Number is based in special edges, is introduced. The kind of natural extension from edges toward vertex and the set of vertices in the way that, the final notion is number, is studied. The result is obtained which is about the study on the classes of graphs in the matter of new notions. There is the extended notion about having edge amid two vertices toward having some edges in the word of neighbor and in another stage going into the atmosphere of having consecutive edges in the terminology of path and in the upper vision going on the notion about path with jargon and buzzword of distance as if the minimal vertices has concluded the new notions with the word, number.

The kind of set which is based on edges, is introduced. The analysis on this set is done in the matter of operation which are the classes of graphs. The general notion which is related to this concept, is up. The set of edges is seen in the matter of common vertex, entitled neighbor edges and the set of edges which has specific condition on the vertices of graphs, entitled ghost set. The kind of viewpoint when the edges are up so the kind of efforts to assign some notions which get the sensible result of edges which make sense about these two types of notions. Notions of having some attributes about vertices concerning edges and edges' attributes to get result about edges in the matter of vertices.

Farmland edge plants can support high butterfly richness. Our objective was determine if, even in farms under intensive cultivation, the diversity of plants (mostly native) in crop edges is enough to sustain a high species richness of butterfly. We characterized the vegetation on the edges of Medicago sativa farms in central Mexico and identified the species of diurnals butterflies (Rhopalocera) associated. Butterflies and plants were counted along transects at the edges of a cul-tivated field during 24 months. We found 2710 individuals of plants, belonging to 48 different species from 24 families; 1749 individuals of diurnal butterflies, belonging to 57 species from six families. Most than half of the plant species found were native flora of central Mexico and with ethnobotanical use. A similarity analysis test showed significant differences in floristic composi-tion between transects. The Canonical Correspondence Analysis between butterfly species and plant families showed three groups. Six butterfly species were migratory and four mexican en-demic species, most of them associated with a group formed by Amaranthaceae, Euphorbiaceae, Annonaceae Lamiaceae Apiaceae and Fabaceae families. The high diversity of plants in our agro-ecosystem plays an important role to sustain a high diversity of butterflies and could be useful as biological corridors.

Active contour models present a robust segmentation approach which make efficient use of specific information about objects in the input data rather than processing all the data. They have been widely used in many applications including image segmentation, object boundary localisation, motion tracking, shape modelling, stereo matching and object reconstruction. In this paper, we investigate the potential of active contour models in extracting roads from Mobile Laser Scanning (MLS) data. The categorisation of active contours based on their mathematical representation and implementation are discussed in detail. We discuss an integrated version in which active contour models are combined to overcome their limitations. We review various active contour based methodologies which have been developed to extract roads and other features from LiDAR and digital imaging datasets. We present a small case study in which an integrated version of active contour models is applied to automatically extract road edges from MLS dataset. An accurate extraction of left and right edges from the tested road section validates the use of active contour models. The present study provides a valuable insight on the potential of active contours for extracting roads and other infrastructures from 3D LiDAR point cloud data.

Cities are small on earth’s surface but they are the most attractive places for people to live and work; cities are developing quickly, thus it’s important to keep it a better quality place to live as it has the major of the economic activities and more job opportunities and other social and economic advantages to be a more green and sustainable place. Seeking to achieve sustainable use of ecosystems and conserve natural resources in the city of Prague; integrating ecological sustainability goals, the political borders as a reflection of urban development in the city, and ecosystems edges in blue and green functions impact the city development, and present opportunities to create strategies for green and blue infrastructure and clarifying threats could slow down the process to achieve the sustainability and greenery application. Also checking possible urban areas for development like brownfields and clarifying their relationship with political borders and ecosystems to find possible areas to add for sustainable green use, which will create better places for people to live and raise the value of life as well.

A Pogorelov polytope is a combinatorial simple 3-polytope realizable in the Lobachevsky (hyperbolic) space as a bounded right-angled polytope. It has no 3- and 4-gons and may have any prescribed numbers of k-gons, k ≥ 7. Any polytope with only 5-, 6- and at most one 7-gon is Pogorelov. For any other prescribed numbers of k-gons, k ≥ 7, we give an explicit construction of a Pogorelov and a non-Pogorelov polytopes. Any Pogorelov polytope different from Löbel polytopes can be constructed from the 5- or the 6-barrel by cuttings off pairs of adjacent edges and connected sums with the 5-barrel along a 5-gon with the intermediate polytopes being Pogorelov. For fullerenes there is a stronger result. Any fullerene different from the 5-barrel and the (5, 0)-nanotubes can be constructed by only cuttings off adjacent edges from the 6-barrel with all the intermediate polytopes having 5-, 6- and at most one additional 7-gon adjacent to a 5-gon. This result can not be literally extended to the latter class of polytopes. We prove that it becomes valid if we additionally allow connected sums with the 5-barrel and 3 new operations, which are compositions of cuttings off adjacent edges. We generalize this result to the case when the 7-gon may be isolated from 5-gons.

For the first time, We do fuzzification the concept of domination in crisp graph on a generalization of fuzzy graph by using membership values of vertices, α-strong edges and edges. In this paper, we introduce the first variation on the domination theme which we call vertex domination. We determine the vertex domination number γ_v for several classes of t-norm fuzzy graphs which include complete t-norm fuzzy graph, complete bipartite t-norm fuzzy graph, star t-norm fuzzy graph and empty t-norm fuzzy graph. The relationship between effective edges and α-strong edges is obtained. Finally, we discuss about vertex dominating set of a fuzzy tree with respect to a t-norm ⨂ by using the bridges and α-strong edges equivalence.

This paper aims to analyze arbitrarily loaded isotropic rectangular thin plates with two opposite edges supported (simply supported or clamped), from which one or both are clamped, and the other edges have arbitrary support conditions. Rectangular thin plates with two opposite edges simply supported are routinely analyzed using for the deflection the simple trigonometric series of Lévy or the double trigonometric series of Navier, while the loads are expanded in Fourier series. In this paper the flexibility method (or force method) of the linear beam theory was applied whereby the unknowns were the bending moments along the opposite edges; in this regard, the primary system was the plate simply supported along the above-mentioned opposite edges and subjected to the external loads, system solved using the Lévy solution, and the redundant system was the plate simply supported along the opposite edges and subjected to bending moments along those edges. In the redundant system, a modified Lévy solution was introduced to account for the edge moments. The compatibility equations (vanishing of the slopes at selected positions of the opposite edges) were set to determine the unknowns and so the efforts in the plate. The results obtained were in good agreement with the exact results.