Hasil untuk "Unlocalized maps (Asian studies only)"

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arXiv Open Access 2025
Camera-Only Bird's Eye View Perception: A Neural Approach to LiDAR-Free Environmental Mapping for Autonomous Vehicles

Anupkumar Bochare

Autonomous vehicle perception systems have traditionally relied on costly LiDAR sensors to generate precise environmental representations. In this paper, we propose a camera-only perception framework that produces Bird's Eye View (BEV) maps by extending the Lift-Splat-Shoot architecture. Our method combines YOLOv11-based object detection with DepthAnythingV2 monocular depth estimation across multi-camera inputs to achieve comprehensive 360-degree scene understanding. We evaluate our approach on the OpenLane-V2 and NuScenes datasets, achieving up to 85% road segmentation accuracy and 85-90% vehicle detection rates when compared against LiDAR ground truth, with average positional errors limited to 1.2 meters. These results highlight the potential of deep learning to extract rich spatial information using only camera inputs, enabling cost-efficient autonomous navigation without sacrificing accuracy.

en cs.CV
arXiv Open Access 2025
A Finite-State Symbolic Automaton Model for the Collatz Map and Its Convergence Properties

Leonard Ben Aurel Brauer

We present a finite-state, deterministic automaton that emulates the Collatz function through digitwise transitions on base-10 representations. Each digit is represented as a symbolic triplet (r, p, c) encoding its value, the parity of the next digit, and an incoming carry propagated from the lower digit. This yields exactly 60 possible local states. The automaton applies local, parity-aware rules that collectively reconstruct the global arithmetic of the Collatz map. We show that all symbolic trajectories converge in finitely many steps to a unique terminal cycle (4, 0, 0) -> (2, 0, 0) -> (1, 0, 0), with all higher digit positions degenerating to the absorbing state (0, 0, 0). This collapse reveals a canonical symbolic normal form of Collatz dynamics. In parallel, a binary view explains the dynamics as alternating bit-length growth and contraction, aligning with known heuristics for Collatz convergence. This structural perspective is further reinforced by a symbolic drift function and a ranking potential that together explain and formalize the convergence process.

en math.GM, cs.FL
arXiv Open Access 2024
Triangulating on Possible Futures: Conducting User Studies on Several Futures Instead of Only One

Antti Salovaara, Leevi Vahvelainen

Plausible findings about futures are inherently difficult to obtain as they require critical, well-informed speculations backed with data. HCI scholars tackle this challenge via user studies wherein futuristic prototypes and other props concretise possible futures for participants. By observing participants' actions, researchers then can 'time travel' to see that future as reality, in action. However, such studies may yield particularised findings, inherent to study's intricacies, and lack broader plausibility. This paper suggests that triangulation of possible futures may help researchers disentangle particularities from more generalisable findings. We explored this approach by conducting a study on two alternative futures of AI-augmented knowledge work. Some findings emerged in both futures while others were particular to only one or the other. This approach enabled cross-checking of plausibility and simultaneously afforded deeper insight. The paper discusses how triangulating possible futures renders HCI studies more future-proof and provides means for reflective anticipation of possible futures.

arXiv Open Access 2024
Quantale-valued maps and partial maps

Lili Shen, Xiaoye Tang

Let $\mathsf{Q}$ be a commutative and unital quantale. By a $\mathsf{Q}$-map we mean a left adjoint in the quantaloid of sets and $\mathsf{Q}$-relations, and by a partial $\mathsf{Q}$-map we refer to a Kleisli morphism with respect to the maybe monad on the category $\mathsf{Q}\text{-}\mathbf{Map}$ of sets and $\mathsf{Q}$-maps. It is shown that every $\mathsf{Q}$-map is symmetric if and only if $\mathsf{Q}$ is weakly lean, and that every $\mathsf{Q}$-map is exactly a map in $\mathbf{Set}$ if and only $\mathsf{Q}$ is lean. Moreover, assuming the axiom of choice, it is shown that the category of sets and partial $\mathsf{Q}$-maps is monadic over $\mathsf{Q}\text{-}\mathbf{Map}$.

arXiv Open Access 2023
Centralizers of non-elliptic univalent self-maps and the embeddability problem in the unit disc

Manuel D. Contreras, Santiago Díaz-Madrigal, Pavel Gumenyuk

The embeddability problem is a very old and hard problem in discrete holomorphic iteration which deals with determining general conditions on a given univalent self-map $\varphi$ of the unit disc $\mathbb D$ in order to be contained in a continuous one-parameter semigroup. In this paper, we tackle this embedding problem by establishing different dichotomy results about the centralizer of $\varphi$ (i.e. the set of all univalent self-maps commuting with $\varphi$) which depend strongly on the dynamical character of $\varphi$. Our approach is, in part, based on a new technique to obtain simultaneous linearizations of two non-elliptic univalent self-maps of the unit disc, which might be interesting on their own. We also introduce and study several closed additive subsemigroups of the complex plane that collect the main features of the centralizer of $\varphi$ and which play a prominent position in those dichotomy results.

en math.CV, math.DS
arXiv Open Access 2023
Before-after safety analysis of a shared space implementation

Federico Orsini, Mariana Batista, Bernhard Friedrich et al.

Shared spaces aim to reduce the dominance of motor vehicles by promoting pedestrian and cyclist activity and minimizing segregation between road users. Despite the intended scope to improve the safety of vulnerable road users, only few works in the literature focused on before after safety evaluations, mainly analyzing changes in users trajectories and speeds, traffic volumes, and conflict counts, which, while useful, cannot univocally quantify road safety. Here, we propose a more advanced methodology, based on surrogate measures of safety and Extreme Value Theory, to assess road safety before and after the implementation of a shared space. The aim is to produce a crash risk estimation in different scenarios, obtaining a quantitative and comprehensive indicator, useful to practitioners for evaluating the safety of urban design solutions. A real world case study illustrates the proposed procedure. Video data were collected on two separate days, before and after a shared space implementation, and were semiautomatically processed to extract road users trajectories. Analysis of traffic volumes, trajectories, speeds and yield ratios allowed to understand the spatial behavior of road users in the two scenarios. Traffic conflicts, identified with an innovative surrogate measure of safety called time to avoided collision point, TTAC, were then used to estimate a Lomax distribution, and therefore to model the probabilistic relationship between conflicts and crashes, eventually retrieving a crash risk estimate. Results show that the analyzed shared space was able to significantly reduce the risk of crashes, and these findings are consistent with the observed changes in users speed and spatial behavior. The analyzed case study and its limitations were useful in highlighting the methodology main features and suggesting practical prescriptions for practitioners.

arXiv Open Access 2023
A PRISMA-driven systematic mapping study on system assurance weakeners

Kimya Khakzad Shahandashti, Alvine B. Belle, Timothy C. Lethbridge et al.

Context: An assurance case is a structured hierarchy of claims aiming at demonstrating that a given mission-critical system supports specific requirements (e.g., safety, security, privacy). The presence of assurance weakeners (i.e., assurance deficits, logical fallacies) in assurance cases reflects insufficient evidence, knowledge, or gaps in reasoning. These weakeners can undermine confidence in assurance arguments, potentially hindering the verification of mission-critical system capabilities. Objectives: As a stepping stone for future research on assurance weakeners, we aim to initiate the first comprehensive systematic mapping study on this subject. Methods: We followed the well-established PRISMA 2020 and SEGRESS guidelines to conduct our systematic mapping study. We searched for primary studies in five digital libraries and focused on the 2012-2023 publication year range. Our selection criteria focused on studies addressing assurance weakeners at the modeling level, resulting in the inclusion of 39 primary studies in our systematic review. Results: Our systematic mapping study reports a taxonomy (map) that provides a uniform categorization of assurance weakeners and approaches proposed to manage them at the modeling level. Conclusion: Our study findings suggest that the SACM (Structured Assurance Case Metamodel) -- a standard specified by the OMG (Object Management Group) -- may be the best specification to capture structured arguments and reason about their potential assurance weakeners.

en cs.SE
arXiv Open Access 2022
Listen to Users, but Only 85% of the Time: How Black Swans Can Save Innovation in a Data-Driven World

Maximilian Speicher

Data-driven design is a proven success factor that more and more digital businesses embrace. At the same time, academics and practitioners alike warn that when virtually everything must be tested and proven with numbers, that can stifle creativity and innovation. This article argues that Taleb's Black Swan theory can solve this dilemma. It shows that online experimentation, and therefore digital design, are fat-tailed phenomena and, hence, prone to Black Swans. It introduces the notion of Black Swan designs -- "crazy" designs that make sense only in hindsight -- along with four specific criteria. To ensure incremental improvements and their potential for innovation, businesses should apply Taleb's barbell strategy: Invest 85-90% of resources into data-driven approaches and 10-15% into potential Black Swans.

en cs.HC
arXiv Open Access 2022
Analysis of the Driving Factors of Implementing Green Supply Chain Management in SME in the City of Semarang

Nanang Adie Setyawan, Hadiahti Utami, Bayu Setyo Nugroho et al.

This study set out to determine what motivated SMEs in Semarang City to undertake green supply chain management during the COVID-19 and New Normal pandemics. The purposive sampling approach was used as the sampling methodology in this investigation. There are 100 respondents in the research samples. The AMOS 24.0 program's structural equation modelling (SEM) is used in this research method. According to the study's findings, the Strategic Orientation variable significantly and favourably affects the Green Supply Chain Management variable expected to have a value of 0.945, and the Government Regulation variable has a positive and strong influence on the variable Green Supply Chain Management with an estimated value of 0.070, the Green Supply Chain Management variable with an estimated value of has a positive and significant impact on the environmental performance variable. 0.504, the Strategic Orientation variable with an estimated value of has a positive and significant impact on the environmental performance variable. 0.442, The Environmental Performance variable is directly impacted positively and significantly by the Government Regulation variable, with an estimated value of 0.041. This significant positive influence is because SMEs in Semarang City have government regulations, along with government support for facilities regarding efforts to implement the concept of environmental concern, causing high environmental performance caused by the optimal implementation of Green supply chain management is built on a collaboration between the government and the supply chain's participants.

arXiv Open Access 2022
Which Factors are associated with Open Access Publishing? A Springer Nature Case Study

Fakhri Momeni, Stefan Dietze, Philipp Mayr et al.

Open Access (OA) facilitates access to articles. But, authors or funders often must pay the publishing costs preventing authors who do not receive financial support from participating in OA publishing and citation advantage for OA articles. OA may exacerbate existing inequalities in the publication system rather than overcome them. To investigate this, we studied 522,411 articles published by Springer Nature. Employing correlation and regression analyses, we describe the relationship between authors affiliated with countries from different income levels, their choice of publishing model, and the citation impact of their papers. A machine learning classification method helped us to explore the importance of different features in predicting the publishing model. The results show that authors eligible for APC waivers publish more in gold-OA journals than others. In contrast, authors eligible for an APC discount have the lowest ratio of OA publications, leading to the assumption that this discount insufficiently motivates authors to publish in gold-OA journals. We found a strong correlation between the journal rank and the publishing model in gold-OA journals, whereas the OA option is mostly avoided in hybrid journals. Also, results show that the countries' income level, seniority, and experience with OA publications are the most predictive factors for OA publishing in hybrid journals.

en cs.DL, cs.LG
arXiv Open Access 2021
You Only Write Thrice: Creating Documents, Computational Notebooks and Presentations From a Single Source

Kacper Sokol, Peter Flach

Academic trade requires juggling multiple variants of the same content published in different formats: manuscripts, presentations, posters and computational notebooks. The need to track versions to accommodate for the write--review--rebut--revise life-cycle adds another layer of complexity. We propose to significantly reduce this burden by maintaining a single source document in a version-controlled environment (such as git), adding functionality to generate a collection of output formats popular in academia. To this end, we utilise various open-source tools from the Jupyter scientific computing ecosystem and operationalise selected software engineering concepts. We offer a proof-of-concept workflow that composes Jupyter Book (an online document), Jupyter Notebook (a computational narrative) and reveal.js slides from a single markdown source file. Hosted on GitHub, our approach supports change tracking and versioning, as well as a transparent review process based on the underlying code issue management infrastructure. An exhibit of our workflow can be previewed at https://so-cool.github.io/you-only-write-thrice/.

en cs.PL, cs.AI
S2 Open Access 2021
The Other Milk: Reinventing Soy in Republican China

M. King

Among the historical gems that Jia-Chen Fu has unearthed in her intricate study of the transformation of soymilk in modern Chinese history is a postcard of skinny Granny Soybean and her four soybean grandkids, armed with sticks, chasing a fat Madame Cow into the front gate of a museum. Printed by the China Nutritional Aid Council, a social welfare organization active from 1939–42, which attempted to produce and distribute soymilk and soybean cakes to children across southwestern China during World War II, the postcard hints at a world where dairy would be doomed to historical obsolescence, while the vigorous and energetic Granny Soybean and her many derivative products would rule the day. Yet this quirky postcard offers more than just an unforgettable image: it also suggests the broader context of national rivalry that underlay all Republican era (1912–1949) attempts to refashion the traditional Chinese drink of soymilk as a nutritious, scientific, modern Chinese beverage. After all, Granny Soybean was not just any generic soybean lady: she was recognizably Chinese, and looked less like a granny than a young, modern Chinese housewife, with her trim black hair coiffed just so, and high-heel wedge sandals at the end of her slender legs. Moreover, the spots on Madame Cow’s back bore a striking resemblance to a map of the Pacific rim, with the East Asian coastline facing off against North America. For Chinese audiences, the postcard drew upon the close association between Western diets and the heavy consumption of dairy products such as cow’s milk, while the soybean was considered a native foodstuff. Fu’s fascinating book examines the scientific worldviews that gathered momentum in the Republican era to create not only the Granny Soybean postcard, but also social welfare organizations, such as the China Nutritional Aid Council. These artifacts and activities resulted from the work of a pioneering generation of nutritional scientists in China, including men like Wu Xian (1893–1959), Chinese biochemist

arXiv Open Access 2020
A User Study to Investigate Semantically Relevant Contextual Information of WWW Images

Fariza Fauzi, Mohammed Belkhatir

The contextual information of Web images is investigated to address the issue of enriching their index characterizations with semantic descriptors and therefore bridge the semantic gap (i.e. the gap between the low-level content-based description of images and their semantic interpretation). Although we are highly motivated by the availability of rich knowledge on the Web and the relative success achieved by commercial search engines in indexing images using surrounding text-based information in webpages, we are aware that the unpredictable quality of the surrounding text is a major limiting factor. In order to improve its quality, we highlight contextual information which is relevant for the semantic characterization of Web images and study its statistical properties in terms of its location and nature considering a classification into five semantic concept classes: signal, object, scene, abstract and relational. A user study is conducted to validate the results. The results suggest that there are several locations that consistently contain relevant textual information with respect to the image. The importance of each location is influenced by the type of webpage as the results show the different distribution of relevant contextual information across the locations for different webpage types. The frequently found semantic concept classes are object and abstract. Another important outcome of the user study shows that a webpage is not an atomic unit and can be further partitioned into smaller segments. Segments containing images are of interest and termed as image segments. We observe that users typically single out textual information which they consider relevant to the image from the textual information bounded within the image segment.

S2 Open Access 2019
The Role of Capital on Islamic Bank Spin-Offs in Indonesia

Muhammad Budi Prasetyo, Rizky Luxianto, R. Baskoro et al.

Research Aims: Some Islamic banks have experienced decreasing performance after spinning off from the parent company, and it is presumed that the amount of capital may have contributed to the decline. Hence, this paper aims to find a minimum amount of capital that Islamic banks must own after spin-offs in order to be able to compete in the market and to achieve excellent performance. Design/Methodology/Approach: We employ the OLS method for small banks (assets below Rp 5 trillion) with variable Capital as the dependent variable and Bank Performance (ROA, ROE, BOPO, and NPL) as the independent variable. We conduct several rounds of regression analysis by including different dummy variables to capture an increase in bank performance when certain capital limits are applied. Various results of the interaction between Capital and Bank Performance are mapped into the frontier line formed by the regression equation. We then compare the frontier results with the actual bank identifier to map the position of each bank relative to the frontier. We add cluster analysis to confirm the results further. Research Findings: Descriptive statistics of the small banks shows that conventional banks perform better in overall performance, efficiency and risk in comparison with the Islamic banks. Several dummy variables are set to represent the size of bank capital (Rp. 800 billion, Rp. 1 trillion, Rp. 1.2 trillion, and Rp. 1.5 trillion), and all dummy variables are significant; the corresponding coefficient reveals that the higher the capital, the better the average performance. Also, the relationship between performance and bank capital is a non-linear (quadratic) relationship that is convex, indicating that capital is not the only critical factor that contributes to the bank’s improvement. The cluster analysis partially confirms that there is a specific pattern of capital in each of the clusters. Theoretical Contribution/Originality: The result of this study is in line with some previous literature on the relationship between capital and bank performance. In banks with small capital, capital has a positive influence on bank performance but has the opposite effect after reaching a certain point. In the literature related to spin-offs in Islamic banking, th ere are only a few studies about the performance of small banks after the spin-off and even fewer (or none) that discuss the critical role of capital and its relationship with the bank’s performance after the spin-off. Our findings support previous studies conducted by Siswantoro (2014). Managerial Implications in the South East Asian Context: With the implementation of the dual banking system in several southeast Asian countries, many conventional banks have Islamic bank subsidiaries. Findings from this research could help banking regulators in the South East Asian countries to carefully re-evaluate their spin-off strategy for the unit bank, especially regarding the limit of capital requirement before the spin-off. The bigger the capital size, the better the performance of the business unit after the spin-off. Research Limitation & Implications: This research only uses variable capital as a determinant for the bank’s performance after spin-offs. However, as suggested by the resulting R-Squared from the regression formula (66%) and the convex trend line of the frontier analysis, other factors may contribute to the banking performance. Future research should include several other indicators for spin-off success, such as parent-subsidiary relationship (Tubke, 2004; Lindholm-Dahlstrand, 2000) and parent’s size (Cristo and Falk, 2006), credit and liquidity position before spin-offs.

7 sitasi en Economics
arXiv Open Access 2019
A systematic mapping study of developer social network research

Steffen Herbold, Aynur Amirfallah, Fabian Trautsch et al.

Developer social networks (DSNs) are a tool for the analysis of community structures and collaborations between developers in software projects and software ecosystems. Within this paper, we present the results of a systematic mapping study on the use of DSNs in software engineering research. We identified 255 primary studies on DSNs. We mapped the primary studies to research directions, collected information about the data sources and the size of the studies, and conducted a bibliometric assessment. We found that nearly half of the research investigates the structure of developer communities. Other frequent topics are prediction systems build using DSNs, collaboration behavior between developers, and the roles of developers. Moreover, we determined that many publications use a small sample size regarding the number of projects, which could be problematic for the external validity of the research. Our study uncovered several open issues in the state of the art, e.g., studying inter-company collaborations, using multiple information sources for DSN research, as well as general lack of reporting guidelines or replication studies.

en cs.SE
arXiv Open Access 2019
Shoulder Surfing: From An Experimental Study to a Comparative Framework

Leon Bošnjak, Boštjan Brumen

Shoulder surfing is an attack vector widely recognized as a real threat - enough to warrant researchers dedicating a considerable effort toward designing novel authentication methods to be shoulder surfing resistant. Despite a multitude of proposed solutions over the years, few have employed empirical evaluations and comparisons between different methods, and our understanding of the shoulder surfing phenomenon remains limited. Barring the challenges in experimental design, the reason for that can be primarily attributed to the lack of objective and comparable vulnerability measures. In this paper, we develop an ensemble of vulnerability metrics, a first endeavour toward a comprehensive assessment of a given method's susceptibility to observational attacks. In the largest on-site shoulder surfing experiment (n = 274) to date, we verify the model on four conceptually different authentication methods in two observation scenarios. On the example of a novel hybrid authentication method based on associations, we explore the effect of input type on the adversary's effectiveness. We provide first empirical evidence that graphical passwords are easier to observe; however, that does not necessarily mean that the observed information will allow the attacker to guess the victim's password easier. An in-depth analysis of individual metrics within the clusters offers insight into many additional aspects of the shoulder surfing attack not explored before. Our comparative framework makes an advancement in evaluation of shoulder surfing and furthers our understanding of observational attacks. The results have important implications for future shoulder surfing studies and the field of Password Security as a whole.

S2 Open Access 2019
Timothy Bruce Mitford. 2018. East of Asia Minor: Rome's hidden frontier. Oxford: Oxford University Press; 978-0-19-814874-6 (volume 1), 978-0-19-872516-9 (volume 2) £225.

J. Crow

Until the mid twentieth century, the study of Roman frontiers beyond continental Europe and Britain was largely the prerogative of military and colonial representatives. InAlgeria,Colonel Baradez (Fossatum Africae), R.G. Goodchild in Libya, and most spectacularly, Père Poidebard (La trace de Rome), the Jesuit father who mapped, with the assistance of the biplanes of the French-Syrian mandate, a palimpsest of Roman to Umayyad sites across the Syrian pre-desert. Poidebard’s map stops abruptly at the Turkish border and it has long been a desideratum of Roman frontier studies to map and study the traces of the Roman frontier on the Upper Euphrates. Timothy Bruce Mitford began his doctoral research on the Euphrates frontier initially under the supervision of Sir Ian Richmond in 1963. His fieldwork commenced at an opportune time since there were already plans to create a series of dams in the river’s vertiginous gorges. Indeed, less than a decade later, the first of these at Keban flooded the only excavated fort on the entire line at Pağnik Öreni, which was never fully published. Numerous articles by Mitford have followed over the years, mostly concerning epigraphy and history, but the full exposition of his researches has had to wait. For much of his career he was a serving naval officer, but with great tenacity he continued an involvement in frontier research, often with a permit and representative from the Turkish ministry of culture. The Cappadocian frontier was no ordinary Roman border. As with Syria, the Mediterranean superpower confronted Iran to the east, initially facing the Parthians and then, from the early third century AD, the Sasanians. In between was a patchwork of buffer states and client kingdoms, including Commagene with its great monument on Nemrut Dağ, and, most significantly, Armenia. Up to the mid first century, Roman control conforms to Luttwack’s model of a ‘hegemonic empire’ to be succeeded by the direct territorial presence of legions and other garrisons at Samosata (Commagene) and farther north at Melitene (Eski Malatya) and Satala (Sadak) and later Trapezous (Trabzon). Roads linked the major garrisons, but the river often did not offer a suitable route as it forced a passage through steep gorges across the high ranges of the Taurus and Armenian Taurus. North from Erzincan, the frontier road struck off towards the Pontic Alps and the Black Sea. Few Roman frontiers presented such challenges of topography and extremes of climate. Yet the political significance of its neighbours ensured that we have extensive written accounts of Roman campaigns including the rare insight of the expedition of a provincial army under its governor Fl. Arrianus.

S2 Open Access 2018
Temporal trends and characteristics of clinical trials for which only one racial or ethnic group is eligible

B. Egleston, O. Pedraza, Y. Wong et al.

Background Increasing diversity in clinical trials may be worthwhile. We examined clinical trials that restricted eligibility to a single race or ethnicity. Methods We reviewed 19,246 trials registered on ClinicalTrials.gov through January 2013. We mapped trial ZIP-codes to U.S. Census and American Community Survey data. The outcome was whether trials required participants to be from a single racial or ethnic group. Results In adjusted analyses, the odds of trials restricting eligibility to a single race/ethnicity increased by 4% per year (95% CI 1.01–1.08, p = .024). Behavioral (5.79% with single race/ethnicity requirements), skin-related (4.49%), and Vitamin D (6.14%) studies had higher rates of single race/ethnicity requirements. Many other trial-specific characteristics, such as funding agency and region of the U.S. in which the trial opened, were associated with eligibility restrictions. In terms of neighborhood characteristics, studies with single race eligibility requirements were more likely to be located in ZIP-codes with greater percentages of those self-reporting the characteristic. For example, 35.2% (SD = 24.9%) of the population self-reported themselves as Black or African American in ZIP-codes with trials requiring participants to be Black/African American, but only 5.9% (SD = 6.9%) self-reported themselves as Black/African American in ZIP-codes with trials that required Asian ethnicity. In ZIP-codes with trials requiring Asian ethnicity, 24.6% (SD = 16.2%) self-reported as Asian. In ZIP-codes with trials requiring Hispanic/Latino ethnicity, 33.3% (SD = 28.5%) self-reported as Hispanic/Latino. Neighborhood level poverty rates and reduced English language ability were also associated with more single race eligibility requirements. Conclusions In selected fields, there has been a modest temporal increase in single race/ethnicity inclusion requirements. Some studies may not fall under regulatory purview and hence may be less likely to include diverse samples. Conversely, some eligibility requirements may be related to health disparities research. Future work should examine whether targeted enrollment criteria facilitates development of personalized medicine or reduces trial access.

3 sitasi en Medicine
arXiv Open Access 2017
Mapping properties of the Hilbert and Fubini--Study maps in Kähler geometry

Yoshinori Hashimoto

Suppose that we have a compact Kähler manifold $X$ with a very ample line bundle $\mathcal{L}$. We prove that any positive definite hermitian form on the space $H^0 (X,\mathcal{L})$ of holomorphic sections can be written as an $L^2$-inner product with respect to an appropriate hermitian metric on $\mathcal{L}$. We apply this result to show that the Fubini--Study map, which associates a hermitian metric on $\mathcal{L}$ to a hermitian form on $H^0 (X,\mathcal{L})$, is injective.

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