Algebraic number fields generated by an infinite family of monogenic trinomials

An Infinite Family of Non-Abelian Monogenic Number Fields

We study non-abelian monogenic algebraic number fields (i.e., non-abelian number fields whose rings of integers have a basis of the form {1, α, α, . . . , αn−1} for some α). There are numerous results about abelian monogenic number fields, yet for the non-abelian case little is understood. As our main result, we find an infinite family of non-abelian monogenic degree 6 number fields.

On Quadratic Fields Generated by Discriminants of Irreducible Trinomials

A. Mukhopadhyay, M. R. Murty and K. Srinivas have recently studied various arithmetic properties of the discriminant ∆n(a, b) of the trinomial fn,a,b(t) = t n + at+ b, where n ≥ 5 is a fixed integer. In particular, it is shown that, under the abc-conjecture, for every n ≡ 1 (mod 4), the quadratic fields Q (√ ∆n(a, b) ) are pairwise distinct for a positive proportion of such discriminants with i...

Decomposition of primes in number fields defined by trinomials

Generated topology on infinite sets by ultrafilters

Let $X$ be an infinite set, equipped with a topology $tau$. In this paper we studied the relationship between $tau$, and ultrafilters on $X$. We can discovered, among other thing, some relations of the Robinson's compactness theorem, continuity and the separation axioms. It is important also, aspects of communication between mathematical concepts.

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...