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18 pages, 1910 KiB  
Article
Hierarchical Learning for Closed-Loop Robotic Manipulation in Cluttered Scenes via Depth Vision, Reinforcement Learning, and Behaviour Cloning
by Hoi Fai Yu and Abdulrahman Altahhan
Electronics 2025, 14(15), 3074; https://doi.org/10.3390/electronics14153074 (registering DOI) - 31 Jul 2025
Abstract
Despite rapid advances in robot learning, the coordination of closed-loop manipulation in cluttered environments remains a challenging and relatively underexplored problem. We present a novel two-level hierarchical architecture for a depth vision-equipped robotic arm that integrates pushing, grasping, and high-level decision making. Central [...] Read more.
Despite rapid advances in robot learning, the coordination of closed-loop manipulation in cluttered environments remains a challenging and relatively underexplored problem. We present a novel two-level hierarchical architecture for a depth vision-equipped robotic arm that integrates pushing, grasping, and high-level decision making. Central to our approach is a prioritised action–selection mechanism that facilitates efficient early-stage learning via behaviour cloning (BC), while enabling scalable exploration through reinforcement learning (RL). A high-level decision neural network (DNN) selects between grasping and pushing actions, and two low-level action neural networks (ANNs) execute the selected primitive. The DNN is trained with RL, while the ANNs follow a hybrid learning scheme combining BC and RL. Notably, we introduce an automated demonstration generator based on oriented bounding boxes, eliminating the need for manual data collection and enabling precise, reproducible BC training signals. We evaluate our method on a challenging manipulation task involving five closely packed cubic objects. Our system achieves a completion rate (CR) of 100%, an average grasping success (AGS) of 93.1% per completion, and only 7.8 average decisions taken for completion (DTC). Comparative analysis against three baselines—a grasping-only policy, a fixed grasp-then-push sequence, and a cloned demonstration policy—highlights the necessity of dynamic decision making and the efficiency of our hierarchical design. In particular, the baselines yield lower AGS (86.6%) and higher DTC (10.6 and 11.4) scores, underscoring the advantages of content-aware, closed-loop control. These results demonstrate that our architecture supports robust, adaptive manipulation and scalable learning, offering a promising direction for autonomous skill coordination in complex environments. Full article
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37 pages, 12322 KiB  
Article
Research on the Evaluation Method of Electrical Stress Limit Capability Based on Reliability Enhancement Theory
by Shuai Zhou, Kaixue Ma, Zhihua Cai, Shoufu Liu, Jian Xiang and Chi Ma
Electronics 2025, 14(15), 3056; https://doi.org/10.3390/electronics14153056 - 30 Jul 2025
Abstract
This study focuses on the evaluation of electrical stress limit capability for 3D-packaged memory (256 M × 72-bit DDR3 SDRAM) (Shanghai Fudan Microelectronics Group Co., Ltd., Shanghai, China). Guided by Reliability Enhancement Theory, this study presents a meticulously designed comprehensive test profile that [...] Read more.
This study focuses on the evaluation of electrical stress limit capability for 3D-packaged memory (256 M × 72-bit DDR3 SDRAM) (Shanghai Fudan Microelectronics Group Co., Ltd., Shanghai, China). Guided by Reliability Enhancement Theory, this study presents a meticulously designed comprehensive test profile that incorporates critical stress parameters, including supply voltage, input clock frequency, electrostatic discharge (ESD) sensitivity, and electrical endurance. Explicit criteria for stress selection, upper/lower bounds, step increments, and duration are established. A dedicated test platform is constructed, integrating automated test equipment (ATE) and ESD sensitivity analyzers with detailed specifications on device selection criteria and operational principles. The functional performance testing methodology is systematically investigated, covering test platform configuration, initialization protocols, parametric testing procedures, functional verification, and acceptance criteria. Extreme-condition experiments—including supply voltage margining, input clock frequency tolerance, ESD sensitivity characterization, and accelerated electrical endurance testing—are conducted to quantify operational and destructive limits. The findings provide critical theoretical insights and practical guidelines for the design optimization, quality control, and reliability enhancement of 3D-packaged memory devices. Full article
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13 pages, 1132 KiB  
Review
M-Edge Spectroscopy of Transition Metals: Principles, Advances, and Applications
by Rishu Khurana and Cong Liu
Catalysts 2025, 15(8), 722; https://doi.org/10.3390/catal15080722 - 30 Jul 2025
Viewed by 45
Abstract
M-edge X-ray absorption spectroscopy (XAS), which probes 3p→3d transitions in first-row transition metals, provides detailed insights into oxidation states, spin-states, and local electronic structure with high element and orbital specificity. Operating in the extreme ultraviolet (XUV) region, this technique provides [...] Read more.
M-edge X-ray absorption spectroscopy (XAS), which probes 3p→3d transitions in first-row transition metals, provides detailed insights into oxidation states, spin-states, and local electronic structure with high element and orbital specificity. Operating in the extreme ultraviolet (XUV) region, this technique provides sharp multiplet-resolved features with high sensitivity to ligand field and covalency effects. Compared to K- and L-edge XAS, M-edge spectra exhibit significantly narrower full widths at half maximum (typically 0.3–0.5 eV versus >1 eV at the L-edge and >1.5–2 eV at the K-edge), owing to longer 3p core-hole lifetimes. M-edge measurements are also more surface-sensitive due to the lower photon energy range, making them particularly well-suited for probing thin films, interfaces, and surface-bound species. The advent of tabletop high-harmonic generation (HHG) sources has enabled femtosecond time-resolved M-edge measurements, allowing direct observation of ultrafast photoinduced processes such as charge transfer and spin crossover dynamics. This review presents an overview of the fundamental principles, experimental advances, and current theoretical approaches for interpreting M-edge spectra. We further discuss a range of applications in catalysis, materials science, and coordination chemistry, highlighting the technique’s growing impact and potential for future studies. Full article
(This article belongs to the Special Issue Spectroscopy in Modern Materials Science and Catalysis)
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21 pages, 1657 KiB  
Article
Heterogeneous-IRS-Assisted Millimeter-Wave Systems: Element Position and Phase Shift Optimization
by Weibiao Zhao, Qiucen Wu, Hao Wei, Dongliang Su and Yu Zhu
Sensors 2025, 25(15), 4688; https://doi.org/10.3390/s25154688 - 29 Jul 2025
Viewed by 152
Abstract
Intelligent reflecting surfaces (IRSs) have attracted extensive attention in the design of future communication networks. However, their large number of reflecting elements still results in non-negligible power consumption and hardware costs. To address this issue, we previously proposed a green heterogeneous IRS (HE-IRS) [...] Read more.
Intelligent reflecting surfaces (IRSs) have attracted extensive attention in the design of future communication networks. However, their large number of reflecting elements still results in non-negligible power consumption and hardware costs. To address this issue, we previously proposed a green heterogeneous IRS (HE-IRS) consisting of both dynamically tunable elements (DTEs) and statically tunable elements (STEs). Compared to conventional IRSs with only DTEs, the unique DTE–STE integrated structure introduces new challenges in optimizing the positions and phase shifts of the two types of elements. In this paper, we investigate the element position and phase shift optimization problems in HE-IRS-assisted millimeter-wave systems. We first propose a particle swarm optimization algorithm to determine the specific positions of the DTEs and STEs. Then, by decomposing the phase shift optimization of the two types of elements into two subproblems, we utilize the manifold optimization method to optimize the phase shifts of the STEs, followed by deriving a closed-form solution for those of the DTEs. Furthermore, we propose a low-complexity phase shift optimization algorithm for both DTEs and STEs based on the Cauchy–Schwarz bound. The simulation results show that with the tailored element position and phase shift optimization algorithms, the HE-IRS can achieve a competitive performance compared to that of the conventional IRS, but with much lower power consumption. Full article
(This article belongs to the Special Issue Design and Measurement of Millimeter-Wave Antennas)
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37 pages, 5345 KiB  
Article
Synthesis of Sources of Common Randomness Based on Keystream Generators with Shared Secret Keys
by Dejan Cizelj, Milan Milosavljević, Jelica Radomirović, Nikola Latinović, Tomislav Unkašević and Miljan Vučetić
Mathematics 2025, 13(15), 2443; https://doi.org/10.3390/math13152443 - 29 Jul 2025
Viewed by 97
Abstract
Secure autonomous secret key distillation (SKD) systems traditionally depend on external common randomness (CR) sources, which often suffer from instability and limited reliability over long-term operation. In this work, we propose a novel SKD architecture that synthesizes CR by combining a keystream of [...] Read more.
Secure autonomous secret key distillation (SKD) systems traditionally depend on external common randomness (CR) sources, which often suffer from instability and limited reliability over long-term operation. In this work, we propose a novel SKD architecture that synthesizes CR by combining a keystream of a shared-key keystream generator KSG(KG) with locally generated binary Bernoulli noise. This construction emulates the statistical properties of the classical Maurer satellite scenario while enabling deterministic control over key parameters such as bit error rate, entropy, and leakage rate (LR). We derive a closed-form lower bound on the equivocation of the shared-secret key  KG from the viewpoint of an adversary with access to public reconciliation data. This allows us to define an admissible operational region in which the system guarantees long-term secrecy through periodic key refreshes, without relying on advantage distillation. We integrate the Winnow protocol as the information reconciliation mechanism, optimized for short block lengths (N=8), and analyze its performance in terms of efficiency, LR, and final key disagreement rate (KDR). The proposed system operates in two modes: ideal secrecy, achieving secret key rates up to 22% under stringent constraints (KDR < 10−5, LR < 10−10), and perfect secrecy mode, which approximately halves the key rate. Notably, these security guarantees are achieved autonomously, without reliance on advantage distillation or external CR sources. Theoretical findings are further supported by experimental verification demonstrating the practical viability of the proposed system under realistic conditions. This study introduces, for the first time, an autonomous CR-based SKD system with provable security performance independent of communication channels or external randomness, thus enhancing the practical viability of secure key distribution schemes. Full article
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25 pages, 3093 KiB  
Article
Research of Hierarchical Vertiport Location Based on Lagrange Relaxation
by Yuzhen Guo, Junjie Yao, Jing Jiang and Dongxiao Qiao
Aerospace 2025, 12(8), 672; https://doi.org/10.3390/aerospace12080672 - 28 Jul 2025
Viewed by 124
Abstract
With the rise of the low-altitude urban traffic system, urban air mobility (UAM) has developed rapidly. As a critical component of the UAM system, the strategic layout of vertiports helps divert ground traffic pressure. To satisfy various demand patterns, different vertiport levels are [...] Read more.
With the rise of the low-altitude urban traffic system, urban air mobility (UAM) has developed rapidly. As a critical component of the UAM system, the strategic layout of vertiports helps divert ground traffic pressure. To satisfy various demand patterns, different vertiport levels are needed, so we focus on the hierarchical vertiport location problem. Considering the capacity limitation, a median location model is established to minimize vertiport construction cost, passenger commuting cost, and penalty cost. For the nonlinear term in the objective function, the Big-M method is employed. Based on the reformulated model, we improve the branch-and-bound algorithm (LVBB) to solve it, where the Lagrange relaxation method is used to decompose the large-scale problem into parallel subproblems and compute the lower bound, and the variable neighborhood search algorithm is used to obtain the upper bound. Numerical experiments are performed in the 11 administrative districts of Nanjing, China. The results demonstrate that the proposed location scheme effectively balances vertiport construction cost and passenger commuting cost while satisfying capacity limitations. It also significantly reduces commuting time to improve passenger satisfaction. This scheme can offer strategic guidance for infrastructure planning in UAM. Full article
(This article belongs to the Special Issue Research and Applications of Low-Altitude Urban Traffic System)
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21 pages, 950 KiB  
Article
A Fuzzy Unit Commitment Model for Enhancing Stability and Sustainability in Renewable Energy-Integrated Power Systems
by Sukita Kaewpasuk, Boonyarit Intiyot and Chawalit Jeenanunta
Sustainability 2025, 17(15), 6800; https://doi.org/10.3390/su17156800 - 26 Jul 2025
Viewed by 231
Abstract
The increasing penetration of renewable energy sources (RESs), particularly solar photovoltaic (PV) sources, has introduced significant uncertainty into power system operations, challenging traditional scheduling models and threatening system reliability. This study proposes a Fuzzy Unit Commitment Model (FUCM) designed to address uncertainty in [...] Read more.
The increasing penetration of renewable energy sources (RESs), particularly solar photovoltaic (PV) sources, has introduced significant uncertainty into power system operations, challenging traditional scheduling models and threatening system reliability. This study proposes a Fuzzy Unit Commitment Model (FUCM) designed to address uncertainty in load demand, solar PV generation, and spinning reserve requirements by applying fuzzy linear programming techniques. The FUCM reformulates uncertain constraints using triangular membership functions and integrates them into a mixed-integer linear programming (MILP) framework. The model’s effectiveness is demonstrated through two case studies: a 30-generator test system and a national-scale power system in Thailand comprising 171 generators across five service zones. Simulation results indicate that the FUCM consistently produces stable scheduling solutions that fall within deterministic upper and lower bounds. The model improves reliability metrics, including reduced loss-of-load probability and minimized load deficiency, while maintaining acceptable computational performance. These results suggest that the proposed approach offers a practical and scalable method for unit commitment planning under uncertainty. By enhancing both operational stability and economic efficiency, the FUCM contributes to the sustainable management of RES-integrated power systems. Full article
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15 pages, 2217 KiB  
Article
Energy-Based Approach for Fatigue Life Prediction of Additively Manufactured ABS/GNP Composites
by Soran Hassanifard and Kamran Behdinan
Polymers 2025, 17(15), 2032; https://doi.org/10.3390/polym17152032 - 25 Jul 2025
Viewed by 232
Abstract
This study examines the effectiveness of energy-based models for fatigue life prediction of additively manufactured acrylonitrile butadiene styrene (ABS)/graphene nanoplatelet (GNP) composites. The effects of varying GNP weight percentages and filament raster orientations on the fatigue life of the samples were investigated theoretically. [...] Read more.
This study examines the effectiveness of energy-based models for fatigue life prediction of additively manufactured acrylonitrile butadiene styrene (ABS)/graphene nanoplatelet (GNP) composites. The effects of varying GNP weight percentages and filament raster orientations on the fatigue life of the samples were investigated theoretically. The required stress and strain values for use in energy-based models were obtained by solving two sets of Neuber and Ramberg–Osgood equations, utilizing the available values of notch strength reduction factors at each load level and the average Young modulus for each composite material. Results revealed that none of the studied energy-based models could accurately predict the fatigue life of the samples across the entire high- and low-cycle fatigue regimes, with strong dependence on the stress ratio (R). Instead, a novel fatigue life prediction model was developed by combining two existing energy-based models, incorporating stress ratio dependence for cases with negative mean stress. This model was tested for R values roughly between −0.22 and 0. Results showed that, for all samples at each raster orientation, most of the predicted fatigue lives fell within the upper and lower bounds, with a factor of ±2 across the entire range of load levels. These findings highlight the reliability of the proposed model for a wide range of R values when mean stress is negative. Full article
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22 pages, 312 KiB  
Article
Selberg’s Inequality and Selberg Operator Bounds in Hilbert Spaces with Applications
by Salma Aljawi, Cristian Conde, Silvestru Sever Dragomir and Kais Feki
Axioms 2025, 14(8), 575; https://doi.org/10.3390/axioms14080575 - 25 Jul 2025
Viewed by 179
Abstract
In the present work, we give a new proof of the well-known Selberg’s inequality in complex Hilbert spaces from an operator-theoretic perspective, establishing its fundamental equivalence with the Cauchy–Bunyakovsky–Schwarz inequality. We also derive several lower and upper bounds for the Selberg operator, including [...] Read more.
In the present work, we give a new proof of the well-known Selberg’s inequality in complex Hilbert spaces from an operator-theoretic perspective, establishing its fundamental equivalence with the Cauchy–Bunyakovsky–Schwarz inequality. We also derive several lower and upper bounds for the Selberg operator, including its norm estimates, refining classical results such as de Bruijn’s and Bohr’s inequalities. Additionally, we revisit a recent claim in the literature, providing a clarification of the conditions under which Selberg’s inequality extends to abstract bilinear forms. Full article
(This article belongs to the Section Mathematical Analysis)
19 pages, 890 KiB  
Article
Characterization of SCOBY and Lactiplantibacillus plantarum ELB90 Fermented Coffee Kombucha from Different Coffee Sources
by Oznur Saroglu, Yagmur Gulce Irmak, Rusen Metin Yildirim and Ayse Karadag
Fermentation 2025, 11(8), 428; https://doi.org/10.3390/fermentation11080428 - 25 Jul 2025
Viewed by 341
Abstract
Coffee kombucha beverages were developed by fermenting various coffee substrates, including instant coffee (I), coffee brews of ground coffee beans (G), and additional spent coffee added ground coffee (GSC) using either SCOBY (S) or Lactiplantibacillus plantarum ELB90 (L), or a combination of both [...] Read more.
Coffee kombucha beverages were developed by fermenting various coffee substrates, including instant coffee (I), coffee brews of ground coffee beans (G), and additional spent coffee added ground coffee (GSC) using either SCOBY (S) or Lactiplantibacillus plantarum ELB90 (L), or a combination of both (SL). The combined SL inoculation did not synergistically enhance the growth of acetic and lactic acid bacteria, nor did it increase the acetic and lactic acid concentrations or improve retention of caffeoylquinic acids (CQA) compared to non-fermented controls stored for the incubation period (7 days). Samples fermented with L better preserved the total CQAs during incubation, notably increasing 3-CQA and 4-CQA in L-fermented G and GSC samples by up to 40%, whereas 5-CQA showed a slight decrease (up to 8%) in L-fermented G and GSC samples. After one week, all fermented samples maintained stable levels of 3-CQA compared to the non-fermented SCG control, with significantly elevated 4-CQA. Caffeic acid was detected only in the bound fraction of beans, exhibiting similar concentrations in both fermented and non-fermented samples. SL-fermented coffees showed significant reductions in caffeine contents, except for I coffee substrate, and spent coffee grounds (SCG) filtered from the SL-fermented sample also had significantly lower caffeine content. Panelists preferred coffee kombucha beverages inoculated with S over those fermented with L, which were rated least appealing. The study concludes that fermentation with specific inoculation cultures could mitigate the degradation of coffee phenolic compounds during storage and facilitate the production of beverages with lower caffeine content, potentially enhancing both functional properties and consumer acceptability. Full article
(This article belongs to the Section Fermentation for Food and Beverages)
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25 pages, 7623 KiB  
Article
ASHM-YOLOv9: A Detection Model for Strawberry in Greenhouses at Multiple Stages
by Yan Mo, Shaowei Bai and Wei Chen
Appl. Sci. 2025, 15(15), 8244; https://doi.org/10.3390/app15158244 - 24 Jul 2025
Viewed by 285
Abstract
Strawberry planting requires different amounts of soil water-holding capacity and fertilizer at different growth stages. Determining the stages of strawberry growth has important guiding significance for irrigation, fertilization, and picking. Quick and accurate identification of strawberry plants at different stages can provide important [...] Read more.
Strawberry planting requires different amounts of soil water-holding capacity and fertilizer at different growth stages. Determining the stages of strawberry growth has important guiding significance for irrigation, fertilization, and picking. Quick and accurate identification of strawberry plants at different stages can provide important information for automated strawberry planting management. We propose an improved multistage identification model for strawberry based on the YOLOv9 algorithm—the ASHM-YOLOv9 model. The original YOLOv9 showed limitations in detecting strawberries at different growth stages, particularly lower precision in identifying occluded fruits and immature stages. We enhanced the YOLOv9 model by introducing the Alterable Kernel Convolution (AKConv) to improve the recognition efficiency while ensuring precision. The squeeze-and-excitation (SE) network was added to increase the network’s capacity for characteristic derivation and its ability to fuse features. Haar wavelet downsampling (HWD) was applied to optimize the Adaptive Downsampling module (Adown) of the initial model, thereby increasing the precision of object detection. Finally, the CIoU function was replaced by the Minimum Point Distance based IoU (MPDIoU) loss function to effectively solve the problem of low precision in identifying bounding boxes. The experimental results demonstrate that, under identical conditions, the improved model achieves a precision of 97.7%, a recall of 97.2%, mAP50 of 99.1%, and mAP50-95 of 90.7%, which are 0.6%, 3.0%, 0.7%, and 7.4% greater than those of the original model, respectively. The parameters, model size, and floating-point calculations were reduced by 3.7%, 5.6% and 3.8%, respectively, which significantly boosted the performance of the original model and outperformed that of the other models. Experiments revealed that the model could provide technical support for the multistage identification of strawberry planting. Full article
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17 pages, 720 KiB  
Article
Involvement of Hormone Receptors, Membrane Receptors and Signaling Pathways in European Gastric Cancers Regarding Subtypes and Epigenetic Alterations: A Pilot Study
by Cynthia Pimpie, Anne Schninzler, Marc Pocard, Véronique Baud and Martine Perrot-Applanat
Biomedicines 2025, 13(8), 1815; https://doi.org/10.3390/biomedicines13081815 - 24 Jul 2025
Viewed by 290
Abstract
Background: Gastric cancer (GC) is a highly heterogeneous disease and remains one of the major causes of cancer-related mortality worldwide. The vast majority of GC cases are adenocarcinomas including diffuse and intestinal GC that may differ in their incidence between Asian and [...] Read more.
Background: Gastric cancer (GC) is a highly heterogeneous disease and remains one of the major causes of cancer-related mortality worldwide. The vast majority of GC cases are adenocarcinomas including diffuse and intestinal GC that may differ in their incidence between Asian and non-Asian cohorts. The intestinal-subtype GC has declined over the past 50 years. In contrast to the intestinal-subtype adenocarcinoma, the incidence of diffuse-subtype GC, often associated with poor overall survival, has constantly increased in the USA and Europe. The aim of this study was to analyze the expression and clinical significance of steroid hormone receptors, two membrane-bound receptors (ERRγ and GPER), and several genes involved in epigenetic alterations. The findings may contribute to revealing events driving tumorigenesis and may aid prognosis. Methods: Using mRNA from diffuse and intestinal GC tumor samples, the expression level of 11 genes, including those coding for sex hormone receptors (estrogen receptors ERα and ERβ), progesterone receptor (PR) and androgen receptor (AR), and the putative relevant ERRγ and GPER receptor were determined by RT-qPCR. Results: In diffuse GC, the expression of ERα, ERβ, PR and AR differed from their expression in the intestinal subtype. The expression of ERα and ERβ was strongly increased in the diffuse subtype compared to the intestinal subtype (×1.90, p = 0.001 and ×2.68, p = 0.002, respectively). Overexpression of ERα and ERβ was observed in diffuse GC (15 and 42%, respectively). The expression levels of PR and AR were strongly decreased in the intestinal subtype as compared to diffuse GC (×0.48, p = 0.005 and ×0.25, p = 0.003, respectively; 37.5% and 56% underexpression). ERα, ERβ, PR and AR showed notable differences for clinicopathological correlation in the diffuse and intestinal GC. A significant decrease of ERα, ERβ, PR and AR in intestinal GC correlated with the absence of lymphatic invasion and lower TNM (I-II). In diffuse GC, among the hormone receptors, increases of ERs and PR mainly correlated with expression of growth factors and receptors (IGF1, FGF7 and FGFR1), and with genes involved in epithelial-mesenchymal transition (VIM and ZEB2) or cell migration (MMP2). Our results also report the strong decreased expression of ERRγ and GPER (two receptors that bind estrogen or xenoestrogens) in diffuse and intestinal subtypes. Conclusions: Our study identified new target genes, namely hormone receptors and membrane receptors (ERRγ and GPER), whose expression is associated with an aggressive phenotype of diffuse GC, and revealed the importance of epigenetic factors (EZH2, HOTAIR, H19 and DNMT1) in gastric cancers. Full article
(This article belongs to the Section Cancer Biology and Oncology)
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19 pages, 894 KiB  
Article
Minimum Spatial Housing Requirements for Human Flourishing
by Karl T. Ulrich
Buildings 2025, 15(15), 2623; https://doi.org/10.3390/buildings15152623 - 24 Jul 2025
Viewed by 296
Abstract
This study defines evidence-based minimum internal floor areas required to support long-term residential use across different household types. It addresses the following question: what is the smallest viable floor area that supports sustained occupancy without persistent stress, conflict, or turnover? An integrative review [...] Read more.
This study defines evidence-based minimum internal floor areas required to support long-term residential use across different household types. It addresses the following question: what is the smallest viable floor area that supports sustained occupancy without persistent stress, conflict, or turnover? An integrative review method was employed, drawing from behavioural studies in environmental psychology, international regulatory standards, and real-world market data. The analysis focuses on essential domestic functions including sleep, hygiene, food preparation, storage, social interaction, and work. Quantitative findings from tenancy surveys, post-occupancy research, and market performance data indicate that residential units below 30 square metres for single occupants and 45 square metres for couples are consistently associated with reduced satisfaction and shorter tenancies. Regulatory minimums across diverse jurisdictions tend to converge near these same thresholds. The study proposes technical minimums of 30, 45, and 60 square metres for one-, two-, and three-person households, respectively. These values reflect functional lower bounds rather than ideal or aspirational sizes and are intended to inform performance-based housing standards. Full article
(This article belongs to the Section Architectural Design, Urban Science, and Real Estate)
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15 pages, 302 KiB  
Article
Extremal Permanents of Laplacian Matrices of Unicyclic Graphs
by Tingzeng Wu, Xiuhong Wang and Xiangshuai Dong
Axioms 2025, 14(8), 565; https://doi.org/10.3390/axioms14080565 - 24 Jul 2025
Viewed by 107
Abstract
The extremal problem of Laplacian permanents of graphs is a classical and challenging topic in algebraic combinatorics, where the inherent #P-complete complexity of permanent computation renders this pursuit particularly intractable. In this paper, we determine the upper and lower bounds of permanents of [...] Read more.
The extremal problem of Laplacian permanents of graphs is a classical and challenging topic in algebraic combinatorics, where the inherent #P-complete complexity of permanent computation renders this pursuit particularly intractable. In this paper, we determine the upper and lower bounds of permanents of Laplacian matrices of unicyclic graphs, and the corresponding extremal graphs are characterized. Furthermore, we also determine the upper and lower bounds of permanents of Laplacian matrices of unicyclic graphs with given girth, and the corresponding extremal graphs are characterized. Full article
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25 pages, 355 KiB  
Article
Each ζ(n), 5 ≤ n ≤ 25, Is Not a Liouville Number
by Sidney A. Morris
Axioms 2025, 14(8), 546; https://doi.org/10.3390/axioms14080546 - 22 Jul 2025
Viewed by 223
Abstract
We prove that for the odd integers n{5,7,9,,25}, the Riemann zeta value ζ(n) is not a Liouville number. Our method applies a general strategy pioneered by Wadim [...] Read more.
We prove that for the odd integers n{5,7,9,,25}, the Riemann zeta value ζ(n) is not a Liouville number. Our method applies a general strategy pioneered by Wadim Zudilin and D.V. Vasilyev. Specifically, we construct families of high-dimensional integrals that expand into rational linear combinations of odd zeta values, eliminate lower-order terms to isolate ζ(n), and apply Nesterenko’s linear independence criterion. We verify the required asymptotic growth and decay conditions for each odd n25, establishing that μ(ζ(n))<, and thus that ζ(n)L. This is the first unified proof covering all odd zeta values up to ζ(25) and highlights the structural barriers to extending the method beyond this point. We also give rigorous upper bounds on μ(ζ(n)) for all odd integers n{5,7,,25}, using multiple integral constructions due to Vasilyev and Zudilin, elimination of lower zeta terms, and the quantitative version of Nesterenko’s criterion. Full article
(This article belongs to the Section Algebra and Number Theory)
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