27 citations · 62 across the 20 of their papers we have counts for
20 papers
Error bounds for the asymptotic expansions of the Jacobi polynomials
Xiao-Min Huang, Yu Lin, Xiang-Sheng Wang +1
This paper aims to derive explicit and computable error bounds for the asymptotic expansion of the Jacobi polynomials as their degree approaches infinity, using an integral method.…
Orthogonal polynomials with periodic recurrence coefficients
Dan Dai, Mourad E. H. Ismail, Xiang-Sheng Wang
In this paper, we study a class of orthogonal polynomials defined by a three-term recurrence relation with periodic coefficients. We derive explicit formulas for the generating fun…
Asymptotics, orthogonality relations and duality for the and -symmetric polynomials in the -Askey scheme
Howard S. Cohl, Roberto S. Costas-Santos, Xiang-Sheng Wang
In this survey we summarize the current state of known orthogonality relations for the and -symmetric and dual subfamilies of the Askey--Wilson polynomials in the -A…
Optimized sparse approximate inverse smoothers for solving Laplacian linear systems
Yunhui He, Jun Liu, Xiang-Sheng Wang
In this paper we propose and analyze new efficient sparse approximate inverse (SPAI) smoothers for solving the two-dimensional (2D) and three-dimensional (3D) Laplacian linear syst…
A Direct Parallel-in-Time Quasi-Boundary Value Method for Inverse Space-Dependent Source Problems
Yi Jiang, Jun Liu, Xiang-Sheng Wang
Inverse source problems arise often in real-world applications, such as localizing unknown groundwater contaminant sources. Being different from Tikhonov regularization, the quasi-…
A PDE-ODE Coupled Spatio-Temporal Mathematical Model for Fire Blight During Bloom
Michael Pupulin, Xiang-Sheng Wang, Messoud A Efendiev +2
Fire blight is a bacterial plant disease that affects apple and pear trees. We present a mathematical model for its spread in an orchard during bloom. This is a PDE-ODE coupled sys…
Error bounds for the asymptotic expansions of the Hermite polynomials
Wei Shi, Gergő Nemes, Xiang-Sheng Wang +1
In this paper, we present explicit and computable error bounds for the asymptotic expansions of the Hermite polynomials with Plancherel--Rotach scale. Three cases, depending on whe…
Supercritical Hopf Bifurcation of Cooperative Predation
Srijana Ghimire, Xiang-Sheng Wang
In this work, we conduct a rigorous analysis on the dynamics of a predator-prey model with cooperative predation. From the root classification of an algebraic equation, we derive e…
A well-conditioned direct PinT algorithm for first-and second-order evolutionary equations
Jun Liu, Xiang-Sheng Wang, Shu-Lin Wu +1
In this paper, we propose a direct parallel-in-time (PinT) algorithm for time-dependent problems with first- or second-order derivative. We use a second-order boundary value method…
Bivariate Lagrange interpolation at the checkerboard nodes
Lihua Cao, Srijana Ghimire, Xiang-Sheng Wang
In this paper, we derive an explicit formula for the bivariate Lagrange basis polynomials of a general set of checkerboard nodes. This formula generalizes existing results of bivar…
Optimal allocation of face masks during the COVID-19 pandemic: a case study of the first epidemic wave in the United States
Jun Liu, Xiang-Sheng Wang
In this paper, we propose a two-group SIR epidemic model to simulate the outcome of stay-at-home policy and wearing face masks during the first COVID-19 epidemic wave in the United…
Asymptotics of partition functions in a fermionic matrix model and of related -polynomials
Dan Dai, Mourad E. H. Ismail, Xiang-Sheng Wang
In this paper, we study asymptotics of the thermal partition function of a model of quantum mechanical fermions with matrix-like index structure and quartic interactions. This part…
Convergence rate for a Gauss collocation method applied to constrained optimal control
William W. Hager, Jun Liu, Subhashree Mohapatra +2
A local convergence rate is established for a Gauss orthogonal collocation method applied to optimal control problems with control constraints. If the Hamiltonian possesses a stron…
Convergence Rate for a Radau hp Collocation Method Applied to Constrained Optimal Control
William W. Hager, Hongyan Hou, Subhashree Mohapatra +1
For unconstrained control problems, a local convergence rate is established for an -method based on collocation at the Radau quadrature points in each mesh interval of the disc…
Uniform Asymptotics of Orthogonal Polynomials Arising from Coherent States
Dan Dai, Weiying Hu, Xiang-Sheng Wang
In this paper, we study a family of orthogonal polynomials arising from nonlinear coherent states in quantum optics. Based on the three-term recurrence relation only,…
Calculating the day of the week: null-days algorithm
Xiang-Sheng Wang
In this paper, we propose a new algorithm of calculating the day of the week for any given century, year, month and day in Gregorian calendar. We provide two simple formulas to con…
Plancherel-Rotach Asymptotics of Second-Order Difference Equations with Linear Coefficients
Xiang-Sheng Wang
In this paper, we provide a complete Plancherel-Rotach asymptotic analysis of polynomials that satisfy a second-order difference equation with linear coefficients. According to the…
Traveling Wave Phenomena in a Kermack-McKendrick SIR model
Haiyan Wang, Xiang-Sheng Wang
We study the existence and nonexistence of traveling waves of general diffusive Kermack-McKendrick SIR models with standard incidence where the total population is not constant. Th…
Plancherel-Rotach asymptotic expansion for some polynomials from indeterminate moment problems
Dan Dai, Mourad E. H. Ismail, Xiang-Sheng Wang
We study the Plancherel--Rotach asymptotics of four families of orthogonal polynomials, the Chen--Ismail polynomials, the Berg-Letessier-Valent polynomials, the Conrad--Flajolet po…
Global Asymptotics of the Meixner Polynomials
X. -S. Wang, R. Wong
Using the steepest descent method for oscillatory Riemann-Hilbert problems introduced by Deift and Zhou [Ann. Math. {\bf 137}(1993), 295-368], we derive asymptotic formulas for the…