and that the children’s health might benefit. Most of the students enjoyed the outdoor mathematics lessons. They were positive towards outdoor education in any subject.

• 58.
Weaknesses of Authentication in Quantum Cryptography and Strongly Universal Hash Functions2010Licentiatavhandling, med artikler (Annet vitenskapelig)

Authentication is an indispensable part of Quantum Cryptography, which is an unconditionally secure key distribution technique based on the laws of nature. Without proper authentication, Quantum Cryptography is vulnerable to “man-in-the-middle” attacks. Therefore, to guarantee unconditional security of any Quantum Cryptographic protocols, the authentication used must also be unconditionally secure. The standard in Quantum Cryptography is to use theWegman-Carter authentication, which is unconditionally secure and is based on the idea of universal hashing.

In this thesis, we first investigate properties of a Strongly Universal hash function family to facilitate understanding the properties of (classical) authentication used in Quantum Cryptography. Then, we study vulnerabilities of a recently proposed authentication protocol intended to rule out a "man-in-the-middle" attack on Quantum Cryptography. Here, we point out that the proposed authentication primitive is not secure when used in a generic Quantum Cryptographic protocol. Lastly, we estimate the lifetime of authentication using encrypted tags when the encryption key is partially known. Under simplifying assumptions, we derive that the lifetime is linearly dependent on the length of the authentication key. Experimental results that support the theoretical results are also presented.

• 59.
Lifetime of Authentication Using Encrypted Tags When the Encryption Key is Partially KnownManuskript (preprint) (Annet vitenskapelig)

Quantum cryptography is an unconditionally secure key growing technique provided that an unconditionally secure authentication protocol is combined with it. This paper is about the study of the lifetime of a message authentication scheme, where a message to be authenticated is first hashed by a secret–but fixed–Strongly Universal hash function then the output is encrypted with a one-time-pad key to generate a tag for the message. If the onetime-pad is completely secret, then the lifetime is exponential in the tag length. If, however, the one-time-pad key is partially known in each authentication round, as is the case in practical quantum key distribution protocols, then the picture is different; because the adversary’s partial knowledge of the one-time-pad key in each authentication round contributes to his/her ability to identify the secret hash function. We estimate the lifetime of this type of authentication. Here the parameters are the length of the key identifying the secret hash function and the amount of knowledge that Eve has on the one-time-pad. A theoretical estimate is presented, along with experimental results that support it.

• 60.
Special Properties of Strongly Universal2 Hash Functions Important in Quantum Cryptography2009Inngår i: AIP Conference Proceedings, ISSN 0094-243X, Foundations of Probability and Physics—5, Växjö, augusti 2008, New York: American Institute of Physics , 2009, Vol. 1101, s. 289-293Konferansepaper (Fagfellevurdert)

Secure message authentication is an important part of Quantum Key Distribution. In this paper we analyze special properties of a Strongly Universal2 hash function family, an understanding of which is important in the security analysis of the authentication used in Quantum Cryptography. We answer the following question: How much of Alices message does Eve need to influence so that the message along with its tag will give her enough information to create the correct tag for her message?

• 61.
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
Philosophy of mathematics in “La Science et l’Hypothèse”, from Henri Poincaré.2017Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
• 62.
Columbia Univ, Dept Math, New York, NY 10027 USA.
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
On the immersion classes of nearby Lagrangians2016Inngår i: Journal of Topology, ISSN 1753-8416, E-ISSN 1753-8424, Vol. 9, nr 1, s. 232-244Artikkel i tidsskrift (Fagfellevurdert)

We show that the transfer map on Floer homotopy types associated to an exact Lagrangian embedding is an equivalence. This provides an obstruction to representing isotopy classes of Lagrangian immersions by Lagrangian embeddings, which, unlike previous obstructions, is sensitive to information that cannot be detected by Floer cochains. We show this by providing a concrete computation in the case of spheres.

• 63.
Örebro universitet, Handelshögskolan vid Örebro universitet.
Örebro universitet, Handelshögskolan vid Örebro universitet.
Behov av stödundervisning i grundskolan: En designbaserad analys av longitudinella data2008Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
• 64.
Högskolan i Jönköping, Tekniska Högskolan, JTH, Matematik.
Strong L1 convergence to equilibrium without entropy conditions for the Boltzmann equation1999Inngår i: Communications in Partial Differential Equations, ISSN 0360-5302, E-ISSN 1532-4133, Vol. 24, nr 7-8, s. 1501-1535Artikkel i tidsskrift (Fagfellevurdert)

The main result of this paper is that for the har dsphere kernel, the solution of the spatially homogenous Boltzmann equation converges strongly in L1 to equilibrium given that the initial data f0 belongs to L1(R3,(1+v^2)dv). This was previously known to be true with the additional assumption that f0logf0 belonged to L1(R3), which corresponds to bounded initial entropy.

• 65.
Högskolan i Halmstad, Sektionen för lärarutbildning (LUT).
Högskolan i Halmstad, Sektionen för lärarutbildning (LUT).
Vilket arbetssätt gynnar förmågan att kommunicera matematik?2012Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
• 66.
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
A priori estimates for solutions of singular perturbations with a turning point1977Inngår i: Studies in applied mathematics (Cambridge), ISSN 0022-2526, E-ISSN 1467-9590, Vol. 56, s. 51-69Artikkel i tidsskrift (Fagfellevurdert)
• 67.
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
Difference approximations for singular perturbations of systems of ordinary differential equations1974Inngår i: Numerische Mathematik, ISSN 0029-599X, E-ISSN 0945-3245, Vol. 22, s. 367-391Artikkel i tidsskrift (Fagfellevurdert)
• 68.
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Matematisk statistik.
Statistical models of breast cancer tumour growth for mammography screening data2012Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
• 69.
A Gröbner basis algorithm for fast encoding of Reed-Müller codes2016Independent thesis Basic level (degree of Bachelor), 10,5 poäng / 16 hpOppgave

In this thesis the relationship between Gröbner bases and algebraic coding theory is investigated, and especially applications towards linear codes, with Reed-Müller codes as an illustrative example. We prove that each linear code can be described as a binomial ideal of a polynomial ring, and that a systematic encoding algorithm for such codes is given by the remainder of the information word computed with respect to the reduced Gröbner basis. Finally we show how to apply the representation of a code by its corresponding polynomial ring ideal to construct a class of codes containing the so called primitive Reed-Müller codes, with a few examples of this result.

• 70.
Linköpings universitet, Institutionen för systemteknik, Kommunikationssystem.
Hide and Seek in a Social Network2017Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave

In this thesis a known heuristic for decreasing a node's centrality scores while maintaining influence, called ROAM, is compared to a modified version specifically designed to decrease eigenvector centrality. The performances of these heuristics are also tested against the Shapley values of a cooperative game played over the considered network, where the game is such that influential nodes receive higher Shapley values. The modified heuristic performed at least as good as the original ROAM, and in some instances even better (especially when the terrorist network behind the World Trade Center attacks was considered). Both heuristics increased the influence score for a given targeted node when applied consecutively on the WTC network, and consequently the Shapley values increased as well. Therefore the Shapley value of the game considered in this thesis seems to be well suited for discovering individuals that are assumed to actively trying to evade social network analysis.

• 71.
Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Samhällsvetenskapliga fakulteten, Institutionen för informationsvetenskap. Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Samhällsvetenskapliga fakulteten, Institutionen för informationsvetenskap.
Re: Long-term survival and mortality in prostate cancer treated with noncurative intent1995Inngår i: UROLGY, Vol. 154, s. 460-465Artikkel i tidsskrift (Fagfellevurdert)
• 72. Abramov, V.
Paal, E.Tallinn University of Technology.Silvestrov, Sergei D.Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.Stolin, A.Chalmers University of Techology.
Proceedings of the 3rd Baltic-Nordic Workshop “Algebra, Geometry, and Mathematical Physics”2008Konferanseproceedings (Fagfellevurdert)
• 73. Abramov, Viktor
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
Preface [Special issue devoted to the 4th Baltic-Nordic Workshop “Algebra, Geometry and Mathematical Physics”]2010Inngår i: Proceedings of the Estonian Academy of Sciences, ISSN 1736-6046, E-ISSN 1736-7530, Vol. 59, nr 4Artikkel i tidsskrift (Fagfellevurdert)
• 74. Abramovic, A.
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik.
General inequalities via isotonic subadditive functionals2007Inngår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 10, nr 1, s. 15-28Artikkel i tidsskrift (Fagfellevurdert)

In this manuscript a number of general inequalities for isotonic subadditive functionals on a set of positive mappings are proved and applied. In particular, it is pointed out that these inequalities both unify and generalize some general forms of the Hö̈lder, Popoviciu, Minkowski, Bellman and Power mean inequalities. Also some refinements of some of these results are proved.

• 75.
University of Haifa.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. University of Tromsø ; The Arctic University of Norway, Narvik.
Fejer and Hermite–Hadamard Type Inequalitiesfor N-Quasiconvex Functions2017Inngår i: Mathematical notes of the Academy of Sciences of the USSR, ISSN 0001-4346, E-ISSN 1573-8876, Vol. 102, nr 5-6, s. 599-609Artikkel i tidsskrift (Fagfellevurdert)

Abstract—Some new extensions and refinements of Hermite–Hadamard and Fejer type inequali-ties for functions which are N-quasiconvex are derived and discussed.

• 76.
Department of Mathematics, University of Haifa.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Some New Refined Hardy Type Inequalities with Breaking Points p = 2 or p = 32014Inngår i: Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation: 22nd International Workshop in Operator Theory and its Applications, Sevilla, July 2011 / [ed] Manuel Cepedello Boiso; Håkan Hedenmalm; Marinus A. Kaashoek; Alfonso Montes Rodríguez; Sergei Treil, Basel: Encyclopedia of Global Archaeology/Springer Verlag, 2014, s. 1-10Konferansepaper (Fagfellevurdert)

For usual Hardy type inequalities the natural “breaking point” (the parameter value where the inequality reverses) is p = 1. Recently, J. Oguntuase and L.-E. Persson proved a refined Hardy type inequality with breaking point at p = 2. In this paper we show that this refinement is not unique and can be replaced by another refined Hardy type inequality with breaking point at p = 2. Moreover, a new refined Hardy type inequality with breaking point at p = 3 is obtained. One key idea is to prove some new Jensen type inequalities related to convex or superquadratic funcions, which are also of independent interest

• 77.
Department of Mathematics, University of Haifa.
Faculty of Textile Technology, University of Zagreb. Faculty of Textile Technology, University of Zagreb. Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Some new refined Hardy type inequalities with general kernels and measures2010Inngår i: Aequationes Mathematicae, ISSN 0001-9054, E-ISSN 1420-8903, Vol. 79, nr 1-2, s. 157-172Artikkel i tidsskrift (Fagfellevurdert)

We state and prove some new refined Hardy type inequalities using the notation of superquadratic and subquadratic functions with an integral operator Ak defined by, where k: Ω1 × Ω2 is a general nonnegative kernel, (Ω1, μ1) and (Ω2, μ2) are measure spaces and,. The relations to other results of this type are discussed and, in particular, some new integral identities of independent interest are obtained.

• 78.
Department of Mathematics, University of Haifa.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Inequalities for averages of quasiconvex and superquadratic functions2016Inngår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 19, nr 2, s. 535-550Artikkel i tidsskrift (Fagfellevurdert)

For n ε ℤ+ we consider the difference Bn-1 (f)-Bn(f):= 1/an n-1/ηi=0 f(ai/an-1)-1/an+1 nηi=0f(ai/an) where the sequences{ai} and {ai-ai-1} are increasing. Some lower bounds are derived when f is 1-quasiconvex and when f is a closely related superquadratic function. In particular, by using some fairly new results concerning the so called "Jensen gap", these bounds can be compared. Some applications and related results about An-1 (f)-An(f):= 1/an n-1/ηi=0 f(ai/an-1)-1/an+1 nηi=0f(ai/an) are also included.

• 79.
Department of Mathematics, University of Haifa.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Some new estimates of the ‘Jensen gap’2016Inngår i: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 2016, artikkel-id 39Artikkel i tidsskrift (Fagfellevurdert)

Let (μ,Ω) be a probability measure space. We consider the so-called ‘Jensen gap’ J(φ,μ,f)=∫ Ω φ(f(s))dμ(s)−φ(∫ Ω f(s)dμ(s)) for some classes of functions φ. Several new estimates and equalities are derived and compared with other results of this type. Especially the case when φ has a Taylor expansion is treated and the corresponding discrete results are pointed out.

• 80.
University of Haifa.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Some new scales of refined Hardy type inequalities via functions related to superquadracity2013Inngår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 16, nr 3, s. 679-695Artikkel i tidsskrift (Fagfellevurdert)

For the Hardy type inequalities the "breaking point" (=the point where the inequality reverses) is p = 1. Recently, J. Oguntoase and L. E. Persson proved a refined Hardy type inequality with a breaking point at p = 2. In this paper we prove a new scale of refined Hardy type inequality which can have a breaking point at any p ≥ 2. The technique is to first make some further investigations for superquadratic and superterzatic functions of independent interest, among which, a new Jensen type inequality is proved

• 81.
University of Haifa, Department of Mathematics.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. University of Zagreb. University of Zagreb.
General inequalities via isotonic subadditive functionals2007Inngår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 10, nr 1, s. 15-28Artikkel i tidsskrift (Fagfellevurdert)

In this manuscript a number of general inequalities for isotonic subadditive functionals on a set of positive mappings are proved and applied. In particular, it is pointed out that these inequalities both unify and generalize some general forms of the Holder, Popoviciu, Minkowski, Bellman and Power mean inequalities. Also some refinements of some of these results are proved.

• 82.
University of Haifa.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
On some new developments of Hardy-type inequalities2012Inngår i: 9th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences: ICNPAA 2012 / [ed] Seenith Sivasundaram, Melville, NY: American Institute of Physics (AIP), 2012, s. 739-746Konferansepaper (Fagfellevurdert)

In this paper we present and discuss some new developments of Hardy-type inequalities, namely to derive (a) Hardy-type inequalities via a convexity approach, (b) refined scales of Hardy-type inequalities with other “breaking points” than p = 1 via superquadratic and superterzatic functions, (c) scales of conditions to characterize modern forms of weighted Hardy-type inequalities.

• 83.
Department of Mathematics, University of Haifa.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
On γ-quasiconvexity, superquadracity and two-sided reversed Jensen type inequalities2015Inngår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 18, nr 2, s. 615-627Artikkel i tidsskrift (Fagfellevurdert)

In this paper we deal with γ -quasiconvex functions when −1γ 0, to derive sometwo-sided Jensen type inequalities. We also discuss some Jensen-Steffensen type inequalitiesfor 1-quasiconvex functions. We compare Jensen type inequalities for 1-quasiconvex functionswith Jensen type inequalities for superquadratic functions and we extend the result obtained forγ -quasiconvex functions to more general classes of functions.

• 84.
Department of Mathematics, University of Haifa.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Some new scales of refined Jensen and Hardy type inequalities2014Inngår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 17, nr 3, s. 1105-1114Artikkel i tidsskrift (Fagfellevurdert)

Some scales of refined Jensen and Hardy type inequalities are derived and discussed. The key object in our technique is ? -quasiconvex functions K(x) defined by K(x)x-? =? (x) , where Φ is convex on [0,b) , 0 < b > ∞ and γ > 0.

• 85.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
Numerical analysis for random processes and fields and related design problems2011Doktoravhandling, med artikler (Annet vitenskapelig)

In this thesis, we study numerical analysis for random processes and fields. We investigate the behavior of the approximation accuracy for specific linear methods based on a finite number of observations. Furthermore, we propose techniques for optimizing performance of the methods for particular classes of random functions. The thesis consists of an introductory survey of the subject and related theory and four papers (A-D).

In paper A, we study a Hermite spline approximation of quadratic mean continuous and differentiable random processes with an isolated point singularity. We consider a piecewise polynomial approximation combining two different Hermite interpolation splines for the interval adjacent to the singularity point and for the remaining part. For locally stationary random processes, sequences of sampling designs eliminating asymptotically the effect of the singularity are constructed.

In Paper B, we focus on approximation of quadratic mean continuous real-valued random fields by a multivariate piecewise linear interpolator based on a finite number of observations placed on a hyperrectangular grid. We extend the concept of local stationarity to random fields and for the fields from this class, we provide an exact asymptotics for the approximation accuracy. Some asymptotic optimization results are also provided.

In Paper C, we investigate numerical approximation of integrals (quadrature) of random functions over the unit hypercube. We study the asymptotics of a stratified Monte Carlo quadrature based on a finite number of randomly chosen observations in strata generated by a hyperrectangular grid. For the locally stationary random fields (introduced in Paper B), we derive exact asymptotic results together with some optimization methods. Moreover, for a certain class of random functions with an isolated singularity, we construct a sequence of designs eliminating the effect of the singularity.

In Paper D, we consider a Monte Carlo pricing method for arithmetic Asian options. An estimator is constructed using a piecewise constant approximation of an underlying asset price process. For a wide class of Lévy market models, we provide upper bounds for the discretization error and the variance of the estimator. We construct an algorithm for accurate simulations with controlled discretization and Monte Carlo errors, andobtain the estimates of the option price with a predetermined accuracy at a given confidence level. Additionally, for the Black-Scholes model, we optimize the performance of the estimator by using a suitable variance reduction technique.

• 86.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
Was it snowing on lake Kassjön in January 4486 BC? Functional data analysis of sediment data.2014Inngår i: Proceedings of the Third International Workshop on Functional and Operatorial Statistics (IWFOS 2014), Stresa, Italy, June 2014., 2014Konferansepaper (Fagfellevurdert)
• 87.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
Umeå universitet, Medicinska fakulteten, Institutionen för samhällsmedicin och rehabilitering, Sjukgymnastik. National Sports Institute of Malaysia. MOX – Department of Mathematics, Politecnico di Milano. Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik. Umeå universitet, Medicinska fakulteten, Institutionen för samhällsmedicin och rehabilitering, Fysioterapi. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik. MOX – Department of Mathematics, Politecnico di Milano.
An inferential framework for domain selection in functional anova2014Inngår i: Contributions in infinite-dimensional statistics and related topics / [ed] Bongiorno, E.G., Salinelli, E., Goia, A., Vieu, P, Esculapio , 2014Konferansepaper (Fagfellevurdert)

We present a procedure for performing an ANOVA test on functional data, including pairwise group comparisons. in a Scheff´e-like perspective. The test is based on the Interval Testing Procedure, and it selects intervals where the groups significantly differ. The procedure is applied on the 3D kinematic motion of the knee joint collected during a functional task (one leg hop) performed by three groups of individuals.

• 88.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
Multivariate piecewise linear interpolation of a random field2011Manuskript (preprint) (Annet vitenskapelig)

We consider a multivariate piecewise linear interpolation of a continuous random field on a-dimensional cube. The approximation performance is measured by the integrated mean square error. Multivariate piecewise linear interpolator is defined by N field observations on a locations grid (or design). We investigate the class of locally stationary random fields whose local behavior is like a fractional Brownian field in mean square sense and find the asymptotic approximation accuracy for a sequence of designs for large N. Moreover, for certain classes of continuous and continuously differentiable fields we provide the upper bound for the approximation accuracy in the uniform mean square norm.

• 89.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
On the error of the Monte Carlo pricing method for Asian option2008Inngår i: Journal of Numerical and Applied Mathematics, ISSN 0868-6912, Vol. 96, nr 1, s. 1-10Artikkel i tidsskrift (Fagfellevurdert)

We consider a Monte Carlo method to price a continuous arithmetic Asian option with a given precision. Piecewise constant approximation and plain simulation are used for a wide class of models based on L\'{e}vy processes. We give bounds of the possible discretization and simulation errors. The sufficient numbers of discretization points and simulations to obtain requested accuracy are derived. To demonstrate the general approach, the Black-Scholes model is studied in more detail. We undertake the case of continuous averaging and starting time zero,  but the obtained results can be applied to the discrete case  and generalized for any time before an execution date. Some numerical experiments and comparison to the PDE based method are also presented.

• 90.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
Piecewise multilinear interpolation of a random field2013Inngår i: Advances in Applied Probability, ISSN 0001-8678, E-ISSN 1475-6064, Vol. 45, nr 4, s. 945-959Artikkel i tidsskrift (Fagfellevurdert)

We consider a piecewise-multilinear interpolation of a continuous random field on a d-dimensional cube. The approximation performance is measured using the integrated mean square error. Piecewise-multilinear interpolator is defined by N-field observations on a locations grid (or design). We investigate the class of locally stationary random fields whose local behavior is like a fractional Brownian field, in the mean square sense, and find the asymptotic approximation accuracy for a sequence of designs for large N. Moreover, for certain classes of continuous and continuously differentiable fields, we provide the upper bound for the approximation accuracy in the uniform mean square norm.

• 91.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
Stratified Monte Carlo quadrature for continuous random fields2015Inngår i: Methodology and Computing in Applied Probability, ISSN 1387-5841, E-ISSN 1573-7713, Vol. 17, nr 1, s. 59-72Artikkel i tidsskrift (Fagfellevurdert)

We consider the problem of numerical approximation of integrals of random fields over a unit hypercube. We use a stratified Monte Carlo quadrature and measure the approximation performance by the mean squared error. The quadrature is defined by a finite number of stratified randomly chosen observations with the partition generated by a rectangular grid (or design). We study the class of locally stationary random fields whose local behavior is like a fractional Brownian field in the mean square sense and find the asymptotic approximation accuracy for a sequence of designs for large number of the observations. For the H¨older class of random functions, we provide an upper bound for the approximation error. Additionally, for a certain class of isotropic random functions with an isolated singularity at the origin, we construct a sequence of designs eliminating the effect of the singularity point.

• 92.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik. Politecnico di Milano, Italy. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik. Politecnico di Milano, Italy. Oslo University, Norway.
Clustering misaligned dependent curves applied to varved lake sediment for climate reconstruction2017Inngår i: Stochastic environmental research and risk assessment (Print), ISSN 1436-3240, E-ISSN 1436-3259, Vol. 31, nr 1, s. 71-85Artikkel i tidsskrift (Fagfellevurdert)

In this paper we introduce a novel functional clustering method, the Bagging Voronoi K-Medoid Aligment (BVKMA) algorithm, which simultaneously clusters and aligns spatially dependent curves. It is a nonparametric statistical method that does not rely on distributional or dependency structure assumptions. The method is motivated by and applied to varved (annually laminated) sediment data from lake Kassjön in northern Sweden, aiming to infer on past environmental and climate changes. The resulting clusters and their time dynamics show great potential for seasonal climate interpretation, in particular for winter climate changes.

• 93.
KTH, Skolan för industriell teknik och management (ITM), Industriell produktion.
KTH, Skolan för elektro- och systemteknik (EES), Centra, Alfvénlaboratoriet.
Plane intersections of rotational ellipsoids2006Inngår i: The American mathematical monthly, ISSN 0002-9890, E-ISSN 1930-0972, Vol. 113, nr 4, s. 336-339Artikkel i tidsskrift (Fagfellevurdert)
• 94.
Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
Skattning av kausala effekter med matchat fall-kontroll data2017Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
• 95.
Högskolan i Jönköping, Högskolan för lärande och kommunikation, HLK, Skolnära forskning, Matematikdidaktik.
Elevers förståelse av likhetstecknet: En studie i årskurs 32016Independent thesis Advanced level (professional degree), 10 poäng / 15 hpOppgave

Studiens syfte är att bilda kunskap om elevers förståelse av likhetstecknet och hur undervisning om likhetstecknet i årskurs 3 kan varieras för att bli så effektiv som möjligt. Syftet ska besvaras genom frågeställningarna: vilka variationsmönster som de studerade eleverna kan möta och vilka kritiska aspekter som elever kan identifiera. Kritiska aspekter är det som elever behöver identifiera för att förstå det som ska läras. Variationsmönster innebär att det som är kritiskt i undervisningen ska varieras för att synliggöras. Studien har sin ansats i variationsteorin, där variationsmönster och kritiska aspekter är centrala begrepp.

En lektion observerades i årskurs 3 och sex elever valdes ut och intervjuades om likhetstecknet. Resultatet av studien visar att eleverna mötte sex kritiska aspekter i undervisningen. I varje kritisk aspekt mötte eleverna ett eller flera variationsmönster. Studien visar också att alla de intervjuade eleverna har en relationell och instrumentell förståelse av likhetstecknet. Eleverna har förståelse av en kritisk aspekt, som den observerade lektionen inte hade berört, nämligen att alla tal måste ingå i en uppgift för att lösningen ska vara korrekt. Fyra av sex elever har förståelse av den kritiska aspekten att det ska vara ekvivalens i en kedja av likheter. Resultatet visar också att elevernas förståelse av likhetstecknet inte är beroende av att de möter variationsmönster i undervisningen, men att de möter de kritiska aspekterna på något sätt.

• 96.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik.
Inequalities for some classes of Hardy type operators and compactness in weighted Lebesgue spaces2016Doktoravhandling, med artikler (Annet vitenskapelig)

This PhD thesis is devoted to investigate weighted differential Hardy inequalities and Hardy-type inequalities with the kernel when the kernel has an integrable singularity, and also the additivity of the estimate of a Hardy type operator with a kernel.The thesis consists of seven papers (Papers 1, 2, 3, 4, 5, 6, 7) and an introduction where a review on the subject of the thesis is given. In Paper 1 weighted differential Hardy type inequalities are investigated on the set of compactly supported smooth functions, where necessary and sufficient conditions on the weight functions are established for which this inequality and two-sided estimates for the best constant hold. In Papers 2, 3, 4 a more general class of $\alpha$-order fractional integrationoperators are considered including the well-known classical Weyl, Riemann-Liouville, Erdelyi-Kober and Hadamard operators. Here 0 < $\alpha$ < 1. In Papers 2 and 3 the boundedness and compactness of two classes of such operators are investigated namely of Weyl and Riemann-Liouville type, respectively, in weighted Lebesgue spaces for 1 < p ≤ q < 1 and 0 < q < p < ∞. As applications some new results for the fractional integration operators of Weyl, Riemann-Liouville, Erdelyi-Kober and Hadamard are given and discussed.In Paper 4 the Riemann-Liouville type operator with variable upper limit is considered. The main results are proved by using a localization method equipped with the upper limit function and the kernel of the operator. In Papers 5 and 6 the Hardy operator with kernel is considered, where the kernel has a logarithmic singularity. The criteria of the boundedness and compactness of the operator in weighted Lebesgue spaces are given for 1 < p ≤ q < ∞ and 0 < q < p < ∞, respectively. In Paper 7 we investigated the weighted additive estimates for integral operators K+ and K¯ defined by

K+ ƒ(x) := ∫ k(x,s) ƒ(s)ds,  K¯ ƒ(x) := ∫ k(x,s)ƒ(s)ds.

It is assumed that the kernel k of the operators K+and K- belongs to the general Oinarov class. We derived the criteria for the validity of these addittive estimates when 1 ≤ p≤ q < ∞

• 97.
Department of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana .
Department of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana. Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Boundedness and compactness of a class of Hardy type operators2016Inngår i: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, nr 1, artikkel-id 324Artikkel i tidsskrift (Fagfellevurdert)

We establish characterizations of both boundedness and of compactness of a general class of fractional integral operators involving the Riemann-Liouville, Hadamard, and Erdelyi-Kober operators. In particular, these results imply new results in the theory of Hardy type inequalities. As applications both new and well-known results are pointed out.

• 98.
Department of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana .
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. UiT, Tromso.
Hardy type inequalities and compactness of a class of integral operators with logarithmic singularities2018Inngår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 21, nr 1, s. 201-215Artikkel i tidsskrift (Fagfellevurdert)

We establish criteria for both boundedness and compactness for some classes of integraloperators with logarithmic singularities in weighted Lebesgue spaces for cases 1 < p 6 q <¥ and 1 < q < p < ¥. As corollaries some corresponding new Hardy inequalities are pointedout.1

• 99.
L. N.Gumilev Eurasian National University, Khazakstan.
L. N.Gumilev Eurasian National University, Khazakstan. Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Additive weighted Lp estimates of some classes of integral operators involving generalized Oinarov Kernels2017Inngår i: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 11, nr 3, s. 683-694Artikkel i tidsskrift (Fagfellevurdert)

Abstract. Inequalities of the formkuK f kq 6C(kr f kp +kvH f kp) , f > 0,are considered, where K is an integral operator of Volterra type and H is the Hardy operator.Under some assumptions on the kernel K we give necessary and sufficient conditions for suchan inequality to hold.1

• 100. Accardi, L
Discussion on "On quantum statistical inference" by Barndorff-Nielsen, Gill and Jupp2003Inngår i: Journal of The Royal Statistical Society Series B-statistical Methodology, ISSN 1369-7412, E-ISSN 1467-9868, Vol. 65, nr 4, s. 805-816s. 805-816Artikkel i tidsskrift (Fagfellevurdert)
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