The objective of the article is to examine the approximative and adjustive uses of the verb dire, which is mostly regarded as an assertive and eventful verb; hence nonapproximative. Meanwhile, in many expressions, in an impersonal use, in negation when the subjunctive mode is used, in the conditional forms, its evidence value is weakened and the verb dire can express approximation. The study is situated in light of the enunciation theory, notably it refers to a notion of modalisation. The corpus was established on the basis of dictionaries, which are representative for normative uses, but we will refer as well to press texts, particularly interviews, where the verb say is frequently used as a marker of the position of the speaker.

This study discusses the cross-cultural re-conceptualization of the slogan ‘I’m lovin’ it’, popularized in Poland by a global fast-food restaurant chain, which occurs in the inter-linguistic transfer between English and Polish. The analytical framework for the study is provided by Cultural Linguistics and the Re-conceptualization and Approximation Theory. The analysis is based on proposals submitted by 45 translators asked to come up with a Polish equivalent of the slogan. The results indicate that because the semantic networks for the meaning of love do not overlap between English and Polish perfectly, attempts at the cross-cultural transfer of the slogan can be approached only as more or less accurate approximations of the original meaning constructed according to culture-specific norms, expectations, and attitudes.

The positive asymptotically stable continuous-time linear systems are approximated by corresponding asymptotically stable discrete-time linear systems. Two methods of the approximation are presented and the comparison of the methods is addressed. The considerations are illustrated by three numerical examples and an example of positive electrical circuit.

The main aim of the study was to determine the goodness of fit between the relaxation function described with a rheological model and the real (experimental) relaxation curves obtained for digital materials fabricated with a Connex 350 printer using the PolyJet additive manufacturing technology. The study involved estimating the uncertainty of approximation of the parameters of the theoretical relaxation curve. The knowledge of digital materials is not yet sufficient; their properties are not so well-known as those of metallic alloys or plastics used as structural materials. Intensive research is thus required to find out more about their behavior in various conditions. From the calculation results, i.e. the uncertainty of approximation of the relaxation function parameters, it is evident that the experimental curves coincide with the curves obtained by means of the solid model when the approximation uncertainty is taken into account. This suggests that the assumed solid model is well-suited to describe a real material.

Wavelet transform becomes a more and more common method of processing 3D signals. It is widely used to analyze data in various branches of science and technology (medicine, seismology, engineering, etc.). In the field of mechanical engineering wavelet transform is usually used to investigate surface micro- and nanotopography. Wavelet transform is commonly regarded as a very good tool to analyze non-stationary signals. However, to analyze periodical signals, most researchers prefer to use well-known methods such as Fourier analysis. In this paper authors make an attempt to prove that wavelet transform can be a useful method to analyze 3D signals that are approximately periodical. As an example of such signal, measurement data of cylindrical workpieces are investigated. The calculations were performed in the MATLAB environment using the Wavelet Toolbox.

Size-dependent dynamic instability of cylindrical nanowires incorporating the effects of Casimir attraction and surface energy is presented in this research work. To develop the attractive intermolecular force between the nanowire and its substrate, the proximity force approximation (PFA) for small separations, and the Dirichlet asymptotic approximation for large separations with a cylinder-plate geometry are employed. A nonlinear governing equation of motion for free-standing nanowires – based on the Gurtin-Murdoch model – and a strain gradient elasticity theory are derived. To overcome the complexity of the nonlinear problem in hand, a Garlerkin-based projection procedure for construction of a reduced-order model is implemented as a way of discretization of the governing differential equation. The effects of length-scale parameter, surface energy and vacuum fluctuations on the dynamic instability threshold and adhesion of nanowires are examined. It is demonstrated that in the absence of any actuation, a nanowire might behave unstably, due to the Casimir induction force.

In the paper a novel mathematical model of electromechanical actuator is presented. It is based on application of Hamiltonian equations in the description of electromechanical energy conversion. It results in employment of flux linkages as state variables in the state space equations. For simplicity only a 3-phase wye connected stator winding without a neutral wire is considered in detail. The procedure can be generalised to any number of phases. Topology-based approach is used in the model implementation. Procedures for evaluation of all quantities (currents, energy/coenergy, electromagnetic torque) present in model equations are described. Eddy currents and hysteresis phenolmenon are neglected in formulation of the model to enable application of state-space description.

The paper presents an algorithm for the construction of an approximation of a highly nonlinear current-flux characteristic of a synchronous reluctance machine. Such an approximation is required in a Hamiltonian model of an electric machine and the constructed approximation is suited to be used in such a model. It employs a simplicial approximation based on irregular points sets in the spaces of currents and fluxes. The sets are constructed by the iterative insertion of new points. Initially the sets contain an arbitrarily small number of elements. The insertion is based on an approximation error calculation. Based on the sets containing possibly small number of elements, the proposed procedure leads to smooth and precise approximation. Due to the nonlinearity of the approximated characteristics, ambiguities can occur. A method for the triangulation refinement of the sets of currents and fluxes that eliminates them is also presented. In the paper, a reluctance machine model using the constructed approximation is described and compared with a model using the approximation based on regular sets.

The article discusses the development of an approximation model of selected plastic and mechanical properties obtained from compression tests of model materials used in physical modeling. The use of physical modeling with the use of soft model materials such as a synthetic wax branch with various modifiers is a popular tool used as an alternative or verification of numerical modeling of bulk metal forming processes. In order to develop an algorithm to facilitate the choice of material model to simulate the behavior of real-metallic materials used in industrial production processes the induction of decision trees was used. First of all, the Statistica program was used for data mining, which made it possible to determine / find the relationship between the percentage of particular constituents of the model material (base material and modifiers) and yield strength, critical and maximum strain, and provide the opportunity to indicate the most important variables determining the shape of the stress – strain curve. Next, using the induction of decision trees, an approximation model was developed, which allowed to create an algorithm facilitating the selection of individual modifying components. The last stage of the research was verification of the correctness of the developed algorithm. The obtained research results indicate the possibility of using decision tree induction to approximate selected properties of modeling materials simulating the behavior of real materials, thus eliminating the need for costly and time-consuming experiments carried out on metallic material.

This paper presents a universal approximation of the unit circle by a polygon that can be used in signal processing algorithms. Optimal choice of the values of three parameters of this approximation allows one to obtain a high accuracy of approximation. The approximation described in the paper has a universal character and can be used in many signal processing algorithms, such as DFT, that use the mathematical form of the unit circle. One of the applications of the described approximation is the DFT linear interpolation method (LIDFT). Applying the results of the presented paper to improve the LIDFT method allows one to significantly decrease the errors in estimating the amplitudes and frequencies of multifrequency signal components. The paper presents the derived formulas, an analysis of the approximation accuracy and the region of best values for the approximation parameters.

The paper presents the modelling measurement results of the load-displacement relation for scaffold stands and bracings. In the case of stands, there are two sections of curves, i.e. a straight-line and curvilinear section, and in the case of bracings, two straight line sections as well as one curvilinear section are distinguished. As a result of analyses, it is concluded that the sections which can be approximated by means of linear functions should be distinguished in graphs, if possible. On the one hand, this results from the evaluation methods of scaffold components. Nevertheless, the determination of elastic-linear scope of components’ operation is useful in engineering practice during computer calculations. Moreover, the method of determining an intersection point between functions, approximating tests results, along with analysis of the impact of polynomial degree, approximating the research results, on the time and effectiveness of the process of approximating functions selection, are all demonstrated in this article. The proposed method can prove useful in all science fields where curves obtained from any research (laboratory test, in situ test, numerical analysis) require approximation or replacement with a simpler description.

Seasonality is a function of a time series in which the data experiences regular and predictable

changes that repeat each calendar year. Two-stage stochastic programming model

for real industrial systems at the case of a seasonal demand is presented. Sampling average

approximation (SAA) method was applied to solve a stochastic model which gave a productive

structure for distinguishing and statistically testing a different production plan. Lingo

tool is developed to obtain the optimal solution for the proposed model which is validated

by Math works Matlab. The actual data of the industrial system; from the General Manufacturing

Company, was applied to examine the proposed model. Seasonal future demand

is then estimated using the multiplicative seasonal method, the effect of seasonality was

presented and discussed. One might say that the proposed model is viewed as a moderately

accurate tool for industrial systems in case of seasonal demand. The current research may

be considered a significant tool in case of seasonal demand. To illustrate the applicability of

the proposed model a numerical example is solved using the proposed technique. ANOVA

analysis is applied using MINITAB 17 statistical software to validate the obtained results.

Bilevel programming problem is a non-convex two stage decision making process in which the constraint region of upper level is determined by the lower level problem. In this paper, a multi-objective indefinite quadratic bilevel programming problem (MOIQBP) is presented. The defined problem (MOIQBP) has multi-objective functions at both the levels. The followers are independent at the lower level. A fuzzy goal programming methodology is employed which minimizes the sum of the negative deviational variables of both the levels to obtain highest membership value of each of the fuzzy goal. The membership function for the objective functions at each level is defined. As these membership functions are quadratic they are linearized by Taylor series approximation. The membership function for the decision variables at both levels is also determined. The individual optimal solution of objective functions at each level is used for formulating an integrated pay-off matrix. The aspiration levels for the decision makers are ascertained from this matrix. An algorithm is developed to obtain a compromise optimal solution for (MOIQBP). A numerical example is exhibited to evince the algorithm. The computing software LINGO 17.0 has been used for solving this problem.

The study aimed to examine the use of Geomagnetic Anomaly Detection (GAD) to locate the buried ferromagnetic pipeline defects without exposing them. However, the accuracy of GAD is limited by the background noise. In the present work, we propose an approximate entropy noise suppression (AENS) method based on Variational Mode Decomposition (VMD) for detection of pipeline defects. The proposed method is capable of reconstructing the magnetic field signals and extracting weak anomaly signals that are submerged in the background noise, which was employed to construct an effective detector of anomalous signals. The internal parameters of VMD were optimized by the Scale–Space algorithm, and their anti-noise performance was compared. The results show that the proposed method can remove the background noise in high-noise background geomagnetic field environments. Experiments were carried out in our laboratory and evaluation results of inspection data were analysed; the feasibility of GAD is validated when used in the application to detection of buried pipeline defects.

Shaft-stator rub and cracks on rotors, which have devastating effects on the industrial equipment, cause nonlinear and in some cases chaotic lateral vibrations. On the other hand, vibrations caused by machinery faults can be torsional in cases such as rub. Therefore, a combined analysis of lateral and torsional vibrations and extraction of chaotic features from these vibrations is an effective approach for rotor vibration monitoring. In this study, lateral and torsional vibrations of rotors have been examined for detecting cracks and rub. For this purpose, by preparing a laboratory model, the lateral vibrations of a system with crack and rub have been acquired. After that, a practical method for measuring the torsional vibrations of the system is introduced. By designing and installing this measurement system, practical test data were acquired on the laboratory setup. Then, the method of phase space reconstruction was used to examine the effect of faults on the chaotic behaviour of the system. In order to diagnose the faults based on the chaotic behaviour of the system, largest Lyapunov exponent (LLE), approximate entropy (ApEn) and correlation dimension were calculated for a healthy system and also for a system with rub and a crack. Finally, by applying these parameters, the chaotic feature space is introduced in order to diagnose the intentionally created faults. The results show that in this space, the distinction between the various defects in the system can be clearly identified, which enables to use this method in fault diagnosis of rotating machinery.