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Localization of nanoscale objects with light singularities [PDF]
NanophotonicsUnprecedented atomic-scale measurement resolution has recently been demonstrated in single-shot optical localization measurements based on deep-learning analyses of diffraction patterns of topologically structured light scattered from objects.
Grant Thomas A. +4 more
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The Sharp Upper Estimate Conjecture for the Dimension δk(V) of New Derivation Lie Algebra
Mathematics, 2022 Hussain, Yau, and Zuo introduced the Lie algebra Lk(V) from the derivation of the local algebra Mk(V):=On/(g+J1(g)+⋯+Jk(g)). To find the dimension of a newly defined algebra is an important task in order to study its properties.
Naveed Hussain +3 more
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Avoidance of Singularity during the Gravitational Collapse with String T-Duality Effects
Universe, 2023 In this paper, we explore the gravitational collapse of matter (dust) under the effect of zero-point length l0. During the gravitational collapse, we neglect the backreaction effect of pre-Hawking radiation (in the sense that it is a small effect and ...
Kimet Jusufi
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Galaxies, 2021 There are a number of publications on relativistic objects dealing either with black holes or naked singularities in the center. Here we show that there exist static spherically symmetric solutions of Einstein equations with a strongly nonlinear scalar ...
Oleksandr Stashko, Valery I. Zhdanov
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The de Broglie–Bohm Quantum Theory and Its Application to Quantum Cosmology
Universe, 2021 We review the de Broglie–Bohm quantum theory. It is an alternative description of quantum phenomena in accordance with all the quantum experiments already performed.
Nelson Pinto-Neto
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Geometrical Properties of the Pseudonull Hypersurfaces in Semi-Euclidean 4-Space
Mathematics, 2021 In this paper, we focus on some geometrical properties of the partially null slant helices in semi-Euclidean 4-space. By structuring suitable height functions, we obtain the singularity types of the pseudonull hypersurfaces, which are generated by the ...
Jianguo Sun, Xiaoyan Jiang, Fenghui Ji
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Mapping the Tilt and Torsion Angles for a 3-SPS-U Parallel Mechanism
Robotics, 2023 This article presents the analysis of a parallel mechanism of type 3-SPS-U. The usual singularity approach is carried out with respect to the Euler angles of the universal joint. However, this approach is computationally expensive especially when stacked
Swaminath Venkateswaran, Damien Chablat
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Numerical solution of Cauchy problems with multiple poles of integer order
Discrete and Continuous Models and Applied Computational Science, 2022 We consider Cauchy problem for ordinary differential equation with solution possessing a sequence of multiple poles. We propose the generalized reciprocal function method.
Aleksandr A. Belov, Nikolay N. Kalitkin
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On singularities of real algebraic sets and applications to kinematics
Open Mathematics, 2020 We address the question of identifying non-smooth points in Vℝ(I){{\bf{V}}}_{{\mathbb{R}}}(I) the real part of an affine algebraic variety. Two simple algebraic criteria will be formulated and proven.
Diesse Marc
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The Borg’s Theorem for Singular Sturm-Liouville Problem with Non-Separated Boundary Conditions [PDF]
Mathematics Interdisciplinary Research, 2023 In this paper, we consider a Sturm-Liouville equation with non-separated boundary conditions on a finite interval. We discuss some properties of solutions of the Sturm-Liouville equation, where the potential function has a singularity in the ...
Maedeh Bagherzadeh, Abdolali Neamaty
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