Action Of Group Research Articles

Substructures of the Weyl group and their physical applications

We study substructures of the Weyl group of conformal transformations of the metric of (pseudo)Riemannian manifolds. These substructures are identified by differential constraints on the conformal factors of the transformations which are chosen such that their composition is associative. Mathematically, apart from rare exceptions, they are partial associative groupoids, not groups, so they do not have an algebra of infinitesimal transformations, but this limitation can be partially circumvented using some of their properties cleverly. We classify and discuss the substructures with two-derivatives differential constraints, the most famous of which being known as the harmonic or restricted Weyl group in the physics literature, but we also show the existence of a lightcone constraint which realizes a proper subgroup of the Weyl group. We then show the physical implications that come from invariance under the two most important substructures, concentrating on classical properties of the energy-momentum tensor and a generalization of the quantum trace anomaly. We also elaborate further on the harmonic substructure, which can be interpreted as partial gauge fixing of full Weyl invariance using BRST methods. Finally, we discuss how to construct differential constraints of arbitrary higher-derivative order and present, as examples, generalizations involving scalar constraints with four and six derivatives.

Strengthening person-centered care through quality improvement: a mixed-methods study examining implementation of the Person-Centered Care Assessment Tool in Zambian health facilities

Introduction Person-centered care (PCC) is considered a fundamental approach to address clients’ needs. There is a dearth of data on specific actions that HIV treatment providers identify as priorities to strengthen PCC. Objective This study team developed the Person-Centered Care Assessment Tool (PCC-AT), which measures PCC service delivery within HIV treatment settings. The PCC-AT, including subsequent group action planning, was implemented across 29 facilities in Zambia among 173 HIV treatment providers. Mixed-methods study objectives included: (1) identify types of PCC-strengthening activities prioritized based upon low and high PCC-AT scores; (2) identify common themes in PCC implementation challenges and action plan activities by low and high PCC-AT score; and (3) determine differences in priority actions by facility ART clinic volume or geographic type. Methods The study team conducted thematic analysis of action plan data and cross-tabulation queries to observe patterns across themes, PCC-AT scores, and key study variables. Results The qualitative analysis identified 39 themes across 29 action plans. A higher proportion of rural compared to urban facilities identified actions related to stigma and clients’ rights training; accessibility of educational materials and gender-based violence training. A higher proportion of urban and peri-urban compared to rural facilities identified actions related to community-led monitoring. Discussion Findings provide a basis to understand common PCC weaknesses and activities providers perceive as opportunities to strengthen experiences in care. Conclusion To effectively support clients across the care continuum, systematic assessment of PCC services, action planning, continuous quality improvement interventions and re-measurements may be an important approach.

Anaerobic recovery of vivianite from waste-activated sludge through combined sludge pre-fermentation and agroforestry biomass-based biochar

The recovery of vivianite through the anaerobic digestion of waste-activated sludge has attracted considerable attention due to its operational simplicity and the high economic value of vivianite. This study concentrated on the recovery of vivianite from anaerobic fermentation systems through a strategy combining sludge pre-fermentation with the waste agricultural and forestry biomass-derived biochar (ZBC). In-depth analyses of the structure and functionality of ZBC were conducted using techniques such as Fourier-transform infrared spectroscopy (FTIR), X-ray photoelectron spectroscopy (XPS), and Raman spectroscopy. The sediment produced after the experiment and the changes in microbial community composition were characterized. The results indicated that pre-fermentation promoted phosphorus release, enhancing the synthesis of vivianite while selectively enriching respiratory and fermentative Fe (III)-reducing microorganisms. When FeOOH was used as the Fe (III) source, ZBC, through its dual action of redox functional groups and graphitization structure, increased the Fe2+ production by 243.6 % in the system dominated by respiratory Fe (III)-reducing bacteria. The optimal dosage of ZBC for the simultaneous recovery of vivianite resources and methane energy was 2.5 g/L. The combined application of pre-fermentation and ZBC provides a novel approach for the efficient recycling of vivianite and offers new insights into the reuse of agroforestry waste biomass resources.

Finite group actions on abelian groups of finite Morley rank

Finite group actions on abelian groups of finite Morley rank

CSI-Otter: isogeny-based (partially) blind signatures from the class group action with a twist

In this paper, we construct the first provably-secure isogeny-based (partially) blind signature scheme. While at a high level the scheme resembles the Schnorr blind signature, our work does not directly follow from that construction, since isogenies do not offer as rich an algebraic structure. Specifically, our protocol does not fit into the linear identification protocol abstraction introduced by Hauck, Kiltz, and Loss (EUROCYRPT’19), which was used to generically construct Schnorr-like blind signatures based on modules such as classical groups and lattices. Consequently, our scheme is provably secure in the random oracle model (ROM) against poly-logarithmically-many concurrent sessions assuming the subexponential hardness of the group action inverse problem. In more detail, our blind signature exploits the quadratic twist of an elliptic curve in an essential way to endow isogenies with a strictly richer structure than abstract group actions (but still more restrictive than modules). The basic scheme has public key size 128 B and signature size 8 KB under the CSIDH-512 parameter sets—these are the smallest among all provably secure post-quantum secure blind signatures. Relying on a new ring variant of the group action inverse problem (rGAIP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsf{rGAIP}$$\\end{document}), we can halve the signature size to 4 KB while increasing the public key size to 512 B. We provide preliminary cryptanalysis of rGAIP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ extsf{rGAIP}} $$\\end{document} and show that for certain parameter settings, it is essentially as secure as the standard GAIP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsf{GAIP}$$\\end{document}. Finally, we show a novel way to turn our blind signature into a partially blind signature, where we deviate from prior methods since they require hashing into the set of public keys while hiding the corresponding secret key—constructing such a hash function in the isogeny setting remains an open problem.

On symmetry adapted bases in trigonometric optimization

The problem of computing the global minimum of a trigonometric polynomial is computationally hard. We address this problem for the case, where the polynomial is invariant under the exponential action of a finite group. The strategy is to follow an established relaxation strategy in order to obtain a converging hierarchy of lower bounds. Those bounds are obtained by numerically solving semi-definite programs (SDPs) on the cone of positive semi-definite Hermitian Toeplitz matrices, which is outlined in the book of Dumitrescu Dumitrescu (2007). To exploit the invariance, we show that the group has an induced action on the Toeplitz matrices and prove that the feasible region of the SDP can be restricted to the invariant matrices, whilst retaining the same solution. Then we construct a symmetry adapted basis tailored to this group action, which allows us to block-diagonalize invariant matrices and thus reduce the computational complexity to solve the SDP.The approach is in its generality novel for trigonometric optimization and complements the one that was proposed as a poster at the ISSAC 2022 conference Hubert et al. (2022) and later extended to Hubert et al. (2024). In the previous work, we first used the invariance of the trigonometric polynomial to obtain a classical polynomial optimization problem on the orbit space and subsequently relaxed the problem to an SDP. Now, we first make the relaxation and then exploit invariance.Partial results of this article have been presented as a poster at the ISSAC 2023 conference Metzlaff (2023).

Research on the Motivation and Effect of Longfor Group's Transformation to Asset-light Operation Mode

Since the real estate marketization reform in 1998, China's real estate industry has continued to focus on asset operation mode, at that time in the golden period of the industry, real estate enterprises only need to hoard a lot of land, wait for the appreciation of the land and then resell, you can get considerable returns. However, in the context of the current slowdown in the economic growth of China's real estate industry, it is difficult for commercial real estate enterprises to continue to operate with heavy assets, so such enterprises begin to seek transformation, and want to change a profit model to match the current market. As a new way for enterprises to accumulate core competence and maximize value, "asset-light operation" model has been highly valued by the academic and business circles. This paper takes Longfor Group, a representative real estate enterprise, as the research object, and makes an in-depth analysis of the company's finance from the perspective of its financial characteristics and financial performance, in order to provide certain theoretical references for the successful application of the transformation and development of similar companies.

Mutations of numerically exceptional collections on surfaces

A conjecture of Bondal–Polishchuk states that, in particular for the bounded derived category of coherent sheaves on a smooth projective variety, the action of the braid group on full exceptional collections is transitive up to shifts. We show that the braid group acts transitively on the set of maximal numerically exceptional collections on rational surfaces up to isometries of the Picard lattice and twists with line bundles. Considering the blow-up of the projective plane in up to 9 points in very general position, these results lift to the derived category. More precisely, we prove that, under these assumptions, a maximal numerically exceptional collection consisting of line bundles is a full exceptional collection and any two of them are related by a sequence of mutations and shifts. The former extends a result of Elagin–Lunts and the latter a result of Kuleshov–Orlov, both concerning del Pezzo surfaces. In contrast, we show in concomitant work (Krah in Invent Math 235(3):1009–1018, 2024) that the blow-up of the projective plane in 10 points in general position admits a non-full exceptional collection of maximal length consisting of line bundles.

Dynamics of the epidemiological Predator-Prey system in advective environments.

This paper aims to establish the existence of traveling wave solutions connecting different equilibria for a spatial eco-epidemiological predator-prey system in advective environments. After applying the traveling wave coordinates, these solutions correspond to heteroclinic orbits in phase space. We investigate the existence of the traveling wave solution connecting from a boundary equilibrium to a co-existence equilibrium by using a shooting method. Different from the techniques introduced by Huang, we directly prove the convergence of the solution to a co-existence equilibrium by constructing a special bounded set. Furthermore, the Lyapunov-type function we constructed does not need the condition of bounded below. Our approach provides a different way to study the existence of traveling wave solutions about the co-existence equilibrium. The existence of traveling wave solutions between co-existence equilibria are proved by utilizing the qualitative theory and the geometric singular perturbation theory. Some other open questions of interest are also discussed in the paper.

Strategies to Obtain Reliable Energy Landscapes from Embedded Multireference Correlated Wavefunction Methods for Surface Reactions.

Embedded correlated wavefunction (ECW) theory is a powerful tool for studying ground- and excited-state reaction mechanisms and associated energetics in heterogeneous catalysis. Several factors are important to obtaining reliable ECW energies, critically the construction of consistent active spaces (ASs) along reaction pathways when using a multireference correlated wavefunction (CW) method that relies on a subset of orbital spaces in the configuration interaction expansion to account for static electron correlation, e.g., complete AS self-consistent field theory, in addition to the adequate partitioning of the system into a cluster and environment, as well as the choice of a suitable basis set and number of states included in excited-state simulations. Here, we conducted a series of systematic studies to develop best-practice guidelines for ground- and excited-state ECW theory simulations, utilizing the decomposition of NH3 on Pd(111) as an example. We determine that ECW theory results are relatively insensitive to cluster size, the aug-cc-pVDZ basis set provides an adequate compromise between computational complexity and accuracy, and that a fixed-clean-surface approximation holds well for the derivation of the embedding potential. Additionally, we demonstrate that a merging approach, which involves generating ASs from the molecular fragments at each configuration, is preferable to a creeping approach, which utilizes ASs from adjacent structures as an initial guess, for the generation of consistent potential energy curves involving open-d-shell metal surfaces, and, finally, we show that it is essential to include bands of excited states in their entirety when simulating excited-state reaction pathways.

Finitistic spaces with the orbit space 𝔽ℙn × 𝕊m

Let [Formula: see text], [Formula: see text] or [Formula: see text], act freely on a finitistic connected space [Formula: see text]. This paper gives the cohomology classification of [Formula: see text] if the mod 2 or rational cohomology of the orbit space [Formula: see text] is isomorphic to the product of a projective space and sphere [Formula: see text], where [Formula: see text] or [Formula: see text], respectively. For a free involution on [Formula: see text], a lower bound of covering dimension of the coincidence set of a continuous map [Formula: see text] is also determined.

A Note on the Entropy for Heisenberg Group Actions on the Torus

A Note on the Entropy for Heisenberg Group Actions on the Torus

One electron is enough: A chemical bonding approach on the hydrogen induced structural transformation in MPd3 (M = Mg, In, Tl) intermetallic compounds

It is crucial to understand the nature of the metal-hydrogen interactions in the intermetallic hydrides in order to develop new hydrogen storage materials with optimum metal-H interactions for desired hydrogen absorption-desorption kinetics. The MPd3 intermetallic compounds (M = Mg, In, Tl) transform to cubic anti-perovskite type (AuCu3-type with hydrogen in the octahedral intersect) structure from ZrAl3-type four-fold ccp-superstructure up on hydrogenation. According to the DFT-based orbital space electronic structure and chemical bonding analysis, this structural transformation is driven by maximizing the coordination of hydrogen surrounded by Pd, forming the Pd (4d) – H (1s), and … Pd–H–Pd … multicenter interactions. These interactions provide sufficient thermodynamic stability for the hydrides to form, with negative binding energies of hydrogen. The binding energies are found to be significantly low, with the possibility of the ease of hydrogen desorption within limited reaction conditions.

Forecasting Customer Actions: Exploring Machine Learning Techniques for Behavior Analysis and Prediction

Modern modelling of today’s consumer behaviour is highly dependent on data mining which mines customers’ data in order to answer specific questions in time. This complexity and uncertainty relating to the consumer be-haviour makes it difficult for us to predict. Therefore, selection of appropri-ate methods is very important. Predictive models can be designed so as to identify specific group or individual actions and thus making them useful marketing tools. However, many models are overly simplistic for they leave out some of the essential factors hence leading to inaccurate forecasting out-comes. Consequently, instead of concentrating on customer behaviour-firm capital structure relationships only a strong association rule mining model should be created using online store data that effectively estimates customer response. Knowing their business clients is crucial when it comes to profitability by aligning the company’s earnings with their concerns. Artificial intelligence (AI) optimizes product location by clustering techniques targeting the right customers. It examines customer behaviour and buying trends utilizing Kaggle’s client membership card records such as Customer ID, age, gender, annual income, spending score among others. This includes basic market analytics based on demographic information like age or income split into groups, however big data superiority over traditional methods cannot be underestimated including machine learning applications such as Customer Seg-mentation Automated Methodology (CSAM), k-means clustering for user segmentation among others. This approach facilitates focused advertising campaigns and development and launch of new products aimed at particular consumer sections.

Holonomy and (stated) skein algebras in combinatorial quantization

The algebra \mathcal{L}_{g,n}(H) was introduced by Alekseev, Grosse, and Schomerus and by Buffe­noir and Roche and quantizes the character variety of the Riemann surface \Sigma_{g,n}\setminus D (where D is an open disk). In this article we define a holonomy map in that quantized setting, which associates a tensor with components in \mathcal{L}_{g,n}(H) to tangles in (\Sigma_{g,n}\setminus\!D) \times [0,1] , generalizing previous works of Buffenoir and Roche and of Bullock, Frohman, and Kania-Bartoszynska. We show that holonomy behaves well for the stack product and the action of the mapping class group; then we specialize this notion to links in order to define a generalized Wilson loop map. Thanks to the holonomy map, we give a geometric interpretation of the vacuum representation of \mathcal{L}_{g,0}(H) on \mathcal{L}_{0,g}(H) . Finally, the general results are applied to the case H=U_{q^2}(\mathfrak{sl}_{2}) in relation to skein theory and the most important consequence is that the stated skein algebra of a compact oriented surface with just one boundary edge is isomorphic to \mathcal{L}_{g,n}(U_{q^2}(\mathfrak{sl}_{2})) . Throughout the paper, we use a graphical calculus for tensors with coefficients in \mathcal{L}_{g,n}(H) which makes the computations and definitions very intuitive.

Comparative Study between Rocuronium And Magnesium Sulfate as Adjutants to Regional Anesthesia for Ophthalmic Surgeries using Peribulbar Block

Abstract Background Peribulbar anesthesia is frequently used in cataract surgeries. Compared to retrobulbar anesthesia, this approach is associated with less significant consequences. However, it has the disadvantages of a slower onset of orbital akinesia and the frequent requirement for block supplementation. Aim of the Work To evaluate the effect of addition of magnesium sulfate and rocuronium to standard local anesthetics mixture on the time of onset of globe and lid akinesia and corneal anesthesia for peribulbar block in ophthalmic surgeries. Patients and Methods This Prospective Double-blinded Randomized Study was carried out in the ophthalmic surgery unit, Ain Shams university hospital from January 2019 to April 2020. After institutional Ethical Board approval and obtaining written informed patients’ consents, 75 patients from both sexes, ASA physical status I-III, aged 40-80 years and having an Axial globe length less than or equals 26 mm scheduled for cataract surgery under peribulbar block were included in the study. Results Our study found statistically significant more rapid onset of action (mean time to start surgery) in rocuronium group (7.00±1.22) than control group and magnesium sulfate group (9.00±1.47 and 9.00±1.15) respectively, (p < 0.001); Moreover, no statistically significant difference was reported between control group and magnesium sulfate group. In addition, no significant difference was reported regarding duration of surgery between groups Conclusion Adding Rocuronium to local anesthetic mixture in peribulbar block during cataract surgery enhances ocular akinesia and corneal anesthesia and reduces the need for supplementary injections with no side effects and that was significantly better than Magnesium sulfate in term of rapid onset and time needed to achieve adequate condition to begin surgery. However, adding Magnesium sulfate showing good results regarding akinesia, corneal anesthesia and need for supplementary injections but it did not significantly fasten the onset of block and hence the time to start surgery.

A Hilbert–Mumford criterion for polystability for actions of real reductive Lie groups

AbstractWe study a Hilbert–Mumford criterion for polystablility associated with an action of a real reductive Lie group G on a real submanifold X of a Kähler manifold Z. Suppose the action of a compact Lie group with Lie algebra $$\mathfrak {u}$$ u extends holomorphically to an action of the complexified group $$U^{\mathbb {C}}$$ U C and that the U-action on Z is Hamiltonian. If $$G\subset U^{\mathbb {C}}$$ G ⊂ U C is compatible, there is a corresponding gradient map $$\mu _\mathfrak {p}: X\rightarrow \mathfrak {p}$$ μ p : X → p , where $$\mathfrak {g}= \mathfrak {k}\oplus \mathfrak {p}$$ g = k ⊕ p is a Cartan decomposition of the Lie algebra of G. Under some mild restrictions on the G-action on X, we characterize which G-orbits in X intersect $$\mu _\mathfrak {p}^{-1}(0)$$ μ p - 1 ( 0 ) in terms of the maximal weight functions, which we viewed as a collection of maps defined on the boundary at infinity ($$\partial _\infty G/K$$ ∂ ∞ G / K ) of the symmetric space G/K. We also establish the Hilbert–Mumford criterion for polystability of the action of G on measures.

Categorifying equivariant monoids

Equivariant monoids are very important objects in many branches of mathematics: they combine the notion of multiplication and the concept of a group action. In this paper we will construct categories which encode the structure borne by monoids with a group action by combining the theory of product and permutation categories (PROPs) and product and braid categories (PROBs) with the theory of crossed simplicial groups. PROPs and PROBs are categories used to encode structures borne by objects in symmetric and braided monoidal categories respectively, whilst crossed simplicial groups are categories which encode a unital, associative multiplication and a compatible group action. We will produce PROPs and PROBs whose categories of algebras are equivalent to the categories of monoids, comonoids and bimonoids with group action using extensions of the symmetric and braid crossed simplicial groups. We will extend this theory to balanced braided monoidal categories using the ribbon braid crossed simplicial group. Finally, we will use the hyperoctahedral crossed simplicial group to encode the structure of an involutive monoid with a compatible group action.

Quantum Annular Homology and Bigger Burnside Categories

As part of their construction of the Khovanov spectrum, Lawson, Lipshitz and Sarkar assigned to each cube in the Burnside category of finite sets and finite correspondences, a finite cellular spectrum. In this paper, we extend this assignment to cubes in Burnside categories of infinite sets. This is later applied to the work of Akhmechet, Krushkal and Willis on the quantum annular Khovanov spectrum with an action of a finite cyclic group: we obtain a quantum annular Khovanov spectrum with an action of the infinite cyclic group.

Homogeneous Spaces and Induced Transformation Groups of S-Topological Transformation Group

Homogeneous Spaces and Induced Transformation Groups of S-Topological Transformation Group