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18 pages, 404 KiB  
Article
Long COVID-19: A Concept Analysis
by Sujata Srikanth, Jessica R. Boulos, Diana Ivankovic, Lucia Gonzales, Delphine Dean and Luigi Boccuto
Infect. Dis. Rep. 2025, 17(4), 90; https://doi.org/10.3390/idr17040090 - 29 Jul 2025
Viewed by 154
Abstract
Background/Objectives: In late 2019, the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) caused a pandemic called the ‘coronavirus disease 2019’ (COVID-19). After the acute SARS-CoV-2 infection, many individuals (up to 33%) complained of unexplained symptoms involving multiple organ systems and were diagnosed [...] Read more.
Background/Objectives: In late 2019, the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) caused a pandemic called the ‘coronavirus disease 2019’ (COVID-19). After the acute SARS-CoV-2 infection, many individuals (up to 33%) complained of unexplained symptoms involving multiple organ systems and were diagnosed as having Long COVID-19 (LC-19). Currently, LC-19 is inadequately defined, requiring the formation of consistent diagnostic parameters to provide a foundation for ongoing and future studies of epidemiology, risk factors, clinical characteristics, and therapy. LC-19 represents a significant burden on multiple levels. The reduced ability of workers to return to work or compromised work efficiency has led to consequences at national, economic, and societal levels by increasing dependence on community services. On a personal scale, the isolation and helplessness caused by the disease and its subsequent impact on the patient’s mental health and quality of life are incalculable. Methods: In this paper, we used Walker and Avants’ eight-step approach to perform a concept analysis of the term “Long COVID-19” and define its impact across these parameters. Results: Using this methodology, we provide an improved definition of LC-19 by connecting the clinical symptomology with previously under-addressed factors, such as mental, psychological, economic, and social effects. This definition of LC-19 features can help improve diagnostic procedures and help plan relevant healthcare services. Conclusions: LC-19 represents a complex and pressing public health challenge with diverse symptomology, an unpredictable timeline, and complex pathophysiology. This concept analysis serves as a tool for improving LC-19 definition, but it remains a dynamic disease with evolving diagnostic and therapeutic approaches, requiring deeper investigation and understanding of its long-term effects. Full article
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18 pages, 774 KiB  
Article
Bayesian Inertia Estimation via Parallel MCMC Hammer in Power Systems
by Weidong Zhong, Chun Li, Minghua Chu, Yuanhong Che, Shuyang Zhou, Zhi Wu and Kai Liu
Energies 2025, 18(15), 3905; https://doi.org/10.3390/en18153905 - 22 Jul 2025
Viewed by 141
Abstract
The stability of modern power systems has become critically dependent on precise inertia estimation of synchronous generators, particularly as renewable energy integration fundamentally transforms grid dynamics. Increasing penetration of converter-interfaced renewable resources reduces system inertia, heightening the grid’s susceptibility to transient disturbances and [...] Read more.
The stability of modern power systems has become critically dependent on precise inertia estimation of synchronous generators, particularly as renewable energy integration fundamentally transforms grid dynamics. Increasing penetration of converter-interfaced renewable resources reduces system inertia, heightening the grid’s susceptibility to transient disturbances and creating significant technical challenges in maintaining operational reliability. This paper addresses these challenges through a novel Bayesian inference framework that synergistically integrates PMU data with an advanced MCMC sampling technique, specifically employing the Affine-Invariant Ensemble Sampler. The proposed methodology establishes a probabilistic estimation paradigm that systematically combines prior engineering knowledge with real-time measurements, while the Affine-Invariant Ensemble Sampler mechanism overcomes high-dimensional computational barriers through its unique ensemble-based exploration strategy featuring stretch moves and parallel walker coordination. The framework’s ability to provide full posterior distributions of inertia parameters, rather than single-point estimates, helps for stability assessment in renewable-dominated grids. Simulation results on the IEEE 39-bus and 68-bus benchmark systems validate the effectiveness and scalability of the proposed method, with inertia estimation errors consistently maintained below 1% across all generators. Moreover, the parallelized implementation of the algorithm significantly outperforms the conventional M-H method in computational efficiency. Specifically, the proposed approach reduces execution time by approximately 52% in the 39-bus system and by 57% in the 68-bus system, demonstrating its suitability for real-time and large-scale power system applications. Full article
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19 pages, 12224 KiB  
Article
A Non-Destructive Method, Micro-CT, Supports the Identification of Three New Casmara Species from Sumatra and Taiwan (Lepidoptera: Ashinagidae)
by In-Won Jeong, Sora Kim and John B. Heppner
Insects 2025, 16(8), 747; https://doi.org/10.3390/insects16080747 - 22 Jul 2025
Viewed by 371
Abstract
Insects exhibit diverse ecological characteristics, but species identification is challenging due to high morphological similarity. Traditional methods require genitalia dissection, which damages specimens and flattens three-dimensional structures, potentially losing key morphological details. In this study, we evaluate the utility of Micro-CT (Computed Tomography) [...] Read more.
Insects exhibit diverse ecological characteristics, but species identification is challenging due to high morphological similarity. Traditional methods require genitalia dissection, which damages specimens and flattens three-dimensional structures, potentially losing key morphological details. In this study, we evaluate the utility of Micro-CT (Computed Tomography) as a non-destructive alternative for species identification by comparing genitalia structures obtained through Micro-CT with those obtained through traditional dissection. Micro-CT enabled three-dimensional reconstructions of male genitalia and aedeagus, providing detailed views from multiple angles without physical damage. The aedeagus was also virtually separated in a digital environment, further enhancing morphological analysis. Using this approach, we identified three new species, Casmara fulvacorona sp. nov. from Sumatra, C. falcatussica sp. nov. and C. fuscatulipa sp. nov. from Taiwan, based on genitalia characteristics. In addition, we provide a checklist of all Casmara Walker, 1863 species reported to date, including these newly described species, to confirm and clarify the distribution of this genus. Our results demonstrate that the additional use of Micro-CT in insect species identification can provide a scientific basis for reviewing and increasing confidence in species identification based on genital dissection. Full article
(This article belongs to the Section Insect Systematics, Phylogeny and Evolution)
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13 pages, 243 KiB  
Article
Complex Riemannian Spacetime and Singularity-Free Black Holes and Cosmology
by John W. Moffat
Axioms 2025, 14(6), 459; https://doi.org/10.3390/axioms14060459 - 12 Jun 2025
Viewed by 587
Abstract
An approach is presented to address singularities in general relativity using a complex Riemannian spacetime extension. We demonstrate how this method can be applied to both black hole and cosmological singularities, specifically focusing on the Schwarzschild and Kerr black holes and the Friedmann–Lemaître–Robertson–Walker [...] Read more.
An approach is presented to address singularities in general relativity using a complex Riemannian spacetime extension. We demonstrate how this method can be applied to both black hole and cosmological singularities, specifically focusing on the Schwarzschild and Kerr black holes and the Friedmann–Lemaître–Robertson–Walker (FLRW) Big Bang cosmology. By extending the relevant coordinates into the complex plane and carefully choosing integration contours, we show that it is possible to regularize these singularities, resulting in physically meaningful, singularity-free solutions when projected back onto real spacetime. The removal of the singularity at the Big Bang allows for a bounce cosmology. The approach offers a potential bridge between classical general relativity and quantum gravity effects, suggesting a way to resolve longstanding issues in gravitational physics without requiring a full theory of quantum gravity. Full article
(This article belongs to the Special Issue Complex Variables in Quantum Gravity)
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15 pages, 633 KiB  
Article
Walking-Age Estimator Based on Gait Parameters Using Kernel Regression
by Tomohito Kuroda, Shogo Okamoto and Yasuhiro Akiyama
Appl. Sci. 2025, 15(11), 5825; https://doi.org/10.3390/app15115825 - 22 May 2025
Viewed by 373
Abstract
Human gait motions differ depending on the age of the person. Previous studies have estimated age categories of walkers or have used age analysis for security or commercial surveillance purposes using images. However, few studies have estimated age from gait parameters alone. We [...] Read more.
Human gait motions differ depending on the age of the person. Previous studies have estimated age categories of walkers or have used age analysis for security or commercial surveillance purposes using images. However, few studies have estimated age from gait parameters alone. We estimated the age of people using kernel regression analysis based on their height, weight, and representative gait parameters, i.e., walking features that are interpretable with relative ease. Samples were obtained from 75 Japanese women aged 20–70 in a database. Through a variable selection based on sensitivity analysis, the established model estimated the ages of the women with a correlation coefficient of 0.78 with their actual ages, and the mean absolute error was 9.99 years. The sensitive variables included the minimum foot clearance, body weight, walking velocity, step width, and stride length. Estimation errors were significantly greater for elderly adults than for young people. Specifically, the mean absolute error for people in their 20s was 7.4 years, whereas that for those over 60 was 13.1 years. The proposed method uses gait parameters that can be measured with wearable devices, such as inertial measurement units; therefore, it offers an accessible approach to estimating a walker’s age with moderate certainty and promoting healthcare awareness in daily life. Full article
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13 pages, 7770 KiB  
Article
Adaptive Navigation of a Smart Walker with Shared Control
by Giuseppe Sutera, Dario Calogero Guastella, Francesco Cancelliere and Giovanni Muscato
Actuators 2025, 14(5), 224; https://doi.org/10.3390/act14050224 - 1 May 2025
Viewed by 620
Abstract
The global surge in the elderly population has increased the awareness of their needs. Supporting mobility and perception is vital to improving their quality of life. This project introduces a prototype of an active smart walker with obstacle avoidance and assistive navigation features [...] Read more.
The global surge in the elderly population has increased the awareness of their needs. Supporting mobility and perception is vital to improving their quality of life. This project introduces a prototype of an active smart walker with obstacle avoidance and assistive navigation features to aid the elderly. The system can plan routes and move in familiar environments, adjusting its actions based on the user’s intentions. To accomplish this, a shared control approach employs a force–torque sensor to gauge the user’s will. The proposed system has been tested in multiple scenarios, replicating a common use in real-world environments. Full article
(This article belongs to the Section Actuators for Robotics)
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10 pages, 2002 KiB  
Case Report
Adult-Onset Syringomyelia in Dandy-Walker Malformation Patients: Clinical Insights and Literature Review
by Bojana Zivkovic, Mirko Micovic, Marko Todorovic, Jelena Kostic and Vladimir Bascarevic
Brain Sci. 2025, 15(5), 456; https://doi.org/10.3390/brainsci15050456 - 26 Apr 2025
Viewed by 761
Abstract
Introduction: The presence of syringomyelia associated with Dandy-Walker malformation is rarely described in adults. Case report: We report a case of a 28-year-old woman with a history of Dandy-Walker malformation who developed syringomyelia. She had been previously treated in childhood with a ventriculoperitoneal [...] Read more.
Introduction: The presence of syringomyelia associated with Dandy-Walker malformation is rarely described in adults. Case report: We report a case of a 28-year-old woman with a history of Dandy-Walker malformation who developed syringomyelia. She had been previously treated in childhood with a ventriculoperitoneal and cystoperitoneal shunt for hydrocephalus, but over time she developed progressive neurological symptoms, including numbness and weakness in the upper extremities. Magnetic resonance imaging revealed a syrinx extending from C4 to T1 associated with large posterior fossa cyst. The patient was treated with cyst fenestration and cystoperitoneal shunts were removed, with complete resolution of symptoms and disappearance of syrinx. Discussion: A literature review revealed only 6 cases of syringomyelia associated with Dandy-Walker malformation in adults. The pathophysiology of this entity is multifactorial and may be related to obstructed cerebrospinal fluid flow, altered pressure dynamics, and formation of arachnoid adhesions. Conclusions: Individualized surgical approaches are essential for optimizing outcomes in this rare condition. Further research is needed to standardize treatment protocols and clarify underlying mechanisms and help to improve the management of these patients. Full article
(This article belongs to the Section Neurosurgery and Neuroanatomy)
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18 pages, 1429 KiB  
Article
Comprehensive Optical Inter-Satellite Communication Model for Low Earth Orbit Constellations: Analyzing Transmission Power Requirements
by Michail Gioulis, Thomas Kamalakis and Dimitris Alexandropoulos
Photonics 2025, 12(4), 392; https://doi.org/10.3390/photonics12040392 - 17 Apr 2025
Viewed by 953
Abstract
Free-space optical communications have emerged as a powerful solution for inter-satellite links, playing a crucial role in next-generation satellite networks. This paper introduces a comprehensive model that enables the dynamic evaluation of optical power requirements for realistic low Earth orbit satellite constellations throughout [...] Read more.
Free-space optical communications have emerged as a powerful solution for inter-satellite links, playing a crucial role in next-generation satellite networks. This paper introduces a comprehensive model that enables the dynamic evaluation of optical power requirements for realistic low Earth orbit satellite constellations throughout the orbital period. Our approach incorporates the constellation architecture, link budget analysis, and optical transceiver design to accurately estimate the power required for sustaining connectivity for both intra- and inter-orbit links. We apply the model considering Walker delta-type constellations of varying densities. We show that in dense constellations, even at high data rates, the required transmission power can be low enough to mitigate the need for optical amplification. Dynamically estimating the power requirements is vital when evaluating energy savings in adaptive scenarios where terminals adaptively change the emitted power depending on the link status. Our model is implemented in Python and is openly available under an open-source license. It can be easily adapted to various alternative constellation configurations. Full article
(This article belongs to the Special Issue Advanced Technologies in Optical Wireless Communications)
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11 pages, 1228 KiB  
Article
Distribution of Rachiplusia nu and Chrysodeixis includens in Bt and Conventional Soybean Fields in Brazil
by Carolina T. D. Godói, Tamylin K. Ishizuka, Guilherme A. Gotardi, Natália R. F. Batista, Luiz H. Marques, Antônio César S. Santos, Mário H. Dal Pogetto, Timothy Nowatzki, Amit Sethi and Mark L. Dahmer
Insects 2025, 16(4), 365; https://doi.org/10.3390/insects16040365 - 1 Apr 2025
Viewed by 763
Abstract
Chrysodeixis includens (Walker, 1858) and Rachiplusia nu (Guenée, 1852) are important defoliating pests belonging to the Plusiinae subfamily in the Western hemisphere. C. includens is a major lepidopteran pest of soybean in the Americas, whereas, until 2021, R. nu was more restricted to [...] Read more.
Chrysodeixis includens (Walker, 1858) and Rachiplusia nu (Guenée, 1852) are important defoliating pests belonging to the Plusiinae subfamily in the Western hemisphere. C. includens is a major lepidopteran pest of soybean in the Americas, whereas, until 2021, R. nu was more restricted to the temperate regions of South America. Recently, reports of R. nu feeding on Cry1Ac soybean and occurring in tropical regions of Brazil have raised questions regarding the distribution of this species. The morphological similarity of the larvae from the two species makes it difficult to correctly identify the species in the field, which may lead to an underestimation of R. nu in Brazilian territory. This study aimed to address these questions by using a molecular approach to identify Plusiinae caterpillars throughout three seasons in non-Bt, Cry1Ac, and Cry1Ac × Cry1F soybean fields. Here, we carried out a comprehensive spatial sampling of the primary soybean-producing regions in Brazil. The results showed that R. nu has been the main Plusiinae occurring in soybean over the last three years, and it was present in all sampled regions. For Cry1Ac and Cry1Ac × Cry1F soybeans, up to 99% of the samples collected in 2023/24 were identified as R. nu. Non-Bt soybeans had higher variations in the proportion of the two species among the regions and across seasons, indicating that populations of C. includens and R. nu are co-occurring throughout the country. This is, to our knowledge, the most robust report assessing the distribution of C. includens and R. nu in Brazil using a molecular tool. This study provides clarification of R. nu occurrence and highlights the importance of pest monitoring from an integrated pest management perspective. Full article
(This article belongs to the Section Insect Pest and Vector Management)
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22 pages, 5048 KiB  
Review
Development in Soil Chronosequence Research from 1994 to 2024: A Bibliometric Analysis Using CiteSpace
by Jingtao Wu, Wenyan Yang, Manman Fan, Huan Zhang, Zhengwei Ye and Muhammad Shaukat
Agriculture 2025, 15(7), 708; https://doi.org/10.3390/agriculture15070708 - 26 Mar 2025
Viewed by 595
Abstract
Soil chronosequences are crucial for understanding pedogenesis and ecosystem dynamics, yet a systematic bibliometric analysis of this field remains absent. To investigate hotspots and trends, this study used CiteSpace to analyze 4075 publications from the Web of Science Core Collection (1994–2024). The results [...] Read more.
Soil chronosequences are crucial for understanding pedogenesis and ecosystem dynamics, yet a systematic bibliometric analysis of this field remains absent. To investigate hotspots and trends, this study used CiteSpace to analyze 4075 publications from the Web of Science Core Collection (1994–2024). The results revealed a steady increase in publications over time, led by the USA (1287 articles) and China (1093 articles). Wardle David A. emerged as the most influential researcher (67,519 citations) for his contributions regarding microbial-driven pedogenic feedbacks. The Chinese Academy of Sciences was the top institution, contributing 13.3% of articles and achieving the highest centrality of 0.21. Geoderma (IF = 5.6) was the most cited journal (2258 citations), with key contributors including Vitousek (530 citations) and Walker (415 citations) from the USA and Wardle (411 citations) from Sweden. Research hotspots in this field were nutrient cycling, vegetation succession/ecological restoration, and soil microbial community dynamics. Three thematic shifts were identified: early focus on conceptual frameworks, expansion to ecological restoration and carbon dynamics, and recent diversification into microbial communities, coastal ecosystems (e.g., mangroves, Spartina alterniflora), and anthropogenic impacts (e.g., heavy metals). The research has evolved significantly from 1994 to 2024, with a growing emphasis on interdisciplinary approaches and practical applications. This analysis provides a comprehensive synthesis of soil chronosequence research, advancing our understanding of pedogenesis and informing sustainable land-management strategies. Full article
(This article belongs to the Section Agricultural Soils)
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9 pages, 158 KiB  
Article
Through the Lens of Kara Walker’s Artwork: Exploring Race, Identity, and Intersectionality in Higher Education
by Veronica Bremer
Genealogy 2025, 9(1), 24; https://doi.org/10.3390/genealogy9010024 - 4 Mar 2025
Viewed by 1100
Abstract
Kara Walker’s art, known for its stark depictions of race, history, and power dynamics, offers an invaluable entry point for discussing race in higher education. Integrating Walker’s work into the humanities classroom allows for critical engagement with historical and contemporary issues of race, [...] Read more.
Kara Walker’s art, known for its stark depictions of race, history, and power dynamics, offers an invaluable entry point for discussing race in higher education. Integrating Walker’s work into the humanities classroom allows for critical engagement with historical and contemporary issues of race, ethnicity, and systemic oppression. Through her use of silhouettes and narratives that expose the brutal legacies of slavery, racism, and colonialism, Walker’s art challenges students to confront uncomfortable truths and foster deeper conversations about intersectionality. Discussing Walker’s art can lead to explorations of how race intersects with class, gender, sexuality, and disability, revealing the layered and compounded experiences of marginalized groups. Through the flipped classroom approach, students were introduced to Kara Walker’s work outside of class through assigned readings and materials. During class time, discussions were facilitated by students themselves, enhancing peer-to-peer learning. The session was led by a pupil responsible for elaborating on Walker’s work and guiding the discussion. In-class time was dedicated to small-group discussions where students critically engaged with the themes in Walker’s art. These groups provided space for more intimate, reflective conversations. After small-group discussions, insights were shared in a larger panel discussion format. This allowed students to synthesize ideas, compare perspectives, and engage with a wider range of interpretations of Walker’s art. By engaging with Walker’s work, students develop a more nuanced understanding of oppression and social justice, making her art a powerful tool for transformative education. Full article
(This article belongs to the Special Issue Tackling Race Inequality in Higher Education)
13 pages, 503 KiB  
Article
Electromagnetic Waves in Cosmological Space–Time II. Luminosity Distance
by Denitsa Staicova and Michail Stoilov
Universe 2025, 11(2), 50; https://doi.org/10.3390/universe11020050 - 5 Feb 2025
Cited by 1 | Viewed by 604
Abstract
In this article, we continue our investigation on how the electromagnetic waves propagate in the Friedman–Lemaître–Robertson–Walker spacetime. Unlike the standard approach, which relies on null geodesics and geometric optics approximation, we derive explicit solutions for electromagnetic waves in expanding spacetime and examine their [...] Read more.
In this article, we continue our investigation on how the electromagnetic waves propagate in the Friedman–Lemaître–Robertson–Walker spacetime. Unlike the standard approach, which relies on null geodesics and geometric optics approximation, we derive explicit solutions for electromagnetic waves in expanding spacetime and examine their implications for cosmological observations. In particular, our analysis reveals potential modifications to the standard luminosity distance formula. Its effect on other cosmological parameters, e.g., the amount of cold dust matter in the Universe, is considered and estimated from Type Ia supernovae data. We see that this alternative model is able to fit the supernova data, but it gives a qualitatively different Universe without a cosmological constant but with stiff or ultra-stiff matter. Full article
(This article belongs to the Special Issue Cosmological Models of the Universe)
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17 pages, 3787 KiB  
Review
Recent Advances in DNA Systems for In Situ Telomerase Activity Detection and Imaging
by Shiyi Zhang, Wenjing Xiong, Shuyue Xu and Ruocan Qian
Chemosensors 2025, 13(1), 17; https://doi.org/10.3390/chemosensors13010017 - 15 Jan 2025
Cited by 2 | Viewed by 1628
Abstract
Telomeres play a key role in maintaining chromosome stability and cellular aging. They consist of repetitive DNA sequences that protect chromosome ends and regulate cell division. Telomerase is a reverse transcriptase enzyme counteracts the natural shortening of telomeres during cell division by extending [...] Read more.
Telomeres play a key role in maintaining chromosome stability and cellular aging. They consist of repetitive DNA sequences that protect chromosome ends and regulate cell division. Telomerase is a reverse transcriptase enzyme counteracts the natural shortening of telomeres during cell division by extending them. Its activity is pivotal in stem cells and cancer cells but absent in most normal somatic cells. Recent advances in biosensor technologies have facilitated the in situ detection of telomerase activity, which is essential for understanding its role in aging and cancer. Techniques such as fluorescence, electrochemistry, and DNA nanotechnology are now being employed to monitor telomerase activity in living cells, providing real-time insights into cellular processes. DNA-based biosensors, especially those incorporating molecular beacons, DNA walkers, and logic gates, have shown promise for enhancing sensitivity and specificity in telomerase imaging. These approaches also facilitate the simultaneous analysis of related cellular pathways, offering potential applications in early cancer detection and precision therapies. This review explores recent developments in intracellular telomerase imaging, highlighting innovative approaches such as DNA-functionalized nanoparticles and multi-channel logic systems, which offer non-invasive, real-time detection of telomerase activity in complex cellular environments. Full article
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20 pages, 304 KiB  
Article
Derivation of Tensor Algebra as a Fundamental Operation—The Fermi Derivative in a General Metric Affine Space
by Michael Tsamparlis
Symmetry 2025, 17(1), 81; https://doi.org/10.3390/sym17010081 - 7 Jan 2025
Viewed by 892
Abstract
The aim of this work is to demonstrate that all linear derivatives of the tensor algebra over a smooth manifold M can be viewed as specific cases of a broader concept—the operation of derivation. This approach reveals the universal role of differentiation, which [...] Read more.
The aim of this work is to demonstrate that all linear derivatives of the tensor algebra over a smooth manifold M can be viewed as specific cases of a broader concept—the operation of derivation. This approach reveals the universal role of differentiation, which simplifies and generalizes the study of tensor derivatives, making it a powerful tool in Differential Geometry and related fields. To perform this, the generic derivative is introduced, which is defined in terms of the quantities Qk(i)(X). Subsequently, the transformation law of these quantities is determined by the requirement that the generic derivative of a tensor is a tensor. The quantities Qk(i)(X) and their transformation law define a specific geometric object on M, and consequently, a geometric structure on M. Using the generic derivative, one defines the tensor fields of torsion and curvature and computes them for all linear derivatives in terms of the quantities Qk(i)(X). The general model is applied to the cases of Lie derivative, covariant derivative, and Fermi derivative. It is shown that the Lie derivative has non-zero torsion and zero curvature due to the Jacobi identity. For the covariant derivative, the standard results follow without any further calculations. Concerning the Fermi derivative, this is defined in a new way, i.e., as a higher-order derivative defined in terms of two derivatives: a given derivative and the Lie derivative. Being linear derivative, it has torsion and curvature tensor. These fields are computed in a general affine space from the corresponding general expressions of the generic derivative. Applications of the above considerations are discussed in a number of cases. Concerning the Lie derivative, it is been shown that the Poisson bracket is in fact a Lie derivative. Concerning the Fermi derivative, two applications are considered: (a) the explicit computation of the Fermi derivative in a general affine space and (b) the consideration of Freedman–Robertson–Walker spacetime endowed with a scalar torsion field, which satisfies the Cosmological Principle and the computation of Fermi derivative of the spatial directions defining a spatial frame along the cosmological fluid of comoving observers. It is found that torsion, even in this highly symmetric case, induces a kinematic rotation of the space axes, questioning the interpretation of torsion as a spin. Finally it is shown that the Lie derivative of the dynamical equations of an autonomous conservative dynamical system is equivalent to the standard Lie symmetry method. Full article
(This article belongs to the Special Issue Advances in Nonlinear Systems and Symmetry/Asymmetry)
19 pages, 404 KiB  
Article
Modeling of (n,m)-Type Minkowski Pythagorean Hodograph Curves with Hopf Map and Applications
by Muhammed Talat Sariaydin and Aziz Yazla
Fractal Fract. 2024, 8(12), 705; https://doi.org/10.3390/fractalfract8120705 - 28 Nov 2024
Viewed by 924
Abstract
In the present paper, regular spacelike spatial Minkowski Pythagorean hodograph (MPH) curves are characterized with rational rotation-minimizing frames (RRMFs). We define an Euler–Rodrigues frame (ERF) for MPH curves and by means of this concept, we reach the definition of MPH curves of type [...] Read more.
In the present paper, regular spacelike spatial Minkowski Pythagorean hodograph (MPH) curves are characterized with rational rotation-minimizing frames (RRMFs). We define an Euler–Rodrigues frame (ERF) for MPH curves and by means of this concept, we reach the definition of MPH curves of type (n,m). Expressing the conditions provided by these curves in the form of a Minkowski–Hopf map that we define; it is aimed to establish a connection with the Lorentz force that occurs during the process of computer numerical control (CNC)-type sinker electronic discharge machines (EDMs). This approach is reinforced by split quaternion polynomials. We give conditions satisfied by MPH curves of low degree to be type (n,m) and construct illustrative examples. In five-axis CNC machines, rotation-minimizing frames are used for tool path planning, and in this way, unnecessary rotations in the tool frame are prevented and tool orientation is provided. Since we obtain MPH curves with RRMF using the ERF, finally we define the Fermi–Walker derivative and parallelism along MPH curves with respect to the ERF and give applications. Full article
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