| 41. |
- Laksman, Efraim, 1983, et al.
(författare)
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The stochastic opportunistic replacement problem, part III: improved bounding procedures
- 2020
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Ingår i: Annals of Operations Research. - : Springer Science and Business Media LLC. - 1572-9338 .- 0254-5330. ; 292:2, s. 711-733
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Tidskriftsartikel (refereegranskat)abstract
- We consider the problem to find a schedule for component replacement in a multi-component system, whose components possess stochastic lives and economic dependencies, such that the expected costs for maintenance during a pre-defined time period are minimized. The problem was considered in Patriksson et al. (Ann Oper Res 224:51–75, 2015), in which a two-stage approximation of the problem was optimized through decomposition (denoted the optimization policy). The current paper improves the effectiveness of the decomposition approach by establishing a tighter bound on the value of the recourse function (i.e., the second stage in the approximation). A general lower bound on the expected maintenance cost is also established. Numerical experiments with 100 simulation scenarios for each of four test instances show that the tighter bound yields a decomposition generating fewer optimality cuts. They also illustrate the quality of the lower bound. Contrary to results presented earlier, an age-based policy performs on par with the optimization policy, although most simple policies perform worse than the optimization policy.
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| 42. |
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| 43. |
- Zhang, Ye, 1984-, et al.
(författare)
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Reconstructing gas distribution maps via an adaptive sparse regularization algorithm
- 2016
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Ingår i: Inverse Problems in Science and Engineering. - : Taylor & Francis. - 1741-5977 .- 1741-5985. ; 24:7, s. 1186-1204
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we present an algorithm to be used by an inspectionrobot to produce a gas distribution map and localize gas sources ina large complex environment. The robot, equipped with a remotegas sensor, measures the total absorption of a tuned laser beam andreturns integral gas concentrations. A mathematical formulation ofsuch measurement facility is a sequence of Radon transforms,which isa typical ill-posed problem. To tackle the ill-posedness, we developa new regularization method based on the sparse representationproperty of gas sources and the adaptive finite-element method. Inpractice, only a discrete model can be applied, and the quality ofthe gas distributionmap depends on a detailed 3-D world model thatallows us to accurately localize the robot and estimate the paths of thelaser beam. In this work, using the positivity ofmeasurements and theprocess of concentration, we estimate the lower and upper boundsof measurements and the exact continuous model (mapping fromgas distribution to measurements), and then create a more accuratediscrete model of the continuous tomography problem. Based onadaptive sparse regularization, we introduce a new algorithm thatgives us not only a solution map but also a mesh map. The solutionmap more accurately locates gas sources, and the mesh map providesthe real gas distribution map. Moreover, the error estimation of theproposed model is discussed. Numerical tests for both the syntheticproblem and practical problem are given to show the efficiency andfeasibility of the proposed algorithm.
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| 44. |
- Bernhoff, Niclas, 1971-
(författare)
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Discrete Velocity Models for Polyatomic Molecules Without Nonphysical Collision Invariants
- 2018
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Ingår i: Journal of statistical physics. - New York : Springer. - 0022-4715 .- 1572-9613. ; 172:3, s. 742-761
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Tidskriftsartikel (refereegranskat)abstract
- An important aspect of constructing discrete velocity models (DVMs) for the Boltzmann equation is to obtain the right number of collision invariants. Unlike for the Boltzmann equation, for DVMs there can appear extra collision invariants, so called spurious collision invariants, in plus to the physical ones. A DVM with only physical collision invariants, and hence, without spurious ones, is called normal. The construction of such normal DVMs has been studied a lot in the literature for single species, but also for binary mixtures and recently extensively for multicomponent mixtures. In this paper, we address ways of constructing normal DVMs for polyatomic molecules (here represented by that each molecule has an internal energy, to account for non-translational energies, which can change during collisions), under the assumption that the set of allowed internal energies are finite. We present general algorithms for constructing such models, but we also give concrete examples of such constructions. This approach can also be combined with similar constructions of multicomponent mixtures to obtain multicomponent mixtures with polyatomic molecules, which is also briefly outlined. Then also, chemical reactions can be added.
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| 45. |
- Casarino, V., et al.
(författare)
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On the variation operator for the Ornstein-Uhlenbeck semigroup in dimension one
- 2023
-
Ingår i: Annali Di Matematica Pura Ed Applicata. - 0373-3114 .- 1618-1891.
-
Tidskriftsartikel (refereegranskat)abstract
- Consider the variation seminorm of the Ornstein-Uhlenbeck semigroup Ht in dimension one, taken with respect to t. We show that this seminorm defines an operator of weak type (1, 1) for the relevant Gaussian measure. The analogous Lp estimates for 1 < p < 8 were already known.
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| 46. |
-
Engineering Mathematics II : Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization
- 2016
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Samlingsverk (redaktörskap) (refereegranskat)abstract
- This book highlights the latest advances in engineering mathematics with a main focus on the mathematical models, structures, concepts, problems and computational methods and algorithms most relevant for applications in modern technologies and engineering. It addresses mathematical methods of algebra, applied matrix analysis, operator analysis, probability theory and stochastic processes, geometry and computational methods in network analysis, data classification, ranking and optimisation.The individual chapters cover both theory and applications, and include a wealth of figures, schemes, algorithms, tables and results of data analysis and simulation. Presenting new methods and results, reviews of cutting-edge research, and open problems for future research, they equip readers to develop new mathematical methods and concepts of their own, and to further compare and analyse the methods and results discussed.The book consists of contributed chapters covering research developed as a result of a focused international seminar series on mathematics and applied mathematics and a series of three focused international research workshops on engineering mathematics organised by the Research Environment in Mathematics and Applied Mathematics at Mälardalen University from autumn 2014 to autumn 2015: the International Workshop on Engineering Mathematics for Electromagnetics and Health Technology; the International Workshop on Engineering Mathematics, Algebra, Analysis and Electromagnetics; and the 1st Swedish-Estonian International Workshop on Engineering Mathematics, Algebra, Analysis and Applications.It serves as a source of inspiration for a broad spectrum of researchers and research students in applied mathematics, as well as in the areas of applications of mathematics considered in the book.
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| 47. |
- Guckenheimer, John, et al.
(författare)
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Rigorous enclosures of a slow manifold
- 2012
-
Ingår i: SIAM Journal on Applied Dynamical Systems. - : Society for Industrial & Applied Mathematics (SIAM). - 1536-0040. ; 11:3, s. 831-863
-
Tidskriftsartikel (refereegranskat)abstract
- Slow-fast dynamical systems have two time scales and an explicit parameter representing the ratio of these time scales. Locally invariant slow manifolds along which motion occurs on the slow time scale are a prominent feature of slow-fast systems. This paper introduces a rigorous numerical method to compute enclosures of the slow manifold of a slow-fast system with one fast and two slow variables. A triangulated first order approximation to the two dimensional invariant manifold is computed “algebraically.” Two translations of the computed manifold in the fast direction that are transverse to the vector field are computed as the boundaries of an initial enclosure. The enclosures are refined to bring them closer to each other by moving vertices of the enclosure boundaries one at a time. As an application we use the method to prove the existence of tangencies of invariant manifolds in the problem of singular Hopf bifurcation and to give bounds on the location of one such tangency.
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| 48. |
- Jorgensen, Palle, et al.
(författare)
-
Operator algebras and representation theory : frames, wavelets and fractals
- 2011
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Ingår i: Oberwolfach Reports. - 1660-8933 .- 1660-8941. ; 8:1, s. 901-978
-
Tidskriftsartikel (refereegranskat)abstract
- Operator Algebras and Representation Theory: Frames, Wavelets and Fractals Organized by: Palle E.T. Jorgensen (1), Gitta Kutyniok (2), Gestur Olafsson (3) and Sergei Silvestrov (4) (1) Department of Mathematics, University of Iowa, IA 52242-1466, IOWA CITY, UNITED STATES(2) Fachbereich Mathematik / Informatik, Universität Osnabrück, Albrechtstr. 28a, 49069, OSNABRÜCK, GERMANY(3) Department of Mathematics, Louisiana State University, LA 70803-4918, BATON ROUGE, UNITED STATES(4) Centre for Mathematical Sciences, Lund University, P.O. Box 118, 22100, LUND, SWEDEN The central focus of the workshop was Kadison-Singer conjecture and its connection to operator algebras, harmonic analysis, representation theory and the theory of fractals. The program was intrinsically interdisciplinary and represented areas with much recent progress. The workshop includes talks on operator theory, wavelets, shearlets, frames, fractals, representations theory and compressed sensing.
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| 49. |
- Kavallaris, Nikos I., et al.
(författare)
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On the impact of noise on quenching for a nonlocal diffusion model driven by a mixture of Brownian and fractional Brownian motions
- 2024
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Ingår i: Discrete and Continuous Dynamical Systems. Series S. - : American Institute of Mathematical Sciences. - 1937-1632 .- 1937-1179. ; 17:3, s. 1222-1268
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper, we study a stochastic parabolic problem involving anonlocal diffusion operator associated with nonlocal Robin-type boundary conditions. The stochastic dynamics under consideration is driven by a mixtureof a classical Brownian and a fractional Brownian motion with Hurst indexH ∈ (1/2, 1). We first establish local in time existence results and then exploreconditions under which the resulting SPDE exhibits finite-time quenching. Using results on the probability distribution of perpetual integral functionals ofBrownian motion as well as tail estimates for the fractional Brownian motionwe provide analytic estimates for certain quantities of interest, such as upperbounds for quenching times and the corresponding quenching probabilities.The existence of global in time solutions is also investigated and as a consequence a lower estimate of the quenching time is also derived. Our analyticalresults demonstrate the non-trivial impact of the noise on the dynamics ofthe system. The analytic results are complemented with a detailed numericalstudy of the model under Dirichlet boundary conditions. A possible application concerning MEMS technology is considered and the implications of theresults in this context are commented upon.
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| 50. |
- Manzetti, Sergio
(författare)
-
Derivation and Numerical analysis of an Attenuation Operator for non-relativistic waves
- 2018
-
Ingår i: Scientific Reports. - New York : Springer Science and Business Media LLC. - 2045-2322. ; 8
-
Tidskriftsartikel (refereegranskat)abstract
- Quantum mechanical models for particles are strictly dependent on the Schrödinger equation, where the solutions and the Hermitian polynomials form a mathematical foundation to derive expectation values for observables. As for all quantum systems, the solutions are derived in discrete energy levels, and yield probability density, the kinetic energy and average momentum. In this study however, an attenuation Hamiltonian is derived by the algebraic relation of the momentum and position operators, and the derived equation, where the attenuation of kinetic energy is the eigenvalue, is studied numerically. The numerical solutions suggest that the change in kinetic energy from one transition to the next proceed in an undular fashion, and not in a definite manner. This suggests that any sub-atomic particle which experiences a transition from one level to the next, does so by both gaining and losing energy in an undular manner before reaching an equilibrium with a new and stabilized kinetic energy. The results show also that the phase of the change in kinetic energy between transitions differs between high and low momenta and that higher levels of momentum attenuate more smoothly than transitions between lower energy levels. The investigated attenuation operator may be important for future pinning and quasipinning approaches and play a role in future quantum information processing. Future research is required on the spectrum of the operator and on its potential analytical solutions.
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