Production rates for various activities and overall construction project duration are significantly influenced by crew formation. Crews are composed of available renewable resources. Construction companies tend to reduce the number of permanent employees, which reduces fixed costs, but at the same time limits production capacity. Therefore, construction project planning must be carried out by means of scheduling methods which allow for resource constrains. Authors create a mathematical model for optimized scheduling of linear construction projects with consideration of resources and work continuity constraints. Proposed approach enables user to select optimal crew formation under limited resource supply. This minimizes project duration and improves renewable resource utilization in construction linear projects. This paper presents mixed integer linear programming to model this problem and uses a case study to illustrate it.

The paper presents a method of priority scheduling that is useful during the planning of multiple-structure construction projects. This approach is an extension of the concept of interactive scheduling. In priority scheduling, it is the planner that can determine how important each of the technological and organisational constraints are to them. A planner's preferences can be defined through developing a ranking list that defines which constraints are the most important, and those whose completion can come second. The planner will be able to model the constraints that appear at a construction site more flexibly. The article presents a general linear programming model of the planning of multiple-structure construction projects, as well as various values of each of the parameters that allow us to obtain different planning effects. The proposed model has been implemented in a computer program and its effectiveness has been presented on a calculation example.

New equivalent conditions of the asymptotical stability and stabilization of positive linear dynamical systems are investigated in this paper. The asymptotical stability of the positive linear systems means that there is a solution for linear inequalities systems. New necessary and sufficient conditions for the existence of solutions of the linear inequalities systems as well as the asymptotical stability of the linear dynamical systems are obtained. New conditions for the stabilization of the resultant closed-loop systems to be asymptotically stable and positive are also presented. Both the stability and the stabilization conditions can be easily checked by the so-called I-rank of a matrix and by solving linear programming (LP). The proposed LP has compact form and is ready to be implemented, which can be considered as an improvement of existing LP methods. Numerical examples are provided in the end to show the effectiveness of the proposed method.

Positively invariant sets play an important role in the theory and applications of dynamical systems. The stability in the sense of Lyapunov of the equilibrium x = 0 is equivalent to the existence of the ellipsoidal positively invariant sets. The constraints on the state and control vectors of dynamical systems can be formulated as polyhedral positively invariant sets in practical engineering problems. Numerical checking method of positive invariance of polyhedral sets is addressed in this paper. The validation of the positively invariant sets can be done by solving LPs which can be easily done numerically. It is illustrated by examples that our checking method is effective. Compared with the now existing algebraic methods, numerical checking method is an attractive method in that it’s easy to be implemented.

A certain non-linear differential equation containing a power of unknown function being the solution is considered with application to selected geotechnical problems. The equation can be derived to a linear differential equation by a proper substitution and properties of operations G and S.

In this paper we present results of systematic and comprehensive simulation analysis of the Tsao & Safonov unfalsified controller for complex robot manipulators. In particular, we show that the controller falsification procedure yields the closedloop unfalsified controller, which accomplishes the control objective, within a finite and relatively short time interval with the number of invocations of linear programming based unfalsified controller selection procedure being relatively small. We also present some conclusions resulting from the investigation of the effect of such elements as manipulator structure complexity, prior knowledge about disturbances, reference trajectory and assigned closed-loop spectrum on unfalsified controller performance and computational complexity.

This paper presents the current stage of the development of EA-MOSGWA – a tool for identifying causal genes in Genome Wide Association Studies (GWAS). The main goal of GWAS is to identify chromosomal regions which are associated with a particular disease (e.g. diabetes, cancer) or with some quantitative trait (e.g height or blood pressure). To this end hundreds of thousands of Single Nucleotide Polymorphisms (SNP) are genotyped. One is then interested to identify as many SNPs as possible which are associated with the trait in question, while at the same time minimizing the number of false detections.

The software package MOSGWA allows to detect SNPs via variable selection using the criterion mBIC2, a modified version of the Schwarz Bayesian Information Criterion. MOSGWA tries to minimize mBIC2 using some stepwise selection methods, whereas EA-MOSGWA applies some advanced evolutionary algorithms to achieve the same goal. We present results from an extensive simulation study where we compare the performance of EA-MOSGWA when using different parameter settings. We also consider using a clustering procedure to relax the multiple testing correction in mBIC2. Finally we compare results from EA-MOSGWA with the original stepwise search from MOSGWA, and show that the newly proposed algorithm has good properties in terms of minimizing the mBIC2 criterion, as well as in minimizing the misclassification rate of detected SNPs.

Given a linear discrete system with initial state x0 and output function yi , we investigate a low dimensional linear systemthat produces, with a tolerance index ǫ, the same output function when the initial state belongs to a specified set, called ǫ-admissible set, that we characterize by a finite number of inequalities. We also give an algorithm which allows us to determine an ǫ-admissible set.

For many years, a digital waveguide model is being used for sound propagation in the modeling of the vocal tract with the structured and uniform mesh of scattering junctions connected by same delay lines. There are many varieties in the formation and layouts of the mesh grid called topologies. Current novel work has been dedicated to the mesh of two-dimensional digital waveguide models of sound propagation in the vocal tract with the structured and non-uniform rectilinear grid in orientation. In this work, there are two types of delay lines: one is called a smaller-delay line and other is called a larger-delay line. The larger-delay lines are the double of the smaller delay lines. The scheme of using the combination of both smaller- and larger-delay lines generates the non-uniform rectilinear two-dimensional waveguide mesh. The advantage of this approach is the ability to get a transfer function without fractional delay. This eliminates the need to get interpolation for the approximation of fractional delay and give efficient simulation for sound wave propagation in the two-dimensional waveguide modeling of the vocal tract. The simulation has been performed by considering the vowels /ɔ/, /a/, /i/ and /u/ in this work. By keeping the same sampling frequency, the standard two-dimensional waveguide model with uniform mesh is considered as our benchmark model. The results and efficiency of the proposed model have compared with our benchmark model.

It is shown that in uncontrollable linear system ẋ = Ax + Bu it is possible to assign arbitrarily the eigenvalues of the closed-loop system with state feedbacks u = Kx, K ∈ ℜ^n⨉m if rank [A B] = n. The design procedure consists in two steps. In the step 1 a nonsingular matrix  M ∈ ℜ^n⨉m is chosen so that the pair (MA,MB) is controllable. In step 2 the feedback matrix K is chosen so that the closed-loop matrix A_c = A  − BK has the desired eigenvalues. The procedure is illustrated by simple example.

We consider the Debreu private ownership economy in which all consumption plans belong to a proper linear subspace of the commodity-price space ℝ^l. This geometric property of consumption sets means that there is a dependency between quantities of some commodities in all consumption plans. Competitive mechanism makes producers adjust their plans of action to the same dependency. It results in the mild evolution of the production sector to offer production plans which are also contained in the given subspace of ℝ^l. Modified production system and the initial consumption system can form an economy in equilibrium. The aim of this paper is to model gentle changes of producers’ activity that give equilibrium in the Debreu economy with consumption system reduced to a proper subspace of ℝ^l without considering additional costs.

Conditions for the positivity of linear electrical circuits composed of resistances, coils, capacitors and voltage (current) sources are established. It is shown that: 1) the electrical circuit composed of resistors, coils and voltage source is positive for any values of their resistances, inductances and source voltages if and only if the number of coils is less or equal to the number of its linearly independent meshes, 2) the electrical circuit is not positive for any values of its resistances, capacitances and source voltages if each its branch contains resistor, capacitor and voltage source, 3) the positive n-meshes electrical circuit with only one inductance in each linearly independent mesh is reachable if all resistances of branches belonging to two linearly independent meshes are zero.

The analysis of the positivity and stability of linear electrical circuits by the use of state-feedbacks is addressed. Generalized Frobenius matrices are proposed and their properties are investigated. It is shown that if the state matrix of an electrical circuit has generalized Frobenius form then the closed-loop system matrix is not positive and asymptotically stable. Different cases of modification of the positivity and stability of linear electrical circuits by state-feedbacks are discussed and necessary conditions for the existence of solutions to the problem are established.