Computation of focus (or focal) values for nonlinear dynamical systems is not only important in theoretical study, but also useful in applications. In this paper, we compare three typical methods for computing focus values, and give a comparison among these methods. Then, we apply these methods to study two practical problems and Hilbert’s 16th problem. We show that these different methods have...

Vasil'ev posed Problem 16.26 in [The Kourovka Notebook: Unsolved Problems in Group Theory, 16th ed.,Sobolev Inst. Math., Novosibirsk (2006).] as follows:Does there exist a positive integer $k$ such that there are no $k$ pairwise nonisomorphicnonabelian finite simple groups with the same graphs of primes? Conjecture: $k = 5$.In [Zvezdina, On nonabelian simple groups having the same prime graph a...

This paper investigates the first part of Hilbert’s 16th problem which asks about topology of the real projective algebraic curves. Using the Rokhlin-Viro-Fiedler method of complex orientation, we obtain new restrictions on the arrangements of ovals of projective algebraic curves of odd degree d = 4k + 1, k ≥ 2, with nests of depth k.

BIFURCATION SET AND LIMIT CYCLES FORMING COMPOUND EYES IN A PERTURBED HAMILTONIAN SYSTEM JIBIN LI AND ZHENRONG LIU In this paper we consider a class of perturbation of a Hamiltonian cubic system with 9 finite critical points . Using detection functions, we present explicit formulas for the global and local bifurcations of the flow . We exhibit various patterns of compound eyes of limit cycles ....

extract: children abuse probably not new phenomena but sever reflection of treble stories in press due to that this issue viewed as a problem which need to special nursing and medical attention.   each person who read new articles may to conclude that children abuse is a phenomenon relevant to twenty century but unfortunately children were abused for centuries. in 16th century a surgeon called ...

The latent toxoplasmosis is usually considered to be asymptomatic, however, this paradigm has never been rigorously tested. Here we searched for symptoms of deterioration of physical health (decrease of weight) in infected people by analysis of clinical records of 758 women tested for toxoplasmosis in the 16th week of gravidity. Toxoplasma-positive women have a lower body weight in the 16th wee...

Periodic motion or oscillation is a common phenomenon which exists in almost all disciplines of physical and engineering systems. Limit cycle is one of the source generating periodic motion, and its study plays an important role in the research of nonlinear dynamical systems. A related wellknown problem to limit cycle is Hilbert’s 16th problem [Hilbert, 1902], which has attracted many mathemati...

Extended Abstract: I will only summarise the evidence for the transmission of the calculus from India to Europe in the 16th c. CE, since it has been considered elsewhere. Briefly, unlike the wild claims of transmission from “Greece”, typically advanced without serious evidence by Western historians in the last three centuries, the standard of evidence I use is a legal standard of evidence which...