17,245 Results Found

We study the properties of the image of a rational surface of revolution under a nonsingular affine mapping. We prove that this image has a notable property, namely that all the affine normal lines, a concept that appears in the context of affine dif...

Modeling non-stationary systems with dynamically evolving data distributions remains a fundamental challenge in modern learning and optimization problems. In this work, we adopt a generalized notion of non-stationarity, where distribution shifts acro...

The polynomial affine model of gravity was proposed as an alternative to metric and metric-affine gravitational models. What, in the beginning, was thought to be a source of unpredictability—the presence of many terms in the action—turned...

Quantization for a probability distribution refers to the idea of estimating a given probability by a discrete probability supported by a finite set. In this article, we consider a probability distribution generated by an infinite system of affine tr...

In this work, we study the relationships between affine manifolds and complex manifolds. We prove that a linear connection and a Riemannian metric on an affine manifold M of dimension n induce a complex structure and a Hermitian metric on both the pr...

Finding affine parameters for null geodesics is often of considerable physical importance, especially when studying null geodesics or dealing with conservation laws and/or averaged energy conditions. But explicitly finding null affine parameters is a...

Our purpose is to study a space $\Pi$ of centered m-planes in n-projective space. Generalized fiberings (with semi-gluing) are investigated. Planar and normal affine connections associated with the space $\Pi$ are set in the generalized fiberings. Fields of...

This article presents an exhaustive classification of metric-affine theories according to their scale symmetries. First it is clarified that there are three relevant definitions of a scale transformation. These correspond to a projective transformati...

In this paper, we review the so-called Myrzakulov Gravity models (MG-N, with N = I, II, …, VIII) and derive their respective metric-affine generalizations (MAMG-N), discussing also their particular sub-cases. The field equations of the theories are o...

The present paper concretizes the models proposed by S. Ri and N. Secelean. S. Ri proposed the construction of the fractal interpolation function (FIF) considering finite systems consisting of Rakotch contractions, but produced no concretization of t...

In this paper, we study centro-affine Lorentzian surfaces $M^2$ in ${ℝ}^3$ which have pseudo-isotropic or lightlike pseudo-isotropic difference tensor. We first show that $M^2$ is pseudo-isotropic if and only if the Tchebychev form $T=0$. In that case, $M^2$ is a an...

Two decades ago, Ngai and Wang introduced a well-known finite type condition (FTC) on the self-similar iterated function system (IFS) with overlaps and used it to calculate the Hausdorff dimension of self-similar sets. In this paper, inspired by Ngai...

In this paper, we studied the limiting regimes $\alpha \to n^{-}$ and $\alpha \to 0^{+}$ in the affine Hardy–Littlewood–Sobolev (HLS) inequalities. Specifically, we established affine logarithmic HLS inequalities and affine Beckner-type l...

We provide a comprehensive overview of metric-affine geometries with spherical symmetry, which may be used in order to solve the field equations for generic gravity theories which employ these geometries as their field variables. We discuss the most...

Let S and $\mathcal{C}$ be affine semigroups in ${\mathbb{N}}^d$ such that $S\subseteq \mathcal{C}$. We provide a characterization for the set $\mathcal{C}\setminus S$ to be finite, together with a procedure and computational tools to check whether such a set is finite and, if so, compute its elements. As...

We study the characteristics of affine vector fields on pseudo-Riemannian manifolds and provide tensorial formulas that characterize these vector fields. Using our approach, we present a straightforward proof that any affine vector field on a compact...

As a newly proposed video coding standard, Versatile Video Coding (VVC) has adopted some revolutionary techniques compared to High Efficiency Video Coding (HEVC). The multiple-mode affine motion compensation (MM-AMC) adopted by VVC saves approximatel...

Geometrically, the affine connection is the main ingredient that underlies the covariant derivative, the parallel transport, the auto-parallel curves, the torsion tensor field, and the curvature tensor field on a finite-dimensional differentiable man...

This paper presents a new encryption technique, which combines affine ciphers and the residue number system. This makes it possible to eliminate the shortcomings and vulnerabilities of affine ciphers, which are sensitive to cryptanalysis, using the a...

We investigated, for the first time, the curve shortening flow in the metric-affine plane and prove that under simple geometric condition (when the curvature of initial curve dominates the torsion term) it shrinks a closed convex curve to a “ro...

The special affine Fourier transform (SAFT) is an extended version of the classical Fourier transform and incorporates various signal processing tools which include the Fourier transforms, the fractional Fourier transform, the linear canonical transf...

Discrete kinetic equations describing binary processes of agglomeration and fragmentation are considered using formal equivalence between the kinetic equations and the geodesic equations of some affinely connected space $\mathbf{A}$ associated with the kinetic...

In this work, we explore a three-dimensional formulation of the polynomial affine model of gravity, which is a model that extends general relativity by relaxing the equivalence principle through the exclusion of the metric from the set of fundamental...

The two-dimensional inverse problem for first-order systems is analysed and a method to construct an affine Lagrangian for such systems is developed. The determination of such Lagrangians is based on the theory of the Jacobi multiplier for the system...

We present a fast 3D analytical affine transformation (F3DAAT) method to obtain polygon-based computer-generated holograms (CGHs). CGHs consisting of tens of thousands of triangles from 3D objects are obtained by this method. We have attempted a revi...

Conventional affine projection (AP) algorithm with a fixed order is subject to a tradeoff between convergence speed and steady-state misalignment. In order to address such problem, a switching mechanism on the order of AP algorithm is proposed by com...

In this paper, we investigate warped products on super quasi-Einstein manifolds under affine connections. We explore their fundamental properties, establish conditions for their existence, and prove that these manifolds can also be nearly quasi-Einst...

In this paper, we introduce and systematically study a new two-parameter family of affine $(q,\eta )$-Gould–Hopper-based Appell polynomials. These polynomials arise by fusing the affine $(q,\eta )$-exponential Gould–Hopper kernel with an inve...

This article deals with Lie algebra $\mathfrak{G}$ of all infinitesimal affine transformations of the manifold $\mathcal{M}$ with an affine connection, its stationary subalgebra $ℌ\subset \mathfrak{G}$, the Lie group $\mathcal{G}$ corresponding to the algebra $\mathfrak{G}$, and its subgroup $\mathcal{H}\subset \mathcal{G}$ correspon...

Affine quantization is a relatively new procedure, and it can solve many new problems. This essay reviews this new, and novel, procedure for particle problems, as well as those of fields and gravity. New quantization tools, which are extremely close...

Batch normalization (BN) has become a foundational component in modern deep neural networks. However, one of its disadvantages is its reliance on batch statistics that may be unreliable or unavailable during inference, particularly under test-time do...

For fixed k ≥ 2 and fixed data alphabet of cardinality m, the hierarchical type class of a data string of length n = k^j for some j ≥ 1 is formed by permuting the string in all possible ways under permutations arising from the isomorphisms of the uniq...

For a self-affine iterated function system (IFS) ${\left\{f_j\right\}}_{j=1}^N$ on ${\mathbb{R}}^d$ defined by $f_j\left(x\right)=A^{-1}(x+d_j)$, where A is an expansive matrix and $d_j\in {\mathbb{R}}^d$, we reveal a novel characterization of the open set and weak separation conditions through the bounded deg...

The subjects of our study are affine hypersurfaces $f:M\to {\mathbb{R}}^{2n+2}$ considered with a transversal vector field C, which is $\tilde{J}$-tangent. By $\tilde{J}$ we understand the canonical paracomplex structure on ${\mathbb{R}}^{2n+2}$. The vector field C induces on the hyper...

Saturated nonlinear affine systems are widely encountered in many engineering fields. Currently, most control methods on saturated nonlinear affine systems are not specifically designed based on sparsity-based control methodologies, and they might re...

Large-scale engineering of the 3D scenes used in BIM, GIS, digital twins, and geospatial web delivery frequently suffer from significant geometric redundancy after export to mesh-based delivery formats, arising in part from the inconsistent reuse of...

In the geometric data model for spatio-temporal data, introduced by Chomicki and Revesz [1], spatio-temporal data are modelled as a finite collection of triangles that are transformed by time-dependent affinities of the plane. To facilitate querying...

In the article, affine-periodic boundary value problem involving fractional derivative is considered. Existence of solutions to a Caputo-type fractional differential inclusion is researched by some fixed-point theorems and set-valued analysis theory....

Given a triangular mesh, we obtain an orthogonality-free analogue of the classical local Zlámal–Ženišek spline procedure with simple explicit affine-invariant formulas in terms of the normalized barycentric coordinates of the...

Calibration transfer is an important field for near-infrared (NIR) spectroscopy in practical applications. However, most transfer methods are constructed with standard samples, which are expensive and difficult to obtain. Taking this problem into acc...

This study proposes a lightweight solution to estimate affine parameters in affine motion compensation. Most of the current approaches start with an initial approximation based on the standard motion estimation, which only estimates the translation p...

The realization of a BRST cohomology of the 4D topological gauge-affine gravity is established in terms of a superconnection formalism. The identification of fields in the quantized theory occurs directly as is usual in terms of superconnection and i...

A critical processing step for AI algorithms is mapping the raw data to a landscape where the similarity of two data points is conveniently defined. Frequently, when the data points are compositions of probability functions, the similarity is reduced...

Affine invariance is one of the most fundamental properties of free-form curves, ensuring that transformations such as translation, scaling, rotation, and shearing preserve the essential characteristics of the geometric shape. It is exploited by almo...

We study the complete, compact, locally affine manifolds equipped with a k-symplectic structure, which are the quotients of ${\mathbb{R}}^{n(k+1)}$ by a subgroup $\mathsf{\Gamma }$ of the affine group $A\left(n\right(k+1\left)\right)$ of ${\mathbb{R}}^{n(k+1)}$ acting freely and properly discontinuously on ${\mathbb{R}}^{n(k+1)}$ and lea...

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 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...

We construct three new families of asymmetric quantum MDS codes from nested Hermitian self-orthogonal generalized Reed–Solomon and extended generalized Reed–Solomon codes over ${\mathbb{F}}_{q^2}$. The construction is developed in three settings: affine p...

Scanning electron microscopes (SEMs) are versatile imaging devices for the micro- and nanoscale that find application in various disciplines such as the characterization of biological, mineral or mechanical specimen. Even though the specimen’s...

Gnaphalium affine D. Don (G. affine), a genus within the genus Gnaphalium of the Asteraceae family, is recognized as a significant medicinal resource. Phytochemical investigations identified various bioactive compounds in G. affine, including flavono...