In this paper I explore the concept of the Domains of Best Approximations. These structures are of interest in the study of Diophantine Approximation as they encode the inequalities that govern how efficiently an irrational point can be approximated by a rational point with a given bound on the (lowest common) denominator. The problem of best approximation can be formulated as follows. Given a ...

the aim of this paper is to give the set of all t -best approximations on fuzzy n-normed spaces and prove some theorems in the sense of vaezpour and karimi [13].

we study the theory of best approximation in tensor product and the direct sum of some lattice normed spacesx_{i}. we introduce quasi tensor product space anddiscuss about the relation between tensor product space and thisnew space which we denote it by x boxtimesy. we investigate best approximation in direct sum of lattice normed spaces by elements which are not necessarily downwardor upward a...

We consider the problem of …nding the best analytic approximation in Smirnov and Bergman norm to general monomials of the type znzm. We show that in the case of approximation to z in the annulus (and the disk) the best approximation is the same for all values of p. Moreover, the best approximations to z in Smirnov and Bergman spaces characterize disks and annuli.

It is shown that for any positive integer n and any function in Lp([0, 1]) with p ∈ [1,∞) there exists a best approximation by linear combinations of n characteristic functions of half-spaces. Further, sequences of such linear combinations converging in distance to the best approximation distance have subsequences converging to the best approximation, i.e., these linear combinations are an appr...

Lifted inference algorithms exploit symmetries in probabilistic models to speed up inference. They show impressive performance when calculating unconditional probabilities in relational models, but often resort to non-lifted inference when computing conditional probabilities, because the evidence breaks many of the model’s symmetries. Recent theoretical results paint a grim picture, showing tha...