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19 pages, 8836 KB  
Article
Exploring Female Volunteer Head and Thorax Kinematics During a Braking Pulse in the Presence of a Steering Wheel
by Lea Siebler, María González-García, Jens Weber, Steffen Peldschus and Sylvia Schick
Appl. Sci. 2026, 16(18), 8905; https://doi.org/10.3390/app16188905 - 8 Sep 2026
Abstract
As driving becomes more automated, the driver–car interaction is changing. The steering wheel, traditionally the main interface between the driver and the vehicle, is reduced to being a part of the environment in autonomous driving. Its influence on kinematic reactions to decelerations without [...] Read more.
As driving becomes more automated, the driver–car interaction is changing. The steering wheel, traditionally the main interface between the driver and the vehicle, is reduced to being a part of the environment in autonomous driving. Its influence on kinematic reactions to decelerations without a prompt to take over control of the vehicle is still unknown. Therefore, low-speed sled tests with seven female volunteers matching 5th or 50th percentile anthropometrics were performed, including three upright trials and two reclined trials at backrest angles of 23° and 45° during a standardized braking pulse. A steering wheel was placed in front of the volunteers to limit available space when moving forward. Kinematic analysis focused on the forward head movement. The study showed that no targeted hand grasping towards the steering wheel occurred in either backrest configuration. Head forward excursion was slightly higher in the first upright trial for some volunteers. Less variation and lower absolute forward excursion of the head were found in the reclined trials. Without the need for a required vehicle takeover, no grasping of the steering wheel was observed among the participants studied. Full article
(This article belongs to the Special Issue Biomechanics and Ergonomics in Prevention of Injuries)
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32 pages, 13647 KB  
Article
Design Trends in Contemporary Polish Catholic Churches Built After 1945, as Illustrated by the Examples of Częstochowa and Kielce
by Małgorzata Doroz-Turek and Aleksandra Repelewicz
Religions 2026, 17(9), 1034; https://doi.org/10.3390/rel17091034 - 3 Sep 2026
Viewed by 254
Abstract
Sacred buildings have constituted a distinctive element of urban space for centuries. Catholic churches have consistently exhibited a monumental character, regardless of the period in which they were constructed. The form of these buildings has been shaped by prevailing architectural styles, ecclesiastical guidelines, [...] Read more.
Sacred buildings have constituted a distinctive element of urban space for centuries. Catholic churches have consistently exhibited a monumental character, regardless of the period in which they were constructed. The form of these buildings has been shaped by prevailing architectural styles, ecclesiastical guidelines, and the political context. This was also the case in Poland, especially during the most recent historical period—the post-war period, encompassing the second half of the 20th century and the early 21th century. During this time, the most significant changes in both the external form and functional organization of churches can be observed. This diversity resulted, among other factors, from the complex socio-economic and political conditions of the communist and post-communist periods, as well as from the revolutionary provisions of the Second Vatican Council. This study presents sacred architecture in two centrally located Polish cities of comparable size—Kielce and Częstochowa. An analysis was carried out of the number of churches and their forms in order to identify similarities and differences. Full article
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23 pages, 21053 KB  
Article
Analysis of PMSM Torque Waveform Discrepancies in a Hardware-in-the-Loop Environment
by Wojciech Pietrowski, Magdalena Puskarczyk and Jan Szymenderski
Electronics 2026, 15(17), 3946; https://doi.org/10.3390/electronics15173946 - 2 Sep 2026
Viewed by 154
Abstract
This paper compares Permanent-Magnet Synchronous Motor (PMSM) torque waveforms measured on a dynamometer test bench and generated by a real-time Hardware-in-the-Loop (HiL) simulation. A nonlinear PMSM model, parameterised using measurements from the physical motor and incorporating magnetic saturation through Look-Up Tables, was implemented [...] Read more.
This paper compares Permanent-Magnet Synchronous Motor (PMSM) torque waveforms measured on a dynamometer test bench and generated by a real-time Hardware-in-the-Loop (HiL) simulation. A nonlinear PMSM model, parameterised using measurements from the physical motor and incorporating magnetic saturation through Look-Up Tables, was implemented on a dSpace HiL platform. Torque signals were evaluated at steady-state operating points of 20, 100, and 200 rpm using time-domain errors, Pearson and Spearman correlations, and FFT-based spectral analysis. An affine gain–offset transformation was applied to separate calibration-related discrepancies from differences caused by dynamic behaviour and unmodelled physical effects. The maximum observed initial discrepancy between dynamometer-measured and HiL-estimated torque was 0.638 Nm. Affine calibration reduced the maximum error by up to 85%, demonstrating that gain and offset mismatches were major contributors to the original error. However, correlation values remained low, and spectral analysis identified substantial differences in harmonic content. The dynamometer signals contained speed-dependent components, including a component near the 24th mechanical harmonic, whereas the HiL signals were dominated by the first mechanical harmonic. The proposed workflow supports mean-torque-oriented HiL validation and identifies priorities for improving model representation, channel scaling, and dynamic testing procedures. Full article
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36 pages, 4980 KB  
Article
Adaptive Physics-Informed Digital Twin-Based Energy Management for Dynamic Inductive Charging of Four-Wheel Drive Fuel Cell Hybrid Electric Vehicles
by Khaled Mammeri, Riad Bouzidi, Brahim Gasbaoui, Houssam Eddine Ghadbane, Habib Benbouhenni, Nicu Bizon and Adrian Tulbure
World Electr. Veh. J. 2026, 17(9), 458; https://doi.org/10.3390/wevj17090458 - 31 Aug 2026
Viewed by 149
Abstract
Dynamic inductive charging (DIC) combined with hybrid energy storage systems (HESSs) and vehicle-to-grid (V2G) capabilities offers a promising pathway toward extended-range electric vehicles with grid integration benefits. However, real-time optimal energy management remains challenging due to multi-axis coil misalignment, component aging, and bidirectional [...] Read more.
Dynamic inductive charging (DIC) combined with hybrid energy storage systems (HESSs) and vehicle-to-grid (V2G) capabilities offers a promising pathway toward extended-range electric vehicles with grid integration benefits. However, real-time optimal energy management remains challenging due to multi-axis coil misalignment, component aging, and bidirectional power flow uncertainty. This paper proposes an adaptive digital twin driven artificial intelligence (AI) energy management framework integrating physics-informed neural networks (PINNs), soft actor critic (SAC) deep reinforcement learning, and model predictive control (MPC) for optimal power distribution among a proton exchange membrane fuel cell (PEMFC), lithium-ion battery, supercapacitor, dynamic wireless charging, and grid interface in four-wheel drive electric vehicles (4WD-EVs). The framework features: (1) a self-evolving digital twin with online learning via Elastic Weight Consolidation (EWC) updating every 50 cycles; (2) a PINN-based state estimator for battery-state estimation, with an average inference time of 1.1 ms and a worst-case latency of 2.8 ms; (3) a hierarchical SAC–MPC strategy with high-level mode selection and low-level power optimization; (4) real-time five-degree-of-freedom WPT misalignment compensation, achieving a mean efficiency of 91.5% under the evaluated dynamic lateral misalignment conditions, with a 50 mm displacement amplitude; (5) degradation-aware V2G optimization generating €582.50/year in revenue while reducing battery aging by 31.8%; and (6) comprehensive techno-economic analysis yielding a discounted payback period of approximately 5.57 years and a net present value of approximately €3777 over a 10-year horizon. Validated through 200+ hours of hardware-in-the-loop (HIL) simulation on the dSPACE/NVIDIA Jetson platform, the proposed approach achieves a 24.3% cost reduction and 31.8% lower battery degradation. The MPC controller exhibits an average execution time of 32.1 ms, a 95th-percentile latency of 44.8 ms, and a worst-case latency of 62.4 ms, while remaining within the 100-ms real-time control deadline. Results demonstrate the viability of adaptive digital twins for next-generation EVs with autonomous charging and multi-source architectures. Full article
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48 pages, 2158 KB  
Article
Enhancing Communication Security in Automotive Software: A Hybrid SecOC and MACsec Integration for SOME/IP over Ethernet
by Omar Mohamed Ali Alm El-Din, Omar Hesham Hanafy, Ashraf El Farghly Salem and Bassem Abdullah
Appl. Sci. 2026, 16(17), 8609; https://doi.org/10.3390/app16178609 - 29 Aug 2026
Viewed by 294
Abstract
Automotive Ethernet networks increasingly rely on SOME/IP within the AUTOSAR Adaptive Platform for service-oriented ECU communication, yet SOME/IP lacks built-in security, exposing systems to Man-in-the-Middle (MitM), replay, spoofing, and eavesdropping attacks. As of AUTOSAR Release R22-11, no standardised security profile addresses both authenticity [...] Read more.
Automotive Ethernet networks increasingly rely on SOME/IP within the AUTOSAR Adaptive Platform for service-oriented ECU communication, yet SOME/IP lacks built-in security, exposing systems to Man-in-the-Middle (MitM), replay, spoofing, and eavesdropping attacks. As of AUTOSAR Release R22-11, no standardised security profile addresses both authenticity and confidentiality for multicast SOME/IP traffic. This paper proposes a hybrid security architecture combining SecOC (CMAC-AES256, instantiated as a vendor-defined security profile) applied to the SOME/IP application Protocol Data Unit (above OSI Layer 4) with IEEE 802.1AE MACsec at the data link layer (Layer 2): SecOC provides end-to-end message authentication and replay protection, while MACsec adds hop-by-hop confidentiality and integrity, which coincides with end-to-end confidentiality only on a single-hop path. The SecOC and MACsec protocol constructions themselves are not modified; only SecOC’s parameter profile deviates from the three predefined profiles. The architecture is evaluated across ten sub-scenarios (five configurations, each tested under unicast and multicast communication; 500 iterations recorded per sub-scenario). For the Hybrid-PSK multicast configuration (Scenario 3a-B), steady-state end-to-end latency adds 27.8 ms (33.89 ms versus the 6.12 ms unsecured-multicast baseline, Scenario 1-B; both figures are measured on the identical two-VM topology using the same half-round-trip method); the worst-case measured 99th percentile of this absolute latency, across all hybrid configurations, is 40.99 ms (Hybrid-RSA multicast, Scenario 3b-B). Of the added overhead, MACsec contributes 11.5% (3.18 ms), isolated by re-running the SecOC-only scenarios on the same two-VM topology used for the hybrid scenarios, and one-time RSA-2048 session establishment adds 25.2 ms to 33.8 ms at startup. Cross-referencing the SecOC path cost against CPU utilisation indicates that most of it is user-space integration overhead rather than cipher execution, a split not isolated by direct microbenchmark. The reported MACsec figure remains an upper bound in one respect: it reflects the Linux kernel software MACsec driver rather than a PHY-offloaded implementation. At this single quiet operating point (64-byte payload, approximately 20 messages/s, two receivers, no background load), the measured worst-case p99 leaves an approximate 9 ms margin against an assumed 50 ms soft real-time budget for ADAS and infotainment messaging; whether this margin survives realistic ECU loading, larger receiver groups, and production-stack constant factors was not evaluated. This margin is also bound to the present, unoptimised software path: because most of the SecOC path cost is user-space integration overhead rather than cipher execution, removing it is projected to widen the margin substantially, so the reported headroom characterises this prototype rather than a ceiling on the architecture. Full article
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18 pages, 282 KB  
Article
Conditional Local Existence and Uniqueness for Impulsive Stochastic Differential Equations with State-Dependent Delay
by Houari Charaf Eddine Bendjellal, Mohamed Belaidi, Zouaoui Chikr Elmezouar, Fatimah Alshahrani, Abderrahmane Belguerna and Hamza Daoudi
Mathematics 2026, 14(17), 3031; https://doi.org/10.3390/math14173031 - 22 Aug 2026
Viewed by 237
Abstract
We consider impulsive stochastic delay differential equations with state-dependent impulse times, where the k-th impulse occurs at a time τ satisfying τ=τku(τ). In generalized Lipschitz and growth conditions for coefficients, establishing existence and [...] Read more.
We consider impulsive stochastic delay differential equations with state-dependent impulse times, where the k-th impulse occurs at a time τ satisfying τ=τku(τ). In generalized Lipschitz and growth conditions for coefficients, establishing existence and uniqueness is conditional on the successive approximations sharing a common finite impulse-time structure. The proof of our main result is based on the successive approximation scheme along with Itô’s isometry and Bihari’s inequality. We prove that the approximating sequence is bounded and convergent in a suitable Banach space, which gives a unique local solution. Full article
(This article belongs to the Section C1: Difference and Differential Equations)
13 pages, 3785 KB  
Article
Comprehensive CT Angiography Assessment of Internal Thoracic Artery Morphometry, Anatomical Relationships, and Perforating Branches
by Selma Cansu Bayrak, Keziban Karacan, Alper Karacan and Mehtap Erdogan
Biomedicines 2026, 14(8), 1863; https://doi.org/10.3390/biomedicines14081863 - 20 Aug 2026
Viewed by 348
Abstract
Background and Objectives: The internal thoracic artery (ITA) is widely used in coronary artery bypass grafting and reconstructive procedures due to its favorable anatomical characteristics. This study aimed to comprehensively evaluate the morphometric features of the ITA using computed tomography angiography and to [...] Read more.
Background and Objectives: The internal thoracic artery (ITA) is widely used in coronary artery bypass grafting and reconstructive procedures due to its favorable anatomical characteristics. This study aimed to comprehensively evaluate the morphometric features of the ITA using computed tomography angiography and to investigate variations according to sex and anatomical side. Materials and Methods: In this retrospective cross-sectional study, thoracic computed tomography angiography images of 72 individuals were analyzed. Bilateral measurements of ITA length, diameter at different intercostal levels, anatomical relationships, and perforating branches were recorded. Results: The mean ITA length was slightly greater on the left side (18.6 ± 2.7 cm) compared to the right (18.3 ± 2.3 cm), without significant sex differences. A progressive decrease in arterial diameter from proximal to distal segments was observed. Statistically significant sex-related differences in diameter were identified, particularly at the 3rd and 4th intercostal spaces (p < 0.05). Distances to adjacent anatomical structures also varied significantly between sexes. Perforating branches were most frequently detected at the 4th intercostal space. Conclusions: The ITA demonstrates notable morphometric variability depending on sex and anatomical side. These findings provide anatomical reference data that may contribute to individualized evaluation of the ITA. Full article
(This article belongs to the Section Molecular and Translational Medicine)
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20 pages, 4599 KB  
Article
“The Axis of Influence”: The Roles of Illustrations in Children’s Literature
by Shai Rudin
Literature 2026, 6(3), 21; https://doi.org/10.3390/literature6030021 - 19 Aug 2026
Viewed by 225
Abstract
Since the 17th century, when illustrations began to appear in children’s schoolbooks, the role of illustrations has undergone a development in concept. It has shifted from a narrow view of illustrations demonstrating the text, as well as lightening up the textual monotony, to [...] Read more.
Since the 17th century, when illustrations began to appear in children’s schoolbooks, the role of illustrations has undergone a development in concept. It has shifted from a narrow view of illustrations demonstrating the text, as well as lightening up the textual monotony, to a broader view of illustrations as a way of perceiving an additional interpretational layer of the meanings inherent in the text. Concurrently, the hierarchy indicating the supremacy of the written text over the illustrations has been undermined, opening the way to viewing children’s stories as a literary work in which the text and the illustrations conduct a complex relationship, together affecting the addressees’ experiencing of the meaning. After five decades of analyzing picturebooks, there are still some gaps between the research on children’s literature and the research on illustrations, whereby the study of children’s literature mainly deals with the textual aspects of works. The present research offers a model examining the functions of illustrations in children’s literature. The model includes a spectrum of layers located on an axis, which may be termed “the axis of influence”. This spectrum begins with illustrations that are limited to a simple description and adhere to the text, and it reaches illustrations that contrast with the text, accompanying it as a “counterpoint”. The illustrations’ modes of function are divided into three groups. The first group is that of illustrations describing the text faithfully. The second group includes illustrations which expand the meaning by providing layers that do not exist in the text: illustrations describing the space in which the protagonists are located; illustrations portraying the inner world of the protagonists; illustrations explicating complex concepts or themes; inclusive illustrations expanding the cultural and social variety of the characters in the story; and illustrations which promote social or national values. The third group includes illustrations subversive to the text, often even contradicting it or promoting a message that does not necessarily adhere to the contents of the text, thereby providing an independent narrative. The existence of an independent narrative leads to a poetic gap, by which there are two narratives dwelling in the same story. The research examines four types of subversive illustrations: illustrations creating gender correction; the implicative illustrations containing a visual subtext; illustrations casting a new light upon the story’s ending; and illustrations voicing a counterpoint to the content delivered in the text. Full article
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37 pages, 6150 KB  
Article
Consumption of Coffee, Tobacco, Opium, and Alcohol in Ottoman Society Through the Eyes of Western Travelers
by Mert Ağaoğlu and Görkem Işık
Soc. Sci. 2026, 15(8), 555; https://doi.org/10.3390/socsci15080555 - 17 Aug 2026
Viewed by 313
Abstract
Drawing on phenomenological observations from an extensive corpus of 68 Western travelogs and memoirs, this study analyzes the Ottoman urban and social fabric from the 15th to the early 20th century through the lens of stimulants and intoxicants. It examines how coffee and [...] Read more.
Drawing on phenomenological observations from an extensive corpus of 68 Western travelogs and memoirs, this study analyzes the Ottoman urban and social fabric from the 15th to the early 20th century through the lens of stimulants and intoxicants. It examines how coffee and tobacco, entering the empire as cultural commodities in the 16th century, transitioned from theological objections to socio-legal legitimacy, fostering the emergence of coffeehouses as dynamic “third spaces” that reproduced social hierarchies. Concurrently, the consumption of alcohol and opium—evaluated from a jurisprudential perspective due to their intoxicating effects—is shown navigating a paradoxical relationship between official prohibitions and civil reality. Rather than replicating the Orientalist imagination that frequently encoded Eastern pleasure rituals through an ontology of inertia and indolence, this paper repositions these practices as constitutive elements of social dynamism, urban identity, and spatial memory. Ultimately, by deciphering the historical dichotomy between constructed Western discourse and the heterogeneous, everyday reality of the empire, this study offers a holistic perspective on Ottoman material culture. Full article
(This article belongs to the Section Community and Urban Sociology)
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1 pages, 129 KB  
Correction
Correction: Şanda and Gün (2026). Tribal Settlement Along the Frontiers: Space, Sovereignty, and Identity in Çıldır and Ardahan (18th and 19th Centuries). Genealogy 10: 36
by Mehmet Nuri Şanda and Doğan Gün
Genealogy 2026, 10(3), 101; https://doi.org/10.3390/genealogy10030101 - 4 Aug 2026
Viewed by 198
Abstract
In the original publication (Şanda and Gün 2026), the Acknowledgments section was inadvertently omitted during the publication process, and the author would like to add the following acknowledgement: [...] Full article
25 pages, 6723 KB  
Article
Meditation and Aspiration at Kagyu Monlam Chenmo in Bodh Gaya
by Malwina Krajewska
Religions 2026, 17(8), 911; https://doi.org/10.3390/rel17080911 - 1 Aug 2026
Viewed by 353
Abstract
This article examines practices of meditation and aspiration performed during the Kagyu Monlam Chenmo in Bodh Gaya, within the Karma Kagyu institutional and devotional network associated with the 17th Karmapa Trinley Thaye Dorje. It focuses on the collective recitation of Samantabhadra’s King of [...] Read more.
This article examines practices of meditation and aspiration performed during the Kagyu Monlam Chenmo in Bodh Gaya, within the Karma Kagyu institutional and devotional network associated with the 17th Karmapa Trinley Thaye Dorje. It focuses on the collective recitation of Samantabhadra’s King of Aspiration Prayers, not only as a liturgical performance, but as a contemplative practice shaped by attention, bodily endurance, repetition, and joint participation. The article argues that Bodh Gaya provides a setting in which meditation is not separated from ritual, place, institution, and religious labour. Drawing on James A. Beckford’s social constructionist approach, I examine how lay and monastic practitioners take part in forming a contemplative space under the Bodhi Tree. Based on long-term ethnographic fieldwork, the article shows how collective aspiration works within a disciplined meditative framework, while allowing individual attention to take shape by accompanying a common ritual rhythm. The Monlam may therefore be understood as a site where lineage continuity is ritually sustained within a specific Karma Kagyu setting. By focusing on aspiration, repetition, and sacred place, the article contributes to discussions of lived Buddhism and to the study of meditation as a social and spatial practice. Full article
(This article belongs to the Special Issue Buddhist Meditation: Culture, Mindfulness, and Rationality)
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16 pages, 19353 KB  
Article
Analysis of Seismo-Ionospheric Anomaly Disturbance Associated with the Mw7.6 Mexico Earthquake on 19 September 2022
by Zhen Li, Baojun Liu, Jing Zhang and Wenjing Liu
Atmosphere 2026, 17(8), 750; https://doi.org/10.3390/atmos17080750 - 31 Jul 2026
Viewed by 296
Abstract
GNSS ionospheric records are valuable measurements of earthquake-related ionospheric anomalies. The deep exploration of GNSS ionospheric data can help to better understand the seismic–ionospheric coupling effect. Thus, we used GNSS ionospheric data to detect and investigate the pre-earthquake ionospheric anomalies of the 7.6 [...] Read more.
GNSS ionospheric records are valuable measurements of earthquake-related ionospheric anomalies. The deep exploration of GNSS ionospheric data can help to better understand the seismic–ionospheric coupling effect. Thus, we used GNSS ionospheric data to detect and investigate the pre-earthquake ionospheric anomalies of the 7.6 magnitude earthquake, which occurred in Mexico on 19 September 2022. A 10.7 cm solar radio flux (F10.7), sunspot number (SSN), and geomagnetic activity indices (Dst and Hp30) are employed to reflect solar and geomagnetic activities, respectively. The result of the sliding quartile range method indicates that there was a ionospheric disturbance over the epicenter on the 10th day prior to the earthquake, and that there were no anomalies observed in solar activity and geomagnetic activity on that day. Meanwhile, the ionospheric anomaly over the epicenter on 15th day before the earthquake was the most significant, but the geomagnetic activity was abnormal on that day. To further distinguish whether the ionospheric disturbance on 15th day was caused by geomagnetic activity or the earthquake, this paper adopts the coherent wavelet to analyze the time-varying relationship between total electron content (TEC) and geomagnetic activity in the time-frequency space. The results show that the correlation and phase relationship between TEC, Dst, and Hp30 remained relatively stable on the 15th day before the earthquake, while the strong correlation between TEC, Dst, and Hp30 suddenly disappeared and the phase relationship sharply changed after the 10th day. This may be due to the influence of the seismic–ionospheric coupling effect, where the abnormal disturbances of TEC may disrupt the pre-existing stable relationship between TEC, Dst, and Hp30. Therefore, we conclude that the TEC anomaly on 10th day before the earthquake might be the precursor to the Mw7.6 Mexico earthquake. Full article
(This article belongs to the Special Issue Advances in Observation and Simulation Studies of Ionosphere)
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29 pages, 1078 KB  
Article
DAO-TDS: Decentralized Autonomous Trusted Data Space for Global Data Circulation
by Yongjian Wang and Aibo Song
Computers 2026, 15(8), 482; https://doi.org/10.3390/computers15080482 - 29 Jul 2026
Viewed by 802
Abstract
Trusted Data Spaces (TDSs) have emerged as the core infrastructure for secure, privacy-preserving data circulation across industries and jurisdictions. However, state-of-the-art TDS implementations suffer from centralized platform monopoly, rigid cross-border governance failure, unfair value distribution, and poor scalability for global-scale collaboration. This paper [...] Read more.
Trusted Data Spaces (TDSs) have emerged as the core infrastructure for secure, privacy-preserving data circulation across industries and jurisdictions. However, state-of-the-art TDS implementations suffer from centralized platform monopoly, rigid cross-border governance failure, unfair value distribution, and poor scalability for global-scale collaboration. This paper proposes DAO-TDS, a novel decentralized autonomous trusted data space paradigm that enables centerless, cryptography-governed, and value-closed-loop data circulation. We make three core contributions: (1) We formalize the first anti-monopoly, incentive-compatible game-theoretic model for distributed TDS governance, with rigorous provable security guarantees; (2) we design an original Proof of Data Contribution (PoDC) consensus mechanism and a post-quantum secure Crypto-DAO governance protocol, with formal security proofs under the Universal Composability (UC) framework; (3) we implement a full prototype of DAO-TDS and conduct comprehensive, reproducible evaluations, showing that it supports 10,000+ distributed nodes with >12,000 TPS and <2 s 99th-percentile confirmation latency, while delivering >80% of generated value to data contributors (vs. <50% in centralized platforms). While the proposed paradigm demonstrates strong performance and security guarantees, it still faces challenges in adaptive cross-jurisdictional compliance and lightweight edge node deployment, which require further investigation. Full article
(This article belongs to the Topic Security and Privacy in Distributed and Trustless Systems)
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23 pages, 382 KB  
Article
Growth Estimates for m-th (m ≥ 1) Derivatives of Algebraic Polynomials in Domains with Piecewise Quasismooth Boundaries
by Cevahir Doğanay Gün, Meerim Imashkyzy and Fahreddin G. Abdullayev
Axioms 2026, 15(8), 562; https://doi.org/10.3390/axioms15080562 - 29 Jul 2026
Viewed by 288
Abstract
In this paper, we investigate the growth behavior of the m-th derivatives (m1) of arbitrary algebraic polynomials in bounded and unbounded domains whose boundaries are piecewise quasismooth curve and possess interior and exterior zero angles of power type, [...] Read more.
In this paper, we investigate the growth behavior of the m-th derivatives (m1) of arbitrary algebraic polynomials in bounded and unbounded domains whose boundaries are piecewise quasismooth curve and possess interior and exterior zero angles of power type, within weighted Lebesgue spaces. We derive estimates for the growth of these derivatives in terms of the characteristics of the weight function, the geometric properties of the boundary, and the tangency exponents of the boundary arcs at their junction points. The obtained estimates are established both in the closure of the bounded domain and at exterior points, while the pointwise estimates in the unbounded domain additionally reflect the location of the point within the domain. Full article
(This article belongs to the Section Mathematical Analysis)
27 pages, 3518 KB  
Article
Filling in the Blanks: The Material Semiotics of Visual Meditation in the Buddhist Qizil Yoga Manual
by Karen O’Brien-Kop
Religions 2026, 17(8), 898; https://doi.org/10.3390/rel17080898 - 28 Jul 2026
Viewed by 416
Abstract
This paper analyses the ‘grammar’, or rules, of meditation practice in the c. 5th-century Qizil Yoga Manual (QYM). The QYM was found in Kucha, a significant location in the Silk Road trade network. Meditation in this text means visual recollection, and the practices [...] Read more.
This paper analyses the ‘grammar’, or rules, of meditation practice in the c. 5th-century Qizil Yoga Manual (QYM). The QYM was found in Kucha, a significant location in the Silk Road trade network. Meditation in this text means visual recollection, and the practices are largely structured around Buddhist Sarvāstivāda sequences with some hints of Mahāyāna or Tantric themes). As with certain Mahāyāna ontologies, the Qizil Yoga Manual meditations emphasize an expansive spatiality, employing a densely populated mental landscape in which images abound. Since visualization requires blank space for projection/construction (whether mental space or the space of the cave), one result is the spatialisation of time. Nonetheless, the QYM is not a text in which temporality is dispensed with, and the meditation formulas also retain a more restrained Sarvāstivāda manual emphasis on visual elements arising and disappearing in temporal sequence—such as we find in the Abhidharmakośabhāṣya or early Sarvāstivāda layers of the Yogācārabhūmiśāstra, such as the ‘Śrāvakabhūmi’. To address the interplay of image proliferation and temporal sequence in the text, this paper engages semiotics, or the study of sign systems. Drawing on both linguistic and visual approaches, a ‘semiotic triangle’ is proposed to acknowledge how ‘mental imagery’ is produced triadically by text, cave and body. Since the primary surviving manuscript of the Qizil Yoga Manual is fragmentary, its meaning can be hard to discern, made doubly so by the distinct cultural character of this Central Asian Buddhist Sanskrit text. Moreover, only when the material context of the manuscript is highlighted, taking into account embodied cave meditation, can the ‘readerly blanks’ be filled in. The goals of this paper are to deepen an ontological understanding of the practices in the Qizil Yoga Manual, and to show how historical textual research in religious studies can be underpinned by methods that are bolder in their theoretical scope, moving beyond the remit of translation projects. Full article
(This article belongs to the Special Issue Buddhist Meditation in Central Asia)
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