Do you want to publish a course? Click here

A study in the geometry of subspaces from Riemann spaces and the problem of immersion

دراسة في هندسة الفضاءات الجزئية من فضاءات ريمان ومسألة الغمر

914   0   0   0.0 ( 0 )
 Publication date 2018
  fields Mathematics
and research's language is العربية
 Created by Shamra Editor




Ask ChatGPT about the research

The thesis topic discusses the geometry of subspaces of Riemann spaces, and it is a work prepared for obtaining a master's degree in mathematics. Our study falls into three chapters that include a reference study and then a study of the immersion issue and the geometry of subspaces from Riemann spaces.



References used
Luther pfahler eisenhart , riemannian geometry , Princeton University (1949)
rate research

Read More

In this paper, we define tensors and space Riemann spaces and fixed curvature, and offer a study of some cases associated with the search topic, the basic function is to study the relationships that remain valid when the coordinates system change to another system.
We prove that the sum A + B of closed subspaces A and B of the inverse limit of finite dimensional vector spaces, V = limVn (n ∈ N) over an algebraically closed field of characteristic 0 is closed. We extend also the basic fact that every ideal of a finite dimensional semisimple Lie algebra has a unique complement to the case of closed ideals of prosemisimple Lie algebras.
in this paper we: defined Riemannian spaces, conformal mappings, Einstein spaces, Riemannian symmetric spaces, Ricci spaces and Ricci symmetric spaces, recall the fundamental properties of these spaces
It is often useful to replace a function with a sequence of smooth functions approximating the given function to resolve minimizing optimization problems. The most famous one is the Moreau envelope. Recently the function was organized using the Br egman distance h D . It is worth noting that Bregman distance h D is not a distance in the usual sense of the term. In general, it is not symmetric and it does not satisfy the triangle inequality The purpose of the research is to study the convergence of the Moreau envelope function and the related proximal mapping depends on Bregman Distance for a function on Banach space. Proved equivalence between Mosco-epi-convergence of sequence functions and pointwise convergence of Moreau-Bregman envelope We also studied the strong and weak convergence of resolvent operators According to the concept of Bregman distance.
It is widely accepted that fine-tuning pre-trained language models usually brings about performance improvements in downstream tasks. However, there are limited studies on the reasons behind this effectiveness, particularly from the viewpoint of stru ctural changes in the embedding space. Trying to fill this gap, in this paper, we analyze the extent to which the isotropy of the embedding space changes after fine-tuning. We demonstrate that, even though isotropy is a desirable geometrical property, fine-tuning does not necessarily result in isotropy enhancements. Moreover, local structures in pre-trained contextual word representations (CWRs), such as those encoding token types or frequency, undergo a massive change during fine-tuning. Our experiments show dramatic growth in the number of elongated directions in the embedding space, which, in contrast to pre-trained CWRs, carry the essential linguistic knowledge in the fine-tuned embedding space, making existing isotropy enhancement methods ineffective.

suggested questions

comments
Fetching comments Fetching comments
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا