Let G =（V, E） be a locally finite connected weighted graph, and ？ be the usual graph Laplacian. In this article, we study blow-up problems for the nonlinear parabolic equation ut = ？u ＋ f（u） on G. The blow-up p...Let G =（V, E） be a locally finite connected weighted graph, and ？ be the usual graph Laplacian. In this article, we study blow-up problems for the nonlinear parabolic equation ut = ？u ＋ f（u） on G. The blow-up phenomenons for ut = ？u ＋ f（u） are discussed in terms of two cases：（i） an initial condition is given;（ii） a Dirichlet boundary condition is given. We prove that if f satisfies appropriate conditions, then the corresponding solutions will blow up in a finite time.展开更多
Applying the Riemann-Roch theorem,we calculate the dimension of a kind of mero- morphicλ-differentials’ space on compact Riemann surfaces.And we also construct a basis of theλ-differentials’ space.As the main resu...Applying the Riemann-Roch theorem,we calculate the dimension of a kind of mero- morphicλ-differentials’ space on compact Riemann surfaces.And we also construct a basis of theλ-differentials’ space.As the main result,the Cauchy type of integral formula on compact Riemann surfaces is established.展开更多
Historically,Chinese characters were used throughout the East Asian region,giving rise to a common cultural sphere.Since early modern times,the written languages of East Asia have developed in a diversity of ways,shap...Historically,Chinese characters were used throughout the East Asian region,giving rise to a common cultural sphere.Since early modern times,the written languages of East Asia have developed in a diversity of ways,shaped by nation,geography and culture,among other factors.Strengthening research on the long-term history of East Asian cultural development is thus very necessary.Komine Kazuaki has long been engaged in the study of medieval Japanese literature.Over the past two decades,he has projected a holistic academic approach to the study of culture in East Asia,conducting comparative research on the classical East Asian cultures.This paper takes a methodological approach to the discussion of the subjects,methods,techniques and goals of such research.In the study of East Asian cultural exchange,comparison enables us to undertake holistic investigations;it is not simply a tactic for unilateral studies.The study of texts and of images can be mutually enhancing;for example,the Japanese emaki is a medium that mixes literature and painting.Methods of researching environmental literature provide new insights for re-interpreting classical and modern literary works.Lastly,we need to examine the value of classical East Asian literature from the standpoint of East Asia as a whole;this is an urgently needed direction in contemporary research in this field.展开更多
基金supported by the National Science Foundation of China(11671401)supported by the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China(17XNH106)
文摘Let G =（V, E） be a locally finite connected weighted graph, and ？ be the usual graph Laplacian. In this article, we study blow-up problems for the nonlinear parabolic equation ut = ？u ＋ f（u） on G. The blow-up phenomenons for ut = ？u ＋ f（u） are discussed in terms of two cases：（i） an initial condition is given;（ii） a Dirichlet boundary condition is given. We prove that if f satisfies appropriate conditions, then the corresponding solutions will blow up in a finite time.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10626054,10701077)the Knowledge Innovation Project of Chinese Academy of Sciences(Grant No.KJCX3-SYW-S03)the National Key Basic Research Project of China(Grant No.2004CB31800,2006CB805905)
文摘Applying the Riemann-Roch theorem,we calculate the dimension of a kind of mero- morphicλ-differentials’ space on compact Riemann surfaces.And we also construct a basis of theλ-differentials’ space.As the main result,the Cauchy type of integral formula on compact Riemann surfaces is established.
文摘Historically,Chinese characters were used throughout the East Asian region,giving rise to a common cultural sphere.Since early modern times,the written languages of East Asia have developed in a diversity of ways,shaped by nation,geography and culture,among other factors.Strengthening research on the long-term history of East Asian cultural development is thus very necessary.Komine Kazuaki has long been engaged in the study of medieval Japanese literature.Over the past two decades,he has projected a holistic academic approach to the study of culture in East Asia,conducting comparative research on the classical East Asian cultures.This paper takes a methodological approach to the discussion of the subjects,methods,techniques and goals of such research.In the study of East Asian cultural exchange,comparison enables us to undertake holistic investigations;it is not simply a tactic for unilateral studies.The study of texts and of images can be mutually enhancing;for example,the Japanese emaki is a medium that mixes literature and painting.Methods of researching environmental literature provide new insights for re-interpreting classical and modern literary works.Lastly,we need to examine the value of classical East Asian literature from the standpoint of East Asia as a whole;this is an urgently needed direction in contemporary research in this field.
