Proper Space Research Articles

Efficient and Stable Deep-Blue 0D Copper-Based Halide TEA2Cu2I4 with Near-Unity Photoluminescence Quantum Yield for Light-Emitting Diodes

Achieving deep-blue light with high color saturation remains a critical challenge in the development of white light-emitting diode (LED) technology, necessitating luminescent materials that excel in efficiency, low toxicity, and stability. Here, we report the synthesis of [N(C2H5)4]2Cu2I4 (TEA2Cu2I4) single crystals (SCs), which exhibit deep-blue photoluminescence (PL) at 450 nm. These crystals are characterized by a significant Stokes shift of 180 nm, a long lifetime of 1.7 μs, and an impressive photoluminescence quantum yield (PLQY) of 96.7% for SCs and 87.2% for polycrystalline films. The zero-dimensional structure is attributed to the proper spacing of triangular inorganic units [Cu2I4]2− by organic cations [N(C2H5)4]+. This structural arrangement facilitates broadband deep-blue light emission with phosphorescent characteristics, as evidenced by temperature-dependent PL and time-resolved photoluminescence (TRPL) measurements. The band gap properties of TEA2Cu2I4 were further elucidated through density functional theory (DFT) computations. Notably, the material exhibited minimal PL intensity degradation after continuous UV irradiation and one month of exposure to ambient conditions. Moreover, the polycrystalline film of TEA2Cu2I4 maintained substantial deep-blue emission even after one year of storage. Utilizing TEA2Cu2I4 thin film, we fabricated an electroluminescent device emitting deep-blue light with high color saturation, featuring CIE coordinates (0.143, 0.076) and a brightness of 90 cd/m2. The exceptional photophysical properties of TEA2Cu2I4 render it a highly promising candidate for optoelectronic applications.

Stress shadow effects in multistage horizontal hydrofracturing of tight reservoirs: a numerical analysis considering perforation cluster spacings and fracturing sequences

AbstractMultistage horizontal fracturing technology of reservoirs has been widely used to enhance tight hydrocarbon resource recovery. Determining the proper perforation cluster spacing is crucial to developing a complex fracture network that connects natural rock fractures and facilitates gas flow in reservoirs. The stress shadow effect that occurs between multiple clusters has a significant effect on the development of the fracture network in reservoirs. The quantification of the stress shadow effect and its influences on the development of fracture networks has not been resolved satisfactorily due to experimental and numerical difficulties with detecting and identifying crack propagation and intersection in deep reservoirs. In this study, we used an adaptive finite element-discrete element method to analyze crack propagation and intersection in tight shale reservoirs by altering perforation spacings and fracture sequences. The effects of five perforation cluster spacings using sequential, simultaneous and parallel fracturing techniques were compared. The non-linear properties of shales, hydromechanical coupling and fluid leak-off effects, proppant transport, dual-rupture criteria of strength and energy, and intersection of hydraulic fractures were taken into account in the simulation. The areas affected by the stress shadow and the optimum perforation cluster spacing in terms of hydraulic fracture propagation lengths, volumes, and microseismic magnitudes were evaluated when adopting different fracturing methods. This study extends the understanding of the impact of the different independent factors that contribute to the stress shadow effect and, therefore, provides new information to help guide wellbore completion design in horizontal fracturing wells.

On the moment measure conjecture

AbstractThe moment measure conjecture of Białynicki-Birula and Sommese gives a combinatorial characterization of all open substacks of a global quotient stack for a torus action on a normal projective variety that admit a proper good moduli space, in other words it characterizes the invariant open subvarieties that admit a proper quotient. In this article we prove the conjecture for actions on smooth varieties. This gives an instance of stability conditions defined by cohomological invariants that are not given by Chern classes of line bundles.

Determining the issues associated with the urban centre: A case of Jalandhar city

Abstract Urban centers often serve as the centers of economic, social, and cultural activity within a region, playing a pivotal role in its development and growth. However, with this centralization comes a myriad of challenges, ranging from infrastructure strains to socio-economic disparities. Jalandhar city, situated in the Indian state of Punjab, exemplifies this complexity as it grapples with various issues associated with its centre. Rapid urbanization and population growth have resulted in increased pressure on transportation networks, utilities, and public services. This paper aims to delve into the multifaceted challenges facing Jalandhar’s city centre, shedding light on the intricacies of urban management and development in the context of a rapidly evolving urban landscape. Traffic congestion, inadequate parking facilities, and overburdened utilities contribute to the deteriorating quality of life for residents and commuters alike. The major problems identified in the study area includes inadequate parking; poor road maintenance; noise and safety issues; unavailability of street lighting, pathways, and proper seating space. Addressing these issues requires comprehensive planning, infrastructure improvements, and community engagement to enhance the overall liveability and functionality of the study area.

Admission Strategy for International New Students at the University of Mataram

Recruiting international students is highly beneficial yet challenging for universities in Indonesia. This study raised research focusing on strategies applied by Indonesian Universities to attract international students' willingness to enroll. It also figured out the challenges and solutions encountered by the students in their initial studies. This study adopted Vincent Tinto's theory about the factors affecting students' academic accomplishments and learning failures. Qualitative design, case study approach, and open-ended questionnaires were implemented. This study invited three staff members of the International Affairs and International Center as the participants. Thematic analysis was adopted utilizing Atlas. Ti software to analyze the data from the respondents following Kawulich's (2004) framework, encompassing Narrative, Coding, Interpretation, Confirmation, and Presentation. The result demonstrated some strategies implemented by Mataram University for international students, such as providing proper facilities, including library and study spaces, access to technology, and a health center. The university also utilizes international alumni to endorse the university in their home country. Alongside the hurdles, the university provides students with a welcoming ceremony that includes a language course, academic orientation, and cultural adaptation programs upon their arrival

Assessment of parental attitude, knowledge and awareness towards preventive dentistry in south zone of Chhatrapati Sambhajinagar: A questionnaire based cross sectional survey

Introduction: Oral health is a pivotal aspect of overall well-being. In early childhood, primary teeth play a vital role in development of speech, chewing, maintaining proper spacing, and guiding the eruption of permanent teeth. Common oral conditions comprise dental caries, malocclusion, childhood caries, and trauma. Aim: The present study was conducted to assess paternal knowledge towards the forestallment of oral conditions and application of preventive dental procedures in children in South zone of Chhatrapati Sambhajinagar. Materials and Methods: A cross-sectional questionnaire was administered to parents of pediatric patients of age group 3 to12 years in South zone of Chhatrapati Sambhajinagar, Maharashtra, with a sample size of 270 participants. A structured questionnaire, comprising 14 questions in English, was developed, translated and back translated into the local language Marathi by experts to ensure better comprehension by the parents. The questionnaire was divided into two sections: the first focused on demographic information, while the second included 14 multiple-choice, close-ended questions. These questions included topics such as preventive treatments for dental caries, childhood caries, topical fluoride application, fluoridated toothpaste, pit and fissure sealants, habit-breaking dental appliances, malocclusion, mouth guards, and space maintainers. Additionally, the survey addressed harmful habits such as thumb-sucking, tongue-thrusting, and nail-biting. Result: 56.6% of parents sought dental care only after experiencing pain. Additionally, parents of paediatric patients have restricted knowledge about preventive dentistry. Conclusion: Parental knowledge about preventive dental procedures is limited, as is the utilization of these measures.

The Primitive Comparison Theorem in characteristic p

We prove an analogue of Scholze’s Primitive Comparison Theorem for proper rigid spaces over an algebraically closed non-archimedean field K of characteristic p. This implies a v-topological version of the Primitive Comparison Theorem for proper finite type morphisms f:X→Y\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f{:}\\,X\\rightarrow Y$$\\end{document} of analytic adic spaces over Zp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {Z}_p$$\\end{document}. We deduce new cases of the Proper Base Change Theorem for p-torsion coefficients and the Künneth formula in this setting.

Combining virtual reality with asymmetric collaborative learning: a case study in chemistry education

The use of Virtual Reality (VR) in education is getting more and more common, especially when hands-on learning experiences have to be delivered. With VR it becomes possible, e.g., to simulate dangerous or costly procedures that could hardly be implemented in real settings. However, engaging large classes in immersive laboratory activities may be difficult, since VR kits are still rather expensive for quantity purchases and may require powerful PCs as well as proper spaces to work. A possible way to deal with these issues could be to combine VR with so-called asymmetric Collaborative Learning (CL). CL is a particularly interesting pedagogical approach, as it make learners work in team to achieve a common educational goal, promoting critical thinking and active learning. In asymmetric CL, in particular, learners use different technologies to interact. When combined with VR, asymmetric CL could be used, e.g., to let some learners get immersed in a virtual environment, while some others actively participate in the experience using a desktop interface. This configuration could allow, in principle, to involve more learners in the same amount of time and with the same number of VR kits, while also letting them benefit of the advantages of CL. Based on these considerations, this paper investigates the impact of CL on VR-based education by leveraging an immersive virtual environment designed to support a laboratory experience in a Chemistry course. A user study was conducted by involving 46 university students enrolled in the course. Objective and subjective metrics were used to compare two education methods, i.e. one in which the students experienced the VR environment in isolation, another one in which pairs of students collaborated with an asymmetric approach. Students’ knowledge acquisition was assessed by means of theoretical quizzes, whereas practical performance was automatically measured during the VR experience. The experimental results showed that trading off VR-based, individual learning for CL may have positive effects on the acquisition of theoretical knowledge, but may be detrimental to the achievement of practical abilities if sufficient exposure to technology cannot be guaranteed.

Real-time scheduling for two-stage assembly flowshop with dynamic job arrivals by deep reinforcement learning

Assembly flowshops differ from flowshops because their jobs have several components that are manufactured in the processing stage and then joined together in the assembly stage. Real-time scheduling of two-stage assembly flowshops is of great significance for many discrete manufacturing companies in customized order fulfilment. Therefore, we study two-stage assembly flowshop scheduling problem with the objective of total tardiness minimization considering dynamic job arrivals using deep reinforcement learning (DRL). First, an architecture of DRL-based real-time scheduling is proposed. Second, we establish a DRL-based real-time scheduling model by designing proper state space, action space and reward function. A scheduling agent is constructed and trained through the proximal policy optimization (PPO) using interactive simulation data. The experimental results show that the trained scheduling agent can learn to choose the appropriate dispatching rules efficiently so as to make a real-time scheduling quickly and effectively. The PPO algorithm outperforms six dispatching rules, genetic algorithm and two DRL algorithms (i.e., DDQN and DDPG) in terms of solution quality and computing speed. The proposed approach is highly applicable to many practical scheduling situations that requires real-time and quick decisions.

Comparative study of RC and ECC beam-column connections with shear deficit spacing under quasi-static conditions

ABSTRACT This study evaluates the seismic performance of beam-column joints using Engineered Cementitious Composite (ECC) compared to Reinforced Concrete (RC) under quasi-static loading. Five full-scale specimens, one control RC specimen and four ECC specimens with varying configurations were tested. The study examines parameters such as load-bearing capacity, ductility, energy dissipation, and cracking behavior. Results revealed that ECC significantly outperformed conventional concrete, increasing the mean ultimate load by 28.96% and ductility by 23.95% in specimens with proper shear spacing. While ECC specimens with shear deficits exhibited 26.75% lower energy dissipation, extending ECC into the plastic hinge zones increased dissipation by 58.06%. These findings demonstrate ECC’s effectiveness in enhancing seismic resilience, particularly in cases with inadequate shear reinforcement, and underscore its potential as a viable alternative to traditional reinforcement strategies.

Crown Width–Tree Height Models for Magnolia grandiflora, Prunus cerasifera, and Acer negundo Growing in Cities in Northeastern Greece

The objective of this study is the development of crown width–tree height (CW-H) models in cities in northeastern Greece, for better urban vegetation management. In the cities of Kavala, Xanthi, Komotini, Alexadroupolis, and Orestiada, in total, 700 trees of Magnolia grandiflora L., Prunus cerasifera Ehrh., and Acer negundo L. were selected. For each selected tree, the total height as well as the minimum and maximum crown diameter were measured, and the average of the minimum and maximum diameter was considered the crown width. The selected CW-H models exhibit satisfactory R2 values of 0.60 and above. There is not a common pattern in the value order (or rank) of R2 among the M. grandiflora, P. cerasifera, and A. negundo CW-H models in the studied cities. A medium-sized tree such as M. grandiflora, a small-medium sized tree such as A. negundo, and a shrub or small tree such as P. cerasifera did not exhibit substantial differences in estimated and observed crown widths. The results of this study will increase our understanding of CW-H allometries. The main use of these models will be in the selection of the proper above-ground spacing of tree lines and in the spatial planning of a tree’s establishment so that no problems arise from its proximity to infrastructure.

WITHDRAWN: Pullout Capacity of Piles in Unsaturated High Plasticity Clayey Soil: An Experimental Model Study

Unsaturated soils exhibit distinct physical and mechanical characteristics compared to dry or saturated soils. Ignoring the influence of unsaturation (matric suction) and assuming either dry or saturated conditions can lead to unreliable predictions of pile behavior in unsaturated soils. In this study, the pullout capacity of different physical model piles driven in an unsaturated Kaolinite-Bentonite matrix is investigated. A series of lab-scale pullout tests were carried out to examine the influence of matric suction, pile type, pile L/D ratio, and undrained cohesion (cu) of soil on the ultimate pullout capacity of model piles. Soil samples were prepared and compacted in a tank, and holes were created using a pile. Four model piles (solid and hollow stainless steel) were driven into the holes, ensuring proper spacing. Incremental loading was applied until the piles slipped out, with displacement measured by an LVDT. The pile pullout capacity increased with increased matric suction and undrained cohesion. The uplift capacity increased by 50 % to 136% as matric suction increased by 157.97% as the compaction state was changed from 0.95 γd(max) on the wet side of optimum moisture content (OMC) to 0.95 γd(max) on the dry side of OMC of the compaction curve. However, for the compaction state of 0.90 γd(max), the matric suction increased by 398.80%, leading to a 275% to 800 % increase in the uplift capacity. As the cohesion of the five samples increased from 17.84 kPa to 137.84 kPa, the uplift capacity of all the model piles increased. In Kaolinite-Bentonite mixes compacted on the dry side of OMC, hollow model piles resisted higher pull-out loads than solid model piles. The increase in uplift capacity was found to be in the range of 11.11% to 75% for different combinations of pile type and compaction density (matric suction). The results from the study imply a strong influence of matric suction, undrained cohesion, L/D ratio, and pile type on pullout capacity for piles driven in unsaturated Kaolinite-Bentonite mix.

A two-level semi-hybrid-mixed model for Stokes–Brinkman flows with divergence-compatible velocity–pressure elements

A two-level version for a recent semi-hybrid-mixed finite element approach for modeling Stokes and Brinkman flows is proposed. In the context of a domain decomposition of the flow region Ω, composite divergence-compatible finite elements pairs in H(div,Ω)×L2(Ω) are utilized for discretizing velocity and pressure fields, using the same approach previously adopted for two-level mixed Darcy and stress mixed elasticity models. The two-level finite element pairs of spaces in the subregions may have richer internal resolution than the boundary normal trace. Hybridization occurs by the introduction of an unknown (traction) defined over element boundaries, playing the role of a Lagrange multiplier to weakly enforce tangential velocity continuity and Dirichlet boundary condition. The well-posedness of the method requires a proper choice of the finite element space for the traction multiplier, which can be achieved after a proper velocity FE space enrichment with higher order bubble fields. The method is strongly locally conservative, yielding exact divergence-free velocity fields, demonstrating pressure robustness, and facilitating parallel implementations by limiting the communication of local common data to at most two elements. Easier coupling strategies of finite elements regarding different polynomial degree or mesh widths are permitted, provided that mild mesh and normal trace consistency properties are satisfied. Significant improvement in computational performance is achieved by the application of static condensation, where the global system is solved for coarse primary variables. The coarse primary variables are a piecewise constant pressure variable over the subregions, velocity normal trace and tangential traction over subdomain interfaces, as well as a real number used as a multiplier ensuring global zero-mean pressure. Refined details of the solutions are represented by secondary variables, which are post-processed by local solvers. Numerical results are presented for the verification of convergence histories of the method.

Investigation of multi-inlet arrangement effect on mesoscale bubble dynamics in the gas–liquid-solid reactor via VOF-DEM

Multi-channel gas–liquid-solid systems have attracted considerable attention across chemical, energy, and biochemical industries due to their potential applications, yet the intricate interplay between different scales of interphase interactions remains complex. This study employs the volume of fluid method coupled with the discrete element method (VOF-DEM) to investigate the multi-scale flow hydrodynamics within gas–liquid-solid systems featuring various inlet arrangements. Following thorough validation of the numerical methodology, the intricate interphase interactions, bubble dynamics, and the influence of multi-channel configurations are examined. The findings elucidate that the presence of a densely packed particle bed fundamentally alters the bubble generation process, inhibiting lateral expansion while promoting vertical growth. Consequently, this phenomenon increases the likelihood of collision and coalescence between adjacent rising bubbles. Additionally, higher Reynolds and Weber numbers facilitate vortex shedding and create open unsteady wakes, thereby enhancing mixing effects within the system. Consequently, it is advisable to adjust both the inlet size and gas flow rate to achieve Reynolds numbers exceeding 3000 and Weber numbers surpassing 10. Moreover, reactor design considerations must include proper channel spacing to mitigate the formation of large merged bubbles, which may enhance local stirring but impede global mixing. Optimizing the spacing between gas inlets enhances lateral bubble extrusion by particles, fosters a meandering ascent for bubbles, and boosts both gas–liquid contact area and gas hold-up. The insights obtained from this study provide valuable contributions to understanding the multi-channel flow behaviors in gas–liquid-solid systems and offer practical guidance for the design and optimization of such reactors.

Urban agriculture as ecosystem services provider: A review

Background: Urban agriculture’s role in mitigating the urban environment deterioration as ecosystem services provider. Urban agriculture adds various functions to different landscape scales, providing numerous benefits if managed correctly. This paper aims to study the role of urban agriculture as ecosystem services provider in mitigating urban environment deterioration. Method: The method that will be used in this article is literature review from articles related to urban agriculture and ecosystem services from provisioning, regulating, services, and cultural. The review is compiled from urban agriculture’s function as ecosystem services provider, such as biodiversity conservation, microclimate regulation, aesthetic function, and food production. Result: In essence, urban agriculture is a diverse and vital solution for cities, and it takes various forms, from private gardens to community plots, addressing challenges like limited public funding and promoting greening initiatives. Urban agriculture plays a key role in biodiversity conservation, contributing to enhanced environmental benefits and the preservation of local habitats. Another crucial role in regulating the complex dynamics of the urban microclimate, offering ecological benefits such as reduced Urban Heat Island effects, wind protection, and pollutant absorption. Beyond its ecological impact, urban agriculture adds aesthetic value to urban spaces, creating visually appealing landscapes and promoting cultural integration. Moreover, it serves as a multifaceted strategy for sustainable urban development, addressing food security, resilience, and well-being. Conclusion: Amidst challenges, such as the threat to urban biodiversity and the need for proper green space management, urban agriculture emerges as a holistic approach, contributing to the visual, cultural, and environmental fabric of cities. Novelty/Originality of this article: This study offers a new perspective on urban agriculture as a multifunctional solution to address urban environmental degradation. By integrating agriculture into the urban landscape, the study reveals the transformative potential for creating greener, more resilient and sustainable cities.

Adoption of Improved Buffalo Husbandry Practices in Peri-Urban Areas of Surat City, Gujarat

The present study was carried out in the peri urban areas of Surat city of Gujarat to find out the adoption of improved buffalo husbandry practices. A random sample of 50 buffalo farm owners were selected and interviewed for the interview schedule prepared about adoption of improved dairy husbandry practices in six major aspects of housing, feeding, breeding, health care, milking and calf rearing management was studied. Housing in separate located place (100%), providing proper floor space (98%) and proper height and ventilation (90%) were more adopted in housing practices. Provision of clean and fresh drinking water (100%), feeding extra ration to advance pregnant animals (64%) and feeding balance concentrate mixture on the basis of milk production (64%) were more adopted in feeding management. In adoption of breeding management, keeping watch on oestrus cycle and heat symptoms of animals (100%), artificial insemination of animals (100%) and practicing pregnancy diagnosis between 60-90 days after service (91%) were more adopted by buffalo owners. Observing animals daily for signs of sickness (100%), timely and regularly vaccination (100%) and treatment of reproductive disorders (75%) were more adopted by respondents in health care management practices. In milking and calf rearing practices, washing pails and hands before milking (100%) and regularity in milking time (100%), early solid feeding (100%) and milk feeding to calves up to three months of age (96%) were more adopted by the buffalo owners.

Spacing and nitrogen application affect Indian oregano (Origanum vulgare L.) biomass, essential oil yield and composition

Oregano offers culinary and medicinal applications for mankind. Due to its vast health benefits, its consumption has been gradually rising in the modern era. Since, the nutrients and proper spacing are critical factors influencing plant growth, current study endeavors to investigate the effects of four different nitrogen levels (N0: 0 kg/ha, N1: 50 kg/ha, N2: 100 kg/ha, and N3: 150 kg/ha) combined with three row spacings (S1 = 45 × 45 cm, S2 = 45 × 30 cm, and S3 = 45 × 15 cm) on the growth and production of oregano, with the goal of optimizing nitrogen levels and spacing for effective cultivation of a recently released Indian oregano variety i.e., CIM-Sudeeksha. The study revealed that the N2S2 treatment (i.e., 100 kg/ha nitrogen and 45 × 30 cm spacing) produced the tallest plants, measuring 63.60±0.79 cm. On the other hand, the N2S3 treatment (i.e., 45×15 cm spacing and 100 kg/ha nitrogen) resulted with the remarkable yields of both fresh and dry herbs and oil, measuring 292.23±2.03 (Fresh herb) and 73.04±2.61 (dry herb) q/ha, 63.37±5.27 (Fresh herb oil), and 56.14±4.14 (Dry herb oil) kg/ha respectively, whereas N3S3 treatment showed highest but insignificantly different dry herb oil content i.e., 56.32±2.42 kg/ha. Also, the chemical composition of N2S2 treatment showed more carvacrol content (56.89 % in fresh and 52.62 % in dry herb) then N2S3 and N3S3 treatment. The results showed that the effects of nitrogen application with rates of 100 kg/ha and 150 kg/ha were similar on almost all agronomic traits and oil yield parameters. Furthermore, the 45×30 cm spacing showed encouraging outcomes, increasing vegetative growth and decreasing plant competition. Given these findings, it is advised to use 45×30 cm spacing and 100 kg/ha nitrogen fertilization for increased Indian oregano production and economical resource utilization.

Wall crossing for K‐moduli spaces of plane curves

AbstractWe construct proper good moduli spaces parametrizing K‐polystable ‐Gorenstein smoothable log Fano pairs , where is a Fano variety and is a rational multiple of the anticanonical divisor. We then establish a wall‐crossing framework of these K‐moduli spaces as varies. The main application in this paper is the case of plane curves of degree as boundary divisors of . In this case, we show that when the coefficient is small, the K‐moduli space of these pairs is isomorphic to the GIT moduli space. We then show that the first wall crossing of these K‐moduli spaces are weighted blow‐ups of Kirwan type. We also describe all wall crossings for degree 4,5,6 and relate the final K‐moduli spaces to Hacking's compactification and the moduli of K3 surfaces.

A geometric p-adic Simpson correspondence in rank one

For any smooth proper rigid space $X$ over a complete algebraically closed extension $K$ of $\mathbb {Q}_p$ we give a geometrisation of the $p$ -adic Simpson correspondence of rank one in terms of analytic moduli spaces: the $p$ -adic character variety is canonically an étale twist of the moduli space of topologically torsion Higgs line bundles over the Hitchin base. This also eliminates the choice of an exponential. The key idea is to relate both sides to moduli spaces of $v$ -line bundles. As an application, we study a major open question in $p$ -adic non-abelian Hodge theory raised by Faltings, namely which Higgs bundles correspond to continuous representations under the $p$ -adic Simpson correspondence. We answer this question in rank one by describing the essential image of the continuous characters $\pi ^{{\mathrm {\acute {e}t}}}_1(X)\to K^\times$ in terms of moduli spaces: for projective $X$ over $K=\mathbb {C}_p$ , it is given by Higgs line bundles with vanishing Chern classes like in complex geometry. However, in general, the correct condition is the strictly stronger assumption that the underlying line bundle is a topologically torsion element in the topological group $\operatorname {Pic}(X)$ .

Extending and improving conical bicombings

We study metric spaces that admit a conical bicombing and thus obey a weak form of non-positive curvature. Prime examples of such spaces are injective metric spaces. In this article, we give a complete characterization of complete metric spaces admitting a conical bicombing by showing that every such space is isometric to a \sigma -convex subset of some injective metric space. In addition, we show that every proper metric space that admits a conical bicombing also admits a consistent bicombing that satisfies certain convexity conditions. This can be seen as a strong indication that a question from Descombes and Lang about improving conical bicombings might have a positive answer. As an application, we prove that any group acting geometrically on a proper metric space with a conical bicombing admits a \mathcal{Z} -structure.