In the paper a linear-quadratic optimization problem (LCTOR) with unseparated two-point boundary conditions is considered. To solve this problem is proposed a new sweep algorithm which increases doubles the dimension of the original system. In contrast to the well-known methods, here it refuses to solve linear matrix and nonlinear Riccati equations, since the solution of such multi-point optimi...

Design process is a key process in forming of product’s cost and if we notify to total design we will see all of the effective parameters in design activities. Design process is contented design planning, design inputs, design outputs, design review, design verification, design validation and design changes. This approach will help us to identify the cost parameters for managing, controlling an...

This chapter deals with constraint-based multidimensional modelling. The model we define integrates a constellation of facts and dimensions. Along each dimension, various hierarchies are possibly defined and the model supports multiple instantiations of dimensions. The main contribution is the definition of intra-dimension constraints between hierarchies of a same dimension as well as inter-dim...

Let $G$ be a simple connected graph. In this paper, Szeged dimension and PI$_v$ dimension of graph $G$ are introduced. It is proved that if $G$ is a graph of Szeged dimension $1$ then line graph of $G$ is 2-connected. The dimensions of five composite graphs: sum, corona, composition, disjunction and symmetric difference with strongly regular components is computed. Also explicit formulas of Sze...

1. Preliminaries In this section we list a few results from the literature that will be utilized in the proof of Theorem 1. Proposition 1 (Lemma 1 in (Ben-David et al., 2010)). Let d be the VC dimension of the hypothesis set H and S1, S2 be two i.i.d. samples of size n from D1 and D2 respectively. Then for any δ > 0 with probability at least 1− δ: disc(D1, D2)≤disc(S1, S2)+2 √ 2d log(2n) + log(...