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## Harmonogramowanie realizacji obiektów liniowych z ograniczoną dostępnością zasobów. = Scheduling linear construction projects with constraints on resource availability

### Abstract

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.
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## Model reduction problem of linear discrete systems: Admissibles initial states

### Abstract

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.
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## A comprehensive approach to double inverted pendulum modelling

### Abstract

The problem of mathematical modelling and indication of properties of a DIP has been investigated in this paper. The aim of this work is to aggregate the knowledge on a DIP modelling using the Euler-Lagrange formalism in the presence of external forces and friction. To indicate the main properties important for simulation, model parameters identification and control system synthesis, analytical and numerical tools have been used. The investigated properties include stability of equilibrium points, a chaos of dynamics and non-minimum phase behaviour around an upper position. The presented results refer to the model of a physical (constructed) DIP system.
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## Influence of different supply modes on the performance of linear induction motors

### Abstract

This paper deals with the modelling of traction linear induction motors (LIMs) for public transportation. The magnetic end effect inherent to these motors causes an asymmetry of their phase impedances. Thus, if the LIM is supplied from the three-phase symmetrical voltage, its phase currents become asymmetric. This effect must be taken into consideration when simulating the LIMs’ performance. Otherwise, when the motor phase currents are assumed to be symmetric in the simulation, the simulation results are in error. This paper investigates the LIM performance, considering the end-effect induced asymmetry of the phase currents, and presents a comparative study of the LIM performance characteristics in both the voltage and the current mode.
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## A new D-stability area for linear discrete-time systems

### Abstract

The paper addresses the problem of constrained pole placement in discrete-time linear systems. The design conditions are outlined in terms of linear matrix inequalities for the Dstable ellipse region in the complex Z plain. In addition, it is demonstrated that the D-stable circle region formulation is the special case of by this way formulated and solved pole placement problem. The proposed principle is enhanced for discrete-lime linear systems with polytopic uncertainties.
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## The application of selected methods of multidimensional comparative analysis to identify value determinants on the example of energy sector companies

### Abstract

The subject of the paper is the analysis of factors determining the value of multi-entity organizations in the energy sector and their ranking according to the degree of impact on this value. For this purpose, statistical methods were used, which are best suited to determine the order of diagnostic features according to a specific criterion. The survey covered companies from the Polish energy sector, while the process itself is based on aggregated data, which represents the financial data of capital groups currently operating in the Polish energy sector. The first part of the article presents a short description of the Polish energy sector, paying particular attention to the organizational structure of the sector, i.e. companies operating on the domestic energy market. The nature of a multi-entity enterprise as a typical economic unit in the sector is described. The second part of the article describes the assumptions of multidimensional comparative analysis (MCA) as a tool for comparing multifunctional units. The MCA makes it possible to find the most important parameters or indicators having the greatest impact on the value of a multi-entity organization, i.e. a capital group. The survey covered four companies from the Polish energy sector: TAURON Polska Energia SA, ENEA SA, ENERGA SA and PGE Polska Grupa Energetyczna SA. The study with the use of MCA was conducted in three stages: - in the first stage, on the basis of information contained in the financial statements, a matrix of diagnostic features was created, describing the financial condition of the examined entity, - in the second stage, the values of diagnostic variables were normalized/unified; two methods of normalization were applied: the method of standardization and zero unitization, - in the third stage, the diagnostic variables were grouped using two methods: the model measure of Hellwig’s development and the non-standard measure of development. The results of the analysis are illustrated by tables and figures.
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## Modelling and Measurement of Folk Guitar: Truss Rod and Strings in Numerical Analysis of Tone

### Abstract

The study makes an attempt to model a complete vibrating guitar including its non-linear features, specifically the tension-compression of truss rod and tension of strings. The purpose of such a model is to examine the influence of design parameters on tone. Most experimental studies are flawed by uncertainties introduced by materials and assembly of an instrument. Since numerical modelling of instruments allows for deterministic control over design parameters, a detailed numerical model of folk guitar was analysed and an experimental study was performed in order to simulate the excitation and measurement of guitar vibration. The virtual guitar was set up like a real guitar in a series of geometrically non-linear analyses. Balancing of strings and truss rod tension resulted in a realistic initial state of deformation, which affected the subsequent spectral analyses carried out after dynamic simulations. Design parameters of the guitar were freely manipulated without introducing unwanted uncertainties typical for experimental studies. The study highlights the importance of acoustic medium in numerical models.
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## Navigation complex with adaptive non-linear Kalman filter for unmanned flight vehicle

### Abstract

A navigation complex of an unmanned flight vehicle of small class is considered. Increasing the accuracy of navigation definitions is done with the help of a nonlinear Kalman filter in the implementation of the algorithm on board an aircraft in the face of severe limitations on the performance of the special calculator. The accuracy of the assessment depends on the available reliable information on the model of the process under study, which has a high degree of uncertainty. To carry out high-precision correction of the navigation complex, an adaptive non-linear Kalman filter with parametric identification was developed. The model of errors of the inertial navigation system is considered in the navigation complex, which is used in the algorithmic support. The procedure for identifying the parameters of a non-linear model represented by the SDC method in a scalar form is used. The developed adaptive non-linear Kalman filter is compact and easy to implement on board an aircraft.
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## Explicit commutativity conditions for second-order linear time-varying systems with non-zero initial conditions

### Abstract

Although the explicit commutativitiy conditions for second-order linear time-varying systems have been appeared in some literature, these are all for initially relaxed systems. This paper presents explicit necessary and sufficient commutativity conditions for commutativity of second-order linear time-varying systems with non-zero initial conditions. It has appeared interesting that the second requirement for the commutativity of non-relaxed systems plays an important role on the commutativity conditions when non-zero initial conditions exist. Another highlight is that the commutativity of switched systems is considered and spoiling of commutativity at the switching instants is illustrated for the first time. The simulation results support the theory developed in the paper.
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## Liptovské Matiašovce-Bochníčky site: A new Neolithic settlement in the region of Liptov (central Slovakia)

### Abstract

In 2017, a new neolithic site was discovered south of the village of Liptovské Matiašovce, on the elevated ridge of the Bochníčky site. Numerous finds of sherds, daub and chipped lithic industry from dominant Jurassic sub-Kraków flint were obtained by a primary survey and a succeeding small evaluation excavation in form of three trenches. Decoration of the thin-walled neolithic pottery of mostly semiglobular shapes points to presence of the younger Linear (musical note) Pottery culture, Želiezovce and rarely the Bükk culture. Unique chipped artifacts made of obsidian are also associated with the last mentioned culture. Part of the chipped lithic industry from the survey belongs to the late Paleolithic and Mesolithic. Among the previously documented rare neolithic settlements from the region of Liptov, the newly discovered site represents the richest neolithic settlement which should be complexly studied. It is being destroyed by ploughing every year.
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## A Low Power and High Performance Hardware Design for Automatic Epilepsy Seizure Detection

### Abstract

An application specific integrated design using Quadrature Linear Discriminant Analysis is proposed for automatic detection of normal and epilepsy seizure signals from EEG recordings in epilepsy patients. Five statistical parameters are extracted to form the feature vector for training of the classifier. The statistical parameters are Standardised Moment, Co-efficient of Variance, Range, Root Mean Square Value and Energy. The Intellectual Property Core performs the process of filtering, segmentation, extraction of statistical features and classification of epilepsy seizure and normal signals. The design is implemented in Zynq 7000 Zc706 SoC with average accuracy of 99%, Specificity of 100%, F1 score of 0.99, Sensitivity of 98% and Precision of 100 % with error rate of 0.0013/hr., which is approximately zero false detection.
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## Pewne rozwiązanie nieliniowego problemu różniczkowego z zastosowaniem do wybranych zagadnień geotechnicznych. = Solution of non-linear differential problem with application to selected geotechnical problems

### Abstract

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.
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## Unfalsified control of manipulators: simulation analysis

### Abstract

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 e#27;ect 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.
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## Performance evaluation of fractional-slot tubular permanent magnet machines with low space harmonics

### Abstract

This paper evaluates the performance of fractional-slot per pole winding configurations for tubular permanent magnet (PM) machines that can effectively eliminate the most undesirable space harmonics in a simple and cost-effective manner. The benefits of the proposed machine topology winding configurations are illustrated through comparison with 9-slot, 10-pole tubular PM machine developed for a free piston energy converter under the same specification and volumetric constraints. It has been shown that the proposed machine topology results in more than 7 times reduction in the eddy current loss in the mover magnets and supporting tube, and hence avoids potential problem of excessive mover temperature and risk of demagnetization.
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## CMOS ECCCII with Linear Tune of Rx and Its Application to Current-Mode Multiplier

### Abstract

In this paper, the second-generation CMOS currentcontrolled- current-conveyor based on differential pair of operational transconductance amplifier has been researched and presented. Since the major improvement of its parasitic resistance at x-port can be linearly controlled by an input bias current, the proposed building block is then called “The Second-Generation Electronically-tunable Current-controlled Current Conveyor” (ECCCI). The applications are demonstrated in form of both 2 quadrant and 4 quadrant current-mode signal multiplier circuits. Characteristics of the proposed ECCCII and its application are simulated by the PSPICE program from which the results are proved to be in agreement with the theory.
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## Producers’ Adjustment Trajectories Resulting in Equilibrium in the Economy with Linear Consumption Sets

### Abstract

We consider the Debreu private ownership economy in which all consumption plans belong to a proper linear subspace of the commodity-price space ℝl. 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 ℝl. 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 ℝl without considering additional costs.
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## Theory of the Stereological Analysis of Spheroid Size Distribution – Validation of the Equations

### Abstract

The paper presents validation tests for method which is used for the evaluation of the statistical distribution parameters for 3D particles’ diameters. The tested method, as source data, uses chord sets which are registered from a random cutting plane placed inside a sample space. In the sample space, there were individually generated three sets containing 3D virtual spheres. Each set had different Cumulative Distribution Function (CDF3) of the sphere diameters, namely: constant radius, normal distribution and bimodal distribution as a superposition of two normal distributions. It has been shown that having only a chord set it is possible, by using the tested method, to calculate the mean value of the outer sphere areas. For the sets of data, a chord method generates quite large errors for around 10% of the smallest nodules in the analysed population. With the increase of the nodule radii, the estimation errors decrease. The tested method may be applied to foundry issues e.g. for the estimation of gas pore sizes in castings or for the estimation of nodule graphite sizes in ductile cast iron.
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## Modeling and Analysis of Mechanical Properties in Structural Steel-DOE Approach

### Abstract

The present work focuses on the modeling and analysis of mechanical properties of structural steel. The effect of major alloying elements namely carbon, manganese and silicon has been investigated on mechanical properties of structural steel. Design of experiments is used to develop linear models for the responses namely Yield strength, Ultimate tensile strength and Elongation. The experiments have been conducted as per the full factorial design where all process variables are set at two levels. The main effect plots showed that the alloying elements Manganese and Silicon have positive contribution on Ultimate tensile strength and Yield strength. However, Carbon and Manganese showed more contribution as compared to Silicon. All three alloying elements are found to have negative contribution towards the response- Elongation. The present work is found to be useful to control the mechanical properties of structural steel by varying the major alloying elements. Minitab software has been used for statistical analysis. The linear regression models have been tested for the statistical adequacy by utilizing ANOVA and statistical significance test. Further, the prediction capability of the developed models is tested with the help of test cases. It is found that all linear regression models are found to be statistically adequate with good prediction capability. The work is useful to foundrymen to choose alloying elements composition to get desirable mechanical properties.
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## Stability analysis of positive linear systems by decomposition of the state matrices into symmetrical and antisymmetrical parts

### Abstract

The stability of positive linear continuous-time and discrete-time systems is analyzed by the use of the decomposition of the state matrices into symmetrical and antisymmetrical parts. It is shown that: 1) The state Metzler matrix of positive continuous-time linear system is Hurwitz if and only if its symmetrical part is Hurwitz; 2) The state matrix of positive linear discrete-time system is Schur if and only if its symmetrical part is Hurwitz. These results are extended to inverse matrices of the state matrices of the positive linear systems.
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## Investigations of Properties of Wax Mixtures Used in the Investment Casting Technology – New Investigation Methods

### Abstract

The results of testing of the selected group of wax mixtures used in the investment casting technology, are presented in the paper. The measurements of the kinetics of the mixtures shrinkage and changes of viscous-plastic properties as a temperature function were performed. The temperature influence on bending strength of wax mixtures was determined.
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## Positive and stable electrical circuits with state-feedbacks

### Abstract

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.
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## Positive electrical circuits and their reachability

### Abstract

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.
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## Robust stability of positive discrete-time linear systems with multiple delays with linear unity rank uncertainty structure or non-negative perturbation matrices

### Abstract

Simple necessary and sufficient conditions for robust stability of the positive linear discrete-time systems with delays with linear uncertainty structure in two cases: 1) unity rank uncertainty structure, 2) non-negative perturbation matrices, are established. The proposed conditions are compared with the suitable conditions for the standard systems. The considerations are illustrated by numerical examples.
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