Application of the admitted Lie group of the \\ classical Boltzmann equation to classification of the \\ Boltzmann equation with a source term [PDF]
arXiv, 2017 The classical Boltzmann equation is an integro-differential equation which describes the time evolution of rarefied gas in terms of a molecular distribution function. For some kinetic problems where it is necessary to add in the Boltzmann equation a source term depending on the independent and dependent variables.
arxiv
Book Review: Theory of Functionals and of Integral and Integro-differential Equations [PDF]
, 1932 Rudolph E. Langer
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On linear functional equations in locally convex linear topological spaces [PDF]
, 1953 Mieczysław Altman
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A solution of a simple functional equation as a basis for readily obtaining certain fundamental formulas in the theory of elliptic functions [PDF]
, 1930 G. W. Starcher
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Functional evolution equations
Journal of Mathematical Analysis and Applications, 2003 AbstractOf concern is the functional evolution equation dudt∈Bu+F(t,ut),t>0,u0=φ(s)∈C1[−r,0];X, where ut(s)=u(t+s), r>0, s∈[−r,0], and X is a real Banach space. It is shown by the method of lines combined with the Crandall–Pazy theorem, that for the initial data u0 in a generalized domain, this equation has a limit solution, which is Lipschitz ...
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Commissioning evaluation of a deviceless 4DCT scanner
Journal of Applied Clinical Medical Physics, EarlyView.Abstract Background The utilization of four‐dimensional computed tomography (4DCT) for radiation therapy has not seen major advances to the method of data binning since shortly after inception. Recently there is increased interest in the utilization of an alternative binning method rather than more established techniques.
Hunter Tillery +2 more
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Journal of Applied Clinical Medical Physics, EarlyView.Abstract Purpose This study evaluates the technical feasibility of adapting a surface monitoring system, designed for conventional four‐dimensional computed tomography (4DCT), to an intelligent, breathing‐adapted 4DCT and examines its potential to expand the currently limited range of supported surrogate systems.
Niklas Lackner +4 more
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On functional equations for Chow polylogarithms [PDF]
arXivChow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality ...
arxiv
Expansions in generalized Appell polynomials, and a class of related linear functional equations [PDF]
, 1929 I. M. Sheffer
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A method for measuring spatial resolution based on clinical chest CT sequence images
Journal of Applied Clinical Medical Physics, EarlyView.Abstract Purpose This study aimed to develop and validate a method for characterizing the spatial resolution of clinical chest computed tomography (CT) sequence images. Methods An algorithm for characterizing spatial resolution based on clinical chest CT sequence images was developed in Matlab (2021b).
Ying Liu +3 more
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