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1

Weak signed Roman k-domination in digraphs

Volkmann Lutz

Opuscula Mathematica

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2024

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Vol. 44, no. 2

285--296

EN

Let k ≥ 1 be an integer, and let D be a finite and simple digraph with vertex set V (D). A weak signed Roman k-dominating function (WSRkDF) on a digraph D is a function f : V (D) → {−1, 1, 2} satisfying the condition that ∑x∈N−[v] f(x) ≥ k for each v ∈ V (D), where N−[v] consists of v and all vertices of D from which arcs go into v. The weight of a WSRkDF f is w(f) = ∑v∈V (D) f(v). The weak signed Roman k-domination number [formula] is the minimum weight of a WSRkDF on D. In this paper we initiate the study of the weak signed Roman k-domination number of digraphs, and we present different bounds on [formula]. In addition, we determine the weak signed Roman k-domination number of some classes of digraphs. Some of our results are extensions of well-known properties of the weak signed Roman domination number [formula] and the signed Roman k-domination number [formula].

2

Parabolic turbulence k-epsilon model with applications in fluid flows through permeable media

Oliveira Hermenegildo Borges de

Opuscula Mathematica

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2024

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Vol. 44, no. 2

197--240

EN

In this work, we study a one-equation turbulence k-epsilon model that governs fluid flows through permeable media. The model problem under consideration here is derived from the incompressible Navier-Stokes equations by the application of a time-averaging operator used in the k-epsilon modeling and a volume-averaging operator that is characteristic of modeling unsteady porous media flows. For the associated initial- and boundary-value problem, we prove the existence of suitable weak solutions (average velocity field and turbulent kinetic energy) in the space dimensions of physics interest.

3

An integrated velocity model application in ST area, Dongying Depression, China

Xie Qinghui, Fan Hongche, Chen Junhao, Rui Zhifeng, Wu Chuan, Tong Yanming

Acta Geophysica

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2024

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Vol. 72, no. 1

141--159

EN

The velocity is not uniformly distributed in ST area of Dongying Depression in China, which varies both horizontally and vertically. In order to obtain accurate time-depth results, it is necessary to find an appropriate velocity model for time-depth conversion according to the actual situation of the study area. First, the characteristics and main affecting factors of velocity variation in the study area were analyzed. Analysis results showed that the velocity is obviously multi-segment in the vertical direction and zoned on the plane, with a larger velocity in the northern part of Shengbei fault and a smaller velocity in the southern part. The main factors affecting the velocity distribution are the burial depth or compaction, sedimentary facies distribution and lithological composition. Then, the velocity model was established by using checkshot data of 30 wells after making synthetic records. We proposed an integrated velocity modeling method that considers the velocity distribution characteristics and matches the geological characteristics well. Above the target layer, the polynomial fitting method was used to calculate the depth of the bottom of Es3. Then, segmental V = v0/k functions were fit to calculate the thickness of each layer. Subsequently, the stripping method was used to calculate the bottom depth layer by layer. Using this method in the study area effectively reduced uncertainty, improved accuracy of time-depth conversion and accurately understood the lateral structure and stratigraphic pattern of the basin, which could facilitate a rapid search for structural traps.

4

A robust inversion of logging-while-drilling responses based on deep neural network

Zhu Gaoyang, Gao Muzhi, Wang Bin

Acta Geophysica

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2024

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Vol. 72, no. 1

129--139

EN

Resistivity inversion plays a significant role in recent geological exploration, which can obtain formation information through logging data. However, resistivity inversion faces various challenges in practice. Conventional inversion approaches are always time-consuming, nonlinear, non-uniqueness, and ill-posed, which can result in an inaccurate and inefficient description of subsurface structure in terms of resistivity estimation and boundary location. In this paper, a robust inversion approach is proposed to improve the efficiency of resistivity inversion. Specifically, inspired by deep neural networks (DNN) remarkable nonlinear mapping ability, the proposed inversion scheme adopts DNN architecture. Besides, the batch normalization algorithm is utilized to solve the problem of gradient disappearing in the training process, as well as the k-fold cross-validation approach is utilized to suppress overfitting. Several groups of experiments are considered to demonstrate the feasibility and efficiency of the proposed inversion scheme. In addition, the robustness of the DNN-based inversion scheme is validated by adding different levels of noise to the synthetic measurements. Experimental results show that the proposed scheme can achieve faster convergence and higher resolution than the conventional inversion approach in the same scenario. It is very significant for geological exploration in layered formations.

5

Novel accessibility metrics based on hierarchical decomposition of transport networks

Kwatra Divya, Rao Kalaga Ramachandra, Bhatnagar Vasudha

Zeszyty Naukowe. Transport / Politechnika Śląska

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2023

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z. 118

139--160

EN

Scientific analysis of public transport systems at the urban, regional, and national levels is vital in this contemporary, highly connected world. Quantifying the accessibility of nodes (locations) in a transport network is considered a holistic measure of transportation and land use and an important research area. In recent years, complex networks have been employed for modeling and analyzing the topology of transport systems and services networks. However, the design of network hierarchy-based accessibility measures has not been fully explored in transport research. Thus, we propose a set of three novel accessibility metrics based on the k-core decomposition of the transport network. Core-based accessibility metrics leverage the network topology by eliciting the hierarchy while accommodating variations like travel cost, travel time, distance, and frequency of service as edge weights. The proposed metrics quantify the accessibility of nodes at different geographical scales, ranging from local to global. We use these metrics to compute the accessibility of geographical locations connected by air transport services in India. Finally, we show that the measures are responsive to changes in the topology of the transport network by analyzing the changes in accessibility for the domestic air services network for both pre-covid and post-covid times.

6

Metody sztucznej inteligencji w zastosowaniu do przewidywania właściwości materiałów

Trzepieciński Tomasz

Stal, Metale & Nowe Technologie

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2023

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nr 11-12

22--29

PL

Naukowcy nieustannie dążą do lepszego zrozumienia, przewidywania i ulepszania pożądanych właściwości materiałów. Jednym z narzędzi, które można w tym celu wykorzystać, jest sztuczna inteligencja.

7

Modeling reliability of systems with repair by stochastic processes with long memory

Filus Jerzy K., Filus Lidia Z.

Safety and Reliability of Systems and Processes

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2023

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Summer Safety and Reliability Seminar 2023

69--78

EN

In modelling reliability of systems with repair by stochastic processes of times between consecutive failures the usual Markovianity assumption was significantly relaxed. Instead of the Markovian stochastic processes, processes with long memory were constructed for the reliability and maintenance applications. The Markovianity restriction on the process’s memory could be omitted as two (relatively) new methods of the processes construction were employed. In this work, one of the two available methods, the ‘method of triangular transformations’, is presented. Other, the ‘method of parameter dependence’, is shortly described in Section 5. Since using an arbitrarily long memory has serious drawbacks in modelling process we, on the other hand, limited it by introducing the notion of k-Markovianity (k = 1,2,…), where the memory is reduced to the last k previous (discrete) time epochs. The discussion of this kind of problems together with construction of some new classes of stochastic processes with discrete time and their reliability application is provided.

8

Advanced extreme learning machine for an hour PV forecast using general weather data

Farid Imam Wahyudi, Priyad Ardyono, Purnomo Mauridhi Hery, Abdillah Muhammad, Tjahjono Anang, Yorino Naoto

Przegląd Elektrotechniczny

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2023

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R. 99, nr 1

134--139

EN

In recent years, Indonesia has placed great attention on the use of renewable energy resources as a way to decrease gas emission. Located at the equator, Indonesia has many advantages in renewable energy resources, especially photovoltaic (PV). Photovoltaic offers a big opportunity to contribute to the power grid, yet it also comes with its challenges. The use of PV involves a major uncertainty as the inputs of PV are weather conditions that are constantly changing. With Indonesia planning to penetrate the PV farm into the power grid, it is necessary to be able to generate an accurate forecast to assist the power grid control operator. Many algorithms are applied to obtain a precise and accurate PV power generation. One of the algorithms generally used by researchers is the conventional back propagation neural network. It is one of the most commonly applied algorithms, yet it also has a complex setting and numerous parameters. To help overcome this issue, extreme learning machine (ELM) is applied alongside with backpropagation neural network (BPNN), resulting in a more promising result. However, the random value for ELM parameters has become another problem of its own. This paper discusses an advanced ELM to obtain a better PV forecast result. The combination of PV input, ambient temperature, global tilted irradiation (GTI), wind direction, wind velocity and humidity are applied on the kernel extreme learning machine (K-ELM). We found that K-ELM proposes a better performance compared to ELM in facing a nonlinear data, along with better learning capability, mapping ability, and an improved efficiency. We also developed the input data using BPNN, ELM and support vector machine (SVM) to compare training, testing and calculation time

PL

W ostatnich latach Indonezja przywiązywała dużą wagę do wykorzystania odnawialnych źródeł energii jako sposobu na zmniejszenie emisji gazów. Położona na równiku Indonezja ma wiele zalet w zakresie odnawialnych źródeł energii, zwłaszcza fotowoltaiki (PV). Fotowoltaika daje duże możliwości wniesienia wkładu w sieć energetyczną, ale wiąże się również z wyzwaniami. Korzystanie z PV wiąże się z dużą niepewnością, ponieważ wejścia PV to stale zmieniające się warunki pogodowe. Ponieważ Indonezja planuje penetrację farmy fotowoltaicznej do sieci energetycznej, konieczne jest wygenerowanie dokładnej prognozy, aby pomóc operatorowi kontroli sieci energetycznej. W celu uzyskania precyzyjnego i dokładnego wytwarzania energii PV stosuje się wiele algorytmów. Jednym z algorytmów powszechnie stosowanych przez badaczy jest konwencjonalna sieć neuronowa wstecznej propagacji. Jest to jeden z najpowszechniej stosowanych algorytmów, ale ma też złożoną nastawę i liczne parametry. Aby rozwiązać ten problem, zastosowano ekstremalną maszynę uczącą (ELM) wraz z siecią neuronową z propagacją wsteczną (BPNN), co daje bardziej obiecujący wynik. Jednak losowa wartość parametrów ELM stała się kolejnym problemem. W niniejszym artykule omówiono zaawansowane ELM w celu uzyskania lepszego wyniku prognozy PV. Kombinacja sygnału wejściowego PV, temperatury otoczenia, napromieniowania globalnego odchylenia (GTI), kierunku wiatru, prędkości wiatru i wilgotności jest stosowana na maszynie ekstremalnego uczenia jądra (K-ELM). Odkryliśmy, że K-ELM proponuje lepszą wydajność w porównaniu do ELM w obliczu danych nieliniowych, a także lepszą zdolność uczenia się, zdolność mapowania i lepszą wydajność. Opracowaliśmy również dane wejściowe za pomocą BPNN, ELM i maszyny wektorów nośnych (SVM) w celu porównania czasu szkolenia, testowania i obliczeń.

9

The effect of Al(III) and Fe(III) ions on the flotation behavior of Kfeldspar with sodium oleate as the collector

Chen Yi, Zhou Jikui, He Guichun, Hu Hongxi, Liu Chao, Yang Jiping, Lyu Xianjin

Physicochemical Problems of Mineral Processing

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2023

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Vol. 59, iss. 6

art. no. 174724

EN

The present study investigates the effects and mechanisms of aluminum (Al(III)) and iron (Fe(III)) ions on the flotation efficiency of potassium feldspar (K-feldspar) within oleate collector systems. The study employs micro-flotation experiments, solution chemistry calculations, zeta potential measurements, and FT-IR and XPS analyses to demonstrate that Al(III) and Fe(III) ions can significantly improve the flotation recovery of K-feldspar by altering its surface charge, bonding properties, and adsorption modes. The study also develops adsorption models for the flotation of K-feldspar activated by Al(III) and Fe(III), revealing the synergistic impacts of metal ion hydrolysis products and sodium oleate in the formation of hydrophobic complexes.

10

Potassium chloride recovery from mechanically activated microcline through the chlorination roasting and leaching route

Alyosif Bahaa, Uysal Turan, Erdemoğlu Murat

Physicochemical Problems of Mineral Processing

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2023

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Vol. 59, iss. 5

art. no. 167500

EN

In this study, effects of mechanical activation in the chlorination roasting and water leaching route known as CaCl2 process and developed for the production of potassium chloride (KCl) from potassium feldspar ores were studied. A microcline containing K-feldspar ore with 10.89% K2O was first intensively dry milled by a planetary ball mill and mixed with calcium chloride (CaCl2) and then roasted at temperatures up to 1000°C to obtain KCl that will be finally dissolved by the water leaching. Potassium recovery by water leaching increased rapidly up to 800°C. At higher temperatures, the recovery decreased fast due to the evaporation of KCl. According to the K recovery values per unit energy consumed, the optimum roasting temperature was determined as 750°C and the milling time was 15 min. It was concluded that intensive milling causes mechanical activation of the microcline to reduce the chlorination roasting temperature, which triggers a rise in the K recovery by the water leaching.

11

Stripe segmentation of oceanic internal waves in SAR images based on Gabor transform and K-means clustering

Qi Kai-Tuo, Zhang Hong-Sheng, Zheng Ying-Gang, Zhang Yu, Ding Long-Yu

Oceanologia

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2023

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Vol. 65 (4)

548--555

EN

Oceanic internal waves are an active ocean phenomenon that can be observed, and their relevant characteristics can be acquired using synthetic aperture radar (SAR). The locations of oceanic internal waves must be determined first to obtain the important parameters of oceanic internal waves from SAR images. An oceanic internal wave segmentation method with integrated light and dark stripes was described in this study. To extract the SAR image characteristics of oceanic internal waves, the Gabor transform was initially used, and then the K-means clustering algorithm was used to separate the light (dark) stripes of oceanic internal waves from the background in the SAR images. The regions of the dark (light) stripes were automatically determined based on the differences between the three classes, that is, the dark stripes, light stripes, and background area. Finally, the locations of the dark (light) stripes were determined by shifting a given distance along the normal direction of the long side with the minimum bounding rectangle of the light (dark) stripes. The best segmentation results were obtained based on the intersection over the union of the images, and the accuracy of segmentation was verified. Furthermore, the effectiveness and practicability of the proposed method in the light and dark stripe segmentation of SAR images of oceanic internal waves were illustrated. The proposed method prepares the foundation for future inversion studies of oceanic internal waves.

12

Wykorzystanie języka R do statystycznej analizy oraz analizy skupień dla danych geochemicznych

Janiga Marek

Nafta-Gaz

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2023

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R. 79, nr 9

576--583

PL

W zagadnieniach geologii naftowej metody statystyczne są szeroko stosowane w petrografii, petrofizyce, geochemii, geomechanice, geofizyce wiertniczej czy sejsmice, a analiza skupień jest istotna w klasyfikacji skał – wyznaczaniu stref o pewnych własnościach, np. macierzystych lub zbiornikowych. Artykuł prezentuje użycie metod statystycznych, w tym metod analizy skupień, w procesach przetwarzania i analizy dużych zbiorów różnorodnych danych geochemicznych. Do analiz statystycznych wykorzystano literaturowe dane z analiz składu chemicznego i izotopowego gazów ziemnych. Wyniki zawierały skład chemiczny gazów ziemnych oraz skład izotopowy. Zastosowano algorytmy tzw. nienadzorowanego uczenia maszynowego do przeprowadzenia analizy skupień. Grupowania było przeprowadzone dwiema metodami: k-średnich oraz hierarchiczną. Do zobrazowania wyników grupowania metodą k-średnich można wykorzystać dwuwymiarowy wykres (funkcja fviz_cluster języka R). Wymiary na wykresie to efekt analizy głównych składowych (PCA) i są one liniową kombinacją cech (kolumn w tabeli). Wynikiem grupowania metodą hierarchiczną jest wykres nazywany dendrogramem. W artykule dodatkowo zaprezentowano wykresy pudełkowe i histogramy oraz macierz korelacji zawierającą współczynniki korelacji Pearsona. Wszystkie prace wykonano z użyciem języka programowania R. Język R, z wykorzystaniem programu RStudio, jest bardzo wygodnym i szybkim narzędziem do statystycznej analizy danych. Przy użyciu tego języka uzyskanie wymienionych powyżej wykresów, tabeli i danych jest szybkie i stosunkowo łatwe. Wyniki analiz składu gazu wydają się mało zróżnicowane. Mimo to dzięki algorytmom k-średnich i hierarchicznym możliwe było pogrupowanie danych geochemicznych na wyraźnie rozdzielne zespoły. Zarówno wartości składu izotopowego, jak i skład chemiczny pozwalają wyznaczyć grupy, które w inny sposób nie byłyby dostrzegalne.

EN

In petroleum geology, statistical methods are widely used in petrography, petrophysics, geochemistry, geomechanics, well log analysis and seismics, and cluster analysis is important for rock classification – determination of zones with certain properties, e.g., source or reservoir. This paper presents the use of the R language for statistical analysis, including cluster analysis, of large sets of diverse geochemical data. Literature data from analyses of chemical and isotopic composition of natural gases were used for statistical analyses. The results included the chemical composition of the natural gases and the isotopic composition. So-called unsupervised machine learning algorithms were used to perform the cluster analysis. Clustering was performed using two methods: k-means and hierarchical. A two-dimensional graph (function fviz_cluster) can be used to illustrate the results of the k-means clustering. The dimensions in the graph are the result of principal component analysis (PCA) and are a linear combination of the features (columns in the table). The result of hierarchical clustering is a graph called a dendrogram. The paper additionally presents box plots and histograms as well as a correlation matrix containing Pearson correlation coefficients. All work was completed using the programming language R. The R language, using the RStudio software, is a very convenient and fast tool for statistical data analysis. Obtaining the above-mentioned graphs, tables and data is quick and relatively easy, using the R language. The results of the analyses of the composition of the gas appear to have little variation. Nevertheless, thanks to k-means and hierarchical algorithms, it was possible to group the geochemical data into clearly separable groups. Both the isotopic composition values and the chemical composition make it possible to delineate groups that would not otherwise be noticeable.

13

An Efficient Controller Placement Algorithm using Clustering in Software Defined Networks

Jacob Joshua, Shinde Sumedha, Narayan D. G.

Journal of Telecommunications and Information Technology

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2023

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nr 4

9--17

EN

Software defined networking (SDN) is an emerging network paradigm that separates the control plane from data plane and ensures programmable network management. In SDN, the control plane is responsible for decision-making, while packet forwarding is handled by the data plane based on flow entries defined by the control plane. The placement of controllers is an important research issue that significantly impacts the performance of SDN. In this work, we utilize clustering techniques to group networks into multiple clusters and propose an algorithm for optimal controller placement within each cluster. The evaluation involves the use of the Mininet emulator with POX as the SDN controller. By employing the silhouette score, we determine the optimal number of controllers for various topologies. Additionally, to enhance network performance, we employ the meeting point algorithm to calculate the best location for placing the controller within each cluster. The proposed approach is compared with existing works in terms of throughput, delay, and jitter using six topologies from the Internet Zoo dataset.

14

An application of machine learning methods to cutting tool path clustering and rul estimation in machining

Zegarra Fabio C., Vargas-Machuca Juan, Roman-Gonzalez Avid, Coronado Alberto M.

Journal of Machine Engineering

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2023

|

Vol. 23, No. 4

5--17

EN

Machine learning has been widely used in manufacturing, leading to significant advances in diverse problems, including the prediction of wear and remaining useful life (RUL) of machine tools. However, the data used in many cases correspond to simple and stable processes that differ from practical applications. In this work, a novel dataset consisting of eight cutting tools with complex tool paths is used. The time series of the tool paths, corresponding to the three-dimensional position of the cutting tool, are grouped according to their shape. Three unsupervised clustering techniques are applied, resulting in the identification of DBA-k-means as the most appropriate technique for this case. The clustering process helps to identify training and testing data with similar tool paths, which is then applied to build a simple two-feature prediction model with the same level of precision for RUL prediction as a more complex four-feature prediction model. This work demonstrates that by properly selecting the methodology and number of clusters, tool paths can be effectively classified, which can later be used in prediction problems in more complex settings.

15

The Effects of Various Organic Materials on Dactylis glomerata Yield and Content of Selected Macroelements

Malinowska Elżbieta, Wiśniewska-Kadżajan Beata, Ostaszewska Urszula, Horaczek Tomasz

Journal of Ecological Engineering

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2023

|

Vol. 24, nr 7

108--118

EN

The aim of the experiment was to assess the effects of various organic materials on Dactylis glomerata yield, on the content of selected macroelements (K, Ca and Mg) and on K:Ca, K:Mg and K:(Ca + Mg) ratios. As a valuable forage plant, Dactylis glomerata (cocksfoot grass) is a common grass in Poland both in grassland and in arable fields. Its rapid spring growth and its resistance to drought, low temperatures, but also to frequent mowing and pests, makes it a common species in meadows, pastures and grassland, both permanent and alternating. In order to achieve the research goal, a three-year pot experiment was established in a greenhouse. The experiment was conducted in a completely random design, in four replications. In the autumn before the experiment, soil was mixed with organic materials (chicken manure, mushroom substrate and rye straw) and put into pots. To selected units, an additional amount of mineral N was applied in the first year and NPK fertilizers in consecutive years. Mineral fertilizers were applied at the beginning of the growing period. Compared to control, the application of mineral and organic fertilizers resulted in a significant increase in Dactylis glomerata yield. The highest biomass yield (average over the growing periods) was recorded on the unit treated with manure, straw and mineral fertilizers (27.64 g•pot-1) and on the one with mushroom substrate applied together with rye straw and mineral fertilizers (26.47 g•pot-1). The K:(Ca+Mg) ratio in the forage was normal and averaged 0.933, but mineral fertilizers, compared to other treatments, narrowed it.

16

Identification of Homogeneous Regions of Specific Minimum Flows in the State of Goiás, Brazil

Basso Raviel, Santana Kássia, Honório Michelle, Costa Isabella, Leitão Sanderson, Albuquerque Antonio, Scalize Paulo

Journal of Ecological Engineering

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2023

|

Vol. 24, nr 4

357--367

EN

Hydrological information is essential for adequate water resources management as well as for water supply, energy supply, water allocation, among other services. However, this information does not always exist in quantity and quality to be used in hydrological or water management studies, and alternative methods are required to estimate minimum flows. Estimation based on homogeneous regions enables to transfer observation data from a known location to a location without data, but in the same region. Since the fluviometric stations in the state of Goiás (Brazil) are not uniformly distributed, the present work aimed at delimiting homogeneous regions of minimum flows, using the cluster grouping method with the K-means algorithm.Thus, 71 fluviometric stations with at least 5 years of continuous data were selected, obtained from the HIDROWEB system. In addition to the observed data, other variables were considered, such as drainage area, perimeter, specific minimum flows Q7,10, Q90, Q95 and average slope. The use of all these variables together with the observed data made it possible to determine,with great accuracy, 5 homogeneous regions of minimum flows based on the cluster analysis, enabling to obtain the minimum flows of reference for each region.In the selected homogeneous regions, it was possible to observe that the regions with the highest values of average slope presented smaller minimum flows, and the same could be observed under inverse conditions, i.e., lower values of average slope had higher minimum flows.It is also noteworthy that river monitoring is deficient in the center-south and center-north parts of the state of Goiás, making water resources management difficult. This fact indicates, therefore, the need to expand the river monitoring system throughout the state, especially in its southern and northern regions.

17

Fast attack detection method for imbalanced data in industrial cyber-physical systems

Huang Meng, Li Tao, Li Beibei, Zhang Nian, Huang Hanyuan

Journal of Artificial Intelligence and Soft Computing Research

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2023

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Vol. 13, No. 4

229--245

EN

Integrating industrial cyber-physical systems (ICPSs) with modern information technologies (5G, artificial intelligence, and big data analytics) has led to the development of industrial intelligence. Still, it has increased the vulnerability of such systems regarding cybersecurity. Traditional network intrusion detection methods for ICPSs are limited in identifying minority attack categories and suffer from high time complexity. To address these issues, this paper proposes a network intrusion detection scheme, which includes an information-theoretic hybrid feature selection method to reduce data dimensionality and the ALLKNN-LightGBM intrusion detection framework. Experimental results on three industrial datasets demonstrate that the proposed method outperforms four mainstream machine learning methods and other advanced intrusion detection techniques regarding accuracy, F-score, and run time complexity.

18

Radii of starlikeness and convexity of generalized k-Bessel functions

Toklu Evrim

Journal of Applied Analysis

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2023

|

Vol. 29, nr 1

171--185

EN

The main purpose of this study is to determine the radii of starlikeness and convexity of the generalized k-Bessel functions for three different kinds of normalization in such away that the resulting functions are analytic in the unit disk of the complex plane. The characterization of entire functions from Laguerre-Pólya class plays a significant role in this paper. Moreover, the interlacing properties of the zeros of the k-Bessel function and its derivative is also useful in the proof of the main results. By making use of the Euler-Rayleigh inequalities for the real zeros of the generalized k-Bessel function, we obtain some tight lower and upper bounds for the radii of starlikeness and convexity of order zero.

19

Bochner formula in generalized (k, μ)-space forms

B Shanmukha

Journal of Applied Analysis

|

2023

|

Vol. 29, nr 2

323--328

EN

In this article, we studied Green’s theorem and the Bochner formula. Further, we apply the Bochner formula to generalized (k, μ)-space forms and show that the generalized (k, μ) space form is either isometric to a sphere or a certain warped product under some geometric conditions.

20

Segmentation of Homogeneous Regions of Gravity Field Properties by Machine Learning Method in Central Area of Vietnam

Thi Hong Phan, Minh Phuong Do, Van Huu Tran

Inżynieria Mineralna

|

2023

|

no. 2, vol. 1

97--102

EN

This paper presents the results of applying the unsupervised learning method (K-means clustering) on the gravity anomaly field in the central region of Vietnam to separate the research area into different clusters, which are homologous in physical properties. In order to achieve the optimal results, the input parameter plays an important role. In this paper, we chose 04 input attributes including the gravity anomalous field attribute, the horizontal gradient attribute, the variance attribute, and the tracing coefficient of the gravity anomalous axis. The obtained results have shown that the research area could be divided into 7 clusters, 9 clusters, 11 clusters, and 13 clusters with close characteristics of the physical properties of the gravity field. The research results show that the Southwest, the Center, and the South of the study area have complex changing physical properties, this result reflects the complicated tectonic activities in these areas with the presence of crumpled and fractured rock layers in different directions and these locations are the potential places to form endogenous mineral deposits of magma origin. The Northwest, the North, and the East parts of the research area witness negligible changes in the field's physical properties, reflecting the stability of the soil and rock layers in this area, with the direction of extending structure from the Northwest to the Southeast. The clustering results according to the K-means unsupervised learning algorithm in central Vietnam initially increase the reliability of the decisions of geologists and geophysicists in interpreting the geological structure and evaluating the origin of deep-hidden mineral deposits in the area.