Action Of Group Research Articles

Group-theoretic analysis of symmetry-preserving deployable structures and metamaterials.

Many deployable structures in nature, as well as human-made mechanisms, preserve symmetry as their configurations evolve. Examples in nature include blooming flowers, dilation of the iris within the human eye, viral capsid maturation and molecular and bacterial motors. Engineered examples include opening umbrellas, elongating scissor jacks, variable apertures in cameras, expanding Hoberman spheres and some kinds of morphing origami structures. In these cases, the structures either preserve a discrete symmetry group or are described as an evolution from one discrete symmetry group to another of the same type as the structure deploys. Likewise, elastic metamaterials built from lattice structures can also preserve symmetry type while passively deforming and changing lattice parameters. A mathematical formulation of such transitions/deployments is articulated here. It is shown that if [Formula: see text] is Euclidean space, [Formula: see text] is a continuous group of motions of Euclidean space and [Formula: see text] is the type of the discrete subgroup of [Formula: see text] describing the symmetries of the deploying structure, then the symmetry of the evolving structure can be described by time-dependent subgroups of [Formula: see text] of the form [Formula: see text], where [Formula: see text] is a time-dependent affine transformation. Then, instead of considering the whole structure in [Formula: see text], a 'sector' of it that lives in the orbit space [Formula: see text] can be considered at each instant in time, and instead of considering all motions in [Formula: see text], only representatives from right cosets in the space [Formula: see text] need to be considered. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 1)'.

Uncountable group of continuous transformations of unit segment preserving tails of Q_2-representation of numbers

We consider two-base Q2-representation of numbers of segment [0;1] which is defined by two bases q0 ∈ (0;1), q1 = 1-q0 and alphabet A={0,1}, (αn) ∈ A × A × .... It is a generalization of classic binary representation q0=1/2. In the article we prove that the set of all continuous bijections of segment [0;1] preserving "tails" of Q2-representation of numbers forms an uncountable non-abelian group with respect to composition such that it is a subgroup of the group of continuous transformations preserving frequencies of digits of Q2-representation of numbers. Construction of such transformations (bijections) is based on the left and right shift operators for digits of Q2-representation of numbers.

Family of 2:1 resonant quasi-periodic distant retrograde orbits in cislunar space

Given the current enthusiasm for lunar exploration, the 2:1 resonant distant retrograde orbit (DRO) in Earth-Moon space is of interest. To gain an in-depth understanding of the complex dynamic environment in cislunar space and provide more options for parking orbits, this paper investigates the existence of quasi-periodic orbits near the 2:1 resonant DRO in the circular restricted three-body problem (CR3BP). Firstly, the numerical computation approach, continuation strategy, and stability analysis method of quasi-periodic orbits are introduced. Then, addressing the primary challenges in the continuation progress, we have developed an adaptive continuation algorithm with automatic adjustment of the step size and the number of discrete points that characterize the invariant torus. Finally, two types of 2D quasi-DROs and their linear stability properties are explored. Using Poincaré sections, we investigated the boundaries of the maximum extent attainable by both 2D quasi-DRO families in the CR3BP at a specific Jacobi energy, confirming that both types of quasi-periodic families have reached their respective boundaries. The algorithm described in this paper is beneficial for facilitating the computation of quasi-periodic families and aids in discovering additional potential dynamical structures.

Jacobian Spheroids, Shallow Encounters, and the Keyhole Map

The study of the dynamics of flybys is featured in several space-mission-related applications, spanning from the design of interplanetary orbits to the computation of impact probabilities with given celestial bodies in planetary protection and defense tasks. While patched-conics, two-body models suffice in accuracy for trajectory planning cases, collision probability assessment requires instead more insightful approaches. High-fidelity simulations have shown impact patterns to happen outside nominally colliding trajectories in terms of two-body analysis, all caused by distant or weak interactions between the given trajectory-celestial body pairs. This work proposes a novel concept of sphere of influence based on the Jacobian of the three-body dynamics, resulting in a wider definition of encounters that encompasses weak interactions up to an arbitrary threshold. The so-defined Jacobian spheroids are then used to construct the Keyhole map, a graphical tool that maps in the orbital elements space both nominal and off-nominal keyholes, i.e., collision paths accounting for three-body weak interactions. The proposed concepts arise from and are compared against the on-ground casualty risk assessment of the European Space Agency’s mission JUICE.

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.

Determinisme Teologi Islam dalam Pola Gerak Sejarah Indonesia

This article discusses the determinism of Islamic theology in shaping the laws and movement patterns of Indonesian history. The aim is to explore how religions in Indonesia play a central role in shaping individual and group actions, as well as determining the movement patterns of modern Indonesian history. This discussion uses the speculative historical philosophy concept of historical determinism. In conclusion, the Indonesia historical driving force or it historical pattern are influenced by the theological ideas of religions in Indonesia, including Islam. This is reflected in the formulation of periodization of Indonesian history which is based on the periodization of Indonesian history, which is built on the basis of power entities characterized by religion and the identity of its rulers which is related to a particular religion. Apart from that, its influence can also be read in the style of historiography that developed in Indonesia which is related to religious affairs.

Quadratic Systems Possessing an Infinite Elliptic-Saddle or an Infinite Nilpotent Saddle

This paper presents a global study of the class [Formula: see text] of all real quadratic polynomial differential systems possessing exactly one elemental infinite singular point and one triple infinite singular point, which is either an infinite nilpotent elliptic-saddle or a nilpotent saddle. This class can be divided into three different families, namely, [Formula: see text] of phase portraits possessing three real finite singular points, [Formula: see text] of phase portraits possessing one real and two complex finite singular points, and [Formula: see text] of phase portraits possessing one real triple finite singular point. Here, we provide a comprehensive study of the geometry of these three families. Modulo the action of the affine group and time homotheties, families [Formula: see text] and [Formula: see text] are three-dimensional and family [Formula: see text] is two-dimensional. We study the respective bifurcation diagrams of their closures with respect to specific normal forms, in sub-sets of real Euclidean spaces. The bifurcation diagram of family [Formula: see text] (resp., [Formula: see text] and [Formula: see text]) yields 1274 (resp., 89 and 14) sub-sets with 91 (resp., 27 and 12) topologically distinct phase portraits for systems in the closure [Formula: see text] (resp., [Formula: see text] and [Formula: see text]) within the representatives of [Formula: see text] (resp., [Formula: see text] and [Formula: see text]) given by a specific normal form.

Insights into critical urban pedestrian dynamics: an observational study spotlighting a small sample of blind pedestrians and electric vehicles

AbstractObservational studies, whether conducted on-site or through simulation, are practical options for investigating and comprehending pedestrian behaviour and validating the findings of similar studies that have already taken place on the same subject. Although they present difficulties in demographic characterisation and personal context, observation represents the adoption of actual behaviour, highlighting the different scenarios, contexts and characteristics of the environment and infrastructure in urban areas. However, with the growth in simulators, surveys, and data protection issues in Europe, field observation is less considered, and several studies have been left aside. Based on observation, this study answers behavioural and demographic questions, namely age and gender, using the data of six pedestrian crossings in Coimbra, Portugal. This experience occurred on different days of the week (the week before lockdown), registering blind (and non-blind) pedestrians' behaviour facing the electric vehicle in 6 crosswalks, 30 min in each crosswalk, morning or afternoon, with favourable weather conditions outside peak hours In total 180 (30*6) minutes were filmed and evaluated. The relationships between responsibility (when one pedestrian is guided by another) and group action in decision-making and crossing behaviour were also investigated. Another relevant aspect studied was the relationship between pedestrians and electric vehicles in different contexts. During the research, an electric vehicle was inserted in the observational experience, circulating in the streets to observe the pedestrians' reaction to the absence of noise. In this context, blind pedestrians were invited to perform crossings in these areas and identify the presence of the electric vehicle, to identify some differences in the behaviour of blind pedestrians and non-blind pedestrians. The results indicate that blind pedestrians tend to be more cautious than non-blind pedestrians, that younger and elderly pedestrians tend to have more dangerous and less calculated behaviours than other road users and that the differences are more perceptible in age than gender. It should be noted that when in a group, especially adolescents, they commit more traffic errors. Furthermore, regarding the absence of noise associated with the electric vehicle, in moments of pedestrian distraction, if the driver is not attentive, there is an increase in the risk of accidents.

Rigidity and geometricity for surface group actions on the circle

Rigidity and geometricity for surface group actions on the circle

On gauge Poisson brackets with prescribed symmetry

Abstract In the context of averaging method, we describe a reconstruction of invariant connection-dependent Poisson structures from canonical actions of compact Lie groups on fibered phase spaces. Some symmetry properties of Wong's type equations are derived from the main results

Exploring estrogen antagonism using CRISPR/Cas9 to generate specific mutants for each of the receptors

Endocrine disruptors are chemicals that have been in the spotlight for some time now. Their modulating action on endocrine signaling pathways made them a particularly interesting topic of research within the field of ecotoxicology. Traditionally, endocrine disrupting properties are studied using exposure to suspected chemicals. In recent years, a major breakthrough in biology has been the advent of targeted gene editing tools to directly assess the function of specific genes. Among these, the CRISPR/Cas9 method has accelerated progress across many disciplines in biology. This versatile tool allows to address antagonism differently, by directly inactivating the receptors targeted by endocrine disruptors. Here, we used the CRISPR/Cas9 method to knock out the different estrogen receptors in zebrafish and we assessed the potential effects this generates during development. We used a panel of biological tests generally used in zebrafish larvae to investigate exposure to compounds deemed as endocrine disrupting chemicals. We demonstrate that the absence of individual functional estrogen receptors (Esr1, Esr2b, or Gper1) does affect behavior, heart rate and overall development. Each mutant line was viable and could be grown to adulthood, the larvae tended to be morphologically grossly normal. A substantial fraction (70%) of the esr1 mutants presented severe craniofacial deformations, while the remaining 30% of esr1 mutants also had changes in behavior. esr2b mutants had significantly increased heart rate and significant impacts on craniofacial morphometrics. Finally, mutation of gper1 affected behavior, decreased standard length, and decreased bone mineralization as assessed in the opercle. Although the exact molecular mechanisms underlying these effects will require further investigations in the future, we added a new concept and new tools to explore and better understand the actions of the large group of endocrine disrupting chemicals found in our environment.

The G-invariant graph Laplacian part II: Diffusion maps

The diffusion maps embedding of data lying on a manifold has shown success in tasks such as dimensionality reduction, clustering, and data visualization. In this work, we consider embedding data sets that were sampled from a manifold which is closed under the action of a continuous matrix group. An example of such a data set is images whose planar rotations are arbitrary. The G-invariant graph Laplacian, introduced in Part I of this work, admits eigenfunctions in the form of tensor products between the elements of the irreducible unitary representations of the group and eigenvectors of certain matrices. We employ these eigenfunctions to derive diffusion maps that intrinsically account for the group action on the data. In particular, we construct both equivariant and invariant embeddings, which can be used to cluster and align the data points. We demonstrate the utility of our construction in the problem of random computerized tomography.

Infrared finite scattering theory: scattering states and representations of the BMS group

Any non-trivial scattering with massless fields in four spacetime dimensions will generically produce an “out” state with memory which gives rise to infrared divergences in the standard S-matrix. To obtain an infrared-finite scattering theory, one must suitably include states with memory. However, except in the case of QED with massive charged particles, asymptotic states with memory that have finite energy and angular momentum have not been constructed for more general theories (e.g. massless QED, Yang-Mills and quantum gravity). To this end, we construct direct-integral representations over the “Lorentz orbit” of a given memory and classify all “orbit space representations” that have well-defined energy and angular momentum. We thereby provide an explicit construction of a large supply of physical states with memory as well as the explicit action of the BMS charges all states. The construction of such states is a key step toward the formulation of an infrared-finite scattering theory. While we primarily focus on the quantum gravitational case, we outline how the methods presented in this paper can be applied to obtain representations of the Poincaré group with memory for more general quantum field theories.

Invariant rings of the special orthogonal group have nonunimodal h-vectors

For [Formula: see text] an infinite field of characteristic other than two, consider the action of the special orthogonal group [Formula: see text] on a polynomial ring via copies of the regular representation. When [Formula: see text] has characteristic zero, Boutot’s theorem implies that the invariant ring has rational singularities; when [Formula: see text] has positive characteristic, the invariant ring is [Formula: see text]-regular, as proven by Hashimoto using good filtrations. We give a new proof of this, viewing the invariant ring for [Formula: see text] as a cyclic cover of the invariant ring for the corresponding orthogonal group; this point of view has a number of useful consequences, for example, it readily yields the [Formula: see text]-invariant and information on the Hilbert series. Indeed, we use this to show that the [Formula: see text]-vector of the invariant ring for [Formula: see text] need not be unimodal.

Group Theoretic Approach towards the Balaban Index of Catacondensed Benzenoid Systems and Linear Chain of Anthracene

In this work, we present the analytical closed forms of the Balaban index for anthracene and catacondensed benzenoid systems using group theoretic techniques. The Balaban index is a distance-based topological index that provides valuable information about the properties of chemical structures. We emphasize the importance of determining analytical closed forms of the Balaban index for catacondensed benzenoid systems and linear chains of anthracene, as it enables a deeper understanding of these systems and their behavior. Our analysis utilizes the group action of the automorphism group of these chains on the set of vertices, which refer to the points where the chains intersect. In future work, we plan to determine the Balaban index of other polymeric linear chains using group theoretic techniques and extend the applications of this index to other fields, such as materials science and biology. It is clear that the Balaban index remains a valuable tool in theoretical and computational chemistry, and its applications are constantly evolving.

THE RIGHT TO RIDE: AN ETHNOGRAPHY OF AN URBAN AND MARGINAL PRACTICE

This text discusses structural aspects of the practice of roller-cart, based on an ethnography conducted in the Metropolitan Region of Belo Horizonte between 2019 and 2022. Initial impressions indicated that the roller-cart movement, with competition teams, associations and event organizers in the city, was a large and coordinated action of a cohesive group of people around the same purpose. With a dense and prolonged stay in the field, I found a movement marked by disputes, interests and multiple appropriations that limit, at the same time as they shape, a community of practice that emerges from a collective, urban and marginal construction. In this sense, this text highlights three structural aspects of the practice of roller-cart: the participation of women in events, based on the notion of the sexed city by Michele Perrot; the territorial disputes of these groups with the orders of the State and Capital, from the perspective of the city as a right, by Henri Lefebvre; and the search for legitimacy of a marginalized practice, through the prism of consumption as a constituent of identities, according to Michel de Certeau. Thus, men and women, adults and children, participate, constitute, and are constituted by a polysemic, contradictory, and essentially situated practice.

Perceptions of Black faculty encounters with racism through a collaborative autoethnographical lens: CRT and moral reasoning perspectives

Foreign-born scholars as allies from non-advantaged minoritized groups have historically provided critical insights about the racism that is directed at Black people in a racially driven U.S. society. The current collaborative autoethnography is based on the intersecting paths of three university faculty, a Black female scholar and two international J-1 scholars, who documented through personal narratives the racism that is directed at Black faculty at PWIs, drawing from critical race and moral reasoning interpretative frameworks. Building on previous research, the narratives shed light on how anti-Black racism persists at PWIs in the form of micro-aggressions and race-based hostility and that humanizing reparation efforts are warranted but may not be sufficient to ensure comprehensive change. Future research must explore the potential impact of group action initiatives among BIPOC and other minoritized faculty groups (national, international) to promote faculty protections in general while challenging anti-Black racism specifically.

Bilateral Multiple Orbital Metastases Successfully Treated with Standalone Stereotactic Radiosurgery: Clinical Image

Bilateral orbital metastases are extremely rare, and no previous literatures have reported bilateral multiple orbital metastases treated with stereotactic radiosurgery (SRS). We present the impressive images of a patient with history of metastatic leiomyosarcoma with newly diagnosed bilateral multiple orbital metastases. The pre-SRS MRI showed a right and two left orbital metastatic lesions. The patient underwent SRS, and the post-SRS MRI at 2-month following SRS showed a decrease in size of the treated lesions. The PET scan at 5 months after the treatment showed no avid F-fluorodeoxyglucose uptakes in the three orbital metastases. The presenting symptoms are all improved after the treatment without no adverse effects from the SRS. Our interesting images show the presence of multiple lesions in the orbital spaces with excellent treatment responses post SRS. This is the first report of a patient who has bilateral and multiple orbital metastases that were successfully treated with standalone SRS.

A fixed-point formula for Dirac operators on Lie groupoids

We study equivariant families of Dirac operators on the source fibers of a Lie groupoid with a closed space of units and equipped with an action of an auxiliary compact Lie group. We use the Getzler rescaling method to derive a fixed-point formula for the pairing of a trace with the K-theory class of such a family. For the pair groupoid of a closed manifold, our formula reduces to the standard fixed-point formula for the equivariant index of a Dirac operator. Further examples involve foliations and manifolds equipped with a normal crossing divisor.

A self-healing polyurethane/imidazole-modified carboxylated graphene oxide composite coating for antifouling and anticorrosion applications

Marine corrosion and biofouling present significant challenges to maintaining maritime vessels and oceanic infrastructure. Developing coatings that integrate anti-fouling, anti-corrosion, and self-healing properties remains a critical issue. This study introduces imidazolium-modified carboxylated graphene (FCGO) into polyurethane coatings (F-PUSS) containing disulfide bonds to address this challenge. The incorporation of FCGO significantly enhances the mechanical properties of the coating, improving tensile stress by 40 % to 20.97 MPa. The barrier properties of FCGO also provide strong corrosion resistance, with |Z|0.01Hz values an order of magnitude higher than the original samples, even after 15 days of immersion in sodium chloride (3.5 wt%). Additionally, F-PUSS retains corrosion resistance after repairs. The synergistic action of imidazole groups and graphene provides excellent antifouling performance with nearly to an alga rate of 100 % and an antimicrobial rate of 96 %. F-PUSS demonstrates remarkable self-healing capabilities, with a healing efficiency of 78 % after 48 h at 60 °C. This study provides valuable insights for designing multifunctional polymer materials with anti-fouling, anti-corrosion, and self-healing functions.