scholarly journals ON THE KAUFFMAN–VOGEL AND THE MURAKAMI–OHTSUKI–YAMADA GRAPH POLYNOMIALS

2012 ◽  
Vol 21 (10) ◽  
pp. 1250098 ◽  
Author(s):  
HAO WU
Keyword(s):  
Simple Circuit ◽  
Graph Polynomials ◽  
Graph Polynomial ◽  
Link Homology ◽  
Kauffman Polynomial ◽  
Colored Link

This paper consists of three parts. First, we generalize the Jaeger Formula to express the Kauffman–Vogel graph polynomial as a state sum of the Murakami–Ohtsuki–Yamada graph polynomial. Then, we demonstrate that reversing the orientation and the color of a MOY graph along a simple circuit does not change the 𝔰𝔩(N) Murakami–Ohtsuki–Yamada polynomial or the 𝔰𝔩(N) homology of this MOY graph. In fact, reversing the orientation and the color of a component of a colored link only changes the 𝔰𝔩(N) homology by an overall grading shift. Finally, as an application of the first two parts, we prove that the 𝔰𝔬(6) Kauffman polynomial is equal to the 2-colored 𝔰𝔩(4) Reshetikhin–Turaev link polynomial, which implies that the 2-colored 𝔰𝔩(4) link homology categorifies the 𝔰𝔬(6) Kauffman polynomial.

scholarly journals On the Degeneracy of the Orbit Polynomial and Related Graph Polynomials

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1643
Author(s):  
Modjtaba Ghorbani ◽  
Matthias Dehmer ◽  
Frank Emmert-Streib
Keyword(s):  
Automorphism Group ◽  
Structural Properties ◽  
Graph Polynomials ◽  
Graph Polynomial ◽  
Related Graph ◽  
Graph Operation ◽  
Counting Polynomial

The orbit polynomial is a new graph counting polynomial which is defined as OG(x)=∑i=1rx|Oi|, where O1, …, Or are all vertex orbits of the graph G. In this article, we investigate the structural properties of the automorphism group of a graph by using several novel counting polynomials. Besides, we explore the orbit polynomial of a graph operation. Indeed, we compare the degeneracy of the orbit polynomial with a new graph polynomial based on both eigenvalues of a graph and the size of orbits.

Metal Bridge Defects Localization by a Tiny Leakage between One of Bridged Signals and VDD (GND)

2014 ◽  
Author(s):  
Chunlei Wu ◽  
Suying Yao
Keyword(s):  
Circuit Model ◽  
Functional Modules ◽  
Semiconductor Technology ◽  
Simple Circuit ◽  
Lock In

Abstract As semiconductor technology continues to advance to smaller dimensions and more complex circuit designs, it is becoming more challenging to locate the resistive short directly between two metal lines (signals) due to a metal bridge defect. Especially these two metal lines are very long and relevant to many functional modules. After studying the failed circuit model, we found there should be a tiny leakage between one of the bridged signals and one of common power signals (such as VDD and GND) on a failed IC compared with the reference one, if there is a metal bridge defect between these two bridged signals. The tiny leakage between one of the bridged signals and one of power signals is an indirect leakage that is a mapping of the direct resistive short between these two bridged signals. The metal bridge defect could be pinpointed with the tiny leakage between one of the bridged signals and one of power signals by Lock-in IR-OBIRCH. It is an easier and faster way to locate the metal bridge defects. In this paper, the basic and simple circuit model with a metal bridge defect will be presented and two cases will be studied to demonstrate how to localize a metal bridge defect by the tiny leakage between one of the bridged signals and one of power signals.

Simple circuit for pacing hearts of experimental animals

1992 ◽  
Vol 262 (6) ◽  
pp. H1939-H1940 ◽  
Author(s):  
G. L. Freeman ◽  
J. T. Colston
Keyword(s):  
Integrated Circuit ◽  
Simple Circuit ◽  
Cardiovascular Research ◽  
Experimental Animals ◽  
Wide Range ◽  
Astable Multivibrator

In this paper we describe a simple pacing circuit which can be used to drive the heart over a wide range of rates. The circuit is an astable multivibrator, based on an LM555 integrated circuit. It is powered by a 9-V battery and is small enough for use in rabbits. The circuit is easily constructed and inexpensive, making it attractive for numerous applications in cardiovascular research.

A Simple Circuit for a Capacitor Dilatometer

1970 ◽  
Vol 41 (7) ◽  
pp. 1103-1103
Author(s):  
V. A. Danilychev
Keyword(s):  
Simple Circuit

scholarly journals FROM RIBBON CATEGORIES TO GENERALIZED YANG–BAXTER OPERATORS AND LINK INVARIANTS (AFTER KITAEV AND WANG)

2013 ◽  
Vol 24 (01) ◽  
pp. 1250126 ◽  
Author(s):  
SEUNG-MOON HONG
Keyword(s):  
The Other ◽  
Polynomial Invariant ◽  
Link Invariants ◽  
Fusion Categories ◽  
New Family ◽  
Kauffman Polynomial ◽  
Twist Structure

We consider two approaches to isotopy invariants of oriented links: one from ribbon categories and the other from generalized Yang–Baxter (gYB) operators with appropriate enhancements. The gYB-operators we consider are obtained from so-called gYBE objects following a procedure of Kitaev and Wang. We show that the enhancement of these gYB-operators is canonically related to the twist structure in ribbon categories from which the operators are produced. If a gYB-operator is obtained from a ribbon category, it is reasonable to expect that two approaches would result in the same invariant. We prove that indeed the two link invariants are the same after normalizations. As examples, we study a new family of gYB-operators which is obtained from the ribbon fusion categories SO (N)2, where N is an odd integer. These operators are given by 8 × 8 matrices with the parameter N and the link invariants are specializations of the two-variable Kauffman polynomial invariant F.

Simple circuit for computing (x2 + y2)[fraction one-half]

1974 ◽  
Vol 10 (22) ◽  
pp. 455
Author(s):  
J.S.C. Tan
Keyword(s):  
Simple Circuit
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