In this paper, we show that there are solutions of degree r the equation Pell–Abel on some real hyperelliptic curve genus g if and only r>g. This result, which is known to experts, has consequences, seem be unknown experts. First, deduce existence a primitive k-differential an with unique zero order k(2g-2) for every (k,g)≠(2,2). Moreover, exists non Weierstrass point n modulo n>2g.

This article provides sufficient conditions for the existence of periodic solutions with nonconstant sign in a family of polynomial, non-autonomous, first-order differential equations that arise as a generalization of the Abel equation of the second kind.

The paper extends the applicability of our Matlab package Chebpack to find (generalized) Chebyshev polynomial approximations of the solutions of some Abel integral equations with algebraic singularities. Numerical examples confirm the efficiency of this approach.

We prove certain optimal systolic inequalities for a closed Riemannian manifold (X, g), depending on a pair of parameters, n and b. Here n is the dimension of X , while b is its first Betti number. The proof of the inequalities involves constructing Abel-Jacobi maps from X to its Jacobi torus T, which are area-decreasing (on b-dimensional areas), with respect to suitable norms. These norms are ...

In most medical AI programs, the use of notions such as causal relationships, temporal patterns, and aggregate disease categories has been limited. Yet studies of clinicians' behavior reveal that a diagnostic or therapeutic program must consider a case at various levels of detail to integrate overall understanding with detailed knowledge. To explore these issues, Ramesh Patil, Peter Szolovits, ...