Automorphism Groups of Circulant Digraphs With Applications to Semigroup Theory

Abstract This paper consider the existence, uniqueness and exponential stability in the pth moment of mild solution for impulsive neutral stochastic integro-differential equations driven simultaneously by fractional Brownian motion and by standard Brownian motion. Based on semigroup theory, the sufficient conditions to ensure the existence and uniqueness of mild solutions are obtained in terms of fractional power of operators and Banach fixed point theorem. Moreover, the pth moment exponential stability conditions of the equation are obtained by means of an impulsive integral inequality. Finally, an example is presented to illustrate the effectiveness of the obtained results.

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Stabilization of the wave equation with a nonlinear delay term in the boundary conditions

Journal of Applied Analysis ◽

10.1515/jaa-2021-2051 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Wassila Ghecham ◽

Salah-Eddine Rebiai ◽

Fatima Zohra Sidiali

Keyword(s):

Wave Equation ◽

Original Problem ◽

Existence Of Solutions ◽

Semigroup Theory ◽

Decay Rates ◽

Uniform Decay ◽

Delay Term ◽

Nonlinear Semigroup Theory ◽

Nonlinear Boundary Feedback ◽

Nonlinear Delay

Abstract A wave equation in a bounded and smooth domain of ℝ n {\mathbb{R}^{n}} with a delay term in the nonlinear boundary feedback is considered. Under suitable assumptions, global existence and uniform decay rates for the solutions are established. The proof of existence of solutions relies on a construction of suitable approximating problems for which the existence of the unique solution will be established using nonlinear semigroup theory and then passage to the limit gives the existence of solutions to the original problem. The uniform decay rates for the solutions are obtained by proving certain integral inequalities for the energy function and by establishing a comparison theorem which relates the asymptotic behavior of the energy and of the solutions to an appropriate dissipative ordinary differential equation.

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Automorphism groups of Hadamard matrices

Journal of Combinatorial Theory ◽

10.1016/s0021-9800(69)80088-8 ◽

1969 ◽

Vol 6 (3) ◽

pp. 279-281 ◽

Cited By ~ 24

Author(s):

William M. Kantor

Keyword(s):

Automorphism Groups ◽

Hadamard Matrices

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Serre’s Property (FA) for automorphism groups of free products

Journal of Group Theory ◽

10.1515/jgth-2019-0140 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Naomi Andrew

Keyword(s):

Automorphism Group ◽

Free Product ◽

Finite Groups ◽

Automorphism Groups ◽

Sufficient Conditions ◽

Free Products ◽

Cyclic Groups ◽

Link Type ◽

Open Case

AbstractWe provide some necessary and some sufficient conditions for the automorphism group of a free product of (freely indecomposable, not infinite cyclic) groups to have Property (FA). The additional sufficient conditions are all met by finite groups, and so this case is fully characterised. Therefore, this paper generalises the work of N. Leder [Serre’s Property FA for automorphism groups of free products, preprint (2018), https://arxiv.org/abs/1810.06287v1]. for finite cyclic groups, as well as resolving the open case of that paper.

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