There are two interesting methods, in the literature, for solving fuzzy linear programming problems in which the elements of coefficient matrix of the constraints are represented by real numbers and rest of the parameters are represented by symmetric trapezoidal fuzzy numbers. The first method, named as fuzzy primal simplex method, assumes an initial primal basic feasible solution is at hand. T...

Maize biomass from agricultural residues can be a substrate for biofuel production. However, commercial breeding programs have focused on grain yield food and feed, whole plant nutritive value silage, with little attention paid directly to stover or composition. Enhancing the energy content of crop higher quality cellulosic ethanol conversion should provide complementary use use. We also questi...

We develop a second order primal-dual method for optimization problems in which the objective function is given by sum of strongly convex twice differentiable term and possibly nondifferentiable regularizer. After introducing an auxiliary variable, we utilize proximal operator nonsmooth regularizer to transform associated augmented Lagrangian into that once, but not twice, continuously differen...

Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. In this paper, we will introduce the secondary radical of a submodule $N$ of $M$ as the sum of all secondary submodules of $M$ contained in $N$, denoted by $sec^*(N)$, and explore the related properties. We will show that this class of modules contains the family of second radicals properly and can be regarded as a dual o...

The aim of the paper is to employ the dual numbers in the multi axes machine error modelling in order to apply the algebraic methods in computations. The calculus of higher order dual numbers allows us to calculate with the appropriate geometric parametrization effectively. We test the model on the phantom data based on the real machine tool. The results of our analysis are used for the geometr...

First, we consider a compact real-analytic irreducible subvariety M in a sphere and its dual variety M. We explain that two matrices of the second fundamental forms for both varieties M and M can be regarded as the inverse matrices of each other. Also generalization in hyperbolic space is explained.