Projective Space Research Articles

Concordance structure set of connected sum of projective spaces

Concordance structure set of connected sum of projective spaces

Minimal Terracini loci in projective space

Minimal Terracini loci in projective space

Local complete intersections and Weierstrass points

This work presents a simple proof that the moduli space of complete integral Gorenstein curves with a prescribed symmetric Weierstrass semigroup becomes a weighted projective space, even for fields of positive characteristic, when the associated monomial curve is a local complete intersection.

On quaternionic bisectional curvature

AbstractIn this article we study the concept of quaternionic bisectional curvature introduced by Chow and Yang in (J Differ Geom 29(2):361–372, 1989) for quaternion-Kähler manifolds. We show that non-negative quaternionic bisectional curvature is only realized for the quaternionic projective space $$\mathbb {H}\textrm{P}^n$$ H P n . We also show that all symmetric quaternion-Kähler manifolds different from $$\mathbb {H}\textrm{P}^n$$ H P n admit quaternionic lines of negative quaternionic bisectional curvature. In particular this implies that non-negative sectional curvature does not imply non-negative quaternionic bisectional curvature. Moreover we give a new and rather short proof of a classification result by A. Gray on compact Kähler manifolds of non-negative sectional curvature.

Period integrals of smooth projective complete intersections as exponential periods

Let X be a smooth projective complete intersection over Q of dimension n−k in the projective space PQn defined by the zero locus of f_(x_)=(f1(x_),⋯,fk(x_)), for given positive integers n and k. For a given primitive homology cycle [γ]∈Hn−k(X(C),Z)0, the period integral is defined to be a linear map from the primitive de Rham cohomology group HdR,primn−k(X(C);Q) to C given by [ω]↦∫γω. The goal of this article is to interpret this period integral as Feynman's path integral of 0-dimensional quantum field theory with the action functional S=∑ℓ=1kyℓfℓ(x_) (in other words, the exponential period with the action functional S) and use this interpretation to develop a formal deformation theory of period integrals of X, which can be viewed as a modern deformation theoretic treatment of the period integrals based on the Maurer-Cartan equation of a dgla (differential graded Lie algebra).

Speed excess and total acceleration: a kinematical approach to entanglement

Abstract The total variance of a spin state is defined as the average of the variances of spin projection measurements along three orthogonal axes. We show that this quantity also gives the squared rotational speed of the state in projective space, averaged over all rotation axes. We compute the addition law, under system composition, for this quantity and find that, in the case of separable states, it is of simple pythagorean form. In the presence of entanglement, we find that the composite state "rotates faster than its parts", thus unveiling a kinematical origin for the correlation of total variance with entanglement. We analyze a similar definition for the acceleration of a state under rotations, for both pure and mixed states, and probe numerically its relation with a wide array of entanglement related measures.

Analysis of Strengthening Beam Structure Case Study on Food Court Building of Ruang Terbuka Hijau (RTH) Project at Alun-Alun Kota Kediri

The Green Open Space (RTH) construction in Kediri City includes a food court building utilizing reinforced concrete structures. During construction, cracking issues occurred in several beam structures due to the inability to bear the design loads effectively, necessitating a strengthening approach. This study aims to develop and evaluate a strengthening method for cracked beam structures by employing concrete jacketing. The specific objective is to improve the structural integrity and load-bearing capacity of these beams to ensure the durability and safety of the building. A concrete jacketing technique was used to reinforce the cracked beams, utilizing K-300 ready-mix concrete and additional reinforcing steel. The study involved structural analysis to assess the load-bearing capacity before and after jacketing, and on-site evaluation was conducted to monitor the method's effectiveness. The findings indicate that the jacketing method significantly increased the beams' bending moment capacity and overall structural strength, successfully addressing the cracks and enhancing the beams' ability to bear the intended loads. The reinforced beams showed improved load distribution and structural resilience performance. Concrete jacketing proved to be an effective method for strengthening the cracked beam structures in the Green Open Space project. The study provides valuable insights for similar future construction projects, suggesting that concrete jacketing can be a reliable reinforcement technique to enhance the durability and safety of building structures.

Exploring Trust Ecology in a Public-Private Partnership for Agricultural Innovation in the United States Bioeconomy

United States (US) federal agencies are endorsing public-private partnerships (PPPs) to link public institutions with industry to develop local supplies of biofuel and build a domestic bioeconomy. Although trust is a critical factor within effective PPPs, few studies have addressed the different types of trust needed to cultivate these partnerships. Employing a mixed-method design, we explore a PPP in the Southeast US through the lens of trust ecology. We describe how participants perceive trust types within different project spaces and how trust changed during the partnership. Our findings highlight the role that different interactive spaces can play in cultivating types of trust that accumulate in an additive fashion. We offer insights on process-design mechanisms and project management strategies that can bolster trust in PPPs.

Idaho libraries to provide private spaces for SUD telehealth treatment

Called the “Third Space Project,” Idaho libraries will provide space for telehealth treatment for substance use disorders (SUDs), with an emphasis on serving rural and high‐need communities. The state Division of Behavioral Health Substance Use Disorder Unit is leading the project in partnership with the Idaho Commission for Libraries (ICfL), with funding by a $500,000 grant from the American Rescue Plan Act's 2021 Substance Use Prevention, Treatment, and Recovery Services Block Grant supplemental.

Transarterial embolization for anterior cranial fossa dural arteriovenous fistula based on multi-modal three-dimensional imaging.

Dural arteriovenous fistula (DAVF) in the anterior cranial fossa (ACF) is known to show a high risk of intracranial hemorrhage. Recently, multi-modal fusion imaging with computed tomography angiography, computed tomography venography, and three-dimensional (3D) rotation angiography have been used preoperatively to ensure anatomical safety. We report on endovascular treatment as a first-line approach for ACFDAVF based on the understanding of vascular anatomy obtained from multi-modal fusion imaging. All patients with ACF-DAVF treated endovascularly as a first-line approach were included in this study. Analyses took into account complications (particularly visual function), immediate angiographic outcomes, and follow-up findings in consecutive patients with ACF-DAVF treated with interventional treatment based on multi-modal fusion imaging. Five patients with ACF-DAVF underwent six sessions of transarterial embolization (TAE) in our institution. The five male patients (mean age, 74.5 years; range, 60-84 years) were treated with liquid embolic agents (Onyx, four procedures; n-butyl 2-cyanoacrylate, two procedures). No difference was seen between preoperative image evaluation and image evaluation during the endovascular procedure, and in all cases, a microcatheter was navigated into a target artery assumed from preoperative multi-modal imaging, allowing treatment completion in a single procedure. In all cases, the shunt disappeared completely and visual function after procedure was maintained. At the last follow-up, all patients showed a modified Rankin scale score of 0 or 1 with no recurrences. Multi-modal fusion imaging facilitates a 3D understanding of the vascular anatomy, allowing TAE as the first-line treatment for ACF-DAVF.

New curvature characterizations for spherical space forms and complex projective spaces

In this paper, we introduce a new positivity notion for curvature of Riemannian manifolds and obtain characterizations for spherical space forms and the complex projective space C P n \mathbb {C}\mathbb {P}^n .

Tangent space functional reconfigurations in individuals at risk for alcohol use disorder

Abstract Human brain function dynamically adjusts to ever-changing stimuli from the external environment. Studies characterizing brain functional reconfiguration are nevertheless scarce. Here we present a principled mathematical framework to quantify brain functional reconfiguration when engaging and disengaging from a stop signal task (SST). We apply tangent space projection (a Riemannian geometry mapping technique) to transform functional connectomes (FCs) of 54 participants and quantify functional reconfiguration using the correlation distance of the resulting tangent-FCs. Our goal was to compare functional reconfigurations in individuals at risk for alcohol use disorder (AUD). We hypothesized that functional reconfigurations when transitioning to/from a task would be influenced by family history of alcohol use disorder (FHA) and other AUD risk factors. Multilinear regression models showed that engaging and disengaging functional reconfiguration were associated with FHA and recent drinking. When engaging in the SST after a rest condition, functional reconfiguration was negatively associated with recent drinking, while functional reconfiguration when disengaging from the SST was negatively associated with FHA. In both models, several other factors contributed to the functional reconfiguration. This study demonstrates that tangent-FCs can characterize task-induced functional reconfiguration, and that it is related to AUD risk.

A remarkable class of elliptic surfaces of amplitude 1 in weighted projective spaces

A remarkable class of elliptic surfaces of amplitude 1 in weighted projective spaces

Roto-Cyclization of 4-Bromopicene in On-Surface Synthesis.

Progress toward single-molecule electronics relies on a thorough understanding of local physico-chemical processes and development of synthetic routines for controlled hetero-coupling. We demonstrate a structurally unexpected ring closure process for a homo-coupled 4,4'-bipicenyl, realized in on-surface synthesis. An initial covalent C-C coupling of 4-bromopicene locks at lower temperatures the position and geometrically shields part of 4,4'-bipicenyl. Employing this effect of shielding might offer a path toward controlled stepwise hetero-coupling. At higher temperatures, a thermally activated three-dimensional rotation upon hydrogen dissociation, a dehydrogenative roto-cyclization, lifts the surface-dimensionality restriction, and leads to the formation of a perylene. Thereby, the shielded molecular part becomes accessible again.

The Living CV project: a model of collaborative learning in third space

The Living CV project is a collaborative initiative launched at a south coast university in the UK, which aims to help students develop their employability skills and evidence their learning outcomes. The project is delivered university-wide from a third space hub, where people from different disciplines and backgrounds come together to work on shared goals. It has therefore provided a way for colleagues across the university to collaborate within third space. In this study we focus on the role of the departmental Living CV Champions and their pivotal role in driving forward this third space project. These champions are situated across the university – in academic departments, in the university’s central Learning and Teaching service and in its career service – but all are working across boundaries and drawing collaborators into the third space of the project. We suggest that the Living CV Champions are also collaboration champions for the institution, in the way in which they support the development of staff networks and knowledge sharing, and therefore the collaborative capital of the institution as a whole. We find that third space projects such as the Living CV can contribute to the development of collaborative capital, act as a gateway for staff to wider communities of practice and build confidence for those engaged in them. In this case study we illustrate one route to achieving this, through a champions model which breaks down traditional academic silos and encourages wider collaboration.

Cyber Resilience Limitations in Space Systems Design Process: Insights from Space Designers

Space technology is integral to modern critical systems, including navigation, communication, weather, financial services, and defence. Despite its significance, space infrastructure faces unique cyber resilience challenges exacerbated by the size, isolation, cost, persistence of legacy systems, and lack of comprehensive cyber resilience engineering standards. This paper examines the engineering challenges associated with incorporating cyber resilience into space design, drawing on insights and experiences from industry experts. Through qualitative interviews with engineers, cybersecurity specialists, project managers, and testers, we identified key themes in engineering methodologies, cybersecurity awareness, and the challenges of integrating cyber resilience into space projects. Participants emphasised the importance of incorporating cybersecurity considerations from the earliest stages of design, advocating for principles such as zero-trust architecture and security by design. Our findings reveal that experts favour Model-Based Systems Engineering (MBSE) and Agile methodologies, highlighting their synergy in developing flexible and resilient systems. The study also underscores the tension between principles-based standards, which offer flexibility but can lead to inconsistent implementation, and compliance-based approaches, which provide clear measures but may struggle to adapt to evolving threats. Additionally, the research recognises significant barriers to achieving cyber resilience, including insider threats, the complexity of testing and validation, and budget constraints. Effective stakeholder engagement and innovative funding models are crucial for fostering a culture of cybersecurity awareness and investment in necessary technologies. This study highlights the need for a comprehensive cyber resilience framework that integrates diverse engineering methodologies and proactive security measures, ensuring the resilience of space infrastructure against emerging cyber threats.

Choosing a promotion channel for a startup project in the modern media space

Relevance. The startup market is becoming increasingly saturated. Effective promotion channels allow you to stand out from the competition and attract the attention of the target audience. Startups often work with a limited budget. Optimizing the choice of promotion channels is critical to maximizing the return on investment. Modern media management covers many platforms (social networks, blogs, video hosting, etc.). Choosing the right channel helps to optimally use resources and ensure maximum visibility. Different channels are suitable for different target groups. An effective choice of promotion channel helps to more accurately reach the desired audience, taking into account its preferences and behavior. Consumers are increasingly paying attention to digital communication channels. Taking into account current trends and preferences allows you to improve interaction with the audience. The influence of social networks and bloggers is becoming an important mechanism for creating trust among consumers. This can significantly increase the recognition of a startup. All this emphasizes the importance of a strategic approach to choosing promotion channels for a successful launch and sustainable growth of a startup project in the modern media landscape.The purpose of the study is to choose a promotion channel for a startup project in the modern media space.Objectives: to substantiate the relevance of choosing a promotion channel for a startup in the modern media space; to study the demand and effectiveness of modern promotion channels; to use in practice the method of multicriteria selection of promotion channels for a startup project; to substantiate the results obtained.Methodology. The research methodology is based on the methods of comparison and comparison, deduction and induction, qualitative and quantitative analysis, as well as the Churchman-Ackoff multi-criteria assessment method.Results. The study substantiates the relevance of choosing a promotion channel for a startup in the modern media space; the demand and effectiveness of modern promotion channels are studied; the method of multi-criteria selection of channels for promoting a startup project was used in practice; the obtained results were substantiated.Conclusions. The effectiveness of the selected channels for promoting a startup project in the modern media space was proven as conclusions.

Half-space results for generalized linear Weingarten hypersurfaces immersed in the real projective space

Half-space results for generalized linear Weingarten hypersurfaces immersed in the real projective space

Infinitely many exotic Lagrangian tori in higher projective spaces

In de Velloso Vianna (J Topol 9(2):535-551, 2016), Vianna constructed infinitely many exotic Lagrangian tori in P2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {P}^2$$\\end{document}. We lift these tori to higher dimensional projective spaces and show that they remain non-symplectomorphic. Our proof is elementary except for an application of the wall-crossing formula of Pascaleff and Tonkonog (Adv Math 361:106850, 2020).

Additive actions on projective hypersurfaces with a finite number of orbits

An induced additive action on a projective variety [Formula: see text] is a regular action of the group [Formula: see text] on [Formula: see text] with an open orbit, which can be extended to a regular action on the ambient projective space [Formula: see text]. In this work, we classify all projective hypersurfaces admitting an induced additive action with a finite number of orbits.