| 1. |
- Strömberg, Ann-Brith, 1961, et al.
(författare)
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Mixed-Integer Linear Optimization: Primal–Dual Relations and Dual Subgradient and Cutting-Plane Methods
- 2020
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Ingår i: Numerical Nonsmooth Optimization: State of the Art Algorithms. - Cham : Springer International Publishing. ; , s. 499-547, s. 499-547
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- This chapter presents several solution methodologies for mixed-integer linear optimization, stated as mixed-binary optimization problems, by means of Lagrangian duals, subgradient optimization, cutting-planes, and recovery of primal solutions. It covers Lagrangian duality theory for mixed-binary linear optimization, a problem framework for which ultimate success—in most cases—is hard to accomplish, since strong duality cannot be inferred. First, a simple conditional subgradient optimization method for solving the dual problem is presented. Then, we show how ergodic sequences of Lagrangian subproblem solutions can be computed and used to recover mixed-binary primal solutions. We establish that the ergodic sequences accumulate at solutions to a convexified version of the original mixed-binary optimization problem. We also present a cutting-plane approach to the Lagrangian dual, which amounts to solving the convexified problem by Dantzig–Wolfe decomposition, as well as a two-phase method that benefits from the advantages of both subgradient optimization and Dantzig–Wolfe decomposition. Finally, we describe how the Lagrangian dual approach can be used to find near optimal solutions to mixed-binary optimization problems by utilizing the ergodic sequences in a Lagrangian heuristic, to construct a core problem, as well as to guide the branching in a branch-and-bound method. The chapter is concluded with a section comprising notes, references, historical downturns, and reading tips.
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| 2. |
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| 3. |
- Silvestrov, Sergei
(författare)
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Interpolation of Normed Abelian Groups and Non-Commutative Integration
- 2012
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Ingår i: Analysis for Science, Engineering and Beyond. - Berlin : Springer Berlin/Heidelberg. - 9783642202353 ; , s. 325-341
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Bokkapitel (refereegranskat)abstract
- This is a concise review concerned first of all with the two pioneering far reaching and in many ways yet to be fully explored important papers by Gunnar Sparr and Jaak Peetre on interpolation of normed abelian groups and on non-commutative integration. These papers introduced a general framework unifying many previously known interpolation results and methods in the ways applicable for non-commutative integration and non-commutative extensions of the function spaces, the directions of importance for example in non-commutative geometry and applications in quantum physics. Whence some notions and methods from these papers have been applied in various contexts, many other methods and ideas are yet to be discovered and developed further. In addition to the concise review of these important works by Jaak Peetre and Gunnar Sparr, a brief review is presented also of some related works on non-commutative spaces and non-commutative integration in the contexts of the theory of operator algebras and non-commutative geometry
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| 4. |
- Dupuch, Marie, et al.
(författare)
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Comparison of Clustering Approaches through Their Application to Pharmacovigilance Terms
- 2013
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Ingår i: Artificial Intelligence in Medicine. Lecture Notes in Computer Science, vol. 7885. - Berlin Heidelberg : Springer. - 9783642383250 - 9783642383267 ; , s. 58-67
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Bokkapitel (refereegranskat)abstract
- In different applications (i.e., information retrieval, filteringor analysis), it is useful to detect similar terms and to provide the possibilityto use them jointly. Clustering of terms is one of the methods whichcan be exploited for this. In our study, we propose to test three methodsdedicated to the clustering of terms (hierarchical ascendant classification,Radius and maximum), to combine them with the semantic distance algorithmsand to compare them through the results they provide whenapplied to terms from the pharmacovigilance area. The comparison indicatesthat the non disjoint clustering (Radius and maximum) outperformthe disjoint clusters by 10 to up to 20 points in all the experiments.
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| 5. |
- Friberg, Jöran, 1934, et al.
(författare)
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More Mathematical Cuneiform Texts of Group 6 from Late Old Babylonian Sippar
- 2016
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Ingår i: Sources and Studies in the History of Mathematics and Physical Sciences. - Cham : Springer International Publishing. ; , s. 371-389
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- In Ch. IV of Neugebauer and Sachs, MCT (1945), A. Goetze divided published Old Babylonian mathematical texts without known provenance into 6 different groups with respect to their Akkadian orthography. Goetze’s classification was later refined and extended by J. Høyrup in LWS (2002), Ch. IX. Groups 5 and 6 were classified by Goetze as “northern”.
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| 6. |
- Pejlare, Johanna, 1976, et al.
(författare)
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Writing the History of Mathematics: Interpretations of the Mathematics of the Past and Its Relation to theMathematics of Today
- 2021
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Ingår i: Handbook of the Mathematics of the Arts and Sciences. - Cham : Springer International Publishing. - 9783319706580 ; , s. 2395-2420
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- In the present chapter, interpretations of the mathematics of the past are problematized, based on examples such as archeological artifacts, as well as written sources from the ancient Egyptian, Babylonian, and Greek civilizations. The distinction between history and heritage is considered in relation to Euler’s function concept, Cauchy’s sum theorem, and the Unguru debate. Also, the distinction between the historical past and the practical past, as well as the distinction between the historical and the nonhistorical relations to the past, are made concrete based on Torricelli’s result on an infinitely long solid from the seventeenth century. Two complementary but different ways of analyzing the mathematics of the past are the synchronic and diachronic perspectives, which may be useful, for instance, regarding the history of school mathematics. Furthermore, recapitulation, or the belief that students’ conceptual development in mathematics is paralleled to the historical epistemology of mathematics, is problematized emphasizing the important role of culture.
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| 7. |
- Friberg, Jöran, 1934, et al.
(författare)
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Three Old Babylonian Recombination Texts of Mathematical Problems without Solution Procedures, Making up Group 2b
- 2016
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Ingår i: Sources and Studies in the History of Mathematics and Physical Sciences. - Cham : Springer International Publishing. ; , s. 421-480
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- YBC 4698 is a mathematical recombination text, a mixed bag of loosely related exercises, all concerned with commercial problems. See the hand copy and conform transliteration in Fig. 11.1.1 below. Since exercises belonging more closely together are sometimes separated from each other in this text, the exercises are numbered in two different ways in the conform transliteration, both in the order they are inscribed on the tablet (## 1-17) and according to their problem types (§§ 1-5).
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| 8. |
- Ostoja-Starzewski, Martin, et al.
(författare)
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Scaling to RVE in Random Media
- 2016
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Ingår i: Advances in Applied Mechanics. - : Academic Press. - 9780128047798 ; , s. 111-211
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Bokkapitel (refereegranskat)abstract
- The problem of effective properties of material microstructures has received considerableattention over the past half a century. By effective (or overall, macroscopic, global) ismeant the response assuming the existence of a representative volume element (RVE)on which a homogeneous continuum is being set up. Since the efforts over the pastquarter century have been shifting to the problem of the size of RVE, this chapterreviews the results and challenges in this broad field for a wide range of materials.For the most part, the approach employed to assess the scaling to the RVE is basedon the Hill–Mandel macrohomogeneity condition. This leads to bounds that explicitlyinvolve the size of a mesoscale domain—this domain also being called a statisticalvolume element (SVE)—relative to the microscale and the type of boundary conditionsapplied to this domain. In general, the trend to pass from the SVE to RVE depends onrandom geometry and mechanical properties of the microstructure, and displayscertain, possibly universal tendencies. This chapter discusses that issue first for linearelastic materials, where a scaling function plays a key role to concisely grasp theSVE-to-RVE scaling. This sets the stage for treatment of nonlinear and or/inelastic randommaterials, including elasto-plastic, viscoelastic, permeable, and thermoelasticclasses. This methodology can be extended to homogenization of random media bymicropolar (Cosserat) rather than by classical (Cauchy) continua as well as to homogenizationunder stationary (standing wave) or transient (wavefront) loading conditions.The final topic treated in this chapter is the formulation of continuum mechanicsaccounting for the violations of second law of thermodynamics, which have been studied on a molecular level in statistical physics over the past two decades. We end with anoverview of open directions and challenges of this research field.
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| 9. |
- Nedic, Mitja, et al.
(författare)
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Herglotz functions and applications in electromagnetics
- 2020
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Ingår i: Advances in Mathematical Methods for Electromagnetics. - : Institution of Engineering and Technology. - 9781785613845 - 9781785613852 ; , s. 491-514
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- Herglotz functions inevitably appear in pure mathematics, mathematical physics, and engineering with a wide range of applications. In particular, they are the pertinent functions to model passive systems, and thus appear in modeling of electromagnetic phenomena in circuits, antennas, materials, and scattering. In this chapter, we review the basic theory of Herglotz functions and its applications to determine sum rules and physical bounds for passive systems.
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| 10. |
- Romano, Luigi, 1994
(författare)
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Steady-State Brush Theory
- 2022
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Ingår i: SpringerBriefs in Applied Sciences and Technology. - Cham : Springer International Publishing. - 2191-530X .- 2191-5318. ; , s. 35-55
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- In steady-state conditions, explicit expressions for tyre characteristics may be derived using the theoretical framework provided by the brush theory. This chapter is, thus, dedicated to addressing the stationary problem from both the local and global perspectives. The fundamental concepts of critical slip and spin are introduced with respect to an isotropic tyre, and the deformation of the bristles inside the contact patch is investigated for different operating conditions of the tyre. Analytical functions describing the tyre forces and moment acting inside the contact patch are obtained for the particular case of a rectangular contact patch. The analysis is qualitative in nature.
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