247 Results Found

In this paper, by extending some $L^p$-norm inequalities to similar inequalities for Orlicz space ($L^{\mathsf{\Phi }}$-norm), we provide equivalent conditions for composition operators to have the shadowing property on the Orlicz space $L^{\mathsf{\Phi }}\left(\mu \right)$. Additionally, we...

We develop isometry and inversion formulas for the Segal–Bargmann transform on odd-dimensional hyperbolic spaces that are as parallel as possible to the dual case of odd-dimensional spheres.

In the paper, we consider holomorphically projective mappings of n-dimensional pseudo-Riemannian Kähler and hyperbolic Kähler spaces. We refined the fundamental linear equations of the above problems for metrics of differentiability class $C^{}$...

In this paper, we modify the $KF$-iteration process into hyperbolic metric spaces where the symmetry condition is satisfied and establish the weak $w^2$-stability and data dependence results for contraction mappings. We also prove some $\Delta$-convergence...

The concept of an endpoint is a relatively new concept compared to the concept of a fixed point. The aim of this paper is to perform a convergence analysis of M—iteration involving $\alpha$—Reich–Suzuki nonexpansive mappings. In this paper, we prove strong...

The theory of quantum mechanical scattering in hyperbolic space is developed. General formulas based on usage of asymptotic form of the solution of the Shrödinger equation in hyperbolic space are derived. The concept of scattering length in hype...

We present a novel application of transcendental equations for nonlinear distance optimization in hyperbolic space. Through asymptotic approximations using Fourier and Taylor series expansions, we obtain approximations for the transcendental equation...

Hyperbolic space has received extensive attention because it can accurately and concisely represent hierarchical data. Currently, for knowledge graph completion tasks, the introduction of exogenous information of entities can enrich the knowledge rep...

We give a topological condition for a generic sliced space to be globally hyperbolic without any hypothesis on lapse function, shift function, and spatial metric.

Recently, source code mining has received increasing attention due to the rapid increase of open-sourced code repositories and the tremendous values implied in this large dataset, which can help us understand the organization of functions or classes...

This study presents a common fixed-point iteration process that includes two asymptotically nonexpansive self-mappings in a hyperbolic space and their delta convergence. To support our results, we provide an example with a comparison table and suffic...

We introduce hyperbolic oscillation spaces and mixed fractional lifting oscillation spaces expressed in terms of hyperbolic wavelet leaders of multivariate signals on ${\mathbb{R}}^d$, with $d\ge 2$. Contrary to Besov spaces and fractional Sobolev spaces with domina...

In this article, we introduce a new mixed-type iterative algorithm for approximation of common fixed points of two multivalued almost contractive mappings and two multivalued mappings satisfying condition $(E)$ in hyperbolic spaces. We consider new con...

The paper shows that it is possible to construct quantum chromodynamics as a rigorous theory on the basis of employment of hyperbolic unitary group $SUh\left(3\right)$, which is a symmetry group for the three-dimensional complex space of the hyperbolic type. Such...

In this paper, we create a family of neural network (NN) operators employing a parametrized and deformed half-hyperbolic tangent function as an activation function and a density function produced by the same activation function. Moreover, we consider...

We first briefly summarize several well-known properties of regular tessellations of the three two-dimensional maximally symmetric manifolds, ${\mathbb{E}}^2$, ${\mathbb{S}}^2$, and ${\mathbb{H}}^2$, by bounded regular tiles. For instance, there exist infinitely many regular tessellations of...

A wide range of new research articles in artificial intelligence, logic programming, and other applied sciences are based on fixed-point theorems. The aim of this article is to present an approximation method for finding the fixed point of generalize...

Phylogenetic placement, used widely in ecological analyses, seeks to add a new species to an existing tree. A deep learning approach was previously proposed to estimate the distance between query and backbone species by building a map from gene seque...

Knowledge representation learning achieves the automatic completion of knowledge graphs (KGs) by embedding entities into continuous low-dimensional vector space. In knowledge graph completion (KGC) tasks, the inter-dependencies and hierarchical infor...

In this paper, we study the initial value problem for a semilinear delay hyperbolic equation in Hilbert spaces with a self-adjoint positive definite operator. The mean theorem on the existence and uniqueness of a bounded solution of this differential...

The current study is devoted to investigating the existence and uniqueness of solutions for a new class of symmetrically coupled system of nonlinear hyperbolic partial-fractional differential equations in generalized Banach spaces in the sense of $\mathrm{\&ps}$...

The six-dimensional pseudo-Euclidean space ${\mathbb{E}}_{3,3}$ with signature $(3,3)$ is proposed as a model of real physical space at the subparticle scale. The conserved quantum characteristics of elementary particles, such as spin, isospin, electric and baryon cha...

This paper is dedicated to the advancement of fixed-point results for multi-valued asymptotically non-expansive maps regarding convergence criteria in complete uniformly convex hyperbolic metric spaces that are endowed with a graph. The famous fixed-...

The target of the multi-hop knowledge base question-answering task is to find answers of some factoid questions by reasoning across multiple knowledge triples in the knowledge base. Most of the existing methods for multi-hop knowledge base question a...

Spirals, tilings, and hyperbolic geometry are important mathematical topics with outstanding aesthetic elements. Nonetheless, research on their aesthetic visualization is extremely limited. In this paper, we give a simple method for creating Escher-l...

We introduce the quantum currents for quantum systems with an SU(1,1) dynamic symmetry group whose evolution is governed by a non-linear Hamiltonian possessing a continuous spectrum and apply them to the analysis of the tunneling dynamics on the hype...

This study presents a novel fifth-order unequal-sized trigonometric weighted essentially non-oscillatory (US-TWENO) scheme and a novel hybrid US-TWENO (HUS-TWENO) scheme with a novel troubled cell indicator in a finite difference framework to address...

Quantitative Geometrical Thermodynamics (QGT) exploits the entropic Lagrangian–Hamiltonian canonical equations of state as applied to entities obeying the holographic principle and exhibiting Shannon information, the creation of which measures...

A body may have a structural, thermal, electromagnetic or optical role. In wave propagation, many models are described for transmission problems, whose solutions are defined in two or more domains. In this paper, we consider an inverse source hyperbo...

Accurate remote determination of the object coordinates in 3D space is one of the main questions in many applications. In one of the most popular methods, such determination of the location of an object uses the measurement by receiving an electromag...

This paper studies synchronization behaviors of two sorts of non-linear fractional-order complex spatio-temporal networks modeled by hyperbolic space-varying PDEs (FCSNHSPDEs), respectively, with time-invariant delays and time-varying delays, includi...

For dimensions two, three and four, we derive hyperbolic complex algebraic structures on the basis of suitably defined vector products and powers which allow in a standard way a series definitions of the hyperbolic vector exponential function. In doi...

A cyclic antipodal pair of a circle is a pair of points that are the intersection of the circle with the diameter of the circle. In this article, a recent proof of Ptolemy’s Theorem—simultaneously in both (i) Euclidean geometry and (ii) t...

The motivation for this talk and paper is related to the classification of the homogeneous simply connected maximal 3-geometries (the so-called Thurston geometries: ${\mathbf{E}}^3$ , ${\mathbf{S}}^3$ , ${\mathbf{H}}^3$ , ${\mathbf{S}}^2\times \mathbf{R}$ , ${\mathbf{H}}^2\times \mathbf{R}$...

In this paper, we consider the recently introduced $CA{T}_p\left(0\right)$ , where the comparison triangles belong to ${\ell }_p$ , for $p\ge 2$ . We first establish an inequality in these nonlinear metric spaces. Then, we use it to prove the...

The ‘projective theory of relativity’ is a theory developed historically by Oswald Veblen and Banesh Hoffmann, Jan Arnoldus Schouten and David van Dantzig. This theory differs radically from Kaluza-Klein/conformal type theories of spaceti...

We study the Hilbert geometry induced by the Siegel disk domain, an open-bounded convex set of complex square matrices of operator norm strictly less than one. This Hilbert geometry yields a generalization of the Klein disk model of hyperbolic geomet...

Univalent functions with asymptotically conformal extension to the boundary form a subclass of functions with quasiconformal extension with rather special features. Such functions arise in various questions of geometric function theory and Teichm&uum...

Ptolemy’s theorem in Euclidean geometry, named after the Greek astronomer and mathematician Claudius Ptolemy, is well known. We translate Ptolemy’s theorem from analytic Euclidean geometry into the Poincaré ball model of analytic h...

Intelligent vehicular networks can not only connect various smart terminals to manned or unmanned vehicles but also to roads and people’s hands. In order to support diverse vehicle-to-everything (V2X) applications in dynamic, intelligent vehicu...

We discuss a formalism where a universe is identified with the support of a wave function propagating through space–time. The dynamics is of a squeezing type, with shrinking in time and expanding in space. As opposed to classical cosmology, the...

For a massive scalar field in a fixed Schwarzschild background, the radial wave equation obeyed by Fourier modes is first studied. After reducing such a radial wave equation to its normal form, we first study approximate solutions in the neighborhood...

We present Hyperbolic Symmetric Hypermodular Neural Operators (ONHSH), a novel operator learning framework for solving partial differential equations (PDEs) in curved, anisotropic, and modularly structured domains. The architecture integrates three c...

A parametric theoretical boundary equation of a period-3 hyperbolic component in the Mandelbrot set is established from a perspective of Euclidean plane geometry. We not only calculate the interior area, perimeter and curvature of the boundary line b...

Hyperbolic embedding can effectively preserve the property of complex networks. Though some state-of-the-art hyperbolic node embedding approaches are proposed, most of them are still not well suited for the dynamic evolution process of temporal compl...

Ptolemy’s Theorem in Euclidean geometry, named after the Greek astronomer and mathematician Ptolemy, is well-known. By means of the relativistic model of hyperbolic geometry, we translate Ptolemy’s Theorem from Euclidean geometry into the...

Relativistic localizing systems that extend relativistic positioning systems show that pseudo-Riemannian space-time geometry is somehow encompassed in a particular four-dimensional projective geometry. The resulting geometric structure is then that o...

In the Euclidean space ${\mathbb{E}}^n$ , hyperplanes, hyperspheres and hypercylinders are the only isoparametric hypersurfaces. These hypersurfaces are also the only ones with chord property, that is, the chord connecting two points on them meets the hy...

We show that in a sliced spacetime $(V,g)$ , global hyperbolicity in V is equivalent to $T_A$ -completeness of a slice, if and only if the product topology $T_P$ , on V, is equivalent to $T_A$ , where $T_A$ denotes the u...

In 1962, H. Yilmaz published a very original paper in which he showed the striking analogy between Lorentz transformations and the effect of illuminant changes on color perception. As a consequence, he argued that a perceived color space endowed with...