Sentence examples for upper dimension of from inspiring English sources

Suppose that (|s|upper dimension of ((X,d,mu)).

Suppose that (|s|upper dimension of ((X,d,mu)).

We point out that the doubling condition (1.2) implies that there exists a positive constant (omega:=log_{2} C) (the upper dimension of μ) such that for all (xin X), (lambdageq1) and (r > 0), begin{aligned} mubigl(B x, lambda r bigr) leq Clambda^{omega} mu bigl(B x,r bigr).

But that number is now related to the upper box or upper Minkowski dimension of ( K_{ Omega cap {mathbb {R}}} ): begin{aligned} dim ^+_M ( U ) := limsup _{ h rightarrow 0 } frac{ n left( sqrt{h}, U right) }{ log left( 1/sqrt{h}right) }, end{aligned}where ( n ( varepsilon, U ) ) is the minimal number of boxes of sides ( varepsilon ) needed to cover U.

However, considering upper dimensions yields to new difficulties essentially from a numerical point of view.

This provides the first example which demonstrates that the time-averaged spreading rates may exceed the upper box-counting dimension of the spectrum.

Noted that if the dimension of upper level variable is high, generating a uniformly spread upper level variables and refining the resulting upper level variable will be computationally expensive.

Furthermore, for the first time for fluid equations, we derive an upper bound on the dimension of the differential system (inertial manifold) which fully reproduces the infinite-dimensional dynamics.

To cope with the inherent memory limitations of online systems and to embed tracking capabilities to the design, an upper bound on the dimension of the linear subspaces is imposed.

Forty-nine anthropometry dimensions were measured consisting of 28 upper body dimensions and 21 of lower body dimensions.

SNP-A: sagittal dimension of the upper maxillary process.