In this article we analyse various methods of value approximation for Prolate Spheroidal Wave Functions (PSWF). As PSWFs are not given by explicit formula, for any application their values need to be calculated based on their properties and connection to other functions. We will focus on three approaches – Legendre polynomials, Eigenvalues of Matrix Operators and Hermite functions. We then create an implementation and test its effectiveness by using is as a base for band limited signal approximation algorithm.
The formulation of a plate finite element with so called ‘physical’ shape functions is revisited. The derivation of the ‘physical’ shape functions is based on Hencky-Bollé theory of moderately thick plates. The considered finite element was assessed in the past, and the tests showed that the solution convergence was achieved in a wide range of thickness to in-plane dimensions ratios. In this paper a holistic correctness assessment is presented, which covers three criteria: the ellipticity, the consistency and the inf-sup conditions. Fulfilment of these criteria assures the existence of a unique solution, and a stable and optimal convergence to the correct solution. The algorithms of the numerical tests for each test case are presented and the tests are performed for the considered formulation. In result it is concluded that the finite element formulation passes every test and therefore is a good choice for modeling plate structural elements regardless of their thickness.
In this paper the application of so called wedge functions is presented to solve two-dimensional simple geometries of magnetostatic and electrostatic problems, e.g. rectangles of varying aspect ratio and with different values of the magnetic permeability μ. Such problems require the use of surface charge density, or segment source, functions of the form ρs = σa-1, where the power parameters, a, have special fractional values. A methodology is presented to determine these special values of a and use them in segment sources on simple geometries, i.e. rectangles of varying aspect ratio, and with different values of the magnetic permeability μ. Wedge solutions are obtained by coupling the strength coefficients of source segments of the same power around an edge. These surface source functions have been used in the analysis of conducting and infinite permeability structures. Here we apply such functions in a boundary integral analysis method to problems having regions of finite permeability.
Two methods for calculating transport parameters in semiconductor superlattices by applying Green’s functions are compared in the paper. For one of the methods, the Wannier functions method, where computations in the complex space and Wannier functions base are required, the Hamiltonian matrix is small in size and its elements depend solely on the energy. For the real space method, as it operates in the floating point domain and uses the Hamiltonian containing the elements dependent both on energy and position, the Hamiltonian matrix is larger in size. The size makes the method computationally challenging. To find the consequences of choosing one of the methods, a direct comparison between the computations, obtained for both methods with the same input parameters, was undertaken. The differences between the results are shown and explained. Selected simulations allowed us to discuss advantages and disadvantages of both methods. The calculations include transport parameters such as the density of states and the occupation functions, with regard to scattering processes where the self-consistent Born approximation was used, as well as the spatial distribution of electron concentration for two superlattices structures. The numerical results are obtained within the non-equilibrium Green’s functions formalism by solving the Dyson and the Keldysh equations.
Starting from consideration that urban intersections are sites with promise for safety and operational improvements, the paper describes the steps taken to develop a crash predictive model for estimating the safety performance of urban unsignalized intersections located in Palermo, Italy. The focus is on unsignalized four-legged one-way intersections widespread in Italian downtowns. The sample considered in the study consist of 92 intersections in Palermo, Italy. For the study were collected crashes occurred in the sites during the years 2006‒2012, geometric design and functional characteristics and traffic flow. Results showed that data were overdispersed and NB1 distributed. In order to account for the correlation within responses Generalized Estimating Equations (GEE) were used under different working correlation matrices.
The process of railway track adjustment is a task which includes bringing, in geometrical terms, the actual track axis to the position ensuring safe and efficient traffic of rail vehicles. The initial calculation stage of this process is to determine approximately the limits of sections of different geometry, i.e. straight lines, arcs and transition curves. This allows to draw up a draft alignment design, which is subject to control the position relative to the current state. In practice, this type of a project rarely meets the requirements associated with the values of corrective alignments. Therefore, it becomes necessary to apply iterated correction of a solution in order to determine the final project, allowing to introduce minor corrections while maintaining the assumed parameters of the route. The degree of complexity of this process is defined by the quality of determining a preliminary draft alignment design. Delimitation of the sections for creation of creating such a design, is usually done by using the curvature diagram (InRail v8.7 Reference Guide [1], Jamka et al [2], Strach [3]), which is, however, sensitive to the misalignment of the track and measurement errors. In their paper Lenda and Strach [4] proposed a new method for creating curvature diagram, based on approximating spline function, theoretically allowing, inter alia, to reduce vulnerability to interference factors. In this study, the method to determine a preliminary draft alignment design for the track with severe overexploitation was used, and thus in the conditions adversely affecting the accuracy of the conducted readings. The results were compared to the ones obtained using classical curvature diagram. The obtained results indicate that the method allows to increase the readability of a curvature graph, which at considerable deregulation of a track takes an irregular shape, difficult to interpret. The method also favourably affects the accuracy of determining the initial parameters of the project, reducing the entire process of calculation.
This paper presents the measurement of vibrational properties of sundatang soundboard. Sundatang is a plucked stringed traditional musical instrument that is popular among the Kadazandusun communities in Sabah, Malaysia. The vibrational properties of the soundboard are measured using CADA-X impact hammering system in a condition where the instrument is without any string. There are two types of sundatang used in this study; one made from acacia and the other from vitex wood. In this measurement, frequency response functions (FRFs) and modal parameters of the top plate and back plate of this instrument are obtained. It is found that in free edge, fundamental frequency of both plates of acacia sundatang is greater than the vitex sundatang in a range of 112 Hz to 230 Hz. However, in clamped edge (attached to its ribs), it was modified to a lower frequency and closer to each other in the range of 55 Hz to 59 Hz. Another finding is the detection of the excitation of similar mode shape at different resonance frequencies. This phenomenon is termed as Different State of Mode (DSM) which is observed may be because the number of testing points is not enough. Findings of this study provide important information to the study of quality development of this instrument
Landfill leachate makes a potential source of ground water pollution. Municipal waste landfill substratum can be used for removal of pollutants from leachate. Model research was performed with use of a sand bed and artificially prepared leachates. Effectiveness of filtration in a bed of specific thickness was assessed based on the total solids content. Result of the model research indicated that the mass of pollutants contained in leachate filtered by a layer of porous soil (mf) depends on the mass of pollutants supplied (md). Determined regression functions indicate agreement with empirical values of variable m′f. The determined regression functions allow for qualitative and quantitative assessment of influence of the analysed independent variables (m′d, l, ω) on values of mass of pollutants flowing from the medium sand layer. Results of this research can be used to forecast the level of pollution of soil and underground waters lying in the zone of potential impact of municipal waste landfill.
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.
The paper presents a description of used methods and exemplary mathematical models which are classified into theoretical-empirical models of thermal processes. Such models encompass equations resulting from the laws of physics and additional empirical functions describing processes for which analytical models are complex and difficult to develop. The principle of developing, advantages and disadvantages of presented models as well as quality prediction assessment were presented. Mathematical models of a steam boiler, a steam turbine as well as a heat recovery steam generator were described. Exemplary calculation results were presented and compared with measurements.
The article presents the process of functional changes in the area of the Metropolis of Poznań, i.e. 22 communes belonging to the Metropolia Poznań Association. The process was examined on the basis of changes in the employment structure and spatially different tendencies and segregation in the scope of dominant functions.
B a c k g ro u n d: Arterial hypertension (HTN) ranks among the most widespread chronic illnesses that affect adults in industrialized societies. The main goal of this study was to describe the control (inhibition) processes among HTN patients, and to evaluate the dynamics of brain activity while the patients were engaged in tasks measuring the cognitive aspect of self-control.
P a r t i c i p a n t s a n d p ro c e d u re: A set of neuropsychological tests (California Verbal Learning Test, Color Trails Test, The Trail Making Test, Controlled Oral Word Association Test), and a fMRI Stroop test (rapid event design) were administered to 40 persons (20 HTN patients and 20 controls). Groups were matched in terms of age, sex, education, smoking history, and waist-to-hip ratio.
R e s u l t s: As revealed by fMRI, the HTN patients demonstrate left-hemisphere asymmetry in inhibitory processes. Also around 90% of patients had problems when completing tasks which rely on verbal and graphomotor aspects of self-control.
C o n c l u s i o n s: The results suggest that both cerebral hemispheres must interact correctly in order to provide successful executive control. The deficiencies in control and executive functioning, which were observed among the patients, prove that HTN negatively affects brain processes that control one’s cognitive activity.
In this paper, it has been shown that any measuring process can be modeled as a process of sampling of signals. Also, a notion of a special kind of functions, called here functions with attributes, has been introduced. The starting point here, in the first of the above themes, is an observation that in fact we are not able to measure and record truly continuously in time any physical quantity. The measuring process can be viewed as going stepwise that is in steps from one instant to another, similarly as a sampling of signals proceeds. Therefore, it can be modeled as the latter one. We discuss this in more detail here. And, the notion of functions with attributes, we introduced here, follows in a natural way from the interpretation of both the measuring process as well as the sampling of signals that we present in this paper. It turns out to be useful.
This article presents methods and algorithms for the computation of isogenies of degree ℓn. Some of these methods are obtained using recurrence equations and generating functions. A standard multiplication based algorithm for computation of isogeny of degree ℓn has time complexity equal to O(n2 M (n log n)), where M(N) denotes the cost of integers of size N multiplication. The memory complexity of this algorithm is equal to O (n log (n log (n))). In this article are presented algorithms for:
where optimality in this context means that, for the given parameters, no other strategy exists that requires fewer operations for computation of isogeny.
Also this article presents a method using generating functions for obtaining the solutions of sequences (um) and (cm) where cm denotes the cost of computations of isogeny of degree ℓum for given costs p; q of ℓ-isogeny computation and ℓ-isogeny evaluation. These solutions are also used in the construction of the algorithms presented in this article.
The article reviews the integrated territorial investments carried out in the Opolskie Voivodeship in the financial perspective 2014-2020. The object of the analysis was the Opole Agglomeration as the only of five functional areas of the Opolskie Voivodeship, where beneficiaries of funds from European Funds are located within this investment policy development policy.
The aim of the study was to examine the relationships of Level -1/Level -2 visual perspective -taking (VPT -1/VPT -2) with theory of mind (ToM) and executive function (EF). Seventy -six adults aged 18 to 48 years participated in the study. To compare the relationships of the two levels of perspective -taking with the aforementioned abilities, the same stimuli were used in both Level -1 and Level -2 trials of the VPT task. ToM abilities were evaluated with the Strange Story task, and EF using the TMT and WCST tests. It was found that controlling for age -related differences, VPT -1 was not associated with either ToM or such components of EF as executive control and set -shifting. VPT -2 was positively related to ToM, but it was not related to EF. The relationship between VPT -2 and ToM was specific, not mediated by domain -general processing capabilities. The obtained results provide further evidence to support the view that distinct mechanisms underlie Level -1 and Level -2 perspective -taking.
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