scholarly journals A New Approach for Vertex Guarding of Planar Graphs

2002 ◽  
Vol 10 (3) ◽  
pp. 189 ◽  
Author(s):  
Branko Kau�i� ◽  
Borut �alik
Keyword(s):  
Planar Graphs ◽  
New Approach

scholarly journals FROM PLANAR GRAPHS TO EMBEDDED GRAPHS - A NEW APPROACH TO KAUFFMAN AND VOGEL'S POLYNOMIAL

2000 ◽  
Vol 09 (08) ◽  
pp. 975-986 ◽  
Author(s):  
RUI PEDRO CARPENTIER
Keyword(s):  
Planar Graph ◽  
Planar Graphs ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Direct Proof ◽  
Connected Components ◽  
Embedded Graphs ◽  
New Approach ◽  
Graphical Calculus ◽  
Embedded Graph

In [4] Kauffman and Vogel constructed a rigid vertex regular isotopy invariant for unoriented four-valent graphs embedded in three dimensional space. It assigns to each embedded graph G a polynomial, denoted [G], in three variables, A, B and a, satisfying the skein relations: [Formula: see text] and is defined in terms of a state-sum and the Dubrovnik polynomial for links. Using the graphical calculus of [4] it is shown that the polynomial of a planar graph can be calculated recursively from that of planar graphs with less vertices, which also allows the polynomial of an embedded graph to be calculated without resorting to links. The same approach is used to give a direct proof of uniqueness of the (normalized) polynomial restricted to planar graphs. In the case B=A-1 and a=A, it is proved that for a planar graph G we have [G]=2c-1(-A-A-1)v, where c is the number of connected components of G and v is the number of vertices of G. As a corollary, a necessary, but not sufficient, condition is obtained for an embedded graph to be ambient isotopic to a planar graph. In an appendix it is shown that, given a polynomial for planar graphs satisfying the graphical calculus, and imposing the first skein relation above, the polynomial extends to a rigid vertex regular isotopy invariant for embedded graphs, satisfying the remaining skein relations. Thus, when existence of the planar polynomial is guaranteed, this provides a direct way, not depending on results for the Dubrovnik polynomial, to show consistency of the polynomial for embedded graphs.

RECURSIVE SAMPLING OF PLANAR GRAPHS AND FRACTAL PROPERTIES OF A TWO-DIMENSIONAL QUANTUM GRAVITY

1990 ◽  
Vol 01 (01) ◽  
pp. 165-179 ◽  
Author(s):  
MICHAEL E. AGISHTEIN ◽  
ALEXANDER A. MIGDAL
Keyword(s):  
Monte Carlo ◽  
Random Graphs ◽  
Planar Graphs ◽  
Two Dimensional ◽  
Cubic Graphs ◽  
New Approach ◽  
Standard Methods ◽  
Fractal Properties ◽  
Dimensional Gravity ◽  
Dynamical Triangulation

We describe a new approach to the Monte-Carlo simulations of two-dimensional gravity. Standard dynamical triangulation technique was combined with results of direct enumeration of the cubic graphs. As a result we were able to build large (128K vertices) statistically independent random graphs directly. The quantitative correspondence between our results and those obtained by standard methods has been observed. The algorithm proved to be so efficient that we were able to conduct all the simulations, which usually require the most powerful computers, on an Iris workstation. An opportunity to generate large random graphs allowed us to observe that the internal geometry of random surfaces is more complicated than simple fractals. External geometry also proved to be rather peculiar.

scholarly journals A new approach to solving three combinatorial enumeration problems on planar graphs

1995 ◽  
Vol 60 (1-3) ◽  
pp. 119-129 ◽  
Author(s):  
Charles J. Colbourn ◽  
J.Scott Provan ◽  
Dirk Vertigan
Keyword(s):  
Planar Graphs ◽  
Combinatorial Enumeration ◽  
New Approach ◽  
Enumeration Problems

The O–C diagrams of minor planets − a new approach to modelling the rotation

1999 ◽  
Vol 173 ◽  
pp. 185-188
Author(s):  
Gy. Szabó ◽  
K. Sárneczky ◽  
L.L. Kiss
Keyword(s):  
Error Analysis ◽  
Time Dependence ◽  
Theoretical Work ◽  
Minor Planet ◽  
Minor Planets ◽  
New Approach ◽  
Preliminary Results ◽  
Ccd Observations

AbstractA widely used tool in studying quasi-monoperiodic processes is the O–C diagram. This paper deals with the application of this diagram in minor planet studies. The main difference between our approach and the classical O–C diagram is that we transform the epoch (=time) dependence into the geocentric longitude domain. We outline a rotation modelling using this modified O–C and illustrate the abilities with detailed error analysis. The primary assumption, that the monotonity and the shape of this diagram is (almost) independent of the geometry of the asteroids is discussed and tested. The monotonity enables an unambiguous distinction between the prograde and retrograde rotation, thus the four-fold (or in some cases the two-fold) ambiguities can be avoided. This turned out to be the main advantage of the O–C examination. As an extension to the theoretical work, we present some preliminary results on 1727 Mette based on new CCD observations.

A New Approach to the Demonstration of Oxidase-Localization Using Tannic Acid Or Catechin

1973 ◽  
Vol 31 ◽  
pp. 698-699
Author(s):  
V. Mizuhira ◽  
Y. Futaesaku
Keyword(s):  
Cross Section ◽  
Tannic Acid ◽  
Elastic Fiber ◽  
The Other ◽  
New Approach ◽  
Tissue Block ◽  
Active Reaction ◽  
The Cross

Previously we reported that tannic acid is a very effective fixative for proteins including polypeptides. Especially, in the cross section of microtubules, thirteen submits in A-tubule and eleven in B-tubule could be observed very clearly. An elastic fiber could be demonstrated very clearly, as an electron opaque, homogeneous fiber. However, tannic acid did not penetrate into the deep portion of the tissue-block. So we tried Catechin. This shows almost the same chemical natures as that of proteins, as tannic acid. Moreover, we thought that catechin should have two active-reaction sites, one is phenol,and the other is catechole. Catechole site should react with osmium, to make Os- black. Phenol-site should react with peroxidase existing perhydroxide.

Processing Immunoperoxidase Labeled Cell Monolayers and Cryostat Sesctions For Electron Microscopy

1985 ◽  
Vol 43 ◽  
pp. 714-715
Author(s):  
K. Chien ◽  
R. Van de Velde ◽  
I.P. Shintaku ◽  
A.F. Sassoon
Keyword(s):  
Cell Monolayer ◽  
Cell Types ◽  
Surface Antigens ◽  
Immunoperoxidase Method ◽  
Reaction Step ◽  
Hot Plate ◽  
Air Drying ◽  
New Approach ◽  
Cell Monolayers ◽  
Glass Slides

Immunoelectron microscopy of neoplastic lymphoma cells is valuable for precise localization of surface antigens and identification of cell types. We have developed a new approach in which the immunohistochemical staining can be evaluated prior to embedding for EM and desired area subsequently selected for ultrathin sectioning.A freshly prepared lymphoma cell suspension is spun onto polylysine hydrobromide- coated glass slides by cytocentrifugation and immediately fixed without air drying in polylysine paraformaldehyde (PLP) fixative. After rinsing in PBS, slides are stained by a 3-step immunoperoxidase method. Cell monolayer is then fixed in buffered 3% glutaraldehyde prior to DAB reaction. After the DAB reaction step, wet monolayers can be examined under LM for presence of brown reaction product and selected monolayers then processed by routine methods for EM and embedded with the Chien Re-embedding Mold. After the polymerization, the epoxy blocks are easily separated from the glass slides by heatingon a 100°C hot plate for 20 seconds.

TEM study of a biofilm on copper corrosion

1996 ◽  
Vol 54 ◽  
pp. 220-221
Author(s):  
W. A. Chiou ◽  
N. Kohyama ◽  
B. Little ◽  
P. Wagner ◽  
M. Meshii
Keyword(s):  
Marine Bacterium ◽  
Culture Medium ◽  
Copper Alloys ◽  
Pure Copper ◽  
Localized Corrosion ◽  
Natural Seawater ◽  
Copper Corrosion ◽  
New Approach ◽  
The Past ◽  
Copper Tolerant

The corrosion of copper and copper alloys in a marine environment is of great concern because of their widespread use in heat exchangers and steam condensers in which natural seawater is the coolant. It has become increasingly evident that microorganisms play an important role in the corrosion of a number of metals and alloys under a variety of environments. For the past 15 years the use of SEM has proven to be useful in studying biofilms and spatial relationships between bacteria and localized corrosion of metals. Little information, however, has been obtained using TEM capitalizing on its higher spacial resolution and the transmission observation of interfaces. The research presented herein is the first step of this new approach in studying the corrosion with biological influence in pure copper.Commercially produced copper (Cu, 99%) foils of approximately 120 μm thick exposed to a copper-tolerant marine bacterium, Oceanospirillum, and an abiotic culture medium were subsampled (1 cm × 1 cm) for this study along with unexposed control samples.

High resolution at low voltage: A new approach

1989 ◽  
Vol 47 ◽  
pp. 76-77
Author(s):  
Arthur V. Jones
Keyword(s):  
Low Voltage ◽  
Emission Sources ◽  
New Approach ◽  
Design Concepts ◽  
Probe Diameter ◽  
Low Voltage Operation ◽  
Sufficient Intensity ◽  
Electron Microscopes ◽  
Scanning Electron Microscopes ◽  
Immersion Type

With the introduction of field-emission sources and “immersion-type” objective lenses, the resolution obtainable with modern scanning electron microscopes is approaching that obtainable in STEM and TEM-but only with specific types of specimens. Bulk specimens still suffer from the restrictions imposed by internal scattering and the need to be conducting. Advances in coating techniques have largely overcome these problems but for a sizeable body of specimens, the restrictions imposed by coating are unacceptable.For such specimens, low voltage operation, with its low beam penetration and freedom from charging artifacts, is the method of choice.Unfortunately the technical dificulties in producing an electron beam sufficiently small and of sufficient intensity are considerably greater at low beam energies — so much so that a radical reevaluation of convential design concepts is needed.The probe diameter is usually given by

Sign in / Sign up

Export Citation Format

Share Document