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- 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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- Johnson, Tomas, 1979-, et al.
(författare)
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On a computer-aided approach to the computation of Abelian integrals
- 2011
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Ingår i: BIT Numerical Mathematics. - : Springer Science and Business Media LLC. - 0006-3835 .- 1572-9125. ; 51:3, s. 653-667
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Tidskriftsartikel (refereegranskat)abstract
- An accurate method to compute enclosures of Abelian integrals is developed. This allows for an accurate description of the phase portraits of planar polynomial systems that are perturbations of Hamiltonian systems. As an example, it is applied to the study of bifurcations of limit cycles arising from a cubic perturbation of an elliptic Hamiltonian of degree four.
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- Manzetti, Sergio
(författare)
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Derivation and Numerical analysis of an Attenuation Operator for non-relativistic waves
- 2018
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Ingår i: Scientific Reports. - New York : Springer Science and Business Media LLC. - 2045-2322. ; 8
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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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- Wang, Siyang, et al.
(författare)
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CONVERGENCE OF FINITE DIFFERENCE METHODS FOR THE WAVE EQUATION IN TWO SPACE DIMENSIONS
- 2018
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Ingår i: Mathematics of Computation. - : American Mathematical Society (AMS). - 0025-5718 .- 1088-6842. ; 87:314, s. 2737-2763
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Tidskriftsartikel (refereegranskat)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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- Asadzadeh, Mohammad, 1952, et al.
(författare)
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ON HP-STREAMLINE DIFFUSION AND NITSCHE SCHEMES FOR THE RELATIVISTIC VLASOV-MAXWELL SYSTEM
- 2019
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Ingår i: Kinetic and Related Models. - : American Institute of Mathematical Sciences (AIMS). - 1937-5093 .- 1937-5077. ; 12:1, s. 105-131
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Tidskriftsartikel (refereegranskat)abstract
- We study stability and convergence of hp-streamline diffusion (SD) finite element, and Nitsche's schemes for the three dimensional, relativistic (3 spatial dimension and 3 velocities), time dependent Vlasov-Maxwell system and Maxwell's equations, respectively. For the hp scheme for the Vlasov-Maxwell system, assuming that the exact solution is in the Sobolev space HS+1(Omega), we derive global a priori error bound of order O(h/p)(s+1/2), where h(= max(K) h(K)) is the mesh parameter and p(= max(K) p(K)) is the spectral order. This estimate is based on the local version with h(K) = diam K being the diameter of the phase-space-time element K and pR-is the spectral order (the degree of approximating finite element polynomial) for K. As for the Nitsche's scheme, by a simple calculus of the field equations, first we convert the Maxwell's system to an elliptic type equation. Then, combining the Nitsche's method for the spatial discretization with a second order time scheme, we obtain optimal convergence of O(h(2) +k(2)), where h is the spatial mesh size and k is the time step. Here, as in the classical literature, the second order time scheme requires higher order regularity assumptions. Numerical justification of the results, in lower dimensions, is presented and is also the subject of a forthcoming computational work [22].
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- Helenius, Ola, 1970, et al.
(författare)
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Measuring temperature within the didactic space of preschool
- 2016
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Ingår i: Nordisk matematikkdidaktikk, NOMAD. - : Nationellt centrum för matematikutbildning (NCM). - 1104-2176. ; 21:4, s. 155-176
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Tidskriftsartikel (refereegranskat)abstract
- The informal character of preschool mathematics, engaged in during children’s play, places complex requirements on preschool teachers. It also leads to challenges in developing appropriate analytical tools for researching teacher work. In this paper a framework, the ”didaktic space”, is described and used to analyse interactions between preschool teachers and children in relationship to mathematical learning situations. An interaction between a preschool teacher and a group of children about how to compare their temperatures is analysed, using this framework. The analysis focuses on how the teacher’s contributions as well as those of the children changed as the role of the mathematics changed. The paper discusses how the didaktic space offers a nuanced understanding of preschool mathematical situations, both to researchers and to teachers.
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| 9. |
- 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, s. 145-151
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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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| 10. |
- 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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