Cohen-Macaulay type of the face poset of a plane graph

1994 ◽  
Vol 10 (2-4) ◽  
pp. 133-138
Author(s):  
Takayuki Hibi
Keyword(s):  
Plane Graph ◽  
The Face

scholarly journals Longest paths in random Apollonian networks and largest r-ary subtrees of random d-ary recursive trees

2016 ◽  
Vol 53 (3) ◽  
pp. 846-856 ◽  
Author(s):  
Andrea Collevecchio ◽  
Abbas Mehrabian ◽  
Nick Wormald
Keyword(s):  
Related Result ◽  
Plane Graph ◽  
Time Step ◽  
Single Vertex ◽  
Planar Triangulation ◽  
The Face ◽  
Longest Paths ◽  
Recursive Trees ◽  
Positive Integers ◽  
Iterative Construction

AbstractLet r and d be positive integers with r<d. Consider a random d-ary tree constructed as follows. Start with a single vertex, and in each time-step choose a uniformly random leaf and give it d newly created offspring. Let 𝒯d,t be the tree produced after t steps. We show that there exists a fixed δ<1 depending on d and r such that almost surely for all large t, every r-ary subtree of 𝒯d,t has less than tδ vertices. The proof involves analysis that also yields a related result. Consider the following iterative construction of a random planar triangulation. Start with a triangle embedded in the plane. In each step, choose a bounded face uniformly at random, add a vertex inside that face and join it to the vertices of the face. In this way, one face is destroyed and three new faces are created. After t steps, we obtain a random triangulated plane graph with t+3 vertices, which is called a random Apollonian network. We prove that there exists a fixed δ<1, such that eventually every path in this graph has length less than t𝛿, which verifies a conjecture of Cooper and Frieze (2015).

scholarly journals Total Face Irregularity Strength of Grid and Wheel Graph under K-Labeling of Type (1, 1, 0)

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Aleem Mughal ◽  
Noshad Jamil
Keyword(s):  
Plane Graph ◽  
Plane Graphs ◽  
Wheel Graph ◽  
Wheel Graphs ◽  
The Face ◽  
Vertex Set ◽  
Positive Integers ◽  
Special Case ◽  
Irregularity Strength

In this study, we used grids and wheel graphs G = V , E , F , which are simple, finite, plane, and undirected graphs with V as the vertex set, E as the edge set, and F as the face set. The article addresses the problem to find the face irregularity strength of some families of generalized plane graphs under k -labeling of type α , β , γ . In this labeling, a graph is assigning positive integers to graph vertices, graph edges, or graph faces. A minimum integer k for which a total label of all verteices and edges of a plane graph has distinct face weights is called k -labeling of a graph. The integer k is named as total face irregularity strength of the graph and denoted as tfs G . We also discussed a special case of total face irregularity strength of plane graphs under k -labeling of type (1, 1, 0). The results will be verified by using figures and examples.

scholarly journals Gaps in the Chromatic Spectrum of Face-Constrained Plane Graphs

10.37236/1588 ◽  
2001 ◽  
Vol 8 (1) ◽  
Author(s):  
Daniel Kobler ◽  
André Kündgen
Keyword(s):  
Plane Graph ◽  
Plane Graphs ◽  
The Face ◽  
Chromatic Spectrum

Let $G$ be a plane graph whose vertices are to be colored subject to constraints on some of the faces. There are 3 types of constraints: a $C$ indicates that the face must contain two vertices of a $C$ommon color, a $D$ that it must contain two vertices of a $D$ifferent color and a $B$ that $B$oth conditions must hold simultaneously. A coloring of the vertices of $G$ satisfying the facial constraints is a strict $k$-coloring if it uses exactly $k$ colors. The chromatic spectrum of $G$ is the set of all $k$ for which $G$ has a strict $k$-coloring. We show that a set of integers $S$ is the spectrum of some plane graph with face-constraints if and only if $S$ is an interval $\{s,s+1,\dots,t\}$ with $1\leq s\leq 4$, or $S=\{2,4,5,\dots,t\}$, i.e. there is a gap at 3.

Why do people believe in a zero-sum economy?

2018 ◽  
Vol 41 ◽  
Author(s):  
Samuel G. B. Johnson
Keyword(s):  
Perspective Taking ◽  
Evolutionary Model ◽  
Everyday Experience ◽  
Coalitional Psychology ◽  
The Face ◽  
Zero Sum

AbstractZero-sum thinking and aversion to trade pervade our society, yet fly in the face of everyday experience and the consensus of economists. Boyer & Petersen's (B&P's) evolutionary model invokes coalitional psychology to explain these puzzling intuitions. I raise several empirical challenges to this explanation, proposing two alternative mechanisms – intuitive mercantilism (assigning value to money rather than goods) and errors in perspective-taking.

Mars: was There an Ancient Eden?

1997 ◽  
Vol 161 ◽  
pp. 203-218 ◽  
Author(s):  
Tobias C. Owen
Keyword(s):  
Positive Answer ◽  
Biogenic Elements ◽  
Habitable Zones ◽  
The Face ◽  
The Origin Of Life ◽  
Early Mars ◽  
Favorable Conditions ◽  
Open Question ◽  
Rocky Planets ◽  
Impact Erosion

AbstractThe clear evidence of water erosion on the surface of Mars suggests an early climate much more clement than the present one. Using a model for the origin of inner planet atmospheres by icy planetesimal impact, it is possible to reconstruct the original volatile inventory on Mars, starting from the thin atmosphere we observe today. Evidence for cometary impact can be found in the present abundances and isotope ratios of gases in the atmosphere and in SNC meteorites. If we invoke impact erosion to account for the present excess of129Xe, we predict an early inventory equivalent to at least 7.5 bars of CO2. This reservoir of volatiles is adequate to produce a substantial greenhouse effect, provided there is some small addition of SO2(volcanoes) or reduced gases (cometary impact). Thus it seems likely that conditions on early Mars were suitable for the origin of life – biogenic elements and liquid water were present at favorable conditions of pressure and temperature. Whether life began on Mars remains an open question, receiving hints of a positive answer from recent work on one of the Martian meteorites. The implications for habitable zones around other stars include the need to have rocky planets with sufficient mass to preserve atmospheres in the face of intensive early bombardment.

Evidence for a shear mechanism for the precipitation of γ-zirconium hydride in zirconium

1978 ◽  
Vol 36 (1) ◽  
pp. 658-659
Author(s):  
G.J.C. Carpenter
Keyword(s):  
Elevated Temperature ◽  
Strain Field ◽  
Zirconium Hydride ◽  
Zirconium Atom ◽  
Atom Diffusion ◽  
Solvus Temperature ◽  
Hexagonal Close Packed ◽  
Partial Dislocations ◽  
The Face

In zirconium-hydrogen alloys, rapid cooling from an elevated temperature causes precipitation of the face-centred tetragonal (fct) phase, γZrH, in the form of needles, parallel to the close-packed <1120>zr directions (1). With low hydrogen concentrations, the hydride solvus is sufficiently low that zirconium atom diffusion cannot occur. For example, with 6 μg/g hydrogen, the solvus temperature is approximately 370 K (2), at which only the hydrogen diffuses readily. Shears are therefore necessary to produce the crystallographic transformation from hexagonal close-packed (hep) zirconium to fct hydride.The simplest mechanism for the transformation is the passage of Shockley partial dislocations having Burgers vectors (b) of the type 1/3<0110> on every second (0001)Zr plane. If the partial dislocations are in the form of loops with the same b, the crosssection of a hydride precipitate will be as shown in fig.1. A consequence of this type of transformation is that a cumulative shear, S, is produced that leads to a strain field in the surrounding zirconium matrix, as illustrated in fig.2a.

A study of interface sliding at F.C.C.-B.C.C. boundaries in a Cu-Zn alloy

1978 ◽  
Vol 36 (1) ◽  
pp. 422-423
Author(s):  
F. Monchoux ◽  
A. Rocher ◽  
J.L. Martin
Keyword(s):  
Face Centered Cubic ◽  
Creep Tests ◽  
High Voltage Electron Microscopy ◽  
Diffusion Treatment ◽  
Voltage Electron ◽  
The Face ◽  
Face Centered ◽  
Interface Sliding ◽  
Zn Alloy ◽  
Made In

Interphase sliding is an important phenomenon of high temperature plasticity. In order to study the microstructural changes associated with it, as well as its influence on the strain rate dependence on stress and temperature, plane boundaries were obtained by welding together two polycrystals of Cu-Zn alloys having the face centered cubic and body centered cubic structures respectively following the procedure described in (1). These specimens were then deformed in shear along the interface on a creep machine (2) at the same temperature as that of the diffusion treatment so as to avoid any precipitation. The present paper reports observations by conventional and high voltage electron microscopy of the microstructure of both phases, in the vicinity of the phase boundary, after different creep tests corresponding to various deformation conditions.Foils were cut by spark machining out of the bulk samples, 0.2 mm thick. They were then electropolished down to 0.1 mm, after which a hole with thin edges was made in an area including the boundary

The glycomes of Caenorhabditis elegans and other model organisms

2002 ◽  
Vol 69 ◽  
pp. 117-134 ◽  
Author(s):  
Stuart M. Haslam ◽  
David Gems ◽  
Howard R. Morris ◽  
Anne Dell
Keyword(s):  
Caenorhabditis Elegans ◽  
Current Knowledge ◽  
Structural Data ◽  
Model Organisms ◽  
Entire Genome ◽  
C Elegans ◽  
The Face ◽  
Area Of Concern ◽  
Nematode Worm

There is no doubt that the immense amount of information that is being generated by the initial sequencing and secondary interrogation of various genomes will change the face of glycobiological research. However, a major area of concern is that detailed structural knowledge of the ultimate products of genes that are identified as being involved in glycoconjugate biosynthesis is still limited. This is illustrated clearly by the nematode worm Caenorhabditis elegans, which was the first multicellular organism to have its entire genome sequenced. To date, only limited structural data on the glycosylated molecules of this organism have been reported. Our laboratory is addressing this problem by performing detailed MS structural characterization of the N-linked glycans of C. elegans; high-mannose structures dominate, with only minor amounts of complex-type structures. Novel, highly fucosylated truncated structures are also present which are difucosylated on the proximal N-acetylglucosamine of the chitobiose core as well as containing unusual Fucα1–2Gal1–2Man as peripheral structures. The implications of these results in terms of the identification of ligands for genomically predicted lectins and potential glycosyltransferases are discussed in this chapter. Current knowledge on the glycomes of other model organisms such as Dictyostelium discoideum, Saccharomyces cerevisiae and Drosophila melanogaster is also discussed briefly.

Supporting the Use of Rudimentary Vocalizations

2014 ◽  
Vol 23 (3) ◽  
pp. 132-139 ◽  
Author(s):  
Lauren Zubow ◽  
Richard Hurtig
Keyword(s):  
Rett Syndrome ◽  
Visual Cues ◽  
Acoustic Analysis ◽  
Eye Gaze ◽  
Research Question ◽  
Primary Research ◽  
Multiple Modalities ◽  
Face To Face ◽  
Perceptual Judgments ◽  
The Face

Children with Rett Syndrome (RS) are reported to use multiple modalities to communicate although their intentionality is often questioned (Bartolotta, Zipp, Simpkins, & Glazewski, 2011; Hetzroni & Rubin, 2006; Sigafoos et al., 2000; Sigafoos, Woodyatt, Tuckeer, Roberts-Pennell, & Pittendreigh, 2000). This paper will present results of a study analyzing the unconventional vocalizations of a child with RS. The primary research question addresses the ability of familiar and unfamiliar listeners to interpret unconventional vocalizations as “yes” or “no” responses. This paper will also address the acoustic analysis and perceptual judgments of these vocalizations. Pre-recorded isolated vocalizations of “yes” and “no” were presented to 5 listeners (mother, father, 1 unfamiliar, and 2 familiar clinicians) and the listeners were asked to rate the vocalizations as either “yes” or “no.” The ratings were compared to the original identification made by the child's mother during the face-to-face interaction from which the samples were drawn. Findings of this study suggest, in this case, the child's vocalizations were intentional and could be interpreted by familiar and unfamiliar listeners as either “yes” or “no” without contextual or visual cues. The results suggest that communication partners should be trained to attend to eye-gaze and vocalizations to ensure the child's intended choice is accurately understood.

Verrucae planae of the face

1971 ◽  
Vol 104 (3) ◽  
pp. 330-330
Author(s):  
R. Lester
Keyword(s):  
The Face
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