Compatible pairs of commuting isometries

On Pairs of Commuting Nilpotent Matrices

Let B be a nilpotent matrix and suppose that its Jordan canonical form is determined by a partition λ. Then it is known that its nilpotent commutator NB is an irreducible variety and that there is a unique partition μ such that the intersection of the orbit of nilpotent matrices corresponding to μ with NB is dense in NB. We prove that map D given by D(λ) = μ is an idempotent map. This answers a...

Commuting pairs of patterns and symmetric realizations

Common fixed point for three pairs of self-maps satisfying weakly commuting and weakly compatible condition in generalized metric spaces

In this paper, we use weakly commuting and weakly compatible conditions of self-mapping pairs, prove some new common fixed point theorems for three pairs of self-maps in the framework of generalized metric spaces. The results presented in this paper generalize the well known comparable results in the literature due to Abbas et al. [M. Abbas, T. Nazir, R. Saadati, Adv. Difference Equ., 2011 (201...

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...

Kidney paired donation with compatible pairs.

We read with great interest the article Gentry et al. (1) which explores the impact of expanding kidney paired donation (KPD) through participation by compatible pairs. In their abstract they argue that this is a new paradigm of KPD and in their conclusion they indicate that the inclusion of recipients with compatible donors will greatly increase the number of incompatible pairs matched through...