A Novel Cluster-Based Routing Technique for Reliable Path Selection in VANET V2V Communication in 5G Using Upper Triangular Matrix Lie Algebra

2021 ◽  
pp. 1-15
Author(s):  
Supriya Sridharan ◽  
Sathyanarayan Goplakrishnan ◽  
Swaminathan Venkatraman
Keyword(s):  
Lie Algebra ◽  
Triangular Matrix ◽  
Path Selection ◽  
V2v Communication ◽  
Upper Triangular Matrix ◽  
Cluster Based Routing ◽  
Reliable Path

scholarly journals Decomposition of Automorphisms of Certain Solvable Subalgebra of Symplectic Lie Algebra over Commutative Rings

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Xing Tao Wang ◽  
Lei Zhang
Keyword(s):  
Automorphism Group ◽  
Commutative Ring ◽  
Lie Algebra ◽  
Triangular Matrix ◽  
Commutative Rings ◽  
Explicit Description ◽  
Upper Triangular Matrix

LetCl+1(R)be the2(l+1)×2(l+1)matrix symplectic Lie algebra over a commutative ringRwith 2 invertible. Thentl+1CR  =  {m-1m-20-m-1T ∣ m̅1is anl+1upper triangular matrix,m̅2T=m̅2,  over  R}is the solvable subalgebra ofCl+1(R). In this paper, we give an explicit description of the automorphism group oftl+1(C)(R).

scholarly journals Accurate and Efficient Derivative-Free Three-Phase Power Flow Method for Unbalanced Distribution Networks

Computation ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 61
Author(s):  
Oscar Danilo Montoya ◽  
Juan S. Giraldo ◽  
Luis Fernando Grisales-Noreña ◽  
Harold R. Chamorro ◽  
Lazaro Alvarado-Barrios
Keyword(s):  
Power Flow ◽  
Triangular Matrix ◽  
Distribution Networks ◽  
Flow Method ◽  
Processing Times ◽  
Three Phase ◽  
Derivative Free ◽  
Upper Triangular Matrix ◽  
Power Flow Problem ◽  
Power Flow Method

The power flow problem in three-phase unbalanced distribution networks is addressed in this research using a derivative-free numerical method based on the upper-triangular matrix. The upper-triangular matrix is obtained from the topological connection among nodes of the network (i.e., through a graph-based method). The main advantage of the proposed three-phase power flow method is the possibility of working with single-, two-, and three-phase loads, including Δ- and Y-connections. The Banach fixed-point theorem for loads with Y-connection helps ensure the convergence of the upper-triangular power flow method based an impedance-like equivalent matrix. Numerical results in three-phase systems with 8, 25, and 37 nodes demonstrate the effectiveness and computational efficiency of the proposed three-phase power flow formulation compared to the classical three-phase backward/forward method and the implementation of the power flow problem in the DigSILENT software. Comparisons with the backward/forward method demonstrate that the proposed approach is 47.01%, 47.98%, and 36.96% faster in terms of processing times by employing the same number of iterations as when evaluated in the 8-, 25-, and 37-bus systems, respectively. An application of the Chu-Beasley genetic algorithm using a leader–follower optimization approach is applied to the phase-balancing problem utilizing the proposed power flow in the follower stage. Numerical results present optimal solutions with processing times lower than 5 s, which confirms its applicability in large-scale optimization problems employing embedding master–slave optimization structures.

scholarly journals Functional identities on upper triangular matrix rings

2020 ◽  
Vol 18 (1) ◽  
pp. 182-193
Author(s):  
He Yuan ◽  
Liangyun Chen
Keyword(s):  
Triangular Matrix ◽  
Matrix Rings ◽  
Unital Ring ◽  
Functional Identities ◽  
Upper Triangular Matrix ◽  
Free Subset

Abstract Let R be a subset of a unital ring Q such that 0 ∈ R. Let us fix an element t ∈ Q. If R is a (t; d)-free subset of Q, then Tn(R) is a (t′; d)-free subset of Tn(Q), where t′ ∈ Tn(Q), $\begin{array}{} t_{ll}' \end{array} $ = t, l = 1, 2, …, n, for any n ∈ N.

scholarly journals Adjacency preserving maps on upper triangular matrix algebras

2003 ◽  
Vol 367 ◽  
pp. 105-130 ◽  
Author(s):  
W.L Chooi ◽  
M.H Lim ◽  
Peter Šemrl
Keyword(s):  
Triangular Matrix ◽  
Matrix Algebras ◽  
Upper Triangular Matrix

Commuting traces of upper triangular matrix rings

2017 ◽  
Vol 91 (3) ◽  
pp. 563-578 ◽  
Author(s):  
Daniel Eremita
Keyword(s):  
Triangular Matrix ◽  
Matrix Rings ◽  
Upper Triangular Matrix

Piecewise Hereditary Triangular Matrix Algebras

2021 ◽  
Vol 28 (01) ◽  
pp. 143-154
Author(s):  
Yiyu Li ◽  
Ming Lu
Keyword(s):  
Positive Integer ◽  
Triangular Matrix ◽  
Derived Categories ◽  
Matrix Algebras ◽  
Tensor Algebras ◽  
Finite Dimensional ◽  
Abelian Categories ◽  
Upper Triangular Matrix ◽  
Orbit Categories ◽  
Finite Dimensional Algebras

For any positive integer [Formula: see text], we clearly describe all finite-dimensional algebras [Formula: see text] such that the upper triangular matrix algebras [Formula: see text] are piecewise hereditary. Consequently, we describe all finite-dimensional algebras [Formula: see text] such that their derived categories of [Formula: see text]-complexes are triangulated equivalent to derived categories of hereditary abelian categories, and we describe the tensor algebras [Formula: see text] for which their singularity categories are triangulated orbit categories of the derived categories of hereditary abelian categories.

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