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By Felli V., Schneider S.

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Additional info for A note on regularity of solutions to degenerate elliptic equations of Caffarelli-Kohn-Nirenberg type

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Stevin thus never held an academic position, but his influence on several generations of his “students” is very profound (Struik, 1981; Fig. 2). Among those we find, directly, Isaac Beeckman, Snellius (Sr. ) and Albert Girard, and indirectly Gregoire de Saint-Vincent, Descartes and Christiaan Huygens. His legacy and influence on further developments was enormous, but he did not receive the proper recognition. ” All in all, these developments in science in the first half of the 17th century would become the cornerstone of the Radical Enlightenment in the Rational Mechanics and Science Rationnelle Unique 33 second half of that century, when the mathematicians De Witt and Hudde would also take important political positions (Israel, 2005).

7. 99"); x1=x; 52 A. Bonanno et al. 1; y1=valutafunz(g,x1); Q1=y1; r=radiceq((x1-A1)^2+(y1-Q1)^2); C1=Circ(Punto(x1,y1),r); FINE; Fig. 7. Output of nefroid as envelope of circles. 4. EXPERIMENTAL CAUSTIC EXPLORATION In this section an experimental device is presented aimed to really illustrate the way in which the emerging caustic curve is formed by the reflected rays. The proposed device is realized by employing easily found materials. , 1997, Michelini 2006). Fig. 8. Experimental device illustrating the geometry of the caustic formation.

Sint quatuor rectae lineae proportionales AB, BC, CD, DE. Nempe ut AB prima ad BC secundam, ita sit AD tertia ad DE quartam. Dico primam AB ad tertiam AD ita esse ut secunda BC ad quartam DE. Qui modus arguendi dicitur permutando (Torricelli 1919–1944, De Proportionibus liber, p. 313) Propositio X. Si fuerint quotcumque, et aliae ipsis aequales numero, quae binae in eadem ratione sumantur, et ex aequo in eadem ratione erunt. Sint quotcumque magnitudines A, B, C, H, et aliae ipsis aequales numero D, E, F, I, quae in eadem ratione sint, si binae sumantur, nempe ut A ad B ita sit D ad E, et iterum ut B ad 24 R.

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A note on regularity of solutions to degenerate elliptic equations of Caffarelli-Kohn-Nirenberg type by Felli V., Schneider S.


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