Simultaneous Determination of Rare Earth Elements by Dual-System Iterative Target Transformation Factor Analysis

Dualcolor systems were used to reduce the collinearity of multicomponent spectra, which is described by the angles between spectra vectors. Combined with iterative target transformation factor analysis, single rare earth element was determined in its mixture. The calculated results show that the average angle between rare earth spectra in one color system(trichloroarsenazorare earths, pH 34) is 45, and that in two color systems(trichloroarsenazorare earths, pH 34, 14) is 215. This technique makes it easy to select the real number of the components in mixtures, and the determination results show dualcolor system method is an effective technique in rare earth mixture analysis.

Reinforcement strength reduction in FEM for mechanically stabilized earth structures

The factor of safety of mechanically stabilized earth(MSE) structures can be analyzed either using limit equilibrium method(LEM) or strength reduction method(SRM) in finite element/difference method. In LEM, the strengths of the reinforcement members and soils are reduced with the same factor. While using the SRM, only soil strength is reduced during the calculation of the factor of safety. This causes inconsistence in calculating the factor of safety of the MSE structures. To overcome this, an iteration method is proposed to consider the strength reduction of the reinforcements in SRM. The method is demonstrated by using PLAXIS, a finite element software. The results show that the factor of safety converges after a few iterations. The reduction of strength has different effects on the factor of safety depending on the properties of the reinforcements and the soil, and failure modes.

Even factors with a bounded number of components in iterated line graphs

We consider even factors with a bounded number of components in the n-times iterated line graphs L^n(G). We present a characterization of a simple graph G such that L^n(G) has an even factor with at most k components, based on the existence of a certain type of subgraphs in G. Moreover, we use this result to give some upper bounds for the minimum number of components of even factors in L^n(G) and also show that the minimum number of components of even factors in L^n(G) is stable under the closure operation on a claw-free graph G, which extends some known results. Our results show that it seems to be NP-hard to determine the minimum number of components of even factors of iterated line graphs. We also propose some problems for further research.

An implicit algorithm based on iterative modified approximate factorization method coupling with characteristic boundary conditions for solving subsonic viscous flows

An algorithm composed of an iterative modified approximate factorization(MAF(k)) method with Navier-Stokes characteristic boundary conditions(NSCBC) is proposed for solving subsonic viscous flows.A transformation on the matrix equation in MAF(k) is made in order to impose the implicit boundary conditions properly.To be in consistent with the implicit solver for the interior domain,an implicit scheme for NSCBC is formulated.The performance of the developed algorithm is investigated using spatially evolving zero pressure gradient boundary layer over a flat plate and a wall jet mixing with a cross flow over a flat plate with a square hole as the test cases.The numerical results are compared to the existing experimental datasets and a number of general correlations,together with other available numerical solutions,which demonstrate that the developed algorithm possesses promising capacity for simulating the subsonic viscous flows with large CFL number.

ITERATIVE ILU PRECONDITIONERS FOR LINEAR SYSTEMS AND EIGENPROBLEMS

Iterative ILU factorizations are constructed,analyzed and applied as preconditioners to solve both linear systems and eigenproblems.The computational kernels of these novel Iterative ILU factorizations are sparse matrix-matrix multiplications,which are easy and efficient to implement on both serial and parallel computer architectures and can take full advantage of existing matrix-matrix multiplication codes.We also introduce level-based and threshold-based algorithms in order to enhance the accuracy of the proposed Iterative ILU factorizations.The results of several numerical experiments illustrate the efficiency of the proposed preconditioners to solve both linear systems and eigenvalue problems.