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1

Simple Derivation of the Hermite Bicubic Patchusing Tensor Product

Skala Vaclav

Machine Graphics and Vision

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2025

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Vol. 34, No. 2

29--38

EN

Bicubic parametric patches are widely used in various geometric applications. These patches are critical in CAD/CAM systems, which are applied in the automotive industry and mechanical and civil engineering. Commonly, Hermite, Bézier, Coons, or NURBS patches are employed in practice. However, the construction of the Hermite bicubic patch is often not easy to explain formally. This contribution presents a new formal method for constructing the Hermite bicubic plate based on the tensor product approach.

2

Discrete interpolation based on the area of possible location of the evolute of a monotone curve

Kholodniak Yuliia, Havrylenko Yevhen, Halko Serhii, Suprun Olena, Miroshnyk Oleksandr, Shchur Taras, Korenko Maroš, Tomporowski Andrzej, Kruszelnicka Weronika, Walichnowska Patrycja

Advances in Science and Technology. Research Journal

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2025

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Vol. 19, no. 9

281--291

EN

Methods for geometric modelling of curves with a given set of properties interpolating point series of complex configuration form the foundation for developing computer-aided design systems for products bounded by functional surfaces. The key characteristics of the interpolating curve, which ensure the necessary surface properties, include a regular change in curvature values and a minimum number of singular points. The article aims to develop a method for generating a sequence consisting of an arbitrarily large number of specified reference points and assigned intermediate points, which can be interpolated by a monotone curve. The positions of intermediate points are determined based on the pre-assigned properties of the interpolating curve, including the positions of normals and curvature values. The correctness of the solutions proposed in the article is validated through the resolution of a test example. The method developed in the paper is a crucial step towards solving the problem of forming a contour that represents, with given accuracy, a curve with specified properties, interpolating a point series of arbitrary configuration.

3

Geostatystyka dla niematematyków. Przewodnik praktyczny – część I

Naworyta Wojciech

Przegląd Geologiczny

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2024

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Vol. 72, nr 7

341--349

EN

Geostatistical tools are useful and even necessary in many fields, not only in geology. The obstacle to their widespread use is the seemingly difficult mathematical foundations with which the teaching of the subject usually begins. Many years of experience and observations allow me to claim that even if geostatistical methods are used, they are often incomplete and imperfect. In a series of three articles, I would like to introduce potential non-mathematicians to the most important methods and tools from the arsenal of spatial statistics and how to use them properly. I will indicate the areas where they can be used, explain whether they can always be used, showwhat decisions should be made during calculations and how to interpret the obtained results. It will not be a compendium, but rather a pocket guide facilitating the reader's first contact with geostatistics. In the first article, in the introduction, I will explain where the title comes from; I will show what geostatistics can be useful for; what is interpolation, is it always possible, when does it make sense and what does its accuracy depend on? I will show how imperfect the research material available to a geologist is and why we should use sophisticated software to solve seemingly simpleproblems. Using a non-obvious example, I will try to explain the phenomenon of autocorrelation, which is important in geostatistics. I will also ask a few questions, the answers to which will be in the next article in this series.

4

Geostatystyka dla niematematyków. Przewodnik praktyczny – część III

Naworyta Wojciech

Przegląd Geologiczny

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2024

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Vol. 72, nr 9

451--459

EN

Geostatistical tools are useful and even necessary in many fields, not only in geology. The obstacle to their widespread use is the seemingly difficult mathematical foundations with which the teaching of the subject usually begins. Many years of experience and observations allow me to claim that even if geostatistical methods are used, they are often incomplete and imperfect. In a series of three articles, I would like to introduce potential non-mathematicians to the most important methods and tools from the arsenal of spatial statistics and how to use them properly. I will indicate the areas where they can be used, explain whether they can always be used, show what decisions should be made during calculations and how to interpret the obtained results. It will not be a compendium, but rather a pocket guide facilitating the reader ’s first contact with geostatistics. In the third article of my series, I will present the kriging procedure - an interpolation method based on geostatistical assumptions. I will list the most important activities and decisions that need to be made when using this method. Creating a model using the kriging method is the basic goal of using geostatistical methods, so in this article I will make extensive use of the content I presented earlier, from interpolation through autocorrelations to the variogram. The latter serves as an important tool in kriging. Using the example of a lignite deposit model, I will show how to interpret the model and the model credibility map.

5

Optimization of the polynomial fifth-order interpolation 1P kernel in the time domain

Milivojević Zoran, Ivković Ratko, Prlinčević Bojan, Kostić Dijana

Przegląd Elektrotechniczny

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2024

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R. 100, nr 10

79--83

EN

In the first part of this paper, the fifth-order polynomial interpolation convolution one-parameter kernel, is presented. After that, optimization of the interpolation kernel in the time domain was performed. The optimization criterion was the minimization of the interpolation error. The minimization of the error was realized by choosing the optimal value of the kernel parameter αopt. Verification of the correctness of the selection of the opt, by experiment was performed. First, test functions with a complex time shape were created. After that, the test functions were interpolated using interpolation kernels with some analysed kernel parameters. Interpolation errors are shown using MSE. Finally, by applying a comparative analysis, the verification of the choice of the optimal kernel parameter αopt was carried out.

PL

W pierwszej części artykułu zaprezentowano jednoparametrowe jądro splotu interpolacji wielomianowej piątego stopnia. Następnie przeprowadzono optymalizację jądra interpolacyjnego w dziedzinie czasu. Kryterium optymalizacji stanowiła minimalizacja błędu interpolacji. Minimalizację błędu realizowano poprzez dobór optymalnej wartości parametru jądra αopt. Weryfikację poprawności wyboru opt przeprowadzono metodą eksperymentalną. W pierwszej kolejności utworzono funkcje testowe o złożonym kształcie czasu. Następnie funkcje testowe interpolowano za pomocą jąder interpolacyjnych z niektórymi analizowanymi parametrami jądra. Błędy interpolacji są pokazywane za pomocą MSE. Na koniec, stosując analizę porównawczą, przeprowadzono weryfikację wyboru optymalnego parametru jądra αopt.

6

Spatiotemporal Assessment of Groundwater Quality in the Oum Rbia Watershed Using GIS-Pro and Water Quality Indices

Ouhakki Hicham, Taouil Hamid, El Fallah Kamal, Zerraf Soufiane, El Mejdoub Nouredine

Journal of Ecological Engineering

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2024

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Vol. 25, nr 11

15--27

EN

Groundwater analysis across the Oum Rbia watershed is currently hampered by technical constraints and high costs. This research aimed to produce comprehensive groundwater quality maps throughout the basin aquifers by integrating the water quality index (WQI) and microbiological quality index (MQI) with GIS-Pro for a spatiotem poral assessment of water quality. Twenty physicochemical parameters, including pH, temperature, conductivity, total dissolved solids, permanganate index, ammonium (NH₄⁺), major cations (Na⁺, K⁺, Ca2⁺, Mg2⁺, Mn2⁺), major anions (Cl-, HCO3-, NO2-, NO2-, CO3-2, SO₄2-), total hardness (TH), total alkalinity (TAC), and total iron (FeT) concentration were analyzed. Additionally, the microbiological parameters, such as the fecal streptococci, fecal coliforms, and total coliforms were investigated. Fieldwork conducted over twelve campaigns during the 2021 and 2022 seasons involved sample collection from fifty-four locations across the six aquifers of the watershed. The comprehensive database facilitated the calculation of both MQI and WQI. Kriging interpolation was utilized to create spatial estimates of these indices beyond the sampling points, enabling the generation of maps that visualize water quality across the study area. WQI indicated that groundwater in most of the studied basin is of excellent quality, though water quality deteriorates in the areas receiving wastewater discharge from urban, industrial, and agricultural activities. The MQI results revealed significant pathogenic germ contamination across a substantial portion of the watershed, intensifying during the summer due to such factors as temperature, river flow, human activities, and seasonal pollution sources. These maps enhance the understanding of water table information for non-experts as well as aid decision-makers in identifying critical areas and developing effective management strategies. However, complexities in water quality and training data influence the accuracy of ArcGIS-Pro predictions, potentially overlooking key factors if the data is insufficient.

7

Spatiotemporal Interpolation of Water Quality Index and Nitrates Using ArcGIS Pro for Surface Water Quality Modeling in the Oum Er-Rabia Watershed

Ouhakki Hicham, El Fallah Kamal, El Mejdoub Nouredine

Ecological Engineering & Environmental Technology

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2024

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Vol. 25, iss. 5

312--323

EN

This study aims to create complete surface water quality maps for the Oum Er Rabia watershed by predicting nitrate (NO3 - ) and water quality index (WQI) values at unsampled locations. Utilizing a combination of NO3 - , IQE data, and ArcGIS Pro software. Water samples were collected from 40 stations across the basin during twelve campaigns conducted in the winter and summer of 2021 and 2022. The database contains the analysis results of 12 parameters measured in 480 samples. The method used to model water quality is interpolation with ArcGIS Pro. The distribution map of nitrate values for all samples shows concentrations ranging from 0.26 to 38.89 mg/L. These values are lower than the admissible level recommended by the Moroccan standard for drinking water (50 mg/L). The resulting map of the modeling shows higher NO3 - concentrations in summur than in winter. The resulting map of the WQI modeling shows that water quality is excellent in most of the Oum Er-Rbia watershed, with the majority of the area falling into the “good” and “excellent” categories. The water quality deterio-rates in certain parts, especially at stations SS3, SS4, SS5, SS8, and PS9, where the water is of poor quality. In the central and eastern parts, the presence of excessively high ammonium concentrations has significantly compromised the water quality, leading to heavy pollution. Exceeding Moroccan drinking water standards, these observed levels likely stem from human activities. Accurate water quality predictions with ArcGIS Pro require considering data quality, historical trends, and spatiotemporal variations. Understanding these limitations ensures responsible and effective tool use. The study concluded that water pollution could be due to proximity to industrial and urban areas. This study’s uniqueness lies in integrating the WQI, NO3 -, and ArcGIS-Pro into maps. This approach makes information accessible to the public and useful for decision-makers to take action at all watershed points.

8

Spatial Analysis of Environmental Factors for Modeling Plant Hopper Potential Risk Prediction

Minh Vo Quang, Quang Truong Chi, Hieu Pham Thi Minh

Ecological Engineering & Environmental Technology

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2024

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Vol. 25, iss. 11

110--117

EN

Agricultural insect pests reduce crop productivity, causing a gap between global food demand and production. Early detection and early response can improve pest control efficiency. The study aimed to investigate the spatial correlations between brown plant hopper (BPH) occurrence and affected factors using field data collection in Can Tho City, Vietnam. The data on cultivation practices and meteorological conditions at 120 weekly monitoring sites at Can Tho city during the rice cropping season of 2016–2017 were collected to find the correlation between the occurrence frequency and density of BPH. Besides, GIS and spatial interpolation were applied to assess the current status of harmful situations, predict the impact trends of crop pests or diseases in space and time to serve a community’s needs, as well as forecast plant protection. As a result, in the 2nd rice cropping stage, the population of brown planthoppers was found to be highly significantly influenced by the following factors: (1) planthopper age, (2) natural enemy density, (3) air temperature, (4) field water level, and (5) number of leaves, which is highly positively correlated with brown hopper density. There is a lower correlation between leaf color code (6) and air humidity (7) and a negative correlation between pesticides used (8). The variables of rice leaf color code (6) and air humidity (7) correlate with the BPH population, although the field water level (4) and leaf count (5) do not correlate for the whole crop. It can be used to predict the changing trend of BPH in rice fields. However, the factors influencing the brown planthopper would determine the accuracy of the prognosis.

9

Influence of interpolation of the method of mixing the liquid in the container on the mixing efficiency

Hebda Aleksander

Sustainable Production, Instrumentation and Engineering Sciences

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2023

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vol. 1, nr 1

9--12

EN

An anthropomorphic robot, i.e. a robot that can reproduce the movements of the human arm, is equipped with various types of interpolation. The ro-bot can be used to mix two liquids enclosed in a shaker mixer. The problem that has to be solved is the selection of the optimal types of interpolation, as well as the sequence of these robot movements that is able to provide better results higher mixing efficiency, in other words amore sustainable approach to the mixing process, using an anthropomorphic robot.The shaker-type container used the shape of a truncated cone has a positive effect on the efficiency of the liquid mixing process. The difference in den-sity between the two liquids contributes to a sustainable approach to the mixing process. It is preferable to use different shaker position with re-spect to the gravitational acceleration vector and to use different linear and arc interpolation. The use of variable position in relations to gravita-tional acceleration vector, due to the shape of the truncated cone of the mixer, will cause chaotic movement of particles inside the shaker, which is a desirable phenomenon, because then both mixed liquids mix quickly

10

Optymalizacja wykorzystania kanału informacyjnego do transmisji danych pomiarowych

Torbus Sławomir Andrzej, Mroczyńska Karolina

Rynek Energii

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2023

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Nr 6

20--25

PL

W pracy zaprezentowano algorytm umożliwiający optymalizację wykorzystania kanału informacyjnego reprezentującego łącze telemetryczne do transmisji sygnałów pomiarowych. Wykorzystano w nim wybrane zagadnienia teorii informacji Shannona oraz interpolację i decymację. Określono trójwymiarową charakterystykę oraz zestaw charakterystyk dwuwymiarowych, które umożliwiają określanie optymalnych warunków pracy łącza telemetrycznego, które gwarantują brak wystąpienia natłoku. Wskazano w jaki sposób należy dobierać współczynniki decymacji i interpolacji, aby zagwarantować optymalne wykorzystanie kanału informacyjnego. Sformułowano wnioski dotyczące zaproponowanego algorytmu.

EN

The work presents an algorithm enabling the optimization of the use of the information channel representing the telemetry link for the transmission of measurement signals. It uses selected issues of Shannon's information theory as well as interpolation and decimation. Three-dimensional characteristics and a set of two dimensional characteristics were determined, which enable the determination of optimal operating conditions ofthe telemetry link, which guarantee the absence of crowding. It was indicated how to select decimation and interpolation coefﬁcients to ensure optimal use of the information channel. Conclusions regarding the proposed algorithm were formulated.

11

Using interpolation method to estimation step and touch voltage in grounding system

Sikora Roman, Markiewicz Przemysław, Mączka Mariusz, Pawłowski Stanisław, Plewako Jolanta

Przegląd Elektrotechniczny

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2023

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R. 99, nr 2

263--266

EN

The article presents a methodology for calculating the step voltage on the ground surface above the grounding grid of an MV/LV substation. The calculations are performed by using the interpolation method based on the knowledge of the electric potential distribution. The electric potential distribution was determined for the grounding grid model using the finite element method in ANSYS program. The interpolating relationship of two variables allows the calculation of step voltage for any location of human feet.

PL

W referacie przedstawiono metodykę obliczenia napięcia korkowego na powierzchni gruntu nad uziomem stacji SN/nN. Obliczenia są wykonywane za pomocą interpolacji w oparciu o znajomość rozkładu potencjału elektrycznego. Rozkład potencjału elektrycznego został wyznaczony dla modelu uziomu z wykorzystaniem metody elementów skończonych w programie ANSYS. Wyznaczona zależność interpolująca dwóch zmiennych pozwala na odliczenie napięcia krokowego dla dowolnej lokalizacji stóp człowieka.

12

Sterowanie plotera w kartezjańskim układzie XY

Nowacki Wiktor, Wiczyński Grzegorz

Poznan University of Technology Academic Journals. Electrical Engineering

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2023

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No. 108

55--64

PL

W artykule przedstawiono zagadnienie sterowania końcówką roboczą dwuosiowego manipulatora w standardowym układzie kartezjańskim. Omówiono możliwość wykonania ruchu point-to-point oraz interpolacji pewnych geometrii tak, aby możliwy był ruch robota wzdłuż określonej trajektorii. Równania matematyczne zaimplementowano na sterowniku z mikrokontrolerem STM32 i przeprowadzono testy na fizycznym urządzeniu, dla którego omówiono konstrukcję mechaniczną oraz istotne aspekty elektroniczne, szczególnie te dotyczące sterowania silnikami i obsługi enkoderów kwadraturowych.

EN

This paper shows basic method of control end-effector for a two-axis manipulator in a standard Cartesian system. The possibility of performing point-to-point motion and interpolating geometric data for possibility of performing electrical motion for specific trajectories was discussed. Mathematical equations implemented on controllers with an STM32 microcontroller and tested on a physical controller. Mechanical details were presented, and important electronic aspects were discussed, especially those regarding motor control and operation of quadrature encoders.

13

Two-dimensional EMD with shape-preserving spline interpolation

Brown Wesley G., Walt Maria D. van der

Journal of Applied Analysis

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2023

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Vol. 29, nr 2

287--296

EN

Empirical mode decomposition (EMD) is a popular, user-friendly, data-driven algorithm to decompose a given (non-stationary) signal into its constituting components, utilizing spline interpolation. This algorithm was first proposed in 1998 in the one-dimensional setting, and it employed standard cubic spline interpolation. Since then, different two-dimensional extensions of EMD have been proposed. In this paper, we consider one of these two-dimensional extensions and adapt it to use a shape-preserving interpolation scheme based on quadratic B-splines, ensuring that monotonicity and concavity in the input data are preserved. Using multiple numerical experiments, we show that this new scheme outperforms the original EMD, both qualitatively and quantitatively.

14

Improvement of the algorithm for setting the characteristics of interpolation monotone curve

Kholodniak Yuliia, Havrylenko Yevhen, Halko Serhii, Hnatushenko Volodymyr, Suprun Olena, Volina Tatiana, Miroshnyk Oleksandr, Shchur Taras

Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska

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2023

|

T. 13, nr 4

44--50

EN

Interpolation of a point series is a necessary step in solving such problems as building graphs de-scribing phenomena or processes, as wellas modelling based on a set of reference points of the line frames defining the surface. To obtain an adequate model, the following conditions are imposed upon the interpolating curve: a minimum number of singular points (kinking points, inflection points or points of extreme curvature) and a regular curvature change along the curve. The aim of the work is to develop the algorithm for assigning characteristics (position of normals and curvature value) to the interpolating curve at reference points, at which the curve complies with the specified conditions. The characteristics of the curve are assigned within the area of their possible location. The possibilities of the proposed algorithm are investigated by interpolating the point series assignedto the branches of the parabola. In solving the test example, deviations of the normals and curvature radii from the corresponding characteristicsof the original curve have been determined. The values obtained confirm the correctness of the solutions proposed in the paper.

PL

Interpolacja szeregu punktowego jest niezbędnym krokiem w rozwiązywaniu takich problemów, jak budowanie grafów opisujących zjawiska lub procesy, a także modelowanie w oparciu o zbiór punktów odniesienia układów liniowychdefiniujących powierzchnię. Aby uzyskać odpowiedni model, na interpolowaną krzywą stawia się następujące warunki: minimalną liczbę punktów osobliwych (punktów załamania, punktów przegięcia lub punktów skrajnej krzywizny) oraz regularną zmianę krzywizny wzdłuż krzywej. Celem pracy jest opracowanie algorytmu przypisania charakterystyk (położenia normalnych i wartości krzywizny) krzywej interpolacyjnej w punktach odniesienia, w których krzywa spełnia określone warunki. Charakterystyki krzywych nadawane są w obszarze ich możliwego położenia. Możliwości proponowanego algorytmu są badane poprzez interpolację szeregów punktów przypisanych do gałęzi paraboli. W rozwiązaniu przykładu testowego wyznaczono odchylenia normalnych i promieni krzywizny od odpowiednich charakterystyk pierwotnej krzywej. Otrzymane wartości potwierdzają poprawność zaproponowanych w pracy rozwiązań.

15

Bernstein-type operators on elliptic domain and their interpolation properties

Iliyas Mohammad, Khan Asif, Mursaleen Mohammad

Demonstratio Mathematica

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2023

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Vol. 56, nr 1

art. no. 20220199

EN

The aim of this article is to construct univariate Bernstein-type operators (BxmG)(x,z) and (BznG)(x,z), their products (PmnG)(x,z) , (QnmG)(x,z) , and their Boolean sums (SmnG)(x,z) , (TnmG)(x,z) on elliptic region, which interpolate the given real valued function G defined on elliptic region on its boundary. The bound of the remainders of each approximation formula of corresponding operators are computed with the help of Peano’s theorem and modulus of continuity, and the rate of convergence for functions of Lipschitz class is computed.

16

Tworzenie map tłumienia propagacyjnego z wykorzystaniem motody IDW

Majewski Bartosz, Malon Krzysztof, Kryk Michał, Kelner Jan M.

Przegląd Telekomunikacyjny + Wiadomości Telekomunikacyjne

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2022

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nr 4

515--518

PL

W nowoczesnych systemach komunikacji bezprzewodowej dąży się do rozwiązań technologicznych mających na celu zwiększenie wydajności sieci radiowych, w tym także bardziej efektywnego wykorzystania zasobów widmowych. Niezmiernie istotnym elementem współczesnych systemów jest budowanie świadomości sytuacyjnej oraz wspieranie funkcji kognitywnych. Możliwe jest to między innymi dzięki zastosowaniu map środowiska radiowego REM reprezentujących złożone i wielodziedzinowe informacje dla zastosowań radia kognitywnego. Jednym z kluczowych obszarów REM są mapy tłumienia propagacyjnego pozwalające na określenie m.in. zasięgów łączności sieci bezprzewodowych oraz poziomów sygnałów radiowych w określonych lokalizacjach. W artykule przedstawiono algorytm budowania map tłumienia propagacyjnego z wykorzystaniem metody interpolacji ważonej odwrotną odległością IDW.

EN

In modern wireless communication systems, technological solutions aim to increase the efficiency of radio networks, including the more effective use of spectrum resources. An essential element of current systems is building situational awareness and supporting cognitive functions. It is possible by using, e.g., Radio Environment Maps (REM), representing complex and multi-domain information for cognitive radio applications. One of the critical areas of REM is propagation attenuation maps allowing for the determination of communication ranges of wireless networks or levels of radio signals in specific locations. The article presents an algorithm for building propagation attenuation maps using the Inverse Distance Weighted (IDW) interpolation method.

17

Ocena efektywności generacji map tłumienia propagacyjnego

Kryk Michał

Przegląd Telekomunikacyjny + Wiadomości Telekomunikacyjne

|

2022

|

nr 4

519--522

PL

Nowoczesne systemy komunikacji bezprzewodowej wykorzystują różne rozwiązania technologiczne w celu zwiększenia wydajności tworzonych sieci radiowych. Obecnie jednym z kierunków pozwalających usprawnić zarządzanie zasobami radiowymi jest wykorzystanie mapy środowiska radiowego (REM). REM są coraz częściej wykorzystywane w mobilnych sieciach doraźnych (MANET), w szczególności w taktycznych sieciach wojskowych. Mapy tłumienia propagacyjnego (PAM) są kluczowymi elementami REM, które pozwalają na określenie zasięgów węzłów sieci radiowej. W niniejszym artykule zostanie przedstawiona ocena efektywności autorskiego algorytmu generowania PAM. Zaproponowany algorytm PAM bazuje na metodzie równań parabolicznych (PEM), interpolacji liniowej oraz profilach terenu wyznaczanych na podstawie map wysokościowych DTED.

EN

Modern wireless communication systems use various technological solutions to increase the efficiency of the created radio networks. Currently, the use of the radio environment map (REM) is one of the directions allowing improvement of radio resource management. REM is being used more often in emerging mobile ad-hoc networks (MANETs), in particular in tactical military networks. Propagation attenuation maps (PAMs) are the key elements of REM in determining the ranges of the radio network nodes. In this paper, an efficiency assessment of PAM generation is presented. The proposed PAM algorithm is based on the parabolic equation method (PEM), linear interpolation, and terrain profiles determined based on the DTED elevation maps.

18

Contribution of GIS in the Mapping, Interpolation and Modeling of Isohypses of the Pliocene Aquifuge of the Free Water Table of the Fez-Meknes Basin

El Fakir Rabia, Mili El Mostafa

Ecological Engineering & Environmental Technology

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2022

|

Vol. 23, iss. 5

272--284

EN

In order to model the water flow of the free Quaternary aquifer of the Fez-Meknes basin, it is essential to determine the precise geometric limits of the aquifer. Indeed, the characterization and representation of the underground structure of the Miocene marl top which forms the aquiclude of the aquifer, constitutes the fundamental step to study and understand its influence on the groundwater flow. This study is facilitated by the available data, which allow to represent the underground formations on isohypses maps. The data base is formed by reconnaissance drillings, and the extraction of marl altitudes from previous geological works. During this work the generation of the marl top elevation map was based on the test of four interpolation methods, which correspond to : Kriging, IDW method, Natural Neighbors, and Topo to Raster, in order to choose the most reliable and best suited to the study area. On the one hand, the calculation of the conformity index between the values measured in the field and the estimated values for each method was successively (0.9796, 0.9848, 0.9814, 0.9842). On the other hand the values of the root mean square error (RMSE) were successively (13.59, 7.42, 21.27, 14.01). The comparison of these results allowed us to choose the IDW interpolation as the most reliable and suitable to interpolate the top of the aquiclude of the free water table of the Fez Meknes basin with a compliance index the highest and a RMSE the lowest compared to other methods.

19

An approach for electrical harmonic analysis based on interpolation DFT

Jiao Lina, Du Yang

Archives of Electrical Engineering

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2022

|

Vol. 71, nr 2

445--454

EN

The discrete Fourier transform (DFT) is the main method of electrical harmonic analysis since it’s easily realized in an embedded system. But there were some difficulties in performing synchronized sampling. The spectral leakage caused by asynchronous sampling affects the accuracy of harmonics analysis. Using window functions and interpolation algorithms can improve the accuracy of harmonics analysis. An approach for electrical harmonic analysis based on the interpolation DFT was proposed. A window function reduces DFT leakage and the interpolation algorithm modifies the calculation results of frequency, amplitude and the initial phase angle. The simulation results indicate that, by using the interpolation DFT electrical harmonic analysis method based on the Hanning window or the Blackman window, the error of calculating amplitudes and frequencies is not greater than 0.5%.

20

Determination and evaluation of spatio-temporal trends on the example of PM10 concentration in Poland (2000-2018)

Jackowska Malwina, Fiedukowicz Anna, Gąsiorowski Jędrzej

Polish Cartographical Review

|

2021

|

Vol. 53. No. 1

37--48

EN

. Increasing amounts of rapidly growing data are the driving force behind proposing and automating new processing, enabling the extraction of useful information from data. One of such possibilities is determining trends to consider in terms of time and space. Thus far, the analysis of these aspects has been separate and lacked automated tools. Therefore, the authors proposed, implemented, and tested a tool for analyzing spatio-temporal linear trends. The tool was tested on PM10 concentration data in the years 2000–2018. The results, presented as cartographic visualization, were then evaluated, both in terms of time and space. The proposed approach facilitates analyzing spatio-temporal trends and assessing their accuracy; it can be developed using other types of analyzed trends or considering additional factors that influence the trend by using cokriging.