Random search algorithm for solving the nonlinear Fredholm integral equations of the second kind. [PDF]
PLoS ONE, 2014 In this paper, a randomized numerical approach is used to obtain approximate solutions for a class of nonlinear Fredholm integral equations of the second kind.
Zhimin Hong, Zaizai Yan, Jiao Yan
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Macroscopicity of quantum superpositions on a one-parameter unitary path in Hilbert space [PDF]
, 2014 We analyze quantum states formed as superpositions of an initial pure product state and its image under local unitary evolution, using two measurement-based measures of superposition size: one based on the optimal quantum binary distinguishability of the
Volkoff, T. J., Whaley, K. B.
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A Multilevel Heterogeneous ADMM Algorithm for Elliptic Optimal Control Problems with L1-Control Cost
Mathematics, 2023 In this paper, elliptic optimal control problems with L1-control cost and box constraints on the control are considered. To numerically solve the optimal control problems, we use the First optimize, then discretize approach.
Xiaotong Chen +3 more
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Discretizing Distributions with Exact Moments: Error Estimate and Convergence Analysis
, 2015 The maximum entropy principle is a powerful tool for solving underdetermined inverse problems. This paper considers the problem of discretizing a continuous distribution, which arises in various applied fields. We obtain the approximating distribution by
Tanaka, Ken'ichiro, Toda, Alexis Akira
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On an Optimal Quadrature Formula for Classes of Functions Given by Modulus of Continuity
Моделирование и анализ информационных систем, 2014 The problem of minimizing the error of a cubature formula on the classes of functions given by modulus of continuity for cubature formulas with fixed nodes on the boundary of gird rectangular localization domain of nodes is considered.
M. Sh. Shabozov
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Uniqueness of the Optimal Nodes of Quadrature Formulae [PDF]
Mathematics of Computation, 1981 We prove the uniqueness of the quadrature formula with minimal error in the space W ~ q r [ a , b ] , 1 > q > ∞ \tilde W_q^r[a,b],1 > q > \infty , of
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Elementary test for non-classicality based on measurements of position and momentum
, 2015 We generalise a non-classicality test described by Kot et al. [Phys. Rev. Lett. 108, 233601 (2010)], which can be used to rule out any classical description of a physical system.
Borregaard, Johannes +2 more
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Construction of Supplemental Functions for Direct Serendipity and Mixed Finite Elements on Polygons
Mathematics, 2023 New families of direct serendipity and direct mixed finite elements on general planar, strictly convex polygons were recently defined by the authors. The finite elements of index r are H1 and H(div) conforming, respectively, and approximate optimally to ...
Todd Arbogast, Chuning Wang
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Magnetic Resonance Guided Radiation Therapy (MRgRT) Prostate Motion and Margins. [PDF]
J Med Radiat SciThis study evaluated intra‐fractional prostate motion during MR‐guided radiotherapy to determine appropriate PTV margins for prostate cancer. Analysis of 18 patients resulted in calculated margins of 3.2 mm (AP), 1.7 mm (LR), and 3.2 mm (SI), supporting the potential for margin reduction with MRgRT. ABSTRACT Introduction Systematic and random errors in
Peng S +7 more
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On optimal quadrature formulae
Journal of Inequalities and Applications, 2000 For integrals involving a nonnegative weight function on a finite interval the author proposes a procedure to construct quadrature formulas which are exact for solutions of linear differential equations and are optimal in the sense of Sard. The author establishes necessary and sufficient conditions for the existence of such formulas.
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