Sentence examples for satisfy the maximal from inspiring English sources

A random variable sequence { X n, n ≥ 1 } is said to satisfy the maximal moment inequality with exponent 2 if for all n ≥ m ≥ 1, there exists a constant C independent of n and m such that E ( max m ≤ k ≤ n | ∑ i = m k X i | 2 ) ≤ C ∑ i = m n EX i 2. (1.2..

Geometrically, this amounts to repositioning the origin at the centroid of the points in q-dimensional space and then rotating the coordinate axes in such a way as to satisfy the maximal variance property.

We repeat 5.3.2 5.3.5, until it is satisfies the maximal number of generations.

Suppose that { a n b n ( Y n − E Y n ), n ≥ 1 } satisfies the maximal moment inequality with exponent 2. Assume that the following two conditions hold: ∑ i = 1 n a i = O ( b n ), (3.1). a n b n = O ( n − 1 / p ) for some  1 ≤ p < 2. (3.2..

Put c n = b n a n for n ≥ 1, 1 < r < 2. Denote Y n = − c n I ( X n < − c n ) + X n I ( | X n | ≤ c n ) + c n I ( X n > c n ), n ≥ 1, and suppose that { a n b n ( Y n − E Y n ), n ≥ 1 } satisfies the maximal moment inequality with exponent 2. Assume that the following two conditions hold: E | X | r < ∞, (3.12).

MAXFLAT FIR low/high pass digital filters are traditionally designed to satisfy the constraints of maximal flatness at the ends of the frequency band.

The aim of this paper is to study the complete moment convergence of moving average process of random sequence under the assumption that the random variables satisfy the Rosenthal type maximal inequality and the weak mean dominating condition.

Let (Phiinmathcal{Y}), the functions φ and Φ satisfy the condition (2.3), then the maximal operator M is bounded from (mathcal{M}^{Phi,varphi}({mathbb{R}^{n}})) to (Wmathcal {M}^{Phi,varphi }({mathbb{R}^{n}})). (Weak version of Spanne type result).

The best CSP solutions are defined to be those which satisfy the global problem to the maximal degree.

Among the MS2 ion bins that satisfy the minimal number of singlet ions, the maximal bin with the maximal mean intensity will be used as the normalize bin to normalize other bins that satisfy both the minimal number of singlet ions and the minimal relative intensity against the normalize bin, are included into the library to represent the MS2 ions for the primary ion.

Here, are polynomials of maximal degree which satisfy the system (3.2a) at inner collocation points (3.5).