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18 p, 605.1 KB |
Integral geometry about the visual angle of a convex set
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Cufí Sobregrau, Julià, 1945- (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Gallego Gómez, Eduardo (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Reventós, Agustí (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we deal with a general type of integral formulas of the visual angle, among them those of Crofton, Hurwitz and Masotti, from the point of view of Integral Geometry. The purpose is twofold: to provide an interpretation of these formulas in terms of integrals of functions with respect to the canonical density in the space of pairs of lines and to give new simpler proofs of them.
2019 - 10.1007/s12215-019-00461-w
Rendiconti del Circolo Matematico di Palermo, Vol. 69 (October 2019) , p. 1115-1130
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18 p, 299.1 KB |
Linear type global centers of linear systems with cubic homogeneous nonlinearities
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García-Saldaña, Johanna Denise (Universidad Católica de la Santísima Concepción. Departamento de Matemática y Física Aplicadas (Chile)) ;
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)
A center p of a differential system in R2 is global if R2\ { p} is filled of periodic orbits. It is known that a polynomial differential system of degree 2 has no global centers. Here we characterize the global centers of the differential systems x˙=ax+by+P3(x,y),y˙=cx+dy+Q3(x,y),with P3 and Q3 homogeneous polynomials of degree 3, and such that the center has purely imaginary eigenvalues, i. [...]
2019 - 10.1007/s12215-019-00433-0
Rendiconti del Circolo Matematico di Palermo, vol. 69 (July 2019) p. 771-785
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14 p, 324.3 KB |
Global dynamics of a virus model with invariant algebraic surfaces
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Dias, Fabio Scalco (Universidade Federal de Itajubá. Instituto de Matemática e Computação (Brazil)) ;
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
In this paper by using the Poincaré compactification in R3 we make a global analysis for the virus system x˙=λ-dx-βxz,y˙=-ay+βxz z˙=ky-μz with (x, y, z) ∈ R3, β> 0, λ, a, d, k and μ are nonnegative parameters due to their biological meaning. [...]
2019 - 10.1007/s12215-019-00417-0
Rendiconti del Circolo Matematico di Palermo, vol. 69 (May 2019) p.535-546
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47 p, 952.2 KB |
An inverse approach to the center problem
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Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Ramírez, Rafael Orlando (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques) ;
Ramírez, Valentín (Universitat de Barcelona)
We consider analytic or polynomial vector fields of the form X=(-y+X)∂∂x+(x+Y)∂∂y, where X= X(x, y)) and Y= Y(x, y)) start at least with terms of second order. It is well-known that X has a center at the origin if and only if X has a Liapunov-Poincaré local analytic first integral of the form H=12(x2+y2)+∑j=3∞Hj, where H = H (x, y) is a homogenous polynomial of degree j. [...]
2019 - 10.1007/s12215-018-0342-1
Rendiconti del Circolo Matematico di Palermo, Vol. 68, Issue 1 (April 2019) , p. 29-64
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