Construction of hyperelliptic function fields of high three-rank

Construction of hyperelliptic function fields of high three-rank

We present several explicit constructions of hyperelliptic function fields whose Jacobian or ideal class group has large 3-rank. Our focus is on finding examples for which the genus and the base field are as small as possible. Most of our methods are adapted from analogous techniques used for generating quadratic number fields whose ideal class groups have high 3-rank, but one method, applicabl...

construction of vector fields with positive lyapunov exponents

in this thesis our aim is to construct vector field in r3 for which the corresponding one-dimensional maps have certain discontinuities. two kinds of vector fields are considered, the first the lorenz vector field, and the second originally introced here. the latter have chaotic behavior and motivate a class of one-parameter families of maps which have positive lyapunov exponents for an open in...

Automorphism groups of hyperelliptic function fields

Smooth Ideals in Hyperelliptic Function Fields Smooth Ideals in Hyperelliptic Function Fields

Recently, several algorithms have been suggested for solving the discrete logarithm problem in the Jacobians of high-genus hyperelliptic curves over nite elds. Some of them have a provable subexponential running time and are using the fact that smooth reduced ideals are suuciently dense. We explicitly show how these density results can be derived. All proofs are purely combinatorial and do not ...

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...