Action Of Group Research Articles

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

Minimizing under relaxed symmetry constraints: Triple and N-junctions

We consider a nonnegative potential $W:\mathbb{R}^2\rightarrow\mathbb{R}$ invariant under the action of the rotation group $C_N$ of the regular polygon with $N$ sides, $N\geq 3$. We assume that $W$ has $N$ nondegenerate zeros and prove the existence of a $N$-junction solution to the vector Allen-Cahn equation. The proof is variational and is based on sharp lower and upper bounds for the energy and on a new pointwise estimate for vector minimizers.

Study on the interior equilibrium point of a special class of 2 × 2 × 2 asymmetric evolutionary games.

Many behavioural interactions in real life involve three individuals. When each individual has two alternative strategies, they can be abstracted into mathematical models by means of asymmetric games. In this paper, we explore a special class of asymmetric games satisfying fixed conditions. Firstly, we analyse two solitary interior equilibrium points and provide the judgement condition for their instability based on the Jacobi matrix local stability analysis method. Secondly, we analyse the interior equilibrium points that are continuously distributed within a line and probe into their stability conditions based on generalized Hamiltonian systems theory. Under the circumstances, the stable interior equilibrium point is surrounded by closed orbits in phase space, which presents an observable stable state where two strategies coexist and fluctuate in each of the three game populations. This work enriches the study of asymmetric games' evolutionary dynamics.

Dynamic Feedback Linearization of Control Systems with Symmetry

Control systems of interest are often invariant under Lie groups of transformations. For such control systems, a geometric framework based on Lie symmetry is formulated, and from this a sufficient condition for dynamic feedback linearizability obtained. Additionally, a systematic procedure for obtaining all the smooth, generic system trajectories is shown to follow from the theory. Besides smoothness and the existence of symmetry, no further assumption is made on the local form of a control system, which is therefore permitted to be fully nonlinear and time varying. Likewise, no constraints are imposed on the local form of the dynamic compensator. Particular attention is given to the consideration of geometric (coordinate independent) structures associated to control systems with symmetry. To show how the theory is applied in practice we work through illustrative examples of control systems, including the vertical take-off and landing system, demonstrating the significant role that Lie symmetry plays in dynamic feedback linearization. Besides these, a number of more elementary pedagogical examples are discussed as an aid to reading the paper. The constructions have been automated in the Maple package DifferentialGeometry.

Testing a radiation-protective polymer composite on the ISS

The article presents the results of polymer composite testing on the Russian segment of the International Space Station (ISS) during 225 days. For the space experiment “Shielding Composite” two cylinder-shaped composite containers were manufactured. Inside the containers there were detectors for dose registration during the orbital space flight. Presents the results of research on the first container, which was lowered to Earth in 2022. As a result of the space experiment “Shielding Composite”, it was found that the attenuation ratio of the absorbed dose of space ionizing radiation (Inner sensor value/Outdoor sensor value) with a shield wall thickness of 10 mm was 0.71 ± 0.02 for container No. 1. There is no induced radiation in the container after its descent to Earth.

The binary actions of simple groups with a single conjugacy class of involutions

Abstract We continue our investigation of binary actions of simple groups. In this paper, we demonstrate a connection between the graph Γ ⁢ ( C ) \Gamma(\mathcal{C}) based on the conjugacy class 𝒞 of the group 𝐺, which was introduced in our previous work, and the notion of a strongly embedded subgroup of 𝐺. We exploit this connection to prove a result concerning the binary actions of finite simple groups that contain a single conjugacy class of involutions.

Coupled Spacecraft Charging Due to Continuous Electron Beam Emission and Impact

Spacecraft charge naturally in orbit due to the plasma environment and the electromagnetic radiation from the sun. By emitting an electron beam, a servicer spacecraft can control its electric potential and also the potential of a neighboring target if the electron beam is aimed at the target spacecraft. In addition, the impacting electron beam excites secondary electrons and x-rays, providing a way to touchlessly sense the potential of the target. Because of the electron beam, the charging dynamics of the two spacecraft are coupled. This paper studies the effects of the beam on the electric potentials using a numerical charging model. It is found that multiple equilibria may exist due to the electron beam. Jumps between equilibrium configurations are possible when the electron beam energy is quickly reduced or when current fluctuations are present. Being aware of multiple equilibrium configurations is important for feedback-based charge control but also enables a new open-loop charge control around one of the equilibria. The effect of the electron beam on the spacecraft potentials is studied for geostationary Earth orbit and cislunar space. It is found that the current applied by the beam to the target may influence remote electric potential sensing methods.

Geometrical interpretation of isospin subalgebras in SU(3)

Ever since new tetrads in four-dimensional Lorentzian curved spacetimes were introduced, many outstanding properties and results have been proven regarding Riemannian geometry, gauge theory or group theory. These tetrads might carry spacetime-kinematic information about particle multiplets. Among other properties, these new tetrads, locally and covariantly diagonalize stress–energy tensors. In the case where particles have an electromagnetic field, the local planes of gauge symmetry served as a tool in order to propose a new gravitational-kinematic interpretation of particle multiplets. The core reason stems from the mathematical fact that all local gauge symmetries associated to the Standard Model have been proven to be isomorphic to local groups of tetrad transformations in four-dimensional Lorentzian spacetimes. Therefore, the different stress–energy tensors have been proven to determine the local gauge geometry as a natural part of Riemannian geometry. The stress–energy tensors determine locally the orthogonal planes such that the rotation on either of them of the local tetrad vectors that span these planes is isomorphic to local tetrad gauge transformations. All these properties put together allow for a reinterpretation presented previously of particle states as particle gravitational-kinematic-spacetime tetrad states in the asymptotically flat limit. We proceed in this paper to study the case where there are [Formula: see text], [Formula: see text] and [Formula: see text] isospin subalgebras or submultiplets within the context of this new Riemannian interpretation of gauge symmetries.

Cohomology-developed matrices: constructing families of weighing matrices and automorphism actions

The aim of this work is to construct families of weighing matrices via their automorphism group action. The matrices can be reconstructed from the 0, 1, 2-cohomology groups of the underlying automorphism group. We use this mechanism to (re)construct the matrices out of abstract group datum. As a consequence, some old and new families of weighing matrices are constructed. These include the Paley conference, the projective space, the Grassmannian, and the flag variety weighing matrices. We develop a general theory relying on low-dimensional group cohomology for constructing automorphism group actions and in turn obtain structured matrices that we call cohomology-developed matrices. This ‘cohomology development’ generalizes the cocyclic and group developments. The algebraic structure of modules of cohomology-developed matrices is discussed, and an orthogonality result is deduced. We also use this algebraic structure to define the notion of quasiproducts, which is a generalization of the Kronecker product.

A Group Action on an R-Module and G-Module

In this work, we introduce and study in the second part a new concept (the main result), which is called a group action on an module; in the third part, the group action on a ring as -module; and in the fourth part, the relation between the -module and the group action on it. We give examples, properties, propositions, theorems, and corollaries about them.

Islamophobia in India and the Racial State

This article focuses on the relationship between nation-making and the emergence of Islamophobia in India. Studies on anti-Muslim violence and Islamophobia in India either tend to dismiss the concept or limit its deployment by identifying it within the actions of Hindu nationalist groups situating their rise as an exception to India’s secular and multicultural trajectory. Premising on the idea that Islamophobia should be understood as the negation of Muslim political subjectivity this article argues that Hindutva is not an aberration. Rather, it is a continuation of the Indian nation-making project with the Muslim placed as the other of this project. Further, the article frames India as a racial state and this argument would include identifying its systemic nature by looking at the sections of the Indian constitutions and constituent assembly debates. Thus, the Indian state will be understood not as a mere facilitator but as an embodiment of Brahminical hegemony that generates racial conflict and divisions and attempts to exclude or eliminate Muslimness through homogenizing or marginalizing processes.