Mapping Theory Research Articles

SOME REMARKS ON SOBOLEV AND BI-SOBOLEV MAPPINGS

In this note, we present the state-of-the-art theory of bi-Sobolev mappings. We recall that f is a Sobolev homeomorphism if f belongs to Wloc1,1∩Hom(Ω;Ω′)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W^{1,1}_\ ext {loc}\\cap \ extrm{Hom}(\\Omega ; \\Omega ')$$\\end{document}, and f is a bi-Sobolev map if and only if f and f-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f^{-1}$$\\end{document} are Sobolev homeomorphisms. This concept, introduced in Hencl et al. (J. Math. Anal. Appl. 355, 22–32 2009), plays a central role in Geometric Function Theory. For instance, we just mention here that maps of bi-Sobolev type are strictly related to the notion of mappings of finite distortion; see, among others, the papers (Hencl and Koskela 2014) Pratelli (Nonlinear Anal. 154, 258–268 2017).

A 2D piecewise-linear discontinuous map arising in stock market modeling: Two overlapping period-adding bifurcation structures

We consider a 2D piecewise-linear discontinuous map defined on three partitions that drives the dynamics of a stock market model. This model is a modification of our previous model associated with a map defined on two partitions. In the present paper, we add more realistic assumptions with respect to the behavior of sentiment traders. Sentiment traders optimistically buy (pessimistically sell) a certain amount of stocks when the stock market is sufficiently rising (falling); otherwise they are inactive. As a result, the action of the price adjustment is represented by a map defined by three different functions, on three different partitions. This leads, in particular, to families of attracting cycles which are new with respect to those associated with a map defined on two partitions. We illustrate how to detect analytically the periodicity regions of these cycles considering the simplest cases of rotation number 1/n,n≥3, and obtaining in explicit form the bifurcation boundaries of the corresponding regions. We show that in the parameter space, these regions form two different overlapping period-adding structures that issue from the center bifurcation line. In particular, each point of this line, associated with a rational rotation number, is an issue point for two different periodicity regions related to attracting cycles with the same rotation number but with different symbolic sequences. Since these regions overlap with each other and with the domain of a locally stable fixed point, a characteristic feature of the map is multistability, which we describe by considering the corresponding basins of attraction. Our results contribute to the development of the bifurcation theory for discontinuous maps, as well as to the understanding of the excessively volatile boom-bust nature of stock markets.

Fractional partial differential variational inequality

In this present paper, we introduce and study a dynamical systems involving fractional derivative operator and nonlocal condition, which is constituted of a fractional evolution equation and a time-dependent variational inequality, and is named as fractional partial differential variational inequality (FPDVI, for short). By employing the estimates involving the one-and two-parameter Mittag-Leffler functions, fixed-point theory for set-value mappings, and non-compactness measure theory, we develop a general framework to establish the existence of smooth solutions to (FPDVI).

Hippocampal and medial prefrontal ensemble spiking represents episodes and rules in similar task spaces

Episodic memory requires the hippocampus and prefrontal cortex to guide decisions by representing events in spatial, temporal, and personal contexts. Both brain regions have been described by cognitive theories that represent events in context as locations in maps or memory spaces. We query whether ensemble spiking in these regions described spatial structures as rats performed memory tasks. From each ensemble, we construct a state-space with each point defined by the coordinated spiking of single and pairs of units in 125-ms bins and investigate how state-space locations discriminate task features. Trajectories through state-spaces correspond with behavioral episodes framed by spatial, temporal, and internal contexts. Both hippocampal and prefrontal ensembles distinguish maze locations, task intervals, and goals by distances between state-space locations, consistent with cognitive mapping and relational memory space theories of episodic memory. Prefrontal modulation of hippocampal activity may guide choices by directing memory representations toward appropriate state-space goal locations.

A spatiotemporal inference model for hazard chains based on weighted dynamic Bayesian networks for ground subsidence in mining areas

Ground subsidence concerns the long-term development of mining areas, and if not addressed effectively, it could gradually evolve into a major issue limiting the future economic development and survival of mining firms and local populations. However, there is unpredictability and uncertainty in the analysis of ground subsidence in mining areas, which is a quantitative and qualitative problem coupled with multiple indicators. By creating a chain relationship between ground subsidence in mining areas, this research provides a spatiotemporal inference model that integrates remote sensing (RS), geographic information system (GIS), and probabilistic map theory. The model uses a dynamic Bayesian framework to integrate the ground subsidence hazard chain in mining areas, standardizes multi-source data using GIS, computes node probabilities, and applies the entropy weight approach to improve model parameters. The Pingshuo mining area in China served as the study area for the model, and the mean values of area under the curve (AUC) and Brier score (BS) of the inferred results were 0.85 and 0.18, respectively, demonstrating that the model had some accuracy and dependability. Further analysis was performed on the impact of weights on the outcomes and the sensitivity of the model to the input nodes. The findings indicated that the spatiotemporal distribution of the results inferred from the model essentially matched the actual circumstance and could offer data assistance for mine safety management. The matching of the subsidence areas was effectively improved by optimizing the model with weights. The accuracy would also grow as the number of input nodes increased. The model proposed in this study is not limited by data, and the structure can be adjusted with the change of disaster chains, which is applicable to the study of multiple uncertainty problems.

Systematic Evaluation of Research Progress in the Textile Field over the Past 10 Years: Bibliometric Study on Smart Textiles and Clothing

Intelligent textile clothing is one of the most popular topics in the field. In recent decades, rapid advances have been made in the area of intelligent textile clothing research, and the intellectual structure pertaining to this domain has significantly evolved. We used CiteSpace 6.2.R4, VOSviewer 1.6.19, to evaluate and visualize the results, analyzing articles, countries, regions, institutions, authors, journals, citations, and keywords. Both a macroscopic sketch and a microscopic characterization of the entire knowledge domain were realized. The aim of this paper is to utilize bibliometric and knowledge mapping theories to identify relevant research papers on the subject of smart textiles and clothing that have been published by the China Knowledge Network Web of Science (WOS) within the last decade. It is concluded that the main topics of smart textile and garment research can be divided into nine categories: wearable electronics, smart textiles, flexible antennas, energy storage, textile actuators, mechanical properties, asymmetric supercapacitors, carbon nanotubes, and fiber extrusion. In addition to the latter analysis, emerging trends and future research foci were predicted. This review will help scientists discern the dynamic evolution of intelligent textile clothing research as well as highlight areas for future research.

Fluidized Bed Co-Melt Granulation: New Insights in the Influence of Process Variables and Validation of Regime Map Theory

Fluidized Bed Co-Melt Granulation: New Insights in the Influence of Process Variables and Validation of Regime Map Theory

A nonlinear African vulture optimization algorithm combining Henon chaotic mapping theory and reverse learning competition strategy

As a new intelligent optimization algorithm, the African vultures optimization algorithm (AVOA) has been widely used in various fields today. However, when solving complex multimodal problems, the AVOA still has some shortcomings, such as low searching accuracy, deficiency on the search capability and tendency to fall into local optimum. In order to alleviate the main shortcomings of the AVOA, a nonlinear African vulture optimization algorithm combining Henon chaotic mapping theory and reverse learning competition strategy (HWEAVOA) is proposed. Firstly, the Henon chaotic mapping theory and elite population strategy are proposed to improve the randomness and diversity of the vulture's initial population; Furthermore, the nonlinear adaptive incremental inertial weight factor is introduced in the location update phase to rationally balance the exploration and exploitation abilities, and avoid individual falling into a local optimum; The reverse learning competition strategy is designed to expand the discovery fields for the optimal solution and strengthen the ability to jump out of the local optimal solution. HWEAVOA and other advanced comparison algorithms are used to solve classical and CEC2022 test functions. Compared with other algorithms, the convergence curves of the HWEAVOA drop faster and the line bodies are smoother. These experimental results show the proposed HWEAVOA is ranked first in all test functions, which is superior to the comparison algorithms in convergence speed, optimization ability, and solution stability. Meanwhile, HWEAVOA has reached the general level in the algorithm complexity, and its overall performance is competitive in the swarm intelligence algorithms.

Mapping Matters - Your Questions Answered

The Layman's Perspective on Technical Theory and Practical Applications of Mapping and Gis

Buffer Stock Practice and Supply Chain Leverage of Sugar Manufacturing Firms in Kenya.

This research paper aimed at establishing the relationship between Buffer stocks Practices and supply chain leverage of sugar manufacturing firms in Kenya. The specific objective of the study was; to determine the effect of buffer stocks practices on supply chain leverage of sugar manufacturing firms in Kenya. The research study was anchored on supply chain road map theory. The research study methodology followed a descriptive approach where; the target population of the study was 241 respondents. A census survey was conducted on all the 15 registered sugar manufacturing firms in Kenya. From the study, 20 respondents were selected for the pilot study, constituting 8%, which is within the recommended range of, 1% to 10% of the population. Data collected was analyzed by both descriptive and inferential statistics using statistical package for social sciences (SPSS Version 28). Descriptive statistics involved calculation of means, frequencies, percentages and standard deviation. Model diagnostic tests such as Normality test, Multicollinearity, Heteroskedastity were also executed for determination of fitness of regression models. Inferential statistics further included the use of Pearson correlation coefficient to determine the extent of relationship between the independent study variables, while multiple regression analysis was used to establish the relationship between dependent variable and independent variables. The results from the analyzed data were then presented using figures, charts, tables and histograms to facilitate data interpretation. Findings from data analysis indicated that green stocks practices significantly affect supply chain leverage of sugar manufacturing firms in Kenya. This yielded a regression model Y = 2.507 + 0.117X. The findings from the regression models indicated that buffer stocks practices, significantly affected supply chain leverage of sugar manufacturing firms in Kenya. The study further recommended that sugar manufacturing firms in Kenya, to keep buffer stocks to overcome any uncertainties in the demand and supply markets and support continuous production even with seasonal variation in the supply of raw materials to ensure full capacity of operations, production efficiency, cost control and environmental protection. As a result idle time for the machines and people will be completely zero rated, through continued production process without a halt, even when there is shortage of raw materials in the market, hence continued supply of sugar products in the market.

Research on the Cyberspace Map and Its Conceptual Model

The cyberspace map, as one of the important tools for describing cyberspace, provides a visual representation of the dynamic and elusive nature of cyberspace. It has become a research hotspot in multiple disciplinary fields. Compared with traditional maps, cyberspace maps lack the guidance of cartography theory and have not yet formed a unified understanding. Clarifying the concept of the cyberspace map and developing a conceptual model of it could enhance people’s unified understanding of cyberspace. Drawing from the perspective of cartography, this paper analyzes the current situation of cyberspace map research, first discussing the characteristics and definition of the cyberspace map and then proposing the conceptual model of a cyberspace map. This model elaborates on the types of map elements and their specific composition, the strength of their element–space association, the mapping of relationships between elements, element symbolization, and map expression. Then, based on the model proposed in this paper, typical maps are compared and analyzed, and design suggestions are provided. Finally, the entire article is summarized. This paper aims to adapt the development trend of cartography to the ternary space, clarify the basic concept of the cyberspace map, promote the development of cyberspace mapping theory, and lay the foundation for future research.

Achromatic elastic metalens for high-performance confocal piezoelectric energy harvesting

In this study, we analytically, numerically, and experimentally investigated a high-performance confocal piezoelectric energy harvesting system. We achieved a significantly enhanced electrical performance through a Mikaelian lens, which achromatically focuses ambient elastic waves, resulting in the formation of a highly amplified strain energy field in the piezoelectric energy harvester. Previous studies on piezoelectric energy harvesting platforms have limitations, such as the focal position changing with operating frequencies and impedance mismatching owing to inclusions or holes. To address these problems, we utilized the self-focusing ability based on the conformal mapping theory and achromatic ability based on the Kirchhoff–Love thin plate theory to design our Mikaelian lens-based piezoelectric energy harvesting platform. The proposed platform demonstrates a remarkable elastic wave focusing ability at an identical focal position for a broad frequency range. The experimentally visualized wave fields matched well with the numerically calculated full-wave harmonic simulation results. We achieved highly amplified output power up to 1.44 mW within a broad range from 40 to 60 kHz out of the same focal point owing to confined elastic wave energy; the output power extracted at this confocal position was up to 3.76 times higher than that extracted at the lens start position. Our highly performance and broadband achromatic piezoelectric energy harvesting platform lays an attractive foundation for designing potential applications, such as wireless sensing, structural health monitoring, and biomedical devices.

Finite/fixed-time synchronization of inertial memristive neural networks by interval matrix method for secure communication

This paper investigates the finite/fixed-time synchronization problem of delayed inertial memristive neural networks (DIMNNs) using interval matrix-based methods within a unified control framework. By employing set-valued mapping and differential inclusion theory, two distinct methods are applied to handle the switching behavior of memristor parameters: the maximum absolute value method and the interval matrix method. Based on these different approaches, two control strategies are proposed to select appropriate control parameters, enabling the system to achieve finite and fixed-time synchronization, respectively. Additionally, the resulting theoretical criteria differ based on the chosen control strategy, with one expressed in algebraic form and the other in the form of linear matrix inequalities (LMIs). Numerical simulations demonstrate that the interval matrix method outperforms the maximum absolute value method in terms of handling memristor parameter switching, achieving faster finite/fixed-time synchronization. Furthermore, the theoretical results are extended to the field of image encryption, where the response system is utilized for decryption and expanding the keyspace.

Exact solutions for submerged von Kármán point vortex streets cotravelling with a wave on a linear shear current

New exact solutions are presented to the problem of steadily travelling water waves with vorticity wherein a submerged von Kármán point vortex street cotravels with a wave on a linear shear current. Surface tension and gravity are ignored. The work generalizes an earlier study by Crowdy & Nelson (Phys. Fluids, vol. 22, 2010, 096601) who found analytical solutions for a single point vortex row cotravelling with a water wave in a linear shear current. The main theoretical tool is the Schwarz function of the wave, and the work builds on a novel framework set out recently by Crowdy (J. Fluid Mech., vol. 954, 2022, A47). Conformal mapping theory is used to construct Schwarz functions with the requisite properties and to parametrize the waveform. A two-parameter family of solutions is found by solving a pair of nonlinear algebraic equations. This system of equations has intriguing properties: indeed, it is degenerate, which radically reduces the number of possible solutions, although the space of physically admissible equilibria is still found to be rich and diverse. For inline vortex streets, where the two vortex rows are aligned vertically, there is generally a single physically admissible solution. However, for staggered streets, where the two vortex rows are offset horizontally, certain parameter regimes produce multiple solutions. An important outcome of the work is that while only degenerate von Kármán point vortex streets can exist in an unbounded simple shear current, a broad array of such equilibria is possible in a shear current beneath a cotravelling wave on a free surface.

Flower-like imide covalent organic framework as an electrochemical platform catcher for simultaneous sensitive detection of trace Pb(II) and Cd(II)

Heavy metal pollution in aquatic environment poses an enormous risk to ecosystems and human health. In this study, a flowerlike covalent organic framework (TpTa-COF) was synthesized by one-step solvothermal method with 2,4,6-triformylphloroglucinol (Tp) and 4, 4-diamino-tribiphenyl (Ta) as building elements. Then it was used as an effective trap to establish an electrochemical sensing platform for simultaneously sensitive detection of trace Pb(II) and Cd(II) in water. This three-dimensional flower-shaped structure exhibited exceptional adsorption capacity, large surface area, high stability, and all of which enhanced the detection sensitivity of the sensor and facilitated full contact between ions and substrate. The high oxygen content in the structure provided abundant active sites for Pb(II) and Cd(II), further enhancing its electrochemical response. The constructed sensor exhibited a linear response to Pb(II) within the concentration range of 3–60 µg/L under the optimal conditions, with a detection limit of 0.16 µg/L. Similarly, a linear response was observed for Cd(II) in the concentration range of 5–60 µg/L, with a detection limit of 0.29 µg/L. Low detection limits, excellent sensitivity, and strong stability were all features of the suggested approach. It has been successfully employed in determining Pb(II) and Cd(II) concentrations in two actual water samples. XPS, SEM-EDS mapping, and density functional theory calculations confirmed that TpTa-COF interacted with metal ions mainly via coordination with carbonyl oxygen atoms in the structure. Overall, these findings will broaden the applications of COF in the field of chemical analysis.

Metaphor production in the bilingual acquisition of English and Polish.

Metaphor acquisition research has focused mostly on metaphor comprehension in monolingual children. Ours is the first study to examine metaphor production in young bilinguals. A quantitative method was employed whereby sixty-two children aged three to six, with English and Polish, were tested on their ability to produce primary (e.g., a long day) and perceptual resemblance metaphors (e.g., You're my sunshine) in response to elicitation tasks. A univariate ANOVA revealed that the main factors to affect the production of conventional metaphors in bilingual children are their chronological age and their verbal skills in both English and Polish. No significant effect was found for nonverbal IQ, metaphor type, or testing language. These results are discussed in the context of both Conceptual Metaphor Theory, which has been concerned with the study of primary (and other conceptual) metaphors, and Structure Mapping Theory, which has focused on the use of perceptual resemblance metaphors. Usage-Based Theory is brought in to explain lexical effects in metaphor production.

Collective action (still) matters: transformation of government social assistance mechanisms during the covid-19 pandemic

This paper analyzed the Makassar government's public policy during the COVID-19 pandemic, namely the social assistance program. In this study, the perspective of stakeholders is taken, in which in this study the community is the main stakeholder. In addition, there are also other stakeholders such as the Social Service, District, sub District, Social Assistance Assistants. This research will explain the implementation of social assistance policies in Mariso District, Makassar and how the community responds to this policy. In addition, in this study, there were protests carried out by social assistance recipient communities in Mariso District, Makassar as a form of disappointment with the implementation of the Social Assistance policy in Mariso District, which proved successful enough to put pressure on so that aspirations and input could be realized and the government evaluated social assistance programs. COVID-19. This research conduct qualitative methods with data collection techniques using interviews with informants, in this case are the stakeholders. This study also uses the Stakeholder Mapping theory which was popularized by Eden, Ackermann and Bryson. This study uses 3 analyzes in this theory, namely 1) Power versus interest grid, 2) Problem-frame stakeholders map and 3) Policy implementation mapping. The Power versus interest grid is used by researchers to see and analyze from the side of interest and power for the community as the main Stakeholder in this research. The Problem-frame stakeholders map is used by researchers to see how the conditions of stakeholders, in this case, are the community. How does the community solve problems in this social assistance program and what actions are taken by the community to solve these problems. Policy implementation mapping is used by researchers to describe the strategies carried out by the community to influence social assistance policies, especially in Mariso District, Makassar.

Jet spaces over Carnot groups

Jet spaces over \mathbb{R}^n have been shown to have a canonical structure of stratified Lie groups (also known as Carnot groups). We construct jet spaces over stratified Lie groups adapted to horizontal differentiation and show that these jet spaces are themselves stratified Lie groups. Furthermore, we show that these jet spaces support a prolongation theory for contact maps, and in particular, a Bäcklund type theorem holds. A byproduct of these results is an embedding theorem that shows that every stratified Lie group of step s + 1 can be embedded in a jet space over a stratified Lie group of step s .

Halogen substituted aurones as potential apoptotic agents: synthesis, anticancer evaluation, molecular docking, ADMET and DFT study

A series of halogen-substituted aurone derivatives (2a-k) were synthesized and evaluated for an anti-proliferative study against NCI 60 cancer cell line panel and showed that most of the compounds predominantly exhibited promising activity against MCF-7. Compound 2e exhibited promising anticancer activity against the MCF-7 cancer cell line with 84.98% percentage growth inhibition in a single dose assay of 10 μM with an IC50 value of 8.157 ± 0.713 μM. In apoptotic assay, the effect of compound 2e on the cell cycle progression indicated that exposure of MCF-7 cells to compound 2e induced a significant disruption in the cell cycle profile including a time-dependent decrease in the cell population at G0/G1 and G2/M phase and arrests the cell cycle at the S phase. In silico, molecular docking ADME and toxicity studies of all compounds were also carried out. The docking study revealed that all the aurone derivatives displayed good docking scores ranging from −7.066 to −8.573. The results of Molecular Electrostatic Potential Mapping (MESP) and Density Functional Theory (DFT) studies of the most active compound 2e and least active compound 2k also favoured the experimental results.

Dynamics of a Predator–Prey Model with Impulsive Diffusion and Transient/Nontransient Impulsive Harvesting

Harvesting is one of the ways for humans to realize economic interests, while unrestricted harvesting will lead to the extinction of populations. This paper proposes a predator–prey model with impulsive diffusion and transient/nontransient impulsive harvesting. In this model, we consider both impulsive harvesting and impulsive diffusion; additionally, predator and prey are harvested simultaneously. First, we obtain the subsystems of the system in prey extinction and predator extinction. We obtain the fixed points of the subsystems by the stroboscopic map theories of impulsive differential equations and analyze their stabilities. Further, we establish the globally asymptotically stable conditions for the prey/predator-extinction periodic solution and the trivial solution of the system, and then the sufficient conditions for the permanence of the system are given. We also perform several numerical simulations to substantiate our results. It is shown that the transient and nontransient impulsive harvesting have strong impacts on the persistence of the predator–prey model.