Embedding variables in finite dimensional models

Embedding variables in finite dimensional models

Global problems associated with the transformation from the Arnowitt, Deser and Misner (ADM) to the Kuchař variables are studied. Two models are considered: The Friedmann cosmology with scalar matter and the torus sector of the 2+1 gravity. For the Friedmann model, the transformations to the Kuchař description corresponding to three different popular time coordinates are shown to exist on the w...

infinite dimensional garch models

مدلهای گارچ در فضاهای هیلبرت پایان نامه حاضر شامل دو بخش می باشد. در قسمت اول مدلهای اتورگرسیو تعمیم یافته مشروط به ناهمگنی واریانس در فضاهای هیلبرت را معرفی، مفاهیم ریاضی مورد نیاز در تحلیل این مدلها در دامنه زمان را مطرح کرده و آنها را مورد بررسی قرار می دهیم. بر اساس پیشرفتهایی که اخیرا در زمینه تئوری داده های تابعی و آماره های عملگری ایجاد شده است، فرآیندهایی که دارای مقادیر در فضاهای ...

Finite Models and Finitely Many Variables

Constructing finite dimensional codes with optical continuous variables

– We show how a qubit can be fault-tolerantly encoded in the infinite-dimensional Hilbert space of an optical mode. The scheme is efficient and realizable with present technologies. In fact, it involves two travelling optical modes coupled by a cross-Kerr interaction, initially prepared in coherent states, one of which is much more intense than the other. At the exit of the Kerr medium, the wea...

Embedding Cycles in Finite Planes

We define and study embeddings of cycles in finite affine and projective planes. We show that for all k, 3 6 k 6 q2, a k-cycle can be embedded in any affine plane of order q. We also prove a similar result for finite projective planes: for all k, 3 6 k 6 q2 + q + 1, a k-cycle can be embedded in any projective plane of order q.