| 1. |
- Sorooshian, Shahryar, 1980, et al.
(författare)
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Expedited analytical hierarchical process for multicriteria decision making
- 2022
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Ingår i: ICIC Express Letters. - 1881-803X. ; 16:2
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Tidskriftsartikel (refereegranskat)abstract
- In this study, a procedure to overcome analytical hierarchical process (AHP) limitations was developed and tested, and a tool created via pairwise comparison chart and weighted sum method hybridization was introduced. In addition, a multicriteria decision-making software was selected to validate the constructed hybrid decision-making tool. The software was formulated based on an established decision-making technique. Data for the comparison analysis were obtained from an ongoing research, and output from the comparison analysis provided evidence for the accuracy of the constructed tool. The proposed hybridized method aligned with AHP reasoning but demonstrated a faster process; hence, it was called ‘expedited AHP’.
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| 2. |
- Berndtsson, Bo, 1950
(författare)
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Probability measures associated to geodesics in the space of kähler metrics
- 2018
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Ingår i: Springer Proceedings in Mathematics and Statistics. - Cham : Springer International Publishing. - 2194-1017 .- 2194-1009. ; 269, s. 395-419
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Konferensbidrag (refereegranskat)abstract
- We associate certain probability measures on R to geodesics in the space HL of positively curved metrics on a line bundle L, and to geodesics in the finite dimensional symmetric space of hermitian norms on H0(X, kL). We prove that the measures associated to the finite dimensional spaces converge weakly to the measures related to geodesics in HL as k goes to infinity. The convergence of second order moments implies a recent result of Chen and Sun on geodesic distances in the respective spaces, while the convergence of first order moments gives convergence of Donaldson’s Z-functional to the Aubin–Yau energy. We also include a result on approximation of infinite dimensional geodesics by Bergman kernels which generalizes work of Phong and Sturm.
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| 3. |
- Xia, Jiacheng, 1991
(författare)
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Vector-valued Eisenstein series of congruence types and their products
- 2019
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Historically, Kohnen and Zagier connected modular forms with period polynomials, and as a consequence of this association concluded that the products of at most two Eisenstein series span all spaces of classical modular forms of level 1. Later Borisov and Gunnells among other authors extended the result to higher levels. We consider this problem for vector-valued modular forms, establish the framework of congruence types and obtain the structure of the space of vector-valued Eisenstein series using tools from representation theory. Based on this development and historic results, we show that the space of vector-valued modular forms of certain weights and any congruence type can be spanned by the invariant vectors of that type tensor at most two Eisenstein series.
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| 4. |
- Sorooshian, Shahryar, 1980, et al.
(författare)
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Performance of the decision-making trial and evaluation laboratory
- 2023
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Ingår i: AIMS Mathematics. - : American Institute of Mathematical Sciences (AIMS). - 2473-6988. ; 8:3, s. 7490-7514
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Tidskriftsartikel (refereegranskat)abstract
- Multiple attribute decision-making (MADM) techniques constitute a practical approach for solving complex problems involving multiple and often conflicting criteria. Decision-making trial and evaluation laboratory (DEMATEL) is a popular MADM technique with both admirers and critics. This study presents a comprehensive review of DEMATEL through bibliometric analysis using the Scopus database. This article examined 3,521 papers published in journals, conferences or books between 1981 and 2023. We examined a few parameters for commenting on the performance of the technique. Among them are research outputs, the network of DEMATEL users, implementation subject areas, research zones, financing opportunities and publication hosts and their impact trends. We conclude from the findings of this study that the DEMATEL is capable of dealing with modern problem-solving in future environments. Although the growth of new MADMs is obvious, based on the gathered data, we forecast that more than 776 documents will be published in 2025 using DEMATEL for problem-solving. This expanding tendency will continue in the future. As distinct MADMs have diverse constraints, foundations, computing complexity and standpoints, which result in different performances, outmoded low-performance MADM techniques must be reported by researchers to continue this paper’s objective to minimize ambiguity among decision-makers and practitioners. To facilitate such a comparison in the future, a quantitative performance coefficient was also developed here.
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| 5. |
- 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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| 6. |
- Kurujyibwami, Celestin
(författare)
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Admissible transformations and the group classification of Schrödinger equations
- 2017
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- We study admissible transformations and solve group classification problems for various classes of linear and nonlinear Schrödinger equations with an arbitrary number n of space variables.The aim of the thesis is twofold. The first is the construction of the new theory of uniform seminormalized classes of differential equations and its application to solving group classification problems for these classes. Point transformations connecting two equations (source and target) from the class under study may have special properties of semi-normalization. This makes the group classification of that class using the algebraic method more involved. To extend this method we introduce the new notion of uniformly semi-normalized classes. Various types of uniform semi-normalization are studied: with respect to the corresponding equivalence group, with respect to a proper subgroup of the equivalence group as well as the corresponding types of weak uniform semi-normalization. An important kind of uniform semi-normalization is given by classes of homogeneous linear differential equations, which we call uniform semi-normalization with respect to linear superposition of solutions.The class of linear Schrödinger equations with complex potentials is of this type and its group classification can be effectively carried out within the framework of the uniform semi-normalization. Computing the equivalence groupoid and the equivalence group of this class, we show that it is uniformly seminormalized with respect to linear superposition of solutions. This allow us to apply the version of the algebraic method for uniformly semi-normalized classes and to reduce the group classification of this class to the classification of appropriate subalgebras of its equivalence algebra. To single out the classification cases, integers that are invariant under equivalence transformations are introduced. The complete group classification of linear Schrödinger equations is carried out for the cases n = 1 and n = 2.The second aim is to study group classification problem for classes of generalized nonlinear Schrödinger equations which are not uniformly semi-normalized. We find their equivalence groupoids and their equivalence groups and then conclude whether these classes are normalized or not. The most appealing classes are the class of nonlinear Schrödinger equations with potentials and modular nonlinearities and the class of generalized Schrödinger equations with complex-valued and, in general, coefficients of Laplacian term. Both these classes are not normalized. The first is partitioned into an infinite number of disjoint normalized subclasses of three kinds: logarithmic nonlinearity, power nonlinearity and general modular nonlinearity. The properties of the Lie invariance algebras of equations from each subclass are studied for arbitrary space dimension n, and the complete group classification is carried out for each subclass in dimension (1+2). The second class is successively reduced into subclasses until we reach the subclass of (1+1)-dimensional linear Schrödinger equations with variable mass, which also turns out to be non-normalized. We prove that this class is mapped by a family of point transformations to the class of (1+1)-dimensional linear Schrödinger equations with unique constant mass.
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| 7. |
- Berman, Robert, 1976
(författare)
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On the strict convexity of the K-energy
- 2019
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Ingår i: Pure and Applied Mathematics Quarterly. - 1558-8599 .- 1558-8602. ; 15:4, s. 983-999
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Tidskriftsartikel (refereegranskat)abstract
- Let (X, L) be a polarized projective complex manifold. We show, by a simple toric one-dimensional example, that Mabuchi's K-energy functional on the geodesically complete space of bounded positive (1, 1)-forms in c(1)(L), endowed with the Mabuchi-Donaldson-Semmes metric, is not strictly convex modulo automorphisms. However, under some further assumptions the strict convexity in question does hold in the toric case. This leads to a uniqueness result saying that a finite energy minimizer of the K-energy (which exists on any toric polarized manifold (X, L) which is uniformly K-stable) is uniquely determined modulo automorphisms under the assumption that there exists some minimizer with strictly positive curvature current.
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| 8. |
- Brandes, Julia, et al.
(författare)
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On generating functions in additive number theory, II: lower-order terms and applications to PDEs
- 2021
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Ingår i: Mathematische Annalen. - : Springer Science and Business Media LLC. - 0025-5831 .- 1432-1807. ; 379, s. 347-76
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Tidskriftsartikel (refereegranskat)abstract
- We obtain asymptotics for sums of the form Sigma(p)(n=1) e(alpha(k) n(k) + alpha(1)n), involving lower order main terms. As an application, we show that for almost all alpha(2) is an element of [0, 1) one has sup(alpha 1 is an element of[0,1)) | Sigma(1 <= n <= P) e(alpha(1)(n(3) + n) + alpha(2)n(3))| << P3/4+epsilon, and that in a suitable sense this is best possible. This allows us to improve bounds for the fractal dimension of solutions to the Schrodinger and Airy equations.
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| 9. |
- Ericsson, Niklas, 1968
(författare)
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A Framework for Approximation of the Stokes Equations in an Axisymmetric Domain
- 2021
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Ingår i: Computational Methods in Applied Mathematics. - : Walter de Gruyter GmbH. - 1609-4840 .- 1609-9389. ; 21:4
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Tidskriftsartikel (refereegranskat)abstract
- We develop a framework for solving the stationary, incompressible Stokes equations in an axisymmetric domain. By means of Fourier expansion with respect to the angular variable, the three-dimensional Stokes problem is reduced to an equivalent, countable family of decoupled two-dimensional problems. By using decomposition of three-dimensional Sobolev norms, we derive natural variational spaces for the two-dimensional problems, and show that the variational formulations are well-posed. We analyze the error due to Fourier truncation and conclude that, for data that are sufficiently regular, it suffices to solve a small number of two-dimensional problems. © 2021 Ericsson, published by De Gruyter 2021.
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| 10. |
- Kim, Inkang, et al.
(författare)
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Toledo invariant of lattices in SU(2,1) via symmetric square
- 2020
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Ingår i: Journal of Mathematical Physics. - : AIP Publishing. - 1089-7658 .- 0022-2488. ; 61:11
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we address the issue of the quaternionic Toledo invariant to study the character variety of two-dimensional complex hyperbolic uniform lattices into SU(n, 2), n ≥ 4. We construct four distinct representations to prove that the character variety contains at least seven distinct components. We also show the existence of holomorphic horizontal lift to various period domains of SU(n, 2).
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