Chebyshev polynomials: From approximation theory to algebra and number theory

Computational Number Theory and Algebra

Proof (Continued from the previous class) We have already shown in the previous class that the algorithm halts after polynomially many executions of the while-loop as the index i can decrease for at most O(n logA) times in step 6. In order to complete the proof, we also need to show that the size of the numerator and denominator of any rational number involved in the computation is polynomially...

Chebyshev Polynomials and Approximation Theory in Theoretical Computer Science and Algorithm Design

I will talk about low degree polynomials that are small on the interval [0,1] but jump up very rapidly outside of that interval. First I’ll try to convince you why you should care about such polynomials, which have a ton of applications in complexity, optimization, learning theory, and numerical linear algebra. In particular, I will introduce the Chebyshev polynomials and then try to explain th...

skopos theory and translating strategies of csis in translaed literary texts from english into persian

abstract translation has become a cultural act which plays a significant role in human life. with the emergence of functional translation theories, and skopos theory in particular, translation has been considered as a purposeful, interpersonal and intercultural activity which is produced for particular recipients and directed by a specific purpose. this purpose determines the translatio...

superstring scatterng from dbranes and wess zumino terms in string theory

دو هدف را برای انجام این پایان نامه دنبال می کنیم . نشان می دهیم که بسط دامنه پراکندگی یک میدان راموند-راموند دو میدان پیمانه ای و یک میدان تاکیونی caat بسط سازگاری است که این نکته بیانگر آنست که بسط تاکیونها که بسط انرژی پایین نیست را یافته ایم و این بسط با بسط aatt,ctta,cta,cttt سازگار است با مقایسه با دامنه پراکندگی تعدادی از تصحیحات کنشهای tachyonic dbi, wess-zumino را می یابیم .

A Computational Introduction to Number Theory and Algebra (Version 2)