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2020
The electric and magnetic fields are easily derived from the vector potential using the relations $$\displaystyle \begin{aligned} \mathbf{E}(\mathbf{r},t)=-\frac{{\partial}\mathbf{A}}{{\partial}t}\\ \mathbf{B}(\mathbf{r},t)=\boldsymbol{\nabla}\mathbf{xA}. \end{aligned} $$
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The electric and magnetic fields are easily derived from the vector potential using the relations $$\displaystyle \begin{aligned} \mathbf{E}(\mathbf{r},t)=-\frac{{\partial}\mathbf{A}}{{\partial}t}\\ \mathbf{B}(\mathbf{r},t)=\boldsymbol{\nabla}\mathbf{xA}. \end{aligned} $$
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Depth of field in light field rendering
Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429), 2004This paper focuses on the sampling problem in light field rendering (LFR) that is a fundamental approach to image based rendering. Quality of LFR depends on a light ray database generated from pre-acquired images, since image synthesis is a process of gathering appropriate light ray data from the database.
Keita Takahashi 0001 +2 more
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1998
Abstract We shall now go rather more deeply into the theory of fields. In many ways a field is the best sort of system to work with, because it is always possible to divide by a non-zero element. The material of this chapter has many uses in the remainder of the book.
A W Chatters, C R Hajarnavis
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Abstract We shall now go rather more deeply into the theory of fields. In many ways a field is the best sort of system to work with, because it is always possible to divide by a non-zero element. The material of this chapter has many uses in the remainder of the book.
A W Chatters, C R Hajarnavis
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1997
We have now given two proofs of the Fundamental Theorem of Algebra. Both of these involved much more analysis (calculus) than algebra. The first relied on the analytic properties of two-variable real-valued functions from advanced calculus as well as the continuity of real polynomials while the second proof followed from the theory of complex analysis.
Benjamin Fine, Gerhard Rosenberger
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We have now given two proofs of the Fundamental Theorem of Algebra. Both of these involved much more analysis (calculus) than algebra. The first relied on the analytic properties of two-variable real-valued functions from advanced calculus as well as the continuity of real polynomials while the second proof followed from the theory of complex analysis.
Benjamin Fine, Gerhard Rosenberger
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On the Field of Definition for a Field of Automorphic Functions: II
The Annals of Mathematics, 1964The purpose of this paper is to complement the main theorems of the previous papers with the same title, referred to hereafter as [FI] and [FII], and to simplify the proofs. In [FI, II], it was shown that a certain abelian extension k of a certain algebraic number field K' can be determined by a family 1(&2) of abelian varieties belonging to a given ...
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Field separation of adjoining therapy fields
Medical Physics, 1981The question of optimal portal separation between two contiguous fields is of importance in radiotherapy. An analytical linear model based on experimental data has been developed for a Co–60 unit (Siemens Gammatron S 65 K). It allows the computation of the separation distance for any combination of field sizes not necessarily having the same source ...
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Phase-Field Modeling of Microstructure Evolution: Recent Applications, Perspectives and Challenges
Progress in Materials Science, 2022Javier Llorca, Damien Tourret
exaly
Epigenetics and Regenerative Medicine
Medical Epigenetics, 2021Hannele Ruohola-Baker, Shiri Levy
exaly