1,570 Results Found

In the present article, we classify conformally flat weakly Ricci-symmetric space-times and obtain that they represent Robertson–Walker space-times. Furthermore, we provethat a Ricci-recurrent weakly Ricci-symmetric space-time is static and a R...

The class of measure spaces which can be represented as unions of Lebesgue-Rohlin spaces with continuous measures contains a lot of important examples, such as ${\mathbb{R}}^n$ for any $n\in \mathbb{N}$ with the Lebesgue measure. In this work we consider symmetric function...

We study the space of continuous linear functionals approximated by weakly symmetric continuous linear functionals on the complex Banach space ${\mathsf{\ell }}_1$ of all absolutely summing complex sequences. We construct the sequence of groups of symmetries on...

There are two aims in this paper. One is to completely characterize complex symmetric and 2-complex symmetric weighted composition operators induced by some special symbols on the weighted Bergman space of the unit ball, and the other is to fully cha...

A general notion of a weakly symmetric continuous linear functional on a Banach space, in the case where the space is ${\ell }_1$ (i.e., the space of all absolutely summable sequences of complex numbers), reduces to a continuous linear functional whose...

Symmetry enables excellent motion performance of compliant mechanisms, such as minimized parasitic motion, reduced cross-axis coupling, mitigated buckling, and decreased thermal sensitivity. However, most existing symmetric compliant mechanisms are h...

This paper investigates pseudo-symmetric space–times within two interrelated frameworks: vacuum $f\left(R\right)$-gravity and Gray’s seven canonical decomposition subspaces. First, it is established that any conformally flat pseudo-symmetric space&nda...

In this paper, we prove some optimal inequalities involving the intrinsic scalar curvature and the extrinsic Casorati curvature of submanifolds in a generalized complex space form with a semi-symmetric non-metric connection and a generalized Sasakian...

In the paper, we consider geodesic mappings of spaces with an affine connections onto generalized symmetric and Ricci-symmetric spaces. In particular, we studied in detail geodesic mappings of spaces with an affine connections onto 2-, 3-, and m- (Ri...

The primary aim of this paper is to establish two sharp geometric inequalities concerning submanifolds of S-space forms equipped with semi-symmetric metric connections (SSMCs). Specifically, we derive new inequalities involving the generalized normal...

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. $\mathcal{I}$-symm...

This study is focused on pioneering new upper bounds on mean curvature and constant sectional curvature relative to the first positive eigenvalue of the generalized Laplacian operator in the differentiable manifolds with a semi-symmetric metric conne...

This study focuses on submanifolds embedded in a conformal Sasakian space form (CSSF) equipped with a quarter-symmetric metric connection (QSMC). Utilizing the framework of generalized normalized $\delta$-Casorati curvature (GNDCC) alongside scalar cu...

In this paper, we consider canonical F-planar mappings of spaces with affine connection onto m-symmetric spaces. We obtained the fundamental equations of these mappings in the form of a closed system of Chauchy-type equations in covariant derivatives...

This paper is devoted to studying approximations of symmetric continuous functions by symmetric analytic functions on a Banach space X with a symmetric basis. We obtain some positive results for the case when X admits a separating polynomial using a...

This paper aims to prove fixed point results for cyclic compatible contraction and Hardy–Rogers cyclic contraction in symmetric spaces. Our results generalize the results of Kumari and Panthi $\left(2016\right)$ proved for cyclic compatible contraction and modifi...

We consider algebras of polynomials and analytic functions that are invariant with respect to semidirect products of groups of bounded operators on Banach spaces with symmetric bases. In particular, we consider algebras of so-called block-symmetric a...

We introduce the concept of radially symmetric pseudo-Finsler spaces, which generalize the notion of symmetric Finsler spaces, and prove that this concept is equivalent to the preservation of flag curvature by parallel transport together with reversi...

In this paper, we study geodesic mappings of spaces with affine connections onto generalized 2-, 3-, and m-Ricci-symmetric spaces. In either case, the main equations for the mappings are obtained as a closed system of linear differential equations of...

The assertion that quantum states of same-type particles have to be symmetrized because they are indistinguishable has led to a debate in the foundations of quantum mechanics around topics like “thisness” of particles and “surplus s...

In the paper we consider almost geodesic mappings of the first type of spaces with affine connections onto generalized 2-Ricci-symmetric spaces, generalized 3-Ricci-symmetric spaces, and generalized m-Ricci-symmetric spaces. In either case the main e...

We consider Banach spaces ${\ell }_p\left(\mathcal{C}\right),$ $1\le p<\infty ,$ where the index set $\mathcal{C}$ is the classical Cantor set and study various groups of symmetries of ${\ell }_p\left(\mathcal{C}\right),$ associated with the binary representation of $\mathcal{C}.$ The main purpose of the paper is t...

The main idea in this article is to establish some fixed and common fixed point results for multivalued ${\mathcal{H}}^{+}$ -type contraction mappings in symmetric spaces. New results are accompanied with illustrative examples. An application of the obtained...

One aim of the paper is to characterize some complex symmetric and 2-complex symmetric bounded weighted superposition operators on Fock spaces respect to the conjugations $\mathcal{J}$ and ${\mathcal{J}}_{r,s,t}$ defined by $\mathcal{J}f\left(z\right)=\overline{f\left(\overline{z}\right)}$ and ${\mathcal{J}}_{r,s,t}f\left(z\right)=t{e}^{sz}\stackrel{}{f\left(\overline{rz+s}\right)}$...

In this paper, we present a fixed-point theorem in $\mathcal{R}$-complete regular symmetric spaces endowed with a locally T-transitive binary relation $\mathcal{R}$ using comparison functions that generalizes several relevant existing results. In addition, we adopt an examp...

The rationale of this work is to introduce the notion of graphical symmetric spaces and some fixed-point results are proved for $\mathcal{H}$-$(\vartheta ,\phi )$-contractions in this setting. The idea of graphical symmetric spaces generalizes various spaces equip...

We construct a countable algebraic basis of the algebra of all symmetric continuous polynomials on the Cartesian product ${\ell }_{p_1}\times \dots \times {\ell }_{p_n},$ where $p_1,\dots ,p_n\in [1,+\infty )$, and ${\ell }_p$ is the complex Banach space of all...

We consider the Banach space $C[0,1]$, which is a symmetric Banach space, and prove the existence and approximation of numerical solutions for a broad class of third-order BVPs. Our approach is based on an integral operator that is constructed using Gr...

Our basic objects will be compact, even-dimensional, locally symmetric Riemannian manifolds with strictly negative sectional curvature. The goal of the present paper is to investigate the prime geodesic theorems that are associated with this class of...

We studied the behavior of nonlinear spinor field within the scope of a static cylindrically symmetric space–time. It is found that the energy-momentum tensor (EMT) of the spinor field in this case possesses nontrivial non-diagonal components....

One of the aims of this paper is to characterize 3-complex symmetric weighted composition operators induced by three types of symbols on the weighted Bergman space of the right half-plane with the conjugation $\mathcal{J}f\left(z\right)=\overline{f\left(\overline{z}\right)}$. It is well known...

A short review of spherically symmetric static regular black holes and spherically symmetric non-singular cosmological space-time is presented. Several models, including new ones, of regular black holes are considered. First, a large class of regular...

This paper develops a Banach space-valued approximation framework based on symmetrized neural network (SNN) operators generated by a deformation-dependent sigmoidal activation function. Symmetry is introduced directly at the activation level through...

This paper investigates the motion planning problem for symmetric UAV cooperative lifting in confined spaces. A dynamic model of the symmetric UAV cooperative lifting system is established, and differential flatness analysis is employed to transform...

To mitigate mutual coupling and enhance the degrees of freedom (DOFs), this paper proposes a two-level large-spacing symmetric nested array (TLSSNA). Unlike conventional nested arrays, the proposed configuration does not restrict the minimum inter-el...

In this paper, we clarify several issues concerning the abstract geometrical formulation of thermodynamics on non-compact symmetric spaces $\mathrm{U}/\mathrm{H}$ that are the mathematical model of hidden layers in the new paradigm of Cartan Neural Networks. We introduc...

This paper defines two new concepts: the concept of multivalued left-weighted mean contractions in the generalized sense of Nadler in a symmetric generalized metric space and the concept of multivalued right-weighted mean contractions in the generali...

This paper presents the results concerning a space of invariants for second type almost geodesic mappings. After discussing the general formulas of invariants for mappings of symmetric affine connection spaces, based on these formulas, invariants for...

In this paper, we investigate densely defined Toeplitz composition operators $T_u{C}_{\phi }$ on the Fock space ${\mathcal{F}}^2$. We completely characterize the $J_{\lambda }$-complex symmetry of such operators and derive necessary and sufficient conditions for normality. We f...

We investigate recurrent, Lie-recurrent, and Hopf lightlike hypersurfaces of an indefinite trans-Sasakian manifold with a semi-symmetric metric connection. In these hypersurfaces, we obtain several new results. Moreover, we characterize that the tota...

To reduce the pollutant emissions of water ecological POI logistics, the water ecological POI logistics route-planning method based on the improved water network space AGNES clustering model and the symmetrical simulated Huffman spatial searching tre...

The Riemannian geometry of the space P_m, of m × m symmetric positive definite matrices, has provided effective...

Today, gene transfer using polymers as transfer vectors is hardly studied. Some polymers have an excellent gene-carrying ability, but their cytotoxic and biocompatibility properties are not suitable for use. Thus, increased insight into the drug spac...

We investigate a backward problem of the time-space fractional symmetric diffusion equation with a source term, wherein the negative Laplace operator $-\Delta$ contained in the main equation belongs to the category of uniformly symmetric ellipti...

We consider an extended phase space formulation for cosmological and spherically symmetric models in which the choice of a given $\overline{\mu }$-scheme can be implemented dynamically. These models are constructed in the context of the relational formalism...

The Schrödinger equation is one of the most basic equations in quantum mechanics. In this paper, we study the convergence of symmetric discretization models for the nonlinear Schrödinger equation in dark solitons’ motion and verify th...

In this paper, we consider conformal mappings of Riemannian spaces onto Ricci-2-symmetric Riemannian spaces and geodesic mappings of spaces with affine connections onto Ricci-2-symmetric spaces. The main equations for the mappings are obtained as a c...

The space–air–ground integrated network (SAGIN) is a key 6G architecture that provides seamless three-dimensional connectivity, exhibiting hierarchical structural symmetry between LEO satellite and HAP layers. Integrating information-cent...

The main goal of this research paper is to investigate contact CR-warped product submanifolds within Sasakian space forms, utilizing a semi-symmetric metric connection. We conduct a comprehensive analysis of these submanifolds and establish several s...

Aiming at the state estimation problem of nonlinear systems (NLSs), the traditional typical nonlinear filtering methods (e.g., Particle Filter, PF) have large errors in system state, resulting in low accuracy and high computational speed. To perfect...