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.
The interest of this paper lies in the estimates of solutions of the three kinds of Gronwail-Bihari integral inequalities:（Ⅰ） y（x）≤f（x）+sum from i=1 to n（g<sub>i</sub>（x）integral from n=0 to x（...The interest of this paper lies in the estimates of solutions of the three kinds of Gronwail-Bihari integral inequalities:（Ⅰ） y（x）≤f（x）+sum from i=1 to n（g<sub>i</sub>（x）integral from n=0 to x（h<sub>i</sub>（d）y（s）ds））,（Ⅱ） y（x）≤f（x）+g（x）φ（integral from n=0 to x（h（s）w（y（s））ds））（Ⅲ） y（x）≤f（x）+sum from i=1 to n(g<sub>i</sub>（x）integral from n=0 to a(h<sub>i</sub>（s）y（s）ds+g<sub>n+1</sub>φ(integral from n=0 to x(h<sub>n+1</sub>（s）w（y（t））ds)).The results include some modifications and generalizations of the results of D. Willett, U. D. Dhongade and Zhang Binggen. Furthermore, applying the conclusion on the above inequalities to a Volterra integral equation and a differential equation, the authors obtain some new better results.展开更多
Let φ be a normal function defined on [0, 1) and A^p(φ) Bergman space weighted with φ~p(|z|)/(1-|z|~2) for 1≤p<∞. The compactnesses of Toeplitz operaters on A^p(φ) are characterized by Carleson measures and o...Let φ be a normal function defined on [0, 1) and A^p(φ) Bergman space weighted with φ~p(|z|)/(1-|z|~2) for 1≤p<∞. The compactnesses of Toeplitz operaters on A^p(φ) are characterized by Carleson measures and operator algebra.展开更多
In this paper, we consider an initial value problem for nonlinear integro-differential equations in a Banach space. First, we give a comparison result between the under and over functions and some comparison principle...In this paper, we consider an initial value problem for nonlinear integro-differential equations in a Banach space. First, we give a comparison result between the under and over functions and some comparison principles. Then, using these results and the Kuratowski measure of noncompactness, we establish the existence theorem of extremal solutions between the under and over functions, and prove that there exists a unique solution between the lower and upper solutions under an additional Lipschitz's condition.展开更多
In this paper,the author establishes the concepts of relative self-compatibility andrelative finite derivability of languages and obtains the relation between self-compatibilityand relative self-compatibility.From thi...In this paper,the author establishes the concepts of relative self-compatibility andrelative finite derivability of languages and obtains the relation between self-compatibilityand relative self-compatibility.From this it is proved that a family of languages isnondeterministically recognizable if and only if it is relatively self-compatible andrelatively finitely derivable to some set of families of langugaes.展开更多
In this paper the concept △-context is introduced,as a generalization of MoritaContext,to give a characterization of nonsingularly relative primitive rings.
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The interest of this paper lies in the estimates of solutions of the three kinds of Gronwail-Bihari integral inequalities:（Ⅰ） y（x）≤f（x）+sum from i=1 to n（g<sub>i</sub>（x）integral from n=0 to x（h<sub>i</sub>（d）y（s）ds））,（Ⅱ） y（x）≤f（x）+g（x）φ（integral from n=0 to x（h（s）w（y（s））ds））（Ⅲ） y（x）≤f（x）+sum from i=1 to n(g<sub>i</sub>（x）integral from n=0 to a(h<sub>i</sub>（s）y（s）ds+g<sub>n+1</sub>φ(integral from n=0 to x(h<sub>n+1</sub>（s）w（y（t））ds)).The results include some modifications and generalizations of the results of D. Willett, U. D. Dhongade and Zhang Binggen. Furthermore, applying the conclusion on the above inequalities to a Volterra integral equation and a differential equation, the authors obtain some new better results.
基金Supported by Doctoral Program Foundation of Higher Education.
文摘Let φ be a normal function defined on [0, 1) and A^p(φ) Bergman space weighted with φ~p(|z|)/(1-|z|~2) for 1≤p<∞. The compactnesses of Toeplitz operaters on A^p(φ) are characterized by Carleson measures and operator algebra.
基金Project supported by the Natural Science Foundation of Shandong Province.
文摘In this paper, we consider an initial value problem for nonlinear integro-differential equations in a Banach space. First, we give a comparison result between the under and over functions and some comparison principles. Then, using these results and the Kuratowski measure of noncompactness, we establish the existence theorem of extremal solutions between the under and over functions, and prove that there exists a unique solution between the lower and upper solutions under an additional Lipschitz's condition.
基金This work was supported in part by Beijing-Hong Kong Academic Exchange Centre.
文摘In this paper,the author establishes the concepts of relative self-compatibility andrelative finite derivability of languages and obtains the relation between self-compatibilityand relative self-compatibility.From this it is proved that a family of languages isnondeterministically recognizable if and only if it is relatively self-compatible andrelatively finitely derivable to some set of families of langugaes.
文摘In this paper the concept △-context is introduced,as a generalization of MoritaContext,to give a characterization of nonsingularly relative primitive rings.
