Coincidences of division fields

control of the optical properties of nanoparticles by laser fields

در این پایان نامه، درهمتنیدگی بین یک سیستم نقطه کوانتومی دوگانه(مولکول نقطه کوانتومی) و میدان مورد مطالعه قرار گرفته است. از آنتروپی ون نیومن به عنوان ابزاری برای بررسی درهمتنیدگی بین اتم و میدان استفاده شده و تاثیر پارامترهای مختلف، نظیر تونل زنی(که توسط تغییر ولتاژ ایجاد می شود)، شدت میدان و نسبت دو گسیل خودبخودی بر رفتار درجه درهمتنیدگی سیستم بررسی شده اشت.با تغییر هر یک از این پارامترها، در...

Supersimple fields and division rings

It is proved that any supersimple field has trivial Brauer group, and more generally that any supersimple division ring is commutative. As prerequisites we prove several results about generic types in groups and fields whose theory is simple.

Fields of Definition for Division Algebras

Let A be a finite-dimensional division algebra containing a base field k in its center F . We say that A is defined over a subfield F0 if there exists an F0-algebra A0 such that A = A0⊗F0 F . We show that: (i) In many cases A can be defined over a rational extension of k. (ii) If A has odd degree n ≥ 5, then A is defined over a field F0 of transcendence degree ≤ 1 2 (n − 1)(n − 2) over k. (iii)...

The Level of Fields and Division Rings

Remodified Bessel Functions via Coincidences and Near Coincidences

By considering a particular probabilistic scenario associated with coincidences, we are led to a family of functions akin to the modified Bessel function of the first kind. These are in turn solutions to a certain family of linear differential equations possessing structural similarities to the modified Bessel differential equation. The Stirling number triangle of the second kind arises quite n...