Dualities for root systems with automorphisms and applications to non-split groups

a new type-ii fuzzy logic based controller for non-linear dynamical systems with application to 3-psp parallel robot

abstract type-ii fuzzy logic has shown its superiority over traditional fuzzy logic when dealing with uncertainty. type-ii fuzzy logic controllers are however newer and more promising approaches that have been recently applied to various fields due to their significant contribution especially when the noise (as an important instance of uncertainty) emerges. during the design of type- i fuz...

commuting and non -commuting graphs of finit groups

فرض کنیمg یک گروه غیر آبلی متناهی باشد . گراف جابجایی g که با نماد نمایش داده می شود ،گرافی است ساده با مجموعه رئوس که در آن دو راس با یک یال به هم وصل می شوند اگر و تنها اگر . مکمل گراف جابجایی g راگراف نا جابجایی g می نامیم.و با نماد نشان می دهیم. گرافهای جابجایی و ناجابجایی یک گروه متناهی ،اولین بار توسطاردوش1 مطرح گردید ،ولی در سالهای اخیر به طور مفصل در مورد بحث و بررسی قرار گرفتند . در ،م...

Groups with unifoml automorphisms

Symmetric Systems and their Applications to Root Systems Extended by Abelian Groups

We investigate the class of root systems R obtained by extending an irreducible root system by a torsion-free group G. In this context there is a Weyl group W and a group U with the presentation by conjugation. We show under additional hypotheses that the kernel of the natural homomorphism U → W is isomorphic to the kernel of U → W, where U ab and W denote the abelianizations of U and W respect...

Root Systems and Coxeter Groups

This is a brief review of root systems and Coxeter groups, intended as background material for a course on double affine Hecke algebras and Macdonald polynomials. They are still incomplete in places. 1. Root systems Much of this material can be found in [Bou]. Let V be a real vector space with a positive definite inner product 〈·, ·〉. If α ∈ V is a non-zero vector, define the reflection sα in t...