This paper considers the differentiability of C 0 semigroups with respect to (w.r.t.) parameters contained in their infinitesimal generators.It is proved that the generalized continuity and strong differentiability ...This paper considers the differentiability of C 0 semigroups with respect to (w.r.t.) parameters contained in their infinitesimal generators.It is proved that the generalized continuity and strong differentiability of their infinitesimal generators w.r.t.parameters imply the differentiability of the C 0 semigroups.The results are applied to the differentiability of the solution of a linear delay differential equation w.r.t.its delays.展开更多
This paper proposes a new continuity model for engineering in rock masses and a new schematic method for reporting the engineering of rock continuity. This method can be used to evaluate the mechanics of every kind of...This paper proposes a new continuity model for engineering in rock masses and a new schematic method for reporting the engineering of rock continuity. This method can be used to evaluate the mechanics of every kind of medium;and is a new way to determine the mechanical parameters used in engineering design in rock masses. In the numerical simulation, the experimental parameters of intact rock were combined with the structural properties of field rock. Theexperimental results for orthogonally-jointed rock are given. The results included the curves of the stress-strain relationship of some rock masses, the curve of the relationship between the dimension Δ and the uniaxial pressure-resistant strength σc of these rock masses, and pictures of the destructive procedure of some rock masses in uniaxial or triaxial tests, etc. Application of the method to engineering design in rock masses showed the potential of its application to engineering practice.展开更多
The effect of adding Cr and Mg on the microstructure and properties of Cu−Ti alloys was examined.Cu−Ti−Cr−Mg alloys were fabricated using vacuum induction melting.The microstructure and phase composition of Cu−Ti−Cr−M...The effect of adding Cr and Mg on the microstructure and properties of Cu−Ti alloys was examined.Cu−Ti−Cr−Mg alloys were fabricated using vacuum induction melting.The microstructure and phase composition of Cu−Ti−Cr−Mg alloys in different aging states were characterized.Additionally,the hardness and electrical conductivity of the materials were investigated.Results show that the precipitation pattern in Cu−Ti−Cr−Mg alloys resembled that of binary Cu−Ti alloys,with Cr and Ti forming the intermetallic compound of Cr_(2)Ti during casting.The introduction of Cr and Mg increased the hardness of the alloy.Increasing the Mg content in the Cu−Ti−Cr−Mg alloy led to grain refinement and fast nucleation of continuous precipitates during the early aging stage.Moreover,the addition of Mg impeded discontinuous precipitate growth by segregating along the precipitate surfaces.Consequently,the Cu−4Ti−0.5Cr−1Mg alloy exhibited limited discontinuous precipitates at the grain boundaries and a gradual decline in hardness during the over-aging period.展开更多
文摘This paper considers the differentiability of C 0 semigroups with respect to (w.r.t.) parameters contained in their infinitesimal generators.It is proved that the generalized continuity and strong differentiability of their infinitesimal generators w.r.t.parameters imply the differentiability of the C 0 semigroups.The results are applied to the differentiability of the solution of a linear delay differential equation w.r.t.its delays.
文摘This paper proposes a new continuity model for engineering in rock masses and a new schematic method for reporting the engineering of rock continuity. This method can be used to evaluate the mechanics of every kind of medium;and is a new way to determine the mechanical parameters used in engineering design in rock masses. In the numerical simulation, the experimental parameters of intact rock were combined with the structural properties of field rock. Theexperimental results for orthogonally-jointed rock are given. The results included the curves of the stress-strain relationship of some rock masses, the curve of the relationship between the dimension Δ and the uniaxial pressure-resistant strength σc of these rock masses, and pictures of the destructive procedure of some rock masses in uniaxial or triaxial tests, etc. Application of the method to engineering design in rock masses showed the potential of its application to engineering practice.
基金supported by the National Natural Science Foundation of China(No.52201226)Fundamental Research Program of Shanxi Province,China(No.202103021223036)+1 种基金the Key Scientific Research Project in Shanxi Province,China(No.202102050201007)the special fund for Science and Technology Innovation Teams of Shanxi Province,China(No.202204051001004)。
文摘The effect of adding Cr and Mg on the microstructure and properties of Cu−Ti alloys was examined.Cu−Ti−Cr−Mg alloys were fabricated using vacuum induction melting.The microstructure and phase composition of Cu−Ti−Cr−Mg alloys in different aging states were characterized.Additionally,the hardness and electrical conductivity of the materials were investigated.Results show that the precipitation pattern in Cu−Ti−Cr−Mg alloys resembled that of binary Cu−Ti alloys,with Cr and Ti forming the intermetallic compound of Cr_(2)Ti during casting.The introduction of Cr and Mg increased the hardness of the alloy.Increasing the Mg content in the Cu−Ti−Cr−Mg alloy led to grain refinement and fast nucleation of continuous precipitates during the early aging stage.Moreover,the addition of Mg impeded discontinuous precipitate growth by segregating along the precipitate surfaces.Consequently,the Cu−4Ti−0.5Cr−1Mg alloy exhibited limited discontinuous precipitates at the grain boundaries and a gradual decline in hardness during the over-aging period.
