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# Lie Groups - Science topic

Explore the latest publications in Lie Groups, and find Lie Groups experts.

Publications related to Lie Groups (10,000)

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This paper proposes a nonlinear stochastic complementary filter design for inertial navigation that takes advantage of a fusion of Ultra-wideband (UWB) and Inertial Measurement Unit (IMU) technology ensuring semi-global uniform ultimate boundedness (SGUUB) of the closed loop error signals in mean square. The proposed filter estimates the vehicle’s...

The symmetries of a Riemann surface Σ \ {a i } with n punctures a i are encoded in its funda-1 mental group π 1 (Σ). Further structure may be described through representations (homomorphisms) 2 of π 1 over a Lie group G as globalized by the character variety C = Hom(π 1 , G)/G. Guided by our 3 previous work in the context of topological quantum com...

In this paper we first construct a Lie group structure on n × n Hankel matrices over R + by Hadamard product and then we find its Lie algebra structure and finally calculate dimension of this manifold over R +. Moreover, we discuss topological properties of this manifold using Frobenious norm. We pointed out the relation between Lie group and Lie a...

The main aim of this note is to prove sharp weighted integral Hardy inequality and conjugate integral Hardy inequality on homogeneous Lie groups with any quasi-norm for the range 1<p≤q<∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepac...

Land vehicles need high-precision navigational systems in which multi-sensor integration may be provided. Moreover, land vehicles regularly use Global Navigation Satellite Systems (GNSS) to estimate their position. Unfortunately, several locations, such as tunnels and inside parking garages, where GNSS signals cannot be detected. Several types of r...

We study the generation of two-qudit entangling quantum logic gates using two techniques in quantum optimal control. We take advantage of both continuous, Lie algebraic control and digital, Lie group control. In both cases, the key is access to a time-dependent Hamiltonian, which can generate an arbitrary unitary matrix in the group SU(d 2). We fin...

Most current methods for determining maneuvers and thrust firing sequences depend on explicit and predetermined commands generated by a combination of on-board systems and ground-based human-in-the-loop methods. For spacecraft and space structures with changing mass properties and thruster configurations, such as the Deep Space Gateway as it change...

Let M 3 {M}^{3} be a strictly almost cosymplectic three-manifold whose Ricci operator is weakly ϕ \phi -invariant. In this article, it is proved that Ricci curvatures of M 3 {M}^{3} are invariant along the Reeb flow if and only if M 3 {M}^{3} is locally isometric to the Lie group E ( 1 , 1 ) E\left(1,1) of rigid motions of the Minkowski 2-space equ...

This work scrutinizes the well-known nonlinear non-classical Sobolev-type wave model which
address the flow of fluid via fractured rock, thermodynamics and many other fields of modern
sciences. The symmetry generators are taking into account the Lie invariance criteria. The
suggested approach produces the three dimensional Lie algebra, where transl...

Generalized BMS (gBMS) is the Lie group of the asymptotic symmetries at null infinity, and is proposed to be a symmetry of the quantum S-matrix. Despite much progress in understanding the symplectic structure at null infinity consistent with the gBMS symmetries, the construction of a radiative phase space where all the physical soft modes and their...

Symmetries and their applications always played an important role in I.E. Segal’s work. I shall exemplify this, starting with his correct proof (at the Lie group level) of what physicists call the “O’Raifeartaigh theorem”, continuing with his incidental introduction in 1951 of the (1953) Inönü-Wigner contractions, of which the passage from AdS (SO(...

In this paper, we discuss the concept of an analytic prolongation of a local Riemannian metric. We propose a generalization of the notion of completeness realized as an analytic prolongation of an arbitrary Riemannian metric. Various Riemannian metrics are studied, primarily those related to the structure of the Lie algebra 𝔤 of all Killing vector...

In this paper, we study the Einstein equation on three-dimensional Lie groups equipped with a left-invariant (pseudo) Riemannian metric and a metric connection with left-invariant vector torsion. We prove that all such Lie groups are either Einstein manifolds with respect to the Levi-Civita connection or conformally flat manifolds.

We report on recent work concerning a new type of generalised Kac-Moody algebras based on the spaces of differentiable mappings from compact manifolds or homogeneous spaces onto compact Lie groups.

Within the extremal black hole attractors arising in ungauged \mathcal{N}≥2 𝒩 ≥ 2 -extended Maxwell Einstein supergravity theories in 3+1 3 + 1 space-time dimensions, we provide an overview of the stratification of the electric-magnetic charge representation space into “large” orbits and related “moduli spaces”, under the action of the (continuous...

The space of representations of a surface group into a given simple Lie group is a very active area of research and is particularly relevant to higher Teichmuller theory. For a closed surface, classical Teichmuller space is a connected component of the moduli space of representations into PSL(2, R) and [Fock-Goncharov:2006] showed that the space of...

This paper studies the robust stabilization of rigid-body attitudes represented by a special orthogonal matrix. A geometric proportional–integral–derivative (PID) controller is proposed with all the input commands defined in the dual space so*(3) of a Lie algebra for left-invariant systems evolving on a Lie group SO(3). Almost global asymptotic sta...

We present a Veronese formulation of the octonionic and split-octonionic pro-jective and hyperbolic planes. This formulation of the incidence planes highlights the relationship between the Veronese vectors and the rank-1 elements of the Albert algebras over octonions and split-octonions, yielding to a clear formulation of the relationship with the...

This article delves into the wave dynamics of the (3+1)-dimensional nonlinear model, which serves as a representation of shallow water waves. This model finds relevance in addressing various natural phenomena such as tides, storms, atmospheric flows, and tsunamis, all linked to shallow water waves. These waves, often called long water waves, exhibi...

In this study, the surface wave in inviscid fluid was analyzed. Starting from Euler equation and mass conservation equation, coupled with a set of boundary conditions, the equations obtained by dimensionless method contain two parameters: amplitude parameter \(\alpha \) and shallowness parameter \(\beta \). Using double-series perturbation analysis...

Let X X be a compact Riemann surface of genus g ≥ 2 g\ge 2 , G G be a semisimple complex Lie group and ρ : G → GL ( V ) \rho :G\to {\rm{GL}}\left(V) be a complex representation of G G . Given a principal G G -bundle E E over X X , a vector bundle E ( V ) E\left(V) whose typical fiber is a copy of V V is induced. A ( G , ρ ) \left(G,\rho ) -Higgs pa...

We explore various formality and finiteness properties in the differential graded algebra models for the Sullivan algebra of piecewise polynomial rational forms on a space. The 1-formality property of the space may be reinterpreted in terms of the filtered and graded formality properties of the Malcev Lie algebra of its fundamental group, while som...

In this current study, a systematic investigation is performed to derive symmetry reductions of conformable time-fractional Schamel-KdV equation via the Lie symmetry method. Using the obtained Lie point symmetries of nonlinear FPDEs the symmetry reduction is generated and utilized for the reduction into an ordinary differential equation. Some solut...

In this comment, we report that a recent paper (Dhiman and Kumar in Eur Phys J Plus 138(3):195, 2023) contains significant errors, omissions, and inaccuracies.

In this paper, we introduce some distinct classes of entangled cat states associated to generalized displaced Fock states. For this purpose, we use the formalism of nonlinear coherent states corresponding to nonlinear oscillator algebra which yields various kinds of $f$-deformed entangled states. We also take a particular class of Gilmore-Perelomov...

A multidimensional projective space with a marked point (center) is considered. On the manifold of projective frames of the given space that are adapted to the center, the action of the stabilizer of the center of the group of projective transformations is introduced. We prove that linear frames, i.e., bases of the tangent vector space of the proje...

Let H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {H}$$\end{document} denote the 3-dimensional Heisenberg Lie group. The main purpose of this paper is to cla...

In this paper, the problem of prescribed values of the operator of sectional curvature on a three-dimensional locally homogeneous Lorentzian manifolds is solved. Necessary and sufficient conditions for the operator of sectional curvature of such manifolds are obtained.

Let G = N ⋊ A, where N is a stratified Lie group and A = R + acts on N via automorphic dilations. We prove that the group G has the Calderón-Zygmund property, in the sense of Hebisch and Steger, with respect to a family of flow measures and metrics. This generalizes in various directions previous works by Hebisch and Steger and Martini, Ottazzi and...

The rigid body displacement mathematical model is a Lie group of the special Euclidean group SE (3). This article is about the Lie algebra se (3) group. The standard exponential map from se (3) onto SE (3) is a natural parameterization of these displacements. In technical applications, a crucial problem is the vector minimal parameterization of man...

In this paper, we consider infinitesimal properties of multidimensional median Bol threewebs with a covariantly constant curvature tensor (webs \({B}_{m}^{\nabla }\)) and lay the foundations for classifying such webs by the rank of the torsion tensor. For three-webs \({B}_{m}^{\nabla }\) of rank ρ, we construct an adapted frame by the Cartan method...

We perform a comprehensive analysis of the symmetry-resolved (SR) entanglement entropy (EE) for one single interval in the ground state of a 1 + 1D conformal field theory (CFT), that is invariant under an arbitrary finite or compact Lie group, G. We utilize the boundary CFT approach to study the total EE, which enables us to find the universal lead...

As a typical kinematic problem, an important criterion for the accuracy of robot-world calibration is whether the rotational and translational parts are calculated separately or not. Solving the kinematic equation separately increases the interest into the decomposition mode of the equation. This paper provides a decomposition mode for Ad(SE(3)) wi...

We provide a unifying theoretical and methodological framework for Lie group symmetry in machine learning from a linear-algebraic viewpoint. The central objects in this work are linear operators describing the finite and infinitesimal transformations of smooth sections of vector bundles with fiber-linear Lie group actions. We explain how these idea...

We consider Anosov subgroups of a semi-simple Lie group, a higher rank generalization of convex cocompact groups. Cocompact domains of discontinuity for these groups in flag manifolds were constructed systematically by Kapovich et al. (Geom Topol 22(1):157–234, 2018). For Δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \use...

The relation between the holonomy along a loop with the curvature form is a well-known fact, where the small square loop approximation of aholonomy Hγ,O is proportional to Rσ. In an attempt to generalize the relation for arbitrary loops, we encounter the following ambiguity. For a given loop γ embedded in a manifold M, Hγ,O is an element of a Lie g...

We prove a statement concerning hyperlinearity for central extensions of property (T) groups in the presence of flexible HS-stability, and more generally, weak ucp-stability. Notably, this result is applied to show that if \({{\,\textrm{Sp}\,}}_{2g} ({\mathbb {Z}})\) is flexibly HS-stable, then there exists a non-hyperlinear group. Further, the sam...

The theory of scaling called finite similitude does not involve dimensional analysis and is founded on a transport-equation approach that is applicable to all of classical physics. It features a countable infinite number of similitude rules and has recently been extended to other types of governing equations (e.g., differential, variational) by the...

In this article, we are concerned with minimal-time optimal problems for the class of controllable linear control system on low-dimensional nonnilpotent solvable Lie groups and their homogeneous spaces.

We establish the $L^p$-$L^q$-boundedness of subelliptic pseudo-differential operators on a compact Lie group $G$. Effectively, we deal with the $L^p$-$L^q$-bounds for operators in the sub-Riemmanian setting because the subelliptic classes are associated to a H\"ormander sub-Laplacian. The Riemannian case associated with the Laplacian is also includ...

The Félix-Tanré rational model [12] for the polyhedral product of a fibre inclusion is considered. In particular, we investigate the rational model for the polyhedral product of a pair of Lie groups corresponding to arbitrary simplicial complex and the rational homotopy group of the polyhedral product. Furthermore, it is proved that for a partial q...

This paper investigates the dynamical and integrability properties and the complete analytical solutions of the well-known SEIR and the SIRV models utilized for the COVID-19 pandemic by employing the partial Hamiltonian method based on Lie group theory. Regarding the model's parameters, two distinct cases are evaluated for each model. The closed-fo...

We call a poset factorable if its characteristic polynomial has all positive integer roots. Inspired by inductive and divisional freeness of a central hyperplane arrangement, we introduce and study the notion of inductive posets and their superclass of divisional posets. It then motivates us to define the so-called inductive and divisional abelian...

Jordan algebras arise naturally in (quantum) information geometry, and we want to understand their role and their structure within that framework. Inspired by Kirillov's discussion of the symplectic structure on coadjoint orbits, we provide a similar construction in the case of real Jordan algebras. Given a real, finite-dimensional, formally real J...

We construct pairs of residually finite groups with isomorphic profinite completions such that one has non-vanishing and the other has vanishing real second bounded cohomology. The examples are lattices in different higher-rank simple Lie groups. Using Galois cohomology, we actually show that $\operatorname {SO}^0(n,2)$ for $n \ge 6$ and the except...

This paper carries out research on the offshore gangway, and introduces the spinor theory method which is simpler to calculate and more comprehensive to describe than the D-H parameter method. Referring to the modeling method of the series manipulator, the exponential product formula is applied to the kinematic analysis of the offshore gangway and...

We present a novel approach to generate Bessel–Gauss modes of arbitrary integer order and well-defined optical angular momentum in a gradient index medium of transverse parabolic profile. The propagation and coherence properties, as well as the quality factor, are studied using algebraic techniques that are widely used in quantum mechanics. It is f...

Dans cette communication, nous dérivons une nouvelle borne de Cramér-Rao intrinsèque pour paramètres et observations vivant sur groupes de Lie. L'expression est obtenue en utilisant les propriétés inhérentes à leur structure. De plus, une expression exacte est obtenue dans le cas où paramètres et observations sont sur SO(2), le groupe de Lie des ma...

The viscous laminar magnetohydrodynamic convective boundary layer flow with the combined effects of chemical reaction and nonlinear velocity slip and linear thermal and concentration slips have been considered across a flat plate in motion. Using a non-dimensional transformation attained by the single parameter continuous group method, the governin...

We show that there exists a quantum compact metric space which underlies the setting of each Sobolev algebra associated to a subelliptic laplacian ∆ =-( X_1^2 + · · · + X _m^2) on a compact connected Lie group G if p is large enough, more precisely under the (sharp) condition p > d α where d is the local dimension of (G, X) and where 0 < α <1. We a...

Let [Formula: see text] be a Kähler manifold and let [Formula: see text] be a compact connected Lie group with Lie algebra [Formula: see text] acting on [Formula: see text] and preserving [Formula: see text]. We assume that the [Formula: see text]-action extends holomorphically to an action of the complexified group [Formula: see text] and the [For...

By calculating inequivalent classical r-matrices for the $$gl(2,{\mathbb {R}})$$ g l ( 2 , R ) Lie algebra as solutions of (modified) classical Yang-Baxter equation ((m)CYBE), we classify the YB deformations of Wess-Zumino-Witten (WZW) model on the $$GL(2,{\mathbb {R}})$$ G L ( 2 , R ) Lie group in twelve inequivalent families. Most importantly, it...

For a finite group $G$ of not prime power order, Oliver showed that the obstruction for a finite CW-complex $F$ to be the fixed point set of a contractible finite $G$-CW-complex is determined by the Euler characteristic $\chi (F)$. (He also has similar results for compact Lie group actions.) We show that the analogous problem for $F$ to be the fixe...

We investigate the differential geometry and topology of four-dimensional Lorentzian manifolds (M, g) equipped with a real Killing spinor \(\varepsilon \), where \(\varepsilon \) is defined as a section of a bundle of irreducible real Clifford modules satisfying the Killing spinor equation with nonzero real constant. Such triples \((M,g,\varepsilon...

We establish a Tukia-type theorem for uniform quasiconformal groups of a Carnot group. More generally we establish a fiber bundle version (or foliated version) of Tukia theorem for uniform quasiconformal groups of a nilpotent Lie group whose Lie algebra admits a diagonalizable derivation with positive eigenvalues. These results have applications to...

Recently, on-orbit service, formation flight, rendezvous and docking, fuel filling, and other close-distance operations have attracted increasing attention from researchers. Traditional control methods assume that the translation and rotation of spacecraft are decoupled, and spacecraft control adopts the serial control mode of alternate attitude an...

The Wahba problem, first proposed by Grace Wahba in 1965, seeks the proper orthogonal matrix (attitude matrix, direction-cosine matrix), which minimizes a cost function built from a set of measured directions observed in a rigid body frame. This problem is essential in multiple aerospace engineering applications that typically involve finding an op...

In physics, two systems that radically differ at short scales can exhibit strikingly similar macroscopic behaviour: they are part of the same long-distance universality class¹. Here we apply this viewpoint to geometry and initiate a program of classifying homogeneous metrics on group manifolds² by their long-distance properties. We show that many m...

Analogues of the classical affine-projective correspondence are developed in the context of statistical manifolds compatible with a radiant vector field. These utilize a formulation of Einstein equations for special statistical structures that generalizes the usual Einstein equations for pseudo-Riemannian metrics and is of independent interest. A c...

This paper derives the dynamic equations of a reduced-order race-car model using Lie-group methods. While these methods are familiar to computational dynamicists and roboticists, their adoption in the vehicle dynamics community is limited. We address this gap by demonstrating how this framework integrates smoothly with the Articulated-Body Algorith...

We discuss Cartan-Schouten metrics (Riemannian or pseudo-Riemannian met-rics that are parallel with respect to the Cartan-Schouten canonical connection) on perfect Lie groups and in particular, on cotangent bundles of simple Lie groups. Applications are foreseen in Information Geometry. Throughout this work, the tangent bundle T G and the cotangent...

The purpose of the present research endeavor is to propose a novel control strategy for a DC-DC electrical converter realized as a switched circuit. The present endeavor is based on an early work by Leonard and Krishnaprasad where a prototypical DC-DC converter was modeled as a state space dynamical system and controlled by an open-loop strategy ba...

Let O(Spin q 1/2 (2n + 1)) and O(SO q (2n + 1)) be the quantized algebras of regular functions on the Lie groups Spin(2n + 1) and SO(2n + 1), respectively. In this article, we prove that the Gelfand-Kirillov dimension of a simple unitarizable O(Spin q 1/2 (2n + 1))-module V Spin t,w is the same as the length of the Weyl word w. We show that the sam...

To address the problem of the expensive and time-consuming annotation of high-resolution remote sensing images (HRRSIs), scholars have proposed cross-domain scene classification models, which can utilize learned knowledge to classify unlabeled data samples. Due to the significant distribution difference between a source domain (training sample set)...

In this paper, the main aim is to consider the boundedness of the nonlinear commutator [b,Mα]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$[b, M_{\alpha}]$\end{documen...

Quantum theory suggests that the three observed gauge groups U(1), SU(2) and SU(3) are related to the three Reidemeister moves: twists, pokes and slides. The background for the relation is provided. It is then shown that twists generate the group U(1), whereas pokes generate SU(2). Emphasis is placed on proving the relation between slides, the Gell...

We prove a generalization of the classical Klein–Maskit combination theorem, in the free product case, in the setting of Anosov subgroups. Namely, if ΓA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidem...

Let G be a compact and connected Lie group. The Hamiltonian G-model functor maps the category of symplectic representations of closed subgroups of G to the category of exact Hamiltonian G-actions. Based on previous joint work with Y. Karshon, the restriction of this functor to the momentum proper subcategory on either side induces a bijection betwe...

We classify compact, connected Hamiltonian and quasi-Hamiltonian manifolds of cohomogeneity one (which is the same as being multiplicity free of rank one). The group acting is a compact connected Lie group (simply connected in the quasi-Hamiltonian case). This work is a concretization of a more general classification of multiplicity free manifolds...

The complete quantum metric of a parametrized quantum system has a real part (usually known as the Provost-Vallee metric) and a symplectic imaginary part (known as the Berry curvature). In this paper, we first investigate the relation between the Riemann curvature tensor of the space described by the metric, and the Berry curvature, by explicit par...

The effects of surface mass flux (suction/injection) and variable viscosity on free-forced convec-tion along a stretching or shrinking permeable plate embedded in a saturated porous medium are investigated through Lie-group analysis for steady two-dimensional flow in this paper. Assumptions are made that the fluid viscosity varies as a linear funct...

A Lie algebra morphism triple is a triple (g,h,ϕ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\mathfrak {g}, \mathfrak {h}, \phi )$$\end{document} consisting of two...

The upshot of nonlinear thermal radiation of steady state MHD heat transfer of Jeffrey nanofluid together with prescribed boundary conditions of interest was studied. Essential fluid properties, dimensionless switch parameters with the assistance of the Lie group method were used to transform the convenient partial differential equations that descr...

J-trajectories are arc-length-parameterized curves in almost Hermitian manifolds, which satisfy the equation ∇γ˙γ˙=qJγ˙\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\...

In this paper, an explicit boundary-type numerical procedure, including a constraint-type fictitious time integration method (FTIM) and a two-point boundary solution of the Lie-group shooting method (LGSM), is constructed to tackle nonlinear nonhomogeneous backward heat conduction problems (BHCPs). Conventional methods cannot effectively overcome n...

We consider nilpotent Lie groups for which the derived subgroup is abelian. We equip them with subRiemannian metrics and we study the normal Hamiltonian flow on the cotangent bundle.
We show a correspondence between normal trajectories and polynomial Hamiltonians in some euclidean space. We use the aforementioned correspondence to give a criterion...

The displacement and motion representation of rigid bodies and multibody systems is one of the principal issues in different research domains like robotics, theoretical kinematics, computer vision, astrodynamics, etc. Higher-order acceleration is crucial in robotic mechanical device design, kinematics, and real-time control. Acquiring higher-order...

Platonization of atomic and nuclear physics could be said to be the theme of this work. The construction of electron configurations of atoms and proton and neutron configurations of atomic physics have considerable analogies and the spectra have essentially the same structure in the standard model. In the TGD framework, the nuclear string model pro...

We present three new coset manifolds named Dixon-Rosenfeld lines that are similar to Rosenfeld projective lines except over the Dixon algebra $$\mathbb {C}\otimes \mathbb {H}\otimes \mathbb {O}$$ C ⊗ H ⊗ O . Three different Lie groups are found as isometry groups of these coset manifolds using Tits’ formula. We demonstrate how Standard Model intera...

We show here in a graphical compact presentation, the fundamental symmetries in physics:
-the fundamental metric rotation group: Lorentz group, and its two fundamental representations as spinors (basic particles) and vectors (basic fields)
-the three symmetry operators C P T, and their breaking
-duality wave-particle
-SU(n) Lie group and Yang-Mills...

Quantum theory suggests that the three observed gauge groups U(1), SU(2) and SU(3) are related to the three Reidemeister moves of knot theory: twists, pokes and slides. The background for the relation is clarified. It is then shown that the twist generates U(1) and that pokes generate SU(2). The emphasis is put on deducing the relation between slid...

The aim of this research paper is to analytically investigate graphene oxide blood base nano°uid with the impact of dynamic viscosity and viscous dissipation. The increased thermal conductivity of nano°uids over regular°uids motivates this research. The basic°ow equations are used to model the°ow problem in nonlinear partial di®erential equations (...

This paper investigates MHD fluid flow and distribution of heat inside a filter chamber during a process of filtering particles from the fluid. A flow model of MHD viscous incompressible fluid inside a filter is studied to seek semi-analytical solutions which are analysed to find flow and heat dynamics that lead to optimal outflow (maximum filtrate...

This manuscript studies the global dynamics of a linear system on a disconnected Lie group. It shows that the connected components of the equilibria form a Lie subgroup, and the dynamics depends on the stability properties of the identity. The main result assures that if the identity is asymptotically stable the system decomposes as component syste...

We completely characterize the pairs of connected Lie groups G>K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G > K$$\end{document} such that rkG-rkK=1\documentclass[...

This work presents a shooting algorithm to compute the periodic responses of geometrically nonlinear structures modelled under the Special Euclidean (SE) Lie group formulation. The formulation is combined with a pseudo-arclength continuation method, while special adaptations are made to ensure compatibility with the SE framework. Nonlinear normal m...

This work presents a shooting algorithm to compute the periodic responses of geometrically nonlinear structures modelled under the Special Euclidean (SE) Lie group formulation. The formulation is combined with a pseudo-arclength continuation method, while special adaptations are made to ensure compatibility with the $SE$ framework. Nonlinear normal...

The study of Ricci solitons and invariant Ricci solitons with connections of various types has garnered much attention from many mathematicians. Metric connections with vector torsion, or semisymmetric connections, were first studied by E. Cartan on (pseudo) Riemannian manifolds. Later, K. Yano and I. Agricola studied tensor fields and geodesic lin...

In his study on the geometry of Lie groups, Rosenfeld postulated a strict relation between all real forms of exceptional Lie groups and the isometries of projective and hyperbolic spaces over the (rank-2) tensor product of Hurwitz algebras taken with appropriate conjugations. Unfortunately, the procedure carried out by Rosenfeld was not rigorous, s...

We prove a Lie 2-group torsor version of the well-known one-one correspondence between fibered categories and pseudofunctors. Consequently, we obtain a weak version of the principal Lie group bundle over a Lie groupoid. The correspondence also enables us to extend a particular class of principal 2-bundles to be defined over differentiable stacks. W...

Quantum mechanical
systems with position dependent masses (PDM) admitting two parametric Lie symmetry groups are classified. Namely,
all PDM systems are specified which, in addition to their invariance w.r.t. a two
parametric Lie group, admit at least one second order integral of motion. The presented classification is partially extended to the mor...

A probability density or distribution function of turbulence has been thought to be symmetric due to the symmetry of the partial differential equations from the first principle. However, the experimental data have shown otherwise by a so-called Taylor correlation function, and this is an unresolved issue. A recent study shows that this probability...

The relations satisfied by symplectic flows and vector fields on phase space are examined in different coordinate bases. It is shown that many relations satisfied by the symplectic matrix Lie group, and its Lie algebra of Hamiltonian matrices, are the coordinate representations (in symplectic coordinates) of coordinate-agnostic tensor relations on...

The complete quantum metric of a parametrized quantum system has a real part (usually known as the Provost-Vallee metric) and a symplectic imaginary part (known as the Berry curvature). In this paper, we first investigate the relation between the Riemann curvature tensor of the space described by the metric, and the Berry curvature, by explicit par...