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1

Accuracy of the application of mobile technologies for measurements made in headings of the Kłodawa Salt Mine

Świerczyńska Ewa Joanna, Kurdek Damian, Jankowska Iwona

Reports on Geodesy and Geoinformatics

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2024

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Vol. 117

55--68

EN

The "Kłodawa" salt mine, due to geological conditions and continuous salt extraction, is subject to a range of measurements documenting the speed of changes in the geometry of the chambers. Cyclic surveys are conducted under challenging conditions several hundred metres underground. Consequently, measurement methods used for determining the parameters of the ongoing clamping should be of high precision but also be resistant to dense dust (in fields of active mining) and strong gusts (near ventilation shafts). The research presented here concerns the analysis of the possibilities of solutions offered by modern technologies in mine conditions. Test measurements were conducted at observation stations using linear bases stabilized with metal pins. The base points were located in the aisles, ceiling, and bottom of the chamber in Field 1 of "Kłodawa" salt mine at the depth of 600m. Point clouds mapping the object were acquired using a Leica RTC360 3D laser scanner and two mobile devices: Motorola G100 smartphone and iPad Pro with LiDAR technology using the Pix4Dcatch application. The accuracy of the point cloud from the Leica RTC360 3D laser scanner was determined by comparing it with classic measurements taken with a Leica Disto laser rangefinder. The repeatability and accuracy of the point cloud from a smartphone were examined using statistical analysis based on Pearson's correlation coefficient and cross-correlation. An attempt was also made to approximate the correlation between the obtained errors and two parameters: the number of images and the size of the object.

2

The discrete, fractional order model of a two-dimensional temperature field using Grünwald-Letnikov definition

Oprzędkiewicz Krzysztof

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2024

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Vol. 72, nr 4

art. no. e150332

EN

In the paper a new, fractional order, discrete model of a two-dimensional temperature field is addressed. The proposed model uses Grünwald-Letnikov definition of the fractional operator. Such a model has not been proposed yet. Elementary properties of the model: practical stability, accuracy and convergence are analysed. Analytical conditions of stability and convergence are proposed and they allow to estimate the orders of the model. Theoretical considerations are validated using exprimental data obtained with the use of a thermal imaging camera. Results of analysis supported by experiments point that the proposed model assures good accuracy and convergence for low order and relatively short memory length.

3

Modified integral transform for solving benney-luke and singular pseudo-hyperbolic equations

Elzaki Tarig M., Chamekh Mourad, Ahmed Shams A.

Acta Mechanica et Automatica

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2024

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Vol. 18, no. 1

139--143

EN

In this article, we propose a technique based on modified double integral transforms used to solve certain equations of materials science, namely Benney–Luke (BL) and singular pseudo-hyperbolic (SP-H) equations. We have established some analytical results. This method can provide accurate one-step solutions, although the equations used may exhibit a singularity in the initial conditions. Some numerical examples have been discussed for illustration and to show the effectiveness of the technique for certain types of equations. We have developed an exact solution in just one step, whereas other approaches require several stages to succeed in a particular solution, making the proposed strategy particularly successful and straightforward to apply to various varieties of the B–L and SP-H equations.

4

Uwarunkowania stosowania strategii dywergencji i konwergencji w przedsiębiorstwach międzynarodowych

Prendke Rafał

Zeszyty Naukowe Politechniki Poznańskiej. Organizacja i Zarządzanie

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2023

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Nr 87

145--160

PL

Procesy globalizacyjne skutkujące przenoszeniem fabryk do innych krajów wymagają od firm zachowania spójności zarówno w zakresie elementów widocznych dla klientów (jakość, marka, produkt), jak i niewidocznych (struktura, kultura organizacyjna, metody zarządzania). Przedmiotem artykułu jest ten drugi, niewidoczny dla klienta obszar. Autor poddał analizie dwie podstawowe strategie interkulturowe stosowane przez firmy: dywergencję i konwergencję. Dywergencja odbierana jako stawiająca na różnorodność i zorientowana na ludzi wydaje się współcześnie wyborem bardziej oczywistym. Presja interesariuszy zmusza jednak firmy do ujednolicania i standaryzowania, co w powszechnej percepcji kojarzy się ze złymi korporacyjnymi praktykami. Konwergencja, jeśli jest stosowana nieumiejętnie, jak pokazują przytoczone w artykule przykłady, prowadzi do kulturowych konfliktów i w konsekwencji zagraża interesom przedsiębiorstwa. Umiejętne łączenie obu tych podejść staje się najważniejszym zadaniem dla menedżerów w międzynarodowych firmach. Autor na podstawie wniosków z własnych badań wyróżnił pięć kluczowych czynników wpływających na przenikanie się dywergencji i konwergencji oraz ich nasilenie.

EN

Globalization processes, resulting in the relocation of enterprises to other countries require companies to maintain consistency in both: elements visible to the customer (such as quality, brand, product etc.) and those invisible (structure, organizational culture, management methods). The subject of the article is that invisible aspect. The author has analyzed two basic strategies used by companies: divergence and convergence, taking into account their possible advantages and disadvantages. Divergence, perceived as focused on diversity, seems to be the more obvious choice nowadays. Pressure from stakeholders, however, forces companies to unify and standardize, which is commonly associated with bad corporate practices. Convergence, if used incompetently, as the examples cited in the article show, leads to cultural clashes and, consequently, threatens the interest of the company. Skillful use of the combination of both approaches, becomes the most important task for managers in international companies. The author, based on his research, has identified five key factors influencing the interpenetration of divergence and convergence and their intensity.

5

On Lq convergence of the Hamiltonian Monte Carlo

Ghosh Soumyadip, Lu Yingdong, Nowicki Tomasz

Journal of Applied Analysis

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2023

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Vol. 29, nr 1

161--169

EN

We establish Lq convergence for Hamiltonian Monte Carlo (HMC) algorithms. More specifically, under mild conditions for the associated Hamiltonian motion, we show that the outputs of the algorithms converge (strongly for 2 ≤ q < ∞ and weakly for 1 < q < 2) to the desired target distribution. In addition, we establish a general convergence rate for an Lq convergence given a convergence rate at a specific q∗, and apply this result to conclude geometric convergence in the Euclidean space for HMC with uniformly strongly logarithmic concave target and auxiliary distributions.We also present the results of experiments to illustrate convergence in Lq.

6

Fourth order computational spline method for two-parameter singularly perturbed boundary value problem

Kambampati Satyanarayana, Emineni Siva Prasad, Reddy M. Chenna Krishna, Kolloju Phaneendra

International Journal of Applied Mechanics and Engineering

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2023

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Vol. 28, no. 4

79--93

EN

The current research work considers a two-parameter singularly perturbed two-point boundary value problem. Here, we suggest a computational scheme derived by using an exponential spline for the numerical solution of the problem on a uniform mesh. The proposed numerical scheme is analyzed for convergence and an accuracy of O(h4) is achieved. Numerical experiments are considered to validate the efficiency of the spline method, and compared comparison with the existing method to prove the superiority of the proposed scheme.

7

Tectonic strain in salt rock mass based on measurements

Szczerbowski Zbigniew, Niedbalski Zbigniew, Bednarek Łukasz

Geology, Geophysics and Environment

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2023

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Vol. 49, no. 2

157--173

EN

The measurement method with the application of an extensometer for the detection of the manifestation of tectonic strain is presented in this paper. The instrument is operated in underground construction for engineering purposes, and the authors applied it in a deeply placed underground old mine gallery in the Bochnia Salt Mine, just at the tectonic boundary of the Outer Carpathians which is commonly considered to be a tectonically active zone. The presented study is characterized by two basic features. The first is the placement of the measurements deep in an old mine which is an environment free of atmospheric factors disturbing the detection of a tectonic signal. The second is a combination of routine measurements carried out for engineering purposes and research measurements enabling the extension of the observation of displacements in the space outside underground workings, inside the rock mass that has been penetrated by extensometer probes. The extensometric measurements have been made using three 7-meter long sections. The results showed the differentiation in the displacement rates of points placed in the side walls: in the southern profile, the annual displacements are approximately 1.5 mm and in the northern one – approximately 1 mm. The combined result corresponds to the amount of the annual convergence value which has been determined by the classical surveys in the excavation where extensometric measurements have been made. What is more, the ongoing displacements in the southern side wall involve the entire part of the rock mass which is penetrated by an extensometric probe, but the displacements in the northern side are only observed in the first 2 m of the penetrated part of the rock mass. This differentiation is interpreted by the authors as being the result of tectonic strain acting from the south exerted by the Carpathians.

8

Comparative Advantage of Yarn and Weaving Industries: Evidence for Türkiye and Top Exporters

Kantur Çiğdem, Türkekul Berna

Fibres & Textiles in Eastern Europe

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2023

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Vol. 31, no. 1

15--24

EN

With the repeal of the MFA agreement, the competitive conditions in yarn and weaving industries have changed. Especially, with the cheap labour of Asian and Far Eastern countries, they have become advantageous in this unrestricted competition environment. Therefore, this study was conducted to help to identify those products where Türkiye and her competitors have comparative advantages. This study mainly focuses on analysing the complementarity and substitutability of selected countries such as Türkiye, India, China and the USA. RTA, RC, RSCA and trade specialisation (TSI) indices were used to evaluate the competitive advantage. The results showed that Türkiye’s competitiveness in cotton yarn and cotton weaving has deteriorated. However, India and China, which are the major countries in the world’s cotton production, have a positive impact on their long-term competitiveness. Moreover, for these countries there is convergence in cotton yarn and divergence in cotton fabric products.

9

Pomiar ruchu górotworu w kopalniach soli

Maj Agnieszka

Prace Instytutu Mechaniki Górotworu PAN

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2022

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T. 24, nr 1-4

61--70

PL

Kopalniane wyrobiska generują zagrożenia. Zapewnienie bezpieczeństwa jest głównym zadaniem nadzoru górniczego. W podziemnych kopalniach soli jednym z głównych zagrożeń jest zagrożenie zawałowe. Jego opanowaniu służy znajomość zachowania się górotworu. Wiedzę tę nabywa się analizując ruch górotworu. W polskich kopalniach soli monitorowany jest on różnymi metodami. Prowadzone są obserwacje niecki osiadań na powierzchni, zaciskania wyrobisk oraz deformacji półek i filarów. W artykule opisano sposoby pomiarów ruchu górotworu z podaniem przykładowych wyników i przedstawiono przykładowe efekty analiz wyników obserwacji.

EN

Excavation voids generate hazards in mines. Ensuring safety is the primary task of mining supervision. One of the main hazards in underground salt mines is the risk of collapse. The analysis of the rock mass movement, through the knowledge of its behaviour, helps to control the collapse hazards. In Polish salt mines, the various methods of the rock mass movements have been used. Observations of subsidence trough on the surface, room closure and deformations of shelves and pillars are carried out. The methods of rock mass motion measurements with the examples of results and the exemplary effects of the analysis of observation results are presented in the article.

10

Comparative analysis of Riemann-Liouville, Caputo-Fabrizio, and Atangana-Baleanu integrals

Shaikh Asif Ali, Qureshi Sania

Journal of Applied Mathematics and Computational Mechanics

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2022

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Vol. 21, nr 1

91--101

EN

This study analyzes the most commonly used operators of the Riemann-Liouville, the Caputo-Fabrizio, and the Atangana-Baleanu integral operators. Firstly, a numerical scheme for the Riemann-Liouville fractional integral has been discussed. Then, two numerical techniques have been suggested for the remaining two operators. The experimental order of convergence for the schemes is further supported by the computations of absolute relative error at the final nodal point over the integration interval [0, T ]. Comparative analysis of the integrals reveals that the Riemann-Liouville fractional integral yields the most minor errors and the most significant experimental order of convergence in the majority of functions, particularly when the fractional-order parameter α → 0. It is worth noting that the Atangana-Baleanu has proved to be an essential operator for solving many dynamical systems that a single RL operator cannot handle. All of the three integral operators coincide with each other for α = 1. Mathematica 11.3 for an Intel(R) Core(TM) i3-4500U procesor running on 1.70 GHz is used to carry out all the necessary computations.

11

Sharp sufficient condition for the convergence of greedy expansions with errors in coefficient computation

Valiullin Artur R., Valiullin Albert R., Solodov Alexei P.

Demonstratio Mathematica

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2022

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Vol. 55, nr 1

254--264

EN

Generalized approximate weak greedy algorithms (gAWGAs) were introduced by Galatenko and Livshits as a generalization of approximate weak greedy algorithms, which, in turn, generalize weak greedy algorithm and thus pure greedy algorithm. We consider a narrower case of gAWGA in which only a sequence of absolute errors {ξn}∞n=1 is nonzero. In this case sufficient condition for a convergence of a gAWGA expansion to an expanded element obtained by Galatenko and Livshits can be written as ∑∞n=1ξ2n<∞ . In the present article, we relax this condition and show that the convergence is guaranteed for ξn=o(1√n) . This result is sharp because the convergence may fail to hold for ξn≍1√n .

12

An accurate and efficient local one-dimensional method for the 3D acoustic wave equation

Wu Mengling, Jiang Yunzhi, Ge Yongbin

Demonstratio Mathematica

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2022

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Vol. 55, nr 1

528--552

EN

We establish an accurate and efficient scheme with four-order accuracy for solving three-dimensional (3D) acoustic wave equation. First, the local one-dimensional method is used to transfer the 3D wave equation into three one-dimensional wave equations. Then, a new scheme is obtained by the Padé formulas for computation of spatial second derivatives and the correction of the truncation error remainder for discretization of temporal second derivative. It is compact and can be solved directly by the Thomas algorithm. Subsequently, the Fourier analysis method and the Lax equivalence theorem are employed to prove the stability and convergence of the present scheme, which shows that it is conditionally stable and convergent, and the stability condition is superior to that of most existing numerical methods of equivalent order of accuracy in the literature. It allows us to reduce computational cost with relatively large time step lengths. Finally, numerical examples have demonstrated high accuracy, stability, and efficiency of our method.

13

Nonlinear Evolutionary PDE-Based Refinement of Optical Flow

Doshi Hirak, Kiran Nori Uday

Machine Graphics and Vision

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2021

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Vol. 30, No. 1/4

45--65

EN

The goal of this paper is to propose two nonlinear variational models for obtaining a refined motion estimation from an image sequence. Both the proposed models can be considered as a part of a generalized framework for an accurate estimation of physics-based flow fields such as rotational and fluid flow. The first model is novel in the sense that it is divided into two phases: the first phase obtains a crude estimate of the optical flow and then the second phase refines this estimate using additional constraints. The correctness of this model is proved using an evolutionary PDE approach. The second model achieves the same refinement as the first model, but in a standard manner, using a single functional. A special feature of our models is that they permit us to provide efficient numerical implementations through the first-order primal-dual Chambolle-Pock scheme. Both the models are compared in the context of accurate estimation of angle by performing an anisotropic regularization of the divergence and curl of the flow respectively. We observe that, although both the models obtain the same level of accuracy, the two-phase model is more efficient. In fact, we empirically demonstrate that the single-phase and the two-phase models have convergence rates of order O(1/N²) and O(1/N) respectively.

14

Trójparametryczna optymalizacja trzonu pełnościennego słupa energetycznego

Wandzik Grzegorz, Potempa Rafał

Inżynieria i Budownictwo

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2021

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R. 77, nr 5-6

195--199

PL

Przedstawiono metodę poszukiwania optymalnego kształtu stalowego słupa energetycznego o konstrukcji powłokowej. Optymalizacja została ograniczona do trzech parametrów: średnicy, zbieżności trzonu, grubości ścianki powłoki. Podstawą analiz jest minimalizacja objętości stali, z użyciem dostosowanej do problemu metody gradientu prostego. Algorytm zastosowano w autorskim programie komputerowym.

EN

The method of searching the optimal shape of a steel high-voltage thin-shell pole was presented. The optimization was limited to three parameters: the diameter, convergence of the shaft, the wall thickness of the shell. The basis of the analysis is the minimization of the steel volume of the pole shaft using the simple gradient descent method adapted to the problem. The algorithm has been implemented in a proprietary computer application.

15

Solving two-dimensional nonlinear fuzzy Volterra integral equations by homotopy analysis method

Georgieva Atanaska

Demonstratio Mathematica

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2021

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Vol. 54, nr 1

11--24

EN

The purpose of the paper is to find an approximate solution of the two-dimensional nonlinear fuzzy Volterra integral equation, as homotopy analysis method (HAM) is applied. Studied equation is converted to a nonlinear system of Volterra integral equations in a crisp case. Using HAM we find approximate solution of this system and hence obtain an approximation for the fuzzy solution of the nonlinear fuzzy Volterra integral equation. The convergence of the proposed method is proved. An error estimate between the exact and the approximate solution is found. The validity and applicability of the HAM are illustrated by a numerical example.

16

Time-domain decomposition for optimal control problems governed by semilinear hyperbolic systems with mixed two-point boundary conditions

Krug Richard, Leugering Günter, Martin Alexander, Schmidt Martin, Weninger Dieter

Control and Cybernetics

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2021

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Vol. 50, No. 4

427--455

EN

In this article, we study the time-domain decomposition of optimal control problems for systems of semilinear hyperbolic equations and provide an in-depth well-posedness analysis. This is a continuation of our work, Krug et al. (2021) in that we now consider mixed two-point boundary value problems. The more general boundary conditions significantly enlarge the scope of applications, e.g., to hyperbolic problems on metric graphs with cycles. We design an iterative method based on the optimality systems that can be interpreted as a decomposition method for the original optimal control problem into virtual control problems on smaller time domains.

17

Neumann boundary optimal control problems governed by parabolic variational equalities

Bollo Carolina M., Gariboldi Claudia M., Tarzia Domingo A.

Control and Cybernetics

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2021

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Vol. 50, No. 2

227--252

EN

We consider a heat conduction problem S with mixed boundary conditions in an n-dimensional domain with regular boundary and a family of problems Sα with also mixed boundary conditions in , where α > 0 is the heat transfer coefficient on the portion of the boundary Г1. In relation to these state systems, we formulate Neumann boundary optimal control problems on the heat flux q which is definite on the complementary portion Г2 of the boundary of Ω. We obtain existence and uniqueness of the optimal controls, the first order optimality conditions in terms of the adjoint state and the convergence of the optimal controls, the system state and the adjoint state when the heat transfer coefficient α goes to infinity. Furthermore, we formulate particular boundary optimal control problems on a real parameter λ, in relation to the parabolic problems S and Sαα

18

Numerical modeling of heat transfer in Al2O3/H2O nanofluid flowing through a Bessel-like converging pipe

Iweka Chukwuka S., Fadodun Olatomide G.

Archives of Thermodynamics

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2021

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Vol. 42, no 2

121--153

EN

This paper studies hydrodynamic and heat transfer performance of Al2O3/H2O nanofluid flowing through a Bessel-like converging pipe in laminar flow regime using the computational fluid dynamic approach. A parametric study was carried out on the effect of Reynolds number (300– 1200), convergence index (0-3) and nanoparticle concentration (0–3%) on the both hydrodynamic and thermal fields. The results showed the pressure drop profile along the axial length of the converging pipes is parabolic compared to the downward straight profile obtained in a straight pipe. Furthermore, an increase in convergence index, Reynolds number and nanoparticle concentration were found to enhance convective heat transfer performance. Also, a new empirical model was developed to estimates the average Nusselt number as a function of aforementioned variables. Finally, the result of the thermohydraulic performance evaluation criterion showed that the usage of Bessel-like converging pipes is advantageous at a low Reynolds number.

19

Adaptive individual weight-gain AVO inversion with smooth nonconvex regularization

Du Siyuan, Zhang Jiashu, Zhang Sheng, Hu Guangmin

Acta Geophysica

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2021

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Vol. 69, no. 4

1199--1213

EN

Amplitude variation with ofset (AVO) inversion is a widely used approach to obtain reliable estimates of elastic parameter in the felds of seismic exploration. However, the AVO inversion is an ill-posed problem because of the band-limited characteristic of seismic data. The regularization constraint plays an important role in improving inversion resolution. Total variation (TV) class regularization based on L1 norm has been introduced in seismic inversion. But, these methods may underestimate the high-amplitude components and obtain low-resolution results. To tackle these issues, we propose to combine a smooth nonconvex regularization approach with adaptive individual weight-gain. Compared with the L1 norm regularizers, the proposed smoothed nonconvex sparsity-inducing regularizers can lead to more accurate estimation for high-amplitude components. Diferent from previous regularization methods, the proposed approach also assigns diferent weight regularization parameters for diferent strata, which we call adaptive individual weight-gain strategy. To ensure sufcient minimization of the constructed objective function, a spectral Polak–Ribière–Polyak conjugate gradient method with line search step size is used. Further, we prove that the proposed algorithm converges to a stationary point. The synthetic data tests illustrate that our approach has improved performance compared with the conventional TV class regularization methods. Field data example further verifes the higher resolution of the proposed approach.

20

Zastosowanie elektronicznych pomiarów odkształceń górotworu na przykładzie wyrobiska KS Bochnia

Szczerbowski Zbigniew, Niedbalski Zbigniew, Jóźwik Mieczysław, Migdas Tomasz, Kawalec Andrzej, Orzeł Karol

Przegląd Górniczy

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2020

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T. 76, nr 1

19--26

PL

Badania deformacji górotworu w rejonie zabytkowej Kaplicy św. Kingi Kopalni Soli „Bochnia” z zastosowaniem elektromagnetycznej sondy ekstensometrycznej dają nową jakość w analizie charakterystyki tego procesu. Pomiary przemieszczeń reperów stanowiących punkty osnowy kopalnianej z zastosowaniem klasycznych przyrządów i instrumentów geodezyjnych pozwalają jedynie na określenie geometrycznych zmian konturu wyrobisk, często wysoko dokładnych. Na bazie wyników klasycznych pomiarów mierniczych niemożliwe jest określanie sposobu propagacji deformacji wewnątrz górotworu. Wykonane badania z zastosowaniem sond ekstensometrycznych umożliwiły opracowanie charakterystyki odkształceń calizny górotworu solnego w KS Bochnia oraz powiązanie tych wyników z wieloletnimi pomiarami geodezyjnymi. Jak dotąd nie ma opracowań, które w wiarygodny sposób przedstawiają sposób rozchodzenia się deformacji w caliźnie górotworu otaczającej wyrobiska. Jak się podejrzewa, jest on poddany dodatkowo naciskom wciąż aktywnych tektonicznie Karpat sąsiadujących ze złożem. Poza aspektem naukowym przybliżenia opisu zjawisk zachodzących wokół wyrobisk podziemnych w KS Bochnia, istotny jest również aspekt praktyczny, który dotyczy sposobu prowadzenia ewentualnych zabezpieczeń zabytkowych wyrobisk.

EN

Measurements of rock mass deformation with application of electromagnetic extensometer in the Saint Kinga Chapel of The Bochnia Salt Mine provided a new quality of in studies of the process’s performance. Measurements of displacements of control points which are consisted of in the mine’s geodetic network with the use of classical device devices and instruments enable to determine of changes of cavities’ contours only, however with high accuracy. The carried out measurements with the use of electromagnetic extensometer supported elaboration of deformation of undisturbed rock mass surrounding the cavity in The Bochnia Salt Mine that could be combined the results with long standing geodetic observations. As far there is no studies which present reliably propagation of deformation within rock salt mass surrounding underground excavations. As suspected, the rock mass is subjected to additional stress of the Carpathians orogeny, neighboring the salt deposit and which is still tectonically active. Apart from the scientific aspect which brings closer the problem depicting propagation of phenomena ongoing around underground cavity in The Bochnia Salt Mine, there is a practical aspect pertaining to of eventual support methods being constructed in the historical excavations.