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This paper aims to prove some fixed-point theorems for a general class of mappings in modular G-metric spaces. The results of this paper generalize and extend several known results to modular G-metric spaces, including the results of Mutlu et al. [1]. Furthermore, the authors produce an example to demonstrate the applicability of the results.

The results of this paper are theoretical and analytical in nature.

The authors established some fixed-point theorems for a general class of mappings in modular G-metric spaces. The results generalize and extend several known results to modular G-metric spaces, including the results of Mutlu et al. [1]. An example was constructed to demonstrate the applicability of the results.

Analytical and theoretical results.

The results of this paper can be applied in science and engineering.

The results of this paper is applicable in certain social sciences.

The results of this paper are new and will open up new areas of research in mathematical sciences.

The purpose of this paper is to establish novel business metrics of laboratory space utilization for a large, multi‐client R&D organization and to describe their use in space planning to meet strategic objectives. The paper aims to show that traditional methods for measuring and managing laboratory space utilization are impractical in a dynamic environment where there are frequent and significant changes in the use of the space.

The integration of disparate databases – financial, facilities management, and project R&D – enables financial performance data to be explicitly resolved to individual laboratory resources. In turn, this allows determination of the efficiency with which laboratory space is being utilized in meeting the organization's financial and strategic objectives.

Unique and actionable insights were generated in applying the methodology. It provided bases for the identification of both over‐ and under‐utilized laboratory spaces, as well as the means of assessing the efficacy with which space assets are being used in achieving the organization's strategic missions.

This departure from more conventional concepts of occupancy‐based metrics of space utilization treats R&D laboratory space explicitly as a business resource.

The emerging business‐based metrics of lab space utilization are proving to be increasingly valuable tools in both short‐term and strategic space planning.

This paper aims mainly at introducing applied statisticians and econometricians to the current research methodology with non-Euclidean data sets. Specifically, it provides the basis and rationale for statistics in Wasserstein space, where the metric on probability measures is taken as a Wasserstein metric arising from optimal transport theory.

The authors spell out the basis and rationale for using Wasserstein metrics on the data space of (random) probability measures.

In elaborating the new statistical analysis of non-Euclidean data sets, the paper illustrates the generalization of traditional aspects of statistical inference following Frechet's program.

Besides the elaboration of research methodology for a new data analysis, the paper discusses the applications of Wasserstein metrics to the robustness of financial risk measures.

This paper proposes a new metric, named Operational Space Efficiency (OpSE), intended to diagnose and quantify the inefficient use of floor space for stocking materials in industrial workstations. OpSE presents a formulation analogous to the well-known Overall Equipment Effectiveness and can be obtained as the product of three distinct indicators: Standard Compliance Effectiveness, Standards Selection Effectiveness and Design Space-usage Effectiveness.

This indicator scrutinizes how usefully floor space in workstations is used to temporarily stock materials in the form of raw materials, semi-finished products, parts and components. It is suited for analyzing fixed-position layouts as well as product layouts typical of repetitive manufacturing settings, such as assembly lines in the automotive sector. The proposed indicator leverages an appropriate loss structure that features those factors affecting floor space utilization in workstations with regard to supplying and stocking materials.

An Italian manufacturer in the field of electro-technology was used as an industrial case study for the application of the methodology. The application shows how the three indicators work in practice, the effectiveness of OpSE and the methodology as a whole, in diagnosing floor space usage inefficiencies and in properly addressing improvement actions of the internal logistics in industrial settings.

The paper scrutinizes some important Key Performance Indicators (KPIs) dealing with space usage efficiency and identifies some significant drawbacks. Then it suggests a new, inclusive structure of losses and a KPI that not only measures efficiency but also allows to identify viable countermeasures.

The authors prove the existence and uniqueness of fixed point of mappings satisfying Geraghty-type contractions in the setting of preordered modular G-metric spaces. The authors apply the results in solving nonlinear Volterra-Fredholm-type integral equations. The results extend generalize compliment and include several known results as special cases.

The results of this paper are theoretical and analytical in nature.

The authors prove the existence and uniqueness of fixed point of mappings satisfying Geraghty-type contractions in the setting of preordered modular G-metric spaces. apply the results in solving nonlinear Volterra-Fredholm-type integral equations. The results extend, generalize, compliment and include several known results as special cases.

The results are theoretical and analytical.

The results were applied to solving nonlinear integral equations.

The results has several social applications.

The results of this paper are new.

With the increasing demand for surveillance and smart transportation, drone technology has become the center of attraction for robotics researchers. This study aims to introduce a new path planning approach to drone navigation based on topology in an uncertain environment. The main objective of this study is to use the Ricci flow evolution equation of metric and curvature tensor over angular Riemannian metric, and manifold for achieving navigational goals such as path length optimization at the minimum required time, collision-free obstacle avoidance in static and dynamic environments and reaching to the static and dynamic goals. The proposed navigational controller performs linearly and nonlinearly both with reduced error-based objective function by Riemannian metric and scalar curvature, respectively.

Topology and manifolds application-based methodology establishes the resultant drone. The trajectory planning and its optimization are controlled by the system of evolution equation over Ricci flow entropy. The navigation follows the Riemannian metric-based optimal path with an angular trajectory in the range from 0° to 360°. The obstacle avoidance in static and dynamic environments is controlled by the metric tensor and curvature tensor, respectively. The in-house drone is developed and coded using C++. For comparison of the real-time results and simulation results in static and dynamic environments, the simulation study has been conducted using MATLAB software. The proposed controller follows the topological programming constituted with manifold-based objective function and Riemannian metric, and scalar curvature-based constraints for linear and nonlinear navigation, respectively.

This proposed study demonstrates the possibility to develop the new topology-based efficient path planning approach for navigation of drone and provides a unique way to develop an innovative system having characteristics of static and dynamic obstacle avoidance and moving goal chasing in an uncertain environment. From the results obtained in the simulation and real-time environments, satisfactory agreements have been seen in terms of navigational parameters with the minimum error that justifies the significant working of the proposed controller. Additionally, the comparison of the proposed navigational controller with the other artificial intelligent controllers reveals performance improvement.

In this study, a new topological controller has been proposed for drone navigation. The topological drone navigation comprises the effective speed control and collision-free decisions corresponding to the Ricci flow equation and Ricci curvature over the Riemannian metric, respectively.

This paper aims to develop a geometry of moral systems. Existing social choice mechanisms predominantly employ simple structures, such as rankings. A mathematical metric among moral systems allows us to represent complex sets of views in a multidimensional geometry. Such a metric can serve to diagnose structural issues, test existing mechanisms of social choice or engender new mechanisms. It also may be used to replace active social choice mechanisms with information-based passive ones, shifting the operational burden.

Under reasonable assumptions, moral systems correspond to computational black boxes, which can be represented by conditional probability distributions of responses to situations. In the presence of a probability distribution over situations and a metric among responses, codifying our intuition, we can derive a sensible metric among moral systems.

Within the developed framework, the author offers a set of well-behaved candidate metrics that may be employed in real applications. The author also proposes a variety of practical applications to social choice, both diagnostic and generative.

The proffered framework, derived metrics and proposed applications to social choice represent a new paradigm and offer potential improvements and alternatives to existing social choice mechanisms. They also can serve as the staging point for research in a number of directions.

In this paper, we use the notion of cyclic representation of a nonempty set with respect to a pair of mappings to obtain coincidence points and common fixed points for a pair of self-mappings satisfying some generalized contraction- type conditions involving a control function in partial metric spaces. Moreover, we provide some examples to analyze and illustrate our main results.

Theoretical method.

We establish some coincidence points and common fixed point results in partial metric spaces.

Results of this study are new and interesting.

The relationship between the child and his/her physical environment is an area of interaction that includes social, psychological and cultural factors along with the spatial experience, perception and behavior of the child. This study is based on the effects of spatial perception and behavior of the child within the physical environment of primary schools. In this direction, the purpose of this paper is to investigate how spatial and physical characteristics of primary school typologies affect the spatial perception and behavior of the child. Also, the parameters affecting spatial perception and behavior are examined.

The question to be investigated is how the spatial and physical characteristics of the school’s physical environment affect the child’s spatial perception and behavior in primary schools with different typologies. Within this scope, Istanbul’s Kagithane region is selected as a case study. Schools are chosen for their similar spatial and dimensional features and similar socio-economic environment. The methodology of the study consists of a literature review, an observational study carried out to discover the interaction between the child and his/her school building and the analysis of the student’s cognitive maps. These maps were evaluated according to topological, projective, metric and imaginative parameters.

The results show spatial organization and physical characteristics of primary school buildings with a structure that allows for change and transformation, and contributes to the physical and cognitive development of children.

This study will provide an opportunity to develop the design of future primary school buildings that can support the spatial perception and spatial experiences of the children.

The purpose of this paper is to introduce the implicit midpoint rule (IMR) of nonexpansive mappings in 2- uniformly convex hyperbolic spaces and study its convergence. Strong and △-convergence theorems based on this algorithm are proved in this new setting. The results obtained hold concurrently in uniformly convex Banach spaces, CAT(0) spaces and Hilbert spaces as special cases.