| 1. |
- Asekritova, Irina, et al.
(författare)
-
Diffractive Index Determination by Tikhonov Regularization on Forced String Vibration Data
- 2009
-
Ingår i: Mathematical modelling of wave phenomena. - Melville, New York : American Institute of Physics. ; , s. 224-232, s. 224-232
-
Konferensbidrag (refereegranskat)abstract
- Wave analysis is efficient for investigating the interior of objects. Examples are ultra sound examination of humans and radar using elastic and electromagnetic waves. A common procedure is inverse scattering where both transmitters and receivers are located outside the object or on its boundary. A variant is when both transmitters and receivers are located on the scattering object. The canonical model is a finite inhomogeneous string driven by a harmonic point force. The inverse problem for the determination of the diffractive index of the string is studied. This study is a first step to the problem for the determination of the mechanical strength of wooden logs. An inverse scattering theory is formulated incorporating two regularizing strategies. The results of simulations using this theory show that the suggested method works quite well and that the regularization methods based on the couple of spaces (L2; H1 ) could be very useful in such problems.
|
|
| 2. |
- Bergman Ärlebäck, Jonas, 1972-
(författare)
-
Designing, implementing and evaluating mathematical modelling modules at the upper secondary level
- 2009
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This study provides an account of how it is possible to work with mathematical models and modelling at the Swedish upper secondary level. It shows how a researcher and two teachers, departing from what is written in the mathematics curriculum document about mathematical models and modelling and the teachers’ mathematics teaching practices, collaborate to design and develop two so called modelling modules. These two modules designed for, and integrated in, the Mathematics C and Mathematics D course respectively, were implemented in the teachers’ classes and the whole process was evaluated. The students’ experiences of working with the modules were also investigated.The conceptual framework used to study this process of design, implementation, and evaluation is built up of design-based research methodology, cultural historical activity theory (CHAT), and co-learning agreement between the researcher and the participants.The teachers as well as the students expressed that they enjoyed working on the modules and found the experience positive and rewarding. However, some doubt concerning the learning outcome on behalf of the students were raised among the teachers, and the wish to incorporate more scheduled time into the modules was expressed by the students.It is concluded that the participating teachers could had difficulties in expressing a clear conception of the notions of mathematical models or modelling and no affirmative conclusions could be drawn that the participation of the teachers changed their attitudes towards mathematical models and modelling. The designing process was often was restrained by constraints originating from the local school context, and working with modelling highlights many systemic tensions in the established school practice. Also, meta-results in form of suggestions of how to resolve different kinds of tensions in order to improve the study design are reported.
|
|
| 3. |
- Bergman Ärlebäck, Jonas, 1972-
(författare)
-
Matematisk modellering i svenska gymnasieskolans kursplaner i matematik 1965-2000
- 2009
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Denna rapport studerar hur begreppen matematisk modell och matematisk modellering behandlats i kursplanerna i matematik för motsvarande svenska gymnasieskolans naturvetenskapliga program mellan åren 1965 och 2000. En översikt över sex kursplaners olika form och innehåll ges och tre olika analyser på tre olika nivåer genomförs; en innehållsanalys, en kvalitativ analys, och en analys som beaktar relationen mellan begreppen modellering, tillämpningar och problemlösning. Analysen visar att matematiska modeller och modellering förekommit implicit sedan kursplanen från 1965, men att begreppen främst i de två senaste kursplanerna lyfts fram explicit och fått en central position i kursplanerna. I den nuvarande kursplanen Gy2000 framgår att matematiska modeller kan tolkas både som ett undervisningsmål i sig och som ett didaktiskt hjälpmedel att lära matematik.
|
|
| 4. |
- Kurujyibwami, Celestin
(författare)
-
Admissible transformations and the group classification of Schrödinger equations
- 2017
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- We study admissible transformations and solve group classification problems for various classes of linear and nonlinear Schrödinger equations with an arbitrary number n of space variables.The aim of the thesis is twofold. The first is the construction of the new theory of uniform seminormalized classes of differential equations and its application to solving group classification problems for these classes. Point transformations connecting two equations (source and target) from the class under study may have special properties of semi-normalization. This makes the group classification of that class using the algebraic method more involved. To extend this method we introduce the new notion of uniformly semi-normalized classes. Various types of uniform semi-normalization are studied: with respect to the corresponding equivalence group, with respect to a proper subgroup of the equivalence group as well as the corresponding types of weak uniform semi-normalization. An important kind of uniform semi-normalization is given by classes of homogeneous linear differential equations, which we call uniform semi-normalization with respect to linear superposition of solutions.The class of linear Schrödinger equations with complex potentials is of this type and its group classification can be effectively carried out within the framework of the uniform semi-normalization. Computing the equivalence groupoid and the equivalence group of this class, we show that it is uniformly seminormalized with respect to linear superposition of solutions. This allow us to apply the version of the algebraic method for uniformly semi-normalized classes and to reduce the group classification of this class to the classification of appropriate subalgebras of its equivalence algebra. To single out the classification cases, integers that are invariant under equivalence transformations are introduced. The complete group classification of linear Schrödinger equations is carried out for the cases n = 1 and n = 2.The second aim is to study group classification problem for classes of generalized nonlinear Schrödinger equations which are not uniformly semi-normalized. We find their equivalence groupoids and their equivalence groups and then conclude whether these classes are normalized or not. The most appealing classes are the class of nonlinear Schrödinger equations with potentials and modular nonlinearities and the class of generalized Schrödinger equations with complex-valued and, in general, coefficients of Laplacian term. Both these classes are not normalized. The first is partitioned into an infinite number of disjoint normalized subclasses of three kinds: logarithmic nonlinearity, power nonlinearity and general modular nonlinearity. The properties of the Lie invariance algebras of equations from each subclass are studied for arbitrary space dimension n, and the complete group classification is carried out for each subclass in dimension (1+2). The second class is successively reduced into subclasses until we reach the subclass of (1+1)-dimensional linear Schrödinger equations with variable mass, which also turns out to be non-normalized. We prove that this class is mapped by a family of point transformations to the class of (1+1)-dimensional linear Schrödinger equations with unique constant mass.
|
|
| 5. |
- Arnlind, Joakim, et al.
(författare)
-
Eigenvalue Dynamics off the Calogero-Moser system
- 2004
-
Ingår i: Letters in Mathematical Physics. - : Springer. - 0377-9017 .- 1573-0530. ; 68:2, s. 121-129
-
Tidskriftsartikel (refereegranskat)abstract
- By finding N(N-1)/2 suitable conserved quantities, free motions of real symmetric N x N matrices X(t), with arbitrary initial conditions, are reduced to nonlinear equations involving only the eigenvalues of X-in contrast to the rational Calogero-Moser system, for which [X(0), X(0)] has to be purely imaginary, of rank one.
|
|
| 6. |
- Arnlind, Joakim, et al.
(författare)
-
Spinning Membranes
- 2004
-
Ingår i: Physics Letters B. - : Elsevier BV. - 0370-2693 .- 1873-2445. ; 599:1-2, s. 118-128
-
Tidskriftsartikel (refereegranskat)abstract
- We present new solutions of the classical equations of motion of bosonic (matrix-)membranes. Those relating to minimal surfaces in spheres provide spinning membrane solutions in AdS(p) X S-q, as well as in flat space-time. Nontrivial reductions of the BMN matrix model equations are also given.
|
|
| 7. |
- Berntsson, Fredrik, 1971-, et al.
(författare)
-
Numerical Solution of Cauchy Problems for Elliptic Equations in "Rectangle-like" Geometries
- 2005
-
Ingår i: FEMLAB Conference,2005. - Stockholm : Comsol AB.
-
Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- We consider two dimensional inverse steady state heat conduction problems in complex geometries. The coefficients of the elliptic equation are assumed to be non-constant. Cauchy data are given on one part of the boundary and we want to find the solution in the whole domain. The problem is ill--posed in the sense that the solution does not depend continuously on the data. Using an orthogonal coordinate transformation the domain is mapped onto a rectangle. The Cauchy problem can then be solved by replacing one derivative by a bounded approximation. The resulting well--posed problem can then be solved by a method of lines. A bounded approximation of the derivative can be obtained by differentiating a cubic spline, that approximate the function in the least squares sense. This particular approximation of the derivative is computationally efficient and flexible in the sense that its easy to handle different kinds of boundary conditions. This inverse problem arises in iron production, where the walls of a melting furnace are subject to physical and chemical wear. Temperature and heat--flux data are collected by several thermocouples located inside the walls. The shape of the interface between the molten iron and the walls can then be determined by solving an inverse heat conduction problem. In our work we make extensive use of Femlab for creating test problems. By using Femlab we solve relatively complex model problems for the purpose of creating numerical test data used for validating our methods. For the types of problems we are intressted in numerical artefacts appear, near corners in the domain, in the gradients that Femlab calculates. We demonstrate why this happen and also how we deal with the problem.
|
|
| 8. |
- Daneva (Mitradjieva), Maria, et al.
(författare)
-
A Comparison of Feasible Direction Methods for the Stochastic Transportation Problem
- 2010
-
Ingår i: Computational optimization and applications. - : Springer Science and Business Media LLC. - 0926-6003 .- 1573-2894. ; 46:3, s. 451-466
-
Tidskriftsartikel (refereegranskat)abstract
- The feasible direction method of Frank and Wolfe has been claimed to be efficient for solving the stochastic transportation problem. While this is true for very moderate accuracy requirements, substantially more efficient algorithms are otherwise diagonalized Newton and conjugate Frank–Wolfe algorithms, which we describe and evaluate. Like the Frank–Wolfe algorithm, these two algorithms take advantage of the structure of the stochastic transportation problem. We also introduce a Frank–Wolfe type algorithm with multi-dimensional search; this search procedure exploits the Cartesian product structure of the problem. Numerical results for two classic test problem sets are given. The three new methods that are considered are shown to be superior to the Frank–Wolfe method, and also to an earlier suggested heuristic acceleration of the Frank–Wolfe method.
|
|
| 9. |
- Eriksson, Sofia, et al.
(författare)
-
Finite difference schemes with transferable interfaces for parabolic problems
- 2018
-
Ingår i: Journal of Computational Physics. - Linköping : Elsevier. - 0021-9991 .- 1090-2716. ; 375, s. 935-949
-
Tidskriftsartikel (refereegranskat)abstract
- We derive a method to locally change the order of accuracy of finite difference schemes that approximate the second derivative. The derivation is based on summation-by-parts operators, which are connected at interfaces using penalty terms. At such interfaces, the numerical solution has a double representation, with one representation in each domain. We merge this double representation into a single one, yielding a new scheme with unique solution values in all grid points. The resulting scheme is proven to be stable, accurate and dual consistent. (C) 2018 Elsevier Inc. All rights reserved.
|
|
| 10. |
- Erlander, Sven, 1934-
(författare)
-
Cost-Minimizing Choice Behavior in Transportation Planning : A Theoretical Framework fo Logit Models
- 2010
-
Bok (övrigt vetenskapligt/konstnärligt)abstract
- This book stems from a desire to understand the underlying assumptions and structureof the choice probability models most often used in transportation planning. The bookinvestigates how far a new way of defining cost minimizing behavior can take us. Allcommonly used choice probability distributions of the logit type – log linear probabilityfunctions – follow from cost minimizing behavior defined in the new way; some newnested models also appear. The new approach provides a deeper understanding of whatis at work in the models. The new way of defining cost minimizing behavior is as follows:cost minimizing behavior pertains if the likelihood (probability) of any independentsample of observations is a decreasing function of the average cost of the sample.Extreme value distributed random variables are not used in the derivation of models. Ameasure of freedom of choice related to the Shannon measure of how much "choice" isinvolved is used to obtain a welfare measure which is equal to composite cost.... more on http://springer.com/978-3-642-11910-1
|
|
