HKU Scholars Hubhttp://hub.hku.hkThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sun, 16 Jun 2019 01:27:32 GMT2019-06-16T01:27:32Z50781- Two-variable Wiman-Valiron theory and its applications to PDEshttp://hdl.handle.net/10722/241392Title: Two-variable Wiman-Valiron theory and its applications to PDEs
Authors: Ng, TW
Abstract: The classical Wiman-Valiron theory is an important tool for the study of entire solutions of ODEs in the complex plane. A two variable version of Wiman-Valiron theory was developed by Peter Fenton in 1995 and it has been applied to study the entire solutions of some PDEs by Peter Fenton and John Rossi very recently. In this talk, we shall explain how their techniques can be used to show that certain PDEs cannot have transcendental entire solutions.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10722/2413922010-01-01T00:00:00Z
- Chebyshev-Blaschke productshttp://hdl.handle.net/10722/241393Title: Chebyshev-Blaschke products
Authors: Ng, TW
Abstract: In a recent joint work with Mingxi Wang, a version of Ritt's theory on the factorization of finite Blaschke products has been developed. In this Ritt's theory on the unit disk, a special class of finite Blaschke products has been introduced as the counterpart of Chebyshev polynomials in Ritt's theory for polynomials. These special finite Blaschke products are therefore called Chebyshev-Blaschke products. In this talk, I will explain the construction of them and also discuss some of their interesting properties.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10722/2413932011-01-01T00:00:00Z
- Critical points of polynomials with random zeroshttp://hdl.handle.net/10722/236885Title: Critical points of polynomials with random zeros
Authors: Ng, TW
Abstract: The study of zero distribution of random polynomials has a long history and is currently a very active research area. Traditionally, the randomness in these polynomials comes from the probability distribution followed by their coe cients. One can introduce randomness in the zeros (instead of the coe cients) of polynomials, and then investigate the locations of their critical points (relative to these zeros). Such a study was initiated by Rivin and the late Schramm in 2001, but only until 2011, Pemantle and Rivin proposed a precise probabilistic framework of it which will rst be explained in this talk. Following this framework, we will consider the problem of nding the zero distributions of the derivatives of random polynomials with i.i.d. zeros following a common distribution supported on a subset of the complex plane. Recently, Sean O'Rourke applied the same framework to study critical points of characteristic polynomial of a random matrix drawn from one of the compact classical matrix groups.
This is a joint work with Pak-Leong Cheung, Jonathan Tsai and Phillip Yam and the
work was supported by the RGC grant HKU 704611P and HKU 703313P.
Description: Organizer: Department of Mathematics, Faculty of Science and Technology, University of Macau (UM); Session 4
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10722/2368852016-01-01T00:00:00Z
- Meromorphic solutions of a third order nonlinear differential equationhttp://hdl.handle.net/10722/137326Title: Meromorphic solutions of a third order nonlinear differential equation
Authors: Conte, R; Ng, TW
Abstract: We prove that all the meromorphic solutions of the nonlinear differential equation c 0u ‴+6 u4+c 1 u "+c 2uu '+c 3 u 3u 3+c 4 u′ +c 5u 2+c 6u+c 7= 0 are elliptic or degenerate elliptic we build them explicitly. © 2010 American Institute of Physics.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10722/1373262010-01-01T00:00:00Z
- Density estimates on composite polynomialshttp://hdl.handle.net/10722/185945Title: Density estimates on composite polynomials
Authors: Cheung, WS; Ng, TW; Tsang, CY
Tue, 20 Aug 2013 00:00:00 GMThttp://hdl.handle.net/10722/1859452013-08-20T00:00:00Z
- A companion matrix approach to the study of zeros and critical points of a polynomialhttp://hdl.handle.net/10722/156163Title: A companion matrix approach to the study of zeros and critical points of a polynomial
Authors: Cheung, WS; Ng, TW
Abstract: In this paper, we introduce a new type of companion matrices, namely, D-companion matrices. By using these D-companion matrices, we are able to apply matrix theory directly to study the geometrical relation between the zeros and critical points of a polynomial. In fact, this new approach will allow us to prove quite a number of new as well as known results on this topic. For example, we prove some results on the majorization of the critical points of a polynomial by its zeros. In particular, we give a different proof of a recent result of Gerhard Schmeisser on this topic. The same method allows us to prove a higher order Schoenberg-type conjecture proposed by M.G. de Bruin and A. Sharma. © 2005 Elsevier Inc. All rights reserved.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10722/1561632006-01-01T00:00:00Z
- Periodic solutions of a derivative nonlinear Schrödinger equation: Elliptic integrals of the third kindhttp://hdl.handle.net/10722/144764Title: Periodic solutions of a derivative nonlinear Schrödinger equation: Elliptic integrals of the third kind
Authors: Chow, KW; Ng, TW
Abstract: The nonlinear Schrödinger equation (NLSE) is an important model for wave packet dynamics in hydrodynamics, optics, plasma physics and many other physical disciplines. The 'derivative' NLSE family usually arises when further nonlinear effects must be incorporated. The periodic solutions of one such member, the Chen-Lee-Liu equation, are studied. More precisely, the complex envelope is separated into the absolute value and the phase. The absolute value is solved in terms of a polynomial in elliptic functions while the phase is expressed in terms of elliptic integrals of the third kind. The exact periodicity condition will imply that only a countable set of elliptic function moduli is allowed. This feature contrasts sharply with other periodic solutions of envelope equations, where a continuous range of elliptic function moduli is permitted. © 2011 Elsevier B.V. All rights reserved.
Description: International Conference on Engineering and Computational Mathematics, The Hong Kong Polytechnic University, Hong Kong, 27–29 May 2009
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10722/1447642011-01-01T00:00:00Z
- Hayman’s classical conjecture on some nonlinear second-order algebraic ODEshttp://hdl.handle.net/10722/217069Title: Hayman’s classical conjecture on some nonlinear second-order algebraic ODEs
Authors: Conte, RMJ; Ng, TW; Wu, C
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10722/2170692015-01-01T00:00:00Z
- Permutable entire functions and their Julia setshttp://hdl.handle.net/10722/75206Title: Permutable entire functions and their Julia sets
Authors: Ng, TW
Abstract: In 1922-23, Julia and Fatou proved that any 2 rational functions f and g of degree at least 2 such that f(g(z)) = g(f(z)), have the same Julia set. Baker then asked whether the result remains true for nonlinear entire functions. In this paper, we shall show that the answer to Baker's question is true for almost all nonlinear entire functions. The method we use is useful for solving functional equations. It actually allows us to find out all the entire functions g which permute with a given f which belongs to a very large class of entire functions. © 2001 Cambridge Philosophical Society.
Mon, 01 Jan 2001 00:00:00 GMThttp://hdl.handle.net/10722/752062001-01-01T00:00:00Z
- An example concerning infinite factorizations of transcendental entire functionshttp://hdl.handle.net/10722/75191Title: An example concerning infinite factorizations of transcendental entire functions
Authors: Ng, TW
Sat, 01 Jan 2000 00:00:00 GMThttp://hdl.handle.net/10722/751912000-01-01T00:00:00Z
- Multivariate Markov Models for the Correlation of Multiple Biological Sequenceshttp://hdl.handle.net/10722/100302Title: Multivariate Markov Models for the Correlation of Multiple Biological Sequences
Authors: Ching, WK; Fung, SL; Ng, KP; Ng, TW
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10722/1003022003-01-01T00:00:00Z
- Fermat functional equations revisitedhttp://hdl.handle.net/10722/253006Title: Fermat functional equations revisited
Authors: Ng, TW
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10722/2530062016-01-01T00:00:00Z
- On the composition of a prime transcendental function and a prime polynomialhttp://hdl.handle.net/10722/156098Title: On the composition of a prime transcendental function and a prime polynomial
Authors: Ng, TW; Yang, CC
Abstract: Let f, g be transcendental entire functions and p, q be nonlinear polynomials with deg p ≠ 3, 6. Suppose that f and p are prime and f(p(z)) = g(q(z)), then f = g ○ L and p = L-1 ○ q, where L is a linear polynomial. Similar results for p(f(z)) = q(g(z)) are also obtained.
Sat, 01 Jan 2000 00:00:00 GMThttp://hdl.handle.net/10722/1560982000-01-01T00:00:00Z
- A double epidemic model for the SARS propagationhttp://hdl.handle.net/10722/144846Title: A double epidemic model for the SARS propagation
Authors: Ng, WT; Turinici, G; Danchin, A
Abstract: Background: An epidemic of a Severe Acute Respiratory Syndrome (SARS) caused by a new coronavirus has spread from the Guangdong province to the rest of China and to the world, with a puzzling contagion behavior. It is important both for predicting the future of the present outbreak and for implementing effective prophylactic measures, to identify the causes of this behavior. Results: In this report, we show first that the standard Susceptible-Infected-Removed (SIR) model cannot account for the patterns observed in various regions where the disease spread. We develop a model involving two superimposed epidemics to study the recent spread of the SARS in Hong Kong and in the region. We explore the situation where these epidemics may be caused either by a virus and one or several mutants that changed its tropism, or by two unrelated viruses. This has important consequences for the future: the innocuous epidemic might still be there and generate, from time to time, variants that would have properties similar to those of SARS. Conclusion: We find that, in order to reconcile the existing data and the spread of the disease, it is convenient to suggest that a first milder outbreak protected against the SARS. Regions that had not seen the first epidemic, or that were affected simultaneously with the SARS suffered much more, with a very high percentage of persons affected. We also find regions where the data appear to be inconsistent, suggesting that they are incomplete or do not reflect an appropriate identification of SARS patients. Finally, we could, within the framework of the model, fix limits to the future development of the epidemic, allowing us to identify landmarks that may be useful to set up a monitoring system to follow the evolution of the epidemic. The model also suggests that there might exist a SARS precursor in a large reservoir, prompting for implementation of precautionary measures when the weather cools down. © 2003 Ng et al; licensee BioMed Central Ltd.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10722/1448462003-01-01T00:00:00Z
- Meromorphic traveling wave solutions of the complex cubic-quintic Ginzburg-Landau equationhttp://hdl.handle.net/10722/156286Title: Meromorphic traveling wave solutions of the complex cubic-quintic Ginzburg-Landau equation
Authors: Conte, RMJ; Ng, TW
Abstract: We look for singlevalued solutions of the squared modulus M of the traveling wave reduction of the complex cubic-quintic Ginzburg-Landau equation. Using Clunie's lemma, we first prove that any meromorphic solution M is necessarily elliptic or degenerate elliptic. We then give the two canonical decompositions of the new elliptic solution recently obtained by the subequation method. © 2012 The Author(s).
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10722/1562862012-01-01T00:00:00Z
- Hayman’s conjecture on factorizable algebraic ODEshttp://hdl.handle.net/10722/228521Title: Hayman’s conjecture on factorizable algebraic ODEs
Authors: Ng, TW
Description: Invited Lecture
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10722/2285212015-01-01T00:00:00Z
- On Finite Blaschke Products Sharing Preimage of Connected Compact Setshttp://hdl.handle.net/10722/227925Title: On Finite Blaschke Products Sharing Preimage of Connected Compact Sets
Authors: Ng, TW
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10722/2279252013-01-01T00:00:00Z
- On Finite Blaschke Products Sharing Preimages of Setshttp://hdl.handle.net/10722/227922Title: On Finite Blaschke Products Sharing Preimages of Sets
Authors: Ng, TW
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10722/2279222013-01-01T00:00:00Z
- Critical points of random polynomials and random finite Blaschke productshttp://hdl.handle.net/10722/227926Title: Critical points of random polynomials and random finite Blaschke products
Authors: Ng, TW
Abstract: The study of zero distribution of random polynomials has a long history and is currently a very
active research area. Traditionally, the randomness in these polynomials comes from the probability
distribution followed by their coefficients. One can introduce randomness in the zeros (instead of
the coefficients) of polynomials, and then investigate the locations of their critical points (relative to
these zeros). Such a study was initiated by Rivin and the late Schramm in 2001, but only until 2011,
Pemantle and Rivin proposed a precise probabilistic framework of it which will first be explained in
this talk. Following this framework, we will consider the problem of finding the zero distributions of the
derivatives of random polynomials and random finite Blaschke products with i.i.d. zeros following a
common distribution supported on a subset of the complex plane. This is a joint work with Pak-Leong
Cheung, Jonathan Tsai and Phillip Yam.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10722/2279262014-01-01T00:00:00Z
- On Finite Blaschke Products Sharing Preimages of Setshttp://hdl.handle.net/10722/227924Title: On Finite Blaschke Products Sharing Preimages of Sets
Authors: Ng, TW
Abstract: In this talk, we shall consider the problem of characterizing those finite Blaschke products sharing
preimage of connected compact subsets with positive hyperbolic capacity of the standard unit disk.
We shall see that this problem is closely related to the factorization of finite Blaschke products (in the
sense of compositions) and also the problem of characterizing polynomials sharing the same Julia set.
To solve this problem, we shall follow T.C. Dinh’s approach to a similar problem for polynomials.This
is a joint work with C.Y. Tsang.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10722/2279242013-01-01T00:00:00Z
- Some Infection Models for the Development of AIDShttp://hdl.handle.net/10722/64486Title: Some Infection Models for the Development of AIDS
Authors: Ching, WK; Cong, Y; Bai, Z; Ng, TW
Abstract: The co-infection of HIV viruses can affect the viral evolution in vivo. Wodarz and Levy
2007 [1] study the effect of HIV co-infection by investigating the values of the virus cytopathicity
when the basic reproductive ratio of the virus and the total number of the target cells reach their
extreme point respectively. Here based on their ideas, we further extended the discussion to a more
general model.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10722/644862008-01-01T00:00:00Z
- Finding all meromorphic solutions of certian third order non-linear autonomous ODEhttp://hdl.handle.net/10722/228299Title: Finding all meromorphic solutions of certian third order non-linear autonomous ODE
Authors: Ng, TW
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10722/2282992010-01-01T00:00:00Z
- The star-shapedness of a generalized numerical rangehttp://hdl.handle.net/10722/227320Title: The star-shapedness of a generalized numerical range
Authors: LAU, PS; Ng, TW; Tsing, NK
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10722/2273202016-01-01T00:00:00Z
- Convexity and star-shapedness of real linear images of special orthogonal orbitshttp://hdl.handle.net/10722/227321Title: Convexity and star-shapedness of real linear images of special orthogonal orbits
Authors: LAU, PS; Ng, TW; Tsing, NK
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10722/2273212016-01-01T00:00:00Z
- Fermat functional equations revisitedhttp://hdl.handle.net/10722/226857Title: Fermat functional equations revisited
Authors: Ng, TW
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10722/2268572016-01-01T00:00:00Z
- Polynomials Versus Finite Blaschke Productshttp://hdl.handle.net/10722/226860Title: Polynomials Versus Finite Blaschke Products
Authors: Ng, TW
Abstract: In this talk, we shall compare polynomials of one complex variable and finite Blaschke products and demonstrate that they share many similar properties. In fact, we will see that one can establish a dictionary between polynomials and finite Blaschke products. This also motivates one to consider some problems in finite Blaschke products, for example, Smale's mean value conjecture for finite Blaschke products.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10722/2268602015-01-01T00:00:00Z
- Fermat functional equations revisitedhttp://hdl.handle.net/10722/226864Title: Fermat functional equations revisited
Authors: Ng, TW
Abstract: The problem of the existence of transcendental meromorphic or entire solutions for the Fermat functional equation f n +g n +h n =1 fn+gn+hn=1 was first studied by Walter Hayman in 1984. It is known that meromorphic (entire) solutions exist for n≤6 n≤6 (n≤5 n≤5) and no meromorphic (entire) solution exists when n≥9 n≥9 (n≥7 n≥7). In this talk we will revisit this problem from a more geometric view point. This is a joint work with Sai-Kee Yeung.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10722/2268642016-01-01T00:00:00Z
- Finiteness of fixed equilibrium configurations of point vortices in the plane with a background flowhttp://hdl.handle.net/10722/202989Title: Finiteness of fixed equilibrium configurations of point vortices in the plane with a background flow
Authors: CHEUNG, PL; Ng, TW
Abstract: For a dynamic system consisting of n point vortices in an ideal plane fluid with a steady, incompressible and irrotational background flow, a more physically significant definition of a fixed equilibrium configuration is suggested. Under this new definition, if the complex polynomial w that determines the aforesaid background flow is non-constant, we have found an attainable generic upper bound $\frac{(m+n-1)!}{(m-1)!\,n_1!\cdots n_{i_0}!}$ for the number of fixed equilibrium configurations. Here, m = deg w, i0 is the number of species, and each ni is the number of vortices in a species. We transform the rational function system arising from fixed equilibria into a polynomial system, whose form is good enough to apply the BKK theory (named after Bernshtein (1975 Funct. Anal. Appl. 9 183–5), Khovanskii (1978 Funct. Anal. Appl. 12 38–46) and Kushnirenko (1976 Funct. Anal. Appl. 10 233–5)) to show the finiteness of its number of solutions. Having this finiteness, the required bound follows from Bézout's theorem or the BKK root count by Li and Wang (1996 Math. Comput. 65 1477–84).
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10722/2029892014-01-01T00:00:00Z
- On Briot-Bouquet differential equationshttp://hdl.handle.net/10722/226859Title: On Briot-Bouquet differential equations
Authors: Ng, TW
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/10722/2268592005-01-01T00:00:00Z
- Exact Meromorphic Stationary Solutions of the Real Cubic Swift-Hohenberg Equationhttp://hdl.handle.net/10722/156285Title: Exact Meromorphic Stationary Solutions of the Real Cubic Swift-Hohenberg Equation
Authors: Conte, BR; Ng, TW; Wong, KK
Abstract: We show that all meromorphic solutions of the stationary reduction of the real cubic Swift-Hohenberg equation are elliptic or degenerate elliptic. We then obtain them all explicitly by the subequation method, and one of them appears to be a new elliptic solution. © 2012 by the Massachusetts Institute of Technology.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10722/1562852012-01-01T00:00:00Z
- On a new singular direction of meromorphic functionshttp://hdl.handle.net/10722/75266Title: On a new singular direction of meromorphic functions
Authors: Hui, G; Hua, ZJ; Ng, TW
Abstract: In this paper, by using Ahlfors' theory of covering surfaces, we establish the existence of a new singular direction for a meromorphic functions f, namely a T direction for f, for which the Nevanlinna characteristic function T(r, f) is used as a comparison function.
Thu, 01 Jan 2004 00:00:00 GMThttp://hdl.handle.net/10722/752662004-01-01T00:00:00Z
- Smale's mean value conjecture for finite Blaschke productshttp://hdl.handle.net/10722/252788Title: Smale's mean value conjecture for finite Blaschke products
Authors: Ng, TW
Description: Invited Speakers
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10722/2527882017-01-01T00:00:00Z
- Relationship between the zeros of two polynomialshttp://hdl.handle.net/10722/144763Title: Relationship between the zeros of two polynomials
Authors: Cheung, WS; Ng, TW
Abstract: In this paper, we shall follow a companion matrix approach to study the relationship between zeros of a wide range of pairs of complex polynomials, for example, a polynomial and its polar derivative or Sz.-Nagy's generalized derivative. We shall introduce some new companion matrices and obtain a generalization of the Weinstein-Aronszajn Formula which will then be used to prove some inequalities similar to Sendov conjecture and Schoenberg conjecture and to study the distribution of equilibrium points of logarithmic potentials for finitely many discrete charges. Our method can also be used to produce, in an easy and systematic way, a lot of identities relating the sums of powers of zeros of a polynomial to that of the other polynomial. © 2009 Elsevier Inc.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10722/1447632010-01-01T00:00:00Z
- Contributed Speakershttp://hdl.handle.net/10722/252789Title: Contributed Speakers
Authors: Ng, TW
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10722/2527892014-01-01T00:00:00Z
- Parametrizations of algebraic curveshttp://hdl.handle.net/10722/75299Title: Parametrizations of algebraic curves
Authors: Beardon, AF; Ng, TW
Abstract: We show that if a pair of meromorphic functions parametrize an algebraic curve
then they have a common right factor, and we use this to derive a variety of results on algebraic curves.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10722/752992006-01-01T00:00:00Z
- A vector - host epidemic modelhttp://hdl.handle.net/10722/75169Title: A vector - host epidemic model
Authors: Ching, WK; Chung, SK; Lau, YK; Ng, TW; Yung, SP
Tue, 01 Jan 2002 00:00:00 GMThttp://hdl.handle.net/10722/751692002-01-01T00:00:00Z
- On Optimal Screening and Quarantining Policy in a Network of Prisonshttp://hdl.handle.net/10722/75308Title: On Optimal Screening and Quarantining Policy in a Network of Prisons
Authors: Bai, ZJ; Ching, WK; Cong, Y; Ng, TW
Abstract: In this paper, we propose mathematical models for the spread of HIV in a network of prisons. We study the effect of both screening prisoners and quarantining infectives. Efficient algorithms based on Newton's method are then developed for computing the equilibrium values of the infectives in each prison. We also give an optimization formulation for obtaining the optimal screening and quarantine policy. The models and algorithms developed can be extended to model the spread of a disease in a general network of connected zones.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10722/753082007-01-01T00:00:00Z
- Prefacehttp://hdl.handle.net/10722/156263Title: Preface
Authors: Hu, PC; Ng, TW
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10722/1562632011-01-01T00:00:00Z
- Graceful labeling for mushroom treeshttp://hdl.handle.net/10722/202983Title: Graceful labeling for mushroom trees
Authors: Chan, TL; Cheung, WS; Ng, TW
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10722/2029832015-01-01T00:00:00Z
- Polynomials versus finite Blaschke productshttp://hdl.handle.net/10722/186798Title: Polynomials versus finite Blaschke products
Authors: Ng, PTW; Tsang, CY
Abstract: In a recent joint work with Mingxi Wang, a version of Ritt's theory on the factorization of finite Blaschke products has been developed. In this Ritt's theory on the unit disk, a special class of finite Blaschke products has been introduced as the counterpart of Chebyshev polynomials in Ritt's theory for polynomials. These special finite Blaschke products are therefore called Chebyshev-Blaschke products. In this talk, I will explain the construction of them and also discuss some of their interesting properties.
Description: The Speaker abstracts’ website is located at http://www.fields.utoronto.ca/programs/scientific/11-12/Blaschke_prod/abstracts.html
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10722/1867982013-01-01T00:00:00Z
- On Modeling SARS in Hong Konghttp://hdl.handle.net/10722/75259Title: On Modeling SARS in Hong Kong
Authors: Ching, WK; Chung, SK; Ng, TW
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10722/752592003-01-01T00:00:00Z
- Imprimitive parametrization of analytic curves and factorizations of entire functionshttp://hdl.handle.net/10722/75222Title: Imprimitive parametrization of analytic curves and factorizations of entire functions
Authors: Ng, TW
Abstract: Let f(z) and g(z) be transcendental entire functions. Fuchs and Song proved that if (f(z), g(z)) parametrizes some complex algebraic curve, then f and g must have a transcendental common right factor. The paper proves this result by a different method that also allows a similar result to be proved for some transcendental curves. This result is then used to solve some factorization problems of entire functions. © 2001 London Mathematical Society.
Mon, 01 Jan 2001 00:00:00 GMThttp://hdl.handle.net/10722/752222001-01-01T00:00:00Z
- A parasite vector-host epidemic model for TSE propagationhttp://hdl.handle.net/10722/75415Title: A parasite vector-host epidemic model for TSE propagation
Authors: Ng, TW; Turinici, G; Ching, WK; Chung, SK; Danchin, A
Abstract: Background: Transmissible spongiform encephalopathies (TSEs) are a family of diseases that infect mammals. They are explained by cross-contamination through an unknown route or from infection of food contaminated with prion proteins (PrPs), natural proteins that take an infectious form contributing to the slow destruction of the animal brain. While the extreme resistance of PrPs to denaturation and proteolysis accounts for a route from the mouth to the brain, the possible role of another route of contamination is explored here. Many diseases are spread by vectors, as seen in plague, typhus, malaria, or dengue. The situation where PrPs would be transmitted by a vector and, from the characteristics of outbreaks, proposed hypotheses about the biological nature of such vectors are explored. Material/Methods: The nontrivial situation where contamination by the vector prevents infection by making the host immune to further vector contamination was analyzed. To investigate the nature of a possible vector, the spread of a disease in a closed population of hosts and vectors where the number of hosts is constant and the vectors multiply in the host was modeled mathematically. In this model, the disease is caused by an infective agent and is spread by a vector, while direct host-to-host spread is not permitted. Results: Concrete values of the parameters of the model were computed from simulation of the BSE outbreak in the UK as a possible example of the process. Conclusions: Microbial vector-borne diseases might play an unexpected role in the spread of epidemics, warranting further exploration. © Med Sci Monit, 2007.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10722/754152007-01-01T00:00:00Z
- On Ritt's factorization of polynomialshttp://hdl.handle.net/10722/75226Title: On Ritt's factorization of polynomials
Authors: Beardon, AF; Ng, TW
Abstract: Ritt has shown that any complex polynomial p can be written as the composition of polynomials p1, . . . , pm, where each pj, is prime in the sense that it cannot be written as a non-trivial composition of polynomials. The factors pj are not unique but the number m of them is, as is the set of the degrees of the pj. The paper extends Ritt's theory and, in particular, a third invariant of the decomposition is introduced.
Sat, 01 Jan 2000 00:00:00 GMThttp://hdl.handle.net/10722/752262000-01-01T00:00:00Z
- The critical values of a polynomialhttp://hdl.handle.net/10722/75257Title: The critical values of a polynomial
Authors: Beardon, AF; Carne, TK; Ng, TW
Abstract: It has been known for a long time that any real sequence y1,..., yn-1 is the sequence of critical values of some real polynomial. Here we show that any complex sequence w1..... wn-1 is the sequence of critical values of some complex polynomial.
Tue, 01 Jan 2002 00:00:00 GMThttp://hdl.handle.net/10722/752572002-01-01T00:00:00Z
- Smale's mean value conjecture for odd polynomialshttp://hdl.handle.net/10722/75277Title: Smale's mean value conjecture for odd polynomials
Authors: Ng, TW
Abstract: In this paper, we shall show that the constant in Smale's mean value theorem can be reduced to two for a large class of polynomials which includes the odd polynomials with nonzero linear term.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10722/752772003-01-01T00:00:00Z
- Phylogenetic analysis reveals a correlation between the expansion of very virulent infectious bursal disease virus and reassortment of its genome segment Bhttp://hdl.handle.net/10722/49034Title: Phylogenetic analysis reveals a correlation between the expansion of very virulent infectious bursal disease virus and reassortment of its genome segment B
Authors: Hon, CC; Lam, TY; Drummond, A; Rambaut, A; Lee, YF; Yip, CW; Zeng, F; Lam, PY; Ng, PTW; Leung, FCC
Abstract: Infectious bursal disease virus (IBDV) is a birnavirus causing immunosuppressive disease in chickens. Emergence of the very virulent form of IBDV (vvIBDV) in the late 1980s dramatically changed the epidemiology of the disease. In this study, we investigated the phylogenetic origins of its genome segments and estimated the time of emergence of their most recent common ancestors. Moreover, with recently developed coalescence techniques, we reconstructed the past population dynamics of vvIBDV and timed the onset of its expansion to the late 1980s. Our analysis suggests that genome segment A of vvIBDV emerged at least 20 years before its expansion, which argues against the hypothesis that mutation of genome segment A is the major contributing factor in the emergence and expansion of vvIBDV. Alternatively, the phylogeny of genome segment B suggests a possible reassortment event estimated to have taken place around the mid-1980s, which seems to coincide with its expansion within approximately 5 years. We therefore hypothesize that the reassortment of genome segment B initiated vvIBDV expansion in the late 1980s, possibly by enhancing the virulence of the virus synergistically with its existing genome segment A. This report reveals the possible mechanisms leading to the emergence and expansion of vvIBDV, which would certainly provide insights into the scope of surveillance and prevention efforts regarding the disease. Copyright © 2006, American Society for Microbiology. All Rights Reserved.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10722/490342006-01-01T00:00:00Z
- Higher-Order, Polar and Sz.-Nagy’s Generalized Derivatives of Random Polynomials with Independent and Identically Distributed Zeros on the Unit Circlehttp://hdl.handle.net/10722/210741Title: Higher-Order, Polar and Sz.-Nagy’s Generalized Derivatives of Random Polynomials with Independent and Identically Distributed Zeros on the Unit Circle
Authors: CHEUNG, PL; Ng, TW; Tsai, HTJ; Yam, SCP
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10722/2107412015-01-01T00:00:00Z
- Recent progress on the unique factorizations of entire functionshttp://hdl.handle.net/10722/100325Title: Recent progress on the unique factorizations of entire functions
Authors: Ng, TW
Sat, 01 Jan 2000 00:00:00 GMThttp://hdl.handle.net/10722/1003252000-01-01T00:00:00Z
- Smale's mean value conjecture and the hyperbolic metrichttp://hdl.handle.net/10722/75369Title: Smale's mean value conjecture and the hyperbolic metric
Authors: Beardon, AF; Minda, D; Ng, TW
Tue, 01 Jan 2002 00:00:00 GMThttp://hdl.handle.net/10722/753692002-01-01T00:00:00Z