趙育求

趙育求，男，博士，中山大學數學系教授。

基本介紹

• 中文名：趙育求
• 畢業院校：中山大學
• 學位/學歷：博士
• 專業方向：複分析和漸近分析
• 任職院校：中山大學

人物經歷

教育背景：中山大學 (理學博士,1994)

研究方向

複分析和漸近分析。

目前主要研究興趣包括: Riemann-Hilbert方法及其套用。隨機矩陣理論及其它數學物理問題。特殊函式與正交多項式。Painleve方程, Heun方程及相關差分方程。

教授課程

數學分析、複變函數

講授過的其它課程：數學物理方程、離散數學、泛函分析、泛函分析II等

學術成果

科研項目

國家基金面上項目（11971489），Painlevé方程及Heun方程的匹配問題和連線公式

國家基金面上項目（11571375），隨機矩陣理論與Painleve方程若干問題研究

國家基金面上項目（10871212），非交換最速下降法的一致漸近研究

國家基金面上項目（10471154），最速下降法及若干相關問題研究

論文

(with Shuai-Xia Xu) Gap probability of the circular unitary ensemble with a Fisher-Hartwig singularity and the coupled Painlev\'{e} V system. (arXiv:1907.11509)

(with Xiao-Min Huang and Yu Lin) Asymptotics of the Charlier polynomials via difference equation methods. (arXiv:1901.06041)

(with Xiao-Bo Wu and Shuai-Xia Xu) Gaussian unitary ensemble with boundary spectrum singularity and σ-form of the Painlevé II equation, Stud. Appl. Math., 140 (2018), 221–251. (arXiv:1706.03174)

(with Wen-Gao Long, Yu-Tian Li and Sai-Yu Liu) Real solutions of the first Painlevé equation with large initial data, Stud. Appl. Math., 139 (2017), 505–532. (arXiv:1612.01350)

(with R. Wong) Special functions, integral equations and Riemann-Hilbert problem, Proc. Amer. Math. Soc., 144 (2016), 4367–4380. (arXiv:1603.05357)

(with Xiao-Bo Wu, Yu Lin and Shuai-Xia Xu) Uniform asymptotics for discrete orthogonal polynomials on infinite nodes with an accumulation point, Anal. Appl. 14 (2016), 705–737. (arXiv:1410.3948)

(with Xiao-Bo Wu, Yu Lin and Shuai-Xia Xu) Plancherel-Rotach type asymptotics of the sieved Pollaczek polynomials via the Riemann-Hilbert approach, J. Approx. Theory 208 (2016), 21–58. (arXiv:1412.8580)

(with Shuai-Xia Xu and Dan Dai) Hankel determinants for a singular complex weight and the first and third Painlevé transcendents, J. Approx.Theory 205 (2016), 64-92. (arXiv:1509.07015)

(with Chun-Ru Zhao and Wen-Gao Long) Proof of a conjecture of Granath on optimal bounds of the Landau constants, J. Approx. Theory 204 (2016), 17-33.(arXiv:1505.00304)

(with Zhao-Yun Zeng) Application of uniform asymptotics to the connection formulas of the fifth Painlevé equation, Appl. Anal. 95 (2016), 390-404. (arXiv:1501.00337)

(with Zhao-Yun Zeng and Shuai-Xia Xu) Painlevé III asymptotics of Hankel determinants for a perturbed Jacobi weight, Stud. Appl. Math. 135 (2015), 347-376. (arXiv:1412.8586)

(with Shuai-Xia Xu) Critical edge behavior in the modified Jacobi ensemble and Painlevé equations, Nonlinearity 28 (2015) 1633-1674.(arXiv:1404.5105)

(with Shuai-Xia Xu and Dan Dai) Painlevé III asymptotics of Hankel determinants for a singularly perturbed Laguerre weight, J. Approx. Theory., 192 (2015) 1-18. (arXiv:1407.7334)

(with Shuai-Xia Xu and Dan Dai) Critical edge behavior and the Bessel to Airy transition in the singularly perturbed Laguerre unitary ensemble, Comm. Math. Phys. 332 (2014), 1257-1296. (arXiv:1309.4354)

(with Yutian Li, Saiyu Liu and Shuaixia Xu) Asymptotics of Landau constants with optimal error bounds, Constr. Approx. 40 (2014), 281-305. (arXiv:1309.4564)

(with Min-Hai Huang) High-frequency uniform asymptotics for the Helmholtz equation in a quarter-plane, Asymptot. Anal. 84 (2013), 1-15.

(with Shuai-Xia Xu) Critical edge behavior in the modified Jacobi ensemble and the Painlevé V transcendents, J. Math. Phys. 54 (2013), 083304, 29 pp.

(with Lihan Liu, Yuehai Qin and Yongzhi Xu) The uniqueness and existence of solutions for the 3D Helmholtz equation in a stratified medium with unbounded perturbation, Math. Methods Appl. Sci. 36 (2013), 2033-2047.

(with Sai-Yu Liu and R.Wong) Uniform treatment of Darboux's method and the Heisenberg polynomials, Proc. Amer. Math. Soc. 141 (2013), 2683-2691. (arXiv:1305.5044)

(with S.-X.Xu) Asymptotics of discrete Painlevé V transcendents via the Riemann-Hilbert approach, Stud. Appl. Math. 130 (2013), 201-231.

(with Yutian Li, Saiyu Liu and Shuaixia Xu) Full asymptotic expansions of the Landau constants via a difference equation approach, Appl. Math. Comput. 219 (2012), 988-995.

(with Lihan Liu, Yuehai Qin and Yongzhi Xu) The uniqueness and existence of solutions for the 3D Helmholtz equation in a step-index waveguide with unbounded perturbation, Math. Methods Appl. Sci. 35 (2012), 857-868.

(with Jian-Rong Zhou and Shuai-Xia Xu) Uniform asymptotics of a system of Szego class polynomials via the Riemann-Hilbert approach, Anal. Appl. 9 (2011), 447-480.

(with Min-Hai Huang) High-frequency asymptotics for the modified Helmholtz equation in a quarter-plane, Appl. Anal. 90 (2011), 1927-1938.

(with Shuai-Xia Xu and Jian-Rong Zhou) Universality for eigenvalue correlations from the unitary ensemble associated with a family of singular weights, J. Math. Phys. 52 (2011), 093302, 14 pp.

(with Jian-Rong Zhou) Asymptotic distributions of the zeros of certain classes of Gauss hypergeometric polynomials, Appl. Math. Comput. 218 (2011), 1153-1159.

(with Shuai-Xia Xu) Painlevé XXXIV asymptotics of orthogonal polynomials for the Gaussian weight with a jump at the edge, Stud. Appl. Math. 127 (2011), 67-105.

(with Shuai-Xia Xu) Resurgence relation and global asymptotic analysis of orthogonal polynomials via the Riemann-Hilbert approach, Sci. China Math. 54 (2011), 661-679.

(with Hong-Yong Wang) Uniform asymptotics and zeros of a system of orthogonal polynomials defined via a difference equation, J. Math. Anal. Appl. 369 (2010), 453-472.

(with R.Wong) Asymptotics of orthogonal polynomials via the Riemann-Hilbert approach, Acta Math. Sci. Ser. B Engl. Ed. 29 (2009), 1005-1034.

(with Jian-Rong Zhou) Uniform asymptotics of the Pollaczek polynomials via the Riemann-Hilbert approach, Proc. R. Soc. Lond. Ser. A 464 (2008), 2091-2112.

(with Xiao-Xi Bai) A uniform asymptotic expansion for Jacobi polynomials via uniform treatment of Darboux's method, J. Approx. Theory 148 (2007), 1-11.

(with Jian-Rong Zhou) An infinite asymptotic expansion for the extreme zeros of the Pollaczek polynomials, Stud. Appl. Math. 118 (2007), 255-279.

Uniform asymptotics for orthogonal polynomials via the Riemann-Hilbert approach, Appl. Anal. 85 (2006), 1165-1176.

(with Jian-Rong Zhou) Uniform asymptotic expansions of the Pollaczek polynomials, J. Comput. Appl. Math. 190 (2006), 37-56.

(with R.Wong) On a uniform treatment of Darboux's method, Constr. Approx. 21 (2005), 225-255.

(with R.Wong) Uniform asymptotic expansion of the Jacobi polynomials in a complex domain, Proc. R. Soc. Lond. Ser. A 460 (2004), 2569-2586.

(with R.Wong) Estimates for the error term in a uniform asymptotic expansion of the Jacobi polynomials, Anal. Appl. 1 (2003), 213-241.

A uniform asymptotic expansion of the single variable Bell polynomials, J. Comput. Appl. Math. 150 (2003), 329-355.

(with R.Wong) Exponential asymptotics of the Mittag-Leffler function, Constr. Approx. 18 (2002), 355-385.

(with R.Wong) Gevrey asymptotics and Stieltjes transforms of algebraically decaying functions, R. Soc. Lond. Proc. Ser. A 458 (2002), 625-644.

(with R.Wong) Smoothing of Stokes's discontinuity for the generalized Bessel function. II, R. Soc. Lond. Proc. Ser. A 455 (1999), 3065-3084.

(with R.Wong) Smoothing of Stokes's discontinuity for the generalized Bessel function, R. Soc. Lond. Proc. Ser. A 455 (1999), 1381-1400.

(with Wei Lin) Bi-analytic functions and their applications in elasticity, Partial differential and integral equations (Newark, DE, 1997), 233-247, ISAAC, 2, Kluwer Acad. Publ., Dordrecht, 1999.

(with Wei Lin) On the plane stress boundary value problem of quasi-static linear thermoelasticity, Acta Math. Appl. Sinica (English Ser.) 13 (1997), 385-394.

On the plane orthotropic stress problem of quasi-static thermoelasticity, J. Elasticity 46 (1997), 199-216.

(with Wei Lin and Yongzhi Xu) Normal modes analysis for sound waves in an ocean with an ice cap and a perfectly reflecting bottom, Appl. Anal. 63 (1996), 167-181.

An exact solution to the plane orthotropic elasticity problem with rectangular boundaries under arbitrary edge forces, Philos. Trans. Roy. Soc. London Ser. A 354 (1996), 2469-2511.

(with Wei Lin) Numerical solution to problems concerning quasi-static thermoelasticity, Appl. Anal. 57 (1995), 221-234.

(with Wei Lin) On the plane problem of orthotropic quasi-static thermoelasticity, J. Elasticity 41 (1995), 161-175.

On plane displacement boundary value problem of quasi-static linear thermoelasticity, Appl. Anal. 56 (1995), 117-129.

The proof of Goka's conjecture, IEEE Trans. Automat. Control 31 (1986), 972–973.