scholarly journals 2K+ Graph Construction Framework: Targeting Joint Degree Matrix and Beyond

2019 ◽  
Vol 27 (2) ◽  
pp. 591-606
Author(s):  
Balint Tillman ◽  
Athina Markopoulou ◽  
Minas Gjoka ◽  
Carter T. Buttsc
Keyword(s):  
Degree Matrix

scholarly journals Bounds of Laplacian Energy of a Hypercube Graph

2018 ◽  
Vol 7 (4.10) ◽  
pp. 582
Author(s):  
K. Ameenal Bibi ◽  
B. Vijayalakshmi ◽  
R. Jothilakshmi
Keyword(s):  
Lower Bounds ◽  
Adjacency Matrix ◽  
Laplacian Matrix ◽  
Positive Semidefinite ◽  
Laplacian Energy ◽  
Eigen Values ◽  
Degree Matrix

Let  Qn denote  the n – dimensional  hypercube  with  order   2n and  size n2n-1. The  Laplacian  L  is defined  by  L = D  where D is  the  degree  matrix and  A is  the  adjacency  matrix  with  zero  diagonal  entries.  The  Laplacian  is a  symmetric  positive  semidefinite.  Let  µ1 ≥ µ2 ≥ ....µn-1 ≥ µn = 0 be the eigen values of  the Laplacian matrix.  The  Laplacian  energy is defined as  LE(G) = . In  this  paper, we  defined  Laplacian  energy  of  a  Hypercube  graph  and  also attained  the  lower  bounds.   

Application and Research of Systematic Cluster in IED Switch Online Condition Monitoring

2014 ◽  
Vol 672-674 ◽  
pp. 2041-2047
Author(s):  
Kai Ma ◽  
Chun Chao Hu ◽  
Shan Qiang Feng ◽  
Shu Feng Tan ◽  
Xu Jiang ◽  
...  
Keyword(s):  
Cluster Analysis ◽  
Control System ◽  
Condition Monitoring ◽  
Cluster Algorithm ◽  
Data Matrix ◽  
Online Information ◽  
Analysis Methods ◽  
Systematic Cluster ◽  
Smart Substation ◽  
Degree Matrix

This paper investigates the application of systematic cluster, one of the cluster analysis methods, in the IED switch online condition monitoring. So far, problems still exsit in the IED switch online condition monitoring based on the control system of smart substation. In order to figure out a relatively stable online model and make classification from the online information of IED switch, this paper firstly fliters and preprocesses the online condition information of IED switch, and uses data matrix to describe the online condition of IED switch. Based on this, the paper inroduces a special dissimilarity degree formula to transfer the data matrix into dissimilarity degree matrix, and conducts analysis with clustering pedigree chart out of systematic cluster algorithm. Finally, the paper verifies the feasibility of systematic cluster in the IED switch online condition monitoring.

Lattice Ordered Evaluation Method of Equipment Response Event to Voltage Sag

2013 ◽  
Vol 336-338 ◽  
pp. 399-403
Author(s):  
Ying Wang ◽  
Da Yang ◽  
Yang Liu ◽  
Ce Chen
Keyword(s):  
Personal Computer ◽  
Evaluation Method ◽  
Interval Number ◽  
Voltage Sag ◽  
Interval Numbers ◽  
Lattice Order ◽  
Possibility Degree ◽  
Upper And Lower Probabilities ◽  
Relationship Of ◽  
Degree Matrix

Considering the multi-valued mapping relationship of equipment response event to voltage sag, a lattice ordered evaluation method is proposed in this study. Each possible resulting state of equipment response event is described by an interval number. The interval numbers is with the characteristics of lattice order presented by the upper and lower probabilities. The possibility degree matrix is introduced to compare resulting states without satisfying the axioms of connectedness. Personal computer is simulated and compared testing results. The results have shown the validity and feasibility.

Canonical Wiener-Hopf and spectral factorization of large-degree matrix polynomials

PAMM ◽  
2014 ◽  
Vol 14 (1) ◽  
pp. 817-818
Author(s):  
Albrecht Böttcher ◽  
Martin Halwass
Keyword(s):  
Large Degree ◽  
Spectral Factorization ◽  
Matrix Polynomials ◽  
Degree Matrix

DEGREE MATRICES AND ESTIMATES FOR EXPONENTIAL SUMS OF POLYNOMIALS OVER FINITE FIELDS

2013 ◽  
Vol 12 (07) ◽  
pp. 1350030 ◽  
Author(s):  
WEI CAO
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Exponential Sums ◽  
Elementary Approach ◽  
Multivariate Polynomial ◽  
Elementary Divisors ◽  
Polynomials Over Finite Fields ◽  
Degree Matrix

Let f be a multivariate polynomial over a finite field and its degree matrix be composed of the degree vectors appearing in f. In this paper, we provide an elementary approach to estimating the exponential sums of the polynomials with positive square degree matrices in terms of the elementary divisors of the degree matrices.

Smith Normal Form of Augmented Degree Matrix and Rational Points on Toric Hypersurface

2013 ◽  
Vol 20 (02) ◽  
pp. 327-332
Author(s):  
Jianming Chen ◽  
Wei Cao
Keyword(s):  
Normal Form ◽  
Finite Field ◽  
Rational Points ◽  
Smith Normal Form ◽  
Degree Matrix

We use the Smith normal form of the augmented degree matrix to estimate the number of rational points on a toric hypersurface over a finite field. This is the continuation of a previous work by Cao in 2009.

A SPECIAL DEGREE REDUCTION OF POLYNOMIALS OVER FINITE FIELDS WITH APPLICATIONS

2011 ◽  
Vol 07 (04) ◽  
pp. 1093-1102 ◽  
Author(s):  
WEI CAO
Keyword(s):  
Finite Field ◽  
Explicit Formula ◽  
Finite Fields ◽  
Rational Points ◽  
Degree Reduction ◽  
Affine Hypersurface ◽  
Special Degree ◽  
Low Degree ◽  
Polynomials Over Finite Fields ◽  
Degree Matrix

Let f be a polynomial in n variables over the finite field 𝔽q and Nq(f) denote the number of 𝔽q-rational points on the affine hypersurface f = 0 in 𝔸n(𝔽q). A φ-reduction of f is defined to be a transformation σ : 𝔽q[x1, …, xn] → 𝔽q[x1, …, xn] such that Nq(f) = Nq(σ(f)) and deg f ≥ deg σ(f). In this paper, we investigate φ-reduction by using the degree matrix which is formed by the exponents of the variables of f. With φ-reduction, we may improve various estimates on Nq(f) and utilize the known results for polynomials with low degree. Furthermore, it can be used to find the explicit formula for Nq(f).

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