Nanoindentation and high resolution electron backscatter diffraction(EBSD) were combined to examine the elastic modulus and hardness of α and β phases,anisotropy in residual elastic stress strain fields and distri...Nanoindentation and high resolution electron backscatter diffraction(EBSD) were combined to examine the elastic modulus and hardness of α and β phases,anisotropy in residual elastic stress strain fields and distributions of geometrically necessary dislocation(GND) density around the indentations within TA15 titanium alloy.The nano-indention tests were conducted on α and β phases,respectively.The residual stress strain fields surrounding the indentation were calculated through crosscorrelation method from recorded patterns.The GND density distribution around the indentation was calculated based on the strain gradient theories to reveal the micro-mechanism of plastic deformation.The results indicate that the elastic modulus and hardness for α p hase are 129.05 GPas and 6.44 GPa,while for β phase,their values are 109.80 GPa and 4.29 GPa,respectively.The residual Mises stress distribution around the indentation is relatively heterogeneous and significantly influenced by neighboring soft β phase.The region with low residual stress around the indentation is accompanied with markedly high a type and prismatic-GND density.展开更多
A crystal plasticity finite element(CPFE)model was established and 2D simulations were carried out to study the relationship between microvoids and the microplasticity deformation behavior of the dual-phase titanium a...A crystal plasticity finite element(CPFE)model was established and 2D simulations were carried out to study the relationship between microvoids and the microplasticity deformation behavior of the dual-phase titanium alloy under high cyclic loading.Results show that geometrically necessary dislocations(GND)tend to accumulate around the microvoids,leading to an increment of average GND density.The influence of curvature in the tip plastic zone(TPZ)on GND density is greater than that of the size of the microvoid.As the curvature in TPZ and the size of the microvoid increase,the cumulative shear strain(CSS)in the primaryα,secondaryα,andβphases increases.Shear deformation in the prismatic slip system is dominant in the primaryαphase.As the distance between the microvoids increases,the interactive influence of the microvoids on the cumulative shear strain decreases.展开更多
Let (X, Xk : k ≥ 1) be a sequence of extended negatively dependent random variables with a common distribution F satisfying EX 〉 0.Let τ be a nonnegative integer-valued random variable, independent of {X, Xk :...Let (X, Xk : k ≥ 1) be a sequence of extended negatively dependent random variables with a common distribution F satisfying EX 〉 0.Let τ be a nonnegative integer-valued random variable, independent of {X, Xk : k ≥ 1}. In this paper, the authors obtain the necessary and sufficient conditions for the random sums Sτ=∑n=1^τ Xn to have a consistently varying tail when the random number τ has a heavier tail than the summands, i.e.,P(X〉x)/P(τ〉x)→0 as x →∞.展开更多
We investigate oscillation of certain second order neutral dynamic equations of Emden-Fowler type with positive and negative coefficients. We use some different techniques and apply Riccati transformation to establish...We investigate oscillation of certain second order neutral dynamic equations of Emden-Fowler type with positive and negative coefficients. We use some different techniques and apply Riccati transformation to establish new oscillatory criteria which include two necessary and sufficient conditions. Moreover, we point out that how the power γ plays its role. Some interesting examples are given to illustrate the versatility of our results.展开更多
Let G be a discrete group, E1 and E2 be two subsets of G with E1 () E2, and e ∈ E2. Denote by TE1 and TE2 the associated Toeplitz algebras. In this paper, it is proved that the natural morphism γE2,E1 from TE1 to TE...Let G be a discrete group, E1 and E2 be two subsets of G with E1 () E2, and e ∈ E2. Denote by TE1 and TE2 the associated Toeplitz algebras. In this paper, it is proved that the natural morphism γE2,E1 from TE1 to TE2 exists as a C*-morphism if and only if E2 is finitely covariant-lifted by E1. Based on this necessary and sufficient condition, some applications are made.展开更多
Checking whether a given formula is an invariant at a given program location(especially,inside a loop) can be quite nontrivial even for simple loop programs,given that it is in general an undecidable property.This is ...Checking whether a given formula is an invariant at a given program location(especially,inside a loop) can be quite nontrivial even for simple loop programs,given that it is in general an undecidable property.This is especially the case if the given formula is not an inductive loop invariant,as most automated techniques can only check or generate inductive loop invariants.In this paper,conditions are identified on simple loops and formulas when this check can be performed automatically.A general theorem is proved which gives a necessary and sufficient condition for a formula to be an invariant under certain restrictions on a loop.As a byproduct of this analysis,a new kind of loop invariant inside the loop body,called inside-loop invariant,is proposed.Such an invariant is more general than an inductive loop invariant typically used in the Floyd-Hoare axiomatic approach to program verification.The use of such invariants for program debugging is explored;it is shown that such invariants can be more useful than traditional inductive loop invariants especially when one is interested in checking extreme/side conditions such as underflow,accessing array/collection data structures outside the range,divide by zero,etc.展开更多
Let {Xni} be an array of rowwise negatively associated random variables and Tnk=k∑i=1 i^a Xni for a ≥ -1, Snk =∑|i|≤k Ф(i/nη)1/nη Xni for η∈(0,1],where Ф is some function. The author studies necessary a...Let {Xni} be an array of rowwise negatively associated random variables and Tnk=k∑i=1 i^a Xni for a ≥ -1, Snk =∑|i|≤k Ф(i/nη)1/nη Xni for η∈(0,1],where Ф is some function. The author studies necessary and sufficient conditions of ∞∑n=1 AnP(max 1≤k≤n|Tnk|〉εBn)〈∞ and ∞∑n=1 CnP(max 0≤k≤mn|Snk|〉εDn)〈∞ for all ε 〉 0, where An, Bn, Cn and Dn are some positive constants, mn ∈ N with mn /nη →∞. The results of Lanzinger and Stadtmfiller in 2003 are extended from the i.i.d, case to the case of the negatively associated, not necessarily identically distributed random variables. Also, the result of Pruss in 2003 on independent variables reduces to a special case of the present paper; furthermore, the necessity part of his result is complemented.展开更多
The purpose of this paper is to derive some pointwise second-order necessary conditions for stochastic optimal controls in the general case that the control variable enters into both the drift and the diffusion terms....The purpose of this paper is to derive some pointwise second-order necessary conditions for stochastic optimal controls in the general case that the control variable enters into both the drift and the diffusion terms.When the control region is convex, a pointwise second-order necessary condition for stochastic singular optimal controls in the classical sense is established; while when the control region is allowed to be nonconvex, we obtain a pointwise second-order necessary condition for stochastic singular optimal controls in the sense of Pontryagin-type maximum principle. It is found that, quite different from the first-order necessary conditions,the correction part of the solution to the second-order adjoint equation appears in the pointwise second-order necessary conditions whenever the diffusion term depends on the control variable, even if the control region is convex.展开更多
The necessary and sufficient conditions are given so that a non-anticipative transformation in Hilbert space is isometric. In terms of second order Wiener process, these conditions assure that a non-anticipative trans...The necessary and sufficient conditions are given so that a non-anticipative transformation in Hilbert space is isometric. In terms of second order Wiener process, these conditions assure that a non-anticipative transformation of Wiener process is a Wiener process, too.展开更多
This paper investigates the controllability problem of time-variant linear stochastic controlsystems.A sufficient and necessary condition is established for stochastic exact controllability,whichprovides a useful alge...This paper investigates the controllability problem of time-variant linear stochastic controlsystems.A sufficient and necessary condition is established for stochastic exact controllability,whichprovides a useful algebraic criterion for stochastic control systems.Furthermore,when the stochasticsystems degenerate to deterministic systems,the algebraic criterion becomes the counterpart for thecomplete controllability of deterministic control systems.展开更多
文摘Nanoindentation and high resolution electron backscatter diffraction(EBSD) were combined to examine the elastic modulus and hardness of α and β phases,anisotropy in residual elastic stress strain fields and distributions of geometrically necessary dislocation(GND) density around the indentations within TA15 titanium alloy.The nano-indention tests were conducted on α and β phases,respectively.The residual stress strain fields surrounding the indentation were calculated through crosscorrelation method from recorded patterns.The GND density distribution around the indentation was calculated based on the strain gradient theories to reveal the micro-mechanism of plastic deformation.The results indicate that the elastic modulus and hardness for α p hase are 129.05 GPas and 6.44 GPa,while for β phase,their values are 109.80 GPa and 4.29 GPa,respectively.The residual Mises stress distribution around the indentation is relatively heterogeneous and significantly influenced by neighboring soft β phase.The region with low residual stress around the indentation is accompanied with markedly high a type and prismatic-GND density.
基金the National Key Research and Development Program of China(No.2021YFB3702603).
文摘A crystal plasticity finite element(CPFE)model was established and 2D simulations were carried out to study the relationship between microvoids and the microplasticity deformation behavior of the dual-phase titanium alloy under high cyclic loading.Results show that geometrically necessary dislocations(GND)tend to accumulate around the microvoids,leading to an increment of average GND density.The influence of curvature in the tip plastic zone(TPZ)on GND density is greater than that of the size of the microvoid.As the curvature in TPZ and the size of the microvoid increase,the cumulative shear strain(CSS)in the primaryα,secondaryα,andβphases increases.Shear deformation in the prismatic slip system is dominant in the primaryαphase.As the distance between the microvoids increases,the interactive influence of the microvoids on the cumulative shear strain decreases.
基金Project supported by the National Natural Science Foundation of China(No.11071182)
文摘Let (X, Xk : k ≥ 1) be a sequence of extended negatively dependent random variables with a common distribution F satisfying EX 〉 0.Let τ be a nonnegative integer-valued random variable, independent of {X, Xk : k ≥ 1}. In this paper, the authors obtain the necessary and sufficient conditions for the random sums Sτ=∑n=1^τ Xn to have a consistently varying tail when the random number τ has a heavier tail than the summands, i.e.,P(X〉x)/P(τ〉x)→0 as x →∞.
基金supported by National Natural Science Foundation of China (Grant No. 11271379)Guangzhou Postdoctoral Science Research Foundation Project (Grant No. gdbsh2014003)
文摘We investigate oscillation of certain second order neutral dynamic equations of Emden-Fowler type with positive and negative coefficients. We use some different techniques and apply Riccati transformation to establish new oscillatory criteria which include two necessary and sufficient conditions. Moreover, we point out that how the power γ plays its role. Some interesting examples are given to illustrate the versatility of our results.
基金Project supported by the National Natural Science Foundation of China (No.10371051).
文摘Let G be a discrete group, E1 and E2 be two subsets of G with E1 () E2, and e ∈ E2. Denote by TE1 and TE2 the associated Toeplitz algebras. In this paper, it is proved that the natural morphism γE2,E1 from TE1 to TE2 exists as a C*-morphism if and only if E2 is finitely covariant-lifted by E1. Based on this necessary and sufficient condition, some applications are made.
基金supported by NSFC-90718041NKBRPC-2005C B321902+1 种基金China Scholarship Council in Chinasupported by the National Science Foundation award CCF-0729097
文摘Checking whether a given formula is an invariant at a given program location(especially,inside a loop) can be quite nontrivial even for simple loop programs,given that it is in general an undecidable property.This is especially the case if the given formula is not an inductive loop invariant,as most automated techniques can only check or generate inductive loop invariants.In this paper,conditions are identified on simple loops and formulas when this check can be performed automatically.A general theorem is proved which gives a necessary and sufficient condition for a formula to be an invariant under certain restrictions on a loop.As a byproduct of this analysis,a new kind of loop invariant inside the loop body,called inside-loop invariant,is proposed.Such an invariant is more general than an inductive loop invariant typically used in the Floyd-Hoare axiomatic approach to program verification.The use of such invariants for program debugging is explored;it is shown that such invariants can be more useful than traditional inductive loop invariants especially when one is interested in checking extreme/side conditions such as underflow,accessing array/collection data structures outside the range,divide by zero,etc.
基金supported by the National Natural Science Foundation of China (No.10871146)the Spanish Ministry of Science and Innovation (No.MTM2008-03129)the Xunta de Galicia,Spain (No.PGIDIT07PXIB300191PR)
文摘Let {Xni} be an array of rowwise negatively associated random variables and Tnk=k∑i=1 i^a Xni for a ≥ -1, Snk =∑|i|≤k Ф(i/nη)1/nη Xni for η∈(0,1],where Ф is some function. The author studies necessary and sufficient conditions of ∞∑n=1 AnP(max 1≤k≤n|Tnk|〉εBn)〈∞ and ∞∑n=1 CnP(max 0≤k≤mn|Snk|〉εDn)〈∞ for all ε 〉 0, where An, Bn, Cn and Dn are some positive constants, mn ∈ N with mn /nη →∞. The results of Lanzinger and Stadtmfiller in 2003 are extended from the i.i.d, case to the case of the negatively associated, not necessarily identically distributed random variables. Also, the result of Pruss in 2003 on independent variables reduces to a special case of the present paper; furthermore, the necessity part of his result is complemented.
基金supported by the National Basic Research Program of China(973 Program)(Grant No.2011CB808002)National Natural Science Foundation of China(Grant Nos.11221101+4 种基金1123100711401404 and 11471231)the Program for Changjiang Scholars and Innovative Research Team in University(Grant No.IRT1273)the Changjiang Scholars Program from the Chinese Education Ministrythe Spanish Science and Innovation Ministry(Grant No.MTM2011-29306)
文摘The purpose of this paper is to derive some pointwise second-order necessary conditions for stochastic optimal controls in the general case that the control variable enters into both the drift and the diffusion terms.When the control region is convex, a pointwise second-order necessary condition for stochastic singular optimal controls in the classical sense is established; while when the control region is allowed to be nonconvex, we obtain a pointwise second-order necessary condition for stochastic singular optimal controls in the sense of Pontryagin-type maximum principle. It is found that, quite different from the first-order necessary conditions,the correction part of the solution to the second-order adjoint equation appears in the pointwise second-order necessary conditions whenever the diffusion term depends on the control variable, even if the control region is convex.
文摘The necessary and sufficient conditions are given so that a non-anticipative transformation in Hilbert space is isometric. In terms of second order Wiener process, these conditions assure that a non-anticipative transformation of Wiener process is a Wiener process, too.
基金supported by the National Natural Science Foundation under Grant Nos.60904029 and 60704002the State Key Laboratory under Grant No.RCS2008ZT002
文摘This paper investigates the controllability problem of time-variant linear stochastic controlsystems.A sufficient and necessary condition is established for stochastic exact controllability,whichprovides a useful algebraic criterion for stochastic control systems.Furthermore,when the stochasticsystems degenerate to deterministic systems,the algebraic criterion becomes the counterpart for thecomplete controllability of deterministic control systems.