The non linearities in the motor of an electrodynamic loudspeaker are still a discussed topic. This paper studies the influence of the force factor variation with the coil displacement on the harmonic and inter-modulation distortions. The real variation is described at least by a linear and a quadratic term. The effect of each term is studied separately, as they don't influence the same kind of frequencies, harmonics or inter-modulation. Both terms considered together result in enhanced effects. The dissymmetry of the Bl variation with regard to the coil centered position has also peculiar effects. This paper presents the method developed to calculate the power of each harmonic and inter-modulation frequency. This allows to compare the obtained values and thus the induced nonlinearities.

This paper presents the classification of musical instruments using Mel Frequency Cepstral Coefficients (MFCC) and Higher Order Spectral features. MFCC, cepstral, temporal, spectral, and timbral features have been widely used in the task of musical instrument classification. As music sound signal is generated using non-linear dynamics, non-linearity and non-Gaussianity of the musical instruments are important features which have not been considered in the past. In this paper, hybridisation of MFCC and Higher Order Spectral (HOS) based features have been used in the task of musical instrument classification. HOS-based features have been used to provide instrument specific information such as non-Gaussianity and non-linearity of the musical instruments. The extracted features have been presented to Counter Propagation Neural Network (CPNN) to identify the instruments and their family. For experimentation, isolated sounds of 19 musical instruments have been used from McGill University Master Sample (MUMS) sound database. The proposed features show the significant improvement in the classification accuracy of the system.

The paper discuss a problem of determination of inductances for AC machine windings when saturation of magnetic circuit is not neglected. For such cases, computation of magnetic field distribution in the machine magnetic circuit is a starting point for post processing procedures leading to various values, among others the co-energy in a given area and linkage fluxes of windings. This paper shows how to determine winding inductances in a nonlinear magnetic circuit from these two values and also how to compute directly nonlinear inductances. Problem is not trivial because such inductances are not uniquely determined as for linear case. In the paper a definition of nonlinear inductances is proposed which makes the choice unique.

Noise spectroscopy and I-V characteristic non-linearity measurement were applied as diagnostic tools in order to characterize the volume and contact quality of positive temperature coefficient (PTC) chip sensors and to predict possible contact failure. Correctly made and stable contacts are crucial for proper sensing. I-V characteristics and time dependences of resistance were measured for studied sensors and, besides the samples with stable resistance value, spike type resistance fluctuation was observed for some samples. These spikes often disappear after about 24 hours of voltage application. Linear I-V characteristics were measured for the samples with stable resistance. The resistance fluctuation of burst noise type was observed for some samples showing the I-V characteristic dependent on the electric field orientation. We have found that the thermistors with high quality contacts had a linear I-V characteristic, the noise spectral density is of 1/f type and the third harmonic index is lower than 60 dB. The samples with poor quality contacts show non-linear I-V characteristics and excess noise is given by superposition of g-r and 1/fn type noises, and the third harmonic index is higher than 60 dB.

The paper presents the author’s non-linear FEM solution of an initially stressless deformed flat frame element, in which the nodes are situated along the axis of the bar initially straight. It has been assumed that each node may sustain arbitrary displacements and rotation. The solution takes into account the effect of shear, the geometrical non-linearity with large displacements (Green-Lagrange’s strain tensor) and moderate rotations (i.e. such ones which allow a linear-elastic behaviour of the material) and alternative small rotations when the second Piola-Kirchhoff stress tensor is applied. This solution is based on [1], concerning beams without any initial bow imperfections. The convergence of the obtained results at different numbers of nodes and Gauss points in the element was tested basing on the example of circular arcs with a central angle of 120°÷180°. The analysis concerned elements with two, three, five, seven, nine and eleven nodes, for the same number of points of numerical integration and also with one more or less. Moreover, the effect of distributing the load on the convergence of the results was analyzed.

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.

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.

Statistical analysis is helpful for better understanding of the processes which take place in agricultural ecosystems. Particular attention should be paid to the processes of crops’ productivity formation under the influence of natural and anthropogenic factors. The goal of our study was to provide new theoretical knowledge about the dependence of vegetable crops’ productivity on water supply and heat income. The study was conducted in the irrigated conditions of the semi-arid cold Steppe zone on the fields of the Institute of Irrigated Agriculture of NAAS, Kherson, Ukraine. We studied the historical data of productivity of three most common in the region vegetable crops: potato, tomato, onion. The crops were cultivated by using the generally accepted in the region agrotechnology. Historical yielding and meteorological data of the period 1990–2016 were used to develop the models of the vegetable crops’ productivity. We used two approaches: development of pair linear models in three categories (“yield – water use”, “yield – sum of the effective air temperatures above 10°C”); development of complex linear regression models taking into account such factors as total water use, and temperature regime during the crops’ vegetation. Pair linear models of the crops’ productivity showed that the highest effect on the yields of potato and onion has the water use index (R2 of 0.9350 and 0.9689, respectively), and on the yield of tomato – temperature regime (R2 of 0.9573). The results of pair analysis were proved by the multiple regression analysis that revealed the same tendencies in the crop yield formation depending on the studied factors.

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.