scholarly journals Fractional powers of quaternionic operators and Kato’s formula using slice hyperholomorphicity

2017 ◽  
Vol 370 (2) ◽  
pp. 1045-1100 ◽  
Author(s):  
Fabrizio Colombo ◽  
Jonathan Gantner
Keyword(s):  
Fractional Powers

scholarly journals Rational Krylov methods for fractional diffusion problems on graphs

2021 ◽  
Author(s):  
Michele Benzi ◽  
Igor Simunec
Keyword(s):  
Analytic Function ◽  
Diffusion Equation ◽  
Graph Laplacian ◽  
Fractional Diffusion ◽  
Singular Matrix ◽  
Krylov Methods ◽  
Fractional Powers ◽  
Directed Networks ◽  
Rank One ◽  
Diffusion Problems

AbstractIn this paper we propose a method to compute the solution to the fractional diffusion equation on directed networks, which can be expressed in terms of the graph Laplacian L as a product $$f(L^T) \varvec{b}$$ f ( L T ) b , where f is a non-analytic function involving fractional powers and $$\varvec{b}$$ b is a given vector. The graph Laplacian is a singular matrix, causing Krylov methods for $$f(L^T) \varvec{b}$$ f ( L T ) b to converge more slowly. In order to overcome this difficulty and achieve faster convergence, we use rational Krylov methods applied to a desingularized version of the graph Laplacian, obtained with either a rank-one shift or a projection on a subspace.

scholarly journals Unitarity of theories containing fractional powers of the d’Alembertian operator

2014 ◽  
Vol 90 (10) ◽  
Author(s):  
E. C. Marino ◽  
Leandro O. Nascimento ◽  
Van Sérgio Alves ◽  
C. Morais Smith
Keyword(s):  
Fractional Powers

scholarly journals Avoiding Fractional Powers over the Natural Numbers

10.37236/6678 ◽  
2018 ◽  
Vol 25 (2) ◽  
Author(s):  
Lara Pudwell ◽  
Eric Rowland
Keyword(s):  
Fixed Point ◽  
Rational Numbers ◽  
Finite Alphabet ◽  
Its Sequence ◽  
Natural Numbers ◽  
Fractional Powers ◽  
Free Word

We study the lexicographically least infinite $a/b$-power-free word on the alphabet of non-negative integers. Frequently this word is a fixed point of a uniform morphism, or closely related to one. For example, the lexicographically least $7/4$-power-free word is a fixed point of a $50847$-uniform morphism. We identify the structure of the lexicographically least $a/b$-power-free word for three infinite families of rationals $a/b$ as well many "sporadic" rationals that do not seem to belong to general families. To accomplish this, we develop an automated procedure for proving $a/b$-power-freeness for morphisms of a certain form, both for explicit and symbolic rational numbers $a/b$. Finally, we establish a connection to words on a finite alphabet. Namely, the lexicographically least $27/23$-power-free word is in fact a word on the finite alphabet $\{0, 1, 2\}$, and its sequence of letters is $353$-automatic.

scholarly journals Fractional powers of operators

1988 ◽  
Vol 40 (2) ◽  
pp. 331-347 ◽  
Author(s):  
Celso MARTINEZ ◽  
Miguel SANZ ◽  
Luis MARCO
Keyword(s):  
Fractional Powers ◽  
Fractional Powers Of Operators
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