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Number of results: 26
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Abstract

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.
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Abstract

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.
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Abstract

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.
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Abstract

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.
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Abstract

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.
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Abstract

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.
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Abstract

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.
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Abstract

BC (Black Carbon), which can be found in the atmosphere, is characterized by a large value of the imaginary part of the complex refractive index and, therefore, might have an impact on the global warming effect. To study the interaction of BC with light often computer simulations are used. One of the methods, which are capable of performing light scattering simulations by any shape, is DDA (Discrete Dipole Approximation). In this work its accuracy was estimated in respect to BC structures using the latest stable version of the ADDA (vr. 1.2) algorithm. As the reference algorithm the GMM (Generalized Multiparticle Mie-Solution) code was used. The study shows that the number of volume elements (dipoles) is the main parameter that defines the quality of results. However, they can be improved by a proper polarizability expression. The most accurate, and least time consuming, simulations were observed for IGT_SO. When an aggregate consists of particles composed of ca. 750 volume elements (dipoles), the averaged relative extinction error should not exceed ca. 4.5%.
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Abstract

The paper presents a new method of surface topology reconstruction from a white light interferogram. The method is based on interferogram modelling by complex exponents (Prony method). The compatibility of white light interferogram and Prony models has already been proven. Effectiveness of the method was tested by modelling and examining reconstruction of tilted and spherical surfaces, and by estimating the reconstruction accuracy.
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Abstract

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.
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Abstract

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.
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Abstract

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.
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Abstract

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.
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Abstract

Heat and mass transfer stretched flow of an incompressible, electrically conducting Jeffrey fluid has been studied numerically. Nanoparticles are suspended in the base fluid and it has many applications such as cooling of engines, thermal absorption systems, lubricants fuel cell, nanodrug delivery system and so on. Temperature dependent variable thermal conductivity with Rosseland approximation is taken into account and suction effect is employed in the boundary conditions. The governing partial differential equations are first transformed into set of ordinary differential equations using selected similarity transformations, which are then solved numerically using Runge-Kutta-Felhberg fourth-fifth order method along with shooting technique. The flow, heat and mass transfer characteristics with local Nusselt number for various physical parameters are presented graphically and a detailed discussion regarding the effect of flow parameters on velocity and temperature profiles are provided. It is found that, increase of variable thermal conductivity, radiation, Brownian motion and thermophoresis parameter increases the rate of heat transfer. Local Nusselt number has been computed for various parameters and it is observed that, in the presence of variable thermal conductivity and Rosseland approximation, heat transfer characteristics are higher as compared to the constant thermal conductivity and linear thermal radiation.
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Abstract

In this article we construct a finite-difference scheme for the three-dimensional equations of the atmospheric boundary layer. The solvability of the mathematical model is proved and quality properties of the solutions are studied. A priori estimates are derived for the solution of the differential equations. The mathematical questions of the difference schemes for the equations of the atmospheric boundary layer are studied. Nonlinear terms are approximated such that the integral term of the identity vanishes when it is scalar multiplied. This property of the difference scheme is formulated as a lemma. Main a priori estimates for the solution of the difference problem are derived. Approximation properties are investigated and the theorem of convergence of the difference solution to the solution of the differential problem is proved.
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Abstract

This article aims to investigate the phenomenon of the rule of law promotion exercised by the EU through the Deep and Comprehensive Free Trade Agreements (DCFTAs). First, the article emphasizes the unique combination of normative and market power the EU uses to diffuse its norms through trade liberalization. Next, it provides an insight into the particularities of the European Neighbourhood Policy as a policy context for the conclusion and implementation of the Association Agreements, including the DCFTAs with Ukraine, Moldova and Georgia, as well as the conceptual problematic and scope of the rule of law as a value the EU seeks to externalize. Using the DCFTAs with Ukraine, Moldova, and Georgia) as a single group case study of the transparency dimension of the rule of law, the central part of the article analyzes the DCFTAs substantive requirements, directed toward promoting transparency in the partner states (while categorizing the requirements into the most general ones; cooperation-related; and discipline-specific) and the legal mechanisms that make these clauses operational (e.g., the institutional framework of the AAs, gradual approximation and monitoring clauses, and the Dispute Settlement Mechanism). In concluding, the article summarizes the state-of-the-art of the rule of law promotion through the DCFTAs, distinguishes the major challenges the respective phenomenon faces, and emphasizes the prospects for and difficulties of using the DCFTAs as an instrument of rule of law promotion.
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Abstract

Sensitivity analysis of the dynamic response of both the designed and the actual models of a slewing superstructure with two masts to the variation of the counterweight mass and the degree of accuracy of the approximation polynomials of the digging resistance was conducted in the paper. Spatial reduced dynamic models of the bucket wheel excavator SchRs 1600 were used as a basis for the presented investigations. Based on the comparative analysis of the calculation results, the following conclusions were drawn: (a) mass of the counterweight has a significantly higher influence on the maximum intensities of accelerations of the referent points than on the spectrum of natural frequencies, (b) the accuracy of approximations of the digging resistance and the maximum values of accelerations differ by an order of magnitude, for the approximation trigonometric polynomial of the same number of harmonics.
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Abstract

This paper derives analytical formulas for the systematic errors of the linear interpolated DFT (LIDFT) method when used to estimating multifrequency signal parameters and verifies this analysis using Monte-Carlo simulations. The analysis is performed on the version of the LIDFT method based on optimal approximation of the unit circle by a polygon using a pair of windows. The analytical formulas derived here take the systematic errors in the estimation of amplitude and frequency of component oscillations in the multifrequency signal as the sum of basic errors and the errors caused by each of the component oscillations. Additional formulas are also included to analyze particular quantities such as a signal consisting of two complex oscillations, and the analyses are verified using Monte-Carlo simulations.
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Abstract

This paper presents the general solution of the least-squares approximation of the frequency characteristic of the data window by linear functions combined with zero padding technique. The approximation characteristic can be discontinuous or continuous, what depends on the value of one approximation parameter. The approximation solution has an analytical form and therefore the results have universal character. The paper presents derived formulas, analysis of approximation accuracy, the exemplary characteristics and conclusions, which confirm high accuracy of the approximation. The presented solution is applicable to estimating methods, like the LIDFT method, visualizations, etc.
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Abstract

The essential parameters for structure integrity assessment in Linear Elastic Fracture Mechanics (LEFM) are Stress Intensity Factors (SIFs). The estimation of SIFs can be done by analytical or numerical techniques. The analytical estimation of SIFs is limited to simple structures with non-complicated boundaries, loads and supports. An effective numerical technique for analyzing problems with singular fields, such as fracture mechanics problems, is the extended finite element method (XFEM). In the paper, XFEM is applied to compute an actual stress field in a two-dimensional cracked body. The XFEM is based on the idea of enriching the approximation in the vicinity of the discontinuity. As a result, the numerical model consists of three types of elements: non-enriched elements, fully enriched elements (the domain of whom is cut by a discontinuity), and partially enriched elements (the so-called blending elements). In a blending element, some but not all of the nodes are enriched, which adds to the approximation parasitic term. The error caused by the parasitic terms is partly responsible for the degradation of the convergence rate. It also limits the accuracy of the method. Eliminating blending elements from approximation space and replacing them with standard elements, together with applying shifted-basis enrichment, makes it possible to avoid the problem. The numerical examples show improvements in results when compared with the standard XFEM approach.
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Abstract

The goal of this paper is to explore and to provide tools for the investigation of the problems of unit-length scheduling of incompatible jobs on uniform machines. We present two new algorithms that are a significant improvement over the known algorithms. The first one is Algorithm 2 which is 2-approximate for the problem Qm|pj  = 1, G = bisubquartic|Cmax. The second one is Algorithm 3 which is 4-approximate for the problem Qm|pj  = 1, G = bisubquartic|ΣCj, where m ∈ {2, 3, 4}. The theory behind the proposed algorithms is based on the properties of 2-coloring with maximal coloring width, and on the properties of ideal machine, an abstract machine that we introduce in this paper.
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Abstract

The formulas have been entered and approved for the calculation of porosity distribution on the thickness of layer of fine-grained mixture during its separation by the inclined flat or vertical cylinder vibro sieves. It has been attained as a result of approximation of tabular information of the obtained numerical computer integration of the specially worked out nonlinear differential equations of the second order in a dimensionless form. For approximation, the function of degree coefficients and index is used for the degrees which are certain by the Aitken's method. Coefficients of the entered analytical dependence are the vibro sieves related to the parameters obtained by mechanical descriptions of the separated material. Coefficients of the entered analytical dependence are related to the parameters of vibro sieves and mechanical descriptions of the separated material. In the case of cylinder vertical vibro sieve the action of centrifugal force is also taken into account. The method of mixture porosity calculation does not need a computer numerical integration of nonlinear differential equations conducted by other authors for solving this problem. Comparison of numerical results of the proposed analytical method of calculation with the ones described in literature, have confirmed its high accuracy results, for the differences do not exceed one percent. The expounded method is universal enough and simple in use, besides it opens the possibilities of subsequent analytical integration of differential equalizations of motion at the calculation of kinematics descriptions of grain flow. The developed method gives the opportunity to also solve the inverse task when, according to experimental measurements of porosity values of grain mixtures on the thickness of movable separated layer, it is needed to find the value of phenomenological permanent that is included in the expressions of coefficients of initial differential equalization. In this way, the adequacy of the mathematical model is improved. The use of approximation of degree considerably simplifies the method of authentication of differential equalization coefficients. In the article, the examples of grain mixture porosity calculation as well as the examples of phenomenological permanent authentication have been resulted after experimental calculations for both the variants of vibro sieves.
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Abstract

In this work we discuss 3D selfconsistent solution of Poisson and Schrödinger equations for electrostatically formed quantum dot. 3D simulations give detailed insight into the energy spectrum of the device and allow us to find values of respective voltages ensuring given number of electrons in the dot. We performed calculations for fully 3D potential and apart from that calculations for the same potential separated into two independent parts, i.e. regarding to the plane of 2DEG and to the direction perpendicular to the meant plane. We found that calculations done for the two independent parts of the potential give good information about quantum dot properties and they are much faster compared to fully 3D simulations.
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Abstract

The analytical method of calculation of a withstand motion of fine-grained mixture is worked out in the vertical cylindrical sieve of vibrocentrifuge. Integration of differential equalization of motion is show out the reserved formulas for the calculation of kinematics descriptions of grain flow. The two-parameter continual model of the state of separation mixture is used in researches, as a heterogeneous continuous environment with variable specific mass (by porosity) on the thickness of movable layer of friable material. Change of specific mass on a radial coordinate in the cylindrical layer of mixture approximated by the function of degree, the coefficients of that are certain by the Aitken's method. Due to such approximation, the analytical decision of differential equalization of the grain flow, shown out with the use of two-parameter rheological dependence, in that the constituent of linear viscid resistance is complemented by the constituent of remaining internal dry friction, proportional overpressure in mixture, is built. An analytical decision is expressed as squaring that is not expressed through elementary functions in closed form, the close method of calculation of integral offers that is why, with the use of partial sum of row of degree. The results got close formulas result in that well comport with the results of numerical computer integration of squaring. Such method the continual models of grain flow on vibrosieves, it is assumed in that friable material is fully confined internal dry friction, are generalized known for, as a result of vibrodilution. The examples of calculations are considered, where influence of different factors is investigational, in particular values of rheological coefficients and change of porosity, on kinematics descriptions. It is set that calculation kinematics descriptions of grain flow substantially depend not only on the thickness of movable layer and rheological constants, and also from the concentration of grains near free surface of the mixture. Thus, worked out here a method of research of vertical grain flow in the cylindrical sieve of vibrocentrifuge can be an alternative to other methods in that for the calculation of motion of grain mixture of variable porosity conducted numerical computer integration of nonlinear differential equalizations.
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