This research addresses the escalating need for lightweight materials, such as aluminum and magnesium alloys, in the aerospace and automotive sectors. The study explores friction stir welding (FSW), a cost-efficient process known for producing high-quality joints in these materials. The experiment involved the welding of dissimilar aluminum alloys (AA5086-H111 to AA6061-T6) using a novel pin tool design with welding parameters such as holding time, pin tool length, tool spindle speed, and linear speed fine-tuned through a design of experiment (DOE) approach. A comparative analysis of two tool designs revealed that the newly introduced design substantially improved mechanical properties, particularly tensile strengths, by 18.2% relative to its predecessor. It is noteworthy that FSW joint efficiency is 83% when using a normal tool design in comparison with 92.2% when using a new tool design at similar FSW parameters. The new tool achieved the parameter values leading to the maximum tensile strength of 317 MPa with 3 mm thickness (Th), 25 s holding time (Tt), 0.1 mm dimension (L), 1600 rpm spindle speed (SS), and 30 mm/min feed velocity (Fr). In comparison, the normal tool achieved a maximum UTS of 285 MPa, 5 mm Th, 25 s Tt, 0.3 mm L, 800 rpm SS, and 90 mm/min Fr. The new tool design, with longitudinal and circular grooves, improves heat input for plastic deformation and alloy mixing during welding. Subsequent analysis of the joint’s microstructure and microhardness shows its similarity to the original alloys. Full article

Indoor microclimate conditions and air pollutant concentrations (O₃, TVOC, CO, CO₂, and particulate matter mass concentrations in six size bins) were measured in the Greek Archaeological Museum of Abdera, which houses priceless works of art from the birthplace of the ancient philosopher Democritus. The monitoring campaign took place during the spring and summer months, when there were the greatest number of visitors. In the exhibition rooms, daily variations in relative humidity ranged from 4% to 10%, and daily variations in air temperature ranged from 0.9 °C to 2.6 °C. These uncontrolled changes may endanger the housed antiquities. The microclimate in the storage rooms varied substantially less than in the exhibition halls due to dehumidifiers and the lack of visitors. Concerning air pollution, indoor O₃ concentrations were higher than the recommended limit values for the conservation of artwork. Even more worrisome are particulate matter mass concentrations above the air quality guidelines. Despite the fact that the building is well insulated and that only artificial lighting is used in the exhibition halls, it is difficult to achieve adequate conditions for the protection of the works of art. Full article

The motion responses, mooring tensions, and submergence depth are the dominant factors for the arrangement of the Submerged Floating Tunnel (SFT) subjected to waves. Generally, the maximum values of motion responses, mooring tensions, and absolute submergence depth are mainly focused on. In the present study, experiments are implemented to measure the motion responses and mooring tensions of the SFT with different mooring patterns and submergence depths under waves with different characteristic wave heights and periods. In order to evaluate the arrangement of the SFT more effectively and comprehensively, besides the maximum values, several new characteristic parameters are introduced. Such parameters account for the motion responses in the frequency domain, the uniformity of the tension distribution, the length of time during which the cable reaches a relaxed condition during wave action, the KC number, the dimensionless period, the wave height, and the submergence depth. The results from the optimization analysis show the following: according to the characteristic values of motion responses and mooring tensions, the pattern of diagonal cables is better than that of diagonal cables + vertical cables; and within the range of the present experiments, there are optimal dimensionless parameters—the dimensionless submergence depth d₀/L_P ≥ 0.15, the KC number ≤ 0.8, or the dimensionless wave height Hs/d₀ ≤ 0.10—for the condition of which the dynamic responses and mooring tensions vary slightly. Full article

Green algae blooms of the genus Ulva are occurring globally and are primarily attributed to anthropogenic factors. At Los Tubos beach in Algarrobo Bay along the central Chilean coast, there have been blooms of these algae that persist almost year-round over the past 20 years, leading to environmental, economic, and social issues that affect the local government and communities. The objective of this study was to characterize the species that form these green tides based on a combination of ecological, morpho-anatomical, and molecular information. For this purpose, seasonal surveys of beached algal fronds were conducted between 2021 and 2022. Subsequently, the sampled algae were analyzed morphologically and phylogenetically using the molecular markers ITS1 and tufA, allowing for the identification of at least five taxa. Of these five taxa, three (U. stenophylloides, U. uncialis, U. australis) have laminar, foliose, and distromatic morphology, while the other two (U. compressa, U. aragoensis) have tubular, filamentous, and monostromatic fronds. Intertidal surveys showed that U. stenophylloides showed the highest relative coverage throughout the seasons and all intertidal levels, followed by U. uncialis. Therefore, we can establish that the green tides on the coast of Algarrobo in Chile are multispecific, with differences in relative abundance during different seasons and across the intertidal zone, opening opportunities for diverse future studies, ranging from ecology to algal biotechnology. Full article

Clickable chemical tools are essential for studying the localization and role of biomolecules in living cells. For this purpose, alkyne-based close analogs of the respective biomolecules are of outstanding interest. Here, in the field of phytosterols, we present the first alkyne derivative of sitosterol, which fulfills the crucial requirements for such a chemical tool as follows: very similar in size and lipophilicity to the plant phytosterols, and correct absolute configuration at C-24. The alkyne sitosterol FB-DJ-1 was synthesized, starting from stigmasterol, which comprised nine steps, utilizing a novel alkyne activation method, a Johnson–Claisen rearrangement for the stereoselective construction of a branched sterol side chain, and a Bestmann–Ohira reaction for the generation of the alkyne moiety. Full article

When an unmanned surface vehicle (USV) navigates in narrow waterway scenarios, its ability to detect vanishing points accurately and quickly is highly important for safeguarding its navigation safety and realizing automated navigation. We propose a novel approach for detecting vanishing points based on an improved lightweight AlexNet. First, a similarity evaluation calculation method based on image texture features is proposed, by which some scenarios are selected from the filtered Google Street Road Dataset (GSRD). These filtered scenarios, together with the USV Inland Dataset (USVID), compose the training dataset, which is manually labeled according to a non-uniformly distributed grid level. Next, the classical AlexNet was adjusted and optimized by constructing sequential connections of four convolutional layers and four pooling layers and incorporating the Inception A and Inception C structures in the first two convolutional layers. During model training, we formulate vanishing point detection as a classification problem using an output layer with 225 discrete possible vanishing point locations. Finally, we compare and analyze the labeled vanishing point with the detected vanishing point. The experimental results show that the accuracy of our method and the state-of-the-art algorithmic vanishing point detector improves, indicating that our improved lightweight AlexNet can be applied in narrow waterway navigation scenarios and can provide a technical reference for autonomous navigation of USVs. Full article

The growing importance of hydrogen as an energy carrier in a future decarbonised energy system has led to a surge in its production plans. However, the development of infrastructure for hydrogen delivery, particularly in the hard-to-abate sectors, remains a significant challenge. While constructing new pipelines entails substantial investment, repurposing existing pipelines offers a cost-effective approach to jump-starting hydrogen networks. Many European countries and, more recently, other regions are exploring the possibility of utilising their current pipeline infrastructure for hydrogen transport. Despite the recent efforts to enhance the understanding of pipeline compatibility and integrity for hydrogen transportation, including issues such as embrittlement, blend ratios, safety concerns, compressor optimisation, and corrosion in distribution networks, there has been limited or no focus on pipeline expansion options to address the low-energy density of hydrogen blends and associated costs. This study, therefore, aims to explore expansion options for existing natural gas high-pressure pipelines through additional compression or looping. It seeks to analyse the corresponding cost implications to achieve an affordable and sustainable hydrogen economy by investigating the utilisation of existing natural gas pipeline infrastructure for hydrogen transportation as a cost-saving measure. It explores two expansion strategies, namely pipeline looping (also known as pipeline reinforcement) and compression, for repurposing a segment of a 342 km × 36 inch existing pipeline, from the Escravos–Lagos gas pipeline system (ELPS) in Nigeria, for hydrogen transport. Employing the Promax^® process simulator tool, the study assesses compliance with the API RP 14E and ASME B31.12 standards for hydrogen and hydrogen–methane blends. Both expansion strategies demonstrate acceptable velocity and pressure drop characteristics for hydrogen blends of up to 40%. Additionally, the increase in hydrogen content leads to heightened compression power requirements until approximately 80% hydrogen in the blends for compression and a corresponding extension in looping length until around 80% hydrogen in the blend for looping. Moreover, the compression option is more economically viable for all investigated proportions of hydrogen blends for the PS1–PS5 segment of the Escravos–Lagos gas pipeline case study. The percentage price differentials between the two expansion strategies reach as high as 495% for a 20% hydrogen proportion in the blend. This study offers valuable insights into the technical and economic implications of repurposing existing natural gas infrastructure for hydrogen transportation. Full article

Alzheimer’s disease (AD) is a progressive neurodegenerative condition. It causes cognitive impairment and memory loss in individuals. Healthcare professionals face challenges in detecting AD in its initial stages. In this study, the author proposed a novel integrated approach, combining LeViT, EfficientNet B7, and Dartbooster XGBoost (DXB) models to detect AD using magnetic resonance imaging (MRI). The proposed model leverages the strength of improved LeViT and EfficientNet B7 models in extracting high-level features capturing complex patterns associated with AD. A feature fusion technique was employed to select crucial features. The author fine-tuned the DXB using the Bayesian optimization hyperband (BOHB) algorithm to predict AD using the extracted features. Two public datasets were used in this study. The proposed model was trained using the Open Access Series of Imaging Studies (OASIS) Alzheimer’s dataset containing 86,390 MRI images. The Alzheimer’s dataset was used to evaluate the generalization capability of the proposed model. The proposed model obtained an average generalization accuracy of 99.8% with limited computational power. The findings highlighted the exceptional performance of the proposed model in predicting the multiple types of AD. The recommended integrated feature extraction approach has supported the proposed model to outperform the state-of-the-art AD detection models. The proposed model can assist healthcare professionals in offering customized treatment for individuals with AD. The effectiveness of the proposed model can be improved by generalizing it to diverse datasets. Full article

Climate change is a notable challenge for agriculture as it affects crop productivity and yield. Increases in droughts, salinity, and soil degradation are some of the major consequences of climate change. The use of microorganisms has emerged as an alternative to mitigate the effects of climate change. Among these microorganisms, dark septate endophytes (DSEs) have garnered increasing attention in recent years. Dark septate endophytes have shown a capacity for mitigating and reducing the harmful effects of climate change in agriculture, such as salinity, drought, and the reduced nutrient availability in the soil. Various studies show that their association with plants helps to reduce the harmful effects of abiotic stresses and increases the nutrient availability, enabling the plants to thrive under adverse conditions. In this study, the effect of DSEs and the underlying mechanisms that help plants to develop a higher tolerance to climate change were reviewed. Full article

The aim of this work is to present the results of research carried out in a city in the interior of São Paulo that sought to understand the health needs of women released from prisons in the region who are cared for at a Center for Attention to Egress and Family (CAEF) as well as the barriers they report in obtaining support, discussing them in light of educational health interventions described in the international literature. This study conducted formative research to identify the themes and issues that should be included in educational material. Data were collected through body-map storytelling and semi-structured interviews with six and twenty women released from prison, respectively, and nine interviews with professionals from the CAEF and the health sector of a women’s penitentiary in the study location. The main health demands of the women identified in the study were chronic diseases, mental health, gynecological problems, and sexually transmitted diseases, which constitute individual barriers and are aggravated by others of a relational, institutional, and political-systemic nature. It is hoped that the present study will inspire new interventions to be considered in the Brazilian context based on these results. Full article

Microenvironment and transcriptional plasticity generate subpopulations within the tumor, and the use of BRAF inhibitors (BRAFis) contributes to the rise and selection of resistant clones. We stochastically isolated subpopulations (C1, C2, and C3) from naïve melanoma and found that the clones demonstrated distinct morphology, phenotypic, and functional profiles: C1 was less proliferative, more migratory and invasive, less sensitive to BRAFis, less dependent on OXPHOS, more sensitive to oxidative stress, and less pigmented; C2 was more proliferative, less migratory and invasive, more sensitive to BRAFis, less sensitive to oxidative stress, and more pigmented; and C3 was less proliferative, more migratory and invasive, less sensitive to BRAFis, more dependent on OXPHOS, more sensitive to oxidative stress, and more pigmented. Hydrogen peroxide plays a central role in oxidative stress and cell signaling, and PRDXs are one of its main consumers. The intrinsically resistant C1 and C3 clones had lower MITF, PGC-1α, and PRDX1 expression, while C1 had higher AXL and decreased pigmentation markers, linking PRDX1 to clonal heterogeneity and resistance. PRDX2 is depleted in acquired BRAFi-resistant cells and acts as a redox sensor. Our results illustrate that decreased pigmentation markers are related to therapy resistance and decreased antioxidant defense. Full article

Tchaikovsky enjoyed composing Yevgeni Onegin. He expressed his fulfillment in a famous letter to Sergey Taneyev. What could his enthusiasm convey about the content of the project? Music criticism has taken Tchaikovsky’s words as proof for the thesis that the opera is connected to autobiographical circumstances. In this mode of thinking, the quality of Tchaikovsky’s music is the result of the composer’s identification with the subject matter. Despite the objection of several Tchaikovsky scholars, the autobiographical paradigm remains very much alive in the reception of Tchaikovsky’s music. As an alternative, Tchaikovsky scholarship has explored a hermeneutical approach that would link his music to its context in Russian society and culture. In this paper, I present another possible reaction to Tchaikovsky’s statement: an exploration of the composer’s approach to musical characterization. Analysis of some key scenes reveals that the definition of characters and situations by musical means is more precise than standard interpretations of the opera would concede. This discovery may lead to a new assessment of characterization as a critical tool to refine the definition of Tchaikovsky’s position in European music history. The method may be applied to examples outside his operatic output, such as Serenade for Strings and the Fifth Symphony. Full article

The hemodynamic relevance of differently located stenoses of the internal jugular veins remains undetermined. It particularly concerns nozzle-like strictures in the upper parts of these veins and stenotic jugular valves located at the end of these veins. This study was aimed at understanding flow disturbances caused by such stenoses. The computational fluid dynamics software Flowsquare+ was used. We constructed 3-dimensional models of the venous outflow, comprising two alternative routes: the tube representing the internal jugular vein and an irregular network representing the vertebral veins. At the beginning of the tube representing the internal jugular vein, differently shaped and sized short strictures representing nozzle-like strictures were built in. At the end of this tube, differently shaped membranes representing the jugular valve were built in. With the use of computational fluid dynamics modeling, we studied how these two obstacles influenced the outflow. We found that the most relevant outflow disturbances were evoked by the nozzle-like strictures in the upper part of the internal jugular vein that were small, long, or asymmetrically positioned. Very tight stenotic valves and septum-like malformed valve were equally hemodynamically relevant. These findings suggest that both upper and lower strictures of the internal jugular vein can be of clinical significance. Full article

The common geometrical (symplectic) structures of classical mechanics, quantum mechanics, and classical thermodynamics are unveiled with three pictures. These cardinal theories, mainly at the non-relativistic approximation, are the cornerstones for studying chemical dynamics and chemical kinetics. Working in extended phase spaces, we show that the physical states of integrable dynamical systems are depicted by Lagrangian submanifolds embedded in phase space. Observable quantities are calculated by properly transforming the extended phase space onto a reduced space, and trajectories are integrated by solving Hamilton’s equations of motion. After defining a Riemannian metric, we can also estimate the length between two states. Local constants of motion are investigated by integrating Jacobi fields and solving the variational linear equations. Diagonalizing the symplectic fundamental matrix, eigenvalues equal to one reveal the number of constants of motion. For conservative systems, geometrical quantum mechanics has proved that solving the Schrödinger equation in extended Hilbert space, which incorporates the quantum phase, is equivalent to solving Hamilton’s equations in the projective Hilbert space. In classical thermodynamics, we take entropy and energy as canonical variables to construct the extended phase space and to represent the Lagrangian submanifold. Hamilton’s and variational equations are written and solved in the same fashion as in classical mechanics. Solvers based on high-order finite differences for numerically solving Hamilton’s, variational, and Schrödinger equations are described. Employing the Hénon–Heiles two-dimensional nonlinear model, representative results for time-dependent, quantum, and dissipative macroscopic systems are shown to illustrate concepts and methods. High-order finite-difference algorithms, despite their accuracy in low-dimensional systems, require substantial computer resources when they are applied to systems with many degrees of freedom, such as polyatomic molecules. We discuss recent research progress in employing Hamiltonian neural networks for solving Hamilton’s equations. It turns out that Hamiltonian geometry, shared with all physical theories, yields the necessary and sufficient conditions for the mutual assistance of humans and machines in deep-learning processes. Full article

We present a deep learning (DL) network-based approach for detecting and semantically segmenting two specific types of tuberculosis (TB) lesions in chest X-ray (CXR) images. In the proposed method, we use a basic U-Net model and its enhanced versions to detect, classify, and segment TB lesions in CXR images. The model architectures used in this study are U-Net, Attention U-Net, U-Net++, Attention U-Net++, and pyramid spatial pooling (PSP) Attention U-Net++, which are optimized and compared based on the test results of each model to find the best parameters. Finally, we use four ensemble approaches which combine the top five models to further improve lesion classification and segmentation results. In the training stage, we use data augmentation and preprocessing methods to increase the number and strength of lesion features in CXR images, respectively. Our dataset consists of 110 training, 14 validation, and 98 test images. The experimental results show that the proposed ensemble model achieves a maximum mean intersection-over-union (MIoU) of 0.70, a mean precision rate of 0.88, a mean recall rate of 0.75, a mean F1-score of 0.81, and an accuracy of 1.0, which are all better than those of only using a single-network model. The proposed method can be used by clinicians as a diagnostic tool assisting in the examination of TB lesions in CXR images. Full article

The pulsed- and steady-pedestal paradigms were designed to track increment thresholds (ΔC) as a function of pedestal contrast (C) for the parvocellular (P) and magnocellular (M) systems, respectively. These paradigms produce contrasting results: linear relationships between ΔC and C are observed in the pulsed-pedestal paradigm, indicative of the P system’s processing, while the steady-pedestal paradigm reveals nonlinear functions, characteristic of the M system’s response. However, we recently found the P model fits better than the M model for both paradigms, using Gabor stimuli biased towards the M or P systems based on their sensitivity to color and spatial frequency. Here, we used two-square pedestals under green vs. red light in the lower-left vs. upper-right visual fields to bias processing towards the M vs. P system, respectively. Based on our previous findings, we predicted the following: (1) steeper ΔC vs. C functions with the pulsed than the steady pedestal due to different task demands; (2) lower ΔCs in the upper-right vs. lower-left quadrant due to its bias towards P-system processing there; (3) no effect of color, since both paradigms track the P-system; and, most importantly (4) contrast gain should not be higher for the steady than for the pulsed pedestal. In general, our predictions were confirmed, replicating our previous findings and providing further evidence questioning the general validity of using the pulsed- and steady-pedestal paradigms to differentiate the P and M systems. Full article

Due to the interaction of accumulated charges on the surface of a test mass with the surrounding electric and magnetic fields, the performance of inertial sensors is affected, necessitating charge management for the test mass. Discharge technology based on Ultraviolet LEDs is internationally recognized as the optimal solution for charge management. Precision driving of Ultraviolet LEDs is considered a key technology in charge management. This paper presents the driving control system used for Ultraviolet LEDs, achieving precision pulse-width-modulation-type current output with controllable pulse width and amplitude. The system generates the pulse-width-controllable pulse voltage signal via analog pulse-width modulation, and subsequently regulates the amplitude of the PWM signal through range switching. To convert the voltage into the pulse-width-modulation-type driving current, the improved Howland current source is employed. The test results demonstrate that the driving control system can output controllable current in the range of 0.01 mA to 10 mA, with a minimum step of 0.01 mA. The accuracy of the current reaches 1%, the stability within 1 h is better than 1%, and the load regulation is better than 2%. The driving control system provides an important reference for the integration of charge management system and the precision drive control method for LEDs. Full article

This study presents the interaction with the human host metabolism of SARS-CoV-2 ORF7b protein (43 aa), using a protein–protein interaction network analysis. After pruning, we selected from BioGRID the 51 most significant proteins among 2753 proven interactions and 1708 interactors specific to ORF7b. We used these proteins as functional seeds, and we obtained a significant network of 551 nodes via STRING. We performed topological analysis and calculated topological distributions by Cytoscape. By following a hub-and-spoke network architectural model, we were able to identify seven proteins that ranked high as hubs and an additional seven as bottlenecks. Through this interaction model, we identified significant GO-processes (5057 terms in 15 categories) induced in human metabolism by ORF7b. We discovered high statistical significance processes of dysregulated molecular cell mechanisms caused by acting ORF7b. We detected disease-related human proteins and their involvement in metabolic roles, how they relate in a distorted way to signaling and/or functional systems, in particular intra- and inter-cellular signaling systems, and the molecular mechanisms that supervise programmed cell death, with mechanisms similar to that of cancer metastasis diffusion. A cluster analysis showed 10 compact and significant functional clusters, where two of them overlap in a Giant Connected Component core of 206 total nodes. These two clusters contain most of the high-rank nodes. ORF7b acts through these two clusters, inducing most of the metabolic dysregulation. We conducted a co-regulation and transcriptional analysis by hub and bottleneck proteins. This analysis allowed us to define the transcription factors and miRNAs that control the high-ranking proteins and the dysregulated processes within the limits of the poor knowledge that these sectors still impose. Full article

The microstructure characteristics of TiAl alloy prepared by laser-directed energy deposition (L-DED) are coarse columnar grains parallel to the building direction, which results in serious mechanical properties and anisotropy and limits its application. In the present study, TiB₂ can be used as an effective grain refiner due to the extremely high Q value (growth inhibition factor; the larger the Q value of an alloying element, the stronger its grain refinement effect.) of B. With TiB₂ addition, TiAl alloys prepared by laser-directed energy deposition with the microstructure of full equiaxed grains were obtained, and the grain size was significantly reduced by about 30% with 0.45 wt.% TiB₂. This value has been further increased to 45% when adding 0.9 wt.% TiB₂. Moreover, the γ_m phase was nearly eliminated and the width of (α2 + γ) lamellar was significantly decreased, which has positive effects on mechanical properties. Meanwhile, TiB₂ precipitates uniformly distribute in the matrix, as a reinforced particle to increase the hardness and compressive strength of the alloys. The microhardness of the TiAl alloy increased with the increasing content of TiB₂. The addition of TiB₂ improved the room and high-temperature compressive properties of TiAl alloy while slightly increasing its ductility. These findings have important guiding significance for expanding the application of TiAl alloys. Full article

Intensive economic and human activities present challenges to the carbon storage capacity of terrestrial ecosystems, particularly in arid regions that are sensitive to climate change and ecologically fragile. Therefore, accurately estimating and simulating future changes in carbon stocks on the northern slope economic belt of Tianshan Mountains (NSEBTM) holds great significance for maintaining ecosystem stability, achieving high-quality development of the economic belt, and realizing the goal of “carbon neutrality” by 2050. This study examines the spatiotemporal evolution characteristics of the NSEBTM carbon stocks in arid regions from 1990 to 2050, utilizing a combination of multi-source data and integrating the Patch-generating Land use Simulation (PLUS) and Integrated Valuation of Ecosystem Services and Trade-offs (InVEST) models. Additionally, an attribution analysis of carbon stock changes is conducted by leveraging land use data. The findings demonstrate that (1) the NSEBTM predominantly consists of underutilized land, accounting for more than 60% of the total land area in the NSEBTM. Unused land, grassland, and water bodies exhibit a declining trend over time, while other forms of land use demonstrate an increasing trend. (2) Grassland serves as the primary reservoir for carbon storage in the NSEBTM, with grassland degradation being the leading cause of carbon loss amounting to 102.35 t over the past three decades. (3) Under the ecological conservation scenario for 2050 compared to the natural development scenario, there was a net increase in carbon storage by 12.34 t; however, under the economic development scenario compared to the natural development scenario, there was a decrease in carbon storage by 25.88 t. By quantitatively evaluating the land use change in the NSEBTM and its impact on carbon storage in the past and projected for the next 30 years, this paper provides scientific references and precise data support for the territorial and spatial decision making of the NSEBTM, thereby facilitating the achievement of “carbon neutrality” goals. Full article

The calculation of satellite orbit involves some very complex formula derivations and expansions, which are very difficult to manually derive and prone to errors. And the efficiency of manual derivation is not high. We can use computer algebra systems to derive complex formulas related to satellite orbits. This can avoid some of the drawbacks of manual derivation and significantly improve computational efficiency and accuracy. In the past, the relationship among three anomalies was generally represented in the form of a trigonometric series with the first eccentricity $e$ as the parameter. In this paper, the trigonometric series with the parameter $m=\frac{1-\sqrt{1-e^2}}{e}$ is used, as determined by the Lagrange conjugate series. We can use the formula of the Lagrange conjugate series to derive the relationship between the true anomaly and elliptic anomaly. And the relationship between the elliptic anomaly and the mean anomaly is derived by using the symbolic iteration method. In this research paper, we calculated the accuracy of the trigonometric series expansion among three types of anomalies at the first eccentricity $e$ equal to values of 0.01, 0.1, and 0.2. The calculation results indicate that the accuracy of the trigonometric series expansion with $m$ as the parameter is better than 10⁻⁵. Moreover, in some cases, the trigonometric series expansion among the three anomalies with $m$ as a parameter is simpler in form than the expansion expressed with parameter $e$. This paper also derived and calculated the symbolic expressions and extreme values of the difference among three anomalies and expressed the extreme values of the difference in the form of a power series of $e$. It can be seen that the extreme value increases with the increase in eccentricity $e$. And the absolute values of the extreme value of the difference between the elliptic anomaly and the mean anomaly, the true anomaly and the elliptic anomaly, and the true anomaly and the mean anomaly increase in this order. When the eccentricity is small, the absolute value of the extreme value of the difference between the true anomaly and the mean anomaly is about twice as large as the elliptic anomaly and the mean anomaly and the true anomaly and the mean anomaly. Full article

Due to the increasing demand for transport of electrical energy, measures for power flow control, congestion management, and higher utilisation of the existing grid play a decisive role in the transformation of the power system. Hence, enormous efforts must be undertaken using measures of congestion management. Modelling and integration of corresponding measures in optimisation tools to support grid and system operation and therewith reduce the resulting efforts become more important. This is especially true because of the high intermittency and decentralisation of renewable generation leading to increased complexity of the power system, higher loading of assets, and a growing need for control over flexible alternating current transmission systems (FACTS) and high-voltage direct current (HVDC) converters. This work therefore describes the implementation of optimised congestion management in an A Mathematical Programming Language (AMPL)-based nonlinear optimisation problem. AMPL is an effective tool to deal with highly complex problems of optimisation and scheduling. Therefore, the modelling of assets and flexibilities for power flow control in AC/DC systems in combination with an innovative grid operation strategy using predefined curative measures for the optimised use of the existing grid is introduced. The nonlinear mathematical optimisation aims at the optimal cost selection of flexibility measures. The application of the optimisation technique in a combined AC/DC system shows the optimal preventive and curative use of measures in operational congestion management. Simulation results prove that, by using predefined curative measures, the volume of cost-intensive preventive measures can significantly be reduced, especially in association with power flow control. Full article