SelectedWorks - Matthew He

Contact

Selected Works of Matthew He

Assistant Dean/Professor, Department of Mathematics

Assistant Dean/Full Professor of the Halmos College of Natural Sciences and Oceanography of Nova Southeastern University in Florida. From 2004 to 2015, Prof. He served as the Director of the Division of Math, Science, and Technology of Farquhar College of Arts and Sciences of the university. He has been a full professor and grand Ph.D. of the World Information Distributed University since 2004, as well as an academician of the European Academy of Informatization. He was a research associate at the Department of Mathematics, Eldgenossische Technische Hochschule, Zurich, Switzerland, and the Department of Mathematics and Theoretical Physics, Cambridge University, Cambridge, England. He was also a visiting professor at the National Key Research Lab of Computational Mathematics of the Chinese Academy of Science and the University of Rome, Italy.

Media Contact Collaborator Mentor

Works
About

×

About Matthew He

Assistant Dean/Full Professor of the Halmos College of Natural Sciences and Oceanography of Nova Southeastern University in Florida. From 2004 to 2015, Prof. He served as the Director of the Division of Math, Science, and Technology of Farquhar College of Arts and Sciences of the university. He has been a full professor and grand Ph.D. of the World Information Distributed University since 2004, as well as an academician of the European Academy of Informatization. He was a research associate at the Department of Mathematics, Eldgenossische Technische Hochschule, Zurich, Switzerland, and the Department of Mathematics and Theoretical Physics, Cambridge University, Cambridge, England. He was also a visiting professor at the National Key Research Lab of Computational Mathematics of the Chinese Academy of Science and the University of Rome, Italy.

Articles (34)

Journal articles written or co-written by Dr. Matthew He.

Neuroevolutional Methods for Decision Support Under Uncertainty (Nina Komleva, Olga Khlopkova and Matthew He) International Journal of Civil Engineering and Technology (2019)

The article presents a comparative analysis of the fundamental neuroevolutional methods, which are widely applied for the intellectualization of the decision making support systems under uncertainty. Based on this analysis the new neuroevolutionary method is ...

On Taylor’s Formula for the Resolvent of a Complex Matrix (Matthew He and Paolo E. Ricci) Computers & Mathematics with Applications (2008)

The resolvent Rλ(A) of a complex r×r matrix A is an analytic function in any domain with empty intersection with the spectrum ΣA of A. The well known Taylor expansion of Rλ(A) in a neighborhood ...

siRNA Drug Delivery by Biodegradable Polymeric Nanoparticles (Xudong Yuan, Ling Li, Appu Rathinavelu, et al.) Journal of Nanoscience and Nanotechnology (2006)

RNA interference (RNAi) is an emerging technology in which the introduction of double-stranded RNA (dsRNA) into a diverse range of organisms and cell types causes degradation of the complementary mRNA. It offers a broad spectrum ...

Genetic Code, Attributive Mappings and Stochastic Matrices (Matthew He) Bulletin of Mathematical Biology (2004)

In this paper we construct three primitive mappings based on three kinds of genetic attribute equivalences. We then apply the mappings and basic addition operation to the universal genetic code to generate three square matrices. ...

Genetic Code, Hamming Distance and Stochastic Matrices (Matthew He, Sergei V. Petoukhov and Paolo E. Ricci) Bulletin of Mathematical Biology (2004)

In this paper we use the Gray code representation of the genetic code C=00, U=10, G=11 and A=01 (C pairs with G, A pairs with U) to generate a sequence of genetic code-based matrices. In ...

3D Nonrigid Motion Analysis Under Small Deformations (Chandra Kambhamettu, Dmitry Goldgof, Matthew He, et al.) Image and Vision Computing (2003)

We present a novel method for estimating motion parameters and point correspondences between 3D surfaces under small nonrigid motion. A vector point function is utilized as the motion parameter, called the displacement function. Differential-geometric changes ...

Fibonacci-Type Polynomials as a Trajectory of a Discrete Dynamical System (Matthew He, Davis P. Simon and Paolo E. Ricci) Rendiconti Del Circolo Matematico Di Palermo (2002)

Families of polynomials which obey the Fibonacci recursion relation can be generated by repeated iterations of a 2×2 matrix,Q2, acting on an initial value matrix,R2. One matrix fixes the recursion relation, while the other one ...

Differential Equation of Appell Polynomials Via the Factorization Method (Matthew He and Paolo E. Ricci) Journal of Computational and Applied Mathematics (2002)

Let {Pn(x)}∞n=0 be a sequence of polynomials of degree n. We define two sequences of differential operators Φn and Ψn satisfying the following properties: By constructing these two operators for Appell polynomials, we determine their ...

Information entropy of orthogonal (Matthew He and P. E. Ricci) Applied Mathematics and Computation, (2002)

On Quadrature Rules Associated with Appell Polynomials (Gabriella Bretti, Matthew He and Paolo E. Ricci) International Journal of Applied Mathematics (2002)

A quadrature rule using Appell polynomials and generalizing both the Euler-MacLaurin quadrature formula and a similar quadrature rule, obtained in Bretti et al [15], which makes use of Euler (instead of Bernoulli) numbers and even ...

Double Helical Sequences and Doubly Stochastic Matrices (Matthew He) Symmetry: Culture and Science: Quarterly of the International Society for the Interdisciplinary Study of Symmetry (ISIS-Symmetry) (2001)

A Model of Balance of Payments Crisis: Monetary Independences as a Determinant of Exchange Rate Disequilibria (Ordean G. Olson and Matthew He) New York Economic Review (2000)

What factors determine a governmentís decision to abandon a currency peg or to continue to use a fixed exchange rate? This question may be logical when one recognizes that governments can borrow international reserves and ...

Relativistic Jacobi Polynomials (Matthew He and P. Natalini) Integral Transforms and Special Functions (1999)

A new polynomials set, of generalized hypergeometric type, is defined. These polynomials, called relativistic Jacobi polynomials (RJP) and denoted by represent an extension of the classical Jacobi orthogonal polynomials in the sense that they reduce ...

Asymptotics of Zeros of Relativistic Hermite Polynomials (Matthew He, K. Pan and Paolo E. Ricci) SIAM Journal on Mathematical Analysis (1997)

The relativistic Hermite polynomial (RHP) is a class of orthogonal polynomials associated with varying weights. We study the asymptotics of the zeros of the RHP when both degree $n$ of polynomials and relativistic parameter $N$ ...

Dynamics of the Zeros of Fibonacci Polynomials (Matthew He, David S. Simon and Paolo Emilio Ricci) Fibonacci Quarterly (1997)

Numerical Results on the Zeros of Generalized Fibonacci Polynomials (Matthew He, P. E. Ricci and D. S. Simon) Calcolo: A Quarterly on Numerical Analysis and Theory of Computation (1997)

We study some fundamental properties of generalized Fibonacci polynomials, by using the properties and characteristics of classical Fibonacci polynomials as a motivation. We derive the generating function and an explicit representation of these polynomials. A ...

The Relativistic Szego Polynomials (Matthew He, S. Noschese and P. E. Ricci) Integral Transforms and Special Functions (1997)

A new relativistic-type polynomiasl system is defined by means of the Relativistic Polynomial (RLP) system , recently introduced by P. Natalini. These polynomials, denoted by , are called Relativistic Generalized Hermite Polynomials (RGHP) because they ...

Zeros' Asymptotic Distribution of Polynomials Orthogonal with Respect to Varying Weights (Matthew He, P. E. Ricci and P. Natalini) Memoirs on Differential Equations and Mathematical Physics (1997)

By using the WKB method, we found the asymptotic distribution of the zeros of some sets of polynomials orthogonal with respect to varying weights, including the so called relativistic orthogonal polynomials.

Explicit Representations of Faber Polynomials for m-Cusped Hypocycloids (Matthew He) Journal of Approximation Theory (1996)

LetFn(z) be Faber polynomials associated with anm-cusped hypocycloid. We derive an explicit algebraic expression forFn(z) via a Cauchy integral formula. Using a differential equation ofFn(z), we precisely representFn(z) in terms of generalized hypergeometric functions.

Asymptotic Distribution of Zeros of Weighted Fibonacci Polynomials (Matthew He and Paolo E. Ricci) Complex Variables, Theory and Application: An International Journal (1996)

Exploiting the relation between the classical Fibonacci polynomials {F n(z)} and a certain weighted Faber polynomials {B n(z,g)} associated with a domain E in complex plane and a weight function g(z), we define weighted Fibonacci ...

The Faber Polynomials for Circular Lunes (Matthew He) Computers & Mathematics with Applications (1995)

We study the Faber polynomials Fn(z) generated by a circular lune symmetric about both axes with vertices at the points z = ±α (0 < α ≤ 2) and exterior angle απ. An explicit expression ...

On the Zeros of Weighted Faber Polynomials (Matthew He) Indian Journal of Mathematics (1995)

Let E be a compact set in the complex plane C containing more than one point and having simply connected complement in the extended complex plane C¯¯¯¯. Denote by Fn(z;g) the Faber polynomial of degree ...

Faber Polynomials for m-Fold Symmetric Domains (Matthew He) Journal of Computational and Applied Mathematics (1994)

The Faber polynomials for a region of the complex plane are of interest as a basis for polynomial approximations to analytic functions. In this paper we study the Faber polynomials associated with m-fold symmetric domains. ...

The Zeros of Faber Polynomials for An M-Cusped Hypocycloid (Matthew He and E. B. Saff) Journal of Approximation Theory (1994)

The Faber polynomials for a region of the complex plane are of interest as a basis for polynomial approximation of analytic functions. In this paper we determine the location, density, and asymptotic behavior of the ...

On Faber Polynomials Generated by an m-star (J. Bartolomeo and Matthew He) Mathematics of Computation (1994)

In this paper, we study the Faber polynomials generated by a regular m-star An explicit and precise expression for is obtained by computing the coefficients via a Cauchy integral formula. The location and limiting distribution ...