1 Contribution to mathematical research
Li Guoping published his first work on the properties of Bessel functions at Sun Yat-sen University, and is famous at home and abroad for his outstanding work in function theory. In 1956, he attended the National 12-year Scientific Vision Planning Conference and was the drafter of the function theory plan. After 1958, he focused his main energy on the application of mathematics to the national economy and national defense construction, actively advocated research on the intersection of mathematics and other science and technology, and proposed the development idea of ??"one subject, two wings".
1.1 Contribution to the theoretical research of semipure functions and integral functions
In 1935, Li Guoping used Blumenthal functional types to conduct an in-depth analysis of infinite semipure functions and gave Nevanlinna's first The new form of the two fundamental theorems promoted the classic Picard-Borel theorem; the annual academic conference of the Japanese Society of Mathematical Physics was held, and Li Guoping was invited to give a report at the conference. He made an exception and accepted Li Guoping as a member of the Japanese Society of Mathematical Physics, and entered the ranks of international young mathematicians. .
Beginning in 1936, in order to standardize the semipure function class, he constructed a new functional type, skillfully proposed the unified theory of the Borel direction of the semipure function and the filled circle, and proposed and solved the problem of heavy values ??and Borel direction and other issues; summarized the theoretical results of the increasingly mature value line at that time.
1.2 Contribution to the study of quasi-analytic functions and function approximation theory
As early as 1939, Li Guoping began research on quasi-analytic function theory, and most of his results were recommended by Montel and published in " Proceedings of the French Academy of Sciences. Two of the closely related papers study a new quasi-analytic function family and a basic theorem of quasi-analytic function theory. They provide unified sequence regularization and function family regularization criteria, establish a new quasi-analytic function theory, and Based on this theory, some new families of accurate analytic functions were derived, and the relationship between the family of holomorphic functions H1 and quasi-analytic properties was demonstrated.
In 1948, he published a number of quasi-analytic criteria for almost periodic functions in the Science Quarterly of Wuhan University, and studied the application of this theory in quasi-analytic solutions to ordinary differential equations. . He is a pioneer in the field of quasi-analytic function and function approximation theory research.
1.3 Contribution to the research on the analytic theory of differential equations and Minkowski-Denjoy function theory
In 1954, he published a long paper on the semipure function Nevanlinna characteristic function T (r, f) and Connect the analytic theory of ordinary differential equations and establish the internal connection between the theory of differential equations and the theory of filled circles and convergence lines of semipure functions. In 1954, he was commissioned by the Ministry of Education to hold a differential equations workshop in Beijing, where he lectured on the theory of ordinary differential equations.
1.4 Contribution to the study of generalized Riemann geometry and mixed quantity analysis
In 1965, Li Guoping and his collaborators generalized the geometric theory of second-order partial differential equations by the great French mathematician Hadamard. Important contributions at a high level. This paper first establishes the generalized Riemann geometry and proves the consistency of the characteristic surface of the system of partial differential equations and the manifold composed of generalized 0-geodesics.
1.5 Contribution to the study of differential difference equations and operator function theory
Li Guoping attaches great importance to the theory and application of differential and difference equations, and has made a series of reports and written A series of papers; summarized in a monograph. In addition, he and his collaborators published many new ideas and important results on function theory in a comprehensive monograph published in 1983.
He has always attached great importance to the study of operator theory in infinite-dimensional spaces. In his monograph "Automorphic Functions and Minkowski Functions" he gave general principles and specific methods for obtaining generalized functions.
2 Contribution to mathematical and physical science research
He hopes to explore a path that connects mathematics with other disciplines. Since the 1960s, Li Guoping has repeatedly emphasized the importance of the work of Chen Shengshen and Yang Zhenning. The theory of relativity is a theory about the interaction of gravity. The gauge field can be regarded as a nonlinear extension of the Maxwell electromagnetic field. It is a basic theory about the four types of interactions (electromagnetic, weak, strong, and gravitational).
2.1 Contribution to the study of fiber bundle integrals and relativistic quantum field theory
In 1963, Li Guoping proposed that external motion should be described by general relativistic quantum field theory, and internal motion should be described by special relativity. The most general model of particles described by quantum field theory. The monograph constructs V(4) Riemann geometry, defines fiber bundle integrals, proves the isomorphism of two Lie algebras of L(4) and Spin(4), and proves that there is a unique fiber bundle integral of tensor-spinor mixing quantity. The existence theorem of fiber bundle integral and its smoothness are proved.
2.2 Contribution to the study of electromagnetic storm theory and mathematical seismology
In 1961, Li Guoping began to use electromagnetic hydrodynamics methods to study storm phenomena. In 1972, he and his collaborators developed the electromagnetic storm theory, which summarized many original results, including a large number of conservation laws, and theoretically explained the impact of magnetic mineral deposits on climate and other issues. These new works promote or supplement some of the international research and theories of magnetohydrodynamics.
In 1976, he began to study the propagation theory of various earthquake waves, studying the similarity with the principle of transmission lines; the results were summarized in the monograph published by him and his collaborators in 1978. This monograph is divided into three volumes: the above content is in the first volume; the second volume is mainly about the transplantation of electromagnetic solid dynamics and the establishment of statistical medium mechanics theory in earthquake research; the third volume is mainly about the approximate solutions of various earthquake mathematical models , numerical solutions and their inversion, especially the pioneering research results on seismic waveguides.
2.3 Contribution to the study of external differential forms and field theory
In 1964, Li Guoping proposed a notation that preserves the vector form in external differential forms. During the Cultural Revolution, the time suffix Continuing, it systematically discusses eight major contents in modern mathematical physics: Newton field, optical field, electromagnetic field, temperature field, solid mechanics field, fluid mechanics field, Einstein field and gauge field. After the Cultural Revolution, he was asked to rewrite Hodge's theory of harmonic integrals, Cartan's theory of external differential forms, and Cartan and Kahler's important theorems on the existence and degrees of freedom of solutions to general systems of equations in external differential forms, and write a book that partially reflected his eight major contents. .
2.4 Contribution to anisotropic band theory and statistical rock mass mechanics research
Since 1972, Li Guoping generalized the effective mass from a scalar to a tensor and used tensor analysis Systematically reconstructed the semiconductor energy band theory, detailed in the papers and monographs written by him and his collaborators. This is an extremely tedious and detailed work involving a large number of calculations; it tests the wisdom and patience of scientific and technological workers, and it has maintained its leading position in the world to this day.
Li Guoping has always been concerned about the construction of the Three Gorges Project and the preliminary scientific research and technical demonstration work of the Yangtze River Academy of Sciences. In 1964, in view of the randomness, dispersion and scale effect of physical point experimental data in geotechnical mechanics, he introduced the concept of geological points and proposed the theoretical framework of rock statistical mechanics.
2.5 Contribution to the study of perturbation theory and n-body problem
In his book "The n-body problem", Li Guoping studied the relativistic correction of the n-body problem in Newton's celestial mechanics. We obtained an accurate solution to the relativistic modified planetary motion of the two-body problem, and formulated a perturbation calculation for the relativistic modified motion of (n-1) planets that only considers the suction effect of the sun on the planets and ignores the attraction between planets. plan.
3 Contribution to systematic scientific research
In 1956, Premier Zhou Enlai personally proposed and presided over, and Li Guoping participated in the formulation of my country's "Twelve-Year Science and Technology Development Plan", which selected " "Computers, Electronics, Semiconductors, and Automation" are the four emergency measures of the "Development Plan", and computer research, production, and education development plans have been formulated. Our country's computer industry started from this, and to meet the needs of the development of automation and large-scale construction, systems engineering quietly emerged.
3.1 Contribution to digital technology and computer development
In 1959, the International Business Machines Corporation of the United States produced the first transistor computer "IBM7090". The second generation of computers - semiconductor transistor computers began to develop rapidly.
In 1958, the Institute of Computer Technology of the Chinese Academy of Sciences successfully trial-produced China's first general-purpose electronic computer. The 709 Research Institute led by him has made indelible and important contributions to national defense construction.
3.2 Contribution to large-scale projects and national defense construction
Since 1964, Li Guoping was invited to lead teachers and students Fan Wentao and other former WISCO Song Ruiyu and Liu Hanyu to participate in the digestion and absorption of early technologies, especially It was mathematical modeling that did a lot of the work. The project started in September 1974, and materials were put into the project at the end of 1978, and the test run was successful in both cases. From the autumn of 1974 to the autumn of 1975, Li Guoping led his students to participate in the technical demonstration work in the early stage of the Gezhouba Project construction. He proposed many new ideas for theoretical research on rock mass mechanics and engineering technology for the study of rock and soil mechanics.
3.3 Contribution to research on mathematical models and industrial automatic control
Li Guoping took the lead in going deep into the front line of production, studying mathematical models and modeling methods, and studying automatic control and system science. 1. Ancient Poetry
When Li Guoping was studying at Sun Yat-sen University, he also took ancient Chinese literature courses concurrently. He studied composing five-character ancient poems and gradually understood the three families of Cao, Ruan and Tao. He chose the word Mu Tao to express his admiration for Yuan Ming. During the Cultural Revolution, Li Guoping and his relatives, friends and students were accused of the most unjust case of the Chinese Academy of Sciences - the "Li Guoping National Treason Group Case". He was brutally criticized as the "principal culprit", and his assistants were unjustly sentenced to long sentences. After the Cultural Revolution, there is a poem "Remembering Ye Shuwu Qianjiang" (1972) that says:
If you laugh at yourself and your head turns gray, how can you live in vain again in this life?
The real gold that has been hammered and refined is there, waiting to be forged to answer the sound of the bells and drums.
He wrote directly that "when I was young, I had great ambitions and loved to listen to the morning bells." Li Guoping responded to his friends' (including his students') requests for poetry and calligraphy. He has written hundreds of poems over the past decades. Before the age of 40, he had compiled hundreds of ancient and modern poems into the "Mu Tao Shi Manuscript", which was destroyed during the Cultural Revolution. In 1990, Mr. Li's 80th birthday, he compiled "Selected Poems of Li Guoping" and was published by Wuhan University Press. The title on the cover page is:
The rose is fragrant silently at midnight, and the colored pen and ink are filled with light;
Hard work has not changed my lifelong wish, and a hundred poems have come true.
Professor Su Buqing, a famous mathematician, once wrote "Ode to the Qing Dynasty":
It is famous all over the world for its fresh sentences and the vertical and horizontal words as if they are spiritual.
I breathe out the rainbow and connect Guangyu, and use my colored pen to purify the world.
Traveling east, west, north and south, I fall asleep frequently in spring, summer, autumn and winter.
In my entire life, I have always preferred chanting. If I lose my pearls and jade, I will live in poverty.
As a preface to "Selected Poems of Li Guoping", it is sincere and genuine. Counting his poems, there are more than a thousand. There are hundreds of poems in "Haiqing Collection of Poems" and more than 200 poems in "Meixiangzhai Ci", all of which were written since 1958 and were later included in the aforementioned "Selected Poems of Li Guoping" published by Wuhan University Press.
2. The art of calligraphy and painting
Another aspect of Li Guoping's lifelong achievements is the large number of poems, calligraphy, paintings and music he wrote over the decades. His poems are based on five-character ancient poems. After 1983, he began to compose lyrics and devoted himself to the study of lyrics. He believed that lyrics were not poems, but actually poems. He first searched for poems from his poems, and then searched for poems from his poems. He wrote two books, "Collection of Poems in Ci" and "One Hundred Poems of Su Dongpo's Poems" to test his theory, which is a comprehensive review of poetry. It is not without evidence. . He also produced a large number of self-made songs, and worked hard to explore the development of Chinese poetry in terms of inheritance and development. Academician Li Guoping has published more than 100 papers and written more than 20 monographs.
Main papers 1. Li Guoping. Properties of the Bessel function - "Natural Science Quarterly of Sun Yat-sen University", 1930.
2. Li Guoping． On meromorphic functions of infinite order. Jap. J. Math. , 1935, 12:1-16.
3. Li Guopi Hg. On the unified theory of meromorphic functions． J. Fac. Univ. Tokyosect. , 1937, 13: 153-286.
4. Li Guoping． Sur les Valeurs multiples et les directions de Borel des fonc-tions meromorphis. C. R． Acad. Sci. , Paris, 1938, 209: 1548-1550.
5. Li Guoping． Surun theoreme fondamental dams la theoriedes fonctionsquasi-analytiques. C R. Acad. Sci. , Paris, 1939, 208: 1625-1627.
6. Li Guoping． Sur des nouvelles Classes quasi-analytiques des fonctions． Ibid, 1939, 208: 1783-1785.
7. Li Guoping. A new theory of nonlinear ordinary differential equations with characteristic functions - "Acta Mathematica Sinica", 1954 (4): 467-478.
8. Li Guoping. Привалов's theorem - "Journal of Natural Sciences of Wuhan University", 1956 (1): 5-10.
9. Li Guoping. Transformation form of Riesz's theorem - "Acta Mathematica Sinica", 1957, 7 (1): 128-131.
10. Li Guoping. A basic theorem in integral function interpolation method - "Acta Mathematica Sinica", 1957, 7(2): 268-270.
11. Li Guoping. Transformation form of Cauchy's inequality - "Acta Mathematica Sinica", 1957, 7(3): 340-345.
12. Li Guoping. Two basic principles and their extension in the theory of analytic function construction - "Acta Mathematica", 1957, 7(3): 327-339.
13. Li Guoping. Several issues in function theory - "Proceedings of the 30th Anniversary of the Founding of the Wuhan Branch of the Chinese Academy of Sciences", 1980.
14. Li Guoping. Fourier variation, Merlin variation and their applications. Institute of Computing Technology, Chinese Academy of Sciences, 1958.
15. Li Guoping. Application of external differential forms in mathematical physics (Ⅰ)-(Ⅲ). Report of the National Symposium on Mathematical Physics, 1977. His main works are "Function Theory Series"
"Mathematical Physics Series"
"Chinese Science in the Ten Years (Mathematics Part), 1949-1959"
"Promotion Application of Riemannian Geometry in Partial Differential Equations"
"Theory of Operator Functions"
"Theory of Abelian Functions"
"The n-body problem 》
"Convergence Line Theory of Semipure Functions"
"Automorphic Functions and Minkowski Functions"
"Modern Function Theory"
"Quasi-Analytical Function Theory"
"Analytical Theory of Differential Equations"
"The Theory of Electromagnetic Storms"
"Mathematical Seismology"
"General Relativity Quantum Field Theory"
"Conductors and Semiconductors"
"Mathematical Models and Industrial Automatic Control" (Volume 1-3)