In this article, we establish the Gauss Green type theorems for Clifford-valued functions in Clifford analysis. The boundary conditions in theorems obtained are very general by using the geometric measure theoretic me...In this article, we establish the Gauss Green type theorems for Clifford-valued functions in Clifford analysis. The boundary conditions in theorems obtained are very general by using the geometric measure theoretic method. The Cauchy-Pompeiu formula for Clifford-valued functions under the weak condition will be derived as their simple application. Furthermore, Cauchy formula for monogenic functions under the weak condition is derived directly from the Cauchy-Pompeiu formula.展开更多
In this paper, we discussed the problem of nonlocal value for nonlinear fractional q-difference equation. The classical tools of fixed point theorems such as Krasnoselskii’s theorem and Banach’s contraction principl...In this paper, we discussed the problem of nonlocal value for nonlinear fractional q-difference equation. The classical tools of fixed point theorems such as Krasnoselskii’s theorem and Banach’s contraction principle are used. At the end of the manuscript, we have an example that illustrates the key findings.展开更多
Characteristics of Mode I crack near the interface of elasticity matched but plasticity and strength mismatched materials differ from those of the crack in a homogenous body. Interface body of different strength influ...Characteristics of Mode I crack near the interface of elasticity matched but plasticity and strength mismatched materials differ from those of the crack in a homogenous body. Interface body of different strength influences the plastic or cohesive zone at the crack tip in parent body. The mathematical model for load line opening of the crack near the interface in linear elastic regime involves singular integrals. The paper presents explicit solution of these integrals with the help of Cauchy’s principal value theorem. Cases of thin and thick welds between the materials are investigated. Solutions of the integrals are well substantiated. Final results are provided in a consolidated form.展开更多
基金supported by NNSF of China(11171260)RFDP of Higher Education of China(20100141110054)
文摘In this article, we establish the Gauss Green type theorems for Clifford-valued functions in Clifford analysis. The boundary conditions in theorems obtained are very general by using the geometric measure theoretic method. The Cauchy-Pompeiu formula for Clifford-valued functions under the weak condition will be derived as their simple application. Furthermore, Cauchy formula for monogenic functions under the weak condition is derived directly from the Cauchy-Pompeiu formula.
文摘In this paper, we discussed the problem of nonlocal value for nonlinear fractional q-difference equation. The classical tools of fixed point theorems such as Krasnoselskii’s theorem and Banach’s contraction principle are used. At the end of the manuscript, we have an example that illustrates the key findings.
文摘Characteristics of Mode I crack near the interface of elasticity matched but plasticity and strength mismatched materials differ from those of the crack in a homogenous body. Interface body of different strength influences the plastic or cohesive zone at the crack tip in parent body. The mathematical model for load line opening of the crack near the interface in linear elastic regime involves singular integrals. The paper presents explicit solution of these integrals with the help of Cauchy’s principal value theorem. Cases of thin and thick welds between the materials are investigated. Solutions of the integrals are well substantiated. Final results are provided in a consolidated form.
