An official website of the United States government
PurposeThe paper aims to determine the rational homotopy type of the total space of projectivized bundles over complex projective spaces using Sullivan minimal models, providing insights into the algebraic structure of these spaces. Design/methodology/approachThe paper utilises techniques from Sullivan’s theory of minimal models to analyse the differential graded algebraic structure of projectivized bundles. It employs algebraic methods to compute the Sullivan minimal model of and establish relationships with the base space. FindingsThe paper determines the rational homotopy type of projectivized bundles over complex projective spaces. Of great interest is how the Chern classes of the fibre space and base space, play a critical role in determining the Sullivan model ofP(E). We also provide the homogeneous space ofP(E)whenn = 2. Finally, we prove the formality ofP(E)over a homogeneous space of equal rank. Research limitations/implicationsLimitations may include the complexity of computing minimal models for higher-dimensional bundles. Practical implicationsUnderstanding the rational homotopy type of projectivized bundles facilitates computations in algebraic topology and differential geometry, potentially aiding in applications such as topological data analysis and geometric modelling. Social implicationsWhile the direct social impact may be indirect, advancements in algebraic topology contribute to broader mathematical knowledge, which can underpin developments in science, engineering, and technology with societal benefits. Originality/valueThe paper’s originality lies in its application of Sullivan minimal models to determine the rational homotopy type of projectivized bundles over complex projective spaces, offering valuable insights into the algebraic structure of these spaces and their associated complex vector bundles.
more »
« less
This content will become publicly available on October 7, 2026
Central values of zeta functions of non-Galois cubic fields
Abstract The Dedekind zeta functions of infinitely many non-Galois cubic fields have negative central values.
more »
« less
- PAR ID:
- 10641966
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Inventiones mathematicae
- ISSN:
- 0020-9910
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract BackgroundPressure-sensitive adhesives (PSAs) are integral to various industrial applications, yet a significant gap remains in accurately assessing their impact properties under dynamic conditions. This limitation hampers the optimization of PSAs for specific uses where impact resistance is critical. ObjectiveThis study aims to develop an experimental method to evaluate the impact properties of PSAs, providing a reliable and reproducible technique to assess their performance. MethodWe designed an experimental setup to simulate real-world impact conditions, incorporating high-speed cameras and an image analysis algorithm to capture the adhesive's behavior under sudden loads. The method's novelty lies in its ability to quantify maximum failure load and adhesion failure mechanisms in the dynamic loading of PSAs. ResultsThe experimental results reveal critical insights into the impact resistance of various PSA formulations, highlighting significant differences in energy dissipation and failure patterns. ConclusionThese findings offer new data not previously available in the literature, enabling a more precise evaluation of PSA performance. The developed method provides a robust framework for assessing the impact properties of PSAs, offering valuable guidance for the design and selection of adhesives in applications requiring enhanced impact resistance. This work bridges the gap between quasi-static testing and realistic dynamic performance, contributing to the advancement of PSA technology.more » « less
-
Abstract AimQuantifying the phylogenetic diversity of temperate trees is essential for understanding the processes that have shaped the modern distribution of temperate broadleaf forest and other major forest biomes. Here, we focus on Fagales, an iconic member of forests worldwide, to uncover global diversity and endemism patterns and investigate the distribution of root nodule symbiosis (RNS), an important morphological specialisation in this clade, as a key factor behind these patterns. LocationGlobal. TaxonFagales. MethodsWe combined phylogenetic data covering 60.2% of living species, fine‐scale distribution models covering 90% of species, and nodulation data covering all species to investigate the distribution of species richness and phylogenetic diversity at fine spatial scales compared to the distribution of RNS. We identify abiotic environmental factors associated with RNS and with Fagales diversity in general. ResultsWe find the highest species richness in temperate east Asia, eastern North America, and equatorial montane regions of Asia and Central America. By contrast, relative phylogenetic diversity (RPD) is highest at higher latitudes, where RNS also predominates. We found a strong spatial structuring of regionalisations of Fagales floras, reflecting distinct Northern and Southern Hemisphere floras (except a unique Afro‐Boreal region), each with distinct RNS‐environment relationships. Main ConclusionsAlthough species richness and phylogenetic regionalisation for Fagales accord well with traditional biogeographic concepts for temperate forests, this is not the case for RPD. RNS is almost universal in the highest RPD regions, which may reflect ecological filtering promoting RNS in these regions. Our results highlight the utility of global‐scale, clade‐specific spatial phylogenetics and its utility for understanding drivers of diversity in species‐rich clades.more » « less
-
Abstract AimUnderstanding and predicting the biological consequences of climate change requires considering the thermal sensitivity of organisms relative to environmental temperatures. One common approach involves ‘thermal safety margins’ (TSMs), which are generally estimated as the temperature differential between the highest temperature an organism can tolerate (critical thermal maximum, CTmax) and the mean or maximum environmental temperature it experiences. Yet, organisms face thermal stress and performance loss at body temperatures below their CTmax,and the steepness of that loss increases with the asymmetry of the thermal performance curve (TPC). LocationGlobal. Time period2015–2019. Major taxa studiedAnts, fish, insects, lizards and phytoplankton. MethodsWe examine variability in TPC asymmetry and the implications for thermal stress for 384 populations from 289 species across taxa and for metrics including ant and lizard locomotion, fish growth, and insect and phytoplankton fitness. ResultsWe find that the thermal optimum (Topt, beyond which performance declines) is more labile than CTmax, inducing interspecific variation in asymmetry. Importantly, the degree of TPC asymmetry increases with Topt. Thus, even though populations with higher Topts in a hot environment might experience above‐optimal body temperatures less often than do populations with lower Topts, they nonetheless experience steeper declines in performance at high body temperatures. Estimates of the annual cumulative decline in performance for temperatures above Toptsuggest that TPC asymmetry alters the onset, rate and severity of performance decrement at high body temperatures. Main conclusionsSpecies with the same TSMs can experience different thermal risk due to differences in TPC asymmetry. Metrics that incorporate additional aspects of TPC shape better capture the thermal risk of climate change than do TSMs.more » « less
-
ObjectivesThis study aimed to examine concurrent polysubstance use of alcohol, tobacco and marijuana and determine correlations with access to marijuana, friend and familial drug use habits, risk perception and the age of initiation associated with the singular use of these substances. DesignA secondary data analysis. SettingUsed the Jamaica National Drug Prevalence Survey 2016 dataset. ParticipantsInvolved the entire dataset comprising 4623 randomly selected respondents between 12 and 65 years old. Outcome measuresPrimary outcome: concurrent polysubstance use recorded as using two or more of alcohol, tobacco and marijuana. Predictor variables include risk perception and age of initiation of singular alcohol, tobacco and marijuana use, ease of marijuana access and family and friend alcohol and illegal drug use. ResultsApproximately 58%–66% of respondents commenced singular alcohol, tobacco or marijuana use under 17. Participants commencing marijuana use at 11 years and under and between 12 and 17 were 3.346 and 4.560 times more likely to report past month concurrent polysubstance use (p=0.030 and p<0.001). Respondents who did not believe that smoking tobacco sometimes (p=0.049), and smoking marijuana sometimes and often was harmful, had increased odds of concurrent polysubstance use (p=0.047 and p<0.001, respectively). Respondents who indicated access to marijuana as easy were significantly more likely to report past month concurrent polysubstance use compared with those who reported access as difficult (p=0.002). Participants who indicated that friends or family members get drunk and take illegal drugs were associated with 1.722 and 1.864 increased odds of reporting past month concurrent polysubstance use (p=0.004 and p=0.017, respectively). ConclusionsDecreased perceived risk, childhood and adolescent age of initiation and easy access to marijuana were significantly associated with polysubstance use among Jamaicans. The influence of friends and family members’ drug and alcohol use behaviours on individuals developing polysubstance use habits further endorses the need for interventions.more » « less
