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• 1.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Science Education and Mathematics.
Lärarstyrd lek i matematikundervisningen: Dess möjligheter och begränsningar för elevens lärande.2018Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis

Avsikten med min studie är att veta hur lärarstyrd lek påverkar matematikundervisningen samt se vilka möjligheter och begränsningar som metoden lärarstyrd lek har. För detta syfte har jag intervjuat ett antal lärare om detta arbetssätt, hur de planerar för en undervisning som bygger på lärarstyrd lek, vad de menar med lärarstyrd lek, vilka möjligheter och begränsningar de ser samt om de märker att de stimulerar eleven i matematikundervisningen med den lärarstyrda leken.Det resultatet som jag ser i min studie är att i huvudsak anser samtliga pedagoger att det finns en positiv påverkan på lärandet när lärarstyrd lek genomförs i undervisningen. De pekar på några begränsande faktorer som tidsbrist, höga arbetsbelastning, problem med elevers sociala sampel. Trots att arbetssättet möter vissa utmaningar så bedömer samtliga pedagoger att lärarstyrd lek i matematikundervisningen ökar elevens motivation i lärandet och gör ämnet roligt och intressant.

• 2.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Science Education and Mathematics.
Det laborativa arbetsmaterialet i matematik i lågstadiet (åk1-3) – vad, vem, när, hur & varför?2016Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis

Syftet med denna studie är att undersöka det laborativa arbetsmaterialets förekomst i matematikundervisningen och ta reda på hur lärare förhåller sig till materialet och användandet av detta i årskurserna 1-3. Undersökningen är huvudsakligen en kvalitativ studie som bygger på 7 enkätfrågor ställda till lärare i lågstadiet. Min undersökning visar att laborativt arbetsmaterial förekommer i matematikundervisningen och används vid genomgångar av lärarna samt vid behov av både elever och lärare. Materialet är både roligt att använda och ett stöd för lärandet. Vissa tyckte dock att det kunde vara jobbigt att plocka fram och städa undan och att eleverna ibland lekte med det. Lärarna gav exempel på kopplingar till läroplanen och de tillfrågade lärarna upplever sig ha tillräcklig kompetens för att kunna bedriva god undervisning för främjandet av elevernas kunskapsutveckling inom ämnet matematik. Det var dock viktigt med ett fungerande erfarenhetsutbyte i arbetslaget samt möjlighet till fortbildning vid behov.

• 3.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Science Education and Mathematics.
En studie som visar i vilket syfte fyra lärare använder utomhusmatematik i förskoleklass-åk32016Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis

Utomhuspedagogik har under de senaste åren ökat inom skolans värld. Jag har upplevt att lärare har börjat prata mer om utomhuspedagogik och använder det mer och mer i undervisningen. Mitt självständiga arbete handlar om hur lärare i grundskolan förskoleklass-åk3 använder sig av utomhusmatematik och i vilket syfte lärarna har när de undervisar inom utomhusmatematik. Studiens syfte är att undersöka i vilket syfte lärare använder utomhusmatematik, vilka positiva respektive negativa sidor de ser/upplever när de undervisar med undervisningsformen samt ett ungefärligt snittvärde på hur många timmar i veckan lärarna använder det. Metoden som tillämpas till denna studie är kvalitativa semistrukturerade intervjuer med fyra verksamma lärare på olika skolor i samma kommun. Resultatet visar att alla lärare jag intervjuade jobbade med utomhusmatematik varje vecka och var positiv till att jobba med det. Lärarna såg också att fler elever fångades upp när de valde att ta ut klassrummet och jobba mer praktiskt. Genom att jobba på detta sätt har alla elever en större chans att jobba mot sina mål samt att eleverna får använda sin lärstil eftersom många olika lärstilar blir möjliga att använda utomhus.

• 4.
Mid Sweden University, Faculty of Human Sciences, Institution of education.
Mid Sweden University, Faculty of Human Sciences, Institution of education.
Intensivundervisning i matematik: Ett sätt att fånga upp elever?2014Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis

Utvecklingen av svenska elevers matematikkunskaper har på senare tid setts som oroande då internationella jämförelser visat på sjunkande resultat. Skolverkets matematiksatsning gav Lillskolan möjlighet att söka, och få, ekonomiskt stöd för ett matematikprojekt som innefattade intensivundervisning i matematik.

• 5.
Université du Luxembourg.
SUNY Stony Brook, New York. Universitá Roma Tor Vergata. Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
Complex vector fields and hypolleptic partial differential operators2010In: Annales de l'Institut Fourier, ISSN 0373-0956, E-ISSN 1777-5310, Vol. 60, no 3, p. 39p. 987-1034Article in journal (Refereed)

We prove a subelliptic estimate for systems of complex vector fields under some assumptions that generalize the essential pseudoconcavity for CR manifolds, that was first introduced by two of the authors; and the Hormander's bracket condition for real vector fields. Applications are given to prove the hypoellipticity of first order systems and second order partial differential operators. Finally we describe a class of compact homogeneous CR manifolds for which the distribution of (0,1) vector fields satisfies a subelliptic estimate.

• 6. Altomani, Andrea
Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
Holomorphic Extension from Weakly Pseudoconcave CR Manifolds2010In: Rendiconti del Seminario Matematico della Universita di Padova, ISSN 0041-8994, E-ISSN 2240-2926, Vol. 123, p. 69-90Article in journal (Refereed)

Let M be a smooth locally embeddable CR manifold, having some CR dimension M and some CR codimension d. We find an improved local geometric condition on M which guarantees, at a point p on M, that germs of CR distributions are smooth functions, and have extensions to germs of holomorphic functions on a full ambient neighborhood of p. Our condition is a form of weak pseudoconcavity, closely related to essential pseudoconcavity as introduced in [HN1]. Applications are made to CR meromorphic functions and mappings. Explicit examples are given which satisfy our new condition, but which are not pseudoconcave in the strong sense. These results demonstrate that for codimension d > 1 there are additional phenomena, which are invisible when d = 1.

• 7. Andersson, M
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Canonical Homotopy Operators for the d-bar complex in strictly pseudoconvex domains1998In: Bulletin de la Societe Mathematique de France, ISSN 0037-9484, Vol. 126, no 2, p. 245-271Article in journal (Refereed)
• 8. Andersson, Mats
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Approximate formulas for canonical homotopy operators for the d-bar complex in strictly pseudoconvex domains2000In: Mathematica Scandinavica, ISSN 0025-5521, Vol. 87, no 2, p. 251-271Article in journal (Refereed)
• 9.
Bergische Universität Wuppertal, Wuppertal, Germany.
University of Bern, Bern, Switzerland. Mid Sweden University, Faculty of Science, Technology and Media, Department of Science Education and Mathematics.
Holomorphic Automorphisms of Danielewski Surfaces II: Structure of the Overshear Group2015In: Journal of Geometric Analysis, ISSN 1050-6926, E-ISSN 1559-002X, Vol. 25, no 3, p. 1859-1889Article in journal (Refereed)

We apply Nevanlinna theory for algebraic varieties to Danielewski surfaces and investigate their group of holomorphic automorphisms. Our main result states that the overshear group, which is known to be dense in the identity component of the holomorphic automorphism group, is a free product.

• 10.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Science Education and Mathematics.
”Sitter det en spik i väggen, väljer jag inte skruvdragaren. Jag tar hammaren.”: En studie om hur lärare inom F-3 använder surfplattor och applikationer i matematikundervisningen2018Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis

Denna studie handlar om hur lärare i årskurs 1-3 använder surfplattor i matematikundervisningen. Syftet med studien är att ta reda på hur surfplattor används och hur lärarna arbetar med olika applikationer. För att få svar på det har kvalitativa intervjuer skett med tre lärare. Lärarna använde surfplattan i matematikundervisningen som ett komplement till den ordinarie undervisningen. Trots att surfplattorna användes som komplement förekom verktyget på hälften av alla matematiklektioner. Ingen av lärarna använde applikationerna utifrån utgivarens rekommendationer om sådana fanns. Fördelarna med verktyget var att det var motiverande för eleverna och de kunde göra fler repetitioner och nöta uppgifter. Nackdelarna var tekniska problem som slut på batteri eller nätverkskrångel.

• 11.
University of St Andrews, Scotland.
University of St Andrews, Scotland. Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.
Sesqui-arrays, a generalisation of triple arrays2018In: The Australasian Journal of Combinatorics, ISSN 1034-4942, Vol. 71, no 3, p. 427-451Article in journal (Refereed)

A triple array is a rectangular array containing letters, each letter occurring equally often with no repeats in rows or columns, such that the number of letters common to two rows, two columns, or a rowand a column are (possibly different) non-zero constants. Deleting the condition on the letters common to a row and a column gives a double array. We propose the term sesqui-array for such an array when only the condition on pairs of columns is deleted. In this paper we give three constructions for sesqui-arrays. Therst gives $(n + 1)\times n^2$ arrays on n(n + 1) letters for $n\geq 2$. (Suchan array for n = 2 was found by Bagchi.) This construction uses Latin squares. The second uses the Sylvester graph, a subgraph of the Hoffman--Singleton graph, to build a good block design for 36 treatments in 42 blocks of size 6, and then uses this in a 736 sesqui-array for 42 letters.We also give a construction for K(K-1)(K-2)/2 sesqui-arrays on K(K-1)/2 letters from biplanes. The construction starts with a block of a biplane and produces an array which satises the requirements for a sesqui-array except possibly that of having no repeated letters in a row or column. We show that this condition holds if and only if the Hussain chains for the selected block contain no 4-cycles. A sufficient condition for the construction to give a triple array is that each Hussain chain is a union of 3-cycles; but this condition is not necessary, and we give a few further examples. We also discuss the question of which of these arrays provide good designs for experiments.

• 12. Bandelt, H J
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics. Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Quasi-median graphs from sets of partitions2002In: Discrete Applied Mathematics, ISSN 0166-218X, E-ISSN 1872-6771, Vol. 122, no 1-3, p. 23-35Article in journal (Refereed)

In studies of molecular evolution, one is typically confronted with the task of inferring a phylogenetic tree from a set X of sequences of length n over a finite alphabet Λ. For studies that invoke parsimony, it has been found helpful to consider the quasi-median graph generated by X in the Hamming graph Λn. Although a great deal is already known about quasi-median graphs (and their algebraic counterparts), little is known about the quasi-median generation in Λn starting from a set X of vertices. We describe the vertices of the quasi-median graph generated by X in terms of the coordinatewise partitions of X. In particular, we clarify when the generated quasi-median graph is the so-called relation graph associated with X. This immediately characterizes the instances where either a block graph or the total Hamming graph is generated.

• 13.
Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM). Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
Relating vocabulary in mathematical tasks to aspects of reading and solving2012In: Evaluation and comparison of mathematical achievement: Dimensions and perspectives. Proceedings of MADIF 8, The Eighth Mathematics Education Research Seminar, Umeå, January 24-25, 2012 / [ed] Christer Bergsten, Eva Jablonka & Manya Raman, Linköping: SMDF , 2012, p. 61-70Conference paper (Refereed)

This paper focuses on relationships between vocabulary in mathematical tasks and aspects of reading and solving these tasks. The paper contains a framework that highlights a number of different aspects of word difficulty as well as many issues to consider when planning and implementing empirical studies concerning vocabulary in tasks, where the aspect of common/uncommon words is one important part. The paper also presents an empirical method where corpora are used to investigate issues of vocabulary in mathematical tasks. The results from the empirical study show that there are connections between different types of vocabulary and task difficulty, but that they seem to be mainly an effect of the total number of words in a task.

• 14.
Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM). Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
Relations between linguistic features and difficulty of PISA tasks in different languages2016In: Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education / [ed] Csíkos, C., Rausch, A., & Szitányi, J., Szeged, Hungary: PME , 2016, p. 125-125Conference paper (Refereed)
• 15.
Umeå Univ, Umeå.
Umeå Univ, Umeå. Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education. Umeå Univ, Umeå.
The role of linguistic features when reading and solving mathematics tasks in different languages2018In: Journal of Mathematical Behavior, ISSN 0732-3123, E-ISSN 1873-8028, Vol. 51, p. 41-55Article in journal (Refereed)

The purpose of this study is to deepen the understanding of the relation between the language used in mathematics tasks and the difficulty in reading and solving the tasks. We examine issues of language both through linguistic features of tasks (word length, sentence length, task length, and information density) and through different natural languages used to formulate the tasks (English, German, and Swedish). Analyses of 83 PISA mathematics tasks reveal that tasks in German, when compared with English and Swedish, show stronger connections between the examined linguistic features of tasks and difficulty in reading and solving the tasks. We discuss if and how this result can be explained by general differences between the three languages.

• 16.
Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
A theoretical model of the connection between the process of reading and the process of solving mathematical tasks2010In: Mathematics and mathematics education: Cultural and social dimensions. Proceedings of MADIF 7 / [ed] C. Bergsten, E. Jablonka & T. Wedege, Linköping, Sweden: Svensk förening för matematikdidaktisk forskning, SMDF , 2010, p. 47-57Conference paper (Refereed)

In this paper we suggest a theoretical model of the connection between the process of reading and the process of solving mathematical tasks. The model takes into consideration different types of previous research about the relationship between reading and solving mathematical tasks, including research about traits of mathematical tasks (a linguistic perspective), about the reading process (a psychological perspective), and about behavior and reasoning when solving tasks (a mathematics education perspective). In contrast to other models, our model is not linear but cyclic, and considers behavior such as re-reading the task.

• 17.
Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
Communicating mathematics or mathematical communication?: An analysis of competence frameworks2012In: Proceedings of the 36th Conference of the International Group for the Psychology of Mathematics Education: Vol. 2: opportunities to learn in mathematics education / [ed] Tai-Yih Tso, 2012, p. 67-74Conference paper (Refereed)

In this study we analyse the communication competence included in two different frameworks of mathematical knowledge. The main purpose is to find out if mathematical communication is primarily described as communication of or about mathematics or if it is (also) described as a special type of communication. The results show that aspects of mathematics are mostly included as the content of communication in the frameworks but the use of different forms of representation is highlighted both in the frameworks and also in prior research as a potential cause for characterising mathematical communication differently than "ordinary" communication.

• 18.
Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
Umeå universitet, Umeå forskningscentrum för matematikdidaktik (UFM).
Språkbrukets roll i matematikundervisningen2014In: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, Vol. 2014, no 1, p. 27-31Article in journal (Other (popular science, discussion, etc.))

Det språk vi använder oss av i matematikklassrummet kan fokuseras på många olika sätt. Språket är också nödvändigt att förhålla sig till vid utvecklingen av sitt matematiska tänkande. Författarna diskuterar här relationer mellan språk och lärande.

• 19.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Science Education and Mathematics.
Vilka undervisningsmetoder använder lärare på högstadiet i praktiken för att hjälpa svaga elever i matematik?2017Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis

Syftet med detta examensarbete är att ta reda på vilka undervisningsmetoder somlärare på högstadiet använder i praktiken för att hjälpa svaga elever i matematik.Examensarbetet inleds med en litteraturstudie om olika typer av matematiskasvårigheter och vilka undervisningsmetoder som är bäst lämpade vid dessa problem.Litteraturstudien omfattar även motivationens betydelse i matematisk undervisning.Därefter har en kvalitativ intervju genomförts på fem erfarna matematiklärare påhögstadiet. Intervjuernas syfte har varit att utröna vilka matematiska svårigheter hoseleverna som lärarna stöter på samt att ta reda på vilka undervisningsmetoder lärarnaanvänder för att hjälpa dessa elever i svårigheter.Intervjuernas resultat har visat på ett antal svårigheter, som lärarna har urskilt, hoseleverna bland andra bristande taluppfattning, svårigheter med algoritmer, bristandebegreppsförståelse. Intervjusvaren har även tagit fram vilka undervisningsmetodersom matematiklärarna använder i skolorna för att hjälpa svaga elever. Några av dessametoder är en till en undervisning, anpassat material och användning av laborativtmaterial. Dessa tre undervisningsmetoder som lärarna i studien använder sig avrekommenderas också av forskningen vid olika typer av matematiska svårigheter.Examensarbetets intervjuundersökning har också visat på lärarnas iakttagelser avelevernas motivation som en nödvändig förutsättning för om olika undervisningsmetoderska ha någon framgång. Svaren från lärarna har även tagit fram enviktig faktor till att elever tappar motivationen, den om elever i för stor utsträckningexponeras för matematiska uppgifter de inte klarar av. Dessa förhållanden ommotivationens betydelse, för om undervisningsmetoderna ska ha någon mening ochatt elever tappar motivationen om de drabbas av för svåra uppgifter, bekräftas avforskningen. En viktig lärdom från detta examensarbete är att det har visatnödvändigheten att matematiklärarna anpassar sin undervisning för olika eleversbehov. Om lärarna inte gör det kommer troligen de svagare eleverna att exponeras föruppgifter de inte klarar av, vilket resulterar i frustration och omotivation.

• 20.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
On canonical homotopy operators for partial derivative in Fock type spaces in C-n2001In: Publicacions Matematiques, ISSN 0214-1493, Vol. 45, no 1, p. 223-233Article in journal (Refereed)

We show that a certain solution operator for partial derivative in a space of forms square integrable against e(-\z\2) is canonical, i.e.. that it gives the minimal solution when applied to a partial derivative -closed form. and gives zero when applied to a form orthogonal to Ker partial derivative.

• 21.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Quadratic convexity1998In: Journal d'Analyse Mathematique, ISSN 0021-7670, Vol. 76, no 1, p. 45-65Article in journal (Refereed)
• 22.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Sticky Graphs - A Tool To Model Self Assembly2004Report (Other scientific)

We define sticky graphs and propose their use in the study of self assembly by means of a grammar-like structure modeling the dynamic behaviour of a system.

• 23.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
The H^p corona theorem in analytic polyhedra1997In: Arkiv för matematik, ISSN 0004-2080, Vol. 35, no 2, p. 225-251Article in journal (Refereed)
• 24.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
The Ball Embedding Property of the Open Unit Disc2011In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 130, no 10, p. 3573-3581Article in journal (Refereed)

We prove that the open unit disc Delta in C satisfies the ball embedding property in C(2); i.e., given any discrete set of discs in C(2) there exists a proper holomorphic embedding Delta hooked right arrow C(2) which passes arbitrarily close to the discs. It is already known that C does not satisfy the ball embedding property in C(2) and that Delta satisfies the ball embedding property in C(n) for n > 2.

• 25.
University of Berne Institute of Mathematics Sidlerstrasse 5 CH-3012 Berne Switzerland.
University of Berne Institute of Mathematics Sidlerstrasse 5 CH-3012 Berne Switzerland.
Embeddings through Discrete Sets of Discs2008In: Arkiv för matematik, ISSN 0004-2080, E-ISSN 1871-2487, Vol. 46, no 2, p. 251-269Article in journal (Refereed)

We investigate whether a Stein manifold M which allows proper holomorphic embedding into ℂ n can be embedded in such a way that the image contains a given discrete set of points and in addition follow arbitrarily close to prescribed tangent directions in a neighbourhood of the discrete set. The infinitesimal version was proven by Forstnerič to be always possible. We give a general positive answer if the dimension of M is smaller than n/2 and construct counterexamples for all other dimensional relations. The obstruction we use in these examples is a certain hyperbolicity condition.

• 26.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Non-equivalent embeddings into complex Euclidean spaces2006In: International Journal of Mathematics, ISSN 0129-167X, Vol. 17, no 9, p. 1033-1046Article in journal (Refereed)

We study the number of equivalence classes of proper holomorphic embeddings of a Stein space X into ℂn. In this paper we prove that if the automorphism group of X is a Lie group and there exists a proper holomorphic embedding of X into ℂn, 0 < dim X < n, then for any k ≥ 0 there exist uncountably many non-equivalent proper holomorphic embeddings Φ: X × ℂk ℂn × ℂk. For k = 0 all embeddings will be proved to satisfy the additional property of ℂn\Φ(X) being (n - dim X)-Eisenman hyperbolic. As a corollary we conclude that there are uncountably many non-equivalent proper holomorphic embeddings of ℂk into ℂn whenever 0 < k < n.

• 27. Borell, Stefan
Proper Holomorphic Disks in the Complement of Varieties in C22008In: Mathematical Research Letters, ISSN 1073-2780, E-ISSN 1945-001X, Vol. 15, no 4, p. 821-826Article in journal (Refereed)
• 28.
Mid Sweden University, Faculty of Human Sciences, Institution of education.
Mid Sweden University, Faculty of Human Sciences, Institution of education.
Algoritmen i matteboken: En litteraturstudie av mängden algoritm- huvudräknings –och övriga uppgifter i matematikböcker för årskurs 32014Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis

Denna uppsats har undersökt mängden algoritmuppgifter, huvudräkningsuppgifter och övriga uppgifter i matematikböckerna för årskurs 3 med syfte att jämföra böckerna och relatera utvecklingen i förhållande till de tre senaste läroplanerna Lgr 80, Lpo 94, Lgr 11.

• 29.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences.
Chemometric tools for enhanced performance in liquid chromatography-mass spectrometry2001Doctoral thesis, monograph (Other scientific)
• 30.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences.
Chromatographic alignment by warping and dynamic programming as a pre-processing tool for PARAFAC modelling of liquid chromatography-mass spectrometry data2002In: Journal of Chromatography A, ISSN 0021-9673, Vol. 961, no 2, p. 237-244Article in journal (Refereed)

Solutes analysed with LC–MS are characterised by their retention times and mass spectra, and quantified by the intensities measured. This highly selective information can be extracted by multiway modelling. However, for full use and interpretability it is necessary that the assumptions made for the model are valid. For PARAFAC modelling, the assumption is a trilinear data structure. With LC–MS, several factors, e.g. non-linear detector response and ionisation suppression may introduce deviations from trilinearity. The single largest problem, however, is the retention time shifts not related to the true sample variations. In this paper, a time warping algorithm for alignment of LC–MS data in the chromatographic direction has been examined. Several refinements have been implemented and the features are demonstrated for both simulated and real data. With moderate time shifts present in the data, pre-processing with this algorithm yields approximately trilinear data for which reasonable models can be made.

• 31.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences.
Peak purity assessment in liquid chromatography-mass spectrometry2001In: Journal of Chromatography A,, ISSN 0021-9673, Vol. 915, no 1/2, p. 43-52Article in journal (Refereed)

Fixed-size moving window evolving factor analysis and base peak chromatograms have been used for peak purity detection in data generated with LC–MS. The two methods were evaluated with both real and simulated data and were found to be fast and complementary to each other. When a possibly impure peak is detected, it is suggested that further information can be obtained from local principal component analysis modelling and comparative mass chromatogram plots.

• 32.
Sapienza Università di Roma, Rome, Italy.
Sapienza Università di Roma, Rome, Italy. Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education. Uniwersytet Jana Kochanowskiego W Kielcach, Kielce, Poland. Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education. Uniwersytet Jana Kochanowskiego W Kielcach, Kielce, Poland.
A novel noncommutative KdV-type equation, its recursion operator, and solitons2018In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 59, no 4, article id 043501Article in journal (Refereed)

A noncommutative KdV-type equation is introduced extending the Bäcklund chart in Carillo et al. [Symmetry Integrability Geom.: Methods Appl. 12, 087 (2016)]. This equation, called meta-mKdV here, is linked by Cole-Hopf transformations to the two noncommutative versions of the mKdV equations listed in Olver and Sokolov [Commun. Math. Phys. 193, 245 (1998), Theorem 3.6]. For this meta-mKdV, and its mirror counterpart, recursion operators, hierarchies, and an explicit solution class are derived.

• 33.
Dipartimento “Scienze di Base e Applicate per l’Ingegneria”, Sapienza - Università di Roma, 16, Via A. Scarpa, Rome, Italy; I.N.F.N. - Sez. Roma1, Gr. IV - Mathematical Methods in NonLinear Physics, Rome, Italy .
Dipartimento “Scienze di Base e Applicate per l’Ingegneria”, Sapienza - Università di Roma, 16, Via A. Scarpa, Rome, Italy. Mid Sweden University, Faculty of Science, Technology and Media, Department of Science Education and Mathematics. Instytut Matematyki, Uniwersytet Jana Kochanowskiego w Kielcach, Poland.
Bäcklund transformations and non-abelian nonlinear evolution equations: A novel bäcklund chart2016In: SIGMA. Symmetry, Integrability and Geometry, ISSN 1815-0659, E-ISSN 1815-0659, Vol. 12, article id 087Article in journal (Refereed)

Classes of third order non-Abelian evolution equations linked to that of Korteweg-de Vries-type are investigated and their connections represented in a non-commutative Bäcklund chart, generalizing results in [Fuchssteiner B., Carillo S., Phys. A 154 (1989), 467-510]. The recursion operators are shown to be hereditary, thereby allowing the results to be extended to hierarchies. The present study is devoted to operator nonlinear evolution equations: general results are presented. The implied applications referring to finite-dimensional cases will be considered separately.

• 34.
Dipartimento “Scienze di Base e Applicate per l’Ingegneria”, Sapienza - Universita di Roma, 16, Via A. Scarpa, 00161 Rome, Italy.
Dipartimento “Scienze di Base e Applicate per l’Ingegneria”, Sapienza - Universita di Roma, 16, Via A. Scarpa, 00161 Rome, Italy. Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education. Instytut Matematyki, Uniwersytet Jana Kochanowskiego w Kielcach, Poland.
Recursion operators admitted by non-Abelian Burgers equations: some remarks2018In: Mathematics and Computers in Simulation, ISSN 0378-4754, E-ISSN 1872-7166, Vol. 147, no SI, p. 40-51Article in journal (Refereed)

The recursion operators admitted by different operator Burgers equations, in the framework of the study of nonlinear evolution equations, are here considered. Specifically, evolution equations wherein the unknown is an operator acting on a Banach space are investigated. Here, the mirror   non-Abelian Burgers equation is considered: it can be written as rt=rxx+2rxrrt=rxx+2rxr. The structural properties of the admitted recursion operator are studied; thus, it is proved to be a strong symmetry for the mirror non-Abelian Burgers equation as well as to be the hereditary. These results are proved via direct computations as well as via computer assisted manipulations; ad hoc routines are needed to treat non-Abelian quantities and relations among them. The obtained recursion operator generates the mirror   non-Abelian Burgers hierarchy. The latter, when the unknown operator rr is replaced by a real valued function reduces to the usual (commutative) Burgers hierarchy. Accordingly, also the recursion operator reduces to the usual Burgers one.

• 35.
Universita Roma La Sapienza.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
A non-commutative operator-hierarchy of Burgers equations and Bäcklund transformations2009In: Series on Advances in Mathematics for Applied Sciences, ISSN 1793-0901, Vol. 82Article in journal (Refereed)
• 36.
Universita Roma La Sapienza.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
Matrix KdV and mKdV hierarchies: Noncommutative soliton solutions and explicit formulae2009Report (Other academic)
• 37.
Univ Roma La Sapienza, Dipartimento Sci Base & Applicate Ingn, Sez Matemat, Rome, Italy .
Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
Matrix Korteweg-de Vries and modified Korteweg-de Vries hierarchies: Noncommutative soliton solutions2011In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 52, no 5, p. Art. no. 053507-Article in journal (Refereed)

The present work continues work on KdV-type hierarchies presented by S. Carillo and C. Schiebold ["Noncommutative Korteweg-de Vries and modified Korteweg-de Vries hierarchies via recursion methods," J. Math. Phys. 50, 073510 (2009)]. General solution formulas for the KdV and mKdV hierarchies are derived by means of Banach space techniques both in the scalar and matrix case. A detailed analysis is given of solitons, breathers, their countable superpositions as well as of multisoliton solutions for the matrix hierarchies. (C) 2011 American Institute of Physics. [doi:10.1063/1.3576185]

• 38.
Universita Roma La Sapienza.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
Noncommutative Korteweg-de Vries and modified Korteweg-de Vries hierarchies via recursion methods2009In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 50, no 7, article id 073510Article in journal (Refereed)

Here, noncommutative hierarchies of nonlinear equations are studied. They represent a generalization to the operator level of corresponding hierarchies of scalar equations, which can be obtained from the operator ones via a suitable projection. A key tool is the application of Baumlcklund transformations to relate different operator-valued hierarchies. Indeed, in the case when hierarchies in 1+1-dimensions are considered, a "Baumlcklund chart" depicts links relating, in particular, the Korteweg-de Vries (KdV) to the modified KdV (mKdV) hierarchy. Notably, analogous links connect the hierarchies of operator equations. The main result is the construction of an operator soliton solution depending on an infinite-dimensional parameter. To start with, the potential KdV hierarchy is considered. Then Baumlcklund transformations are exploited to derive solution formulas in the case of KdV and mKdV hierarchies. It is remarked that hierarchies of matrix equations, of any dimension, are also incorporated in the present framework.

• 39.
Dipartimento di Scienze di Base e Applicate per l'Ingegneria Sez. Matematica, SAPIENZA Università di Roma, Rome, Italy.
Mid Sweden University, Faculty of Science, Technology and Media, Department of applied science and design.
On the recursion operator for the noncommutative Burgers hierarchy2012In: Journal of Nonlinear Mathematical Physics, ISSN 1402-9251, E-ISSN 1776-0852, Vol. 19, no 1, p. Art. no. 1250003-Article in journal (Refereed)

The noncommutative Burgers recursion operator is constructed via the ColeHopf transformation, and its structural properties are studied. In particular, a direct proof of its hereditary property is given. © S. Carillo and C. Schiebold.

• 40.
Universita Roma I La Sapienza.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
Recursion techniques and explicit solutions of integrable noncommutative hierarchies2010In: Proceedings WASCOM 2009 / [ed] A. Greco, S. Rionero, T. Ruggeri, 2010, p. 74-80Conference paper (Refereed)
• 41.
Universität Jena.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences.
Ein direkter Ansatz zur Untersuchung von Solitonengleichungen2000In: Jahresbericht der Deutschen Mathematiker-Vereinigung (Teubner), ISSN 0012-0456, E-ISSN 1869-7135, Vol. 102, no 3, p. 102-148Article in journal (Refereed)
• 42.
Universität Jena.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences.
Nonlinear equations in soliton physics and operator ideals1999In: Nonlinearity, ISSN 0951-7715, E-ISSN 1361-6544, Vol. 12, no 2, p. 333-364Article in journal (Refereed)

An operator-theoretic method for the investigation of nonlinear equations in soliton physics is discussed comprehensively. Originating from pioneering work of Marchenko, our operator-method is based on new insights into the theory of traces and determinants on operator ideals. Therefore, we give a systematic and concise approach to some recent developments in this direction which are important in the context of this paper. Our method is widely applicable. We carry out the corresponding arguments in detail for the Kadomtsev-Petviashvili equation and summarize the results concerning the Korteweg-de Vries and the modified Korteweg-de Vries equation as well as for the sine-Gordon equation. Exactly the same formalism works in the discrete case, as the treatment of the Toda lattice, the Langmuir and the Wadati lattice shows.

• 43.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Comparison of the pluricomplex and the classical Green funcions1998In: The Michigan mathematical journal, ISSN 0026-2285, E-ISSN 1945-2365, Vol. 45, no 2, p. 399-407Article in journal (Refereed)
• 44.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Comparison of the pluricomplex and the classical Green functions1997Report (Other academic)
• 45.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics. Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Jensen measures, hyperconvexity and boundary behaviour of the pluricomplex Green function1999In: Annales Polonici Mathematici, ISSN 0066-2216, Vol. 71, no 1, p. 87-103Article in journal (Refereed)

We characterise hyperconvexity in terms of Jensen measures with barycentre at a boundary point. We also give an explicit formula for the pluricomplex Green function in the Hartogs' triangle. Finally we study the behaviour of the pluricomplex Green function $g(z,w)$ as the pole $w$ tends to a boundary point.

• 46. Carlsson, Linus
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Spectrum of certain Banach algebras and б-problems2007In: Annales Polonici Mathematici, ISSN 0066-2216, Vol. 90, no 1, p. 51-58Article in journal (Refereed)
• 47.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
A comparison priciple for the complex Monge-Ampere operator2003Book (Other academic)

A comparison priniple for the complex Monge-Ampere operator

• 48.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
A general Dirichlet problem for the Complex Monge-Ampere operator2006Report (Other academic)
• 49.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Approximation of plurisubharmonic functions in hyperconvex domains2006Report (Other academic)
• 50.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Boundary values of plurisubharmonic functions2004Book (Other academic)
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