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• 101.
Alternative confidence intervals for the total of a skewed biological population2003Rapport (Annet vitenskapelig)
• 102.
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)

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.

• 103.
An optimal calibration distance leading to optimal regression estimator2003Rapport (Annet vitenskapelig)
• 104.
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)

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.

• 105.
CDU: R2 Optimeringsmetoder för resursfördelning inom Dr&Uh-verksamhet väg2003Inngår i: CDU-dagen,2003, 2003Konferansepaper (Annet vitenskapelig)
• 106. Kjøp publikasjonen >>
Computation of Thermal Development in Injection Mould Filling, based on the Distance Model2002Licentiatavhandling, monografi (Annet vitenskapelig)

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.

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• 107. Kjøp publikasjonen >>
Multi-year maintenance optimisation for paved public roads - segment based modelling and price-directive decomposition2007Doktoravhandling, monografi (Annet vitenskapelig)

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.

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• 108.
Multiyear planning of public road maintenance2003Inngår i: GOR2003,2003, 2003Konferansepaper (Annet vitenskapelig)
• 109.
An iterative solution method for p-harmonic functions on finite graphs with an implementation2009Independent thesis Advanced level (degree of Master (One Year)), 20 poäng / 30 hpOppgave

In this paper I give a description and derivation of Dirichlet's problem, a boundary value problem, for p-harmonic functions on graphs and study an iterative method for solving it.The method's convergence is proved and some preliminary results about its speed of convergence are presented.There is an implementation accompanying this thesis and a short description of the implementation is included. The implementation will be made available on the internet at http://www.mai.liu.se/~anbjo/pharmgraph/ for as long as possible.

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• 110. Andreev, A.
Averaged Moduli of Smoothness and Runge-Kutta Methods2005Inngår i: Mathematica Balkanica, ISSN 0350-2007, Vol. 19, s. 293-304Artikkel i tidsskrift (Fagfellevurdert)
• 111.
Malardalen Univ, Sweden; Mittag Leffler Inst, Sweden.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten. Mittag Leffler Inst, Sweden. Umea Univ, Sweden; Mittag Leffler Inst, Sweden.
Restricted completion of sparse partial Latin squares2019Inngår i: Combinatorics, probability & computing, ISSN 0963-5483, E-ISSN 1469-2163, Vol. 28, nr 5, s. 675-695Artikkel i tidsskrift (Fagfellevurdert)

An n x n Martial Latin square P is called dense if each row and column has at mostan non-empty cells and each symboloccurso n times in P. An x n arrayA where each cell contains subset of {1, ..., n} is a (beta n, beta n, beta n)-array if each symbol occurs at most beta n times in each row and column and each cell contains a set of size at most beta n. Combining the notions of completing partial Latin squared and avoiding arrays, we prose that there are constants alpha, beta amp;gt; 0 such that, for every positive integer n, if P is an alpha-dense n x n partial a square, A is an n x n (beta n, beta n, beta n)-array and no cell of P contains a symbol that ppears in the corresponing cell of A, then there is a completiong of P that avoids A; that is, there is a Latin square L that agrees with P on every non-empty of P, and for each i, j satisfying 1 amp;lt;= i, j, amp;lt;= n, the symbol in position (i, j) in L does not appear in the corresponding cell of A.

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• 112.
Department of Biometry and Engineering SLU.
Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Matematisk statistik. Department of Biometry and Engineering SLU.
Estimation of banded covariance matrices in a multivariate normal distribution2008Rapport (Annet vitenskapelig)
• 113.
Energy and Technology, Swedish University of Agricultural Sciences, Uppsala, Sweden.
Asymptotic distribution of the estimators of a harmonic component in a multivariate time series under m-dependence2011Rapport (Annet vitenskapelig)

Multivariate time series with definite harmonic structure is considered, in the special case when the marginal univariate time series are independent and asymptotically stationary to second order. The asymptotic distribution of the estimators of a harmonic component under \$m\$-dependence is found

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• 114.
Programmering som en problemlösningsmetod i ämnet matematik inom gymnasieskolan2018Independent thesis Basic level (professional degree), 10 poäng / 15 hpOppgave

Skolverket införde år 2017 ett nytt kursmoment inom ämnet matematik, som var att programmering ska användas som metod för problemlösning. Lärarkåren har delade meningar om implementeringen av programmering, eftersom en del lärare anser att det redan har varit svårt att hinna med det centrala innehållet, och nu med det nya kursmoment, blir lärarna oroliga för att det finns en risk att det nya kursmomentet kommer leda till tidsbrist i undervisningen.Studiens syfte är att sammanställa forskningsresultat om hur programmering som problemlösningsmetod påverkar elevers problemlösning i matematik. Frågeställningen är ”Hur påverkar elevers problemlösningsförmåga av att programmering används som problemlösningsmetod i ämnet matematik i gymnasieskolan?”.Metoden är en allmän litteraturstudie, där nio stycken vetenskapliga artiklar ingår i urvalet.Enligt skollagen ska undervisning baseras på vetenskaplig forskning och beprövade erfarenheter. Litteraturstudien visar att forskningslitteraturen dokumenterar positiva effekter på problemlösningsförmågan av att använda programmering som problemlösningsmetod.

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• 115.
Computation of Autonomous Safety Maneuvers Using Segmentation and Optimization2019Licentiatavhandling, med artikler (Annet vitenskapelig)

This thesis studies motion planning for future autonomous vehicles with main focus on passenger cars. By having automatic steering and braking together with information about the environment, such as other participants in the traffic or obstacles, it would be possible to perform autonomous maneuvers while taking limitations of the vehicle and road–tire interaction into account. Motion planning is performed to find such maneuvers that bring the vehicle from the current state to a desired future state, here by formulating the motion-planning problem as an optimal control problem. There are a number of challenges for such an approach to motion planning; some of them are how to formulate the criterion in the motion planning (objective function in the corresponding optimal control problem), and how to make the solution of motion-planning problems efficient to be useful in online applications. These challenges are addressed in this thesis.

As a criterion for motion-planning problems of passenger vehicles on doublelane roads, it is investigated to use a lane-deviation penalty function to capture the observation that it is dangerous to drive in the opposing lane, but safe to drive in the original lane after the obstacle. The penalty function is augmented with certain additional terms to address also the recovery behavior of the vehicle. The resulting formulation is shown to provide efficient and steady maneuvers and gives a lower time in the opposing lane compared to other objective functions. Under varying parameters of the scenario formulation, the resulting maneuvers are changing in a way that exhibits structured characteristics.

As an approach to improve efficiency of computations for the motion-planning problem, it is investigated to segment motion planning of the full maneuver into several smaller maneuvers. A way to extract segments is considered from a vehicle dynamics point of view, and it is based on extrema of the vehicle orientation and the yaw rate. The segmentation points determined using this approach are observed to allow efficient splitting of the optimal control problem for the full maneuver into subproblems.

Having a method to segment maneuvers, this thesis further studies methods to allow parallel computation of these maneuvers. One investigated method is based on Lagrange relaxation and duality decomposition. Smaller subproblems are formulated, which are governed by solving a low-complexity coordination problem. Lagrangian relaxation is performed on a subset of the dynamic constraints at the segmentation points, while the remaining variables are predicted. The prediction is possible because of the observed structured characteristics resulting from the used lane-deviation penalty function. An alternative approach is based on adoption of the alternating augmented Lagrangian method. Augmentation of the Lagrangian allows to apply relaxation for all dynamic constraints at the segmentation points, and the alternating approach makes it possible to decompose the full problem into subproblems and coordinating their solutions by analytically solving an overall coordination problem. The presented decomposition methods allow computation of maneuvers with high correspondence and lower computational times compared to the results obtained for solving the full maneuver in one step.

1. Segmentation and Merging of Autonomous At-the-Limit Maneuvers for Ground Vehicles
Åpne denne publikasjonen i ny fane eller vindu >>Segmentation and Merging of Autonomous At-the-Limit Maneuvers for Ground Vehicles
2018 (engelsk)Inngår i: Proceedings of the 14th International Symposium on Advanced Vehicle Control, Beijing, July 16-20, 2018, 2018, s. 1-6Konferansepaper, Publicerat paper (Fagfellevurdert)
##### Abstract [en]

To decrease the complexity of motion-planning optimizations, a segmentation and merging strategy for maneuvers is proposed. Maneuvers that are at-the-limit of friction are of special interest since they appear in many critical situations. The segmentation pointsare used to set constraints for several smaller optimizations for parts of the full maneuver, which later are merged and compared withoptimizations of the full maneuver. The technique is illustrated for a double lane-change maneuver.

##### Emneord
vehicle automation and control, ground vehicle motion-planning, aggressive maneuvers
##### Identifikatorer
urn:nbn:se:liu:diva-152222 (URN)
##### Konferanse
The 14th International Symposium on Advanced Vehicle Control, Beijing, July 16-20, 2018
Tilgjengelig fra: 2018-10-22 Laget: 2018-10-22 Sist oppdatert: 2019-11-21bibliografisk kontrollert
2. Efficient Motion Planning for Autonomous Vehicle Maneuvers Using Duality-Based Decomposition
Åpne denne publikasjonen i ny fane eller vindu >>Efficient Motion Planning for Autonomous Vehicle Maneuvers Using Duality-Based Decomposition
2019 (engelsk)Inngår i: IFAC PAPERSONLINE, ELSEVIER , 2019, Vol. 52, nr 5, s. 78-84Konferansepaper, Publicerat paper (Fagfellevurdert)
##### Abstract [en]

A method to decompose a motion-planning problem into several segments is presented. It is based on a modification of the original problem, such that certain variables at the splitting points are considered to be precomputed and thus fixed and the remaining variables are obtained by performing Lagrange relaxation. The resulting dual problem is split into several subproblems, allowing parallel computation. The method is formalized as a computational algorithm and evaluated in a safety critical double lane-change situation. The resulting maneuver has close-to-optimal behavior and, for certain initialization strategies, it is obtained in shorter computational time compared to computing the full maneuver in one step. (C) 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

##### sted, utgiver, år, opplag, sider
ELSEVIER, 2019
##### Emneord
trajectory and path planning; autonomous vehicles; duality-based decomposition; motion control; safety; intelligent transportation systems
##### Identifikatorer
urn:nbn:se:liu:diva-161215 (URN)10.1016/j.ifacol.2019.09.013 (DOI)000486629500014 ()
##### Konferanse
9th IFAC International Symposium on Advances in Automotive Control (AAC)

Funding Agencies|Wallenberg AI, Autonomous Systems and Software Program (WASP) - Knut and Alice Wallenberg Foundation

Tilgjengelig fra: 2019-10-25 Laget: 2019-10-25 Sist oppdatert: 2019-11-21
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Computation of Autonomous Safety Maneuvers Using Segmentation and Optimization
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• 116.
Linköpings universitet, Institutionen för systemteknik, Fordonssystem. Linköpings universitet, Tekniska fakulteten. Lund Univ, Sweden. Linköpings universitet, Institutionen för systemteknik, Fordonssystem. Linköpings universitet, Tekniska fakulteten.
Efficient Motion Planning for Autonomous Vehicle Maneuvers Using Duality-Based Decomposition2019Inngår i: IFAC PAPERSONLINE, ELSEVIER , 2019, Vol. 52, nr 5, s. 78-84Konferansepaper (Fagfellevurdert)

A method to decompose a motion-planning problem into several segments is presented. It is based on a modification of the original problem, such that certain variables at the splitting points are considered to be precomputed and thus fixed and the remaining variables are obtained by performing Lagrange relaxation. The resulting dual problem is split into several subproblems, allowing parallel computation. The method is formalized as a computational algorithm and evaluated in a safety critical double lane-change situation. The resulting maneuver has close-to-optimal behavior and, for certain initialization strategies, it is obtained in shorter computational time compared to computing the full maneuver in one step. (C) 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

• 117.
Linköpings universitet, Institutionen för fysik, kemi och biologi, Biologi. Linköpings universitet, Tekniska fakulteten. Polismyndigheten - Nationellt Forensiskt Centrum.
Linköpings universitet, Institutionen för datavetenskap, Statistik. Linköpings universitet, Filosofiska fakulteten. Polismyndigheten - Nationellt Forensiskt Centrum. Polismyndigheten - Nationellt Forensiskt Centrum.
Interpretation of DNA Evidence: Implications of Thresholds Used in the Forensic Laboratory2014Konferansepaper (Annet vitenskapelig)

Evaluation of forensic evidence is a process lined with decisions and balancing, not infrequently with a substantial deal of subjectivity. Already at the crime scene a lot of decisions have to be made about search strategies, the amount of evidence and traces recovered, later prioritised and sent further to the forensic laboratory etc. Within the laboratory there must be several criteria (often in terms of numbers) on how much and what parts of the material should be analysed. In addition there is often a restricted timeframe for delivery of a statement to the commissioner, which in reality might influence on the work done. The path of DNA evidence from the recovery of a trace at the crime scene to the interpretation and evaluation made in court involves several decisions based on cut-offs of different kinds. These include quality assurance thresholds like limits of detection and quantitation, but also less strictly defined thresholds like upper limits on prevalence of alleles not observed in DNA databases. In a verbal scale of conclusions there are lower limits on likelihood ratios for DNA evidence above which the evidence can be said to strongly support, very strongly support, etc. a proposition about the source of the evidence. Such thresholds may be arbitrarily chosen or based on logical reasoning with probabilities. However, likelihood ratios for DNA evidence depend strongly on the population of potential donors, and this may not be understood among the end-users of such a verbal scale. Even apparently strong DNA evidence against a suspect may be reported on each side of a threshold in the scale depending on whether a close relative is part of the donor population or not. In this presentation we review the use of thresholds and cut-offs in DNA analysis and interpretation and investigate the sensitivity of the final evaluation to how such rules are defined. In particular we show what are the effects of cut-offs when multiple propositions about alternative sources of a trace cannot be avoided, e.g. when there are close relatives to the suspect with high propensities to have left the trace. Moreover, we discuss the possibility of including costs (in terms of time or money) for a decision-theoretic approach in which expected values of information could be analysed.

• 118.
Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Ekonomiska informationssystem.
A note on the Erard & Feinstein tax audit model Manuskript (preprint) (Annet vitenskapelig)

This paper introduces a new method for the determination of near-optimal audit strategies with the Erard & Feinstein model. It is demonstrated that the solution method presented by Erard & Feinstein does not lead to optimal audit strategies. The new method simulates taxpayer behaviour for a class of audit functions among which the best function is selected. Using a simple class of functions, the resulting strategies are superior to those obtained with the Erard & Feinstein method.

The simulation method can easily handle variations of the model, for instance with involuntary taxpayer errors as well as with partially discrete true income distributions.

• 119.
Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Ekonomiska informationssystem. Linköpings universitet, Filosofiska fakulteten.
Audit strategy for temporary parental benefit2012Rapport (Annet (populærvitenskap, debatt, mm))

The aim of this project is to study the possibility to apply audit strategies developed for taxation on fraud and involuntary errors in the social benefit sector. The efficiency of different audit strategies is compared using a computer-based optimization algorithm.

Two types of audit strategies are used in this study. One is to adapt the audit intensity to the propensity for errors and fraud in different segments of the group studied. The other type of audit strategy is based on adaptation of behaviour through information concerning the audit intensity. A model for determination of optimal tax audit strategies of the latter type was developed by Erard & Feinstein in 1994.

This study is based on data from a large study of temporary parental benefit performed by the Institute for Evaluation of Labour Market and Education Policy (Institutet för arbetsmarknadspolitisk utvärdering, IFAU) in 2006.

The study has shown that it is possible to apply the Erard & Feinstein model on benefit fraud. However, the solution method developed by Erard & Feinstein has proven to be non-optimal. A new solution method based on simulation has been developed and used in the study.

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• 120.
Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Ekonomiska informationssystem. Linköpings universitet, Filosofiska fakulteten.
Kontrollstrategi för tillfällig föräldrapenning2011Rapport (Annet (populærvitenskap, debatt, mm))
• 121.
Elevers attittyder till matematik: En jämförande studie mellan årskurs 3 och 62012Independent thesis Advanced level (professional degree), 10 poäng / 15 hpOppgave

I dagens samhälle förekommer en nedåtgående trend där intresset för och kunskapen om matematik sjunker. Matematikkunnande utvecklas bland annat genom en lust och nyfikenhet som gör att människan vill utforska ämnet vilket innebär att kunskap och intresse är tätt sammankopplat. En möjlig anledning till den sjunkande kunskapsnivån skulle därför kunna vara en allt mer negativ attityd gentemot matematikämnet. Detta är en studie, baserat på en enkätundersökning, som riktar in sig på just elevers attityder till matematik. Dess syfte är att undersöka hur elevers attityd till matematik, i årskurs 3 och 6, ser ut med avseende på intresse, motivation, tilltro till den egna förmågan och oro, fyra viktiga faktorer för inlärning. Studien behandlar huruvida det förekommer några uppenbara skillnader mellan dessa två elevgrupper. Resultatet visar att eleverna i årskurs 3 har en mer positiv attityd gentemot matematik än vad eleverna i årskurs 6 har, vilket stämmer överens med tidigare forskning. Den mest uppenbara skillnaden som studien visat är inom delområdena intresse och yttre motivation där en signifikant skillnad mellan årskurserna förekom. Studien har vidare visat att eleverna i båda årskurserna har en relativt hög tilltro till sin egen förmåga samt låg oro i samband med matematikämnet.

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• 122.
Department of Applied Mathematics and Statistics, Stony Brook University, USA .
Institute of Computer Science, Freie Universität Berlin, Germany . Institute of Computer Science, Universität Bayreuth, Germany . Department of Applied Mathematics and Statistics, Stony Brook University, USA . Helsinki Institute for Information Technology, CS Dept, University of Helsinki, Finland . Institute of Computer Science, Freie Universität Berlin, Germany . Department of Computer Science, Stony Brook University, USA .
Convex transversals2014Inngår i: Computational Geometry, ISSN 0925-7721, Vol. 47, nr 2, s. 224-239Artikkel i tidsskrift (Fagfellevurdert)

We answer the question initially posed by Arik Tamir at the Fourth NYU Computational Geometry Day (March, 1987): “Given a collection of compact sets, can one decide in polynomial time whether there exists a convex body whose boundary intersects every set in the collection?”

We prove that when the sets are segments in the plane, deciding existence of the convex stabber is NP-hard. The problem remains NP-hard if the sets are regular polygons. We also show that in 3D the stabbing problem is hard when the sets are balls. On the positive side, we give a polynomial-time algorithm to find a convex transversal of a maximum number of pairwise-disjoint segments in 2D if the vertices of the transversal are restricted to a given set of points. Our algorithm also finds a convex stabber of the maximum number of a set of convex pseudodisks in the plane.

The stabbing problem is related to “convexity” of point sets measured as the minimum distance by which the points must be shifted in order to arrive in convex position; we give a PTAS to find the minimum shift in 2D, and a 2-approximation in any dimension. We also consider stabbing with vertices of a regular polygon – a problem closely related to approximate symmetry detection.

• 123.
Energy estimates and variance estimation for hyperbolic stochastic partial differentialequations2011Independent thesis Advanced level (professional degree), 30 poäng / 45 hpOppgave

In this thesis the connections between the boundary conditions and the vari- ance of the solution to a stochastic partial differential equation (PDE) are investigated. In particular a hyperbolical system of PDE’s with stochastic initial and boundary data are considered. The problem is shown to be well- posed on a class of boundary conditions through the energy method. Stability is shown by using summation-by-part operators coupled with simultaneous- approximation-terms. By using the energy estimates, the relative variance of the solutions for different boundary conditions are analyzed. It is concluded that some types of boundary conditions yields a lower variance than others. This is verified by numerical computations.

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• 124.
Low Dimensional Matrix Representations for Noncommutative Surfaces of Arbitrary Genus2020Inngår i: Mathematical physics, analysis and geometry, ISSN 1385-0172, E-ISSN 1572-9656, Vol. 23, nr 2, artikkel-id 12Artikkel i tidsskrift (Fagfellevurdert)

In this note, we initiate a study of the finite-dimensional representation theory of a class of algebras that correspond to noncommutative deformations of compact surfaces of arbitrary genus. Low dimensional representations are investigated in detail and graph representations are used in order to understand the structure of non-zero matrix elements. In particular, for arbitrary genus greater than one, we explicitly construct classes of irreducible two and three dimensional representations. The existence of representations crucially depends on the analytic structure of the polynomial defining the surface as a level set in Double-struck capital R-3.

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• 125.
Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden .
Representation theory of C  -algebras for a higher-order class of spheres and tori2008Inngår i: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 49, s. 053502-1-053502-13, artikkel-id 053502Artikkel i tidsskrift (Fagfellevurdert)

We construct C  -algebras for a class of surfaces that are inverse images of certain polynomials of arbitrary degree. By using the directed graph associated with a matrix, the representation theory can be understood in terms of “loop” and “string” representations, which are closely related to the dynamics of an iterated map in the plane. As a particular class of algebras, we introduce the “Hénon algebras,” for which the dynamical map is a generalized Hénon map, and give an example where irreducible representations of all dimensions exist.

• 126.
An axiomatic approach to gradients with applications to Dirichlet and obstacle problems beyond function spaces2016Inngår i: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 134, s. 70-104Artikkel i tidsskrift (Fagfellevurdert)

We develop a framework for studying variational problems in Banach spaces with respect to gradient relations, which encompasses many of the notions of generalized gradients that appear in the literature. We stress the fact that our approach is not dependent on function spaces and therefore applies equally well to functions on metric spaces as to operator algebras. In particular, we consider analogues of Dirichlet and obstacle problems, as well as first eigenvalue problems, and formulate conditions for the existence of solutions and their uniqueness. Moreover, we investigate to what extent a lattice structure may be introduced on ( ordered) Banach spaces via a norm-minimizing variational problem. A multitude of examples is provided to illustrate the versatility of our approach. (C) 2015 Elsevier Ltd. All rights reserved.

• 127.
Institut des Hautes Études Scientifiques, Le Bois-Marie 35, route de Chartres, F-91440, Bures-sur-Yvette, France och Max Planck Institute for Gravitational Physics, Am Mühlenberg 1, D-14476, Golm, Germany .
Laboratoire de MIA, 4, rue des Frères Lumière, Université de Haute-Alsace, F-68093, Mulhouse, France . Université du Luxembourg, FSTC 162a, avenue de la Faïencerie, L-1511, Luxembourg City, Luxembourg . Department of Mathematics, KTH, S-10044, Stockholm, Sweden . Max Planck Institute for Gravitational Physics, Am Mühlenberg 1, D-14476, Golm, Germany .
Noncommutative Riemann Surfaces by Embeddings in R32009Inngår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 288, s. 403-429Artikkel i tidsskrift (Fagfellevurdert)

We introduce C-Algebras of compact Riemann surfaces Σ  as non-commutative analogues of the Poisson algebra of smooth functions on Σ  . Representations of these algebras give rise to sequences of matrix-algebras for which matrix-commutators converge to Poisson-brackets as N → ∞. For a particular class of surfaces, interpolating between spheres and tori, we completely characterize (even for the intermediate singular surface) all finite dimensional representations of the corresponding C-algebras

• 128.
Department of Mathematics, Royal Institute of Technology, Lindstedtsvägen 25 S-10044 Stockholm, Sweden.
Laboratoire de MIA, Université de Haute-Alsace, 4, rue des Frères Lumière, F-68093 Mulhouse, France. Department of Mathematics, Royal Institute of Technology, Lindstedtsvägen 25 S-10044 Stockholm, Sweden och Laboratoire de MIA, Université de Haute-Alsace, 4, rue des Frères Lumière, F-68093 Mulhouse, France. Department of Mathematics, Royal Institute of Technology, Lindstedtsvägen 25 S-10044 Stockholm, Sweden. Max Planck Institute for Gravitational Physics, Albert Einstein Institute, Am Mühlenberg 1 D-14476 Golm., Germany.
Fuzzy Riemann surfaces2009Inngår i: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, Vol. 2009, nr 024, s. 1-17Artikkel i tidsskrift (Fagfellevurdert)

We introduce C-Algebras (quantum analogues of compact Riemann surfaces), defined by polynomial relations in non-commutative variables and containing a real parameter that, when taken to zero, provides a classical non-linear, Poisson-bracket, obtainable from a single polynomial C(onstraint) function. For a continuous class of quartic constraints, we explicitly work out finite dimensional representations of the corresponding C-Algebras.

• 129.
Department of Mathematics, Royal Institute of Technology, 100 44, Stockholm, Sweden .
Laboratoire de MIA, 4 rue des Frères Lumière, Univ. deHaute-Alsace, 68093, Mulhouse, France . Department of Mathematics, Royal Institute of Technology, 100 44, Stockholm, Sweden . Department of Physics and Center for Theoretical Physics, Seoul National University, 151-747, Seoul, South Korea .
Goldfish Geodesics and Hamiltonian Reduction of Matrix Dynamics2008Inngår i: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 84, s. 89-98Artikkel i tidsskrift (Fagfellevurdert)

We describe the Hamiltonian reduction of a time-dependent real-symmetric N×N matrix system to free vector dynamics, and also provide a geodesic interpretation of Ruijsenaars–Schneider systems. The simplest of the latter, the goldfish equation, is found to represent a flat-space geodesic in curvilinear coordinates.

• 130.
Korea Institute Adv Study, South Korea. Royal Institute Technology, Sweden.
Noncommutative Minimal Surfaces2016Inngår i: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 106, nr 8, s. 1109-1129Artikkel i tidsskrift (Fagfellevurdert)

We define noncommutative minimal surfaces in the Weyl algebra, and give a method to construct them by generalizing the well-known Weierstrass representation.

• 131.
A noncommutative catenoid2018Inngår i: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 108, nr 7, s. 1601-1622Artikkel i tidsskrift (Fagfellevurdert)

A noncommutative algebra corresponding to the classical catenoid is introduced together with a differential calculus of derivations. We prove that there exists a unique metric and torsion-free connection that is compatible with the complex structure, and the curvature is explicitly calculated. A noncommutative analogue of the fact that the catenoid is a minimal surface is studied by constructing a Laplace operator from the connection and showing that the embedding coordinates are harmonic. Furthermore, an integral is defined and the total curvature is computed. Finally, classes of left and right modules are introduced together with constant curvature connections, and bimodule compatibility conditions are discussed in detail.

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• 132.
Institut des Hautes Études Scientif iques, Le Bois-Marie, 35, Route de Chartres, 91440 Bures-sur-Yvette, France.
Eidgenössische Technische Hochschule, 8093 Zürich, Switzerland (on leave of absence from Kungliga Tekniska Högskolan, 100 44 Stockholm, Sweden).
Discrete Minimal Surface Algebras2010Inngår i: SIGMA. Symmetry, Integrability and Geometry, ISSN 1815-0659, E-ISSN 1815-0659, Vol. 6, nr 042, s. -18Artikkel i tidsskrift (Fagfellevurdert)

We consider discrete minimal surface algebras (DMSA) as generalized noncommutative analogues of minimal surfaces in higher dimensional spheres. These algebras appear naturally in membrane theory, where sequences of their representations are used as a regularization. After showing that the defining relations of the algebra are consistent, and that one can compute a basis of the enveloping algebra, we give several explicit examples of DMSAs in terms of subsets of sln (any semi-simple Lie algebra providing a trivial example by itself). A special class of DMSAs are Yang-Mills algebras. The representation graph is introduced to study representations of DMSAs of dimension d ≤ 4, and properties of representations are related to properties of graphs. The representation graph of a tensor product is (generically) the Cartesian product of the corresponding graphs. We provide explicit examples of irreducible representations and, for coinciding eigenvalues, classify all the unitary representations of the corresponding algebras.

• 133.
Department of Mathematics, Royal Institute of Technology, Stockholm, 100 44, Sweden .
Department of Mathematics, Royal Institute of Technology, Stockholm, 100 44, Sweden .
EIGENVALUE DYNAMICS, FOLLYTONS AND LARGEN LIMITS OF MATRICES2006Inngår i: Applications of Random Matrices in Physics / [ed] Édouard Brézin, Vladimir Kazakov, Didina Serban, Paul Wiegmann, Anton Zabrodin, Springer, 2006, 211, s. 89-94Kapittel i bok, del av antologi (Fagfellevurdert)

How do the eigenvalues of a “free” hermitian N × N matrix X(t) evolve in time? The answer is provided by the rational Calogero-Moser systems [5, 13] if (!) the initial conditions are chosen such that i[X(0),Ẋ(0)] has a non-zero eigenvalue of multiplicity N–1; for generic X(0),Ẋ(0) the question remained unanswered for 30 years.

• 134.
Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden.
Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden.
Eigenvalue-Dynamics off the Calogero–Moser System2004Inngår i: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 68, s. 121-129Artikkel i tidsskrift (Fagfellevurdert)

By finding N(N− 1)/2 suitable conserved quantities, free motions of real symmetric N×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),Xd(0)] has to be purely imaginary, of rank one.

• 135.
Department of Mathematics, Royal Institute of Technology, 10044 Stockholm, Sweden.
Department of Mathematics, Royal Institute of Technology, 10044 Stockholm, Sweden. Albert-Einstein-Institut, Am Mühlenberg 1, D-14476 Golm, Germany.
Spinning membranes2004Inngår i: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 599, nr 1-2, s. 118-128Artikkel i tidsskrift (Fagfellevurdert)

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 AdSp×SqAdSp×Sq, as well as in flat space–time. Nontrivial reductions of the BMN matrix model equations are also given.

• 136.
University of Tubingen, Germany.
Pseudo-Riemannian Geometry in Terms of Multi-Linear Brackets2014Inngår i: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 104, nr 12, s. 1507-1521Artikkel i tidsskrift (Fagfellevurdert)

We show that the pseudo-Riemannian geometry of submanifolds can be formulated in terms of higher order multi-linear maps. In particular, we obtain a Poisson bracket formulation of almost (para-)Kahler geometry.

• 137.
Université de Haute-Alsace, France. Université de Haute-Alsace, France. Mälardalens Högskola, Västerås, Sweden.
Structure and Cohomology of 3-Lie Algebras Induced by Lie Algebras2014Inngår i: ALGEBRA, GEOMETRY AND MATHEMATICAL PHYSICS (AGMP), SPRINGER , 2014, Vol. 85, s. 123-144Konferansepaper (Fagfellevurdert)

The aim of this paper is to compare the structure and the cohomology spaces of Lie algebras and induced 3-Lie algebras.

• 138.
Max Planck Institute for Gravitational Physics (AEI), Am Mühlenberg 1, D-14476 Golm, Germany.
Université de Haute Alsace, Laboratoire de Mathématiques, Informatique et Applications, 4, rue des Frères Lumière F-68093 Mulhouse, France . Mälardalen University, Division of Applied Mathematics, The School of Education, Culture and Communication, Box 883, 721 23 Västerås, Sweden och Centre for Mathematical Sciences, Lund University, Box 118, 221 00 Lund, Sweden .
Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras2011Inngår i: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 52, artikkel-id 123502Artikkel i tidsskrift (Fagfellevurdert)

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

• 139.
Max Planck Institute for Gravitational Physics (AEI), Am Mühlenberg 1, D-14476 Golm, Germany.
Laboratoire de Mathématiques, Informatique et Applications, Université de Haute Alsace, 4, rue des Frères Lumière, F-68093 Mulhouse, France . Centre for Mathematical Sciences, Lund University, Box 118, SE-221 00 Lund, Sweden .
Ternary Hom–Nambu–Lie algebras induced by Hom–Lie algebras2010Inngår i: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 51, s. 043515-1-043515-11, artikkel-id 43515Artikkel i tidsskrift (Fagfellevurdert)

The need to consider n  -ary algebraic structures, generalizing Lie and Poisson algebras, has become increasingly important in physics, and it should therefore be of interest to study the mathematical concepts related to n  -ary algebras. The purpose of this paper is to investigate ternary multiplications (as deformations of n  -Lie structures) constructed from the binary multiplication of a Hom–Lie algebra, a linear twisting map, and a trace function satisfying certain compatibility conditions. We show that the relation between the kernels of the twisting maps and the trace function plays an important role in this context and provide examples of Hom–Nambu–Lie algebras obtained using this construction.

• 140.
Mathematical Physics, Royal Institute of Technology, SE-106 91, Stockholm, Sweden .
Mathematical Physics, Royal Institute of Technology, SE-106 91, Stockholm, Sweden .
Trace Extensions, Determinant Bundles, and Gauge Group Cocycles2002Inngår i: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 62, nr 2, s. 101-110Artikkel i tidsskrift (Fagfellevurdert)

We study the geometry of determinant line bundles associated with Dirac operators on compact odd-dimensional manifolds. Physically, these arise as (local) vacuum line bundles in quantum gauge theory. We give a simplified derivation of the commutator anomaly formula using a construction based on noncyclic trace extensions and associated nonmultiplicative renormalized determinants.

• 141.
Albert Einstein Institute, Golm, Germany..
Centre for Mathematical Sciences, Lund University, Box 118, 221 00 Lund, Sweden .
Affine transformation crossed product type algebras and noncommutative surfaces2009Inngår i: Operator structures and dynamical systems :: July 21-25 2008, Lorentz Center, Leiden, the Netherlands, satellite conference of the fifth European Congress of Mathematics, American Mathematical Society (AMS), 2009, 503, s. 1-25Kapittel i bok, del av antologi (Fagfellevurdert)

Several classes of *-algebras associated to teh action of an affine transformation are considered, and an investigation of the interplay between the different classes is initiated. Connections are established that relate representations of *-algebras, geometry of algebraic surfaces, dynamics of affine transformations, graphs and algebras coming from a quantization procedure of Poisson structures. In particular, algebras related to surgaced being inverse images of fourth order polynomials (in $\mathbb{R}^3$) are studied in detail, and a close link between representation theory and geometric properties is established for compact as well as non-compact surfaces.

• 142.
Riemannian curvature of the noncommutative 3-sphere2017Inngår i: Journal of Noncommutative Geometry, ISSN 1661-6952, E-ISSN 1661-6960, Vol. 11, nr 2, s. 507-536Artikkel i tidsskrift (Fagfellevurdert)

In order to investigate to what extent the calculus of classical (pseudo-) Riemannian manifolds can be extended to a noncommutative setting, we introduce pseudo-Riemannian calculi of modules over noncommutative algebras. In this framework, it is possible to prove an analogue of Levi-Civitas theorem, which states that there exists at most one torsion-free and metric connection for a given (metric) module, satisfying the requirements of a real metric calculus. Furthermore, the corresponding curvature operator has the same symmetry properties as the classical Riemannian curvature. As our main motivating example, we consider a pseudo-Riemannian calculus over the noncommutative 3-sphere and explicitly determine the torsion-free and metric connection, as well as the curvature operator together with its scalar curvature.

• 143.
Examples of infinity harmonic functions having singular lines2006Rapport (Annet vitenskapelig)
• 144.
Five Geometric Principles for Injection Molding2003Inngår i: International polymer processing, ISSN 0930-777X, E-ISSN 2195-8602, Vol. 18, nr 1, s. 91-94Artikkel i tidsskrift (Fagfellevurdert)

A condensed presentation of some results of a geometric character, concerning the injection molding of plastics, is given here. The author has derived these results from mathematical arguments and some simplifying assumptions, besides the usual Hele-Shaw flow conditions.

The presentation here is intended for readers with an interest in polymer processing, rather than mathematics, so that the mathematical derivations are omitted in some cases, and sketchy in other cases. Instead we try to explain the results using figures, intuitive arguments and a few inevitable formulas. Since the experimental verification of the results is still very incomplete, we prefer to present them as proposed principles. Comments and suggestions for improvement are very welcome.

• 145.
INTERPOLATION UNDER A GRADIENT BOUND2009Inngår i: JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, ISSN 1446-7887, Vol. 87, nr 1, s. 19-35Artikkel i tidsskrift (Fagfellevurdert)

This paper deals with the interpolation of given real boundary values into a bounded domain in Euclidean n-space, under a prescribed gradient bound. It is well known that there exist an upper solution (ail inf-convolution) and a lower solution (a sup-convolution) to this problem, provided that a certain compatibility condition is satisfied. If the upper and lower solutions coincide somewhere in the domain, then several interesting consequences follow. They are considered here. Basically, the upper and lower solutions must be regular wherever they coincide.

• 146.
Interpolation under a gradient bound and infimal convolutions2007Rapport (Annet vitenskapelig)
• 147.
On certain minimax problems and Pontryagin’s maximum principle2010Inngår i: Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, E-ISSN 1432-0835, Vol. 37, nr 1-2, s. 99-109Artikkel i tidsskrift (Fagfellevurdert)

This paper deals with minimax problems for nonlinear differential expressions involving a vector-valued function of a scalar variable under rather conventional structure conditions on the cost function. It is proved that an absolutely minimizing (i.e. globally and locally minimizing) function is continuously differentiable. A minimizing function is also continuously differentiable, provided a certain extra condition is satisfied. The variational method of V.G. Boltyanskii, developed within optimal control theory, is adapted and used in the proof. The case of higher order derivatives is also considered.

• 148.
On certain minimax problems and the Pontryagin maximum principle2008Rapport (Annet vitenskapelig)

• 149.
On Production Planning and Activity Periods2015Rapport (Annet vitenskapelig)

Consider a company which produces and sells a certain product on a market with highly variable demand. Since the demand is very high during some periods, the company will produce and create a stock in advance before these periods. On the other hand it costs money to hold a big stock, so that some balance is needed for optimum. The demand is assumed to be known in advance with sufficient accuracy. We use a technique from optimal control theory for the analysis, which leads to so-called activity periods. During such a period the stock is positive and the production is maximal, provided that the problem starts with zero stock, which is the usual case. Over a period of one or more years, there will be a few activity periods. Outside these periods the stock is zero and the policy is to choose production = the smaller of [demand, maximal production]. The “intrinsic time length” is a central concept. It is simply the maximal time a unit of the product can be stored before selling without creating a loss.

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• 150.
Production planning, activity periods and passivity periods2015Rapport (Annet vitenskapelig)

Consider a company which produces and sells a certain product on a market with highly variable demand. Since the demand is very high during some periods, the company will produce and create a stock in advance before these periods. On the other hand it costs money to hold a big stock, so that some balance is needed for optimum. The demand is assumed to be known in advance with sufficient accuracy. We use a technique from optimal control theory for the analysis, which leads to so-called activity periods. During such a period the stock is positive and the production is maximal, provided that the problem starts with zero stock, which is the usual case. Over a period of one or more years, there will be a few activity periods. Outside these periods the stock is zero and the policy is to choose production = the smaller of [demand, maximal production]. The “intrinsic time length” is a central concept. It is simply the maximal time a unit of the product can be stored before selling without creating a loss.

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