Assume that X and Y are real Banach spaces with the same finite dimension.In this paper we show that if a standard coarse isometry f:X→Y satisfies an integral convergence condition or weak stability on a basis,then t...Assume that X and Y are real Banach spaces with the same finite dimension.In this paper we show that if a standard coarse isometry f:X→Y satisfies an integral convergence condition or weak stability on a basis,then there exists a surjective linear isometry U:X→Y such that∥f(x)−Ux∥=o(∥x∥)as∥x∥→∞.This is a generalization about the result of Lindenstrauss and Szankowski on the same finite dimensional Banach spaces without the assumption of surjectivity.As a consequence,we also obtain a stability result forε-isometries which was established by Dilworth.展开更多
Anti-plane punch-through shear test and anti-planefour-point bending test are used to study the crack initiation and propagation under anti-plane shear (Mode Ⅲ) loading. The tensile and shear stresses at the crack ti...Anti-plane punch-through shear test and anti-planefour-point bending test are used to study the crack initiation and propagation under anti-plane shear (Mode Ⅲ) loading. The tensile and shear stresses at the crack tip are calculated by finite element method. The results show that under Mode Ⅲ loading the maximum principal stress σ1 at crack tip is smaller or a little larger than the maximum shear stress τmax. Since the tensile strength of brittle rock is much lower than its shear strength, σ1 is easy to reach its critical value before τmax reaches its critical value and thus results in Mode I fracture. The fracture trajectory is helicoid and the normal direction of tangential plane with the fractured helicoid is along the predicted direction of the maximum principal stress at the notch tip. It is further proved that Mode Ⅰ instead of Mode Ⅲ fracture occurs in brittle rock under Mode Ⅲ loading. The fracture mode depending on the fracture mechanism must be distinguished from the loading form.展开更多
Strain and stress were simulated using finite element method(FEM)for threeⅢ-V-on-Insulator(Ⅲ-VOI)structures,i.e.,InP/SiO2/Si,InP/Al2O3/SiO2/Si,and GaAs/Al2O3/SiO2/Si,fabricated by ion-slicing as the substrates for o...Strain and stress were simulated using finite element method(FEM)for threeⅢ-V-on-Insulator(Ⅲ-VOI)structures,i.e.,InP/SiO2/Si,InP/Al2O3/SiO2/Si,and GaAs/Al2O3/SiO2/Si,fabricated by ion-slicing as the substrates for optoelectronic devices on Si.The thermal strain/stress imposes no risk for optoelectronic structures grown on InPOI at a normal growth temperature using molecular beam epitaxy.Structures grown on GaAsOI are more dangerous than those on InPOI due to a limited critical thickness.The intermedia Al2O3 layer was intended to increase the adherence while it brings in the largest risk.The simulated results reveal thermal stress on Al2O3 over 1 GPa,which is much higher than its critical stress for interfacial fracture.InPOI without an Al2O3 layer is more suitable as the substrate for optoelectronic integration on Si.展开更多
基金Supported by National Natural Science Foundation of China(11731010 and 12071388)。
文摘Assume that X and Y are real Banach spaces with the same finite dimension.In this paper we show that if a standard coarse isometry f:X→Y satisfies an integral convergence condition or weak stability on a basis,then there exists a surjective linear isometry U:X→Y such that∥f(x)−Ux∥=o(∥x∥)as∥x∥→∞.This is a generalization about the result of Lindenstrauss and Szankowski on the same finite dimensional Banach spaces without the assumption of surjectivity.As a consequence,we also obtain a stability result forε-isometries which was established by Dilworth.
基金Project (50374073)supported by the National Natural Science Foundation of China project (2002032256)supported bythe Postdoctor Science Foundation of China
文摘Anti-plane punch-through shear test and anti-planefour-point bending test are used to study the crack initiation and propagation under anti-plane shear (Mode Ⅲ) loading. The tensile and shear stresses at the crack tip are calculated by finite element method. The results show that under Mode Ⅲ loading the maximum principal stress σ1 at crack tip is smaller or a little larger than the maximum shear stress τmax. Since the tensile strength of brittle rock is much lower than its shear strength, σ1 is easy to reach its critical value before τmax reaches its critical value and thus results in Mode I fracture. The fracture trajectory is helicoid and the normal direction of tangential plane with the fractured helicoid is along the predicted direction of the maximum principal stress at the notch tip. It is further proved that Mode Ⅰ instead of Mode Ⅲ fracture occurs in brittle rock under Mode Ⅲ loading. The fracture mode depending on the fracture mechanism must be distinguished from the loading form.
基金Project supported by the National Key Research and Development Program of China(Grant No.2017YFE0131300)the National Natural Science Foundation of China(Grant Nos.U1732268,61874128,11622545,61851406,11705262,and 61804157)+5 种基金the Frontier Science Key Program of the Chinese Academy of Sciences(Grant No.QYZDY-SSW-JSC032)the Chinese-Austrian Cooperative Research and Development Project(Grant No.GJHZ201950)the Science and Technology Innovation Action Plan Program of Shanghai,China(Grant No.17511106202)the Program of Shanghai Academic Research Leader,China(Grant No.19XD1404600)the Sailing Program of Shanghai,China(Grant Nos.19YF1456200 and 19YF1456400)the K C Wong Education Foundation(Grant No.GJTD-2019-11).
文摘Strain and stress were simulated using finite element method(FEM)for threeⅢ-V-on-Insulator(Ⅲ-VOI)structures,i.e.,InP/SiO2/Si,InP/Al2O3/SiO2/Si,and GaAs/Al2O3/SiO2/Si,fabricated by ion-slicing as the substrates for optoelectronic devices on Si.The thermal strain/stress imposes no risk for optoelectronic structures grown on InPOI at a normal growth temperature using molecular beam epitaxy.Structures grown on GaAsOI are more dangerous than those on InPOI due to a limited critical thickness.The intermedia Al2O3 layer was intended to increase the adherence while it brings in the largest risk.The simulated results reveal thermal stress on Al2O3 over 1 GPa,which is much higher than its critical stress for interfacial fracture.InPOI without an Al2O3 layer is more suitable as the substrate for optoelectronic integration on Si.
