scholarly journals A Unified Methodology for the Generalisation of the Geometry of Features

2021 ◽  
Vol 10 (3) ◽  
pp. 107
Author(s):  
Anna Barańska ◽  
Joanna Bac-Bronowicz ◽  
Dorota Dejniak ◽  
Stanisław Lewiński ◽  
Artur Krawczyk ◽  
...  
Keyword(s):  
Spatial Data ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Banach Fixed Point Theorem ◽  
Digital Cartography ◽  
Complex Process ◽  
Source Data ◽  
Before And After ◽  
Feature Geometry ◽  
Fully Automatic

The development of generalisation (simplification) methods for the geometry of features in digital cartography in most cases involves the improvement of existing algorithms without their validation with respect to the similarity of feature geometry before and after the process. It also consists of the assessment of results from the algorithms, i.e., characteristics that are indispensable for automatic generalisation. The preparation of a fully automatic generalisation for spatial data requires certain standards, as well as unique and verifiable algorithms for particular groups of features. This enables cartographers to draw features from these databases to be used directly on the maps. As a result, collected data and their generalised unique counterparts at various scales should constitute standardised sets, as well as their updating procedures. This paper proposes a solution which consists in contractive self-mapping (contractor for scale s = 1) that fulfils the assumptions of the Banach fixed-point theorem. The method of generalisation of feature geometry that uses the contractive self-mapping approach is well justified due to the fact that a single update of source data can be applied to all scales simultaneously. Feature data at every scale s < 1 are generalised through contractive mapping, which leads to a unique solution. Further generalisation of the feature is carried out on larger scale spatial data (not necessarily source data), which reduces the time and cost of the new elaboration. The main part of this article is the theoretical presentation of objectifying the complex process of the generalisation of the geometry of a feature. The use of the inherent characteristics of metric spaces, narrowing mappings, Lipschitz and Cauchy conditions, Salishchev measures, and Banach theorems ensure the uniqueness of the generalisation process. Their application to generalisation makes this process objective, as it ensures that there is a single solution for portraying the generalised features at each scale. The present study is dedicated to researchers concerned with the theory of cartography.

Some fixed point results for (β-ψ1-ψ2)-contractive conditions in ordered b-metric-like spaces

Filomat ◽  
2017 ◽  
Vol 31 (14) ◽  
pp. 4587-4612 ◽  
Author(s):  
S.K. Padhan ◽  
Rao Jagannadha ◽  
Hemant Nashine ◽  
R.P. Agarwal
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Existence Of Solution ◽  
Distance Functions ◽  
Point Boundary ◽  
Contractive Mappings ◽  
Altering Distance

This paper extends and generalizes results of Mukheimer [(?,?,?)-contractive mappings in ordered partial b-metric spaces, J. Nonlinear Sci. Appl. 7(2014), 168-179]. A new concept of (?-?1-?2)-contractive mapping using two altering distance functions in ordered b-metric-like space is introduced and basic fixed point results have been studied. Useful examples are illustrated to justify the applicability and effectiveness of the results presented herein. As an application, the existence of solution of fourth-order two-point boundary value problems is discussed and rationalized by a numerical example.

scholarly journals On Fuzzy Extended Hexagonal b-Metric Spaces with Applications to Nonlinear Fractional Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2032
Author(s):  
Sumaiya Tasneem Zubair ◽  
Kalpana Gopalan ◽  
Thabet Abdeljawad ◽  
Bahaaeldin Abdalla
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Feasible Solution ◽  
Banach Fixed Point Theorem ◽  
Nonlinear Fractional Differential Equations ◽  
Research Article ◽  
Fractional Differential

The focus of this research article is to investigate the notion of fuzzy extended hexagonal b-metric spaces as a technique of broadening the fuzzy rectangular b-metric spaces and extended fuzzy rectangular b-metric spaces as well as to derive the Banach fixed point theorem and several novel fixed point theorems with certain contraction mappings. The analog of hexagonal inequality in fuzzy extended hexagonal b-metric spaces is specified as follows utilizing the function b(c,d): mhc,d,t+s+u+v+w≥mhc,e,tb(c,d)∗mhe,f,sb(c,d)∗mhf,g,ub(c,d)∗mhg,k,vb(c,d)∗mhk,d,wb(c,d) for all t,s,u,v,w>0 and c≠e,e≠f,f≠g,g≠k,k≠d. Further to that, this research attempts to provide a feasible solution for the Caputo type nonlinear fractional differential equations through effective applications of our results obtained.

scholarly journals The evolution of European stunt art (50–70s of the twentieth century)

2021 ◽  
Author(s):  
Nazar Mayboroda
Keyword(s):  
Film Industry ◽  
Professional Activity ◽  
French Cinema ◽  
Scientific Methods ◽  
Russian Art ◽  
Professional Activities ◽  
French Film ◽  
Complex Process ◽  
Before And After ◽  
General Scientific

The purpose of the article is to identify the specifics of the formation and development of stunt art in French cinema of the 1950-1970s; analyze the contribution to the process of formation in the European film industry stunt as a profession of French actors and performers of film stunts. Methodology. The scientific provisions of the article are reasoned at the level of the totality of general scientific methods of cognition and approaches of modern art history. The historical, analytical and typological methods were applied, which contributed to determining the specifics of the professionalization process of stunt art in the French film industry in the 1950-1970s, as well as the typological features of cinema stunts of the leading French stuntmen; a method of comparative analysis (to identify the characteristic signs of stunt activities before and after professionalization) and other. Scientific novelty. For the first time in Russian art criticism, the process of development and professionalization of stunt art in European cinema of the 1950-1970s has been studied. on the example of the evolution of French historical stunt scenes (films “cloak and sword”), adventure and detective films; reviewed and analyzed the professional activities of C. Carlier, R. Julien, J. Delamard and other French stuntmen of this period; revealed the influence of American stunt performers, the specifics of the development of French stunt art, as well as characterized the evolution of stunt techniques, the use of existing ones and the development of new safety methods for their implementation. Conclusions. The content and nature of professional stunt activities in the context of cinematic art are non-static, since its dynamism is determined by the stunt status in the continuous qualification system. The stunt man is the stunt developer, stunt coordinator (stunt director), and the head of the stunt troupe. In the 50–70s. XX century in French cinema, a complex process of professionalization of stunt art took place, the motivation of which was the need to assimilate professional knowledge, skills, abilities, and expand the experience of professional activity. The specifics of the French movie stunts by C. Carlier, R. Julien, J. Delamard, and I. Cipher are manifested in originality, exposure to the viewer with a degree of risk, and a specially refined aesthetics.

scholarly journals On New Type of F -Contractive Mapping for Quasipartial b -Metric Spaces and Some Results of Fixed-Point Theorem and Application

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
A. M. Zidan ◽  
Asma Al Rwaily
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Banach’S Fixed Point Theorem ◽  
Contractive Type ◽  
New Type

In this paper, we introduce the concept of new type of F -contractive type for quasipartial b-metric spaces and some definitions and lemmas. Also, we will prove a new fixed-point theorem in quasipartial b -metric spaces for F -contractive type mappings. In addition, we give an application which illustrates a situation when Banach’s fixed-point theorem for complete quasipartial b -metric spaces cannot be applied, while the conditions of our theorem are satisfying.

scholarly journals On Intuitionistic Fuzzy 2-Metric Spaces

2018 ◽  
Vol 22 ◽  
pp. 01024
Author(s):  
Elif Güner ◽  
Vildan Çetkin ◽  
Halis Aygün
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Intuitionistic Fuzzy

In this study, we first recall the notion of an intuitionistic fuzzy 2-metric space and fundamental definitions with several illustrative examples. Then we define the notion of δ−chainable space and (δ,λ)−uniform locally contractive mapping between intuitionistic fuzzy 2-metric spaces. After that, by using the proposed concepts, we obtain a few fixed point theorems of self-mappings defined on this spaces.

Before-and-After Empirical Bayes Evaluation of Citywide Installation of Driver Feedback Signs

2020 ◽  
Vol 2674 (4) ◽  
pp. 419-427
Author(s):  
Mingjian Wu ◽  
Karim El-Basyouny ◽  
Tae J. Kwon
Keyword(s):  
Traffic Safety ◽  
Spatial Data ◽  
Empirical Bayes ◽  
Large Scale ◽  
Low Cost ◽  
Cost Effective ◽  
Before And After ◽  
Feedback Sign ◽  
Driver Feedback ◽  
Road Segments

Speeding is a leading factor that contributes to approximately one-third of all fatal collisions. Over the past decades, various passive/active countermeasures have been adopted to improve drivers’ compliance to posted speed limits to improve traffic safety. The driver feedback sign (DFS) is considered a low-cost innovative intervention that is being widely used, in growing numbers, in urban cities to provide positive guidance for motorists. Despite their documented effectiveness in reducing speeds, limited literature exists on their impact on reducing collisions. This study addresses this gap by designing a before-and-after study using the empirical Bayes method for a large sample of urban road segments. Safety performance functions and yearly calibration factors are developed to quantify the sole effectiveness of DFS using large-scale spatial data and a set of reference road segments within the city of Edmonton, Alberta, Canada. Likewise, the study followed a detailed economic analysis based on three collision-costing criteria to investigate if DFS was indeed a cost-effective intervention. The results showed significant collision reductions that ranged from 32.5% to 44.9%, with the highest reductions observed for severe speed-related collisions. The results further attested that the benefit–cost ratios, combining severe and property-damage-only collisions, ranged from 8.2 to 20.2 indicating that DFS can be an extremely economical countermeasure. The findings from this study can provide transportation agencies in need of implementing cost-efficient countermeasures with a tool they need to design a long-term strategic deployment plan to ensure the safety of traveling public.

scholarly journals Pentagonal Cone b-metric Spaces over Banach Algebras and Fixed Point Theorem of Generalized Lipschitz Mapping

2018 ◽  
Vol 22 ◽  
pp. 01003 ◽  
Author(s):  
Abba Auwalu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Banach Algebras ◽  
Lipschitz Mapping ◽  
Banach Fixed Point Theorem ◽  
Cone Metric ◽  
Generalized Lipschitz Mapping

In this paper, we introduce the concept of pentagonal cone b-metric space over Banach algebras as a generalization of cone metric space over Banach algebras and many of its generalizations. Furthermore, we prove Banach fixed point theorem in such a space. Our result unify, complement and/or generalized some recent results in the papers [1–7], and many others. We provide some examples to elucidate the validity and superiority of our results.

scholarly journals On the weakly(α, ψ, ξ)-contractive condition for multi-valued operators in metric spaces and related fixed point results

2016 ◽  
Vol 14 (1) ◽  
pp. 167-180 ◽  
Author(s):  
Marwan Amin Kutbi ◽  
Wutiphol Sintunavarat
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Binary Relation ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Contractive Condition ◽  
Integral Type

AbstractThe aim of this paper is to introduce the concept of a new nonlinear multi-valued mapping so called weakly (α, ψ, ξ)-contractive mapping and prove fixed point results for such mappings in metric spaces. Our results unify, generalize and complement various results from the literature. We give some examples which support our main results while previous results in literature are not applicable. Also, we analyze the existence of fixed points for mappings satisfying a general contractive inequality of integral type. Many fixed point results for multi-valued mappings in metric spaces endowed with an arbitrary binary relation and metric spaces endowed with graph are given here to illustrate the results in this paper.

scholarly journals Spatial distribution of pedestrian-motor vehicle collisions before and after pedestrian countdown signal installation in Toronto, Canada

2017 ◽  
Vol 25 (2) ◽  
pp. 110-115 ◽  
Author(s):  
Linda Rothman ◽  
Marie-Soleil Cloutier ◽  
Alison K Macpherson ◽  
Sarah A Richmond ◽  
Andrew William Howard
Keyword(s):  
Spatial Distribution ◽  
Spatial Patterns ◽  
Spatial Data ◽  
Motor Vehicle ◽  
Spatial Data Analysis ◽  
Motor Vehicle Collisions ◽  
Vehicle Collisions ◽  
Point Patterns ◽  
Kernel Density Estimates ◽  
Before And After

BackgroundPedestrian countdown signals (PCS) have been installed in many cities over the last 15 years. Few studies have evaluated the effectiveness of PCS on pedestrian motor vehicle collisions (PMVC). This exploratory study compared the spatial patterns of collisions pre and post PCS installation at PCS intersections and intersections or roadways without PCS in Toronto, and examined differences by age.MethodsPCS were installed at the majority of Toronto intersections from 2007 to 2009. Spatial patterns were compared between 4 years of police-reported PMVC prior to PCS installation to 4 years post installation at 1864 intersections. The spatial distribution of PMVC was estimated using kernel density estimates and simple point patterns examined changes in spatial patterns overall and stratified by age. Areas of higher or lower point density pre to post installation were identified.ResultsThere were 14 911 PMVC included in the analysis. There was an overall reduction in PMVC post PCS installation at both PCS locations and non-PCS locations, with a greater reduction at non-PCS locations (22% vs 1%). There was an increase in PMVC involving adults (5%) and older adults (9%) at PCS locations after installation, with increased adult PMVC concentrated downtown, and older adult increases occurring throughout the city following no spatial pattern. There was a reduction in children’s PMVC at both PCS and non-PCS locations, with greater reductions at non-PCS locations (35% vs 48%).ConclusionsResults suggest that the effects of PCS on PMVC may vary by age and location, illustrating the usefulness of exploratory spatial data analysis approaches in road safety. The age and location effects need to be understood in order to consistently improve pedestrian mobility and safety using PCS.

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