By Luc Tartar
Homogenization isn't approximately periodicity, or Gamma-convergence, yet approximately realizing which powerful equations to take advantage of at macroscopic point, understanding which partial differential equations govern mesoscopic degrees, with no utilizing chances (which break actual reality); as an alternative, one makes use of a number of topologies of vulnerable variety, the G-convergence of Sergio Spagnolo, the H-convergence of François Murat and the writer, and a few chargeable for the looks of nonlocal results, which many theories in continuum mechanics or physics guessed wrongly.
For a greater figuring out of twentieth century technology, new mathematical instruments has to be brought, just like the author’s H-measures, editions through Patrick Gérard, and others but to be chanced on.
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Example text
Seeing then the chaotic situation which resulted from the search for the mathematical laws followed by nature, I think that it is the role of mathematicians interested in other sciences to create a little order, and for doing that I found that the mathematical theory of homogenization, as I developed it with Fran¸cois MURAT,49 contains many ideas which should help putting a lot of things on a sounder basis. A few people pretended that some of my results were already known, and it could be possible, but more likely those who made these claims did not understand what mathematics is about, and if they knew that there cannot be a mathematical result before there is a definition of what one is looking for, they would probably say that some results were conjectured, instead of proven.
He worked as a telegrapher, in Denmark, in Newcastle upon Tyne, England, and then did research on his own, living in the South of England. We owe to him the simplified version of the Maxwell equation using vector calculus, as he replaced by a set of 4 equations in 2 variables what MAXWELL had written as a set of 20 equations in 20 variables, so that I prefer to call it the Maxwell–Heaviside equation. 44 Sesqui is a prefix meaning one and a half, and sesqui-linear is the complex analogue of bilinear: one has linearity in one variable, but anti-linearity in the other variable, which is counted for half in respect to linearity.
20 1 Why Do I Write? ,80 MITTAG-LEFFLER,81 MUHAMMAD,82 ´ ,83 Paul (apostle),84 Peter (apostle),85 Napol´eon I = BONAPARTE, NEEL 78 John the Baptist, Jewish preacher and ascetic, 30. According to the gospels, he was a cousin of Jesus of Nazareth. 79 Louis Stanislas Xavier de France, 1755–1824, count of Provence, was king of France from 1814 to 1824, under the name of Louis XVIII. 80 M. (Mahendranath GUPTA), Bengali teacher, 1854–1932. , and was the author of The Gospel of Ramakrishna [57]. 81 Magnus G¨ osta MITTAG-LEFFLER, Swedish mathematician, 1846–1927.