Quantitative law of diffusion induced fracture

Through dimension analysis, an almost analytical model for the maximum diffusion induced stress（DIS）and critical temperature（or concentration） difference at which cracks begin to initiate in the diffusion process is developed. It interestingly predicts that the spacing of diffusioninduced cracks is constant, independent of the thickness of specimen and the temperature difference. These conclusions are validated by our thermal shock experiments on alumina plates. Furthermore, the proposed model can interpret observed hierarchical crack patterns for high temperature jump cases, and a three-stage relation between the residual strength and the temperature difference. The prediction for crack spacing can guide the biomimetic thermal-shockfailure proof design, in which the hard platelets smaller than the predicted diffusion induced by constant crack-spacing are embedded in a soft matrix, and, therefore, no fracture will happen. This may guide the design of the thermal protection system and the lithium ion battery. Finally we present the maximum normalized DISes for various geometry and boundary conditions by single-variable curves for the stressindependent diffusion process and two-variable contour plots for the stress-dependent diffusion process, which can provideengineers and materialists a simple and easy way to quickly evaluate the reliability of related materials and devices.

Genetic Algorithms of Structural Fuzzy Reliability Index

In this paper the simple generation algorithms are improved. According to the geometric meaning of the structural reliability index, a method is proposed to deal with the variables in the standard normal space. With consideration of variable distribution, the correlation coefficient of the variables and its fuzzy reliability index, the feasibility and the reliability of the algorithms are proved with an example of structural reliability analysis and optimization.

Composition Cesàro Operator on the Normal Weight Zygmund Space in High Dimensions

Let n>1 and B be the unit ball in n dimensions complex space C^(n).Suppose thatφis a holomorphic self-map of B andψ∈H(B)withψ(0)=0.A kind of integral operator,composition Cesàro operator,is defined by T_(φ)ψ(f)(z)=∫^(1)0f[φ(tz)]Rψ(tz)dt/t,f∈(B)z∈B.In this paper,the authors characterize the conditions that the composition Cesàro operator T_φ,ψis bounded or compact on the normal weight Zygmund space Z_μ(B).At the same time,the sufficient and necessary conditions for all cases are given.

Composition operators on the normal weight Dirichlet type space in the unit disc

Let p>0 andνbe a normal function on[0,1).In this paper,several equivalent characterizations are given for which composition operators are bounded or compact on the normal weight Dirichlet type space D_(ν)^(p)(D)in the unit disc.

On Almost Isometric Embedding from C(Ω) into C_0(Ω_0)

In this paper we give the sufficient and necessary condition for the existence of any almost isometric operator from C（Ω） into C0（Ω0）. As a corollary, we show that there is no e-isometry from 1 any abstract M space with a strong unit into C0（Г） if 0 〈 e 〈 1/9.