In this paper, solutions of Riemann boundary value problems with nodes are extended to the case where they may have singularties of high order at the nodes. Moreover, further extension is discussed when the free term ...In this paper, solutions of Riemann boundary value problems with nodes are extended to the case where they may have singularties of high order at the nodes. Moreover, further extension is discussed when the free term of the problem involved also possesses singularities at the nodes. As an application, certain singular integral equation is discussed.展开更多
In this article, by introducing characteristic singular integral operator and associate singular integral equations （SIEs）, the authors discuss the direct method of solution for a class of singular integral equation...In this article, by introducing characteristic singular integral operator and associate singular integral equations （SIEs）, the authors discuss the direct method of solution for a class of singular integral equations with certain analytic inputs. They obtain both the conditions of solvability and the solutions in closed form. It is noteworthy that the method is different from the classical one that is due to Lu.展开更多
This study addresses the morphometric variables that determine the sediment yield in Wadi AI-Arja through the analysis of the impact of different morphometric characteristics along the course of the valley on its sedi...This study addresses the morphometric variables that determine the sediment yield in Wadi AI-Arja through the analysis of the impact of different morphometric characteristics along the course of the valley on its sediment yield, as well as the analysis of spatial and formal dimensions and morphologies of the basin and its relationship to the sediment yield. The study also addresses the size of variation in the volume of sediment yield of the river tributaries that make up the water network of the valley under the differences of its mor- phometric and hydrological characteristics. The study found several results, most notably： The classification of Wadi AI-Arja basin according to the hypsometric integral value （72.1%） within an uneven topography, which in- creases the force of the erosive activity and the size of the sediment yield if the basin was exposed to moist climatic periods. The study also showed the presence of convergence in the intra-spaces between the river tributaries in the water network. This increases the volume of water flows when these tributaries meet with each other and thus increasing their erosive ability and sediment yield. The study also showed the presence of marked variation in the sediment yield of the river tributaries depending on the differences in its morphometric characteristics. The results of the step-wise regression analysis confirmed the importance of the morphometric and hydrological variables, and plant coverage in interpreting the variation in the size of the sediment yield of the river tributaries of different stream order in Wadi AI-Arja basin, where these variables interpreted 43% of the total variation, with statistical significance less than 0.05.展开更多
Under the appropriate hypotheses subject to the unknown function and the free term, by means of our Lemma, we prove the rationality of order at x = ∞ on two sides for the characteristic singular integral equations wi...Under the appropriate hypotheses subject to the unknown function and the free term, by means of our Lemma, we prove the rationality of order at x = ∞ on two sides for the characteristic singular integral equations with solutions having singularities of higher order on the real axis X. We transform the equations into solving equivalent Riemann boundary value problems with solutions having singularities of higher order and with additional conditions on X. The solutions and the solvable conditions for the former are obtained from the latter.展开更多
文摘In this paper, solutions of Riemann boundary value problems with nodes are extended to the case where they may have singularties of high order at the nodes. Moreover, further extension is discussed when the free term of the problem involved also possesses singularities at the nodes. As an application, certain singular integral equation is discussed.
基金Project was supported by RFDP of Higher Education and NNSF of China, SF of Wuhan University
文摘In this article, by introducing characteristic singular integral operator and associate singular integral equations （SIEs）, the authors discuss the direct method of solution for a class of singular integral equations with certain analytic inputs. They obtain both the conditions of solvability and the solutions in closed form. It is noteworthy that the method is different from the classical one that is due to Lu.
文摘This study addresses the morphometric variables that determine the sediment yield in Wadi AI-Arja through the analysis of the impact of different morphometric characteristics along the course of the valley on its sediment yield, as well as the analysis of spatial and formal dimensions and morphologies of the basin and its relationship to the sediment yield. The study also addresses the size of variation in the volume of sediment yield of the river tributaries that make up the water network of the valley under the differences of its mor- phometric and hydrological characteristics. The study found several results, most notably： The classification of Wadi AI-Arja basin according to the hypsometric integral value （72.1%） within an uneven topography, which in- creases the force of the erosive activity and the size of the sediment yield if the basin was exposed to moist climatic periods. The study also showed the presence of convergence in the intra-spaces between the river tributaries in the water network. This increases the volume of water flows when these tributaries meet with each other and thus increasing their erosive ability and sediment yield. The study also showed the presence of marked variation in the sediment yield of the river tributaries depending on the differences in its morphometric characteristics. The results of the step-wise regression analysis confirmed the importance of the morphometric and hydrological variables, and plant coverage in interpreting the variation in the size of the sediment yield of the river tributaries of different stream order in Wadi AI-Arja basin, where these variables interpreted 43% of the total variation, with statistical significance less than 0.05.
基金Supported by the National Natural Science Foundation of China (10471107)the Specialized Research Fund for the Doctoral Program of Higher Education of China (20060486001)
文摘Under the appropriate hypotheses subject to the unknown function and the free term, by means of our Lemma, we prove the rationality of order at x = ∞ on two sides for the characteristic singular integral equations with solutions having singularities of higher order on the real axis X. We transform the equations into solving equivalent Riemann boundary value problems with solutions having singularities of higher order and with additional conditions on X. The solutions and the solvable conditions for the former are obtained from the latter.
