Mapping Properties Research Articles

Some chaoticity properties of the Henon and the Lozi maps and comparison between them

In this paper, we note there are some chaotic and general properties of Henon and Lozi maps, In this work, we introduce some general properties of the Henon and Lozi maps, and we study the type of fixed points concerning the parameter spaces. has been studied chaotic properties of Henon and Lozi maps, we show that the Henon and Lozi maps have sensitive depends on initial condition by using the software (Matlab). we investigate its transitivity of it by varying the parameter of maps.

Mapping using <i>p</i>-holomorphic functions

In this paper, the properties of p-holomorphic maps are considered. An analog of Rolle’s theorem and a global p-diffeomorphism theorem for p-holomorphic functions are found. A modified Carathéodoryʼs theorem (conformal mapping) for p-holomorphic mappings is obtained. We prove the theorems of the mapping of rectangular domains and the compact exhaustion of bounded domains.

Domain Adaptive Land-Cover Classification via Local Consistency and Global Diversity

Unsupervised domain adaptive (UDA) land-cover classification has recently gained more and more attention. UDA aimed to learn a model from the annotated source data and the unlabeled target data that can perform well on the target domain. The existing UDA frameworks based on adversarial training and self-training methods have boosted this field a lot. However, these methods almost all originate from the computer vision field, and they ignore the very nature of high-resolution remote sensing (HRS) images. The core insight of this paper is that a good land-cover classification result always has strong local consistency and good global diversity, which makes it possible to construct a metric representing the properties of good land-cover mapping, to improve the existing UDA algorithms. Firstly, based on this finding, we prove that local consistency and global diversity can be measured by the Frobenius norm and nuclear norm, respectively. Secondly, we propose a novel local consistency and global diversity metric (LCGDM), which can be easily integrated into the existing UDA frameworks. Finally, the experiments conducted on the LoveDA data set prove the validity of the proposed metric, which can not only improve the overall land-cover mapping but also the category-wise prediction.

Конусное обобщение теоремы Банаха и накрывание вдоль кривых

This work is devoted to the study of the covering property of linear and nonlinear mappings of Banach spaces. We consider linear continuous operators acting from one Banach space to another. For a given operator, it is shown that for any point y_0 from the relative interior of the image of a given convex closed cone there exists a conical neighborhood of y_0, with respect to which the given operator has the covering property at zero with a covering constant depending on the point y0: We provide an example showing that for a linear continuous operator the covering property with respect to the image of a given cone at zero may fail, i. e. the statement of Banach’s theorem on an open mapping may not hold for restrictions of linear continuous operators to closed convex cones. We obtain a corollary of the obtained theorem for the case when the target space is finite-dimensional. Moreover, nonlinear twice differentiable mappings of Banach spaces are considered. For them, conditions for local covering along a certain curve with respect to a given cone are presented. The corresponding sufficient conditions are formulated in terms of 2 -regular directions. They remain meaningful even in the case of degeneracy of the first derivative of the mapping under consideration at a given point.

Contra M -Continuous Maps in Neutrosophic Soft Topological Spaces

In this paper, we introduce, study, and explain some of the properties of neutrosophic soft contraM-continuous mappings and irresolute maps in neutrosophic soft topological spaces.

Phase transition for piecewise linear fibonacci bimodal map

<abstract><p>In this paper we concern with the Fibonacci bimodal maps. We first study the topological properties of the Fibonacci bimodal maps in the context of kneading map and give an equivalent description of Fibonacci combinatorics. Then we construct a one-parameter family $ f_{\lambda} $ of countably piecewise linear Fibonacci bimodal maps depending on the parameter $ \lambda $ which are all odd functions. By a random walk argument on its induced Markov map, we will show that a phase transition occurs from Lebesgue conservative to Lebesgue dissipative behaviors.</p></abstract>

Neural Network Normal Estimation and Bathymetry Reconstruction From Sidescan Sonar

Sidescan sonar intensity encodes information about changes in the surface normal of the seabed. However, other factors such as seabed geometry as well as its material composition also affect the return intensity. One can model these intensity changes in a forward direction from the surface normals from a bathymetric map and physical properties to the measured intensity, or alternatively one can use an inverse model which starts from the intensities and models the surface normals. Here, we use an inverse model which leverages deep learning's ability to learn from data; a convolutional neural network is used to estimate the surface normal from the sidescan. Once this information is estimated, a bathymetric map can be reconstructed through an optimization framework that also includes altimeter readings to provide a sparse depth profile as a constraint. Implicit neural representation learning was recently proposed to represent the bathymetric map in such an optimization framework. In this article, we use a neural network to represent the map and optimize it under constraints of altimeter points and estimated surface normal from sidescan. By fusing multiple observations from different angles from several sidescan lines, the estimated results are improved through optimization. We demonstrate the efficiency and scalability of the approach by reconstructing a high-quality bathymetry using sidescan data from a large sidescan survey. We compare the proposed data-driven inverse model approach of modeling a sidescan with a forward Lambertian model. We assess the quality of each reconstruction by comparing it with data constructed from a multibeam sensor.

Boundedness of Fractional Integrals on Hardy Spaces Associated with Ball Quasi-Banach Function Spaces

Let $X$ be a ball quasi-Banach function space on ${\mathbb R}^n$ and $H_X({\mathbb R}^n)$ the Hardy space associated with $X$, and let $\alpha\in(0,n)$ and $\beta\in(1,\infty)$. In this article, assuming that the (powered) Hardy--Littlewood maximal operator satisfies the Fefferman--Stein vector-valued maximal inequality on $X$ and is bounded on the associate space of $X$, the authors prove that the fractional integral $I_{\alpha}$ can be extended to a bounded linear operator from $H_X({\mathbb R}^n)$ to $H_{X^{\beta}}({\mathbb R}^n)$ if and only if there exists a positive constant $C$ such that, for any ball $B\subset \mathbb{R}^n$, $|B|^{\frac{\alpha}{n}}\leq C \|\mathbf{1}_B\|_X^{\frac{\beta-1}{\beta}}$, where $X^{\beta}$ denotes the $\beta$-convexification of $X$. Moreover, under some different reasonable assumptions on both $X$ and another ball quasi-Banach function space $Y$, the authors also consider the mapping property of $I_{\alpha}$ from $H_X({\mathbb R}^n)$ to $H_Y({\mathbb R}^n)$ via using the extrapolation theorem. All these results have a wide range of applications.

Flat modules and coherent endomorphism rings relative to some matrices

<abstract><p>Let $ N $ be a left $ R $-module with the endomorphism ring $ S = \text{End}(_{R}N) $. Given two cardinal numbers $ \alpha $ and $ \beta $ and a matrix $ A\in S^{\beta\times\alpha} $, $ N $ is called flat relative to $ A $ in case, for each $ x\in l_{N^{(\beta)}}(A) = \{u\in N^{(\beta)} \mid uA = 0\} $, there are a positive integer $ k $, $ y\in N^{k} $ and a $ k\times \beta $ row-finite matrix $ C $ over $ S $ such that $ CA = 0 $ and $ x = yC $. It is shown that $ N_{S} $ is flat relative to a matrix $ A $ if and only if $ l_{N^{(\beta)}}(A) $ is generated by $ N $. $ S $ is called left coherent relative to $ A $ if Ker$ (_{S}S^{(\beta)}\to _{S}S^{(\beta)}A) $ is finitely generated. It is shown that $ S $ is left coherent relative to $ A $ if and only if Hom$ _{R}(N, l_{N^{n}}(A)) $ is a finitely generated left $ S $-module if and only if $ l_{N^{n}}(A) $ has an add$ (N) $-precover (add$ (N) $ denotes the category of all direct summands of finite direct sums of copies of $ _{R}N $). Regarding applications, new necessary and sufficient conditions for epic (monic, having the unique mapping property) add$ (N) $-precovers of $ l_{N^{(\beta)}}(A) $ are investigated. Also, some new characterizations of left $ n $-semihereditary rings and von Neumann regular rings are given.</p></abstract>

Rough pseudodifferential operators on Hardy spaces for Fourier integral operators

We prove mapping properties of pseudodifferential operators with rough symbols on Hardy spaces for Fourier integral operators. The symbols a(x,η) are elements of C r* S m1,δ classes that have limited regularity in the x variable. We show that the associated pseudodifferential operator a(x, D) maps between Sobolev spaces ℌ s,pFIO (ℝn) and ℌ t,pFIO (ℝn) over the Hardy space for Fourier integral operator ℌ pFIO (ℝn). Our main result implies that for m = 0, δ =l/2 and r > n − 1, a(x, D) acts boundedly on ℌ pFIO (ℝn) for all p ∈ (1, ∞).

A Generalized Newton Method for Subgradient Systems

This paper proposes and develops a new Newton-type algorithm to solve subdifferential inclusions defined by subgradients of extended real-valued prox-regular functions. The proposed algorithm is formulated in terms of the second order subdifferential of such functions that enjoy extensive calculus rules and can be efficiently computed for broad classes of extended real-valued functions. Based on this and on the metric regularity and subregularity properties of subgradient mappings, we establish verifiable conditions ensuring the well-posedness of the proposed algorithm and its local superlinear convergence. The obtained results are also new for the class of equations defined by continuously differentiable functions with Lipschitzian gradients ([Formula: see text] functions), which is the underlying case of our consideration. The developed algorithms for prox-regular functions and their extension to a structured class of composite functions are formulated in terms of proximal mappings and forward–backward envelopes. Besides numerous illustrative examples and comparison with known algorithms for [Formula: see text] functions and generalized equations, the paper presents applications of the proposed algorithms to regularized least square problems arising in statistics, machine learning, and related disciplines. Funding: Research of P. D. Khanh is funded by Ho Chi Minh City University of Education Foundation for Science and Technology [Grant CS.2022.19.20TD]. Research of B. Mordukhovich and V. T. Phat was partly supported by the U.S. National Science Foundation [Grants DMS-1808978 and DMS-2204519]. The research of B. Mordukhovich was also supported by the Air Force Office of Scientific Research [Grant 15RT0462] and the Australian Research Council under Discovery Project DP-190100555. This work was supported by the Air Force Office of Scientific Research [Grant 15RT0462].

Dynamical Property of the Shift Map under Group Action

Firstly, we introduced the concept of G ‐ Lipschitz tracking property, G ‐ asymptotic average tracking property, and G ‐ periodic tracking property. Secondly, we studied their dynamical properties and topological structure and obtained the following conclusions: (1) let X , d be compact metric G ‐ space and the metric d be invariant to G . Then, σ has G ¯ ‐ asymptotic average tracking property; (2) let X , d be compact metric G ‐ space and the metric d be invariant to G . Then, σ has G ¯ ‐ Lipschitz tracking property; (3) let X , d be compact metric G ‐ space and the metric d be invariant to G . Then, σ has G ¯ ‐ periodic tracking property. The above results make up for the lack of theory of G ‐ Lipschitz tracking property, G ‐ asymptotic average tracking property, and G ‐ periodic tracking property in infinite product space under group action.

Mapping properties of operator-valued Bergman projections

In this paper, we study the boundedness theory for Bergman projection in the operator-valued setting. More precisely, let D \mathbb {D} be the open unit disk in the complex plane C \mathbb {C} and M \mathcal {M} be a semifinite von Neumann algebra. We prove that ‖ P ( f ) ‖ L 1 , ∞ ( N ) ≤ C ‖ f ‖ L 1 ( N ) , \begin{equation*} \|P(f)\|_{L_{1,\infty }(\mathcal {N})}\leq C \|f\|_{L_1(\mathcal {N})}, \end{equation*} where N = L ∞ ( D ) ⊗ ¯ M \mathcal {N}=L_{\infty }(\mathbb {D})\bar {\otimes }\mathcal {M} and P P denotes the Bergman projection. Consequently, P P is bounded on L p ( N ) L_{p}(\mathcal {N}) with 1 > p > ∞ 1>p>\infty . As applications, we also obtain Kolmogorov and Zygmund inequalities for the Bergman projection P P .

Mappings and Finite Product of Pairwise Expandable Spaces

In this work, we intend to study certain mappings in bitopological spaces such as pairwise perfect and pairwise countably perfect mappings that possess the property (E). Some properties of such mappings are provided which have helped us to obtain some finite product theorems concerning with pairwise expandable and almost pairwise expandable spaces. Two illustrative examples are given to demonstrate the effectiveness of some proposed results.

On a contraction-like property of dismantlable graphs

In a recent paper, Baradol, Gopal and Radenović (2020) study the contraction properties of mappings on rectangular metric spaces endowed with a digraph. In this paper, we show that a class of mappings on dismantlable undirected graphs have a natural contraction-like property acting on a spanning tree of the graph. We propose further characterizations of dismantlable graphs and apply our results to pursuit-evasion games on graphs.

Remarks on Martio's conjecture

We introduce a certain integrability condition for the reciprocal of the Jacobian determinant which guarantees the local homeomorphism property of quasiregular mappings with a small inner dilatation. This condition turns out to be sharp in the planar case. We also show that every branch point of a quasiregular mapping with a small inner dilatation is a Lebesgue point of the differential matrix of the mapping.

L p -bounds for Fourier integral operators on the torus

In this paper, we investigate the mapping properties of periodic Fourier integral operators in -spaces. The operators are considered associated to periodic symbols (with limited regularity) in the sense of Ruzhansky and Turunen.

Digital watermarking by utilizing the properties of self-organization map based on least significant bit and most significant bit

<p><span lang="EN-US">Information security is one of the most important branches concerned with maintaining the confidentiality and reliability of data and the medium for which it is transmitted. Digital watermarking is one of the common techniques in this field and it is developing greatly and rapidly due to the great importance it represents in the field of reliability and security. Most modern watermarking systems, however, use the self-organization map (SOM), which is safer than other algorithms because an unauthorized user cannot see the result of the SOM's training. Our method presents a semi-fragile watermark under spatial domain using least significant bit (LSB) and by relying on most significant bit (MSB) when the taken values equal to (2 or 4 bits) depending on the characteristics of SOM through developing the so-called best matching unit (BMU) which working to determine the best location for concealment. As a result, it shows us the ability of the proposed method to maintain the quality of the host with the ability to retrieve data, whether it is a binary image or a secret message.</span></p>

Mapping properties for operators on Herz-Morrey and Herz-Morrey-Hardy spaces

Mapping properties for operators on Herz-Morrey and Herz-Morrey-Hardy spaces

Dendrite Net with Acceleration Module for Faster Nonlinear Mapping and System Identification

Nonlinear mapping is an essential and common demand in online systems, such as sensor systems and mobile phones. Accelerating nonlinear mapping will directly speed up online systems. Previously the authors of this paper proposed a Dendrite Net (DD) with enormously lower time complexity than the existing nonlinear mapping algorithms; however, there still are redundant calculations in DD. This paper presents a DD with an acceleration module (AC) to accelerate nonlinear mapping further. We conduct three experiments to verify whether DD with AC has lower time complexity while retaining DD’s nonlinear mapping properties and system identification properties: The first experiment is the precision and identification of unary nonlinear mapping, reflecting the calculation performance using DD with AC for basic functions in online systems. The second experiment is the mapping precision and identification of the multi-input nonlinear system, reflecting the performance for designing online systems via DD with AC. Finally, this paper compares the time complexity of DD and DD with AC and analyzes the theoretical reasons through repeated experiments. Results: DD with AC retains DD’s excellent mapping and identification properties and has lower time complexity. Significance: DD with AC can be used for most engineering systems, such as sensor systems, and will speed up computation in these online systems.