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Содержание:

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Обращаю внимание на последнюю главу: она носит привычный для меня учебный характер, там приведены подробные выводы формул и подробные же описания численных методов.

Выражаю благодарность всем друзьям за разнообразную поддержку и прошу способствовать рекламе среди заинтересованных слоев читателей:))

Аннотация:

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Не по моей части, но вдруг кому-то пригодится. Завлекают разобранными примерами:))

A Spectral Theory of Scalar Volterra Equations https://arxiv.org/abs/2503.06957
David Darrow, George Stepaniants
Volterra integral and integro-differential equations have been extensively studied in both pure mathematics and applied science. In one direction, developments in analysis have yielded far-ranging existence, uniqueness, and regularity results. In the other, applications in science have inspired a substantial library of practical techniques to deal with such equations.
The present work connects these research areas by examining five large classes of linear Volterra equations: integral and integro-differential equations with completely monotone (CM) kernels, corresponding to linear viscoelastic models; those with positive definite (PD) kernels, corresponding to partially-observed quantum systems; difference equations with PD kernels; a class of generalized delay differential equations; and a class of generalized fractional differential equations. We develop a system of correspondences between these problems, showing that all five can be understood within the same, spectral theory. We leverage this theory to recover practical, closed-form solutions of all five classes, and we show that interconversion yields a natural, continuous involution within each class. Our work unifies several results from science: the interconversion formula of Gross, recent results in viscoelasticity and operator theory for integral equations of the second type, classical formulas for Prony series and fractional differential equations, and the convergence of Prony series to CM kernels. Finally, our theory yields a novel, geometric construction of the regularized Hilbert transform, extends it to a wide class of infinite measures, and reveals a natural connection to delay and fractional differential equations.
We leverage our theory to develop a powerful, spectral method to handle scalar Volterra equations numerically, and illustrate it with a number of practical examples.
Comments: 79 pages, 15 figures

Кто-нибудь из уважаемых читателей имел дело с гистограммами в логарифмическом масштабе? Это когда бины одинаковые по ширине на логарифмической оси абсцисс?

Очень хорошая статья! А некоторые у меня тут в ЖЖ даже отрицали, ссылаясь при этом на "Теоретическую физику и астрофизику" Гинзбурга, хотя там утверждается как раз противоположное, т.е. что таки излучает.

Once more about radiation from uniformly accelerating charge https://arxiv.org/abs/2503.00064
E. T. Akhmedov, M. N. Milovanova
We consider an electric charge uniformly accelerating along x direction and moving with constant velocity along y direction. We show that in the co-accelerating along x direction Rinder's frame this charge creates non-zero Poynting vector, which, however, does not lead to a non-vanishing flux through an infinitely distant surface. Furthermore, we show that in the laboratory Minkowski frame such a charge creates a stress energy flux that does not vanish at infinity. We interpret these observations as that while the Rindler's frame corresponds to the static zone around the charge, the Minkowski frame does contain the wave zone. We give detailed calculations and explanations concluding that uniformly accelerating charge does radiate
Comments: 17 pages

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