Sentence examples for exists the operator from inspiring English sources

If its inverse exists, the operator inverse can be applied to both sides of (53), which will lead to an explicit equation for the change in the thermal variable, (dot {varsigma }).

We show that the points x where (f^{prime }(x+)) and (f^{prime } x-)) exist, the operators (M_{n}(f;x)) converge to the function (f(x)), as (nrightarrow infty ).

Therefore, by the Banach inverse operator theorem, there exists the inverse operator (P_{0}^{-1} :L_{2} (mathbb{R}_ ;H to W_{2,K}^{4} (mathbb{R}_ ;H)), and this operator is bounded.

The spectral radius of the operator is less than one, then there exists the bounded operator and we can write (3.21) in the form.

Suppose that there exists the bounded operator (K Erightarrow E) given by K:= Biggl[I-sum_{i=1}^{n}c_{i} varpi(t_{i}) Biggr]^{-1}.

If there exists the shift operator δ satisfying Definition 2.7, then we say the group ((mathbb{T}, Pi,F,delta)) is a matched space for the time scale (mathbb{T}).

Furthermore, we assume that all functions under consideration are left continuous and that there exists the Cauchy operator U ( t, s ) ( 0 ≤ s ≤ t ) of the linear equation d u 1 d t = A ( t ) u 1. (3).

If the spectral radius or, more roughly, the norm of the operator are less than one, then there exists the inverse bounded operator which is of course positive.

Here the vector h belongs to the tangent cone to the set ({ xin X:F x)=0 } ) at (x^{ast}) and p is taken so large (if it ever exists) that the operator (Psi_{p}(x^{ast},h)) turns out to be surjective (the so-called p-regularity condition).

Furthermore, not only do the UEs connect to the network, but also a wide range of devices, such as, sensors and robots, will co-exist, and the operator may have further degrees of freedom to coordinate the functionalities of these devices.

As it stands, almost no regulations regarding security procedures exist for the operators of tourist and charter helicopters in New York City, several industry officials said yesterday.