38 research outputs found
A Three-Dimensional Voting System in Hong Kong
The voting system in the Legislative Council of Hong Kong (Legco) is
sometimes unicameral and sometimes bicameral, depending on whether the bill is
proposed by the Hong Kong government. Therefore, although without any
representative within Legco, the Hong Kong government has certain degree of
legislative power --- as if there is a virtual representative of the Hong Kong
government within the Legco. By introducing such a virtual representative of
the Hong Kong government, we show that Legco is a three-dimensional voting
system. We also calculate two power indices of the Hong Kong government through
this virtual representative and consider the -dimension and the
-dimension of Legco. Finally, some implications of this Legco model to the
current constitutional reform in Hong Kong will be given
Meromorphic solutions of a third order nonlinear differential equation
We prove that all the meromorphic solutions of the nonlinear differential
equation c0 u"' + 6 u^4 + c1 u" + c2 u u' + c3 u^3 + c4 u'+ c5 u^2 + c6 u +c7=0
are elliptic or degenerate elliptic, and we build them explicitly.Comment: 12 pages, to appear, Journal of Mathematical Physic
Smale's mean value conjecture for finite Blaschke products
Motivated by a dictionary between polynomials and finite Blaschke products,
we study both Smale's mean value conjecture and its dual conjecture for finite
Blaschke products in this paper. Our result on the dual conjecture for finite
Blaschke products allows us to improve a bound obtained by V. Dubinin and T.
Sugawa for the dual mean value conjecture for polynomials.Comment: To appear in an issue of Journal of Analysis denoted to the
Proceedings of the Conference on Modern Aspects of Complex Geometry
(MindaFest)
Hayman's classical conjecture on some nonlinear second order algebraic ODEs
In this paper, we study the growth, in terms of the Nevanlinna characteristic
function, of meromorphic solutions of three types of second order nonlinear
algebraic ordinary differential equations. We give all their meromorphic
solutions explicitly, and hence show that all of these ODEs satisfy the {\it
classical conjecture} proposed by Hayman in 1996.Comment: 15 pages, to appear, Complex variables and elliptic equation
A Uniqueness Theorem for Holomorphic Mappings in the Disk Sharing Totally Geodesic Hypersurfaces
In this paper, we prove a Second Main Theorem for holomorphic mappings in a
disk whose image intersects some families of nonlinear hypersurfaces (totally
geodesic hypersurfaces with respect to a meromorphic connection) in the complex
projective space . This is a generalization of Cartan's Second
Main Theorem. As a consequence, we establish a uniqueness theorem for
holomorphic mappings which intersects many totally geodesic
hypersurfaces