Main Part Research Articles

Improved deep belief network for estimating mango quality indices and grading: A computer vision-based neutrosophic approach

ABSTRACT This research introduces a revolutionary machinet learning algorithm-based quality estimation and grading system. The suggested work is divided into four main parts: Ppre-processing, neutroscopic model transformation, Feature Extraction, and Grading. The raw images are first pre-processed by following five major stages: read, resize, noise removal, contrast enhancement via CLAHE, and Smoothing via filtering. The pre-processed images are then converted into a neutrosophic domain for more effective mango grading. The image is processed under a new Geometric Mean based neutrosophic approach to transforming it into the neutrosophic domain. Finally, the prediction of TSS for the different chilling conditions is done by Improved Deep Belief Network (IDBN) and based on this; the grading of mango is done automatically as the model is already trained with it. Here, the prediction of TSS is carried out under the consideration of SSC, firmness, and TAC. A comparison between the proposed and traditional methods is carried out to confirm the efficacy of various metrics.

Detecting communities with multiple topics in attributed networks via self-supervised adaptive graph convolutional network

Attributed networks which have topology information and attribute information simultaneously are very common in the real world, e.g., online social networks and co-authorship networks. Community detection in attribute networks is a very valuable research topic. Although there is already a lot of work focused on it, but most of existing approaches still face two key challenges: topology information and attribute information fusion, and multiple topics community detection. To effectively address these challenges, in this paper we devise an approach called SSAGCN, which adopts the self-supervised learning paradigm using the autoencoder architecture. Specifically, SSAGCN comprises three main parts: adaptive graph convolutional network (AGCN) encoder, modularity maximization and dual decoder. AGCN uses two GCNs with shared parameters and the attention mechanism to fuse topology information and attribute information automatically. To drive AGCN encoder to uncover community structure, we select the modularity maximization as the optimization objective. The dual decoder is applied to reconstruct both topology structure and network attributes. By introducing the joint training strategy, SSAGCN is able to discover multiple topics community through the end-to-end manner. Extensive experiments are conducted on nine benchmark attributed networks, and the results illustrate not only the superiority of SSAGCN over state-of-the-art approaches, but also its good ability of community-topic analysis. For the reproducibility, we release the source code at https://github.com/GDM-SCNU/SSAGCN.

Analysis of thermophysical and transport properties of nanofluids using machine learning algorithms

Accurate calculations of thermophysical properties (TPP) and fluid transport properties are crucial for solving and enhancing a myriad of heat and mass transfer issues, particularly in the field of engineering and associated disciplines. This is even more significant in the case of advanced fluids, such as nanofluids, which play a pivotal role in the progression of new technologies. The significance of TPP in heat transfer studies is undeniable, yet there is a notable scarcity of reliable TPP values for nanofluids that can be uniformly applied to numerous problems and complex industrial systems. This shortage poses a unique challenge for nanofluids. The current study introduces NanoFluid Explorer (NanoFEx), a comprehensive MATLAB-based database specifically designed to catalog the TPP of nanofluids. The database is divided into two main parts. The first part employs Gaussian regression, supported by experimental data derived from existing literature, using kernel functions commonly used for this type of analysis. The second part features a neural network, designed for efficiency, that is trained on the aforementioned database and supplemented by an additional database formed from the Gaussian-regression output. This setup allows NanoFEx to recapture TPP values for nanofluids that may be absent in the existing literature. The preliminary findings demonstrate that NanoFEx could prove to be an invaluable resource for both theoretical and experimental researchers studying heat and mass transfer in nanofluids. Moreover, NanoFEx confirms thermodynamically consistent values with any discrepancies attributed to finite-precision computations. Furthermore, NanoFEx achieved over 93% accuracy in predicting key properties. The novelty and relevance of this study stem from the comprehensiveness of the experimental results database. In summary, this research provides an extensive and, to the best of the authors' knowledge, the most reliable dataset currently available for TPP of nanofluids. This significant contribution aims to unify nanofluid TPP research and optimize experimental processes while setting a crucial standard for future nanofluid applications.

Formaldehyde observations of the Perseus Molecular Cloud

ABSTRACT Large-scale observations of the Perseus Molecular Cloud (MC) with Nanshan 26-m telescope are presented using the 6 cm ortho-H2CO (110–111) transition. As a probe of dense gas at low temperatures, the H2CO absorption extends over the main parts of the Perseus MC. A comparison of the H2CO absorption line with the 12CO and 13CO (J = 1–0) emissions shows that the H2CO and CO are similarly distributed over the Perseus but that H2CO correlates better with 13CO. Comparison with the Herschel-derived H2 column density shows that both the 13CO and H2CO column densities vary linearly with the H2 column density. The main parameters of H2CO absorption line data show a log-normal distribution, which suggests that the strong non-thermal line-broadening results from large-scale supersonic turbulence related to the star formation. Formaldehyde absorption serves well as a tracer of star formation activity and also the H2CO-to-13CO and H2CO-to-H2 abundances systematically trace the star formation activity in the six subregions of Perseus MC. The H2CO abundances anticorrelate with the number of prestellar and protostellar cores and the IRIS 12 μm flux in the six subregions and reveal the star formation history in the Perseus MC.

An artistic perspective on individual space–time flows

ABSTRACT Cartographically, there are now many ways of depicting the spatiotemporal life of human individuals, from flow and animated maps to 3D space-time cubes. However, these scientifically led representations have limited expressive potential for the emotional and inner life of these individuals. Artistic visual forms have been identified as a resource to bring such qualitative communication to and alongside maps. In the ‘Journey as a Flow' project we attempt to represent the geometry and motivation of everyday human motion in relation to various points in the environment and within an environment of other individual flows. We have produced various visual artwork sketches in order to understand the wide range of environmental flows of an individual as well as one's perception of them. We used the space-time cube (i.e. time-geographic aquarium) as a starting point, dictated by the need to create a functional tool in which space and time were both visible, as well as having potential as a 3D tangible object for physical exhibition. This forms the basis for analyses of displacement, interaction and perception. All the modifications of this established geospatial visualisation are inspirations and incorporations from art disciplines. The project outputs therefore include inspirations from cine-plastic art and Escher’s perspective drawings, but the main part of it draws from the Italian renaissance concept of the image conceived as a framed window through which we look at the world. The idea of central perspective has also been used to portray spaces as a flow toward a specific destination. The overall set of representations depict a dynamic version of human lives, while the set of various metaphors deployed drive an artistic interpretation of how some people can perceive (their own / other) flows during their journey. A transformation has therefore occurred from a temporal flow would be conventionally spatial to one that assumes platial properties (i.e. an individually led geography of place).

The effects of tibial tuberosity avulsion and repair on tibial plateau angle in dogs

ABSTRACT Aims To assess whether tibial tuberosity avulsion injury and subsequent surgical repair in skeletally immature dogs are associated with changes in tibial plateau angle (TPA) at skeletal maturity. Methods Skeletally mature (> 18 months of age) dogs that had previously undergone unilateral surgery when 4–8 months of age to repair tibial tuberosity avulsion were enrolled. Bilateral, mediolateral stifle radiographs were taken. TPA was measured digitally from the radiographs independently by two readers and compared between sides within dogs. As the number of dogs that would be enrolled for the main part of the study was unknown, to understand how the variation between left and right stifles within dogs would affect the power of the main study, 29 client-owned, skeletally mature dogs without stifle pathology were recruited prior to the main study for bilateral, mediolateral projection stifle radiographs. Variation in the differences in TPA between left and right stifles was used to estimate the likely power of the major part of the study for different numbers of enrolled dogs. Results From 29 dogs enrolled in the power assessment, the SD of the differences between left and right stifles was 2.1°. With 10 dogs (20 stifles) enrolled within the main part of the study, and if the SD of the differences between operated and non-operated stifles within a dog was the same as the SD of the differences between non-operated stifles within a dog (2.1°), the study would have power ≥ 0.8 if the mean difference in TPA between operated and non-operated stifles was ≥ 2.1°. Ten dogs were enrolled in phase II of the study. In 8/10 of these dogs, the TPA in the operated stifle was less than in the non-operated stifle. The mean TPA on the operated stifle was 6.4° less than on the non-operated stifle (95% CI = 2.4–10.3° less; p = 0.002). For surgery between 4 and 8 months of age, TPA at maturity increased by 2.7° (95% CI = 1.1–4.3°; p = 0.001) for each additional month of age at surgery. Conclusions and clinical relevance Based on this study, surgical repair of tibial tuberosity avulsion in skeletally immature dogs is associated with a smaller TPA at skeletal maturity. However, causality cannot be established from this cross-sectional study, and this association may be because stifles with a smaller TPA are predisposed to tibial tuberosity avulsion.

Optimized short-term load forecasting in residential buildings based on deep learning methods for different time horizons

The aim of this paper is to develop machine learning based framework to short-term load forecasting with high accuracy for residential building. The purpose is to develop a predictive model that assists energy companies in achieving a balance between energy consumption and generation by effectively managing the energy demand of consumers. The originality of this paper lies in two main parts. First, it analyzes effective relevant features such as time, calendar, and weather using a correlation matrix. Next, an optimized eXtreme gradient boosting model is employed to select key features, reducing the complexity of the training model. The second part proposes an intelligent parallel structure that utilizes gated recurrent units and convolutional neural networks for short-term load forecasting in different resolutions with minimal errors. The precise selection of hyperparameters significantly influences error prediction and accuracy. The metaheuristic-search-based algorithm, particle swarm optimization, is applied to find the optimal configuration for tunable parallel proposed model hyperparameters. The main results of this study demonstrate that the intelligent predictive model performs better than the latest models discussed in recent literature. The evaluation was conducted on a real-time time series dataset called Mashhad data. The model achieved impressive results in terms of standard metrics such as root mean square error of 44.28, mean absolute error of 29.32, mean absolute percentage error of 3.11 %, and R2 of 0.9229 % for the next 24 h. The benefits of this novel model play a crucial role in accurate short-term load forecasting, as well as in the decision-making and operations of power companies and smart grid.

Generalized Polynomials on Semigroups

Abstract This article has two main parts. In the first part we show that some of the basic theory of generalized polynomials on commutative semi-groups can be extended to all semigroups. In the second part we show that if a sub-semigroup S of a group G generates G in the sense that G = S · S −1, then a generalized polynomial on S with values in an Abelian group H can be extended to a generalized polynomial on G into H. Finally there is a short discussion of the extendability of exponential functions and generalized exponential polynomials.

An experimental study of hydrogen implantation to minerals: Role of the solar wind as a source of water in terrestrial bodies

The solar wind is a possible source for hydrogen and other volatiles on planetary bodies. To better understand the role of the solar wind during the volatile acquisition of planetary materials, we conducted hydrogen implantation experiments on olivine, orthopyroxene, quartz single crystals. Depth profiles of hydrogen concentration after implantation are determined by the Nuclear Resonance Reaction Analysis. We find that energetic hydrogen particles penetrate into the sample and accumulate at a certain depth. The hydrogen concentration increases with the hydrogen fluence until a “saturation level” is attained. Hydrogen saturation level (e.g., ∼10–20 at.% in olivine, equivalent to 0.5–1.2 wt%) far exceeds the equilibrium solubility in the bulk crystal at a similar thermodynamic condition (∼10−22 wt%). The results of olivine show that the hydrogen penetration depth increases whereas the saturation level decreases (weakly) with the beam energy. Hydrogen saturation level also depends on the mineral species in the order: olivine > orthopyroxene > quartz. The experimental results can be applied to explain some observations on the high surface water content of some planetary bodies including Itokawa asteroid and the Moon. We also explore the possibility of hydrogenated dusts by the solar wind implantation as a source for water on terrestrial planets. We conclude that if all dusts were exposed to the solar wind and all implanted hydrogen were converted to water, then >10 ocean masses would have been acquired for Earth by ∼100 years. However, the main part of the proto-planetary disk was not exposed to the solar wind and dusts could have been hydrogenated only when they were far from the equatorial plane of the disk. We discuss a possible mechanism to transport the hydrogenated dusts to the disk interior via turbulent mixing. Also, our experimental results and the mass dependence of the particle energies in the solar wind suggest that the D/H ratio of the dusts exposed to the solar wind will be higher than the solar wind value.

Numerical simulation of airflow temperature field and cooling in high temperature coal seam working face

With the continuous extension of coal mining depth, the risk of heat exhaustion from high temperatures gets worse. In this paper, we first identified the main heat sources of the high-temperature coal seam working face. The effects of air supply volume on the temperature evolution of working face were then investigated by numerical simulation. The air supply volume to effectively cool the working face was calculated using a new method, sigma heat difference. A mechanical cooling method, an air cooler in the intake airway, was proposed, and the accuracy of the sigma heat difference method was confirmed through numerical simulation and field measurements. The results show that: (1) The aggregate thermal energy emitted by the heat sources located in the mining working face is 688.2177 kW, with mechanical equipment heat dissipation accounting for the main part; (2) The numerical simulation shows that the temperature of the airflow of the roadway steadily drops as the airflow velocity from the inlet airway increases. Yet extremely high inlet airflow velocities lead to narrower change ranges of the air temperature of the working face; (3) The air supply volume required to effectively cool the working face is determined by the sigma heat difference method to be 1972.2 m3/min, which provides a basis for numerical simulation of inlet air velocity for cooling; (4) The Field measurement and numerical modelling demonstrate that the sigma heat difference method is reasonable. The research conclusions provide theoretical guidance for dealing with heat hazards in coal mining faces.

ICT sector electricity consumption and greenhouse gas emissions – 2020 outcome

The Information and Communication Technology (ICT) sector has gained much attention in the discussions on climate change, as it could impact global emissions both positively and negatively. The objective of the present study is to provide estimates for the 2020 use stage electricity consumption and ICT sector's total lifecycle greenhouse gas (GHG) emissions divided in three main parts: user devices including internet-of-things, networks and data centers. The study builds on a high number of data sources including measured and reported data from 150 companies that is estimated to cover about 80% of network subscriptions, about 55% of data center electricity, and about 35% of upstream GHG emissions. To understand the development, the results are put into the perspective of earlier studies. In conclusion, the ICT sector used about 4% of the global electricity in the use stage and represented about 1.4% of the global GHG emissions in 2020. The use stage electricity consumption and the total GHG emissions have increased since 2015, but the impact per subscription has decreased. The user devices accounted for over half of all GHG emissions, with equal parts relating to use stage and other lifecycle stages. For networks and data centers, the use stage GHG emissions are dominating. The electricity consumption and GHG emissions are also estimated for the closely related areas Entertainment and Media (including e.g., TVs), paper media, and cryptocurrencies.

Market movement prediction using chart patterns and attention mechanism

The new concept of forecasting market movements is introduced to fill the gap in stock price forecasting that uses a fixed time window. The candlestick data are grouped into waves before being input into the Transformer model to capture many different chart patterns and provide longer price movement patterns for better feature extraction. This work is divided into two main parts. The first part is wave extraction, for which we propose a new algorithm for grouping candlestick data into waves. The second part deals with Transformer modeling. The result of this work has shown that the Transformer model trained using wave series can help traders reduce their losses and choose a suitable trading strategy based on the prediction results. The model trading result of the test set has earned about 19.8% (using fixed 1 contract size per order) which is better than using MACD signal which can give earning of 12.5%.

Garlic-derived compounds: Epigenetic modulators and their antitumor effects.

Cancer is a highly heterogeneous disease that poses a serious threat to human health worldwide. Despite significant advances in the diagnosis and treatment of cancer, the prognosis and survival rate of cancer remain poor due to late diagnosis, drug resistance, and adverse reactions. Therefore, it is very necessary to study the development mechanism of cancer and formulate effective therapeutic interventions. As widely available bioactive substances, natural products have shown obvious anticancer potential, especially by targeting abnormal epigenetic changes. The main active part of garlic is organic sulfur compounds, of which diallyl trisulfide (DATS) content is the highest, accounting for more than 40% of the total composition. The garlic-derived compounds have been recognized as an antioxidant for cancer prevention and treatment. However, the molecular mechanism of the antitumor effect of garlic-derived compounds remains unclear. Recent studies have identified garlic-derived compound DATS that plays critical roles in enhancing CpG demethylation or promoting histone acetylation as an epigenetic inhibitor. Here, we review the therapeutic progress of garlic-derived compounds against cancer through epigenetic pathways.

Identification of wheel track in the wheat field

Agriculture machinery navigating along permanent traffic lanes in the farmland may avoid causing extensive soil compaction. However, the permanent traffic lanes are frequently covered up or eliminated by following tillage practices. It is necessary to identify the wheel tracks designed as permanent traffic lanes in order to ensure the agriculture machinery travels along the designated wheel tracks when cultivating the field. This study proposed an identification method of wheel tracks based on the morphological characteristics of wheel tracks and the environmental conditions around the wheel tracks in the wheat fields. The proposed method first utilized the maximum interclass variance to identify the contours of the main part of the wheel track and the shadow regions around the wheel track’s edges. The main part of the wheel tracks was then separated from interference pixels by moving the centerline of the main part of the wheel track, which was derived by skeleton algorithm and curve fitting, towards the right or left edge of the wheel track at a specific distance. In a morphological opening operation, specific linear and circular structural elements were used to segment the shadow regions along the edge of the wheel track. The remaining wheel track was finally recognized by computing the complement of the region identified. After achieving the segmentation of wheel tracks, many reference points near the outside of the wheel track edge in the original image were chosen as fiducial points for evaluating the differences between the actual value and the recognized wheel track edge. The evaluation was based on computing the root mean squared error (RMSE) and the mean absolute error (MAE) of coordinates of reference points and recognized wheel track edge. The results showed that the largest RMSE and MAE were 24.01 pixels (0.0045 m) and 17.32 pixels (0.0032 m), respectively. The low values of RMSE and MAE reveal that the accuracy of the algorithm developed in this study is high, and using this algorithm may segment the wheel track in the wheat field accurately.

A compensation approach for magnetic encoder error based on improved deep belief network algorithm

Magnetic encoders are an important part of industrial automation control systems and are widely used in industrial production. In this paper, a magnetic encoder is designed for angle detection during robot arm motion, but the accuracy is not high in practical applications. Through experiments, it is found that the main error compensation methods at present cannot effectively improve the accuracy of this encoder. Therefore, a hybrid prediction model based on decomposition strategy and deep learning prediction method is proposed in this paper. The hybrid prediction model structure is divided into two main parts: feature engineering based on the variational modal decomposition (VMD) method and a deep belief network prediction model based on particle swarm optimization. Through theoretical analysis, this paper introduces temperature into the prediction feature sequence, and effectively reduces the interference of errors on the prediction results through feature engineering. Experiments prove that the proposed model has excellent compensation effect, improving the accuracy from 0.22° to 0.0025°. The RMSE, Max_error and accuracy (σ) of the proposed model are optimal when compared with the mainstream error compensation methods, such as long short-term memory networks (LSTM), support vector machines (SVM) and deep belief networks (DBN). This proves that the proposed hybrid prediction model has a great improvement in the compensation effect of this magnetic encoder. Our work provides a promising approach that can provide unparalleled value in improving the accuracy of magnetic encoders.

ПОДАТКОВА ЗВІТНІСТЬ: СУТНІСТЬ ТА ПОРЯДОК СКЛАДАННЯ

The article analyzes the approaches of leading national scholars to the definition of the concept of "tax reporting". The author characterizes the necessity of tax reporting, since it characterizes the status of an enterprise's obligations related to the accrual and payment of taxes and other mandatory payments. Tax reporting is submitted to the tax authorities.
 The purpose of the article is to deepen theoretical research on the essence of the concept of "tax reporting", to disclose the methodology of its preparation with a view to improving its quality, reliability and objectivity.
 Summarizing the approaches of scholars to the essence of tax reporting, it is worth noting three approaches. According to the first one, tax reporting is considered as a set of documents containing information on the calculation of tax liabilities; according to the second one, it is considered as a set of actions of the taxpayer on preparation and submission of reports; according to the third one, it is considered as a set of consolidated interrelated indicators characterizing the activities of the enterprise for a certain period.
 Having studied the essence of the concept of "tax reporting", we propose to supplement Article 14 of the Tax Code of Ukraine with the following definition: tax reporting is reporting containing information on the tax liabilities of an enterprise by type of tax and fees.
 The Ministry of Finance of Ukraine regulates tax reporting by establishing forms of tax returns, calculations and reports by type of tax and fee.
 The tax reporting procedure can be divided into 4 stages: Stage 1 - selection of the required form of tax reporting in accordance with the type of tax/fee; Stage 2 - preparation of a tax return for the tax/fee, i.e., entering data directly; Stage 3 - verification of the document for correctness of preparation, compliance of the entered data with the accounting data, correctness of determination of the tax base, taxable object, tax rate; Stage 4 - signing of tax reports.
 Based on the study of tax reporting on national taxes and fees, it should be noted that not all forms contain information on the procedure for their preparation. For the preparation of individual forms by type of tax and fees, notes are used after the main part of the tax reporting. Therefore, we believe that the central executive body that ensures the formation and implementation of the state financial policy should develop recommendations on the preparation of tax reporting forms for those taxes and fees that do not have them, as this will contribute to better coverage of information on tax liabilities and significantly reduce the number of pages of tax reports.

The Groundwater Resources in the Mazovian Lowland in Central Poland during the Dry Decade of 2011–2020

This article addresses the issue of droughts in recent years in Poland and their impact on the state of groundwater resources. This paper presents the challenges arising from the increasing demand for the use of groundwater for irrigation in agriculture, supplementing water shortages, and potential threats to the water supply of rural waterworks. The main part of this paper focuses on a small catchment area in the Mazovian Lowland, which is one of the driest regions in the country. This article includes definitions, characteristics, and causes of hydrologic and hydrogeologic droughts during the period 2011–2020. In the discussed area, there is generally one groundwater level of the Quaternary age, primarily recharged by rainfall infiltration, which is utilized by all dug wells and a number of drilled wells. The source material consisted of daily measurements of groundwater levels with a free surface from three piezometers located in different land use areas (forest, agricultural, and sparse development). Additionally, daily flows of the Zagożdżonka River at the Płachty Stare gauge station were examined, where the drying of the riverbed in the upper reaches has been observed in recent years. This study investigated the dynamics of hydrogeologic droughts in renewable groundwater resources and the rate of their decline in relation to hydrologic droughts of surface waters.

The Impact of Technological Pedagogical Content Knowledge (TPACK) on Learning Outcomes: A Bibliometric Review

<span lang="EN-AU">This study aims to analyze the research landscape regarding Technological Pedagogical Content Knowledge (TPACK) which is related to learning outcomes, using the bibliometric analysis method. The data used comes from the Scopus database. After going through the four stages of the process (identification, screening, eligibility, and inclusion), 41 relevant data were obtained. The results showed that the most publications related to TPACK and learning outcomes occurred in 2022 with a total of 6 publications. Meanwhile, the most cited publication occurred in 2017 with 267 citations. The United States has had a major influence on TPACK research and study outcomes. The research focus is divided into three main parts, namely 1) engineering and curriculum; 2) teaching and student; and 3) technology integration. Several new themes in this field include self-regulation, children learning, self-assessment, teaching strategies, learning activities and educational computing. However, the TPACK keywords which were the most dominant in the three research focuses were not directly connected with the three new theme keywords, namely self-regulation, children learning, and teaching strategies</span><span lang="IN">.</span>

Enhanced Solutions to Intuitionistic Fuzzy Multiobjective Linear Fractional Optimization Problems via Lexicographic Method

Optimization involving fuzzy numbers generally, and intuitionistic fuzzy numbers particularly is more and more an essential part of any computational intelligence method; and might be of interest in modeling fuzzy control systems, or carrying out a fuzzy sensitivity analysis. The recent literature includes many research papers related to both theoretical modelling, and practical implementation of fuzzy decision support systems. Fuzzy optimization is one of the main part in such decisionmaking tools. A realistic solution to a fuzzy optimization problem is always desired, and similarly, a Pareto optimal solution to a multiple objective optimization problem is always a need. In this paper we analyze the shortcomings; and eliminate the weaknesses of a solution approach from the literature proposed by Moges et al. in 2023. Firstly, Moges et al. used an accuracy function to de-fuzzify the original intuitionistic fuzzy optimization problem; then linearized the obtained crisp problem; and finally involved fuzzy goals to solve the derived multiple objective linear problem. We present two faulty key points of their approach, namely the de-fuzzification and linearization steps; prove the inappropriateness of their results; and propose some improvements. The final aim in addressing the first key point is to clarify the border between defuzzifications made in accordance to true theoretical statements, and those made for modeling reasons. The methodological improvement we propose is related to the second key point and it assures that Pareto optimal solutions - highly required in multiple objective optimization - are obtained. To illustrate our point of view, we use a numerical example from the literature, and report better numerical results derived by the improved methodology.

On some algebraic properties related to Heron type operator means on positive definite cones of C⁎-algebras

In this paper we consider certain algebraic properties concerning variants of the Heron mean on positive definite cones of general C⁎-algebras. Those variants are the Kubo-Ando type Heron mean and the Wasserstein mean. The main part of the investigation concerns associativity properties. We present a number of results that show how far operations related to those two kinds of means are from being associative. Many of our results can also be viewed as characterizations of central positive definite elements or as characterizations of commutative C⁎-algebras.