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  • 1. Abramov, V.
    et al.
    Paal, E.Tallinn University of Technology.Silvestrov, Sergei D.Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Stolin, A.Chalmers University of Techology.
    Proceedings of the 3rd Baltic-Nordic Workshop “Algebra, Geometry, and Mathematical Physics”2008Conference proceedings (editor) (Refereed)
  • 2.
    Arnlind, Joakim
    et al.
    Max Planck Institute for Gravitational Physics (AEI), Am Mühlenberg 1, D-14476 Golm, Germany.
    Makhlouf, Abdenacer
    Université de Haute Alsace, Lab. de Mathématiques Informatique et Applications, 4, rue des Frères Lumière, F-68093 Mulhouse, France.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication.
    Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras2011In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 52, no 12, p. 123502-Article in journal (Refereed)
    Abstract [en]

    As n-ary operations, generalizing Lie and Poisson algebras, arise in many different physical contexts, it is interesting to study general ways of constructing explicit realizations of such multilinear structures. Generically, they describe the dynamics of a physical system, and there is a need of understanding their quantization. Hom-Nambu-Lie algebras provide a framework that might be an appropriate setting in which n-Lie algebras (n-ary Nambu-Lie algebras) can be deformed, and their quantization studied. We present a procedure to construct (n + 1)-ary Hom-Nambu-Lie algebras from n-ary Hom-Nambu-Lie algebras equipped with a generalized trace function. It turns out that the implications of the compatibility conditions, that are necessary for this construction, can be understood in terms of the kernel of the trace function and the range of the twisting maps. Furthermore, we investigate the possibility of defining (n + k)-Lie algebras from n-Lie algebras and a k-form satisfying certain conditions. (C) 2011 American Institute of Physics. [doi:10.1063/1.3653197]

  • 3.
    Ataguema, H.
    et al.
    Universit́e de Haute Alsace, France .
    Makhlouf, A.
    Universit́e de Haute Alsace, France .
    Silvestrov, S. D.
    Lund University.
    Generalization of n-ary Nambu algebras and beyond2009In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 50, no 8, p. Article number 083501-Article in journal (Refereed)
    Abstract [en]

    The aim of this paper is to introduce n-ary Hom-algebra structures generalizing the n-ary algebras of Lie type including n-ary Nambu algebras, n-ary Nambu-Lie algebras and n-ary Lie algebras, and n-ary algebras of associative type including n-ary totally associative and n-ary partially associative algebras. We provide examples of the new structures and present some properties and construction theorems. We describe the general method allowing one to obtain an n-ary Hom-algebra structure starting from an n-ary algebra and an n-ary algebra endomorphism. Several examples are derived using this process. Also we initiate investigation of classification problems for algebraic structures introduced in the article and describe all ternary three-dimensional Hom-Nambu-Lie structures with diagonal homomorphism.

  • 4.
    Li, H.
    et al.
    Royal Institute of Technology, Sweden.
    Ji, X.
    Royal Institute of Technology, Sweden.
    Yan, Jinyue
    Mälardalen University, School of Sustainable Development of Society and Technology. Royal Institute of Technology, Sweden.
    A new modification on RK EOS for gaseous CO2 and gaseous mixtures of CO2 and H2O2006In: International journal of energy research (Print), ISSN 0363-907X, E-ISSN 1099-114X, Vol. 30, no 3, p. 135-148Article in journal (Refereed)
    Abstract [en]

    To develop an equation of state with simple structure and reasonable accuracy for engineering application, Redlich-Kwong equation of state was modified for gaseous CO2 and CO2-H2O mixtures. In the new modification, parameter a of gaseous CO2 was regressed as a function of temperature and pressure from recent reliable experimental data in the range: 220-750 K and 0.1-400 MPa. Moreover, a new mixing rule was proposed for gaseous CO2-H2O mixtures. To verify the accuracy of the new modification, densities were calculated and compared with experimental data. The average error is 1.68% for gaseous CO2 and 0.93% for gaseous mixtures of CO2 and H2O. Other thermodynamic properties, such as enthalpy and heat capacities of CO2 and excess enthalpy of gaseous CO2-H2O mixtures, were also calculated; results fit experimental data well, except for the critical region.

  • 5.
    Malyarenko, Anatoliy
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Ostoja-Starzewski, Martin
    University of Illinois at Urbana-Champaign.
    Tensor Random Fields in Continuum Mechanics2018In: Encyclopedia of Continuum Mechanics / [ed] Altenbach, Holm and Öchsner, Andreas, Berlin, Heidelberg: Springer Berlin/Heidelberg, 2018, p. 1-9Chapter in book (Refereed)
  • 6.
    Malyarenko, Anatoliy
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Ostoja-Starzewski, Martin
    University of Illinois at Urbana-Champaign, USA.
    Tensor-Valued Random Fields in Continuum Physics2016In: Materials with internal structure: Multiscale and Multifield Modeling and Simulation / [ed] P. Trovalusci, Berlin/Heidelberg: Springer Science+Business Media B.V., 2016, p. 75-88Chapter in book (Refereed)
    Abstract [en]

    This article reports progress on homogeneous isotropic tensor random fields (TRFs) for continuum mechanics. The basic thrust is on determinin most general representations of the correlation functions as well as their spectral expansions. Once this is accomplished, the second step is finding the restrictionsdictated by a particular physical application. Thus, in the case of fields of material properties (like conductivity and stiffness), the restriction resides in the positive-definiteness, whereby a connection to experiments and/or computational micromechanics can be established. On the other hand, in the case of fields of dependent properties (e.g., stress, strain and displacement), restrictions are due to the respective field equations.

  • 7.
    Monsefi, Farid
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Otterskog, Magnus
    Mälardalen University, School of Innovation, Design and Engineering. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Direct and Inverse Computational Methods for Electromagnetic Scattering in Biological Diagnostics2013Report (Other academic)
    Abstract [en]

    Scattering theory has had a major roll in twentieth century mathematical physics. Mathematical modeling and algorithms of direct,- and inverse electromagnetic scattering formulation due to biological tissues are investigated. The algorithms are used for a model based illustration technique within the microwave range. A number of methods is given to solve the inverse electromagnetic scattering problem in which the nonlinear and ill-posed nature of the problem are acknowledged.

  • 8.
    Ostoja-Starzewski, Martin
    et al.
    University of Illinois in Urbana-Champaigne, USA.
    Malyarenko, Anatoliy
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Continuum Mechanics beyond the Second Law of Thermodynamics2014In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 1470, no 2171, p. 1-17, article id 20140531Article in journal (Refereed)
    Abstract [en]

    The results established in contemporary statistical physics indicating that, on very small space and time scales, the entropy production rate may be negative, motivate a generalization of continuum mechanics. On account of the fluctuation theorem, it is recognized that the evolution of entropy at a material point is stochastically (not deterministically) conditioned by the past history, with an increasing trend of average entropy production. Hence, the axiom of Clausius-Duhem inequality is replaced by a submartingale model, which, by the Doob decomposition theorem, allows classification of thermomechanical processes into four types depending on whether they are conservative or not and/or conventional continuum mechanical or not. Stochastic generalizations of thermomechanics are given in the vein of either thermodynamic orthogonality or primitive thermodynamics, with explicit models formulated for Newtonian fluids with, respectively, parabolic or hyperbolic heat conduction. Several random field models of the martingale component, possibly including spatial fractal and Hurst effects, are proposed. The violations of the second law are relevant in those situations in continuum mechanics where very small spatial and temporal scales are involved. As an example, we study an acceleration wavefront of nanoscale thickness which randomly encounters regions in the medium characterized by a negative viscosity coefficient.

  • 9.
    Prytz, Kjell
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    A laborative model of geomagnetism as an example of creative learning2015In: Physics Education, ISSN 0031-9120, E-ISSN 1361-6552, Vol. 50, no 6, p. 699-705Article in journal (Refereed)
    Abstract [en]

    Creative learning is discussed with respect to a specific physics topic. A teaching example, based on an apparatus that demonstrates the standard dynamo model of geomagnetism, is presented. It features many of the basic physics concepts within the syllabus of electromagnetism at high-school and university.

    To stimulate conceptual learning and to invite student explorations, the apparatus is designed to exhibit simplicity and transparency. Due to the connection to natural phenomena and to engineering applications it promotes a holistic view of physics. The apparatus is therefore useful for practising creative learning.

  • 10.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Foundations of Santilli's Lie-Isotopic Theory2010In: Numerical Analysis and Applied Mathematics (AIP Conference Proceedings), American Institute of Physics (AIP), 2010, p. 860-863Conference paper (Refereed)
    Abstract [en]

    The need and benefits of new universal mathematical and especially algebraic and operator structures and methods in all branches and levels of modem physics from experiments to fundamentals is nowdays widely recognized. The far reaching pioneering discoveries of R. M. Santilli extend significantly the Lie analysis and operator methods and models of modem physics opening new areas of applications with possible essential improvements and revisions in models in particle physics and cosmology. In this article, some fundamental aspects of Lie-Santilli isotopic theory and relevant references are presented.

  • 11.
    Silvestrov, Sergei
    et al.
    Lund University.
    Paal, EugenTallinn University of Technology, Estonia.Abramov, ViktorUniversity of Tartu, Estonia.Stolin, AlexanderChalmers.
    Generalized Lie theory in mathematics, physics and beyond2009Collection (editor) (Refereed)
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