scholarly journals On the Number of Faces and Radii of Cells Induced by Gaussian Spherical Tessellations

2021 ◽  
Author(s):  
Eric Lybrand ◽  
Anna Ma ◽  
Rayan Saab
Keyword(s):  
Number Of Faces

A ten-faced hexangulaconulariid from Cambrian Stage 2 of South China

2021 ◽  
pp. 1-8
Author(s):  
Junfeng Guo ◽  
Jian Han ◽  
Heyo Van Iten ◽  
Zuchen Song ◽  
Yaqin Qiang ◽  
...  
Keyword(s):  
New Genus ◽  
Radial Symmetry ◽  
New Taxon ◽  
Three Gorges ◽  
Substantial Variation ◽  
The Three Gorges ◽  
Apical Half ◽  
Lateral Margins ◽  
Number Of Faces ◽  
Extinct Group

Abstract Hexangulaconulariids (Cambrian stages 1–2) are an extinct group of medusozoan polyps having a biradially symmetrical, fan-shaped periderm that is distinct from those of medusozoan polyps showing three-, four-, five-, or six-fold radial symmetry. Hexangulaconulariids exhibit substantial variation in gross morphology, including variation in the number of faces on each of the two major sides of the periderm. An intermediate taxon of hexangulaconulariids with ten faces (five on each major side) was expected. Here we describe a new hexangulaconulariid, Decimoconularia isofacialis new genus new species from Bed 5 of the Yanjiahe Formation (Cambrian Stage 2) in the Three Gorges area of Hubei Province, China. The new taxon differs from other hexangulaconulariids (Arthrochites, Hexaconularia, and Septuconularia) mainly in possessing a total of ten faces. The two lateral margins are each marked by a ridge in about the apertural half of the periderm and by a collinear furrow in about the apical half, while the five faces on each major side are bounded by a furrow in about the apertural half and by a collinear ridge in about the apical half. Among hexangulaconulariids, Decimoconularia and Septuconularia may be more closely related to each other than either genus is to Arthrochites or Hexaconularia. UUID: http://zoobank.org/ca270a3b-25ee-4d1f-bdeb-91a963370e70

scholarly journals Typical emotional expression in children’s drawings of the human face

2021 ◽  
Author(s):  
Eleonora Cannoni ◽  
Giuliana Pinto ◽  
Anna Silvia Bombi
Keyword(s):  
Emotional Expression ◽  
Visual Cues ◽  
Age Groups ◽  
Emotional Expressions ◽  
Basic Emotions ◽  
Preferential Expression ◽  
Human Figure ◽  
Figure Drawings ◽  
Number Of Faces ◽  
Human Faces

AbstractThis study was aimed at verifying if children introduce emotional expressions in their drawings of human faces, and if a preferential expression exists; we also wanted to verify if children’s pictorial choices change with increasing age. To this end we examined the human figure drawings made by 160 boys and 160 girls, equally divided in 4 age groups: 6–7; 8–9; 10–11; 12–13 years; mean ages (SD in parentheses) were: 83,30 (6,54); 106,14 (7,16) 130,49 (8,26); 155,40 (6,66). Drawings were collected with the Draw-a-Man test instructions, i.e. without mentioning an emotional characterization. In the light of data from previous studies of emotion drawing on request, and the literature about preferred emotional expressions, we expected that an emotion would be portrayed even by the younger participants, and that the preferred emotion would be happiness. We also expected that with the improving ability to keep into account both mouth and eyes appearance, other expressions would be found besides the smiling face. Data were submitted to non-parametric tests to compare the frequencies of expressions (absolute and by age) and the frequencies of visual cues (absolute and by age and expressions). The results confirmed that only a small number of faces were expressionless, and that the most frequent emotion was happiness. However, with increasing age this representation gave way to a variety of basic emotions (sadness, fear, anger, surprise), whose representation may depend from the ability to modify the shapes of both eyes and mouth and changing communicative aims of the child.

scholarly journals MULTIPARAMETRIC OPTIMIZATION OF THE SHAPE AND THICKNESS OF INSULATED ENERGY EFFICIENT CONSTRUCTED BUILDING WITH A SPECIFIC NUMBER OF FACES

2021 ◽  
pp. 196-204
Author(s):  
Viacheslav Martynov
Keyword(s):  
Energy Efficiency ◽  
Energy Efficient ◽  
Heat Losses ◽  
Geometrical Parameters ◽  
Energy Efficient Buildings ◽  
Multiparametric Optimization ◽  
Heat Influx ◽  
Number Of Faces ◽  
The Given ◽  
First Time

To calculate the optimal parameters of outbuildings, a mathematical model and method for optimizing the shape and resistance of heat transfer for opaque and transparent structures with a certain constant number of faces, building volume and amount of insulation to minimize the thermal balance of enclosing structures with the environment during the heating period In the course of calculations the geometrical parameters of translucent, opaque structures in the heat-insulating shell of buildings are determined taking into account heat losses, heat influx from solar radiation by the criterion of ensuring minimum heat losses through enclosing structures, rational parameters (buildings) The given technique and mathematical models should be used in the future in the design of energy efficient buildings in the reconstruction and thermal modernization of buildings. This will increase their energy efficiency and, accordingly, the energy efficiency class of buildings. For the research faceted attached building in the form of a triangular pyramid, the reduction in heat loss was 14.82 percent only due to the optimization of the shape and redistribution of the insulation. Similar results were obtained for other initial forms. For the first time, a computerized method was proposed, an algorithm and application package Optimparam for multiparameter shape optimization and insulation of translucent and opaque structures for outbuildings with a given number of arbitrarily arranged faces were developed.

scholarly journals Omega Index of Line and Total Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Musa Demirci ◽  
Sadik Delen ◽  
Ahmet Sinan Cevik ◽  
Ismail Naci Cangul
Keyword(s):  
Line Graph ◽  
Graph Invariant ◽  
Original Graph ◽  
Total Graph ◽  
Graph Classes ◽  
Number Of Faces

A derived graph is a graph obtained from a given graph according to some predetermined rules. Two of the most frequently used derived graphs are the line graph and the total graph. Calculating some properties of a derived graph helps to calculate the same properties of the original graph. For this reason, the relations between a graph and its derived graphs are always welcomed. A recently introduced graph index which also acts as a graph invariant called omega is used to obtain such relations for line and total graphs. As an illustrative exercise, omega values and the number of faces of the line and total graphs of some frequently used graph classes are calculated.

The quantum polyhedra and the volume spectrum

2017 ◽  
Vol 14 (09) ◽  
pp. 1750125
Author(s):  
Ahmida Bendjoudi ◽  
Noureddine Mebarki
Keyword(s):  
Hilbert Space ◽  
Arbitrary Number ◽  
Number Of Faces

The Bohr–Sommerfeld volume spectrum of polyhedron with arbitrary number of faces is computed. Some spacial cases (the three, four and five valent node Hilbert space) are studied.

Convex cores of measures on R d

2001 ◽  
Vol 38 (1-4) ◽  
pp. 177-190 ◽  
Author(s):  
Imre Csiszár ◽  
F. Matúš
Keyword(s):  
Borel Measure ◽  
Convex Sets ◽  
Probability Measures ◽  
Countable Number ◽  
Borel Sets ◽  
Finite Borel Measure ◽  
Number Of Faces ◽  
Convex Core

We define the convex core of a finite Borel measure Q on R d as the intersection of all convex Borel sets C with Q(C) =Q(R d). It consists exactly of means of probability measures dominated by Q. Geometric and measure-theoretic properties of convex cores are studied, including behaviour under certain operations on measures. Convex cores are characterized as those convex sets that have at most countable number of faces.

scholarly journals Optimal number of faces for fast self-folding kirigami

2020 ◽  
Vol 3 (1) ◽  
Author(s):  
H. P. M. Melo ◽  
C. S. Dias ◽  
N. A. M. Araújo
Keyword(s):  
Optimal Number ◽  
Number Of Faces

Colouring of Trivalent Polyhedra

1965 ◽  
Vol 17 ◽  
pp. 659-664 ◽  
Author(s):  
Anton Kotzig
Keyword(s):  
Convex Polyhedron ◽  
Number Of Faces

By an Euler polyhedron of valence three or a trivalent convex polyhedron in Euclidean 3-space (4) we mean in the present paper an Euler polyhedron in the sense of Steinitz (8, p. 113), such that each vertex is incident with exactly three edges.In the present paper we establish a theorem concerning the colouring of trivalent polyhedra. A specialization of this theorem solves the following problem implicit in Eberhard (1, p. 84): Does there exist a trivalent Euler polyhedron with an odd number of faces such that the number of edges incident with any face is divisible by three?

The number of faces of the tridiagonal Birkhoff polytope

2009 ◽  
Vol 161 (6) ◽  
pp. 867-877 ◽  
Author(s):  
L. Costa ◽  
C. M. da Fonseca ◽  
E. A. Martins
Keyword(s):  
Birkhoff Polytope ◽  
Number Of Faces

Abstract Voronoi Diagrams from Closed Bisecting Curves

2017 ◽  
Vol 27 (03) ◽  
pp. 221-240
Author(s):  
Cecilia Bohler ◽  
Rolf Klein ◽  
Chih-Hung Liu
Keyword(s):  
Voronoi Diagrams ◽  
Connected Components ◽  
Voronoi Region ◽  
Jordan Curves ◽  
Intersection Points ◽  
Number Of Faces

We present the first algorithm for constructing abstract Voronoi diagrams from bisectors that are unbounded or closed Jordan curves. It runs in expected [Formula: see text] many steps and [Formula: see text] space, where [Formula: see text] is the number of sites, [Formula: see text] denotes the average number of faces (connected components) per Voronoi region in any diagram of a subset of [Formula: see text] sites, and [Formula: see text] is the maximum number of intersection points between any two related bisectors.

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