Rectangular Space Research Articles

Some Results on Multivalued Proximal Contractions with Application to Integral Equation

In this manuscript, for the purpose of investigating the coincidence best proximity point, best proximity point, and fixed point results via alternating distance ϕ, we discuss some multivalued (ϕ−Fτ)CP and (ϕ−Fτ)BP−proximal contractions in the context of rectangular metric spaces. To ascertain the coincidence best proximity point, best proximity point, and the fixed point for single-valued mappings, we reduce these findings using (Fτ)CP and (Fτ)BP−proximal contractions. To make our work more understandable, examples of both single- and multivalued mappings are provided. These examples support our core findings, which rely on coincidence points, as well as the corollaries that address fixed point conclusions. In the final phase of our study, we use the obtained results to verify that a solution to a Fredholm integral equation exists. This application highlights the theoretical framework we built throughout our study.

Metasurface inspired printed dual‑port MIMO antenna system with LP to CP conversion features for millimeter wave n260 band applications

A cutting-edge antenna system has been developed for new radio (NR) millimeter wave operating from 36.0 to 40.0 GHz frequency range 2 (FR 2) n260 band applications. This innovative system incorporates metasurface-inspired printed dual-port MIMO technology, which includes LP to CP conversion features. The positional orientation of the elements of the MIMO antenna with stacked metasurface provoked the spatial diversity. To convert linearly polarised (LP) waves to circularly polarised (CP) waves, the metasurface layer is suspended above the MIMO antenna. LP to CP polarisation conversion occurs when the conducting strip and rectangular space between strips on the substrate generate π/2 phase-shifted electric field components (Ex and Ey). The proposed stepped impedance-fed antenna elements and metasurface are fabricated on commercially available high-frequency laminates using a double-layer printed circuit board (PCB) fabrication facility. The test findings exhibit a satisfactory level of concurrence with the calculated/measured findings regarding scattering parameters, diversity performance parameters, and realized gain. The result is a highly efficient and versatile antenna system that is ideal for advanced engineering applications.

Fixed Point Results for Geraghty Type Contractions in Extended Rec-tangular Fuzzy <i>b</i>-metric Space with an Application

The aim of this paper is to define the notions of extended fuzzy b-metric spaces, fuzzy rectangular b-metric spaces and extended fuzzy rectangular b-metric spaces and to establish certain fixed point results in these settings utilizing Geraghty type contractions. We also furnished an example which illustrates our main result. To show the authenticity of our results we provide an application involving fuzzy integral equation. The obtained results generalize many existing results in the literature.

Experimental backward integration for state-dependent differential Riccati equation (SDDRE): A case study on flapping-wing flying robot

Backward integration (BI) is a classical approach for solving optimal control arising from linear quadratic regulator (LQR) design in differential form. It proposes a two-round solution, the first one starting from a final boundary condition to the initial one to generate the optimal gain, and the next one, solving the control system in a forward loop. Implementation of the BI on the nonlinear optimal control, the state-dependent differential Riccati equation (SDDRE), is a challenge since in the backward loop, the state information is missing and is not straightforward like the LQR. Hence, a control for backward motion is required to regulate the system from the terminal to the initial desired states. While there have been some valuable works on the theoretical implementation of the BI in simulations for the SDDRE, this approach has not been reported in experiments for the best knowledge of the authors. Here in this work, the SDDRE is solved using the BI and two backward and forward solution steps, and it is experimentally applied for a flapping-wing flying robot (FWFR). The execution of the control system is done onboard using Raspberry Pi 4B as the processor which has limited computational capacity. The trajectory tracking of a line in a closed limited space is proposed for the FWFR flight. The objective is to position the robot bird at the corner of the rectangular limited space with minimum error in translation. The results have been presented for 21 flights to show the repeatability and presented the best-case minimum error of 10 (cm) at the end of the trajectory, in the YZ-plane. Considering approximately 12 (m) flight path, the error is found less than 1 percent of the travel distance. The results were compared with forward integration to confirm the correctness of the computation. The experimental flight dataset, MATLAB simulation codes, and experimental Python codes are available as supplementary material for this work in the online version of the paper.

Common Fixed Point Theorems in Extended Rectangular b-Metric Spaces

In this paper, we establish common fixed point theorems for quadruple weakly compatible mappings satisfying a new generalized contraction condition. Our results generalize the corresponding result of Budi Nurwahyu et al. [6]. Non-trivial examples are further provided to support the hypotheses of our results.

A Study of Boundedness in rectangular fuzzy n-normed spaces

A Study of Boundedness in rectangular fuzzy n-normed spaces

Passive Visual Odometry of Mobile Transport Robots in Production Areas Using Anchor Points

The article considers the problem of determining the orientation of mobile transport robots, which are now actively used in almost all areas of industry. They make it possible to intensify production, free personnel from performing routine operations, and exclude the influence of the human factor from work. Based on the analysis of various variants of active orientation methods involving the use of binocular video systems installed on the vehicles themselves, it is proposed to use a passive orientation detection system. It includes a single stationary monocular video system, the replacement of onboard video systems on mobile robots with simple radiation sensors, as well as the use of anchor points in the area of their movement. The order of choice of anchor points in solving the problem of orientation of a mobile transport robot using a monocular video system, in particular for a rectangular interior space, is considered. Calculation formulas for determining the coordinates of the sensor from the pixel coordinates of its image obtained from a monocular video camera are determined. The general sequence of actions for determining the orientation of a mobile robotic platform is also considered. Unlike active systems, this method makes it possible to significantly simplify the hardware, significantly facilitate the analysis of the current position of the mobile robot and thereby reduce the computational complexity of calculations due to the fact that there is no need to use a complex mathematical apparatus. It is being replaced by simpler two-dimensional geometric calculations. This approach, due to the unified management, makes it possible to effectively coordinate the actions of a group of mobile transport robots when they are used together, greatly simplifies the solution of a number of tasks for optimizing the intra-shop movement of mobile vehicles.

The impact of room shape on affective states, heartrate, and creative output

The architectural design of space can deeply impact an individuals' mood, physiology, and mental health. While previous research has predominantly focused on elements like nature and lighting within architectural spaces, there is a growing literature base that also investigates the psychological and neurophysiological impacts of geometrical properties of architectural spaces. Employing virtual reality technology, the study sought to investigate the effects of curved and rectangular architectural spaces on affective states, heart rate, and creativity.A total of 35 participants were exposed to two distinct virtual environments: a curved room and a rectangular room. Participants' self-reported mood was assessed using the Positive and Negative Affect Schedule (PANAS-Long Form). Heart rate was monitored using a pulse oximeter, and creative output was evaluated using the Guilford Alternative Uses Task (GAUT).Statistical comparisons between the two room types indicated that participants experienced higher positive affect and lower negative affect in the curved room condition compared to the rectangular room condition. Furthermore, heart rate measurements revealed lower physiological arousal in the curved room. Additionally, participants exhibited higher creative output in the curved room as opposed to the rectangular room.These findings align with previous literature on the influence of geometric factors on affective responses. The implications of this study are significant as they pertain to individuals' daily environments and their impact on health and well-being. The positive influence of curved room geometry on mood, arousal, and creativity emphasises the importance of considering room layout and design in various settings, such as workplaces and educational environments. Architects and designers can utilise these findings to inform their decisions and promote neuroarchitecture that enhances positive emotional experiences and productivity.

A fixed point result on an extended neutrosophic rectangular metric space with application

In this paper, we propose the notion of extended neutrosophic rectangular metric space and prove some fixed point results under contraction mapping. Finally, as an application of the obtained results, we prove the existence and uniqueness of the Caputo fractional differential equation.

Commuting and weakly commuting maps in generalized rectangular metric spaces

Commuting and weakly commuting maps in generalized rectangular metric spaces

Some New Results of Fixed Points on Fuzzy Rectangular b-Metric Like Spaces

Some New Results of Fixed Points on Fuzzy Rectangular b-Metric Like Spaces

Existence of coincidence and common fixed points for extended rectangular b-metric spaces

Existence of coincidence and common fixed points for extended rectangular b-metric spaces

Scientific Analysis and Conservation Treatment of the Ancestral Tablet Excavated from the Site of Gongpyeong, Seoul

Scientific analysis and conservation treatment were conducted on two ancestral tablets excavated in whole form the site of the 15th and 16th districts (B area) in Gongpyeong, Seoul. As a result of scientific analysis, a rectangular empty space was confirmed inside the ancestral tablet that could not be seen with the naked eye. It was a form of manufacturing and combining a main body and a prop composed of the front side and the back side, and the tree species of all the members of the two ancestral tablets were identified as Castanea spp.. It is supposed that the two ancestral tablets excavated from the Gongpyeong site were manufactured in accordance with the standard and shape similar to the contents of “Garye”, which has records on the production of ancestral tablets. The excavated ancestral tablets were immersed to the final 40% using PEG#2000 by applying the PEG immersion method, and dried using a vacuum freeze dryer. After drying, disparate things such as PEG and soil remaining on the surface were removed, and PEG#4000 15% (in ethyl alcohol) was applied to the surface once to the surface to strengthen the surface. A slight crack was observed in a part of a prop of one of the two ancestral tablets, and it was restored using epoxy-based resin, color-matched, and conservation treatment was completed.

Common Fixed Point Results For Quadruple Transformations In Vector Valued Rectangular Metric Spaces

In this manuscript, we consider vector valued Rectangular metric space in which metric is Riesz space valued. We establish the existence of common fixed point results for four self-maps in vector valued rectangular metric space. Established results extend and generalize several fixed point results for scalar valued case in the literature.

Fixed Point Theorems in Rectangular b-Metric Space Endowed with a Partial Order

The purpose of this paper is to present some fixed-point results for self-generalized contractions in ordered rectangular b-metric spaces. We also provide some examples that illustrate the non-triviality and richness of this area of research.

Exploring Fuzzy Triple Controlled Metric Spaces: Applications in Integral Equations

In this article, we delve into the study of fuzzy triple controlled metric spaces, investigating their properties and presenting a range of illustrative examples. We emphasize the broader applicability of this concept in comparison to fuzzy rectangular metric spaces and fuzzy rectangular b-metric spaces. By introducing the novel concept of (α-ψ)-fuzzy contractive mappings, we derive fixed point results specifically designed for complete fuzzy triple controlled metric spaces. Our theorems extend and enrich previous findings in this field. Additionally, we demonstrate the practical significance of our study by applying our findings to the solution of an integral equation and providing an example of its application. Furthermore, we propose potential avenues for future research endeavors.

Learning utility of smart school learning space: the impact of spatial factors via visual stated preference method

ABSTRACT In the era of Education 4.0, the development of smart schools represents a significant step forward. Learning spaces are critical to the success of smart school construction in primary and secondary schools, due to their significant impact on school-age children. This study focuses on identifying key spatial factors that influence students’ psychological preferences and learning utility in smart learning spaces. To achieve this, a visual stated preference method was employed to design a questionnaire, which was used to survey primary and secondary school students in Harbin, China. The resulting data was analyzed using a discrete choice model, which enabled the measurement of the utility levels of different learning space factors. The results show that students’ learning space preferences are significantly influenced by a variety of spatial factors, with the combination mode of classrooms and outdoors having the highest level of influence, followed by a completely open interface, U-shape seating layout, zoned color tone, and the combination mode of classrooms and corridors; the students surveyed show a significant negative preference for heteromorphic spaces compared to rectangular spaces. The discussion recommends the design of smart learning spaces around key spatial factors to enhance the utility of student learning.

A note on the fixed point theorem of F-contraction mappings in rectangular M-metric space

A note on the fixed point theorem of F-contraction mappings in rectangular M-metric space

On the coupled dynamics of vertical cladding panels and industrial frame structures subject to out-of-plane seismic loading

Industrial facilities typically consist in large-span single-storey prefabricated buildings having a rectangular floor space. Frame structures made with either steel, timber or precast concrete members are mostly employed to support the roof, while cladding panels create the building enclosure. Their interaction with the frame typically plays a relevant role in the overall building dynamics, potentially leading under seismic excitation to both local and global collapses. Experience shows that a critical component failure is that of the panel-frame connection. Current design approaches classify the panels as “non-structural members” and the forces at the connections induced by the out-of-plane seismic loading are evaluated with approximate expressions. Neglecting the dynamic interaction between the panel and the frame, however, may lead to an oversimplified description of the mechanical problem and inaccurate estimates of the forces at the connections. To overcome these drawbacks, in this work a different approach is pursued in which the interaction between the fundamental sway mode of the frame and the out-of-plane motion of the cladding panel is studied within a rigorous mechanical setting. The focus is on the very frequent case of vertical cladding panels, supported at the ground and retained out-of-plane by the frame. Starting from the development of the equations of motion for the coupled frame-panel structure, a minimal set of parameters controlling the dynamics of the system is identified. The spectral properties of the structure are analytically investigated to gain a clear insight on the coupled frame-panel structure. This is characterized by frequency veering and hybridization between the mode deforming the frame and the local modes of the panel. The system response for seismic excitation, then, is studied with a stochastic approach. Parametric analyses focusing on the values of the forces at the top and bottom connections of the panel and on the lateral displacement of the frame show that while the frame drift is controlled mainly by the first mode of the coupled frame-panel system, the top and bottom connection forces of the panel require at least consideration of the first two modes of the coupled system. This information is of great importance in deriving a reduced model of the coupled system. The proposed procedure allows for a thorough understanding of the coupled system dynamic response, and represents a viable alternative to derive the design response quantities of interest.

Stability analysis for complex-valued neural networks with fractional order

In the context of complex-valued rectangular b-metric spaces, the present study investigates the stability of complex-valued neural networks (CVNNs) with fractional order. Using the generalized contraction principle, we address the suitable condition for uniform stability of fractionally ordered CVNNs and establish the existence and uniqueness of the equilibrium point. Few numerical results are presented to show the feasibility and correctness of the results presented.