In this paper, we present the preconditioned mixed-type splitting iterative method for solving the linear systems, Ax = b, where A is a Z-matrix. And we give some comparison theorems to show that the convergence rate of the preconditioned mixed-type splitting iterative method is faster than that of the mixed-type splitting iterative method. Finally, we give a numerical example to illustrate our...

We describe a representation of linear mixed-effects models using a sparse semidefinite matrix. This representation provides for efficient evaluation of the profiled log-likelihood or profiled restricted loglikelihood of the model, given the relative precision parameters for the random effects. The evaluation is based upon the LDLT form of the Cholesky decomposition of the augmented sparse repr...

In this study, we investigated the effect of using large TiO2 nanoparticles in the matrix of small nanoparticles to improve the performance of dye-sensitized solar cells (DSSCs), as light scatter to increase the light harvesting. The mixed powder was deposited by electrophoretic deposition (EPD) on FTO (F-SnO2 coated glass). It is shown that adding small quantity of larger...

In this paper, we present an application of intuitionistic fuzzyprogramming to a two person bi-matrix game (pair of payoffs matrices) for thesolution with mixed strategies using linear membership and non-membershipfunctions. We also introduce the intuitionistic fuzzy(IF) goal for a choiceof a strategy in a payoff matrix in order to incorporate ambiguity of humanjudgements; a player wants to max...

For a generic n-degree polynomial system which contains n+1 polynomials in n variables, we give the construction of the generic mixed Cayley-Sylvester resultant matrix. There are n− 1 generic mixed Cayley-Sylvester resultant matrices between the classical Cayley resultant matrix and the classical Sylvester resultant matrix. The entries of these new resultant matrix are of degree m(1 < m < n + 1...

Four equivalent approaches of estimating variance components from mixed-model equations including the relationship matrix are presented. One procedure involves simultaneous diagonalization of the coefficient matrix (Z'MZ) and the inverse of the numerator relationship matrix (A-1). After simultaneous diagonalization, the absorbed coefficient matrix of the mixed-model equations is diagonal, so so...

– The Brunn-Minkowski theory is a central part of convex geometry. At its foundation lies the Minkowski addition of convex bodies which led to the definition of mixed volume of convex bodies and to various notions and inequalities in convex geometry. Its origins were in Minkowski’s joining his notion of mixed volumes with the Brunn-Minkowski inequality, which dated back to 1887. Since then it h...

Polysulfone-based mixed matrix membranes (MMMs) incorporated with silica nanoparticles are a new generation material under ongoing research and development for gas separation. However, the attributes of better-performing MMM cannot be precisely studied experimental conditions. Thus, it requires an atomistic scale study to elucidate separation performance silica/polysulfone MMMs. As most work em...

Mixed matrix membranes containing metal-organic frameworks have attracted large attention owing to the combined advantages of high separation performance and easy processability. In this work, CO2-philic zirconium metal organic framework UiO-66 and UiO-66-NH2 nanocrystals were synthesized and embedded into polyether block amide (PEBA) polymer membranes for CO2 separation. It can be found that a...