Space Mapping Research Articles

Well-Posedness of the Schrödinger–Korteweg–de Vries System with Robin Boundary Conditions on the Half-Line

The Schrödinger–Korteweg–de Vries (SKdV) system can describe the nonlinear dynamics of phenomena such as Langmuir and ion acoustic waves, which are highly valuable for studying wave behavior and interactions. The SKdV system has wide-ranging applications in physics and applied mathematics. In this article, we investigate the local well-posedness of the SKdV system with Robin boundary conditions and polynomial terms in the Sobolev space. We want to enhance the applicability of this type of SKdV system. Our verification process is as follows: We estimate Fokas solutions for the Robin problem with external forces. Next, we define an iteration map in suitable solution space and prove the iteration map is a contraction mapping and onto some closed ball B(0,r). Finally, by the contraction mapping theorem, we obtain the uniqueness solution. Moreover, we show that the data-to-solution map is locally Lipschitz continuous and conclude with the well-posedness of the SKdV system.

Invariants for Second Type Almost Geodesic Mappings of Symmetric Affine Connection Space

Invariants for Second Type Almost Geodesic Mappings of Symmetric Affine Connection Space

Existence of solution of a system of non-linear differential inclusions with non-local, integral boundary conditions via fixed points of hybrid contractions

In the present article, we have introduced the notions of γ-admissibility for the pair of q-ROF set-valued maps and admissible hybrid q-ROF Z\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal{Z}$\\end{document}-contraction. Notions introduced in the article generalizes the existing concepts in fuzzy literature. Common fixed point result for a pair of γ-admissible q-ROF mappings in b-metric spaces utilizing the introduced contraction is presented. A nontrivial example to support the obtained results is also included. As an application, we have discussed the existence of solution of system of non-linear n-th order differential inclusions with non-local and integral boundary conditions.

Spatial syntax analysis on the renewal of the external space of mining heritage buildings —— A case study of Zollverein Coal Mine Industrial Complex

ABSTRACT The renovation of external spaces of mining heritage buildings should respect their historical and cultural value and be adapted to the specific characteristics of the mining area for spatial restructuring and functional replacement. Current research often relies on subjective experience and focuses on qualitative analysis, lacking in-depth quantitative analysis. Building upon the summary of research on mining heritage exterior spaces and spatial syntax studies, this paper proposes a research methodology that quantitatively analyzes the accessibility and integration of mining heritage exterior spaces using spatial syntax convex space and axis map models. Taking the exterior connecting spaces and characteristic spaces before and after the renovation of the German Zollverein Coal Mine Industrial Complex as the research objects, the impact of spatial location on different circulation organizations and functions of spatial places is visually expressed, providing a more intuitive explanation of the complex relationships in mining heritage exterior spaces. The research findings reveal that the spatial syntax model is adaptable in evaluating the renovation of mining heritage exterior spaces, with spaces exhibiting high integration being essentially consistent with key and highly utilized exterior spaces within the renovated mining area. In summary, it can be concluded that the integration of mining heritage exterior spaces and consequently the utilization rate and value can be improved through spatial “Connection”, “Growth”, and “Darning”, thereby offering direct reference for subsequent research and practical organization of mining heritage architectural exterior space renewal.

Asymptotic fuzzy contractive mappings in fuzzy metric spaces

Asymptotic fuzzy contractive mappings in fuzzy metric spaces

Modelling and optimization method for energy saving of computer numerical control machine tools under operating condition

The widespread application of machine tools in industry results in very high energy consumption. In order to save energy, it is an effective means to reduce the processing power while improving the processing efficiency of machine tools. Since milling parameters directly affect machine performance, the selection of suitable milling parameters is particularly important. In this regard, this study proposes an integrated modelling and optimization method for energy saving of computer numerical control (CNC) machine tools under operating condition. Firstly, the operating condition of the CNC machine are analyzed and the processing power and efficiency mathematical models are established based on the four milling parameters (n, fz, ae, ap). Subsequently, the Pareto optimal solution is introduced to establish an optimization model integrating the processing power and time. To solve the optimization problem, an adaptive chaotic multi-objective chimp algorithm with fast convergence and satisfactory optimization is proposed considering three aspects: search space, convergence factor, and chaotic mapping. Afterwards, further degrees of freedom and sensitivity analyses were carried out on the constructed model using the Sobol method. Finally, comparative analysis and validation are conducted through simulation cases and actual processing experiments, respectively. The results show that both validation scenarios have the same conclusion. Compared with three existing algorithms, the proposed method reduces the processing power by 5.63 %, 4.65 % and 4.51 % and improves the processing efficiency by 27.88 %, 15.11 % and 15.31 %, respectively. Based on the above enhancements, the energy consumption is reduced by 58.21 %, 45.54 % and 41.45 % respectively.

Exploring Machine Learning for Urban Green Space Mapping in Smart Cities: A Scoping Review

Exploring Machine Learning for Urban Green Space Mapping in Smart Cities: A Scoping Review

Fixed Point Methodologies for ψ-Contraction Mappings in Cone Metric Spaces over Banach Algebra with Supportive Applications

The explicit aim of this manuscript is to obtain fixed point consequences under novel ψ-contraction mappings in a complete cone metric space over Banach algebra. We connect and relate different fixed point theorems by using the idea of ψ-contraction mappings, providing a thorough viewpoint that deepens our comprehension of this topic. Our theorems generalize and unify many results in the scientific literature. These prospective extensions offer intriguing research directions and have the potential to further advance the study of fixed point theory. The investigation of examples plays an extremely crucial role in verifying the effectiveness and validity of our theoretical results. Moreover, to support the theoretical results, some examples are investigated to emphasize these results. Ultimately, the existence and uniqueness of the solution to the Urysohn integral and nonlinear fractional differential equation are cooperated as applications to provide an authoritative basis for dealing with actual problems that include these equations.

Inverse mapping of quantum properties to structures for chemical space of small organic molecules

Computer-driven molecular design combines the principles of chemistry, physics, and artificial intelligence to identify chemical compounds with tailored properties. While quantum-mechanical (QM) methods, coupled with machine learning, already offer a direct mapping from 3D molecular structures to their properties, effective methodologies for the inverse mapping in chemical space remain elusive. We address this challenge by demonstrating the possibility of parametrizing a chemical space with a finite set of QM properties. Our proof-of-concept implementation achieves an approximate property-to-structure mapping, the QIM model (which stands for “Quantum Inverse Mapping”), by forcing a variational auto-encoder with a property encoder to obtain a common internal representation for both structures and properties. After validating this mapping for small drug-like molecules, we illustrate its capabilities with an explainability study as well as by the generation of de novo molecular structures with targeted properties and transition pathways between conformational isomers. Our findings thus provide a proof-of-principle demonstration aiming to enable the inverse property-to-structure design in diverse chemical spaces.

Fast hybrid method for solving variational inequalities beyond monotonicity in real Banach spaces

In this work, we introduce a new inertial hybrid algorithm that combines the subgradient extragradient, Halpern, and S-iteration methods. We provide an approximate solution to variational inequality and common fixed point problem of relatively non-expansive mappings in real Banach spaces, where our cost operator is Lipschitz continuous and quasimonotone, and our step size is self-adaptive, non-monotone, and non-reliant on any line-search principle. We provide two strong convergence results with (and without) recourse to the monotonicity property, and further conduct several relevant numerical experiments to reveal the efficiency of our method over others in the literature.

Quantum Lefschetz Without Curves

Abstract Given one quasi-smooth derived space cut out of another by a section of a 2-term complex of bundles, we give two formulae for its virtual cycle. They are modelled on the the $p$-fields construction of Chang–Li and the Quantum Lefschetz principle, and recover these when applied to moduli spaces of (stable or quasi-) maps. When the complex is a single bundle we recover the results of Kim–Kresch–Pantev.

Some Common Fixed Point Results of Tower Mappings in (Pseudo)modular Metric Spaces

In this paper, we prove the existence and uniqueness of common fixed point of tower type contractive mappings in complete metric (pseudo)modular spaces involving the theoretic relation. However, the newly introduced contraction in this paper further characterize and includes in their full strength several existing results in metrical fixed point theory. Some nontrivial supportive examples were given to justify our result. Our results generalize, improve, and unify some existing results.

A Method with Double Inertial Type and Golden Rule Line Search for Solving Variational Inequalities

In this work, we study a new line-search rule for solving the pseudomonotone variational inequality problem with non-Lipschitz mapping in real Hilbert spaces as well as provide a strong convergence analysis of the sequence generated by our suggested algorithm with double inertial extrapolation steps. In order to speed up the convergence of projection and contraction methods with inertial steps for solving variational inequalities, we propose a new approach that combines double inertial extrapolation steps, the modified Mann-type projection and contraction method, and the line-search rule, which is based on the golden ratio (5+1)/2. We demonstrate the efficiency, robustness, and stability of the suggested algorithm with numerical examples.

Weight Decompositions on Algebraic Models for Mapping Spaces and Homotopy Automorphisms

We obtain restrictions on the rational homotopy types of mapping spaces and of classifying spaces of homotopy automorphisms by means of the theory of positive weight decompositions. The theory applies, in particular, to connected components of holomorphic maps between compact Kähler manifolds as well as homotopy automorphisms of Kähler manifolds.

Deep Embedding Koopman Neural Operator-Based Nonlinear Flight Training Trajectory Prediction Approach

Accurate flight training trajectory prediction is a key task in automatic flight maneuver evaluation and flight operations quality assurance (FOQA), which is crucial for pilot training and aviation safety management. The task is extremely challenging due to the nonlinear chaos of trajectories, the unconstrained airspace maps, and the randomization of driving patterns. In this work, a deep learning model based on data-driven modern koopman operator theory and dynamical system identification is proposed. The model does not require the manual selection of dictionaries and can automatically generate augmentation functions to achieve nonlinear trajectory space mapping. The model combines stacked neural networks to create a scalable depth approximator for approximating the finite-dimensional Koopman operator. In addition, the model uses finite-dimensional operator evolution to achieve end-to-end adaptive prediction. In particular, the model can gain some physical interpretability through operator visualization and generative dictionary functions, which can be used for downstream pattern recognition and anomaly detection tasks. Experiments show that the model performs well, particularly on flight training trajectory datasets.

Common best proximity point theorems in Hausdorff topological spaces

In the present paper, we have obtained common best proximity point theorems of nonself maps in Hausdorff topological space. Further, our results extend the results due to Gerald F. Jungck, thereby proving a generalized version of Kirk’s theorem (J. London Math. 1(1):107–111, 1969).

The Banach Fixed Point Theorem: selected topics from its hundred-year history

On June 24, 1920 Stefan Banach presented his doctoral dissertation titled O operacjach na zbiorach abstrakcyjnych i ich zastosowaniach do równañ całkowych (On operations on abstract sets and their applications to integral equations) to the Philosophy Faculty of Jan Kazimierz University in Lvov. He passed his PhD examinations in mathematics, physics and philosophy, and in January 1921 he became a doctor. A year later, he published the results of his doctorate in Fundamenta Mathematicae. Among them there was the theorem known today as the Banach Fixed Point Theorem or the Banach Contraction Principle. It is one of the most famous theorems in mathematics, one of many under the name of Banach. It concerns certain mappings (called contractions) of a complete metric space into itself and it gives the conditions sufficient for the existence and uniqueness of a fixed point of such mapping. In 2022 we had a centenary of publishing this theorem. In the paper, we want to present its most important modifications and generalizations, several contractive conditions, the converse theorems and some applications. It is not possible to provide complete information about what has been written during the last hundred years about the Banach Fixed Point Theorem and we are just trying to touch on some breakthrough moments in the development of the metric fixed point theory. The main purpose of this article is to organize the knowledge on this subject and to elaborate a broad bibliography which all interested persons can refer to.

Frequency regulation feasible region assessment and optimization of wind farm based on data-driven model predictive control

With the integration of large-scale wind turbines (WTs) into grids via electronic interfaces, power system operators have necessitated frequency support from wind farms. Due to the large number of WTs and their complex dynamic characteristics, it is necessary to assess the primary frequency regulation (PFR) capability and construct feasible region of wind farms. In order to cope with the problems of incomplete parameters, analytical solving complexity and the coupling influence of power system regulation characteristics, this paper develops a data-driven state space mapping linear model predictive control (MPC) to assess the maximum PFR capability of wind farms and reasonably distribute coefficients to WTs. Besides, a coordinated iteration framework between dispatching center and wind farms is proposed to further optimize the wind farm regulation feasible region. The simulation results verify that the proposed method has the advantages of independence from physical parameters, fast analytical solution, and lower requirements of training samples on limited scenarios.

Research on laser communication ranging Integration and VLC nonlinear compensation technology

Abstract Visible light communication (VLC) is a new spectrum communication technology that provides a new direction to solve spectrum resource problems. The nonlinearity problem in VLC will lead to a significant reduction in the performance of the communication system. To solve this problem, this paper studies the integration of laser communication ranging and VLC nonlinear compensation technology based on analyzing the principles of ranging methods and factors affecting ranging performance. Aiming at the problem that the complexity of the Random Fourier Features Kernel adaptive filter (RFF-KAF) method will increase significantly as the dimension of the mapping space increases, we introduce some second-order Volterra series square terms into the input vector of RFF-KAF and propose an improved prediction method. Experimental simulation results show that the method proposed in this article can greatly improve the performance of the RFF-KAF method while maintaining the same mapping space dimension. Compared with obtaining similar performance by increasing the mapping space dimension, the cost of this method is greatly reduced.

Chemical spaces of taste and odor

AbstractThe thesis provides a draft map of the chemical space of chemosensory active molecules in foods and enables, by application of cheminformatics approaches, the deduction of general principles of raw material influence and processing on the sensory perception of complex food systems. The summarized data supports the development of analytical methods targeting the efficient quantitation of key compounds, provides a database for screening of chemosensory receptor agonists and facilitates the optimization of in‐silico tools for prediction of receptor activation determining sensory quality and biological function.