For certain Dirichlet series almost surely(a.s.)of order(R) ρ∈(0,∞)in the right-halfplane,a.s.every point of the imaginary axis is a Borel point of order ρ+1 and with no finiteexoeptional value.
Reasoning expressions are those which express the reaasoning procedure by means ofonly deduction rules and the initial formulas(axioms or assumptions)without the helpof any intermediate results.They express the proced...Reasoning expressions are those which express the reaasoning procedure by means ofonly deduction rules and the initial formulas(axioms or assumptions)without the helpof any intermediate results.They express the procedure systematically,completely andconcisely.The deduction rules are mappings from formulas(premises)to formula(conclusion).The elementary rules are certain propositional connectives(but notnecessarily truth functions)while the higher rules are certain quantifiers.Besides,thedetachment rule is an inverse of the connective implication,and is itself the kernel ofdeduction method;while another inverse of implication(i.e.the suggestion rule)is thekernel of induction method.展开更多
The followunh results are proved in this paper1)If a real quadratic differential system has two strong foci,then around them therecannot appear(2n,2m)distribution of non-semi-stable limit cycles,where n and m arenatur...The followunh results are proved in this paper1)If a real quadratic differential system has two strong foci,then around them therecannot appear(2n,2m)distribution of non-semi-stable limit cycles,where n and m arenatural numbers.2)If a real quadratic differential system has two strong foci of different stability,then around them there cannot appear(2n,2m)distribution of non-semi-stable limitcycles,where n and m are natural numbers.展开更多
In this paper the author establishes the following1.If M^n(n≥3)is a connected Riemannian manifold,then the sectional curvatureK(p),where p is any plane in T^x(M),is a function of at most n(n-1)/2 variables.Moreprecis...In this paper the author establishes the following1.If M^n(n≥3)is a connected Riemannian manifold,then the sectional curvatureK(p),where p is any plane in T^x(M),is a function of at most n(n-1)/2 variables.Moreprecisely,K(p)depends on at most n(n-1)/2 parameters of group SO(n).2.Lot M^n(n≥3)be a connected Riemannian manifold.If there exists a point x ∈ Msuch that the sectional curvature K(p)is independent of the plane p∈T_x(M),then M is aspace of constant curvature.This latter improves a well-known theorem of F.Schur.展开更多
In this paper,singular integral equations with upper and lower translations arediscussed and the equivalence for solving them in and are shown.Equations with asingle pair of upper and lower translations are studied ...In this paper,singular integral equations with upper and lower translations arediscussed and the equivalence for solving them in and are shown.Equations with asingle pair of upper and lower translations are studied in detail.Their solutions as wellas the conditions of solvability are obtained.The method used consists of transferringthem to boundary value problems of analytic functions in upper and lower half-planesand then solving the latter.展开更多
In this paper,based on previous results,the Riemann-Hilbert boundary valueproblems with general forms for overdetermined elliptic equations of first order are consi-dered.The characteristic of modified function space ...In this paper,based on previous results,the Riemann-Hilbert boundary valueproblems with general forms for overdetermined elliptic equations of first order are consi-dered.The characteristic of modified function space is given.It is proved that there existsa unique solution for modified problem of the problem which we discuss.By the way,itis pointed out that there are great differences between overdetermined elliptic systems andfirst order elliptei systems in the plane.展开更多
基金Projects Supported by the National Natural Science Foundation of China.
文摘For certain Dirichlet series almost surely(a.s.)of order(R) ρ∈(0,∞)in the right-halfplane,a.s.every point of the imaginary axis is a Borel point of order ρ+1 and with no finiteexoeptional value.
文摘Reasoning expressions are those which express the reaasoning procedure by means ofonly deduction rules and the initial formulas(axioms or assumptions)without the helpof any intermediate results.They express the procedure systematically,completely andconcisely.The deduction rules are mappings from formulas(premises)to formula(conclusion).The elementary rules are certain propositional connectives(but notnecessarily truth functions)while the higher rules are certain quantifiers.Besides,thedetachment rule is an inverse of the connective implication,and is itself the kernel ofdeduction method;while another inverse of implication(i.e.the suggestion rule)is thekernel of induction method.
文摘The followunh results are proved in this paper1)If a real quadratic differential system has two strong foci,then around them therecannot appear(2n,2m)distribution of non-semi-stable limit cycles,where n and m arenatural numbers.2)If a real quadratic differential system has two strong foci of different stability,then around them there cannot appear(2n,2m)distribution of non-semi-stable limitcycles,where n and m are natural numbers.
基金Projects Supported by the Natural Science Funds of china.
文摘In this paper the author establishes the following1.If M^n(n≥3)is a connected Riemannian manifold,then the sectional curvatureK(p),where p is any plane in T^x(M),is a function of at most n(n-1)/2 variables.Moreprecisely,K(p)depends on at most n(n-1)/2 parameters of group SO(n).2.Lot M^n(n≥3)be a connected Riemannian manifold.If there exists a point x ∈ Msuch that the sectional curvature K(p)is independent of the plane p∈T_x(M),then M is aspace of constant curvature.This latter improves a well-known theorem of F.Schur.
基金Project Supported by the Natural Science Funds of National Committee of Science and Technology.
文摘In this paper,singular integral equations with upper and lower translations arediscussed and the equivalence for solving them in and are shown.Equations with asingle pair of upper and lower translations are studied in detail.Their solutions as wellas the conditions of solvability are obtained.The method used consists of transferringthem to boundary value problems of analytic functions in upper and lower half-planesand then solving the latter.
基金Supported by NSF and supported in part by Science and Technology Development Foundation of Shanghai.
文摘In this paper,based on previous results,the Riemann-Hilbert boundary valueproblems with general forms for overdetermined elliptic equations of first order are consi-dered.The characteristic of modified function space is given.It is proved that there existsa unique solution for modified problem of the problem which we discuss.By the way,itis pointed out that there are great differences between overdetermined elliptic systems andfirst order elliptei systems in the plane.
