Department of Mathematical, Physical, and Engineering Sciences

Science and Technology Building, Room 311B

210-784-2262 |qhan@tamusa.edu

Dr. Han received his B.S. and first Ph.D. in pure mathematics from Shandong University, China in 2008, and his second Ph.D. in theoretic applied mathematics from Houston in 2012 under the guidance of Professor James Giles Auchmuty, who was a tenured professor of mathematics at Indiana University Bloomington, a fellow of the Australian Mathematical Society, and a former member of the Institute for Advanced Study (IAS) at Princeton University.

Dr. Han, prior to A&M-SA, held a 3-year postdoctoral scholar position at Worcester Polytechnic Institute. In addition, he had visiting experiences at Yamagata University, Japan (Aug 2006~Aug 2007); the Fields Institute at University of Toronto, Canada (Nov 2008); the Institute for Mathematics and Its Applications at University of Minnesota, Twin Cities (May~June 2014); and Purdue University (June 2015).

Dr. Han considers himself an entry-level mathematics researcher, believes the beauty of mathematics as the creation of God and enjoys learning mathematics, and now is interested in control and numerical analysis of partial differential equations, and Diophantine approximation and Nevanlinna theory.

Dr. Han is frequently invited as an anonymous referee for internationally well-recognized scientific journals, and has been serving as an appointed reviewer for the American Mathematical Society, MathSciNet since Oct 2013 with a number of important work assigned and reviewed. He has regularly presented research at the American Mathematical Society meetings, and currently serves as a member of the Texas Differential Equations Conference organizing committee.

Dr. Han has taught a wide range of courses in the U.S. including finite mathematics, college algebra, college algebra corequisite model, business algebra, business calculus, pre-calculus, the entire calculus series, mathematical structures and proofs, ordinary differential equations, linear algebra and matrices, discrete mathematics, real analysis, complex analysis, probability, statistics (both introductory and advanced), and calculus of variations.

Dr. Han uses Jesus Christ as the model in his teaching to serve students, and believes everyone can learn some mathematics. He is devoted to the inspiration and interaction with students for their appreciation of the distinctive beauty of mathematics, particularly interested in mentoring undergraduate projects that lead to good research work such as published in *Involve*.

Dr. Han serves in several A&M-SA capacities including as the MATH1314: College Algebra coordinator before Fall 2020 and the interim Mathematics Program coordinator in Fall 2020, as well as a member of three Quality Enhancement Plan (QEP) committees on Quantitative Reasoning (QR).

Dr. Han is married to Dr. Jingbo Liu (who is a mathematics researcher in algebra and number theory, and is a long-term collaborator in providing a good-quality education to our students), and currently they have one lovely daughter Jacquelyn https://apps.tamusa.edu/course-information/Profile/Faculty/394?=Jingbo-Liu Dr. Liu and Dr. Han are both the first generation college students (and blessed the first generation Ph.D.s) in their families.

**Doctoral Genealogy within 10 Generations: **https://www.genealogy.math.ndsu.nodak.edu/

Sir George Gabriel Stokes (University of Cambridge 1841, President of the Royal Society 1885-1890, Fellow of the Royal Society of Edinburgh) ↓

John William Strutt (University of Cambridge 1868, Fellow of the Royal Society, the Winner of the Nobel Prize in Physics 1904) ↓

Sir Joseph John Thomson (University of Cambridge 1883, President of the Royal Society 1915-1920, the Winner of the Nobel Prize in Physics 1906) ↓

Ernest Rutherford (University of Cambridge, Fellow of the Royal Society, Fellow of the Royal Society of Edinburgh, the Winner of the Nobel Prize in Chemistry 1908) ↓

Archibald Vivian Hill (University of Cambridge 1909, Fellow of the Royal Society, 1 of the 2 Winners of the Nobel Prize in Physiology or Medicine 1922) ↓

Sir Ralph Howard Fowler (University of Cambridge 1915, Fellow of the Royal Society, 1 of the 2 Winners of the Nobel Prize in Physics 1983) ↓

Subrahmanyan Chandrasekhar (University of Cambridge 1933, Fellow of the Royal Society, 2 of the 2 Winners of the Nobel Prize in Physics 1983) ↓

Norman Ronald Lebovitz (University of Chicago 1961) ↓

James Giles Auchmuty (University of Chicago 1970) ↓

Qi Han (University of Houston 2012)

All my publications follow the tradition in mathematics research listing authors on joint work in alphabetical order, with the exceptions accommodating some of my co-authors from China, Mainland due to unusual circumstances/practices (American Mathematical Society guidelines; mathematics authorship on wikipedia)

**• **Wei Chen, Qi Han and Qiong Wang. On generalized Fermat Diophantine functional and partial differential equations in * C^{2}*.

**•** Qi Han. Compact Sobolev-Slobodeckij embeddings and positive solutions to fractional Laplacian equations. *Advances in Nonlinear Analysis, 11 (2022), 432-453*. (DOI)

**•** Wei Chen and Qi Han. On entire solutions to eikonal-type partial differential equations. *Journal of Mathematical Analysis and Applications**, 506 (2022), Article 124704*. (DOI)

**•** Qi Han and Jingbo Liu. Algebraic differential independence regarding the Riemann ** ζ**-function and the Euler

**•** Qi Han. Compact Sobolev embeddings and positive solutions to a quasilinear equation with mixed nonlinearities. *Journal of Mathematical Analysis and Applications, 481 (2020), Article 123150**. *(DOI)

** Second Part:** Qi Han. Elliptic variational problems with mixed nonlinearities. *Mathematical Methods in the Applied Sciences, 43 (2020), 1675-1684. *(DOI)

**•** Wei Chen, Qi Han and Jingbo Liu. On Fermat Diophantine functional equations, little Picard theorem, and beyond. *Aequationes Mathematicae, 93 (2019), 425-432*. (DOI)

**• **Wei Chen and Qi Han. A non-integrated hypersurface defect relation for meromorphic maps over complete Kähler manifolds into projective algebraic varieties. *Kodai Mathematical Journal,* *41* *(2018),* *284-300*. (DOI)

** ****Please read and compare:** Do Duc Thai and Si Duc Quang. Non-integrated defect of meromorphic maps on Kähler manifolds. *Mathematische Zeitschrift, 292 (2019), 211-229*. https://link.springer.com/article/10.1007/s00209-018-2179-x

**• **Qi Han. Compact embedding results of Sobolev spaces and existence of positive solutions to quasilinear equations. *Bulletin* *des* *Sciences* *Mathématiques**,* *141* *(2017),* *46-71*. (DOI)

**• **Wei Chen, Qi Han and Jingjing Qu. On Cartan's theorem for linear operators. *Mathematische Nachrichten, 290 (2017), 2560-2566*. (DOI)

**• **Qi Han. Some uniqueness results related to ** L**-functions.

** Please read and compare:** Weichuan Lin and Katsuya Ishizaki. A "3IM+1CM'' result for periodic meromorphic functions. *Journal of Mathematical Analysis and Applications, 466 (2018), 726-732*. https://www.sciencedirect.com/science/article/pii/S0022247X18305018

**• **Qi Han. Compact embedding results of Sobolev spaces and positive solutions to an elliptic equation. *Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 146 (2016), 693-721*. (DOI)

**• **Qi Han. On the first exterior * p*-harmonic Steklov eigenvalue.

**• **Qi Han. Positive solutions of elliptic problems involving both critical Sobolev nonlinearities on exterior regions. *Monatshefte für Mathematik, 176 (2015), 107-141; addendum 177 (2015), 325-327*. (DOI1, DOI2)

**• **Qi Han. A hypersurface defect relation for a family of meromorphic maps on a generalized ** p**-parabolic manifold.

**• **Giles Auchmuty and Qi Han. Representations of solutions of Laplacian boundary value problems on exterior regions. *Applied Mathematics and Optimization, 69 (2014), 21-45*. (DOI)

**• **Giles Auchmuty and Qi Han. Spectral representations of solutions of linear elliptic equations on exterior regions. *Journal of Mathematical Analysis and Applications, 398 (2013), 1-10*. (DOI)

**• **Qi Han. A defect relation for meromorphic maps on generalized ** p**-parabolic manifolds intersecting hypersurfaces in complex projective algebraic varieties.

**• **Qi Han. On complex analytic solutions of the partial differential equation * (u_{z1})^{m} + (u_{z2})^{m} = u^{m}*.

** Please read and compare:** Feng Lü and Zhen Li. Meromorphic solutions of Fermat type partial differential equations. *Journal of Mathematical Analysis and Applications, 478 (2019), 864-873*. https://www.sciencedirect.com/science/article/pii/S0022247X19304664

**• **Xiaotian Bai and Qi Han. On a result of H. Fujimoto. *Kyoto Journal of Mathematics, 49 (2009), 631-643*. (DOI)

**• **Qi Han and Hongxun Yi. On the uniqueness problems of entire functions and their linear differential polynomials. *Kodai Mathematical Journal**, 30 (2007), 61-73*. (DOI)

**• **Qi Han, Seiki Mori and Kazuya Tohge. On results of H. Ueda and G. Brosch concerning the unicity of meromorphic functions. *Journal of Mathematical Analysis and Applications, 335 (2007), 915-934*. (DOI)

** **

Photo courtesy of **Randy Leyva** from RLP Photography.

**Office Hours for Spring 2022: ****Monday, Wednesday and Friday 8:00am-8:40am; Monday and Wednesday 3:45pm-4:45pm.**

**HAPC Advising for Spring 2022: Monday and Wednesday 10:00am-10:40am.**

**Math Major Advising for Spring 2022: Monday and Wednesday 2:00pm-3:30pm.**

Subject | Number | Section | Description | Term | Syllabus |
---|---|---|---|---|---|

MATH | 2313 | 2 | Calculus I | Spring 2022 | Syllabi |

MATH | 4390 | 1 | Advanced Topics in Mathematics | Spring 2022 | Syllabi |

MATH | 3325 | 1 | Intro to Mathematical Proofs | Spring 2022 | Syllabi |

MATH | 2313 | 1 | Calculus I | Spring 2022 | Syllabi |