Author
Samuel Goldberg
Bio: Samuel Goldberg is an academic researcher. The author has contributed to research in topics: Initial value problem & Mathematics. The author has an hindex of 2, co-authored 2 publications receiving 4137 citations.
Topics: Initial value problem, Mathematics
Papers
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4,135 citations
17 Oct 2022
TL;DR: In this article , the Erdős similarity problem was studied on the real line with positive measure and it was shown that every measurable subset of a set contains a similar copy of an infinite geometric progression.
Abstract: . We study some variants of the Erdős similarity problem. We pose the question if every measurable subset of the real line with positive measure contains a similar copy of an infinite geometric progression. We construct a compact subset 𝐸 of the real line such that 0 is a Lebesgue density point of 𝐸 , but 𝐸 does not contain any (non-constant) infinite geometric progression. We give a sufficient density type condition that guarantees that a set contains an infinite geometric progression. By slightly improving a recent result of Bradford, Kohut and Mooroogen [1], we construct a closed set 𝐹 ⊂ [ 0 , ∞) such that the measure of 𝐹 ∩[ 𝑡,𝑡 + 1 ] tends to 1 at infinity but 𝐹 does not contain any infinite arithmetic progression. We also slightly improve a more general recent result by Kolountzakis and Papageorgiou [2] for more general sequences. WegiveasufficientconditionthatguaranteesthatagivenCantortypesetcontains at least one infinite geometric progression with any quotient between 0 and 1. This can be applied to most symmetric Cantor sets of positive measure.
2 citations
2 citations
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TL;DR: In this paper, a method for finding the optical flow pattern is presented which assumes that the apparent velocity of the brightness pattern varies smoothly almost everywhere in the image, and an iterative implementation is shown which successfully computes the Optical Flow for a number of synthetic image sequences.
10,727 citations
TL;DR: In this article, it is shown that these features can be obtained by constructing a matrix with a certain property U, i.e., property U is a property of the solution of the Riemann problem.
8,174 citations
TL;DR: In this article, a second-order extension of the Lagrangean method is proposed to integrate the equations of ideal compressible flow, which is based on the integral conservation laws and is dissipative, so that it can be used across shocks.
6,630 citations
Book•
01 Jan 2002TL;DR: The CLAWPACK software as discussed by the authors is a popular tool for solving high-resolution hyperbolic problems with conservation laws and conservation laws of nonlinear scalar scalar conservation laws.
Abstract: Preface 1. Introduction 2. Conservation laws and differential equations 3. Characteristics and Riemann problems for linear hyperbolic equations 4. Finite-volume methods 5. Introduction to the CLAWPACK software 6. High resolution methods 7. Boundary conditions and ghost cells 8. Convergence, accuracy, and stability 9. Variable-coefficient linear equations 10. Other approaches to high resolution 11. Nonlinear scalar conservation laws 12. Finite-volume methods for nonlinear scalar conservation laws 13. Nonlinear systems of conservation laws 14. Gas dynamics and the Euler equations 15. Finite-volume methods for nonlinear systems 16. Some nonclassical hyperbolic problems 17. Source terms and balance laws 18. Multidimensional hyperbolic problems 19. Multidimensional numerical methods 20. Multidimensional scalar equations 21. Multidimensional systems 22. Elastic waves 23. Finite-volume methods on quadrilateral grids Bibliography Index.
5,791 citations
25 Feb 2004
TL;DR: The instructor's manual to a work which introduces the fundamental principles of meteorology, explaining storm dynamics and the dynamics of climate and its global implications is described in this paper, where the authors present a detailed discussion of the relationship between meteorology and climate.
Abstract: The instructor's manual to a work which introduces the fundamental principles of meteorology, explaining storm dynamics and the dynamics of climate and its global implications.
4,185 citations