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  • 1.
    Abdallah, Nancy
    University of Nice Sophia Antipolis, CNRS, LJAD, UMR 7351, 06100 Nice, Franc.
    On Hodge Theory of Singular Plane Curves2016In: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 59, no 3, p. 449-460Article in journal (Refereed)
    Abstract [en]

    The dimensions of the graded quotients of the cohomology of a plane curve complement U = P-2/C with respect to the Hodge filtration are described in terms of simple geometrical invariants. The case of curves with ordinary singularities is discussed in detail. We also give a precise numerical estimate for the difference between the Hodge filtration and the pole order filtration on H-2(U, C).

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  • 2.
    Abdallah, Nancy
    University of Nice.
    On Plane Curves with Double and Triple Points2016In: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 119, no 1, p. 60-72Article in journal (Refereed)
  • 3.
    Abdallah, Nancy
    et al.
    University of Borås, Faculty of Textiles, Engineering and Business.
    Altafi, Nasrin
    Department of Mathematics, KTH Royal Institute of Technology, S-100 44 Stockholm, Sweden; Department of Mathematics and Statistics, Queen's University, Kingston, Ontario, K7L 3N6, Canada.
    Iarrobino, Anthony
    Department of Mathematics, Northeastern University, Boston, MA 02115, USA.
    Seceleanu, Alexandra
    Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588, USA.
    Yaméogo, Joachim
    Université Côte d'Azur, CNRS, LJAD, France.
    Lefschetz properties of some codimension three Artinian Gorenstein algebras2023In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 625, p. 28-45Article in journal (Refereed)
    Abstract [en]

    Codimension two Artinian algebras have the strong and weak Lefschetz propertiesprovided the characteristic is zero or greater than the socle degree. It is open to whatextent such results might extend to codimension three Artinian Gorenstein algebras. De-spite much work, the strong Lefschetz property for codimension three Artinian Gorensteinalgebra has remained largely mysterious; our results build on and strengthen some of theprevious results. We here show that every standard-graded codimension three ArtinianGorenstein algebra A having maximum value of the Hilbert function at most six has thestrong Lefschetz property, provided that the characteristic is zero. When the characteris-tic is greater than the socle degree of A, we show that A is almost strong Lefschetz, theyare strong Lefschetz except in the extremal pair of degrees.

  • 4.
    Abdallah, Nancy
    et al.
    University of Borås, Faculty of Textiles, Engineering and Business.
    Emsalem, Jacques
    Paris, France.
    Iarrobino, Anthony
    Department of Mathematics, Northeastern University, Boston, MA, 02115, USA.
    Nets of conics and associated Artinian algebras of length 72023In: European Journal of Mathematics, ISSN 2199-675X, E-ISSN 2199-6768, Vol. 9, no 2, article id 22Article in journal (Refereed)
    Abstract [en]

    We classify the orbits of nets of conics under the action of the projective linear group and we determine the specializations of these orbits, using geometric and algebraic methods. We study related geometric questions, as the parametrization of planar cubics. We show that Artinian algebras of Hilbert function H=(1,3,3,0) determined by nets, can be smoothed—deformed to a direct sum of fields; and that algebras of Hilbert function H=(1,r,2,0), determined by pencils of quadrics, can also be smoothed. This portion is a translation and update of a 1977 version, a typescript by the second two authors that was distributed as a preprint of University of Paris VII. In a new Historical Appendix A we describe related work prior to 1977. In an Update Appendix B we survey some developments since 1977 concerning nets of conics, related geometry, and deformations of Artinian algebras of small length.

  • 5.
    Abdallah, Nancy
    et al.
    University of Borås, Faculty of Textiles, Engineering and Business.
    Emsalem, Jacques
    Northeastern Univ, Dept Math, Boston.
    Iarrobino, Anthony
    Northeastern Univ, Dept Math, Boston.
    Yaméogo, Joachim
    Univ Cote Azur, CNRS, LJAD, Nice, France.
    Limits of graded Gorenstein algebras of Hilbert function $$(1,3^k,1)$$2024In: European Journal of Mathematics, ISSN 2199-675X, E-ISSN 2199-6768, Vol. 10, no 1, article id 9Article in journal (Refereed)
    Abstract [en]

    Let R= k [x, y, z], the polynomial ring over a field k. Several of the authors previously classified nets of ternary conics and their specializations over an algebraically closed field, Abdallah et al. (Eur J Math 9(2), Art. No. 22, 2023). We here show that when k is algebraically closed, and considering the Hilbert function sequence T =(1,3(k),1), k >= 2 (i.e. T = (1, 3, 3, ... , 3, 1) where k is the multiplicity of 3), then the family GT parametrizing graded Artinian algebra quotients A = R/I of R having Hilbert function T is irreducible, and G(T) is the closure of the family Gor(T) of Artinian Gorenstein algebras of Hilbert function T. We then classify up to isomorphism the elements of these families Gor(T) and of G(T). Finally, we give examples of codimension 3 Gorenstein sequences, such as (1, 3, 5, 3, 1), for which G(T) has several irreducible components, one being the Zariski closure of Gor(T).

  • 6.
    Abdallah, Nancy
    et al.
    Linköpings Universitet.
    Hansson, Mikael
    Linköpings Universitet.
    Hultman, Axel
    Linköpings Universitet.
    Topology of posets with special partial matchings2019In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 348, p. 255-276Article in journal (Refereed)
    Abstract [en]

    Special partial matchings (SPMs) are a generalisation of Brenti's special matchings. Let a pircon be a poset in which every non-trivial principal order ideal is finite and admits an SPM. Thus pircons generalise Marietti's zircons. We prove that every open interval in a pircon is a PL ball or a PL sphere. It is then demonstrated that Bruhat orders on certain twisted identities and quasiparabolic W-sets constitute pircons. Together, these results extend a result of Can, Cherniaysky, and Twelbeck, prove a conjecture of Hultman, and confirm a claim of Rains and Vazirani.

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  • 7.
    Abdallah, Nancy
    et al.
    Linköpings Universitet.
    Hultman, Axel
    Linköpings Universitet.
    Combinatorial invariance of Kazhdan–Lusztig–Vogan polynomials for fixed point free involutions2017In: Journal of Algebraic Combinatorics, ISSN 0925-9899, E-ISSN 1572-9192, Vol. 47, no 4, p. 543-560Article in journal (Refereed)
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  • 8.
    Abdallah, Nancy
    et al.
    University of Borås, Faculty of Textiles, Engineering and Business.
    Schenck, Hal
    Free resolutions and Lefschetz properties of some Artin Gorenstein rings of codimension four2024In: Journal of symbolic computation, ISSN 0747-7171, E-ISSN 1095-855X, Vol. 121, p. 102257-102257, article id 102257Article in journal (Refereed)
    Abstract [en]

    In (Stanley, 1978), Stanley constructs an example of an Artinian Gorenstein (AG) ring A with non-unimodal H-vector (1,13,12,13,1). Migliore-Zanello show in (Migliore and Zanello, 2017) that for regularity r=4, Stanley's example has the smallest possible codimension c for an AG ring with non-unimodal H-vector.

    The weak Lefschetz property (WLP) has been much studied for AG rings; it is easy to show that an AG ring with non-unimodal H-vector fails to have WLP. In codimension c=3 it is conjectured that all AG rings have WLP. For c=4, Gondim shows in (Gondim, 2017) that WLP always holds for r≤4 and gives a family where WLP fails for any r≥7, building on Ikeda's example (Ikeda, 1996) of failure for r=5. In this note we study the minimal free resolution of A and relation to Lefschetz properties (both weak and strong) and Jordan type for c=4 and r≤6.

  • 9.
    Abdallah, Nancy
    et al.
    University of Borås, Faculty of Textiles, Engineering and Business.
    Schenck, Hal
    Department of Mathematics, Auburn University, Auburn, AL, 36849, USA.
    Nets in P^2 and Alexander Duality2023In: Discrete & Computational Geometry, ISSN 0179-5376, E-ISSN 1432-0444Article in journal (Refereed)
    Abstract [en]

    A net in P^2 is a configuration of lines A and points X satisfying certain incidence properties. Nets appear in a variety of settings, ranging from quasigroups to combinatorial design to classification of Kac–Moody algebras to cohomology jump loci of hyperplane arrangements. For a matroid M and rank r, we associate a monomial ideal (a monomial variant of the Orlik–Solomon ideal) to the set of flats of M of rank ≤r. In the context of line arrangements in P^2, applying Alexander duality to the resulting ideal yields insight into the combinatorial structure of nets.

  • 10.
    Al-Mulla, S Y Youssif
    University of Borås, School of Engineering.
    Spin Dependent Exchange Scattering from Ferromagnetic Materials2008Conference paper (Other academic)
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  • 11.
    Alrud, Bengt
    University of Borås, School of Engineering.
    Fractal spectral measures in two dimensions2011Doctoral thesis, monograph (Other academic)
  • 12. Anderson, D.
    et al.
    Andersson, F.
    Andersson, Peter
    University of Borås, School of Engineering.
    Billander, A.
    Desaix, Mats
    University of Borås, School of Engineering.
    The optimal journey from A to B2008In: American Journal of Physics, ISSN 0002-9505, E-ISSN 1943-2909, Vol. 76, no 9, p. 863-866Article in journal (Refereed)
    Abstract [en]

    How fast can you comfortably travel between two points A and B? This question is formulated as a minimization problem of a functional where the discomfort is quantified in terms of the integral of the square of the acceleration between A and B. The problem is solved in terms of the corresponding Euler-Lagrange equation and approximately using a direct variational approach based on trial functions and Ritz optimization. The main purpose of the analysis is to introduce undergraduate students to variational calculus in an interesting and pedagogical way.

  • 13. Anderson, D
    et al.
    Desaix, Mats
    University of Borås, Faculty of Textiles, Engineering and Business.
    Introduction to direct variational and moment methods and an application to the Child–Langmuir law2015In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 36, no 6Article in journal (Refereed)
    Abstract [en]

    A short introduction is given of direct variational methods and its relation to Galerkin and moment methods, all flexible and powerful approaches for finding approximate solutions of difficult physical equations. A pedagogical application of moment methods is given to the physically and technically important Child–Langmuir law in electron physics. The analysis is shown to provide simple, yet accurate, approximate solutions of the two-dimensional problem (a problem which does not allow an exact analytical solution) and illustrates the usefulness and the power of moment methods.

  • 14. Anderson, D.
    et al.
    Desaix, Mats
    University of Borås, School of Engineering.
    Lisak, M.
    Rasch, J.
    Galerkin approach to approximate solutions of some nonlinear oscillator equations2010In: American Journal of Physics, ISSN 0002-9505, E-ISSN 1943-2909, Vol. 78, no 9, p. 920-924Article in journal (Refereed)
    Abstract [en]

    An analysis based on the Galerkin method is given of some nonlinear oscillator equations that have been analyzed by several other methods, including harmonic balance and direct variational methods. The present analysis is shown to provide simple yet accurate approximate solutions of these nonlinear equations and illustrates the usefulness and the power of the Galerkin method. (C) 2010 American Association of Physics Teachers.

  • 15.
    Anderson, Dan
    et al.
    Chalmers .
    Desaix, Mats
    University of Borås, Faculty of Textiles, Engineering and Business.
    Approximate solution of a Thomas-Fermi model equation for bulk self-gravitating stellar objects in two dimensions2017In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 38, p. 1-8, article id 015406Article in journal (Refereed)
    Abstract [en]

    Direct variational methods are used to find simple approximate solutions of the Thomas–Fermi equations describing the properties of self-gravitating radially symmetric stellar objects both in the non-relativistic and ultra-relativistic cases. The approximate solutions are compared and shown to be in good agreement with exact and numerically obtained solutions.

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  • 16.
    Andersson, Fredrik
    et al.
    Lunds universitet.
    Morimoto, Yoshinori
    Kyoto University.
    Wittsten, Jens
    Kyoto University.
    A variational formulation for interpolation of seismic traces with derivative information2015In: Inverse Problems, Vol. 31, no 5, article id 055002Article in journal (Refereed)
    Abstract [en]

    We construct a variational formulation for the problem of interpolating seismic data in the case of missing traces. We assume that we have derivative information available at the traces. The variational problem is essentially the minimization of the integral over the smallest eigenvalue of the structure tensor associated with the interpolated data. This has the physical meaning of penalizing the local presence of more than one direction in the interpolation. The variational problem is used to justify the solutions of a non-standard anisotropic diffusion problem as reasonable interpolated images. We show existence and uniqueness for this type of anisotropic diffusion. In particular, the uniqueness property is important as it guarantees that the solution can be obtained by the numerical schemes we propose.

  • 17. Andersson, L
    et al.
    Petersen, G
    Johnson, P
    Ståhl, Fredrik
    University of Borås, School of Health Science.
    A web tool for finding gene candidates associated with experimentally induced arthritis in rat2005In: Arthritis Research & Therapy, ISSN 1478-6354, E-ISSN 1478-6362, Vol. 7, no 3, p. R485-R492Article in journal (Refereed)
    Abstract [en]

    Rat models are frequently used for finding genes contributing to the arthritis phenotype. In most studies, however, limitations in the number of animals result in a low resolution. As a result, the linkage between the autoimmune experimental arthritis phenotype and the genomic region, that is, the quantitative trait locus, can cover several hundred genes. The purpose of this work was to facilitate the search for candidate genes in such regions by introducing a web tool called Candidate Gene Capture (CGC) that takes advantage of free text data on gene function. The CGC tool was developed by combining genomic regions in the rat, associated with the autoimmune experimental arthritis phenotype, with rat/human gene homology data, and with descriptions of phenotypic gene effects and selected keywords. Each keyword was assigned a value, which was used for ranking genes based on their description of phenotypic gene effects. The application was implemented as a web-based tool and made public at http://ratmap.org/cgc. The CGC application ranks gene candidates for 37 rat genomic regions associated with autoimmune experimental arthritis phenotypes. To evaluate the CGC tool, the gene ranking in four regions was compared with an independent manual evaluation. In these sample tests, there was a full agreement between the manual ranking and the CGC ranking for the four highest-ranked genes in each test, except for one single gene. This indicates that the CGC tool creates a ranking very similar to that made by human inspection. The exceptional gene, which was ranked as a gene candidate by the CGC tool but not in the manual evaluation, was found to be closely associated with rheumatoid arthritis in additional literature studies. Genes ranked by the CGC tools as less likely gene candidates, as well as genes ranked low, were generally rated in a similar manner to those done manually. Thus, to find genes contributing to experimentally induced arthritis, we consider the CGC application to be a helpful tool in facilitating the evaluation of large amounts of textual information.

  • 18. Aneja, Arun
    et al.
    Pal, Rudrajeet
    University of Borås, Swedish School of Textiles.
    Militky, Jiri
    Kupka, Karel
    Kremenakova, Dana
    Torstensson, Håkan
    University of Borås, Swedish School of Textiles.
    Textile Thru the Looking Glass: A Novel Perspective2013Conference paper (Other academic)
    Abstract [en]

    Today, textiles and fiber science in US, Europe and Japan from its once lofty perch in the global economy, stands in stark contrast to its preeminent position of few decades ago. Its influence on the society as a whole has eroded enormously. Many of the synthetic fiber products that once fuelled the rapid growth of the industry have become mature commodity products now characterized by low growth and lower profit margins. To add to the current dilemma, organizational ‘health’ and growth processes are constantly threatened in this era of turbulence. Thus the drive for survival and success has translated, in recent times, to quest for resiliency – to survive and thrive in turbulences. On the other hand, most managers and academicians agree that innovation ensures superior organizational performance while recent research has shown that most resilient companies can dynamically orchestrate diverse innovation strategies. Resiliency in such a context has become a prerequisite for a sustained long term business prosperity fuelled by diverse technological innovations. This has intensified the organization’s search for differentiated products and services, processes, business models, technology, strategies etc. pushing firms to gain competitive advantage and also to develop new knowledge and innovation performance to drive sustainable growth. Organizations now follow multiple innovation strategies to pragmatically devise their innovation repertoire for delivering growth, hence, success in turbulent times while emphasizing resiliency. What does the future hold and how can we reverse the trend to achieve and sustain the impressive credentials of the past? To understand the significance of what the future may hold, and to reverse the downward spiral of the industry, we must evaluate the successes and failures of the past and come to grips with rapid global changes and turbulences currently underway. The present article seeks to explore such an inexorable phenomenon of quantifying and correlating innovation and business resiliency over a time line, from the annual financial data of 35 healthy and unhealthy companies along with 5 textile companies over a span of few decades. These are then extrapolated with certain predictive capabilities to suggest future trends and strategies for the textile companies. Learning from these companies, if adopted, will yield capacity to transform the scenario. Assessments and classification of the economic health of a company is typically made based on some quantity derived from selected indices, such as Altman’s Z-score. These methods can describe an instantaneous status, or a “time snap” of an economical subject but lack information about the time-dynamics of the assessment, which is important for investors, shareholders and the management. We suggest using historical data to estimate current trends in the form of the first and second time-derivative of the appropriate quantity in the time domain. This new information is independent on the quantity itself and beside more precise description can be used as new predictor to improve effectiveness of classification of successful and unsuccessful subjects. This approach is further discussed in this paper.

  • 19.
    Atanasiu, Dragu
    University of Borås, Faculty of Textiles, Engineering and Business.
    Linear Algebra: Core Topics for the First Course2020 (ed. 1)Book (Refereed)
    Abstract [en]

    The book is an introduction to linear algebra intended as a textbook for the first course in linear algebra. In the first six chapters we present the core topics: matrices, the vector space ℝn, orthogonality in ℝn, determinants, eigenvalues and eigenvectors, and linear transformations. The book gives students an opportunity to better understand linear algebra in the next three chapters: Jordan forms by examples, singular value decomposition, and quadratic forms and positive definite matrices.

    In the first nine chapters everything is formulated in terms of ℝn. This makes the ideas of linear algebra easier to understand. The general vector spaces are introduced in Chapter 10. The last chapter presents problems solved with a computer algebra system. At the end of the book we have results or solutions for odd numbered exercises.

  • 20.
    Atanasiu, Dragu
    University of Borås, School of Engineering.
    Spectral Measures on Compacts of Characters of a Semigroup2010Conference paper (Refereed)
  • 21.
    Atanasiu, Dragu
    University of Borås, School of Engineering.
    The Disc Algebra and a Moment Problem2007In: Function Spaces: Fifth Conference on Function Spaces, May 16-20, 2006, Southern Illinois University, Edwardsville, Illinois, American Mathematical Society , 2007, p. 53-56Chapter in book (Other academic)
  • 22.
    Atanasiu, Dragu
    et al.
    University of Borås, Faculty of Textiles, Engineering and Business.
    Bengtsson, Anders
    University of Borås, Faculty of Textiles, Engineering and Business.
    Modern differential- och integralkalkyl2015 (ed. 1)Book (Refereed)
  • 23.
    Atanasiu, Dragu
    et al.
    University of Borås, Faculty of Textiles, Engineering and Business.
    Mikusinski, Piotr
    University of Central Florida.
    A bridge to linear algebra2019 (ed. 1)Book (Refereed)
    Abstract [en]

    The book makes a first course in linear algebra more accessible to the majority of students and it assumes no prior knowledge of the subject. It provides a careful presentation of particular cases of all core topics. Students will find that the explanations are clear and detailed in manner. It is considered as a bridge over the obstacles in linear algebra and can be used with or without the help of an instructor.While many linear algebra texts neglect geometry, this book includes numerous geometrical applications. For example, the book presents classical analytic geometry using concepts and methods from linear algebra, discusses rotations from a geometric viewpoint, gives a rigorous interpretation of the right-hand rule for the cross product using rotations and applies linear algebra to solve some nontrivial plane geometry problems.Many students studying mathematics, physics, engineering and economics find learning introductory linear algebra difficult as it has high elements of abstraction that are not easy to grasp. This book will come in handy to facilitate the understanding of linear algebra whereby it gives a comprehensive, concrete treatment of linear algebra in R² and R³. This method has been shown to improve, sometimes dramatically, a student's view of the subject.

  • 24.
    Atanasiu, Dragu
    et al.
    University of Borås, Faculty of Textiles, Engineering and Business.
    Mikusinski, Piotr
    Department of Mathematics,University of Central Florida, Orlando, FL, USA.
    An elementary operational calculus2015In: Mathematical Gazette, ISSN 0025-5572, Vol. 99, no 544Article in journal (Refereed)
  • 25.
    Atanasiu, Dragu
    et al.
    University of Borås, School of Engineering.
    Mikusinski, Piotr
    Fourier transform of Radon measures on a locally compact group2010In: Integral transforms and special functions, ISSN 1065-2469, E-ISSN 1476-8291, Vol. 21, no 11, p. 815-821Article in journal (Refereed)
    Abstract [en]

    A space of generalized functions is constructed that allows us to generalize Bochner's theorem so that all Radon measures on a locally compact group are in a one-to-one correspondence with elements of that space of generalized functions. This defines a Fourier transform for all Radon measures on a locally compact group.

  • 26.
    Atanasiu, Dragu
    et al.
    University of Borås, School of Engineering.
    Mikusinski, Piotr
    On the fourier transform, Boehmians, and distributions2007In: Colloquium Mathematicum, ISSN 0010-1354, E-ISSN 1730-6302, Vol. 108, no 2, p. 263-276Article in journal (Refereed)
    Abstract [en]

    We introduce some spaces of generalized functions that are defined as generalized quotients and Boehmians. The spaces provide simple and natural frameworks for extensions of the Fourier transform.

  • 27.
    Atanasiu, Dragu
    et al.
    University of Borås, School of Engineering.
    Mikusinski, Piotr
    The Fourier transform of Lévy measures on a semigroup2008In: Integral transforms and special functions, ISSN 1065-2469, E-ISSN 1476-8291, Vol. 19, no 8, p. 537-543Article in journal (Refereed)
  • 28.
    Atanasiu, Dragu
    et al.
    University of Borås, School of Engineering.
    Mikusinski, Piotr
    Nemzer, Dennis
    An algebraic approach to tempered distributions2011In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 384, no 2, p. 307-319Article in journal (Refereed)
    Abstract [en]

    A space of pseudoquotients is introduced that is shown to be isomorphic to the space of tempered distributions on RN. The Fourier transform is defined as a map from the space of pseudoquotients to the space of tempered distributions and as a transformation on pseudoquotients.

  • 29.
    Atanasiu, Dragu
    et al.
    University of Borås, School of Engineering.
    Mikusinski, Piotr
    Siple, Angela
    Pseudoquotients on commutative Banach algebras2014In: Banach Journal of Mathematical Analysis, ISSN 1735-8787, Vol. 8, no 2, p. 60-66Article in journal (Refereed)
    Abstract [en]

    We consider pseudoquotient extensions of positive linear functionals on a commutative Banach algebra A and give conditions under which the constructed space of pseudoquotients can be identified with all Radon measures on the structure space A.

  • 30.
    Atanasiu, Dragu
    et al.
    University of Borås, Faculty of Textiles, Engineering and Business.
    Mikusiński, Piotr
    University of Central Florida, USA.
    Linear Algebra: Core Topics for the Second Course2023Book (Other academic)
    Abstract [en]

    This is a book for the second course in linear algebra whereby students are assumed to be familiar with calculations using real matrices. To facilitate a smooth transition into rigorous proofs, it combines abstract theory with matrix calculations. This book presents numerous examples and proofs of particular cases of important results before the general versions are formulated and proved. The knowledge gained from a particular case, that encapsulates the main idea of a general theorem, can be easily extended to prove another particular case or a general case. For some theorems, there are two or even three proofs provided. In this way, students stand to gain and study important results from different angles and, at the same time, see connections between different results presented in the book.

  • 31.
    Atanasiu, Dragu
    et al.
    University of Borås, School of Engineering.
    Nemzer, Dennis
    Extending the Laplace Transform2008In: Mathematics Student, ISSN 0025-5742, Vol. 77, p. 203-212Article in journal (Refereed)
  • 32.
    Beach, Dennis
    et al.
    University of Borås, School of Education and Behavioural Science.
    Player-Koro, Catarina
    University of Borås, School of Education and Behavioural Science.
    Authoritative Knowledge in Initial Teacher Education: Studying the Role of Subject Textbooks through Two Ethnographic Studies of Mathematics Teacher Education.2012In: Journal of Education for Teaching, ISSN 0260-7476, E-ISSN 1360-0540, Vol. 38, no 2, p. 115-125Article in journal (Refereed)
    Abstract [en]

    Two related ethnographic research projects on mathematics teacher education in Sweden are presented in this paper. They represent a response to recent policy developments that reaffirm the value of authoritative subject studies content as the central and most important component in the professional knowledge base of would-be teachers and concomitant increases in the amount of subject studies in teacher education. These policy changes, in Sweden at least, lack scientific research support and the article argues that these policies need to be seriously rethought, as the increased emphasis on subject content may undermine the development of key professional skills.

  • 33.
    Becker, Simon
    et al.
    University of Cambridge.
    Embree, Mark
    Virginia Tech.
    Wittsten, Jens
    University of Borås, Faculty of Textiles, Engineering and Business.
    Zworski, Maciej
    University of California at Berkeley.
    Mathematics of magic angles in a model of twisted bilayer graphene2022In: Probability and Mathematical Physics, ISSN 2690-0998, Vol. 3, no 1, p. 69-103Article in journal (Refereed)
    Abstract [en]

    We provide a mathematical account of the recent letter by Tarnopolsky, Kruchkov and Vishwanath (Phys. Rev. Lett.122:10 (2019), art. id. 106405). The new contributions are a spectral characterization of magic angles, its accurate numerical implementation and an exponential estimate on the squeezing of all bands as the angle decreases. Pseudospectral phenomena due to the nonhermitian nature of operators appearing in the model considered in the letter of Tarnopolsky et al. play a crucial role in our analysis.

  • 34.
    Bengtsson, Anders
    University of Borås, School of Engineering.
    Light-front higher-helicity interactions2012In: Fortschritte der Physik. Special Issue: Proceedings of the XVIIthe European Workshop on String Theory 2011, Padua, Italy, 4-9 September 2011 (part 2), Wiley , 2012, p. 1038-1043Conference paper (Refereed)
    Abstract [en]

    The reformulation, using Fock space vertex operators, of the original light-front cubic interaction terms for higher spin gauge fields is reviewed with comments on quantum higher spin gravity. The formalism is generalized to all orders in the interaction. The ensuing recursive equations for the higher order vertices, if they can be explicitly solved, will encode all interaction data into a denumerable set of rational functions of p+, the overall transverse momentum structure being fixed already at the kinematical level. A more thorough exposition can be found in the archive.

  • 35.
    Bengtsson, Anders
    University of Borås, School of Engineering.
    Systematics of Higher-spin Light-front Interactions2012In: arXivArticle in journal (Other academic)
    Abstract [en]

    The original cubic interaction terms for higher spin gauge fields in four dimensions and their reformulation using Fock space vertex operators is reviewed. As a new result, the complete list of all cubic vertex functions in D=4 is derived. It is observed, contrary to what would have been expected, that the non-linear dynamical Poincar\'e transformations do not restrict the cubic interactions beyond what is required by kinematics. The role of the SU(1,1) algebra of tracelessness constraints is clarified. It is shown that higher spin fields couple non-minimally to gravity at the cubic level in D=4 light-front dynamics. Based on a detailed analysis of the structure of the light-front Poincar\'e algebra, the formalism is then generalized to all orders in the interaction. The interacting theory, being a deformation of the free theory, takes the form of a strongly homotopy Lie algebra. It is conjectured that the ensuing recursive equations, if they can be explicitly solved, will encode all interaction data into a denumerable set of functions of p+, the overall transverse momentum structure being fixed already at the kinematical level.

  • 36.
    Bengtsson, Anders
    et al.
    University of Borås, School of Engineering.
    Brink, Lars
    Kim, Sung-Soo
    Counterterms in Gravity in the Light-Front Formulation and a D=2 Conformal-like Summetry in Gravity2013In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, Vol. 2013, no 3Article in journal (Other academic)
    Abstract [en]

    In this paper we discuss gravity in the light-front formulation (light-cone gauge) and show how possible counterterms arise. We find that Poincare invariance is not enough to find the three-point counterterms uniquely. Higher-spin fields can intrude and mimic three-point higher derivative gravity terms. To select the correct term we have to use the remaining reparametrization invariance that exists after the gauge choice. We finally sketch how the corresponding programme for N=8 Supergravity should work.

  • 37.
    Bengtsson, Magnus
    et al.
    University of Borås, Faculty of Textiles, Engineering and Business.
    Waidringer, Jonas
    University of Borås, Faculty of Textiles, Engineering and Business.
    A proposed method using GPU based SDO to optimize retail warehouses2022Conference paper (Refereed)
    Abstract [en]

    Research in warehouse optimization has gotten increased attention in the last few years due to e-commerce. The warehouse contains a waste range of different products. Due to the nature of the individual order, it is challenging to plan the picking list to optimize the material flow in the process. There are also challenges in minimizing costs and increasing production capacity, and this complexity can be defined as a multidisciplinary optimization problem with an IDF nature. In recent years the use of parallel computing using GPGPUs has become increasingly popular due to the introduction of CUDA C and accompanying applications in, e.g., Python. 

    In the case study at the company in the field of retail, a case study including a system design optimization (SDO) resulted in an increase in throughput with well over 20% just by clustering different categories and suggesting in which sequence the orders should be picked during a given time frame. 

    The options provided by implementing a distributed high-performance computing network based on GPUs for subsystem optimization have shown to be fruitful in developing a functioning SDO for warehouse optimization. The toolchain can be used for designing new warehouses or evaluating and tuning existing ones. 

  • 38. Björklund, Camilla
    et al.
    Grevholm, Barbro
    Häggström, Johan
    Kjellström, Katarina
    Löfwall, Stefan
    Norén, Eva
    Olofsson, Gunilla
    Persson, Elisabeth
    University of Borås, School of Education and Behavioural Science.
    Persson, Lars-Erik
    Persson, Per-Eskil
    Riesbeck, Eva
    Taflin, Eva
    Lära och undervisa matematik: från förskoleklass till årskurs 62012Book (Other academic)
  • 39.
    Carlsson, Marcus
    et al.
    Lunds universitet.
    Wittsten, Jens
    Kyoto University.
    A Note on holomorphic functions and the fourier-laplace transform2017In: Mathematica Scandinavica, Vol. 120, no 2, p. 225-248Article in journal (Refereed)
    Abstract [en]

    We revisit the classical problem of when a given function, which is analytic in the upper half plane C+, can be written as the Fourier transform of a function or distribution with support on a half axis (-infinity, b], b is an element of R. We derive slight improvements of the classical Paley-Wiener-Schwartz Theorem, as well as softer conditions for verifying membership in classical function spaces such as H-P (C+).

  • 40.
    Carlsson, Marcus
    et al.
    Lunds universitet.
    Wittsten, Jens
    Kyoto University.
    The Dirichlet problem for standard weighted Laplacians in the upper half plane2016In: Journal of Mathematical Analysis and Applications, Vol. 436, no 2, p. 868-889Article in journal (Refereed)
    Abstract [en]

    In this paper the Dirichlet problem for a class of standard weighted Laplace operators in the upper half plane is solved by means of a counterpart of the classical Poisson integral formula. Boundary limits and representations of the associated solutions are studied within a framework of weighted spaces of distributions. Special attention is given to the development of a, suitable uniqueness theory for the Dirichlet problem under appropriate growth constraints at infinity. (C) 2015 Elsevier Inc. All rights reserved.

  • 41.
    Chung, Yong Moo
    et al.
    Department of Applied Mathematics, Hiroshima University, Higashi-Hiroshima, 739-8527, Japan.
    Nakano, Yushi
    Department of Mathematics, Tokai University, Kanagawa, 259-1292, Japan.
    Wittsten, Jens
    University of Borås, Faculty of Textiles, Engineering and Business. Centre for Mathematical Sciences, Lund University, 221 00 Lund, Sweden.
    Quenched limit theorems for random U(1) extensions of expanding maps2023In: Discrete and Continuous Dynamical Systems, ISSN 1078-0947, E-ISSN 1553-5231, Vol. 43, no 1, p. 338-377Article in journal (Refereed)
    Abstract [en]

    In this paper we provide quenched central limit theorems, large deviation principles and local central limit theorems for random U(1) extensions of expanding maps on the torus. The results are obtained as special cases of corresponding theorems that we establish for abstract random dynamical systems. We do so by extending a recent spectral approach developed for quenched limit theorems for expanding and hyperbolic maps to be applicable also to partially hyperbolic dynamics.

  • 42.
    Darányi, Sándor
    University of Borås, Swedish School of Library and Information Science.
    First- and second-order change as symmetry and symmetry breaking in folklore text content evolution: From Heraclitus to Lévi-Strauss2007Conference paper (Refereed)
    Abstract [en]

    We distinguish between first- and second order change and identify the former with perpetual alternation on an existential plane, the second with moving out into existential space. The first type can be demonstrated by two antagonistic processes inherent in a Markov chain of two pairs of complementary values: the chain gradually alternates between the opposite terminal states and the pattern is symmetrical. Such an existential plane catches an essential feature of Heraclitus’ philosophy, and can be illustrated by examples from classical Greek mythology. The same material also exemplifies Lévi-Strauss’ formula of myth, symmetrical in its weak and asymmetrical in 2 its canonical form. Since the weak form equals the orbit of a Klein group, we hypothesize that the canonical form, and thereby symmetry breaking, can be generated by element exchange between two respective Klein groups. The framework for such processes is text variation in folklore, described by ethnosemiotics.

    Download full text (pdf)
    FULLTEXT01
  • 43.
    Darányi, Sándor
    University of Borås, Swedish School of Library and Information Science.
    Látvány és jelentés: Budapesti épuletszobrok elemzése és fejlödéstörténeti modellezése2007Conference paper (Other academic)
  • 44.
    Darányi, Sándor
    et al.
    University of Borås, Swedish School of Library and Information Science.
    Wittek, Peter
    University of Borås, Swedish School of Library and Information Science.
    Connecting the Dots: Mass, Energy, Word Meaning, and Particle-Wave Duality2012Conference paper (Refereed)
    Abstract [en]

    With insight from linguistics that degrees of text cohesion are similar to forces in physics, and the frequent use of the energy concept in text categorization by machine learning, we consider the applicability of particle-wave duality to semantic content inherent in index terms. Wave-like interpretations go back to the regional nature of such content, utilizing functions for its representation, whereas content as a particle can be conveniently modelled by position vectors. Interestingly, wave packets behave like particles, lending credibility to the duality hypothesis. We show in a classical mechanics framework how metaphorical term mass can be computed.

    Download full text (pdf)
    FULLTEXT01
  • 45.
    Darányi, Sándor
    et al.
    University of Borås, Swedish School of Library and Information Science.
    Wittek, Peter
    University of Borås, Swedish School of Library and Information Science.
    On Information, Meaning, Space and Geometry2009In: Exploration of Space, Technology and Spatiality: Interdisciplinary Perspectives / [ed] Susan Turner, E. D. P. Turner, Hersey: Idea Group , 2009Chapter in book (Other academic)
    Abstract [en]

    We offer a few general considerations, with theoretical overtones, working toward the definition and generation of a geometric language for practical purposes, prominently for information retrieval. This chapter is a non-mathematical introduction to the mathematical modelling of meaning of both words and sentences, outlining already existing components of such an endeavour, and hinting at directions of synthesis.

  • 46.
    Darányi, Sándor
    et al.
    University of Borås, Swedish School of Library and Information Science.
    Wittek, Peter
    University of Borås, Swedish School of Library and Information Science.
    Dobreva, Milena
    Position paper: Adding a 5M layer to the 5S model of digital libraries.2010Conference paper (Refereed)
    Abstract [en]

    We expect radical changes in document ( rst and foremost text) representation for digital libraries (DL) leading to new applications for documents processing.

    Download full text (pdf)
    FULLTEXT01
  • 47.
    Darányi, Sándor
    et al.
    University of Borås, Swedish School of Library and Information Science.
    Wittek, Peter
    University of Borås, Swedish School of Library and Information Science.
    Kitto, Kirsty
    The Sphynx's new riddle: How to relate the canonical formula of myth to quantum interaction2013Conference paper (Refereed)
    Abstract [en]

    We introduce Claude Lévi Strauss' canonical formula (CF), an attempt to rigorously formalise the general narrative structure of myth. This formula utilises the Klein group as its basis, but a recent work draws attention to its natural quaternion form, which opens up the possibility that it may require a quantum inspired interpretation. We present the CF in a form that can be understood by a non-anthropological audience, using the formalisation of a key myth (that of Adonis) to draw attention to its mathematical structure. The future potential formalisation of mythological structure within a quantum inspired framework is proposed and discussed, with a probabilistic interpretation further generalising the formula.

    Download full text (pdf)
    FULLTEXT01
  • 48.
    Dencker, Nils
    et al.
    Lunds universitet.
    Wittsten, Jens
    Kyoto University.
    On the Microlocal Properties of the Range of Systems of Principal Type2013In: Communications in Partial Differential Equations, Vol. 38, no 3, p. 410-454Article in journal (Refereed)
    Abstract [en]

    The purpose of this paper is to study microlocal conditions for inclusion relations between the ranges of square systems of pseudodifferential operators which fail to be locally solvable. The work is an extension of earlier results for the scalar case in this direction, where analogues of results by L. Hormander about inclusion relations between the ranges of first order differential operators with coefficients in C which fail to be locally solvable were obtained. We shall study the properties of the range of systems of principal type with constant characteristics for which condition () is known to be equivalent to microlocal solvability.

  • 49.
    Desaix, Mats
    et al.
    University of Borås, School of Engineering.
    Andersson, Dan
    Lisak, Mietek
    Eigenvalues of the Zakharov-Shabat scattering problem for two separated sech-shaped pulses2008In: Physics Letters A, ISSN 0375-9601, E-ISSN 1873-2429, Vol. 372, no 14, p. 2386-2390Article in journal (Refereed)
  • 50. Eivani, S
    et al.
    Saedpanah, Fardin
    Department of Mathematics, University of Kurdistan, Iran.
    Strong convergence of spectral Galerkin method for the linear stochastic wave equation with additive noise2014Conference paper (Refereed)
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