This doctoral thesis is an extension and deepening of the early work of V. volterra (Vo 1terra) and others. He extended the first and second kinds of integral equations that mathematicians paid close attention to at that time to the form with differentiation. Then, the integral differential equation is transformed into the second kind of integral equation by using the integral transformation formula established by boekhoff. Under the given boundary conditions, he extended the application scope of the "limit process" method actively advocated by volterra, obtained the necessary and sufficient conditions for the existence and uniqueness of the solution of the integro-differential equation studied, and obtained the properties of the equation and its solution under the boundary conditions. In this paper, the properties of * * * yoke and self * * * yoke, and the properties of Green's function are also discussed by using limit method and spectrum theory.
After the defense was passed, Hu Mingfu submitted this doctoral thesis to the American Mathematical Society. Boekhoff and e, who were in charge of the American Mathematical Society at that time. Professor h Moore appreciates his work very much. 19 18 10 in June, this paper was published in the prestigious Journal of the American Mathematical Society (Volume 19, No.4).
Hu Mingfu's doctoral thesis occupies an important position in the history of modern mathematics in China. 1947, Li Zhongyan pointed out in the article "Arithmetic in China for 30 Years" that Hu Mingfu's doctoral thesis was "the earliest arithmetic paper published by China people in the United States". Professor Chen Shengshen, who has personally experienced and is familiar with the development of mathematics in China in the early 20th century, pointed out when talking about the situation of mathematics in China around 1927: "Only Mr. Hu Mingfu and Mr. Jiang Lifu (both of whom are at Harvard) in China have obtained their doctorates abroad. Mr. Mingfu has made great contributions to the organization of China Science Society and the publication of Science magazine. Unfortunately, he died soon after returning to China, and he could not make greater contribution to the development of mathematics in China. His thesis and Mr. Yu Dayou's thesis on mathematical logic seem to be the earliest articles published by China people in major foreign mathematical magazines. "
1928 Science magazine's special issue commemorating the first anniversary of Hu Mingfu's death (No.6, Volume 13), Mingfu's commemorative album edited by the Mathematical Physics Research Association of Datong University, reprinted his doctoral thesis in English. Yan Jici, a student of Hu Mingfu, also wrote an article "Analysis of Dr. Hu Mingfu's Thesis" for Science magazine. Hu Mingfu has a strong ideal of saving the country by science and cares about the future and destiny of the motherland. He initiated and established the "China Student Politics Research Association" at Cornell University in June of 19 12 1 year, together with overseas students from China, to do research on tax system. On June 19 14, 10, Hu Mingfu, Zhao Yuanren, Ren Hongjuan, Zhou Ren, Bing Zhi and Yang Xingfo, who were studying at Cornell University in the United States, decided to organize a science society and take the form of a company for the time being. They had to pay a share capital of five dollars as the capital for publishing magazines. Hu Mingfu, Ren Hongjuan and Yang Xingfo were entrusted to draft the prospectus. The articles of association they drafted are as follows: "Articles of association of the scientific society: (1) Name this society as the scientific society. (2) Purpose: Learn to establish the monthly magazine Science with the purpose of advocating science, advocating industry, investigating nouns and disseminating knowledge. " During the summer vacation of 19 14, Hu Mingfu, Ren Hongjuan and Zhao Yuanren wrote articles for Science day and night. During the summer vacation, Hu Mingfu wrote 10 articles for the first three issues of Science, covering many subjects, such as the law of gravity, the position of arithmetic in science, the world view of modern science, modern pure geometry, lightening (hydrogen) gas with alloys, flowering plants above snowflakes and so on. Hu Mingfu is also responsible for heavy editing work such as reviewing manuscripts, unifying formats, and modifying punctuation marks. He also serves as an accountant and manages finance. In less than a few months, the number of members of the Science Society has increased to more than 70, and its share capital has reached 500 US dollars. The manuscript of the magazine has been prepared for three issues, only to be distributed. 19 15 1 China's first comprehensive modern science magazine, Science Monthly, finally met the people of China. The magazine adopts international scientific symbols and is printed horizontally from left to right, which is common all over the world. It is widely selected, lively and refreshing, and is recognized as the most influential scientific magazine in China in the first half of the 20th century.
19 15 In the spring, the Council of Science Society appointed Hu Mingfu, Ren Hongjuan and Zou Bingwen to draft a new chapter. 10 year125 October, their draft articles of association were passed, and the science society was changed to "China science society". The purpose of China Science Society is to contact and study the academic circles, so as to draw a map of scientific development in China. Hu Mingfu was elected as a director of the first board of directors and concurrently served as an accountant (until 1925).
19 18, the Chinese science society moved back to the motherland from the United States, and Hu Mingfu continued to serve the Chinese science society. Hu Mingfu believes that their generation grew up in China, which is suffering greatly. In order to make China rich and strong, they must be willing to be "coolies" for China to open the way for science. In addition to serving the Chinese Science Society wholeheartedly, Hu Mingfu also wrote academic papers in Science magazine, introducing advanced western science and technology, and made many contributions to the dissemination of science. 1924, Wang, director of the Compilation Institute of Shanghai Commercial Press, hired Hu Mingfu as the director of the Mathematics Correspondence Society. Hu Mingfu contacted a group of math teachers in Nanjing and Shanghai, and together with several editors of the Commercial Press, he presided over the compilation of a number of popular math books. He also translated and published popular science books such as the Science Outline, and compiled teaching materials such as calculus and advanced analysis.
1965438+In July, 2008, in view of the confusion in the translation of scientific terms and terms imported from the West in recent years, the academic circles set up a scientific term review committee. Entrusted by the Science Society of China, Hu Mingfu and Jiang Lifu worked together to formulate mathematical terms (then called arithmetic terms). In order to do this work well, Hu Mingfu put forward many good suggestions, such as determining the standard of mathematical nouns, "the old names of Chinese and Japanese nouns that are barely available will remain the same, and they will be changed as appropriate if they are nominally irrelevant or have obstacles to the system", "calculating nouns, compiling a Chinese and western dictionary and index", and how to accurately translate nouns. Together with Jiang Lifu, He Lu, Hu Dunfu and Wu Zaiyuan, he investigated the terms of elementary geometry, plane triangle, analytic geometry, space geometry, projective geometry, algebra, calculus and function theory. In the preface of Arithmetic Terminology published by 1938, he wrote: "This article was written off, and Hu replied to Jiang Junlifu's meticulous work on arithmetic terminology, regretting his early death, but it was not completed." Mr. Jiang Lifu and later Mr. Jiang Zehan, who presided over the examination and approval of mathematical terms, have repeatedly mentioned Hu Mingfu's work in mathematical terms and spoke highly of it. Hu Mingfu once thought about how to develop science and put forward many original opinions, involving science and technology policy and philosophy of science. 19 15, Hu mingfu wrote a paper on the policy of sending overseas students in recent years-a report for ordinary citizens and people who are interested in studying abroad, and carefully studied the situation of sending overseas students in boxer indemnity since 1909. He believes that it is not a good policy for Tsinghua to dominate the university. Students should be selected within the scope of China, and everyone should not choose the length of study abroad, schools and majors before going abroad. He also analyzed the rise and fall of China and Japan from the study abroad policy, and proposed that the study abroad policy should be formulated from the perspective of the future and destiny of the country.
19 16, Hu Mingfu published "Scientific Methodology-Outline and Essentials of Scientific Method and Spirit", holding that scientific method is the essence of science. "Why is science different from others?" That is, in the Scientific Method, "the only spirit of scientific method is" seeking truth ","this spirit directly affects human thinkers, and it is nothing but superstition and obedience ",and thinks that it is this scientific spirit that China needs. On the issue of saving the country by science, he expounded the relationship between scientific realism and practicality, and refuted the view of developing science for quick success and instant benefit with facts in the history of science. In this article, he also introduced Poincare's scientific aesthetic thought and Mach's economic thinking principle.
In Methodology of Science II-Laws of Science, Hu Mingfu expounded his philosophy of science that was not noticeable in the West at that time. He pointed out: "scientific law (theory) is the truth of nature? There is a lot to study. " He came to the conclusion that scientific theory is only probabilistic, but a statistical law: "husband's scientific law is nothing more than the truth of the past." You can predict the future according to the past, purely assuming the principle, only based on past experience, the number of opportunities is very large, so you can rely on it. Husband is more important than the scientific law, that is, the machine depends on it. Later, he also pointed out in his papers "Probability Theory" and "Error Theory": "The application of scientific laws and regulations ... to the future belongs to the scope of probability. "