Space Mapping Research Articles

Some results related to common fixed point of four maps in f-metric spaces

The purpose of this paper is to present some existence and uniqueness results for some common fixed points of four mappings in F-metric spaces that satisfy the generalized conditions. Whereas, the new proposed two theorems allow to generalize and improve some theorems published in many previous papers related to fixed point in F-metric spaces. Indeed, the basics of the two new theorems proposed in this paper include a generalization and improvement of the previous well-known theorems in metric space, F-metric space and class of F-metric spaces, leading to more flexibility in their understanding and their applications. Furthermore, the proposed theorems allow overcoming the weak contraction type faced in the common fixed point theorem in the setting of F-metric spaces. Some examples are presented to prove that the proposed theorems are complementary and applicable where the existence and uniqueness of common fixed points of four mappings in F-metric spaces in the form of integrals are obtained.

The approximation property for the predual of weighted spaces of holomorphic mappings on Banach spaces

In this paper, we investigate the approximation property for the predual of the weighted space of holomorphic mappings, where is a countable family of weights defined on a balanced open subset U of a Banach space E. We introduce a locally convex topology on and show that is topologically isomorphic to for a suitably restricted family . As a consequence, certain characterizations of the approximation property for the space are proved.

Application of cross-channel multiscale permutation entropy in measuring multichannel data complexity.

Entropy is a pivotal concept in nonlinear dynamics, revealing chaos, self-organization, and information transmission in complex systems. Permutation entropy, due to its computational efficiency and lower data length requirements, has found widespread use in various fields. However, in the age of multi-channel data, existing permutation entropy methods are limited in capturing cross-channel information. This paper presents cross-channel multiscale permutation entropy algorithm, and the proposed algorithm can effectively capture the cross-channel information of multi-channel dataset. The major modification lies in the concurrent frequency counting of specific events during the calculation steps. The algorithm improves phase space reconstruction and mapping, enhancing the capability of multi-channel permutation entropy methods to extract cross-channel information. Simulation and real-world multi-channel data analysis demonstrate the superiority of the proposed algorithm in distinguishing different types of data. The improvement is not limited to one specific algorithm and can be applied to various multi-channel permutation entropy variants, making them more effective in uncovering information across different channels.

Urban recreational green spaces dynamics and implications in the Bonaberi Neighbourhood of Douala IV Municipality, Cameroon

Globally, urban recreational green spaces constitute a major environmental resource of urban landscapes. These greeneries are suffering from shrinkages and transformations due to pressures on more urban land needed for housing, commercial and industrial purposes and uncontrolled urbanization. This study was conducted to assess the spatiotemporal variations and extent of transformations within the urban green spaces and their associated implications in the Bonaberi neighbourhood of Douala IV Municipality. To achieve this, empirical data was collected through field visits, in-depth interviews with urban authorities and mapping of urban green spaces for 2003 and 2022. Two hundred inhabitants were purposively sampled while local council authorities and other stakeholders were interviewed in the Douala IV Municipality. This was complemented by secondary data obtained from the Douala Urban Council. The collected data were analyzed using descriptive and inferential statistical techniques and results revealed that the rapid transformation and decrease of urban green spaces in terms of spatiotemporal nature is a function of expansion and uncontrolled urban settlements. The shrinkage in urban green spaces in the Douala IV municipality has resulted in loss of biodiversity, increase in urban heat islands, atmospheric pollution, unattractiveness of the environment, crimes, mental and physical health issues. This was x-rayed by the poorly arranged green spaces, littered with wastes and having multiple paths used by motorists, pedestrians and vendor activities. This study concludes that greeneries remain a vital environmental resource, thus, recommending effective application of planning policies to restrict their encroachment. Additionally, greeneries should be treated among the top priorities of the development agenda of urban planning authorities as enshrined in the Sustainable Development Goal 11.

Josephy’s Theorem, Revisited

The main goal of this note is to characterize the necessary and sufficient conditions for a composition operator to act between spaces of mappings of bounded Wiener variation in a normed-valued setting. The necessary and sufficient conditions for local boundedness of such operators are also discussed.

Weak ψ-Contractions on Directed Graphs with Applications to Integral Equations

This article deals with a few outcomes ensuring the fixed points of a weak (G,ψ)-contraction map of metric spaces comprised with a reflexive and transitive digraph G. To validate our findings, we furnish several examples. The findings we obtain enable us to seek out the unique solution of a nonlinear integral equation. The outcomes presented herewith sharpen, subsume, unify, improve, enrich, and compile a number of existing theorems.

Investigating the missing-wedge problem in small-angle X-ray scattering tensor tomography across real and reciprocal space.

Small-angle-scattering tensor tomography is a technique for studying anisotropic nanostructures of millimetre-sized samples in a volume-resolved manner. It requires the acquisition of data through repeated tomographic rotations about an axis which is subjected to a series of tilts. The tilt that can be achieved with a typical setup is geometrically constrained, which leads to limits in the set of directions from which the different parts of the reciprocal space map can be probed. Here, we characterize the impact of this limitation on reconstructions in terms of the missing wedge problem of tomography, by treating the problem of tensor tomography as the reconstruction of a three-dimensional field of functions on the unit sphere, represented by a grid of Gaussian radial basis functions. We then devise an acquisition scheme to obtain complete data by remounting the sample, which we apply to a sample of human trabecular bone. Performing tensor tomographic reconstructions of limited data sets as well as the complete data set, we further investigate and validate the missing wedge problem by investigating reconstruction errors due to data incompleteness across both real and reciprocal space. Finally, we carry out an analysis of orientations and derived scalar quantities, to quantify the impact of this missing wedge problem on a typical tensor tomographic analysis. We conclude that the effects of data incompleteness are consistent with the predicted impact of the missing wedge problem, and that the impact on tensor tomographic analysis is appreciable but limited, especially if precautions are taken. In particular, there is only limited impact on the means and relative anisotropies of the reconstructed reciprocal space maps.

Fixed Point Results for New Classes of k-Strictly Asymptotically Demicontractive and Hemicontractive Type Multivalued Mappings in Symmetric Spaces

Fixed point theory is a significant area of mathematical analysis with applications across various fields such as differential equations, optimization, and dynamical systems. Recently, multivalued mappings have gained attention due to their ability to model more complex and realistic problems. ln this work, novel classes of nonlinear mappings called k-strictly asymptotically demicontractive-type and asymptotically hemicontractive-type multivalued mappings are introduced in real Hilbert spaces that are symmetric spaces. In addition, we discuss the weak and strong convergence results by considered modified algorithms, and a demiclosedness property, for these classes of mappings are proved. Several non-trivial examples are demonstrated to validate the newly defined mappings. Consequently, the results and iterative methods obtained in this study improve and extend several known outcomes in the literature.

([formula omitted])-contractive and ([formula omitted])-contractive mapping based fixed point theorems in fuzzy bipolar metric spaces and application to nonlinear Volterra integral equations

In this paper, we introduce some novel concepts within the realm of fuzzy bipolar metric spaces, namely (αη)-contractive type covariant mappings and contravariant mappings, and (βχ)-contractive type covariant mappings. We establish some fixed point theorems that demonstrate both the existence and uniqueness of fixed points for (αη)-contractive type covariant mappings and contravariant mappings, and for (βχ)-contractive type covariant mappings in complete fuzzy bipolar metric spaces utilizing the triangular property. Additionally, to substantiate the findings, some illustrative examples and consequential outcomes are presented. Furthermore, the proven results serve to extend, generalize, and enhance the corresponding outcomes documented in existing literature. A practical application of these findings in the context of non-linear Volterra integral equations is demonstrated, solidifying and reinforcing the credibility of the established results. Overall, this paper contributes to the understanding of fixed point theory in the context of fuzzy bipolar metric spaces and highlights the significance of (αη)-contractive mappings and (βχ)-contractive mappings in this domain.

Nanoscopic analysis of rapid thermal annealing effects on InGaN grown over Si(111)

This study explores the impact of rapid thermal annealing (RTA) on InxGa1-xN grown over Si(111) by molecular beam epitaxy (MBE). Through X-ray diffraction (XRD) and reciprocal space map (RSM) characterization, notable shifts in diffraction peaks were observed post-annealing, suggesting alterations of the Indium content in the nanostructures. Morphological assessments using scanning electron microscopy (SEM) and atomic force microscopy (AFM) indicated that RTA could smooth the surface of the samples, though some instances of degradation were also noted. Energy-dispersive X-ray spectroscopy (EDS) showed further stoichiometric modification following annealing. Photoluminescence spectroscopy (PL) revealed notable shifts and increases in the intensity of the InxGa1-xN peaks, indicating the formation of regions with high Indium or Gallium concentration. The presence of these enriched regions was particularly evident from the peaks at around 540 nm and 433 nm, suggesting significant changes in the material's composition. Transmission electron microscopy combined with electron energy loss spectroscopy (TEM-EELS) corroborated the presence of In-rich and Ga-rich areas, affirming the phenomenon of Indium surface segregation. So, this study contributes to understanding the behavior of InxGa1-xN nanostructures under rapid thermal annealing, providing insights for advanced optoelectronic applications.

Enhanced ICD-10 code assignment of clinical texts: A summarization-based approach

BackgroundAssigning International Classification of Diseases (ICD) codes to clinical texts is a common and crucial practice in patient classification, hospital management, and further statistics analysis. Current auto-coding methods mainly transfer this task to a multi-label classification problem. Such solutions are suffering from high-dimensional mapping space and excessive redundant information in long clinical texts. To alleviate such a situation, we introduce text summarization methods to the ICD coding regime and apply text matching to select ICD codes. MethodWe focus on the tenth revision of the ICD (ICD-10) coding and design a novel summarization-based approach (SuM) with an end-to-end strategy to efficiently assign ICD-10 code to clinical texts. In this approach, a knowledge-guided pointer network is purposed to distill and summarize key information in clinical texts precisely. Then a matching model with matching-aggregation architecture follows to align the summary result with code, tuning the one-vs-all scenario to one-vs-one matching so that the large-label-space obstacle laid in classification approaches would be avoided. ResultThe 12,788 ICD-10 coded discharge summaries from a Chinese hospital were collected to evaluate the proposed approach. Compared with existing methods, the purposed model achieves the greatest coding results with Micro AUC of 0.9548, MRR@10 of 0.7977, Precision@10 of 0.0944, and Recall@10 of 0.9439 for the TOP-50 Dataset. Results on the FULL-Dataset remain consistent. Also, the proposed knowledge encoder and applied end-to-end strategy are proven to facilitate the whole model to gain efficacy in selecting the most suitable code. ConclusionThe proposed automatic ICD-10 code assignment approach via text summarization can effectively capture critical messages in long clinical texts and improve the performance of ICD-10 coding of clinical texts.

Certain Fixed Point Results via Contraction Mappings in Neutrosophic Semi-Metric Spaces

In this work, the authors introduce the concept of neutrosophic semi-metric spaces and prove several common fixed-point theorems for countable and uncountable family of mappings via an implicit relation of contractive and integral type by utilizing locally integrable functions. These results improve and generalize the several results in the existing literature. Further, the authors present some non-trivial examples to support our main results. Mathematics Subject Classification: 46S40, 47H10, 54H25.

Food city Ho Chi Minh City: designing relational mapping of the culture of place

ABSTRACT This research investigates the novel design and implementation of a relational mapping of city spaces, based on research conducted in Ho Chi Minh City, Vietnam. The experimental mapping employs relational methods of exploration to document and understand the city. A special Memefest mapping workshop used food as a key medium for some of the relationships that underpin the culture, community, and the city itself. This paper outlines the design of a sensory based exploration and creative mapping of food culture in Ho Chi Minh City and puts special emphasis in the atmospheres that are created through the relations between food, community, and the structures that underlie these. Lastly the paper shows an example of installations and explains how they work as (post) representational maps of relations and atmospheres.

On the matricial truncated moment problem. II

We continue the study of truncated matrix-valued moment problems begun in [12]. Let q∈N. Suppose that (X,X) is a measurable space and E is a finite-dimensional vector space of measurable mappings of X into Hq, the Hermitian q×q matrices. A linear functional Λ on E is called a moment functional if there exists a positive Hq-valued measure μ on (X,X) such that Λ(F)=∫X〈F,dμ〉 for F∈E.In this paper a number of special topics on the truncated matricial moment problem are treated. We restate a result from [11] to obtain a matricial version of the flat extension theorem. Assuming that X is a compact space and all elements of E are continuous on X we characterize moment functionals in terms of positivity and obtain an ordered maximal mass representing measure for each moment functional. The set of masses of representing measures at a fixed point and some related sets are studied. The class of commutative matrix moment functionals is investigated. We generalize the apolar scalar product for homogeneous polynomials to the matrix case and apply this to the matricial truncated moment problem.

Encoding of 2D Self-Centered Plans and World-Centered Positions in the Rat Frontal Orienting Field.

The neural mechanisms of motor planning have been extensively studied in rodents. Preparatory activity in the frontal cortex predicts upcoming choice, but limitations of typical tasks have made it challenging to determine whether the spatial information is in a self-centered direction reference frame or a world-centered position reference frame. Here, we trained male rats to make delayed visually guided orienting movements to six different directions, with four different target positions for each direction, which allowed us to disentangle direction versus position tuning in neural activity. We recorded single unit activity from the rat frontal orienting field (FOF) in the secondary motor cortex, a region involved in planning orienting movements. Population analyses revealed that the FOF encodes two separate 2D maps of space. First, a 2D map of the planned and ongoing movement in a self-centered direction reference frame. Second, a 2D map of the animal's current position on the port wall in a world-centered reference frame. Thus, preparatory activity in the FOF represents self-centered upcoming movement directions, but FOF neurons multiplex both self- and world-reference frame variables at the level of single neurons. Neural network model comparison supports the view that despite the presence of world-centered representations, the FOF receives the target information as self-centered input and generates self-centered planning signals.

Aromaticity in the Spectroscopic Spotlight of Hexaphyrins.

Spectroscopic properties are commonly used in the experimental evaluation of ground- and excited-state aromaticity in expanded porphyrins. Herein, we investigate if the defining photophysical properties still hold for a diverse set of hexaphyrins with varying redox states, topologies, peripheral substitutions, and core-modifications. By combining TD-DFT calculations with several aromaticity descriptors and chemical compound space maps, the intricate interplay between structural planarity, aromaticity, and absorption spectra is elucidated. Our results emphasize that the general assumption that antiaromatic porphyrinoids exhibit significantly attenuated absorption bands as compared to aromatic counterparts does not hold even for the unsubstituted hexaphyrin macrocycles. To connect the spectroscopic properties to the hexaphyrins' aromaticity behaviour, we analyzed chemical compound space maps defined by the various aromaticity indices. The intensity of the Q-band is not well described by the macrocyclic aromaticity. Instead, the degeneracy of the frontier molecular orbitals, the HOMO-LUMO gap, and the |ΔHOMO-ΔLUMO|2 values appear to be better indicators to identify hexaphyrins with enhanced light-absorbing abilities in the near-infrared region. Regions with highly planar hexaphyrin structures, both aromatic and antiaromatic, are characterized by an intense B-band. Hence, we advise using a combination of global and local aromaticity descriptors rooted in different criteria to assess the aromaticity of expanded porphyrins instead of solely relying on the absorption spectra.

(Keynote) Automated / Autonomous Platforms for Synthesis, Purification, and Characterization of Quantum Dots

Controlling composition, structure, and thus properties of nanomaterials continues to be of importance to numerous fields. For example, applications of quantum dots range from displays and bioimaging, to metal nanoparticles for (electro-) catalytic conversions. The vastness of synthesis parameter space, in combination with still limited understanding of the nucleation and growth mechanisms for many quantum dots systems still hampers progress in identifying nanomaterials with desired properties for existing and newly envisioned purposes. Furthermore, the identification of optimal synthesis recipes for these nanostructures remains a major hurdle.This presentation will report on the development and application a number of enabling capabilities for the synthesis and characterization of quantum dots, achieved through reactor engineering. We demonstrate how the use of automated flow reactors not only helps in run-to-run reproducibility but also in uncovering mechanistic information. Examples include reactors with dedicated nucleation, growth, and shell formation zones, and investigation that revealed mechanistic insight of how water concentration affects QD synthesis outcome. We also employed an autonomous flow reactor system to map synthesis parameter space of specific QD systems, a project that relied on fast, fully automated in-situ characterization using UV-vis or photo-luminescence in combination with multi-step machine learning workflows The utility of flow reactors, however, is limited when considering chemistries with longer reaction times. Hence, more recently we developed a fully automated batch reactor for parameter space mapping of QD synthesis via hot injection, the most frequently used method in both QD research and production at scale. This batch platform is being augmented with purification capabilities, to address some of the challenges of in-line, in-situ characterization of raw reaction mixtures, and to enable using advanced optical and structural characterization methods to provide insight into the actual structure of the QD materials.

Inertial subgradient projection techniques for solving a class of bilevel equilibrium problems

ABSTRACT In this paper, we introduce a new algorithm for solving bilevel equilibrium problems with nonexpansive and pseudocontractive mappings in a real Hilbert space. The proposed algorithm is based on subgradient method with Armijo-type linesearch process, subgradient method, and inertial projection techniques. By choosing the suitable regular parameters, we prove strong convergence of the algorithm under classical conditions of the cost bifunctions.

Impulsive integro‐differential inclusions with nonlocal conditions: Existence and Ulam's type stability

This article focuses on the existence and Ulam–Hyers–Rassias stability outcomes pertaining to a specific category of impulsive integro‐differential inclusions (with instantaneous and non‐instantaneous impulses). These problems are examined using resolvent operators, drawing from the Grimmer perspective. Our analysis is based on Bohnenblust–Karlin's and Darbo's fixed point theorems for multivalued mappings in Banach spaces. Additionally, we provide an illustrative example to reinforce and demonstrate the validity of our findings.

Divisors and curves on logarithmic mapping spaces

We determine the rational class and Picard groups of the moduli space of stable logarithmic maps in genus zero, with target projective space relative a hyperplane. For the class group we exhibit an explicit basis consisting of boundary divisors. For the Picard group we exhibit a spanning set indexed by piecewise-linear functions on the tropicalisation. In both cases a complete set of boundary relations is obtained by pulling back the WDVV relations from the space of stable curves. Our proofs hinge on a controlled technique for manufacturing test curves in logarithmic mapping spaces, opening up the topology of these spaces to further study.