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Näslund, Reinhold
Publications (10 of 11) Show all publications
Näslund, R. (2005). Some studies within applied mathematics with focus on conditional symmetries of partial differential equations and bending waves in plates (ed.). (Licentiate dissertation). Paper presented at . Luleå: Luleå tekniska universitet
Open this publication in new window or tab >>Some studies within applied mathematics with focus on conditional symmetries of partial differential equations and bending waves in plates
2005 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This is thesis in mathematics with special focus on applied mathematics and mathematical physics. There is an introduction (in Svedish), two papers and two addendums to the first paper. The second paper is published in an international journal. The purpose of the introduction is to sketch in an informal way some of the basic ideas and concepts concerning the use of symmetry methods for solving differential equations (DE). Roughly speaking, a symmetry of an object is a mapping (a transformation), which leaves the objekt unchanged, i.e. the object is mapped to itself. A symmetry of a DE is a group of transformations that maps the set of all solutions to the DE on itself. A special solution is mapped to another solution or to itself. We have omitted some mathematical details and no attemtemts are made to make the introduction completely rigorous. We discuss the connection between some ad hoc methods for solving special types of DE and symmetry groups, how symmetry groups can be used to lower the order of a DE, or to obtain similarity solutions to a PDE. A number of illustrative examples are concidered. There are also some historical notes. In paper 1 we have calculated conditional Q-symmetries of a class of nonlinear wave equations with a variable wave speed. This class o wave equations have many applications in the study of wave propagation in different areas, for example in the studies of one-dimensional gas flow, shallow water theory and electromagnetic transmission lines. By using the obtained conditional Q-symmetry generators to get similarity "ansatzes" and reductions to ordinary differential equations we have obtained several solutions which can not be obtained by the classical method of Sophus Lie. In an addendum we discuss with help of conditional symmetries connections between the linear heat equation and some nonlinear evolution equations.In particular, we show the relation between the well-known Cole-Hopf transformation, which transforms Burgers' equation to the linear heat equation and a corresponding conditional Q-symmetry to the linear heat equation. In paper 2 we used the general form of the standard Kirchoff plate equation for an anisotrophic plate to derive integral representation formulas for describing the propagation of bending waves in infinite plates.We started with the most general case with an anisotrophic plate and very modest restrictions on the outher force. After that we concidered various special cases and obtained both new and well-known formulas. For example in the simplest case with an isotrophic plate then the outher force is an unit impulse both in space and time we obtained the clasical Boussinesq solution. Our starting point was to use Fourier analysis. Some of our results contains a Fourier transform as factor in the integrand, which in some cases can be simplified. We also proved some cruical formulas, which are of great importance for this paper. Moreover we have compared theoretical results with experimental data and the agreement was very good.

Place, publisher, year, edition, pages
Luleå: Luleå tekniska universitet, 2005. p. 123
Series
Licentiate thesis / Luleå University of Technology, ISSN 1402-1757 ; 2005:28
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-25750 (URN)af456060-90c8-11db-8975-000ea68e967b (Local ID)af456060-90c8-11db-8975-000ea68e967b (Archive number)af456060-90c8-11db-8975-000ea68e967b (OAI)
Note
Godkänd; 2005; 20061221 (haneit)Available from: 2016-09-30 Created: 2016-09-30 Last updated: 2017-11-24Bibliographically approved
Näslund, R. (2003). On conditional Q-symmetries of some quasilinear hyperbolic wave equation (ed.). Paper presented at . Luleå: Luleå tekniska universitet
Open this publication in new window or tab >>On conditional Q-symmetries of some quasilinear hyperbolic wave equation
2003 (English)Report (Other academic)
Abstract [en]

The quasilinear hyperbolic equation utt = [f(u)ux]x, f 2 C2(<) is studied and conditional Q-symmetries are calculated for different f. Reductions to ordinary differential equations are performed using these symmetry properties which lead to some explicit solutions of the hyperbolic equation for different f.

Place, publisher, year, edition, pages
Luleå: Luleå tekniska universitet, 2003. p. 21
Series
Gula serien, ISSN 1400-4003 ; 2003:11
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-25288 (URN)e8da4c48-1692-4e26-a3ca-528700cee53b (Local ID)e8da4c48-1692-4e26-a3ca-528700cee53b (Archive number)e8da4c48-1692-4e26-a3ca-528700cee53b (OAI)
Note
Godkänd; 2003; 20120118 (ysko)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved
Dunkels, A., Klefsjö, B., Nilsson, I. & Näslund, R. (2002). Mot bättre vetande i matematik (3ed.). Paper presented at . Lund: Studentlitteratur AB
Open this publication in new window or tab >>Mot bättre vetande i matematik
2002 (Swedish)Book (Other (popular science, discussion, etc.))
Place, publisher, year, edition, pages
Lund: Studentlitteratur AB, 2002. p. 214 Edition: 3
National Category
Didactics Reliability and Maintenance
Research subject
Mathematics Education; Quality Technology and Management
Identifiers
urn:nbn:se:ltu:diva-16722 (URN)d88c62e0-84bc-11dd-8275-000ea68e967b (Local ID)91-44-01919-X (ISBN)d88c62e0-84bc-11dd-8275-000ea68e967b (Archive number)d88c62e0-84bc-11dd-8275-000ea68e967b (OAI)
Note

Godkänd; 2002; 20080917 (ysko)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-02-05Bibliographically approved
Erlandsson, O., Lagerkrans, S., Näslund, R. & Vuorinen, E. (2000). Maskinhandboken (ed.). Paper presented at . Lund: Studentlitteratur AB
Open this publication in new window or tab >>Maskinhandboken
2000 (Swedish)Book (Other academic)
Place, publisher, year, edition, pages
Lund: Studentlitteratur AB, 2000. p. 503
National Category
Mathematical Analysis Other Materials Engineering
Research subject
Mathematics; Engineering Materials
Identifiers
urn:nbn:se:ltu:diva-16559 (URN)753858a0-0774-11dc-b09b-000ea68e967b (Local ID)91-44-60071-2 (ISBN)753858a0-0774-11dc-b09b-000ea68e967b (Archive number)753858a0-0774-11dc-b09b-000ea68e967b (OAI)
Note
Godkänd; 2000; Bibliografisk uppgift: Anmärkningar: Svensk bearb. och övers. från danska av: Maskin ståbi / Helge Krex 2. tr., 2006; 20070521 (cira)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-03-05Bibliographically approved
Andersson, L., Grennberg, A., Hedberg, T., Näslund, R., Persson, L.-E., von Sydow, B. & Söderkvist, I. (1999). Linjär algebra med geometri. Paper presented at . Lund: Studentlitteratur AB
Open this publication in new window or tab >>Linjär algebra med geometri
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1999 (Swedish)Book (Other (popular science, discussion, etc.))
Place, publisher, year, edition, pages
Lund: Studentlitteratur AB, 1999. p. 488
National Category
Mathematical Analysis Computational Mathematics
Research subject
Mathematics; Scientific Computing
Identifiers
urn:nbn:se:ltu:diva-16705 (URN)cfe42a50-25b4-11dc-b6d3-000ea68e967b (Local ID)91-44-00972-0 (ISBN)cfe42a50-25b4-11dc-b6d3-000ea68e967b (Archive number)cfe42a50-25b4-11dc-b6d3-000ea68e967b (OAI)
Note

Godkänd; 1999; 20070628 (ysko)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-03-08Bibliographically approved
Lindblom, O., Näslund, R., Persson, L.-E. & Fällström, K.-E. (1997). A study of bending waves in infinite and anisotropic plates (ed.). Paper presented at . Applications of Mathematics, 42(3), 213-232
Open this publication in new window or tab >>A study of bending waves in infinite and anisotropic plates
1997 (English)In: Applications of Mathematics, ISSN 0862-7940, E-ISSN 1572-9109, Vol. 42, no 3, p. 213-232Article in journal (Refereed) Published
Abstract [en]

In this paper we present a unified approach to obtain integral representation formulas for describing the propagation of bending waves in infinite plates. The general anisotropic case is included and both new and well-known formulas are obtained in special cases (e.g. the classical Boussinesq formula). The formulas we have derived have been compared with experimental data and the coincidence is very good in all cases

National Category
Mathematical Analysis Applied Mechanics
Research subject
Mathematics; Experimental Mechanics
Identifiers
urn:nbn:se:ltu:diva-15467 (URN)10.1023/A:1022469605398 (DOI)efae3da0-6fe1-11db-962b-000ea68e967b (Local ID)efae3da0-6fe1-11db-962b-000ea68e967b (Archive number)efae3da0-6fe1-11db-962b-000ea68e967b (OAI)
Note
Godkänd; 1997; 20061026 (cira)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved
Sundkvist, J. & Näslund, R. (1991). Reglerteknik: formelsamling (ed.). Paper presented at . Lund: Studentlitteratur AB
Open this publication in new window or tab >>Reglerteknik: formelsamling
1991 (Swedish)Book (Other (popular science, discussion, etc.))
Place, publisher, year, edition, pages
Lund: Studentlitteratur AB, 1991. p. 72
National Category
Control Engineering Mathematical Analysis
Research subject
Control Engineering; Mathematics
Identifiers
urn:nbn:se:ltu:diva-16553 (URN)6f2b1151-372c-40b5-b8a9-e9b535a90518 (Local ID)91-44-33781-7 (ISBN)6f2b1151-372c-40b5-b8a9-e9b535a90518 (Archive number)6f2b1151-372c-40b5-b8a9-e9b535a90518 (OAI)
Note
Godkänd; 1991; 20110411 (ysko)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved
Dunkels, A., Ekblom, H., Hednerg, T., Näslund, R. & Persson, L.-E. (1990). Flervariabelanalys med numeriska metoder. Paper presented at . Lund: Studentlitteratur AB
Open this publication in new window or tab >>Flervariabelanalys med numeriska metoder
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1990 (Swedish)Book (Other (popular science, discussion, etc.))
Place, publisher, year, edition, pages
Lund: Studentlitteratur AB, 1990. p. 470
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-16704 (URN)cfdafb00-90fe-11dc-9a81-000ea68e967b (Local ID)91-44-32231-3 (ISBN)cfdafb00-90fe-11dc-9a81-000ea68e967b (Archive number)cfdafb00-90fe-11dc-9a81-000ea68e967b (OAI)
Note

Godkänd; 1990; 20071112 (evan)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-02-05Bibliographically approved
Andersson, L., Grennberg, A., Hedberg, T., Näslund, R., Persson, L.-E. & von Sydow, B. (1990). Linjär algebra med geometri (2ed.). Paper presented at . Lund: Studentlitteratur AB
Open this publication in new window or tab >>Linjär algebra med geometri
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1990 (Swedish)Book (Other (popular science, discussion, etc.))
Place, publisher, year, edition, pages
Lund: Studentlitteratur AB, 1990. p. 502 Edition: 2
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-16486 (URN)3e82c840-9103-11dc-9a81-000ea68e967b (Local ID)91-44-32241-0 (ISBN)3e82c840-9103-11dc-9a81-000ea68e967b (Archive number)3e82c840-9103-11dc-9a81-000ea68e967b (OAI)
Note

Godkänd; 1990; 20071112 (evan)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-02-08Bibliographically approved
Dunkels, A., Ekblom, H., Hedberg, T., Näslund, R. & Persson, L.-E. (1987). Flervariabelanalys med numeriska metoder för tekniska högskolor. Paper presented at . Luleå: Luleå tekniska universitet
Open this publication in new window or tab >>Flervariabelanalys med numeriska metoder för tekniska högskolor
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1987 (Swedish)Book (Other (popular science, discussion, etc.))
Place, publisher, year, edition, pages
Luleå: Luleå tekniska universitet, 1987. p. 471
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-16483 (URN)3c3dd390-90fe-11dc-9a81-000ea68e967b (Local ID)91-86998-24-2 (ISBN)3c3dd390-90fe-11dc-9a81-000ea68e967b (Archive number)3c3dd390-90fe-11dc-9a81-000ea68e967b (OAI)
Note

Godkänd; 1987; 20071112 (evan)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-02-05Bibliographically approved
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