Secondary Metabolites of Elaeagnus thunbergii

Chemistry of Natural Compounds -     

Endochronic analysis for finite elasto-plastic deformation and application to metal tube under torsion and metal rectangular block under biaxial compression

The ordinary differential constitutive equations of endochronic theory are extended to simulate elasto-plastic deformation in the range of finite strain using the concept of corotational rate. Different corotational stress rates (Jaumann, Cotter-Rivlin, Truesdell, Dienes and Mandel) are incorporated into the theory. In addition, a new formulation of the plastic spin, which can be used in the Mandel stress rate, is derived. Theoretical simulations of the axial effects for various materials subjected to simple and pure torsional loading cases are discussed in this study. It is shown that the endochronic theory incorporated with the Mandel stress rate yields the most satisfactory result, as indicated from comparison with the experimental data found in literature.

Finally, theoretical investigation of the deformation subjected to finite proportional and non-proportional biaxial compression is presented. The true relationship between stress and strain can be converted to a nominal stress-strain relationship for biaxial loading through the explicit transformation equations derived in this paper. Experimental data tested by Khan and Wang [1990] (“An Experimental study of Large finite Plastic Deformation in Annealed 1100 Aluminum During Proportional and Non-proportional Biaxial Compression” Int. J. Plasticity, 6, 485) are suitably described by the theory demonstrated from a comparison with the theoretical prediction according to rigid-plastic and elastic-plastic models employed by Huang and Khan [1991]. “An Analysis of Finite Elastic-Plastic Deformation under Biaxial Compression”, Int. J. Plasticity, 7, 219).     

A phenomenological theory for elastic superconductors

The purpose of the present study is to develop a phenomenological theory for elastic superconductors that is based on a rigorous thermodynamical internal variable theory in which the concept of complex internal variable is introduced to include the phase effect of quantum mechanics. Two phenomena of superconductivity, i.e., perfect conductivity and perfect diamagnetism, can be explained in the formulation. In the equilibrium state, this theory can be reduced to the well-known Ginzburg-Landau (GL) theory. Upon linearizing the field equations, boundary conditions and constitutive equations, the governing equations of the rigid-body state and the perturbed state are obtained. These equations then serve to analyze the effect of the hydrostatic deformation on the penetration depth, the GL coherence length and the critical field.     

DRDF analysis of wide-angle x-ray scattering of natural rubber

A differential radial distribution function (DRDF) of molten natural rubber (NR) was derived from its wide-angle x-ray scattering (WAXS) data. Three peaks with Bragg spacings 4.85, 2.31, and 1.23 Å corresponding, respectively, to interchain, C₁-C₃ and C₁ -C₂ distances are present in the corrected WAXS curve. The derived DRDF, which is shown to be greatly improved than the ones published so far, contains six peaks located at 1.51, 2.48, 3.98, 5.68, 10.65, and 15.25 Å. Maximum contributions of intramolecular atomic distances to the radial distribution peaks were estimated and compared with the experimental results. The comparison shows that the first three peaks are intramolecular in origin and the remaining peaks are predominantly due to intermolecular regularities. A periodicity of an approximately constant interval of 5.26 Å is found between the intermolecular peaks and is attributable to the organizations of more or less parallel chain segments in the material. This finding provided additional evidence for the presence of local lateral ordering to the extent of about 30 Å in molten-state natural rubber.     

Incorporating the learning effect into data envelopment analysis to measure MSW recycling performance

The effect of organizational learning, which results in continuous improvement of organizational performance over time, has been widely discussed. The cumulative learning effect may form as a source of intellectual capital. Thus far, the static data envelopment analysis (DEA) model has not been used to examine the longitudinal learning effect. Therefore, a two-stage approach is developed together with the estimation of a latent learning effect using time-series data; the estimated learning effect is then used as an input in the DEA Slacks-Based Measure (SBM) model. The proposed DEA SBM model can be used to investigate the efficiency of the organizational learning effect of Municipal Solid Waste (MSW) recycling systems.     

Uniform partition extensions,a generating functions perspective

In this paper, a bivariate generating function CF(x, y) =f(x)-yf(xy)1-yis investigated, where f(x)= n 0fnxnis a generating function satisfying the functional equation f(x) = 1 + r j=1 m i=j-1aij xif(x)j.In particular, we study lattice paths in which their end points are on the line y = 1. Rooted lattice paths are defined. It is proved that the function CF(x, y) is a generating function defined on some rooted lattice paths with end point on y = 1. So, by a simple and unified method, from the view of lattice paths, we obtain two combinatorial interpretations of this bivariate function and derive two uniform partitions on these rooted lattice paths.