Symmetric Spaces Research Articles

Quadratic Killing tensors on symmetric spaces which are not generated by Killing vector fields

Quadratic Killing tensors on symmetric spaces which are not generated by Killing vector fields

Two‐sided estimates of Lebesque constants for Hölder spaces

AbstractA two‐sided estimate of Lebesgue constants is proposed for the Hölder space , constructed from the modulus of continuity of the th order calculated in the symmetric space . Choosing different function spaces , we obtain new criteria for the convergence of classical Fourier series.

Quantum geometrical properties of topological materials

The momentum space of topological insulators and topological superconductors is equipped with a quantum metric defined from the overlap of neighboring valence band states or quasihole states. We investigate the quantum geometrical properties of these materials within the framework of Dirac models and differential geometry. Their momentum space is found to be always a maximally symmetric space with a constant Ricci scalar, and the vacuum Einstein equation is satisfied in 3D with a finite cosmological constant. For linear Dirac models, several geometrical properties are found to be independent of the band gap, including a peculiar straight line geodesic, constant volume of the curved momentum space, and the exponential decay form of the nonlocal topological marker, indicating the peculiar yet universal quantum geometrical properties of these models.

Continuous asymmetric Doob inequalities in noncommutative symmetric spaces

Let (M,τ) be a noncommutative probability space equipped with a filtration (Mt)t∈[0,1] whose union is w⁎-dense in M, and let (Et)t∈[0,1] be the associated conditional expectations. We prove in the present paper that if the symmetric space E∈Int[Lp,Lq] with 1<p≤q<2 and E is 2(1−θ)-convex and w-concave with p<w<2, then the following holds:‖(Et(x))t∈[0,1]‖E(M;ℓ∞θ)≤CE,θ‖x‖HEc,x∈HEc(M) provided 1−p/2<θ<1. Similar result holds for x∈HEr(M). Moreover, if E∈Int[Lp,Lq] with 1<p≤q<2 and E is w-concave with 2<w<2p/(2−p), then for each x∈E(M) there exist y, z∈E(M) such that x=y+z and‖(Et(y))t∈[0,1]‖E(M;ℓ∞c)+‖(Et(z))t∈[0,1]‖E(M;ℓ∞r)≤cE‖x‖E(M). These results can be considered as continuous analogues of those due to Randrianantoanina et al. [33]. One of the key ingredients in our proof is a new decomposition theorem of E(M)-modules for general symmetric space E, which extends the known result of Junge and Sherman.

A Theorem on k-Expansive Mapping and its Fixed Point in G𝐽 𝑆 – Metric Space

Objectives: To find a fixed point of k-expansive mapping on GJS-metric space by establishing a theorem on it and to prove the uniqueness of such a fixed point. Methods: A theorem for the k-expansive map on GJS-metric space is established by generalizing an existing contractive condition theorem. Generalization is done by replacing the contractive condition with an expansive type of condition. Findings: Certain conditions that have to be satisfied by a k-expansive mapping for the existence and uniqueness of fixed points in GJS-metric space were found in this article. An example is also given to illustrate the existence of a fixed point. Novelty: GJS-metric space is a new metric space that has been established recently. Furthermore, the fixed point theorem of k-expansive mapping on GJS - metric space has not yet been proved by anyone, and hence it is proved in this article. 2020 Mathematics Subject Classification: 47H10, 54H25. Keywords: GJS-Metric space; Symmetric GJS-Metric space; GJS-Continuous function; GJS-Cauchy sequence; Expansive mapping; k-Expansive mapping

Estimates for Certain Rough Multiple Singular Integrals on Triebel–Lizorkin Space

This paper focuses on studying the mapping properties of singular integral operators over product symmetric spaces. The boundedness of such operators is established on Triebel–Lizorkin spaces whenever their rough kernel functions belong to the Grafakos and Stefanov class. Our findings generalize, extend and improve some previously known results on singular integral operators.

Investigations on the growth, spectral, optical, electrical, thermal and nonlinear optical properties of L-valine itaconic acid single crystal

A nonlinear optical single crystal of L-Valine Itaconic Acid (LVIA) was grown at room temperature from an aqueous solution by using the slow evaporation method. The grown crystal was undergone X-ray diffraction investigation, which confirm that the crystal belongs to orthorhombic system with the non-centro symmetric Pbca space group. This single crystal contains several functional groups, according to FTIR spectroscopic analysis there were identified. By analyzing the crystal's UV–visible spectrum, based on its optical transparency this crystal may use for optoelectronic device manufacturing. The emission happens at 553 nm wavelength, according to the photoluminescence spectrum. Thermo gravimetric and differential thermal analytical studies helps us to measure title crystal melting point and thermal stability. At various temperatures, the dielectric property of the crystal was found out. The Kurtz-powder method has been used to study the phenomenon of Second Harmonic Generation (SHG) in the crystal.

Plücker coordinates and the Rosenfeld planes

The exceptional compact hermitian symmetric space EIII is the quotient E6/Spin(10)×Z4U(1). We introduce the Plücker coordinates which give an embedding of EIII into CP26 as a projective subvariety. The subvariety is cut out by 27 Plücker relations. We show that, using Clifford algebra, one can solve this over-determined system of relations, giving local coordinate charts to the space.Our motivation is to understand EIII as the complex projective octonion plane (C⊗O)P2, whose construction is somewhat scattered across the literature. We will see that the EIII has an atlas whose transition functions have clear octonion interpretations, apart from those covering a sub-variety X∞ of dimension 10. This subvariety is itself a hermitian symmetric space known as DIII, with no apparent octonion interpretation. We give detailed analysis of the geometry in the neighbourhood of X∞.We further decompose X=EIII into F4-orbits: X=Y0∪Y∞, where Y0∼(OP2)C is an open F4-orbit and is the complexification of OP2, whereas Y∞ has co-dimension 1, thus EIII could be more appropriately denoted as (OP2)C‾. This decomposition appears in the classification of equivariant completion of homogeneous algebraic varieties by Ahiezer [2].

Geometry of Selberg's bisectors in the symmetric space SL(n,R)/SO(n,R)$SL(n,\mathbb {R})/SO(n,\mathbb {R})$

AbstractI study several problems about the symmetric space associated with the Lie group . These problems are connected to an algorithm based on Poincaré's Fundamental Polyhedron Theorem, designed to determine generalized geometric finiteness properties for subgroups of . The algorithm is analogous to the original one in hyperbolic spaces, while the Riemannian distance is replaced by an ‐invariant premetric. The main results of this paper are twofold. In the first part, I focus on questions that occurred in generalizing Poincaré's Algorithm to my symmetric space. I describe and implement an algorithm that computes the face‐poset structure of finitely sided polyhedra, and construct an angle‐like function between hyperplanes. In the second part, I study further questions related to hyperplanes and Dirichlet–Selberg domains in my symmetric space. I establish several criteria for the disjointness of hyperplanes and classify particular Abelian subgroups of based on whether their Dirichlet–Selberg domains are finitely sided or not.

Harmonic Riemannian submersions between Riemannian symmetric spaces of noncompact type

AbstractWe construct harmonic Riemannian submersions that are retractions from symmetric spaces of noncompact type onto their rank‐one totally geodesic subspaces. Among the consequences, we prove the existence of a nonconstant, globally defined complex‐valued harmonic morphism from the Riemannian symmetric space associated to a split real semisimple Lie group. This completes an affirmative proof of a conjecture of Gudmundsson.

Figurative Narratives in Political Blogging: Linguocognitive Perspective

Introduction. Recent years have seen a significant shift towards the pervasive use of figurative narratives in mediated political communication. Narrative practices, previously analyzed exclusively within the framework of literary theory, have become a kind of «language games» of modern politicians in their communication with potential voters and opponents, debates and intricate negotiation processes. The article analyzes figurative narratives of the English- and German-speaking political blogs as a powerful linguistic-cognitive tool for mediated political communication. The purpose of the paper is deep semantic analysis of figurative narratives of political blogs, which, as the authors claim, is a promising direction of research due to the narrative nature of human reasoning. The paper argues that the skillful use of figurative narrative practices based on archetypical plots and cultural references makes it possible to manipulate the consciousness of the electorate to achieve political goals.Methodology and sources. Methodologically, the study is based on the cognitive-discursive approach to narrative analysis and the basic principles of the neural theory of language and metaphor.Results and discussion. Pointing to the manipulative effect of metaphorical framing in narrative, the authors attempt to present a holistic view of narrative as a tool for the formation of political views. The study is based on the premise that narrative employs the rich structure of human representations of events and actions, and the type of metaphor promoted in the narrative affects human understanding of events and the adoption of certain positions on an important public issue by readers of political blogs. The set of metaphors, politicians use, forms a special type of cultural narrative, which the authors interpret as an extended metaphorical narrative.Conclusion. Summarizing the effects of using metaphorically framed narratives in politics, the authors conclude that the narrative communication strategy in political blogging is a targeted impact on a communication partner by referring to various narrative plots; the modification or transformation of the potential and diversity of political narratives, as well as their effectiveness, speaks in favor of their use in domestic and foreign policy communication to contribute to a symmetrical communication space aimed at successful cooperation rather than confrontation.

2-Rotund norms for unconditional and symmetric sequence spaces

A reflexive Banach space with an unconditional basis admits an equivalent 1-unconditional 2R norm and embeds into a reflexive space with a 1-symmetric 2R norm. Partial results on 1-symmetric 2R renormings of spaces with a symmetric basis are obtained.

Some norm estimates for the triangular projection on the space of bounded linear operators between two symmetric sequence spaces

Some norm estimates for the triangular projection on the space of bounded linear operators between two symmetric sequence spaces

I-Symmetric Spaces and the π-Images of Metric Spaces

Symmetric spaces and sn-symmetric spaces, as a generalization of metric spaces, have many important properties and have been widely discussed. We consider characterizations and mapping properties of sn-symmetric spaces under ideal convergence. I-symmetric spaces and I-sn-symmetric spaces are defined and studied. These not only generalize some classical results on symmetric spaces but also provide new directions to study generalized metric spaces using the notion of ideal convergence. As an application of I-sn-symmetric spaces, some relevant properties of statistical convergence are obtained. Some unanswered questions in this field are raised.

Black holes and wormholes beyond classical general relativity

In the paper only Static Spherically Symmetric space–times in four dimension are considered within modified gravity models. The non-singular static metrics, including black holes not admitting a de Sitter core in the center and traversable wormholes, are reconsidered within a class of higher-order F(R), satisfying the constraints F(0)=dFdR(0)=0. Furthermore, making use of the so called effective field theory formulation of gravity, the quantum corrections to Einstein–Hilbert action due to higher-derivative terms related to curvature invariants are investigated. In particular, in the case of Einstein–Hilbert action plus cubic curvature Goroff–Sagnotti contribution, the second order correction in the Goroff–Sagnotti coupling constant is computed. In general, it is shown that the effective metrics, namely Schwarzschild expression plus small quantum corrections are related to black holes, and not to traversable wormholes. In this framework, within the approximation considered, the resolution of singularity for r=0 is not accomplished. The related properties of these solutions are investigated.

On controllability of driftless control systems on symmetric spaces

On controllability of driftless control systems on symmetric spaces

Occasionally Weakly Compatible Maps and Common Fixed Point Theorems in Certain New Generalized Symmetric Space

Occasionally Weakly Compatible Maps and Common Fixed Point Theorems in Certain New Generalized Symmetric Space

Special affine connections on symmetric spaces

Special affine connections on symmetric spaces

Fixed Point Results for New Classes of k-Strictly Asymptotically Demicontractive and Hemicontractive Type Multivalued Mappings in Symmetric Spaces

Fixed point theory is a significant area of mathematical analysis with applications across various fields such as differential equations, optimization, and dynamical systems. Recently, multivalued mappings have gained attention due to their ability to model more complex and realistic problems. ln this work, novel classes of nonlinear mappings called k-strictly asymptotically demicontractive-type and asymptotically hemicontractive-type multivalued mappings are introduced in real Hilbert spaces that are symmetric spaces. In addition, we discuss the weak and strong convergence results by considered modified algorithms, and a demiclosedness property, for these classes of mappings are proved. Several non-trivial examples are demonstrated to validate the newly defined mappings. Consequently, the results and iterative methods obtained in this study improve and extend several known outcomes in the literature.

Subconvexity of twisted Shintani zeta functions

Previously the authors proved subconvexity of Shintani's zeta function enumerating class numbers of binary cubic forms. Here we return to prove subconvexity of the Maass form twisted version. The method demonstrated here has applications to the subconvexity of some of the twisted zeta functions introduced by F. Sato. The argument demonstrates that the symmetric space condition used by Sato is not necessary to estimate the zeta function in the critical strip.