Action Of Group Research Articles

Higher Chow cycles on a family of Kummer surfaces

Abstract We construct a collection of families of higher Chow cycles of type $(2,1)$ on a two-dimensional family of Kummer surfaces, and prove that for a very general member, they generate a subgroup of rank $\ge 18$ in the indecomposable part of the higher Chow group. Construction of the cycles uses a finite group action on the family, and the proof of their linear independence uses Picard–Fuchs differential operators.

Finite odometer factors of rank one group actions

In this paper, we give explicit conditions characterizing the Følner rank one group actions that factor onto a finite odometer; those that factor onto an arbitrary, but specified odometer, and those that factor onto an unspecified odometer. We also give explicit conditions describing the Følner rank one actions that are conjugate to a specific odometer, and those that are conjugate to some odometer. These conditions are based on cutting and stacking procedures used to generate the action, and generalize results given by Foreman, Gao, Hill, Silva and Weiss for rank one Z-actions.

Planets similar in size are often dissimilar in interior

The number of discovered exoplanets now exceeds 5500 allowing statistical analyses of planetary systems. Multi-planet systems are mini-laboratories of planet formation and evolution, and analysing their system architectures can help us to constrain the physics of these processes. Recent works have found evidence of significant intrasystem uniformity in planet properties such as radius, mass, and orbital spacing, collectively termed ‘peas in a pod’ trends. In particular, correlations in radius and mass have been interpreted as implying uniformity in planet bulk density and composition within a system. However, the samples used to assess trends in mass tend to be small and biased. In this paper, we re-evaluate correlations in planet properties in a large sample of systems with at least two planets for which mass and radius have been directly measured, and therefore bulk density can be calculated. Our sample was assembled using the most up-to-date exoplanet catalogue data, and we compute the relevant statistics while using a procedure to ‘weight’ the data points according to measurement precision. We find a moderate correlation in radius and a weak correlation in the densities of adjacent planets. However, masses of neighbouring planets show no overall correlation in our main sample and a weak correlation among pairs of planets similar in size or pairs restricted to Mp<100 M⊕, Rp<10 R⊕. Similarly, we show that the intrasystem dispersion in radius is typically less than that in mass and density. We identify ranges in stellar host properties that correlate with stronger uniformity in pairs of adjacent planets: low Teff for planet masses, and low metallicity and old age for planet densities. Furthermore, we explore whether peas in a pod trends extend into planet compositions or interior structures. For small neighbouring planets with similar radii, we show that their masses and interior structures are often disparate, indicating that even within the same system, similarity in radii is not necessarily a good proxy for similarity in composition or the physical nature of the planets.

Group actions and higher topological complexity of lens spaces

Group actions and higher topological complexity of lens spaces

Lagrangian approach for analysis of acoustic energy transport in open cavity flows

The energy transport in aero-acoustics is investigated in the Lagrangian frame. First, based on finite-time Lyapunov exponent (FTLE) and momentum potential theory, a Lagrangian approach is proposed to identify transport barriers of acoustic energy. Specifically, the method, named relative flux gradient (RFG), is presented in detail. Then, to verify the method, it is applied to analytical fields, showing that it could reveal the wavefronts and energy transport barriers depending on the time interval of computation. Moreover, RFG is applied to analyze a simulated flow field of an open cavity flow, and the results are compared with the Lagrangian coherent structures identified by FTLE, demonstrating great similarity. Importantly, the differences between the structures are further analyzed, illustrating several transport channels that correspond to the Rossiter mode and showing a complex interaction between acoustic and vorticity modes. Finally, the relationship between the identified transport barriers and the acoustic behaviors in Eulerian frame is studied in detail. The results show that the transport barriers identified by RFG significantly impact the orbits in phase space, and in particular, RFG has the potential to illustrate and analyze the transport of acoustic energy in complex flow fields in a quantitative way: one method for direct analysis of acoustic phenomena in complex flow regions.

Feasibility Analysis of a CubeSat Mission for Space Rider Observation and Docking

AbstractIn the last few years, the number of orbiting satellites has increased exponentially, in particular due to the development of the New Space Economy. Even if this phenomenon makes the space more accessible, bringing a great contribution to the scientific, economic and technological fields, on the other hand it contributes to the overpopulation of the space background. Therefore, it is necessary to develop new techniques to manage the space environment, such as in orbit servicing, which is a procedure that aims to refuel and repair satellites to extend their operational life. A first step to reach this goal is to inspect closely the object of interest to study its features. In this framework, the Space Rider Observer Cube (SROC) mission is being developed. SROC is a payload that will be deployed by Space Rider (SR), an uncrewed and reusable robotic spacecraft designed by ESA (European Space Agency). SROC is a 12U CubeSat, whose goal is to carry out inspection manoeuvres around SR, then re-enter on board using a safe docking system to come back to Earth. The feasibility of a mission similar to SROC has been simulated during a university class, starting from the definition of the system requirements with particular focus on the analysis of the payloads and subsystems, to ensure the achievement of the mission goals. In particular, the CubeSat is equipped with an imaging payload to capture high resolution images of Space Rider surface and a docking mechanism. Then, the design of the orbit and the simulation of the effects of the space environment on the CubeSat have been studied using GMAT, SYSTEMA, MATLAB and other numerical tools. The results of the study are useful for future missions, aiming to inspect orbiting objects, such as operative satellites for in orbit servicing, space debris and dead satellites to study their geometries and plan their removal.

Where Are the Water Worlds? Identifying Exo-water-worlds Using Models of Planet Formation and Atmospheric Evolution

Planet formation models suggest that the small exoplanets that migrate from beyond the snowline of the protoplanetary disk likely contain water-ice-rich cores (∼50% by mass), also known as water worlds. While the observed radius valley of the Kepler planets is well explained by the atmospheric dichotomy of the rocky planets, precise measurements of the mass and radius of the transiting planets hint at the existence of these water worlds. However, observations cannot confirm the core compositions of those planets, owing to the degeneracy between the density of a bare water-ice-rich planet and the bulk density of a rocky planet with a thin atmosphere. We combine different formation models from the Genesis library with atmospheric escape models, such as photoevaporation and impact stripping, to simulate planetary systems consistent with the observed radius valley. We then explore the possibility of water worlds being present in the currently observed sample by comparing them with simulated planets in the mass–radius–orbital period space. We find that the migration models suggest ≳10% and ≳20% of the bare planets, i.e., planets without primordial H/He atmospheres, to be water-ice-rich around G- and M-type host stars, respectively, consistent with the mass–radius distributions of the observed planets. However, most of the water worlds are predicted to be outside a period of 10 days. A unique identification of water worlds through radial velocity and transmission spectroscopy is likely to be more successful when targeting such planets with longer orbital periods.

Expression and characterization of a novel β-1,4-endoglucanase from Bacillus subtilis strain isolated from a pulp and paper mill wastewater

The production of fermentable sugars from lignocellulosic biomass is achieved by the synergistic action of a group of enzymes called cellulases. Cellulose is a long chain of chemically linked glucoses by β-1,4 bonds. The enzyme β-1,4-endoglucanase is the first cellulase involved in the degradation, breaking the bond of the amorphous regions. A β-1,4-endoglucanase enzyme with high activity was obtained from a Bacillus subtilis strain isolated from wastewater of a pulp and paper mill. Sequencing and bioinformatic analysis showed that the gene amplified by PCR consisting of 1407 nucleotides and coding for a β-1,4-endoglucanase enzyme of approximately 55 kDa. The open reading frame (ORF) encoding the mature endoglucanase (eglS) was successfully inserted in a modified cloning plasmid (pITD03) and into the pYD1 plasmid used for its expression in yeast. Carboxymethylcellulose (CMC) plate assay, SDS-PAGE, and zymogram confirmed the production and secretion by the transformed E. coli BL21-SI strain of a 39 kDa β-1,4-endoglucanase consistent with the catalytic domain without the cellulose-binding module (CBM). The results showed that the truncated β-1,4-endoglucanase had higher activity and stability.

High time effective detection strategy for geosynchronous orbital space debris

After the formation of a multi-satellite network in a hypersynchronous orbit, it has the ability to continuously and in real-time observe the GEO band, which is an ideal way to solve blind spots and semi-backlight observations and improve the system’s high time-effective coverage ability. In response to the application limitations of high-orbit real-time monitoring constellations in hypersynchronous orbits, such as the large number of satellites in the network, high requirements for satellite detection capability, large field of view, and high launch and orbit cost, this paper proposes a constellation system efficiency analysis method that comprehensively covers both time and space dimensions. Based on this, optimization analysis of satellite detection capability, detection field of view, number of satellites, and orbit height is carried out. Finally, three constellation optimization schemes are provided, which are a semi-major axis of 60000 km with seven satellites, a semi-major axis of 55000 km with eight satellites, and a semi-major axis of 50000 km with ten satellites. The three constellation optimization schemes can provide a reference for the development of space-based high-orbit situational awareness in the future.

Designing precision measurement of the gravitational Aharonov-Bohm effect in microgravity

The gravitational Aharonov-Bohm (GAB) effect serves as the gravitational counterpart to the electromagnetic Aharonov-Bohm effect. Despite the concept’s inception in 1967, a rigorous experimental test of the GAB effect remains elusive. While recent endeavors with ground-based apparatus show promise in uncovering hints of the GAB effect, we propose a precise yet practical experiment to deterministically measure the GAB phase shift using cold atom interferometry in a microgravity environment, such as an orbital space station or drop tower. We conduct a thorough analysis of the experiment’s principles and derive key parameters. Our calculations suggest that it is feasible to precisely measure a significant GAB phase shift within known engineering constraints. Additionally, our design of the cold atom interferometer possesses a unique sensitivity to potential but insensitivity to force, which can be further refined to effectively mitigate adverse effects associated with nonzero inertial forces acting on the cold atoms. These endeavors will ultimately pave the way for experimental exploration into the quantum nature of gravity.

Mumford-Tate groups of 1-motives and Weil pairing

We show how the geometry of a 1-motive M (that is existence of endomorphisms and relations between the points defining it) determines the dimension of its motivic Galois group Galmot(M). Fixing periods matrices ΠM and ΠM⁎ associated respectively to a 1-motive M and to its Cartier dual M⁎, we describe the action of the Mumford-Tate group of M on these matrices. In the semi-elliptic case, according to the geometry of M we classify polynomial relations between the periods of M and we compute exhaustively the matrices representing the Mumford-Tate group of M. This representation brings new light on Grothendieck periods conjecture in the case of 1-motives.

Effect of social capital on enrolment of informal sector occupational groups in the national health insurance scheme in Ghana: a cross-sectional survey

BackgroundEnrolment of informal sector workers in Ghana’s National Health Insurance Scheme (NHIS) is critical to achieving increased risk-pooling and attainment of Universal Health Coverage. However, the NHIS has struggled over the years to improve enrolment of this subpopulation. This study analysed effect of social capital on enrolment of informal sector workers in the NHIS.MethodsA cross-sectional survey was conducted among 528 members of hairdressers and beauticians, farmers, and commercial road transport drivers’ groups. Descriptive statistics, principal component analysis, and multinomial logit regression model were used to analyse the data.ResultsSocial capital including membership in occupational group, trust, and collective action were significantly associated with enrolment in the NHIS, overall. Other factors such as household size, education, ethnicity, and usual source of health care were, however, correlated with both enrolment and dropout. Notwithstanding these factors, the chance of enrolling in the NHIS and staying active was 44.6% higher for the hairdressers and beauticians; the probability of dropping out of the scheme was 62.9% higher for the farmers; and the chance of never enrolling in the scheme was 22.3% higher for the commercial road transport drivers.ConclusionsSocial capital particularly collective action and predominantly female occupational groups are key determinants of informal sector workers’ participation in the NHIS. Policy interventions to improve enrolment of this subpopulation should consider group enrolment, targeting female dominated informal sector occupational groups. Further studies should consider inclusion of mediating and moderating variables to provide a clearer picture of the relationship between occupational group social capital and enrolment in health insurance schemes.

Complex spherical designs from group orbits

We consider the general question of when all orbits under the unitary action of a finite group give a complex spherical design. Those orbits which have large stabilisers are then good candidates for being optimal complex spherical designs. This is done by developing the general theory of complex designs and associated (harmonic) Molien series for group actions. As an application, we give explicit constructions of some putatively optimal real and complex spherical t-designs.

Residue maps, Azumaya algebras, and buildings

The goal of this note is to give an explicit formula for the residues of twists of the matrix algebra in terms of the twisting cocycle. Combined with the Fixed Point Theorem for actions of finite groups on affine buildings, this leads to a quick proof of the well-known characterization of unramified algebras in terms of Azumaya algebras.

A generalization of a result on generating functions of modified Laguerre polynomial by using the notion of partial quasibilinear generating function

In his paper [2], Chongdar obtained an extension (Theorem 3) of the result on bilateral generating functions involving modified Laguerre polynomial stated in Theorem 1 of Ghosh [3]. In this article, the present authors have made an attempt to present a further generalization of the extension obtained by Chongdar [2] by means of the theory of one parameter group of continuous transformations as well as using the concepts of partial quasibilateral generating function [4] involving some special functions.

Topologically free actions and ideals in twisted Banach algebra crossed products

We generalize the influential $C^*$ -algebraic results of Kawamura–Tomiyama and Archbold–Spielberg for crossed products of discrete groups actions to the realm of Banach algebras and twisted actions. We prove that topological freeness is equivalent to the intersection property for all reduced twisted Banach algebra crossed products coming from subgroups, and in the untwisted case to a generalized intersection property for a full $L^p$ -operator algebra crossed product for any $p\in [1,\,\infty ]$ . This gives efficient simplicity criteria for various Banach algebra crossed products. We also use it to identify the prime ideal space of some crossed products as the quasi-orbit space of the action. For amenable actions we prove that the full and reduced twisted $L^p$ -operator algebras coincide.

Apport des aides technologiques dans l’extraction des corps étrangers orbitaires

Background: Removal of orbital foreign bodies is a surgical challenge. The purpose of this study is to report our experience in the removal of orbital foreign bodies and to evaluate the usefulness of various technological aids in their removal.Materials and Methods: We conducted a single-center retrospective study at Nice University Hospital (France) from January 2017 to December 2023. All patients undergoing surgery for an orbital foreign body during the study period were included. Data recorded included the nature of the orbital foreign body, its size, location, surgical route, outcome (success, partial success, failure), and technological aids used (intraoperative navigation, intraoperative imaging scope, orbital magnet). Concurrently, we designed a dedicated orbital magnet, which was tested in the anatomy laboratory and in two of our patients.Results: Six patients, all young men, were included during the study period. Removal was successful, partially successful, or unsuccessful in one-third of cases, respectively. Failure was associated with orbital foreign bodies located in the intraconal or posterior orbital space. Preoperatively, the use of a “low-artifact” scanner allowed us to better determine the exact size and shape of the orbital foreign body. Intraoperative navigation was not accurate enough, due to the mobility of the orbital bodies within the orbital fat. In our experience, intraoperative scope imaging was more accurate. The use of a dedicated orbital magnet was successfully tested in the anatomy laboratory and allowed the removal of a small orbital foreign body in one of our patients. Intraoperative surgical videos are provided.Conclusion: Vegetal orbital foreign bodies must be systematically removed. Removal of non-vegetal orbital foreign bodies should be considered on a case-by-case basis based on their size, best assessed using a “low artifact” scanner, their location, and their intrinsic ferromagnetism. Intraoperative navigation does not appear useful, while intraoperative scope imaging does. A dedicated orbital magnet might be helpful in removing ferromagnetic orbital foreign bodies. However, an orbital magnet may be ineffective in removing intraorbital bullets, since they are made primarily of an alloy of copper and lead.

Community governance during the Shanghai COVID-19 lockdown I: the roles and actions of residents’ committees

ABSTRACT Residents’ committees (RCs) are crucial in China’s “dynamic zero-COVID” policy. They were at the frontline of combating the pandemic yet received wide criticism, drawing controversies to their roles and actions as grassroots organizations or extensions of state control. To further understand RCs in China’s community governance, this research conceptualizes RCs as street-level bureaucrats (SLBs), capable of exercising discretion and policy entrepreneurship, and argues that RCs are the “intermediary space” between the state and society. Questionnaire surveys and structured interviews were used to examine RCs’ roles and their discretion and policy entrepreneurship during the city-wide lockdown in Shanghai, China, in the Spring of 2022. Results suggest that RC staff, volunteers, and residents tend to perceive RCs’ roles differently. Although RC staff might have considered themselves government representatives, they also reported the need to address residents’ needs when implementing policies. At the same time, they actively used discretion, mobilized volunteers, established temporary systems, and helped with residents’ spontaneous group actions, all without directly violating epidemic policies. These insights suggest new ways to understand the nuances of China’s community governance.

Square-integrable representations and the coadjoint action of solvable Lie groups

Abstract We characterize the square-integrable representations of (connected, simply connected) solvable Lie groups in terms of the generalized orbits of the coadjoint action. We prove that the normal representations corresponding, via the Pukánszky correspondence, to open coadjoint orbits are type I, not necessarily square-integrable representations. We show that the quasi-equivalence classes of type I square-integrable representations are in bijection with the simply connected open coadjoint orbits, and the existence of an open coadjoint orbit guarantees the existence of a compact open subset of the space of primitive ideals of the group. When the nilradical has codimension 1, we prove that the isolated points of the primitive ideal space are always of type I. This is not always true for codimension greater than 2, as shown by specific examples of solvable Lie groups that have dense, but not locally closed, coadjoint orbits.

Uncertainty-driven mixture convolution and transformer network for remote sensing image super-resolution

Recently, convolutional neural networks (CNNs) and Transformer-based Networks have exhibited remarkable prowess in the realm of remote sensing image super-resolution (RSISR), delivering promising results in the field. Nevertheless, the effective fusion of the inductive bias inherent in CNNs and the long-range modeling capabilities encapsulated within the Transformer architecture remains a relatively uncharted terrain in the context of RSISR endeavors. Accordingly, we propose an uncertainty-driven mixture convolution and transformer network (UMCTN) to earn a performance promotion. Specifically, to acquire multi-scale and hierarchical features, UMCTN adopts a U-shape architecture. Utilizing the dual-view aggregation block (DAB) based residual dual-view aggregation group (RDAG) in both encoder and decoder, we solely introduce a pioneering dense-sparse transformer group (DSTG) into the latent layer. This design effectively eradicates the considerable quadratic complexity inherent in vanilla Transformer structures. Moreover, we introduce a novel uncertainty-driven Loss (UDL) to steer the network’s attention towards pixels exhibiting significant variance. The primary objective is to elevate the reconstruction quality specifically in texture and edge regions. Experimental outcomes on the UCMerced LandUse and AID datasets unequivocally affirm that UMCTN achieves state-of-the-art performance in comparison to presently prevailing methodologies.