Cofinal elementary extensions

We investigate some properties of ordered structures that are related to their having cofinal elementary extensions. Special attention is paid to models of some very weak fragments of Peano Arithmetic.     

Genetic Algorithm for the Jump Number Scheduling Problem

This paper introduces genetic algorithms for the jump number scheduling problem. Given a set of tasks subject to precedence constraints, the problem is to construct a schedule to minimize the number of jumps. We show that genetic algorithms outperform the previously known Knuth and Szwarcfiter's exhaustive search algorithm when applied to some classes of orders in which no polynomial time algorithms exist in solving the jump number problem. Values for various parameters of genetic jump number algorithms are tested and results are discussed.     

Influence of chain extension on the compatibilization and properties of recycled poly(ethylene terephthalate)/linear low density polyethylene blends

Polymeric methylene diphenyl diisocyanate (PMDI) was added as chain extender to a blend of recycled poly(ethylene terephthalate) (R-PET) and linear low density polyethylene (LLDPE) with compatibilizer of maleic anhydride-grafted poly(styrene-ethylene/butadiene-styrene) (SEBS-g-MA). Hydroxyl end groups of PET can react with both isocyanate groups of PMDI and maleic anhydride groups of SEBS-g-MA, which are competing reactions during reactive extrusion. The compatibility and properties of the blends with various contents of PMDI were systemically evaluated and investigated. WAXD results and SEM observations indicated that chain extension inhibits the reaction between PET and SEBS-g-MA. As the PMDI content increased, the morphology of dispersed phase changed from droplet dispersion to rodlike shape and then to an irregular structure. The DSC results showed that the crystallinity of PET decreased in the presence of PMDI, and the glass transition temperature (T_g) of PET increased with addition of 0-0.7 w% PMDI. The impact strength of the blend with 1.1 w% PMDI increased by 120% with respect to the blend without PMDI, accompanied by only an 8% tensile strength decrease. It was demonstrated that the chain extension of PET with PMDI in R-PET/LLDPE/SEBS-g-MA blends not only decreased the compatibilization effect of SEBS-g-MA but also hindered the crystallization of PET.     

Strain hardening behavior of polymer blends with fibril morphology

We investigate the rheological behavior of the polymer blends with fibril morphology, with special focus on the effect of fibril morphology on the extensional properties under uniaxial extension. We add a small amount of the dispersed phase to the matrix, and control the blend morphology by changing the viscosity ratio. When the fibril morphology is maintained, the blend shows not only a significant increase of the extensional viscosity but the strain hardening behavior. The extensional viscosity increases depending on the aspect ratio of the fibers, while the strain hardening behavior originates from the restricted stretching of deformable fibers, which has been confirmed theoretically by introducing the concept of rigidity of the fiber. It suggests a way to induce the strain hardening behavior by introducing deformable fibrils into the matrix, that is, by the design of polymer blends with a small amount of dispersed phase such that the fibril structure is maintained.     

Creeping flow of viscoplastic materials through a planar expansion followed by a contraction

In this work, the creeping flow of a viscoplastic fluid through a planar channel with an expansion followed by a contraction is analyzed numerically. The solution of the conservation equations of mass and momentum is obtained via the finite volume method. In order to model the non-Newtonian behavior of the fluid, it was used the generalized Newtonian fluid constitutive equation. The viscosity function was the one proposed by Souza Mendes and Dutra [Souza Mendes, P.R., Dutra, E.S.S., 2004. Viscosity function for yield-stress liquids. Appl. Rheol. 14, 296–302]. The yielded and unyielded regions are obtained for several combinations of rheological parameters. The influence of these parameters on pressure drop through the cavity is also obtained and analyzed.     

A rigid line in a confocal elliptic inhomogeneity embedded in an infinite medium under antiplane shear

An effective method is developed and used to investigate the antiplane problem of a rigid line in a confocal elliptic inhomogeneity embedded in an infinite medium. The analytical solution is obtained. The proposed method is based upon the use of conformal mapping and the theorem of analytic continuation. Special solutions which are verified by comparison with existing ones are provided. Finally, the characteristics of stress singularity at the tip of the rigid line inhomogeneity are analyzed and the extension forces for the crack and the rigid line inhomogeneity are derived. The project supported by the National Natural Science Foundation of China, the State Education Commission Foundation and the Failure Mechanics Lab of SEdC.     

Pseudo global energy released locally by crack extension involving multiscale reliability

The energy release rate criterion, being mono scale by definition, is incompatible with the failure behavior of solids that are inherently dual, if not, multiscale. Time span of reliability is scale sensitive and can be addressed with consistency only by use of transitional functions that are designed to transform a function from one scale to another. A pseudo transitional energy release rate G^∗ is defined to address the cross-scaling properties of energy release rate. The reliability of such a function is found to fall quickly when the scale range deviates from that of micro-macro. In general, the time span of reliability based on G^* shortens considerably within the nano-micro and pico-nano scale ranges, resulting in fast turnover of system usability. Prediction accuracy tends to be scale range specific. Stress or strain based criteria are also mono scale. They may be adequate for some situations at the macroscopic scale, but can be ambiguous for multiscale problems. These situations are analyzed by application of the principle of least variance in conjunction with the R-integrals.Accelerated test data for the equivalent of 20 years’ fatigue crack growth in 2024-T3 aluminum panels were analyzed using the mutliscale reliability model. A time span plateau within the micro-macro range is from 8 to 17 years. This corresponds to the reliable portion of prediction, while the terminal 3 years are regarded as unreliable. A similar time span plateau were also found from 4 to 6 years within the nano-micro scale range. And an even smaller plateau hovering around 1.2 years were found for the pico-nano scale range. Time span of reliable prediction narrows with down sized scale range. The overlapping ends of the scale ranges are rendered unreliable as anticipated. These regions can be suppressed by the addition of meso scale ranges. Reference can be made to past discussions related to multiscaling and mesomechanics.     

A NEW METHOD TO DETERMINE THE R-CURVE OF CERAMICS-FRACTURE GRATING METHOD

The etching technique of the single-lined zero-thickness specimen grating is applied tothe surface of the SiC fiber toughening Si_3N_4 ceramic composite specimen.The position of the crackand the crack length during the process of crack extension when the load is applied and gradually in-creased can be determined by recording the output voltage value of the Wheatstone bridge in which theceramic specimen with the fracture grating on is located.The crack-growth-resistance(R-curve) of thismaterialis thus obtained.     

多小波采样定理的拓展

采样定理在数字信号通讯中发挥了十分重要的作用,因为信号通常由它的离散采样数据来恢复.Han Bin等人在[J.Comput.Appl.Math.,2009,227:254-270]中构造了广义插值加细函数向量.本文研究与广义插值加细函数向量有关的采样定理的拓展问题.具体而言,对于已知的广义插值d-加细函数向量φ=(φ_1,…,φ_r)~T,即φe(m/r+k)=δ_kδ_(e-1-m),k∈Z,m=0,1,…,r-1,e=1,…,r我们将构造一组函数{φ_(r+1),…,φ_(dr)},使得φ~ロ=(φ~T,φ_(r+1),…,φ_(dr))~T也是d-加细的,而且满足φ_e(m/(dr)+k)=δ_kδ_(θ_(d,r(e)-m))k∈Z,m=0,1,…,dr-1,e=r+1,…,dr,其中θ_(d,r(e))=e-r+R_(e-1-r,d-1),R_(e-1-r,d-1)=「(e-1-r)/(d-1)」.我们建立与φ~■有关的采样定理.显然,φ的多小波子空间采样定理的适用范围得到了拓展.给出φ~■的多小波子空间采样级数的截断误差估计.     

Ore Extensions of Quasi-Baer Rings

We first study the quasi-Baerness of R[x; σ, δ] over a quasi-Baer ring R when σ is an automorphism of R, obtaining an affirmative result. We next show that if R is a right principally quasi-Baer ring and σ is an automorphism of R with σ(e) = e for any left semicentral idempotent e ∈ R, then R[x; σ, δ] is right principally quasi-Baer. As a corollary, we have that R[x; δ] over a right principally quasi-Baer ring R is right principally quasi-Baer. Finally, we give conditions under which the quasi-Baernesses (right principal quasi-Baernesses) of R and R[x; σ, δ] are equivalent.