Sentence examples for be a shift operator from inspiring English sources

Let δ be a shift operator under Definition  2.7.

Then the operator (delta (s,t)) associated with (e_{Pi^in Pi ^) is said to be a shift operator on the set (mathbb{T}^).

holds for any sequence solution {u(n)} of (1.2), where, P is a shift operator defined as P u i ( p ) = u i ( p + 1 ) for i ∈ N and p ∈ ℤ+.

A popular approach in this category is based on non-negative matrix factor deconvolution (NMFD) [26, 32, 43], in which the above equation is expressed using matrix convolution with a shift operator " m→" as: boldsymbol{Y} = sumlimits_{m=0}^{M-1},,boldsymbol{{H}_{m}{overset{m rightarrow}{boldsymbol{S}}}, (5).

Then the operator δ associated with (e_{Pi^in Pi^) is said to be shift operator on the set (mathbb{T}^).

We do this as follows:4 let (sigma : {mathbb {R}}^{ infty } rightarrow {mathbb {R}}^{ infty } ) be the shift operator, and first define a homotopy of the identity map of ({mathbb {R}}^{ infty } {setminus } { 0 }) to the constant map with value (e_1).

Under Definition 2.9, the complete closedness of time scales in Example 2.5 can be well described, that is, δ for (mathbb{T}_{1}) is a positive-direction shift operator, δ for (mathbb{T}_{2}) is a negative-direction shift operator.

Given a bounded sequence of complex numbers { α n : n ∈ Z } (called weights), let T be the bilateral weighted shift on an infinite dimensional Hilbert space operator H = l 2, with the canonical orthonormal basis { e n : n ∈ Z }, defined by T e n = α n e n + 1 for all n ∈ Z. Lemma 2.10 Let T be a bilateral weighted shift operator with weights { α n : n ∈ Z }.

where is the backward shift operator and is a generating function.

(38) This shift operator is a unitary operation and it can be realized experimentally by using fundamental quantum gates [6, 20].

We follow the notation of Griffiths and Tavaré (1995) and use several operators to denote the changes of sample configuration: S is the shift operator that can be operated on a specific haplotype h k or the entire haplotype set T. Specifically, S h k represents the haplotype obtained by deleting the first mutation coordinate of haplotype h k.