scholarly journals Transcendence, automata theory and gamma functions for polynomial rings

2002 ◽  
Vol 101 (1) ◽  
pp. 39-51 ◽  
Author(s):  
Zhi-Ying Wen ◽  
Jia-Yan Yao
Keyword(s):  
Automata Theory ◽  
Polynomial Rings ◽  
Gamma Functions

scholarly journals A ratio of finitely many gamma functions and its properties with applications

2021 ◽  
Vol 115 (2) ◽  
Author(s):  
Feng Qi ◽  
Wen-Hui Li ◽  
Shu-Bin Yu ◽  
Xin-Yu Du ◽  
Bai-Ni Guo
Keyword(s):  
Gamma Functions

scholarly journals Integrable and Chaotic Systems Associated with Fractal Groups

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 237
Author(s):  
Rostislav Grigorchuk ◽  
Supun Samarakoon
Keyword(s):  
Operator Algebras ◽  
Probabilistic Approach ◽  
Schur Complement ◽  
Automata Theory ◽  
Random Schrödinger Operators ◽  
Rational Maps ◽  
Holomorphic Dynamics ◽  
Von Neumann ◽  
Intermediate Growth ◽  
Quasi Crystals

Fractal groups (also called self-similar groups) is the class of groups discovered by the first author in the 1980s with the purpose of solving some famous problems in mathematics, including the question of raising to von Neumann about non-elementary amenability (in the association with studies around the Banach-Tarski Paradox) and John Milnor’s question on the existence of groups of intermediate growth between polynomial and exponential. Fractal groups arise in various fields of mathematics, including the theory of random walks, holomorphic dynamics, automata theory, operator algebras, etc. They have relations to the theory of chaos, quasi-crystals, fractals, and random Schrödinger operators. One important development is the relation of fractal groups to multi-dimensional dynamics, the theory of joint spectrum of pencil of operators, and the spectral theory of Laplace operator on graphs. This paper gives a quick access to these topics, provides calculation and analysis of multi-dimensional rational maps arising via the Schur complement in some important examples, including the first group of intermediate growth and its overgroup, contains a discussion of the dichotomy “integrable-chaotic” in the considered model, and suggests a possible probabilistic approach to studying the discussed problems.

scholarly journals PI degree parity in q-skew polynomial rings

2008 ◽  
Vol 319 (10) ◽  
pp. 4199-4221 ◽  
Author(s):  
Heidi Haynal
Keyword(s):  
Polynomial Rings ◽  
Skew Polynomial Rings ◽  
Skew Polynomial

scholarly journals New fractional inequalities of Hermite–Hadamard type involving the incomplete gamma functions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Pshtiwan Othman Mohammed ◽  
Thabet Abdeljawad ◽  
Dumitru Baleanu ◽  
Artion Kashuri ◽  
Faraidun Hamasalh ◽  
...  
Keyword(s):  
Convex Functions ◽  
Special Functions ◽  
Integral Inequalities ◽  
Fractional Operators ◽  
Gamma Functions ◽  
Incomplete Gamma Functions ◽  
Type Integral

AbstractA specific type of convex functions is discussed. By examining this, we investigate new Hermite–Hadamard type integral inequalities for the Riemann–Liouville fractional operators involving the generalized incomplete gamma functions. Finally, we expose some examples of special functions to support the usefulness and effectiveness of our results.

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