When a frequency domain sensor is under the effect of an input stimulus, there is a frequency shift at its output. One of the most important advantages of such sensors is their converting a physical input parameter into time variations. In consequence, changes of an input stimulus can be quantified very precisely, provided that a proper frequency counter/meter is used. Unfortunately, it is well known in the time-frequency metrology that if a higher accuracy in measurements is needed, a longer time for measuring is required. The principle of rational approximations is a method to measure a signal frequency. One of its main properties is that the time required for measuring decreases when the order of an unknown frequency increases. In particular, this work shows a new measurement technique, which is devoted to measuring the frequency shifts that occur in frequency domain sensors. The presented research result is a modification of the principle of rational approximations. In this work a mathematical analysis is presented, and the theory of this new measurement method is analysed in detail. As a result, a new formalism for frequency measurement is proposed, which improves resolution and reduces the measurement time.

Analytical and numerical nonlinear solutions for rotating variable-thickness functionally graded solid and annular disks with viscoelastic orthotropic material properties are presented by using the method of successive approximations. Variable material properties such as Young’s moduli, density and thickness of the disk, are first introduced to obtain the governing equation. As a second step, the method of successive approximations is proposed to get the nonlinear solution of the problem. In the third step, the method of effective moduli is deduced to reduce the problem to the corresponding one of a homogeneous but anisotropic material. The results of viscoelastic stresses and radial displacement are obtained for annular and solid disks of different profiles and graphically illustrated. The calculated results are compared and the effects due to many parameters are discussed.

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.

Deriving the formulas for strain components, we are assuming, that cross-section of a rod being rotated in space during deformation does not need to be perpendicular to deformed centroid line. This not a quite intuitive assumption allows for more compact and easier formulas for strain tensor or equilibrium equations. Derived transformations between actual and initial coordinate system, components of strain tensor and virtual works principle for investigated spatially curved beams of bisymmetric cross-section are shown in this paper. Conformity with other models from referenced literature is also shown.

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.

Functional properties of some electrical devices are expressed in the form of a dependence between parameters defining a given aspect of device duty or work circumstance (e.g. breakdown voltage): contacts distance for a circuit breaker, current (voltage for voltage limiters or reaction time), and load current for over current protection. Such characteristics are obtained experimentally, usually in a set of test series, each performed with a fixed independent parameter. Results of each series generate sets of data for estimation of statistical properties of a dependent parameter: distribution, expected value, variance and confidence interval. These statistics concern one point of the tested characteristic, so to get data of it as a whole, that would satisfy the needs for designing an electrical system, a large number of tests can be necessary. The way to reduce the number of tests may consists in: defining the characteristic not as a series of points, but as an analytical function with some specific parameters. This can be combined with aggregation of results of all tests in one set of data for estimation of statistical properties of the mentioned parameter. This paper presents an application of the above approach to tests of time-current characteristics of fuses.

We derive exact and approximate controllability conditions for the linear one-dimensional heat equation in an infinite and a semi-infinite domains. The control is carried out by means of the time-dependent intensity of a point heat source localized at an internal (finite) point of the domain. By the Green’s function approach and the method of heuristic determination of resolving controls, exact controllability analysis is reduced to an infinite system of linear algebraic equations, the regularity of which is sufficient for the existence of exactly resolvable controls. In the case of a semi-infinite domain, as the source approaches the boundary, a lack of L2-null-controllability occurs, which is observed earlier by Micu and Zuazua. On the other hand, in the case of infinite domain, sufficient conditions for the regularity of the reduced infinite system of equations are derived in terms of control time, initial and terminal temperatures. A sufficient condition on the control time, heat source concentration point and initial and terminal temperatures is derived for the existence of approximately resolving controls. In the particular case of a semi-infinite domain when the heat source approaches the boundary, a sufficient condition on the control time and initial temperature providing approximate controllability with required precision is derived.