Department of Pharmaceutical Chemistry, California Institute for Quantitative Biomedical Research, Mission Bay Genentech Hall, 600 16th Street, University of California, San Francisco, CA 94143-2240, USA Department of Biopharmaceutial Sciences, California Institute for Quantitative Biomedical Research, Mission Bay Genentech Hall, 600 16th Street, University of California, San Francisco, CA 9414...

These highly informal lecture notes aim at introducing and explaining several closely related problems on zeros of analytic functions defined by ordinary differential equations and systems of such equations. The main incentive for this study was its potential application to the tangential Hilbert 16th problem on zeros of complete Abelian integrals. The exposition consists mostly of examples ill...

In this paper, we consider the problem of determining exact number periodic orbits for polynomial planar flows. This is a variant Hilbert’s 16th problem. Using natural definition computability, show that noncomputable on one hand and, other hand, computable uniformly set all structurally stable systems defined unit disk. We also prove there family which does not have sharp upper bound its orb...

Within last century the study of cycles of twodimensional quadratic systems was stimulated by 16th Hilbert’s problem and its different variants [Hilbert, 1902; Lloyd, 1988; Blows & Perko, 1994; Ilyashenko, 2002; Chen & Wang, 1979; Shi, 1980]. The development of asymptotical methods for investigation of cycles of quadratic systems is facilitated by the fractionally-quadratic transformations, whi...

Correction Following the publication of the original supplement article [1], it was brought to our attention that the supplement title unfortunately contains an error: “Proceedings of the 16th Annual UT-KBRIN Bioinformatics Summit 2016: proceedings” should instead read “Proceedings of the 16th Annual UT-KBRIN Bioinformatics Summit 2017: proceedings”. The correct title has been included in this ...

© 2006 The Author. Journal Compilation © 2006 The Nautical Archaeology Society. Published by Blackwell Publishing Ltd. 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA. Blackwell Publishing Ltd F. Castro: RISING and NARROWING: 16TH-CENTURY PORTUGUESE GEOMETRIC ALGORITHMS NAUTICAL ARCHAEOLOGY, 35.2 Rising and Narrowing: 16th-Century Geometric Algorithms used to...

In this paper, we prove the existence of twelve small (local) limit cycles in a planar system with third-degree polynomial functions. The best result so far in literature for a cubic order planar system is eleven limit cycles. The system considered in this paper has a saddle point at the origin and two focus points which are symmetric about the origin. This system was studied by the authors and...

This paper is devoted to analytical and numerical investigation of limit cycles in twodimensional polynomial quadratic systems. The appearance of modern computers permits one to use a numerical simulation of complicated nonlinear dynamical systems and to obtain new information on a structure of their trajectories. However the possibilities of naive approach, based on the construction of traject...