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  • 51.
    Amankwah, Henry
    et al.
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Larsson, Torbjörn
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Textorius, Björn
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Rönnberg, Elina
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Open-Pit Production Scheduling - Suggestions for Lagrangian Dual Heuristic and Time Aggregation ApproachesManuskript (preprint) (Annet vitenskapelig)
    Abstract [en]

    Open-pit production scheduling deals with the problem of deciding what and when to mine from an open-pit, given potential profits of the different fractions of the mining volume, pit-slope restrictions, and mining capacity restrictions for successive time periods. We give suggestions for Lagrangian dual heuristic approaches for the open-pit production scheduling problem. First, the case with a single mining capacity restriction per time period is considered. For this case, linear programming relaxations are solved to find values of the multipliers for the capacity restrictions, to be used in a Lagrangian relaxation of the constraints. The solution to the relaxed problem will not in general satisfy the capacity restrictions, but can be made feasible by adjusting the multiplier values for one time period at a time. Further, a time aggregation approach is suggested as a way of reducing the computational burden of solving linear programming relaxations, especially for largescale real-life mine problems. For the case with multiple capacity restrictions per time period we apply newly developed conditions for optimality and nearoptimality in general discrete optimization problems to construct a procedure for heuristically constructing near-optimal intermediate pits.

  • 52.
    Amsallem, David
    et al.
    Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305-4035, USA.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Energy Stable Model Reduction of Neurons by Non-negative Discrete Empirical Interpolation2016Inngår i: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 38, nr 2, s. B297-B326Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The accurate and fast prediction of potential propagation in neuronal networks is of prime importance in neurosciences. This work develops a novel structure-preserving model reduction technique to address this problem based on Galerkin projection and nonnegative operator approximation. It is first shown that the corresponding reduced-order model is guaranteed to be energy stable, thanks to both the structure-preserving approach that constructs a distinct reduced-order basis for each cable in the network and the preservation of nonnegativity. Furthermore, a posteriori error estimates are provided, showing that the model reduction error can be bounded and controlled. Finally, the application to the model reduction of a large-scale neuronal network underlines the capability of the proposed approach to accurately predict the potential propagation in such networks while leading to important speedups.

    Fulltekst (pdf)
    fulltext
  • 53.
    Amsallem, David
    et al.
    Department of Aeronautics and Astronautics, Stanford University, Stanford, USA.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska högskolan.
    High-order accurate difference schemes for the Hodgkin-Huxley equations2012Rapport (Annet vitenskapelig)
    Abstract [en]

    A novel approach for simulating potential propagation in neuronal branches with high accuracy is developed. The method relies on high-order accurate dierence schemes using the Summation-By-Parts operators with weak boundary and interface conditions applied to the Hodgkin-Huxley equations. This work is the rst demonstrating high accuracy for that equation. Several boundary conditions are considered including the non-standard one accounting for the soma presence, which is characterized by its own partial dierential equation. Well-posedness for the continuous problem as well as stability of the discrete approximation is proved for all the boundary conditions. Gains in terms of CPU times are observed when high-order operators are used, demonstrating the advantage of the high-order schemes for simulating potential propagation in large neuronal trees.

    Fulltekst (pdf)
    High-order accurate difference schmes for the Hodgkin-Huxley equations
  • 54.
    Amsallem, David
    et al.
    Department of Aeronautics and Astronautics, Stanford University, USA.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska högskolan.
    High-order accurate difference schemes for the Hodgkin-Huxley equations2013Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 252, s. 573-590Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A novel approach for simulating potential propagation in neuronal branches with high accuracy is developed. The method relies on high-order accurate difference schemes using the Summation-By-Parts operators with weak boundary and interface conditions applied to the Hodgkin–Huxley equations. This work is the first demonstrating high accuracy for that equation. Several boundary conditions are considered including the non-standard one accounting for the soma presence, which is characterized by its own partial differential equation. Well-posedness for the continuous problem as well as stability of the discrete approximation is proved for all the boundary conditions. Gains in terms of CPU times are observed when high-order operators are used, demonstrating the advantage of the high-order schemes for simulating potential propagation in large neuronal trees.

    Fulltekst (pdf)
    fulltext
  • 55.
    Andersen, Lisa
    et al.
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Tebring, Sandra
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Metakognitiva förmågors påverkan på elevers prestationer i matematisk problemlösning2018Independent thesis Basic level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Problemlösning är en central matematisk förmåga och anses av många vara matematikens kärna. I ett försök att finna svar på hur den optimala undervisningen i problemlösning borde bedrivas, uppkom idén att studera elevers prestationer inom problemlösning kopplat till metakognition. Metakognition kan beskrivas som tänkande över det egna tänkandet och är en nödvändig förmåga i flera olika sammanhang. Denna litteraturstudie har till syfte att undersöka om metakognitiv förmåga påverkar elevers prestationer i matematisk problemlösning.Studien utgår från åtta artiklar som hittades via databasen UniSearch och det är dessa åtta artiklar som utgör resultatet. Artiklarnas metoder skiljer sig från varandra då vissa jämför elevers metakognitiva förmåga med deras prestationer inom problemlösning, medan andra testar effekten av olika undervisningsmetoder baserade på metakognition. Trots detta visar studiens resultat på att det finns ett samband mellan god metakognitiv förmåga och att prestera väl inom matematisk problemlösning. Utifrån detta dras slutsatsen att det är av stor vikt att elever får undervisning i metakognition, speciellt de svaga eleverna.

    Fulltekst (pdf)
    fulltext
  • 56.
    Andersen, Lisa
    et al.
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska fakulteten.
    Tebring, Sandra
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska fakulteten.
    Metakognitiva strategier vid lösning av rika matematiska problem: Vilka strategier används och vilka för problemlösningsprocessen framåt?2020Independent thesis Advanced level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Sammanfattningsvis handlar denna studie om relationen mellan metakognition och matematisk problemlösning.Metakognition betyder kortfattat förmågan att tänka över det egna tänkandet och har visat sig vara en central del avarbete med problemlösning. Syftet med studien var att undersöka vilka metakognitiva strategier som elever användervid arbete med rika matematiska problem samt hur dessa påverkar huruvida problemlösningsprocessen förs framåt.Studien bygger på fyra observationer av 13 elever i årskurs åtta som arbetade med rika matematiska problem. Resultatet kodades med hjälp av ett analysverktyg som skapades med stöd i tidigare forskning och studien kom framtill att de vanligaste strategierna som eleverna använde var att identifiera relevant information samt att hitta ”nyckeln”i problemet. Dessa strategier var också de som förde problemlösningsprocessen framåt. Avslutningsvis dras slutsatsenatt elever som lyckas i sin problemlösning använder många olika metakognitiva strategier och att de behärskar detvå vanligaste strategierna, vilket leder till att de kan komma vidare i problemlösningen.

    Fulltekst (pdf)
    fulltext
  • 57.
    Andersson, Carina
    Linköpings universitet, Matematiska institutionen.
    Taluppfattning: En undersökning av elevers förståelse av decimaltal2006Independent thesis Basic level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [sv]

    I detta examensarbete har jag studerat hur elever i år 6 tänker vid decimalform inom taluppfattningens område. Begreppet taluppfattning är ett mycket brett område där det dessutom finns många olika uppfattningar om vad som ingår i begreppet. Därför har jag fokuserat mitt arbete på övergången från heltal till decimaltal. Syftet med undersökningen är att belysa vikten av att lärare har goda matematiska och metodiska kunskaper, hur elever utvecklar sin taluppfattning och förhoppningsvis ge lite tips och idéer som kan användas i undervisningen med elever. Studien omfattar en litteraturgenomgång som behandlar begreppet taluppfattning där jag delat upp kapitlet i tre underrubriker: Vad innebär det att elever har en grundläggande taluppfattning? Hur utvecklar elever en god taluppfattning? Vilka speciella svårigheter finns vid övergången från heltal till decimaltal? Under metoddelen skriver jag om hur pilot- och huvudundersökningen gjordes innan läsaren får ta del av undersökningarnas resultat. Resultatet av undersökningen är att många elever har svårt för övergången från heltal till decimaltal. Det finns tre moment i förståelsen av positionssystemet som tycks orsaka större svårigheter och det är platssiffrans värde, multiplikation med tal mindre än ett och uppskattning av rimligheten av svaret i en beräkning. Uppsatsen innehåller också ett avsnitt om vad vi lärare kan göra för att underlätta elevers förståelse för övergången från heltal till decimaltal.

    Fulltekst (pdf)
    FULLTEXT01
  • 58. Andersson, Carina
    et al.
    Losand, Elin
    Bergman Ärlebäck, Jonas
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Att uppleva räta linjer och grafer – erfarenheter från ett forskningsprojekt2015Inngår i: Nämnaren 2014:4, nr 1, s. 21-27Artikkel i tidsskrift (Annet (populærvitenskap, debatt, mm))
  • 59.
    Andersson, Fredrik
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Edgar, S.B.
    Existence of Lanczos potentials and superpotentials for the Weyl spinor/tensor2001Inngår i: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 18, nr 12, s. 2297-2304Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A new and concise proof of existence - emphasizing the very natural and simple structure - is given for the Lanczos spinor potential LABCA' of an arbitrary symmetric spinor WABCD defined by WABCD = 2?(AA' LBCD)A', this proof is easily translated into tensors in such a way that it is valid in four-dimensional spaces of any signature. In particular, this means that the Weyl spinor ?ABCD has Lanczos potentials in all spacetimes, and furthermore that the Weyl tensor has Lanczos potentials on all four-dimensional spaces, irrespective of signature. In addition, two superpotentials for WABCD are identified: the first TABCD (= T(ABC)D) is given by LABCA' = ?A'DTABCD, while the second HABA'B' (= H(AB)(A'B')) (which is restricted to Einstein spacetimes) is given by LABCA' = ? (AB' HBC)A'B'. The superpotential TABCD is used to describe the gauge freedom in the Lanczos potential.

  • 60.
    Andersson, Fredrik
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Edgar, S.B.
    Local existence of symmetric spinor potentials for symmetric (3,1)-spinors in Einstein space-times2001Inngår i: Journal of Geometry and Physics, ISSN 0393-0440, E-ISSN 1879-1662, Vol. 37, nr 4, s. 273-290Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We investigate the possibility of existence of a symmetric potential HABA'B'=H(AB)(A'B') for a symmetric (3,1)-spinor LABCA', e.g., a Lanczos potential of the Weyl spinor, as defined by the equation LABCA'=?(AB'H BC)A'B'. We prove that in all Einstein space-times such a symmetric potential HABA'B' exists. Potentials of this type have been found earlier in investigations of some very special spinors in restricted classes of space-times. A tensor version of this result is also given. We apply similar ideas and results by Illge to Maxwell's equations in a curved space-time. © 2001 Elsevier Science B.V.

  • 61.
    Andersson, Fredrik
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Edgar, SB
    Linkoping Univ, Dept Math, S-58183 Linkoping, Sweden.
    Spin coefficients as Lanczos scalars: Underlying spinor relations2000Inngår i: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 41, nr 5, s. 2990-3001Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    It has been conjectured by Lopez-Bonilla and co-workers that there is some linear relationship between the NP spin coefficients and the Lanczos scalars, and examples have been given for a number of different classes of space-times. We show that in each of those examples a Lanczos potential can be defined in a very simple way directly from the spinor dyad. Although some of these examples seem to have no deeper geometric meaning, we emphasize that there are structural links between Lanczos potential and spin coefficients which we highlight in some other examples. In particular we show that the direct identification of Lanczos potentials with spin coefficients is possible for some important classes of space-times while the direct identification of Lanczos potentials with the properly weighted spin coefficients is also possible for several important classes of space-times. In both of these cases we obtain the necessary and sufficient conditions on the spin coefficients for such identifications to be possible, which enables us to test space-times directly. (C) 2000 American Institute of Physics. [S0022-2488(00)03104-2].

  • 62.
    Andersson, Hanna
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Den flippade läxan: En systematisk litteraturstudie av läxor i det flippade matematikklassrummet2018Independent thesis Basic level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Syftet med denna litteraturstudie är att redogöra för läxans roll i det flippade matematiklassrummet. Arbetsmetoden ”Flippat klassrum” karaktäriseras av en förflyttning av traditionella föreläsningar ut ur klassrummet. Direkta instruktioner ges istället som läxa, ”flippad läxa”, ofta i form av videoföreläsningar. Litteraturstudien baserar sig på nio artiklar och behandlar den flippade matematikläxans utformning, elevers åsikter om arbetsmetoden, och vilka fördelar respektive nackdelar flippad läxa har i förhållande till traditionell läxa. ”Flippad läxa” är fortfarande är ett relativt outforskat begrepp, vilket gör det svårt att dra generella slutsatser. Studiens resultat tyder dock på att metoden kan ha flera fördelar, bland annat i att videoföreläsningar som läxa ger eleverna ett större ansvar för sitt eget lärande, och att videons bestämda speltid har potential att minska skillnaden i den tid, som olika elever använder för att göra samma läxa.

    Fulltekst (pdf)
    fulltext
  • 63.
    Andersson, Jonathan
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Asymptotic behavior and effective boundaries forage-structured population models in aperiodically changing environment2017Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    Human activity and other events can cause environmental changes to the habitat of organisms. The environmental changes effect the vital rates for a population. In order to predict the impact of these environmental changes on populations, we use two different models for population dynamics. One simpler linear model that ignores environmental competition between individuals and another model that does not. Our population models take into consideration the age distribution of the population and thus takes into consideration the impact of demographics. This thesis generalize two theorems, one for each model, developed by Sonja Radosavljevic regarding long term upper and lower bounds of a population with periodic birth rate ; see [6] and [5]. The generalisation consist in including the case where the periodic part of the birth rate can be expressed with a finite Fourier series and also infinite Fourier series under some constraints. The old theorems only considers the case when the periodic part of the birth rate can be expressed with one cosine term. From the theorems we discover a connection between the frequency of oscillation and the effect on population growth. From this derived connection we conclude that periodical changing environments can have both positive and negative effects on the population.

    Fulltekst (pdf)
    fulltext
  • 64.
    Andersson, Jonathan
    et al.
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Kozlov, Vladimir
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Radosavljevic, Sonja
    Stockholm Resilience Centre, Stockholm University, Stockholm, Sweden.
    Tkachev, Vladimir
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Wennergren, Uno
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Biologi. Linköpings universitet, Tekniska fakulteten.
    Density-Dependent Feedback in Age-Structured Populations2019Inngår i: Journal of Mathematical Sciences, ISSN 1072-3374, E-ISSN 1573-8795, Vol. 242, nr 1, s. 2-24Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The population size has far-reaching effects on the fitness of the population, that, in its turn influences the population extinction or persistence. Understanding the density- and age-dependent factors will facilitate more accurate predictions about the population dynamics and its asymptotic behaviour. In this paper, we develop a rigourous mathematical analysis to study positive and negative effects of increased population density in the classical nonlinear age-structured population model introduced by Gurtin \& MacCamy in the late 1970s. One of our main results expresses the global stability of the system in terms of the newborn function only. We also derive the existence of a threshold population size implying the population extinction, which is well-known in population dynamics as an Allee effect.

  • 65.
    Andersson, Lars-Erik
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    A quasistatic frictional problem with normal compliance penalization term1999Inngår i: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 37, s. 689-705Artikkel i tidsskrift (Fagfellevurdert)
  • 66.
    Andersson, Lars-Erik
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Critical bounds for frictional rate- and wedging problems2010Konferansepaper (Annet vitenskapelig)
  • 67.
    Andersson, Lars-Erik
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Existence and uniqueness for thermoelastic contact2013Inngår i: Encyclopedia of Thermal Stresses / [ed] Hetnarski, Richard B., Springer, 2013, s. -6643Kapittel i bok, del av antologi (Annet vitenskapelig)
    Abstract [en]

    The Encyclopedia of Thermal Stresses is an important interdisciplinary reference work.  In addition to topics on thermal stresses, it contains entries on related topics, such as the theory of elasticity, heat conduction, thermodynamics, appropriate topics on applied mathematics, and topics on numerical methods. The Encyclopedia is aimed at undergraduate and graduate students, researchers and engineers. It brings together well established knowledge and recently received results. All entries were prepared  by leading experts from all over the world, and are presented in an easily accessible format. The work is lavishly illustrated, examples and applications are given where appropriate, ideas for further development abound, and the work will challenge many students and researchers to pursue new results of their own. This work can also serve as a one-stop resource for all who need succinct, concise, reliable and up to date information in short encyclopedic entries, while the extensive references will be of interest to those who need further information. For the coming decade, this is likely to remain the most extensive and authoritative work on Thermal Stresses

  • 68.
    Andersson, Lars-Erik
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Existence results for quasistatic contact problems with Coulomb friction2000Inngår i: Applied mathematics and optimization, ISSN 0095-4616, E-ISSN 1432-0606, Vol. 42, nr 2, s. 169-202Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We prove the existence of a solution for an elastic frictional, quasistatic, contact problem with a Signorini non-penetration condition and a local Coulomb friction law. The problem is formulated as a time-dependent variational problem and is solved by the aid of an established shifting technique used to obtain increased regularity at the contact surface. The analysis is carried out by the aid of auxiliary problems involving regularized friction terms and a so-called normal compliance penalization technique.

  • 69.
    Andersson, Lars-Erik
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Quasistatic frictional contact problems with finitely many degrees of freedom.1999Rapport (Annet vitenskapelig)
    Abstract [en]

    In the present paper results on existence and uniqueness of solutions to discrete frictional quasi-static unilateral contact problems are given under a condition that the coefficients of friction are smaller than a certain upper bound. This upper bound is defined in terms of an influence matrix for the contact nodes. The results of existence and uniqueness may be ordered into two classes depending on whether regularity conditions for the applied forces are imposed or not. For general loading which has a time derivative almost everywhere it is shown that a solution exists which satisfies governing equations for almost all times. Uniqueness of the solution has been shown only when the problem is restricted to two degrees of freedom. For a loading which is right piecewise analytic, additional results can be obtained. For instance, if each contact node has only two degrees of freedom a unique solution which satisfies governing equeations for all times exists. For the constructed solutions a priori estimates of the displacement field and its time derivate in terms of the applied forces are also given.

    Fulltekst (pdf)
    Quasistatic frictional contact problems with finitely many degrees of freedom
  • 70.
    Andersson, Lars-Erik
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Quasistatic frictional contact problems with finitely many degrees of freedom. Existence and uniqueness2002Inngår i: WE-Hereus Seminar on Contact and Fracture Problems,2002, 2002Konferansepaper (Annet vitenskapelig)
  • 71.
    Andersson, Lars-Erik
    et al.
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Barber, J R.
    University of Michigan, MI USA.
    Ahn, Y-J
    Samsung SDI Central Research Centre, South Korea.
    Attractors in Frictional Systems Subjected to Periodic Loads2013Inngår i: SIAM Journal on Applied Mathematics, ISSN 0036-1399, E-ISSN 1095-712X, Vol. 73, nr 3, s. 1097-1116Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper explores the effect of initial conditions on the behavior of coupled frictional elastic systems subject to periodic loading. Previously, it has been conjectured that the long term response will be independent of initial conditions if all nodes slip at least once during each loading cycle. Here, this conjecture is disproved in the context of a simple two-node system. Counter examples are presented of “unstable” steady-state orbits that repel orbits starting from initial conditions that are sufficiently close to the steady state. The conditions guaranteeing stability of such steady states are shown to be more restrictive than those required for the rate problem to be uniquely solvable for arbitrary derivative of the external loading. In cases of instability, the transient orbit is eventually limited either by slip occurring at both nodes simultaneously, or by one node separating. In both cases a stable limit cycle is obtained. Depending on the slopes of the constraint lines, the limit cycle can involve two periods of the loading cycle, in which case it appears to be unique, or it may repeat every loading cycle, in which case distinct limit cycles are reached depending on the sign of the initial deviation from the steady state. In the case of instability an example is given of a loading for which a quasi-static evolution problem with multiple solutions exists, whereas all rate problems are uniquely solvable.

    Fulltekst (pdf)
    fulltext
  • 72.
    Andersson, Lars-Erik
    et al.
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Barber, J. R.
    University of Michigan, MI 48109 USA.
    Ponter, A. R. S.
    University of Leicester, England.
    Existence and uniqueness of attractors in frictional systems with uncoupled tangential displacements and normal tractions2014Inngår i: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 51, nr 21-22, s. 3710-3714Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider the class of two or three-dimensional discrete contact problems in which a set of contact nodes can make frictional contact with a corresponding set of rigid obstacles. Such a system might result from a finite element discretization of an elastic contact problem after the application of standard static reduction operations. The Coulomb friction law requires that the tractions at any point on the contact boundary must lie within or on the surface of a friction cone, but the exact position of any stuck node (i.e., a node where the tractions are strictly within the cone) depends on the initial conditions and/or the previous history of loading. If the long-term loading is periodic in time, we anticipate that the system will eventually approach a steady periodic cycle. Here we prove that if the elastic system is uncoupled, meaning that changes in slip displacements alone have no effect on the instantaneous normal contact reactions, the time-varying terms in this steady cycle are independent of initial conditions. In particular, we establish the existence of a unique permanent stick zone T comprising the set of all nodes that do not slip after some finite number of cycles. We also prove that the tractions and slip velocities at all nodes not contained in T approach unique periodic functions of time, whereas the (time-invariant) slip displacements in T may depend on initial conditions. Typical examples of uncoupled systems include those where the contact surface is a plane of symmetry, or where the contacting bodies can be approximated locally as half spaces and Dundurs mismatch parameter beta = 0. An important consequence of these results is that systems of this kind will exhibit damping characteristics that are independent of initial conditions. Also, the energy dissipated at each slipping node in the steady state is independent of initial conditions, so wear patterns and the incidence of fretting fatigue failure should also be so independent.

  • 73.
    Andersson, Lars-Erik
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Khludnev, Alexander
    Lavrentiev Institute of Hydrodynamics Russian Academie of Sciences, Novosibirsk.
    On crack crossing a contact boundary. Fictitious domain method and invariant integrals (Russian) .2008Inngår i: Siberian journal of industrial mathematics, ISSN 1560-7518, Vol. 11, nr 3, s. 15-29Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

        

  • 74.
    Andersson, Lars-Erik
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Klarbring, Anders
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Institutionen för konstruktions- och produktionsteknik, Mekanik.
    A review of the theory of static and quasi-static frictional contact problems in elasticity2001Inngår i: Philosophical Transactions. Series A: Mathematical, physical, and engineering science, ISSN 1364-503X, E-ISSN 1471-2962, Vol. 359, s. 2519-2539Artikkel i tidsskrift (Fagfellevurdert)
  • 75.
    Andersson, Lars-Erik
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Klarbring, Anders
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Institutionen för konstruktions- och produktionsteknik, Mekanik.
    A Survey of Basic Mathematical Results for Frictional Contact Problems2001Inngår i: From Convexity to Nonconvexity / [ed] Robert P Gilbert; P D Panagiotopoulos; P M Pardalos, Dordrecht/Boston/London: Kluwer , 2001, s. -392Kapittel i bok, del av antologi (Annet vitenskapelig)
    Abstract [en]

    Contains a collection of invited papers dedicated to the memory of two great mathematicians, Gaetano Fichera and Panagis Panagiotopoulos. The book is centered around the seminal research of G Fichera on the Signorini problem, hemivariational inequalities, nonsmooth global optimization, and regularity results for variational inequatities.

  • 76.
    Andersson, Lars-Erik
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Klarbring, Anders
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Institutionen för konstruktions- och produktionsteknik, Mekanik.
    Existence and uniqueness for quasistatic contact problems with friction2001Inngår i: CMIS 2001, third Contact Mechanics International Symposiium,2001, Dordrecht: Kluwer , 2001, s. 245-Konferansepaper (Fagfellevurdert)
  • 77.
    Andersson, Lars-Erik
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Klarbring, Anders
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Institutionen för konstruktions- och produktionsteknik, Mekanik.
    Existence and Uniquness of Steady State Solutions in Thermoelastic Contact with Frictional Heating2004Inngår i: International Congress of Theoretical and Applied Mechanics,2004, 2004, s. 215-215Konferansepaper (Fagfellevurdert)
  • 78.
    Andersson, Lars-Erik
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Klarbring, Anders
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Institutionen för konstruktions- och produktionsteknik, Mekanik.
    Quasi-static Frictional Contact of Discrete Mechanical Structures2000Inngår i: European journal of mechanics. A, Solids, ISSN 0997-7538, E-ISSN 1873-7285, Vol. 19, s. S61-S67Artikkel i tidsskrift (Fagfellevurdert)
  • 79.
    Andersson, Lars-Erik
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Klarbring, Anders
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Institutionen för konstruktions- och produktionsteknik, Mekanik.
    Barber, J.R.
    Department of Mechanical Engineering University of Michigan.
    Ciavarella, M.
    CEMEC-PoliBA.
    On the existence and uniqueness of steady state solutions in thermoelastic contact with frictional heating2005Inngår i: Proceedings of the Royal Society of Edinburgh. Section A Mathematics, ISSN 0308-2105, E-ISSN 1473-7124, Vol. 461, nr 2057, s. 1261-1282Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    It is well known that contact and friction in thermoelasticity result in mathematical problems which may lack solutions or have multiple solutions. Previously, issues related to thermal contact and issues related to frictional heating have been discussed separately. In this work, the two effects are coupled. Theorems of existence and uniqueness of solutions in two or three space dimensions are obtained - essentially extending, to frictional heating, results due to Duvaut, which were built on Barber's heat exchange conditions. Two qualitatively different existence results are given. The first one requires that the contact thermal resistance goes to zero at least as fast as the inverse of the contact pressure. The second existence theorem requires no such growth condition, but requires instead that the frictional heating, i.e. the sliding velocity times the friction coefficient, is small enough. Finally, it is shown that a solution is unique if the inverse of the contact thermal resistance is Lipschitz continuous and the Lipschitz constant, as well as the frictional heating, is small enough.

  • 80.
    Andersson, Lars-Erik
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Klarbring, Anders
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Institutionen för konstruktions- och produktionsteknik, Mekanik.
    Barber, J.R.
    University of Michigan.
    Ciavarella, M.
    Politecnio di Bari.
    Thermoelastic Contact with Frictional Heating2006Inngår i: Nonsmooth Mechanics and Analysis,2003, New York: Springer Science+business Media, inc. , 2006, s. 61-Konferansepaper (Fagfellevurdert)
  • 81.
    Andersson, Lars-Erik
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Peters, T.J.
    Computer Science Engineering University of Connecticut.
    Stewart, N.F.
    Dept IRO Universite de Montreal.
    Equivalence of topological form for curvilinear geometric objects2000Inngår i: International journal of computational geometry and applications, ISSN 0218-1959, Vol. 10, nr 6, s. 609-622Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Given a curvilinear geometric object in R3, made up of properly-joined parametric patches defined in terms of control points, it is of interest to know under what conditions the object will retain its original topological form when the control points are perturbed. For example, the patches might be triangular BΘzier surface patches, and the geometric object may represent the boundary of a solid in a solid-modeling application. In this paper we give sufficient conditions guaranteeing that topological form is preserved by an ambient isotopy. The main conditions to be satisfied are that the original object should be continuously perturbed in a way that introduces no self-intersections of any patch, and such that the patches remain properly joined. The patches need only have C0 continuity along the boundaries joining adjacent patches. The results apply directly to most surface modeling schemes, and they are of interest in several areas of application.

  • 82.
    Andersson, Lars-Erik
    et al.
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Pinto da Costa, A.
    University of Lisbon, Portugal.
    Agwa, M. A.
    Zagazig University, Egypt.
    Existence and uniqueness for frictional incremental and rate problems - sharp critical bounds2016Inngår i: Zeitschrift für angewandte Mathematik und Mechanik, ISSN 0044-2267, E-ISSN 1521-4001, Vol. 96, nr 1, s. 78-105Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We investigate frictional contact problems for discrete linear elastic structures, in particular the quasistatic incremental problem and the rate problem. It is shown that sharp conditions on the coefficients of friction for unique solvability of these problems are the same. We also give explicit expressions of these critical bounds by using a method of optimization. For the case of two spatial dimensions the conditions are formulated as a huge set of non symmetric eigenvalue problem. A computer program for solving these problems was designed and used to compute the critical bounds for some structures of relative small size, some of which appeared in the literature. The results of a variety of numerical experiments with uniform and non uniform distributions of the frictional properties are presented. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

  • 83.
    Andersson, Lars-Erik
    et al.
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Rietz, Andreas
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Existence theorems for noncoercive incremental contact problems with Coulomb friction2006Inngår i: Analysis and Simulation of Contact Problems / [ed] Peter Wriggers and Udo Nackenhorst, Springer Berlin/Heidelberg, 2006, s. 121-128Kapittel i bok, del av antologi (Annet vitenskapelig)
    Abstract [en]

    For static or incremental contact problems with Coulomb friction there are satisfactory and well known existence results for the coercive case, i.e., when the elastic body is anchored so that rigid body motions are not possible, see [3, 1, 6, 7, 2]. The articles by Jaruusek and Cocu, [7, 2] indeed contain results for the noncoercive case, i.e., when rigid body motions are possible. However, the compatibility conditions which are used to ensure the existence of a solution, are the same that guarantee that the corresponding contact problem without friction has a solution. The condition is essentially that the applied force field should push the elastic body towards the obstacle. One of few previous articles containing friction-dependent compatibility conditions is.

  • 84.
    Andersson, Lars-Erik
    et al.
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Stewart, Neil F.
    Université de Montréal, Montréal, Canada.
    Introduction to the Mathematics of Subdivision Surfaces2010Bok (Annet vitenskapelig)
    Abstract [en]

    Subdivision surfaces permit a designer to specify the approximate form of a surface defining an object and to refine and smooth the form to obtain a more useful or attractive version of the surface.

    A considerable amount of mathematical theory is required to understand the characteristics of the resulting surfaces, and this book

    • provides a careful and rigorous presentation of the mathematics underlying subdivision surfaces as used in computer graphics and animation, explaining the concepts necessary to easily read the subdivision literature;

    • organizes subdivision methods into a unique and unambiguous hierarchy to facilitate insight and understanding;

    • gives a broad discussion of the various methods and is not restricted to questions related to regularity of subdivision surfaces at so-called extraordinary points.

    Introduction to the Mathematics of Subdivision Surfaces is excellent preparation for reading more advanced texts that delve more deeply into special questions of regularity. The authors provide exercises and projects at the end of each chapter. Course material, including solutions to the exercises, is available on an associated Web page.

  • 85.
    Andersson, Lars-Erik
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Stewart, Neil F.
    IRO Universite de Montreal.
    Zidani, M.
    IRO Universite de Montreal.
    Conditions for use of a non-selfintersection conjecture2006Inngår i: Computer Aided Geometric Design, ISSN 0167-8396, E-ISSN 1879-2332, Vol. 23, nr 7, s. 599-611Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Volino and Thalmann have published a conjecture proposing sufficient conditions for non-selfintersection of surfaces. Such conditions may be used in solid modeling, computer graphics, and other application areas, as a basis for collision-detection algorithms. In this paper we clarify certain of the hypotheses of the proposed theorem, and give a proof. A brief summary of possible pitfalls related to using the conditions, when the hypotheses of the formal theorem given here are not satisfied, is also given. We also give examples, and show that the theorem can be extended to domains that are not simply connected. © 2006 Elsevier B.V. All rights reserved.

  • 86.
    Andersson, Lars-Erik
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Stewart, Neil F.
    Departement IRO Universite de Montreal.
    Zidani, Malika
    Departement IRO Universite de Montreal.
    Error analysis for operations in solid modeling in the presence of uncertainty2008Inngår i: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 29, nr 2, s. 811-826Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The problem of maintaining consistent representations of solids in computer-aided design and of giving rigorous proofs of error bounds for operations such as regularized Boolean intersection has been widely studied for at least two decades. One of the major difficulties is that the representations used in practice not only are in error but are fundamentally inconsistent. Such inconsistency is one of the main bottlenecks in downstream applications. This paper provides a framework for error analysis in the context of solid modeling, in the case where the data is represented using the standard representational method, and where the data may be uncertain. Included are discussions of ill-condition, error measurement, stability of algorithms, inconsistency of defining data, and the question of when we should invoke methods outside the scope of numerical analysis. A solution to the inconsistency problem is proposed and supported by theorems: it is based on the use of Whitney extension to define sets, called Quasi-NURBS sets, which are viewed as realizations of the inconsistent data provided to the numerical method. A detailed example illustrating the problem of regularized Boolean intersection is also given.    

  • 87.
    Andersson, Lars-Erik
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Stewart, N.F.
    IRO Universite de Montreal.
    Zidani, M.
    IRO Universite de Montreal.
    Proof of a non-selfintersection conjecture2006Rapport (Annet vitenskapelig)
  • 88.
    Andersson, Mats
    et al.
    Linköpings universitet, Institutionen för medicinsk teknik, Medicinsk informatik. Linköpings universitet, Tekniska högskolan.
    Burdakov, Oleg
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Knutsson, Hans
    Linköpings universitet, Institutionen för medicinsk teknik, Medicinsk informatik. Linköpings universitet, Tekniska högskolan.
    Zikrin, Spartak
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Global search strategies for solving multilinear least-squares problems2012Inngår i: Sultan Qaboos University Journal for Science, ISSN 1027-524X, Vol. 17, nr 1, s. 12-21Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The multilinear least-squares (MLLS) problem is an extension of the linear leastsquares problem. The difference is that a multilinear operator is used in place of a matrix-vector product. The MLLS is typically a large-scale problem characterized by a large number of local minimizers. It originates, for instance, from the design of filter networks. We present a global search strategy that allows for moving from one local minimizer to a better one. The efficiency of this strategy is illustrated by results of numerical experiments performed for some problems related to the design of filter networks.

    Fulltekst (pdf)
    TR2011-17
  • 89.
    Andersson, Mats
    et al.
    Linköpings universitet, Institutionen för medicinsk teknik, Medicinsk informatik. Linköpings universitet, Tekniska högskolan.
    Burdakov, Oleg
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Knutsson, Hans
    Linköpings universitet, Institutionen för medicinsk teknik, Medicinsk informatik. Linköpings universitet, Tekniska högskolan.
    Zikrin, Spartak
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska högskolan.
    Global Search Strategies for Solving Multilinear Least-squares Problems2011Rapport (Annet vitenskapelig)
    Abstract [en]

    The multilinear least-squares (MLLS) problem is an extension of the linear least-squares problem. The difference is that a multilinearoperator is used in place of a matrix-vector product. The MLLS istypically a large-scale problem characterized by a large number of local minimizers. It originates, for instance, from the design of filter networks. We present a global search strategy that allows formoving from one local minimizer to a better one. The efficiencyof this strategy isillustrated by results of numerical experiments performed forsome problems related to the design of filter networks.

    Fulltekst (pdf)
    Global Search Strategies for Solving Multilinear Least-squares Problems
  • 90.
    Andersson, Mats
    et al.
    Linköpings universitet, Institutionen för medicinsk teknik. Linköpings universitet, Tekniska högskolan.
    Burdakov, Oleg
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Knutsson, Hans
    Linköpings universitet, Institutionen för medicinsk teknik, Medicinsk informatik. Linköpings universitet, Tekniska högskolan.
    Zikrin, Spartak
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska högskolan.
    Sparsity Optimization in Design of Multidimensional Filter Networks2013Rapport (Annet vitenskapelig)
    Abstract [en]

    Filter networks is a powerful tool used for reducing the image processing time, while maintaining its reasonably high quality.They are composed of sparse sub-filters whose low sparsity ensures fast image processing.The filter network design is related to solvinga sparse optimization problem where a cardinality constraint bounds above the sparsity level.In the case of sequentially connected sub-filters, which is the simplest network structure of those considered in this paper, a cardinality-constrained multilinear least-squares (MLLS) problem is to be solved. If to disregard the cardinality constraint, the MLLS is typically a large-scale problem characterized by a large number of local minimizers. Each of the local minimizers is singular and non-isolated.The cardinality constraint makes the problem even more difficult to solve.An approach for approximately solving the cardinality-constrained MLLS problem is presented.It is then applied to solving a bi-criteria optimization problem in which both thetime and quality of image processing are optimized. The developed approach is extended to designing filter networks of a more general structure. Its efficiency is demonstrated by designing certain 2D and 3D filter networks. It is also compared with the existing approaches.

    Fulltekst (pdf)
    Sparsity Optimization in Design of Multidimensional Filter Networks (revised version)
  • 91.
    Andersson, Mats
    et al.
    Linköpings universitet, Institutionen för medicinsk teknik, Medicinsk informatik. Linköpings universitet, Tekniska högskolan. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV.
    Burdakov, Oleg
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Knutsson, Hans
    Linköpings universitet, Institutionen för medicinsk teknik, Medicinsk informatik. Linköpings universitet, Tekniska högskolan.
    Zikrin, Spartak
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Sparsity Optimization in Design of Multidimensional Filter Networks2015Inngår i: Optimization and Engineering, ISSN 1389-4420, E-ISSN 1573-2924, Vol. 16, nr 2, s. 259-277Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Filter networks are used as a powerful tool used for reducing the image processing time and maintaining high image quality.They are composed of sparse sub-filters whose high sparsity ensures fast image processing.The filter network design is related to solvinga sparse optimization problem where a cardinality constraint bounds above the sparsity level.In the case of sequentially connected sub-filters, which is the simplest network structure of those considered in this paper, a cardinality-constrained multilinear least-squares (MLLS) problem is to be solved. Even when disregarding the cardinality constraint, the MLLS is typically a large-scale problem characterized by a large number of local minimizers, each of which is singular and non-isolated.The cardinality constraint makes the problem even more difficult to solve.

    An approach for approximately solving the cardinality-constrained MLLS problem is presented.It is then applied to solving a bi-criteria optimization problem in which both thetime and quality of image processing are optimized. The developed approach is extended to designing filter networks of a more general structure. Its efficiency is demonstrated by designing certain 2D and 3D filter networks. It is also compared with the existing approaches.

    Fulltekst (pdf)
    fulltext
  • 92.
    Andersson, Per Gösta
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Matematisk statistik.
    A conditional perspective of weighted variance estimation of regression estimator2003Rapport (Annet vitenskapelig)
  • 93.
    Andersson, Per Gösta
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Matematisk statistik.
    A conditional perspective of weighted variance estimation of the optimal regression estimator2006Inngår i: Journal of Statistical Planning and Inference, ISSN 0378-3758, E-ISSN 1873-1171, Vol. 136, nr 1, s. 221-234Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The estimation of the variance for the GREG (general regression) estimator by weighted residuals is widely accepted as a method which yields estimators with good conditional properties. Since the optimal (regression) estimator shares the properties of GREG estimators which are used in the construction of weighted variance estimators, we introduce the weighting procedure also for estimating the variance of the optimal estimator. This method of variance estimation was originally presented in a seemingly ad hoc manner, and we shall discuss it from a conditional point of view and also look at an alternative way of utilizing the weights. Examples that stress conditional behaviour of estimators are then given for elementary sampling designs such as simple random sampling, stratified simple random sampling and Poisson sampling, where for the latter design we have conducted a small simulation study. © 2004 Elsevier B.V. All rights reserved.

  • 94.
    Andersson, Per Gösta
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Matematisk statistik.
    Alternative confidence intervals for the total of a skewed biological population2003Rapport (Annet vitenskapelig)
  • 95.
    Andersson, Per Gösta
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Matematisk statistik.
    Alternative confidence intervals for the total of a skewed biological population2004Inngår i: Ecology, ISSN 0012-9658, E-ISSN 1939-9170, Vol. 85, nr 11, s. 3166-3171Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In a 1999 Ecology article, T. G. Gregoire and O. Schabenberger addressed the problem of obtaining truly symmetric confidence intervals for the total of a positively skewed biological population under simple random sampling. Their simulation study revealed that the skewness induced a substantial positive correlation between the estimator of the total and the estimator of its variance. This caused the standard nominally symmetric t-based intervals, based on approximate normality of the estimator of the total, to be highly unbalanced, i.e., intervals much more often missed from below than from above. To better cope with this situation I suggest an alternative confidence interval procedure that takes into account and adjusts for the induced correlation. A simulation study based on one of the populations used by Gregoire and Schabenberger shows that the resulting adjusted intervals have more balanced noncoverage probabilities and often higher coverage probability than the standard intervals in cases of substantial correlation. I also provide an example of an unequal probability design using auxiliary information, where there is much less need for an adjustment.

  • 96.
    Andersson, Per Gösta
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Matematisk statistik.
    Thorburn, Daniel
    An optimal calibration distance leading to optimal regression estimator2003Rapport (Annet vitenskapelig)
  • 97.
    Andersson, Per Gösta
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Matematisk statistik.
    Thorburn, Daniel
    Department of Statistics Stockholm universitet.
    An Optimal Calibration Distance Leading to the Optimal Regresion Estimator2005Inngår i: Survey methodology, ISSN 0714-0045, Vol. 31, nr 1, s. 95-99Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    When there is auxiliary information in survey sampling, the design based optimal regression estimator of a finite population mean is known to be at least asymptocially more effective than the corresponding GREG estimator . We show that the optimal estimator can be seen as a calibration estimator.

  • 98.
    Andersson, Per-Åke
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Optimeringslära.
    CDU: R2 Optimeringsmetoder för resursfördelning inom Dr&Uh-verksamhet väg2003Inngår i: CDU-dagen,2003, 2003Konferansepaper (Annet vitenskapelig)
  • 99.
    Andersson, Per-Åke
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Computation of Thermal Development in Injection Mould Filling, based on the Distance Model2002Licentiatavhandling, monografi (Annet vitenskapelig)
    Abstract [en]

    The heat transfer in the filling phase of injection moulding is studied, based on Gunnar Aronsson’s distance model for flow expansion ([Aronsson], 1996).

    The choice of a thermoplastic materials model is motivated by general physical properties, admitting temperature and pressure dependence. Two-phase, per-phase-incompressible, power-law fluids are considered. The shear rate expression takes into account pseudo-radial flow from a point inlet.

    Instead of using a finite element (FEM) solver for the momentum equations a general analytical viscosity expression is used, adjusted to current axial temperature profiles and yielding expressions for axial velocity profile, pressure distribution, frozen layer expansion and special front convection.

    The nonlinear energy partial differential equation is transformed into its conservative form, expressed by the internal energy, and is solved differently in the regions of streaming and stagnant flow, respectively. A finite difference (FD) scheme is chosen using control volume discretization to keep truncation errors small in the presence of non-uniform axial node spacing. Time and pseudo-radial marching is used. A local system of nonlinear FD equations is solved. In an outer iterative procedure the position of the boundary between the “solid” and “liquid” fluid cavity parts is determined. The uniqueness of the solution is claimed. In an inner iterative procedure the axial node temperatures are found. For all physically realistic material properties the convergence is proved. In particular the assumptions needed for the Newton-Mysovskii theorem are secured. The metal mould PDE is locally solved by a series expansion. For particular material properties the same technique can be applied to the “solid” fluid.

    In the circular plate application, comparisons with the commercial FEM-FD program Moldflow (Mfl) are made, on two Mfl-database materials, for which model parameters are estimated/adjusted. The resulting time evolutions of pressures and temperatures are analysed, as well as the radial and axial profiles of temperature and frozen layer. The greatest differences occur at the flow front, where Mfl neglects axial heat convection. The effects of using more and more complex material models are also investigated. Our method performance is reported.

    In the polygonal star-shaped plate application a geometric cavity model is developed. Comparison runs with the commercial FEM-FD program Cadmould (Cmd) are performed, on two Cmd-database materials, in an equilateral triangular mould cavity, and materials model parameters are estimated/adjusted. The resulting average temperatures at the end of filling are compared, on rays of different angular deviation from the closest corner ray and on different concentric circles, using angular and axial (cavity-halves) symmetry. The greatest differences occur in narrow flow sectors, fatal for our 2D model for a material with non-realistic viscosity model. We present some colour plots, e.g. for the residence time.

    The classical square-root increase by time of the frozen layer is used for extrapolation. It may also be part of the front model in the initial collision with the cold metal mould. An extension of the model is found which describes the radial profile of the frozen layer in the circular plate application accurately also close to the inlet.

    The well-posedness of the corresponding linearized problem is studied, as well as the stability of the linearized FD-scheme.

    Fulltekst (pdf)
    FULLTEXT01
  • 100.
    Andersson, Per-Åke
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Multi-year maintenance optimisation for paved public roads - segment based modelling and price-directive decomposition2007Doktoravhandling, monografi (Annet vitenskapelig)
    Abstract [sv]

    I avhandlingen studeras hur kostnadseffektiva underhålls- (uh-)planer för belagd väg kan genereras, på basis av information om aktuellt vägytetillstånd och funktionella modeller för kostnads- och tillståndsförändringar, delvis utvecklade i samarbete med svenska Vägverket (VV). Tilltänkt användning är på strategisk och programnivå, innan mer detaljerad objektinformation finns att tillgå. Till skillnad från hittills använda modeller, så genereras individuella uh-planer för varje vägsegment (en homogen vägsträcka vad gäller aktuellt beläggningstillstånd och beläggningshistorik), i kontinuerliga tillstånds- och åtgärdsrum. Genom användning av Lagrangerelaxerande optimeringsteknik, så kan de speciella nytto/kostnads-kvot-villkor som VV ålägger varje uh-objekt naturligen hanteras med dualpriser för budgetvillkoren. Antalet vägsegment som konkurrerar om budgetmedlen är vanligtvis stort. Data från VV:s Vägdatabank för Värmland har använts, omfattande ca 9000 vägsegment. Genom den stora datamängden har datorprogrammen implementerats för parallellbearbetning. Under avhandlingsarbetet har projektet beviljats tillgång till Monolith PCklustret vid NSC. För att kunna reducera optimeringskörtiderna har modell- och metodutveckling varit nödvändig. Genom att aggregera vägsegmenten till vägklasser har goda startvärden på dualpriserna erhållits. Genom utvecklingen av en speciell restvärdesrutin har den explicit behandlade tidsperioden kunnat reduceras. Vid lösandet av det duala subproblemet har speciell uppmärksamhet ägnats åt de diskretiseringseffekter som uppstår i metoden dynamisk programmering. En typ av tillämpning avser ett delvägnät, exempelvis en väg. Valideringsstudier har genomförts på väg 63 i Värmland – med lovande men inte tillfredsställande resultat (se nedan). En speciell modell för samordnat uh beaktar stordriftsfördelarna vid samtidig åtgärd på en hel vägsträcka. Den andra huvudtypen av studier gäller ett helt nätverk. Flera metodtyper har tillämpats, både för att lösa de relaxerade optimeringsproblemen och för att generera uhplaner som uppfyller budgetvillkoren. För en anständig diskretisering är körtiderna för hela Värmland mindre än 80 CPU-timmar. Genom en a posteriori primal heuristik reduceras kraven på parallellbearbetning till ett litet PC-kluster. Avhandlingen studerar vidare effekterna av omfördelade budgetmedel samt en övergång till en transparent, stokastisk modell – vilka båda visar små avvikelser från basmodellen.

    Optimeringsresultaten för Värmland indikerar att budgetnivåer på ca 40% av Värmlands verkliga uh-budget är tillräckliga. Dock saknas viktiga kostnadsdrivande faktorer i denna första modellomgång, exempelvis vissa funktionella prestanda (säkerhet), all miljöpåverkande prestanda (buller etc.) och strukturell prestanda (ex.vis bärighet, som enbart modelleras via ett åldersmått). För ökad tilltro till PMS i allmänhet och optimering i synnerhet, bör avvikelserna analyseras ytterligare och leda till förbättringar vad gäller tillståndsmätning, tillståndseffekt- & kostnadsmodellering samt matematisk modellering & implementering.

    Fulltekst (pdf)
    FULLTEXT01
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