ALGEBRAIC CONNECTIVITY OF LOLLIPOP GRAPHS: A NEW APPROACH

2014 ◽  
Vol 06 (02) ◽  
pp. 1450028
Author(s):  
D. KALITA
Keyword(s):  
Linear Algebra ◽  
Unicyclic Graph ◽  
Algebraic Connectivity ◽  
New Approach ◽  
Pendent Vertex

The unicyclic graph Cn,gobtained by appending a cycle Cgof length g to a pendent vertex of a path on n - g vertices is the lollipop graph on n vertices. In [Algebraic connectivity of lollipop graphs, Linear Algebra Appl.434 (2011) 2204–2210], Guo et al. proved that a( Cn,g-1) < a( Cn,g) for g ≥ 4, where a( Cn,g) is the algebraic connectivity of Cn,g. In this paper, we present a new approach which is quite different from that of Guo et al. in proving a( Cn,g-1) < a( Cn,g) for g ≥ 4.

scholarly journals The Orderings of Bicyclic Graphs and Connected Graphs by Algebraic Connectivity

10.37236/434 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Jianxi Li ◽  
Ji-Ming Guo ◽  
Wai Chee Shiu
Keyword(s):  
Linear Algebra ◽  
Laplacian Matrix ◽  
Algebraic Connectivity ◽  
Connected Graphs ◽  
Unicyclic Graphs ◽  
Smallest Eigenvalue ◽  
Bicyclic Graphs

The algebraic connectivity of a graph $G$ is the second smallest eigenvalue of its Laplacian matrix. Let $\mathscr{B}_n$ be the set of all bicyclic graphs of order $n$. In this paper, we determine the last four bicyclic graphs (according to their smallest algebraic connectivities) among all graphs in $\mathscr{B}_n$ when $n\geq 13$. This result, together with our previous results on trees and unicyclic graphs, can be used to further determine the last sixteen graphs among all connected graphs of order $n$. This extends the results of Shao et al. [The ordering of trees and connected graphs by their algebraic connectivity, Linear Algebra Appl. 428 (2008) 1421-1438].

USING WAVELETS TO EXTEND QUANTUM DYNAMICS CALCULATIONS TO TEN OR MORE DEGREES OF FREEDOM

2003 ◽  
Vol 02 (01) ◽  
pp. 65-72 ◽  
Author(s):  
BILL POIRIER
Keyword(s):  
Phase Space ◽  
Linear Algebra ◽  
Quantum Dynamics ◽  
Degrees Of Freedom ◽  
Orthonormal Basis ◽  
Direct Calculation ◽  
Elliptic Partial Differential Equations ◽  
New Approach ◽  
Truncation Scheme ◽  
Simple Phase

A customizable, orthonormal basis for solving the multidimensional Schrödinger equation is constructed using modified Wilson–Daubechies wavelets, and a simple phase space truncation scheme. Unprecedented numerical efficiency is achieved, enabling a ten-dimensional direct calculation of nearly 600 eigenvalues to be performed. Higher dimensionalities are possible using more sophisticated linear algebra techniques. The new approach is ideally suited to rovibrational spectroscopy applications, but can be used in any context where elliptic partial differential equations are involved.

Trajectory tracking of mobile robots in dynamic environments—a linear algebra approach

Robotica ◽  
2009 ◽  
Vol 27 (7) ◽  
pp. 981-997 ◽  
Author(s):  
Andrés Rosales ◽  
Gustavo Scaglia ◽  
Vicente Mut ◽  
Fernando di Sciascio
Keyword(s):  
Mobile Robots ◽  
Dynamic Model ◽  
Linear Algebra ◽  
Controller Design ◽  
Tracking Error ◽  
Dynamic Environments ◽  
Field Method ◽  
New Approach ◽  
Algebra Approach ◽  
New Strategy

SUMMARYA new approach for navigation of mobile robots in dynamic environments by using Linear Algebra Theory, Numerical Methods, and a modification of the Force Field Method is presented in this paper. The controller design is based on the dynamic model of a unicycle-like nonholonomic mobile robot. Previous studies very often ignore the dynamics of mobile robots and suffer from algorithmic singularities. Simulation and experimentation results confirm the feasibility and the effectiveness of the proposed controller and the advantages of the dynamic model use. By using this new strategy, the robot is able to adapt its behavior at the available knowing level and it can navigate in a safe way, minimizing the tracking error.

A new approach to the concept of linearity. Some elements for a multiplicative linear algebra

2018 ◽  
Vol 97 (1-2) ◽  
pp. 109-119 ◽  
Author(s):  
Fernando Córdova-Lepe ◽  
Rodrigo Del Valle ◽  
Karina Vilches
Keyword(s):  
Linear Algebra ◽  
New Approach

scholarly journals On Euler-Lagrange's Equations: A New Approach

2020 ◽  
Vol 21 (2) ◽  
pp. 359
Author(s):  
G. E. O. Giacaglia ◽  
W. Q. Lamas
Keyword(s):  
Differential Geometry ◽  
Dynamical Systems ◽  
Linear Algebra ◽  
Mechanical Systems ◽  
Rigid Bodies ◽  
New Approach ◽  
New Formalism ◽  
Separate Part ◽  
Lagrange’S Equations ◽  
Lagrange's Equations

A new formalism is proposed to study the dynamics of mechanical systems composed of N connected rigid bodies, by introducing the concept of $6N$-dimensional composed vectors. The approach is based on previous works by the authors where a complete formalism was developed by means of differential geometry, linear algebra, and dynamical systems usual concepts. This new formalism is a method for the description of mechanical systems as a whole and not as each separate part. Euler-Lagrange's Equations are easily obtained by means of this formalism.

On the Calculation of the Moore–Penrose and Drazin Inverses: Application to Fractional Calculus

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2501
Author(s):  
Khosro Sayevand ◽  
Ahmad Pourdarvish ◽  
José A. Tenreiro Machado ◽  
Raziye Erfanifar
Keyword(s):  
Fractional Calculus ◽  
Iterative Method ◽  
Linear Algebra ◽  
Computational Cost ◽  
Numerical Linear Algebra ◽  
Diffusion Equations ◽  
Smooth Solutions ◽  
Third Order ◽  
New Approach

This paper presents a third order iterative method for obtaining the Moore–Penrose and Drazin inverses with a computational cost of O(n3), where n∈N. The performance of the new approach is compared with other methods discussed in the literature. The results show that the algorithm is remarkably efficient and accurate. Furthermore, sufficient criteria in the fractional sense are presented, both for smooth and non-smooth solutions. The fractional elliptic Poisson and fractional sub-diffusion equations in the Caputo sense are considered as prototype examples. The results can be extended to other scientific areas involving numerical linear algebra.

scholarly journals Observable Operator Models

2016 ◽  
Vol 36 (1) ◽  
Author(s):  
Ilona Spanczér
Keyword(s):  
Stochastic Processes ◽  
Hidden Markov Models ◽  
Linear Algebra ◽  
Markov Models ◽  
Learning Algorithm ◽  
Hidden Markov ◽  
New Approach ◽  
Efficient Learning ◽  
Better Than

This paper describes a new approach to model discrete stochastic processes, called observable operator models (OOMs). The OOMs were introduced by Jaeger as a generalization of hidden Markov models (HMMs). The theory of OOMs makes use of both probabilistic and linear algebraic tools, which has an important advantage: using the tools of linear algebra a very simple and efficient learning algorithm can be developed for OOMs. This seems to be better than the known algorithms for HMMs. This learningalgorithm is presented in detail in the second part of the article.

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