| 1. |
- Sorooshian, Shahryar, 1980, et al.
(author)
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Expedited analytical hierarchical process for multicriteria decision making
- 2022
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In: ICIC Express Letters. - 1881-803X. ; 16:2, s. 145-151
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Journal article (peer-reviewed)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. |
- Sorooshian, Shahryar, 1980, et al.
(author)
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Performance of the decision-making trial and evaluation laboratory
- 2023
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In: AIMS Mathematics. - : American Institute of Mathematical Sciences (AIMS). - 2473-6988. ; 8:3, s. 7490-7514
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Journal article (peer-reviewed)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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| 3. |
- Brubaker, Ben, et al.
(author)
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Colored vertex models and Iwahori Whittaker functions
- 2024
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In: Selecta Mathematica, New Series. - : Springer Nature. - 1420-9020 .- 1022-1824. ; 30:4
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Journal article (peer-reviewed)abstract
- We give a recursive method for computing all values of a basis of Whittaker functions for unramified principal series invariant under an Iwahori or parahoric subgroup of a split reductive group G over a nonarchimedean local field F. Structures in the proof have surprising analogies to features of certain solvable lattice models. In the case G=GLr we show that there exist solvable lattice models whose partition functions give precisely all of these values. Here ‘solvable’ means that the models have a family of Yang–Baxter equations which imply, among other things, that their partition functions satisfy the same recursions as those for Iwahori or parahoric Whittaker functions. The R-matrices for these Yang–Baxter equations come from a Drinfeld twist of the quantum group Uq(gl^(r|1)), which we then connect to the standard intertwining operators on the unramified principal series. We use our results to connect Iwahori and parahoric Whittaker functions to variations of Macdonald polynomials.
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| 4. |
- Berman, Robert, 1976
(author)
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On the strict convexity of the K-energy
- 2019
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In: Pure and Applied Mathematics Quarterly. - 1558-8599 .- 1558-8602. ; 15:4, s. 983-999
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Journal article (peer-reviewed)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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| 5. |
- Brandes, Julia, et al.
(author)
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On generating functions in additive number theory, II: lower-order terms and applications to PDEs
- 2021
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In: Mathematische Annalen. - : Springer Science and Business Media LLC. - 0025-5831 .- 1432-1807. ; 379, s. 347-76
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Journal article (peer-reviewed)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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| 6. |
- Ericsson, Niklas, 1968
(author)
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A Framework for Approximation of the Stokes Equations in an Axisymmetric Domain
- 2021
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In: Computational Methods in Applied Mathematics. - : Walter de Gruyter GmbH. - 1609-4840 .- 1609-9389. ; 21:4
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Journal article (peer-reviewed)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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| 7. |
- Gourevitch, D., et al.
(author)
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EULERIANITY OF FOURIER COEFFICIENTS OF AUTOMORPHIC FORMS
- 2021
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In: Representation Theory. - : American Mathematical Society (AMS). - 1088-4165. ; 25, s. 481-507
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Journal article (peer-reviewed)abstract
- We study the question of Eulerianity (factorizability) for Fourier coefficients of automorphic forms, and we prove a general transfer theorem that allows one to deduce the Eulerianity of certain coefficients from that of another coefficient. We also establish a `hidden' invariance property of Fourier coefficients. We apply these results to minimal and next-to-minimal automorphic representations, and deduce Eulerianity for a large class of Fourier and Fourier-Jacobi coefficients. In particular, we prove Eulerianity for parabolic Fourier coefficients with characters of maximal rank for a class of Eisenstein series in minimal and next-to-minimal representations of groups of ADE-type that are of interest in string theory.
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| 8. |
- Kim, Inkang, et al.
(author)
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Toledo invariant of lattices in SU(2,1) via symmetric square
- 2020
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In: Journal of Mathematical Physics. - : AIP Publishing. - 1089-7658 .- 0022-2488. ; 61:11
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Journal article (peer-reviewed)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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| 9. |
- Wang, Siyang, et al.
(author)
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CONVERGENCE OF FINITE DIFFERENCE METHODS FOR THE WAVE EQUATION IN TWO SPACE DIMENSIONS
- 2018
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In: Mathematics of Computation. - : American Mathematical Society (AMS). - 0025-5718 .- 1088-6842. ; 87:314, s. 2737-2763
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Journal article (peer-reviewed)abstract
- When using a finite difference method to solve an initial-boundary-value problem, the truncation error is often of lower order at a few grid points near boundaries than in the interior. Normal mode analysis is a powerful tool to analyze the effect of the large truncation error near boundaries on the overall convergence rate, and has been used in many research works for different equations. However, existing work only concerns problems in one space dimension. In this paper, we extend the analysis to problems in two space dimensions. The two dimensional analysis is based on a diagonalization procedure that decomposes a two dimensional problem to many one dimensional problems of the same type. We present a general framework of analyzing convergence for such one dimensional problems, and explain how to obtain the result for the corresponding two dimensional problem. In particular, we consider two kinds of truncation errors in two space dimensions: the truncation error along an entire boundary, and the truncation error localized at a few grid points close to a corner of the computational domain. The accuracy analysis is in a general framework, here applied to the second order wave equation. Numerical experiments corroborate our accuracy analysis.
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| 10. |
- Zhao, D., et al.
(author)
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Low Phase-Rank Approximation
- 2022
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In: Linear Algebra and Its Applications. - : Elsevier BV. - 0024-3795. ; 639, s. 177-204
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Journal article (peer-reviewed)abstract
- In this paper, we propose and solve low phase-rank approximation problems, which serve as a counterpart to the well-known low-rank approximation problem and the Schmidt-Mirsky theorem. It is well known that a nonzero complex number can be specified by its gain and phase, and while it is generally accepted that the gains of a matrix may be defined by its singular values, there is no widely accepted definition for its phases. In this work, we consider sectorial matrices, whose numerical ranges do not contain the origin, and adopt the canonical angles of such matrices as their phases. Similarly to the rank of a matrix being defined as the number of its nonzero singular values, we define the phase-rank of a sectorial matrix as the number of its nonzero phases. While a low-rank approximation problem is associated with the matrix arithmetic mean, it turns out that a natural parallel for the low phase-rank approximation problem is to use the matrix geometric mean to measure the approximation error. Importantly, we derive a majorization inequality between the phases of the geometric mean and the arithmetic mean of the phases, similarly to the Ky-Fan inequality for eigenvalues of Hermitian matrices. A characterization of the solutions to the proposed problem, with the same flavor as the Schmidt-Mirsky theorem, is then obtained in the case where both the objective matrix and the approximant are restricted to be positive-imaginary. In addition, we provide an alternative formulation of the low phase-rank approximation problem using geodesic distances between sectorial matrices. The two formulations give rise to the exact same set of solutions when the involved matrices are additionally assumed to be unitary. © 2022 Elsevier Inc.
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