Sentence examples for unique operator from inspiring English sources

The unique operator that merges the operations of differentiating and integrating with respect to the radius of the hypercubical function is given by ∂ ± m ∂ r ± m H C ( k, n, r ) ≡ D ± m H C ( k, n. r ).

In that sense we define and, where appropriate, use a unique operator with which we merge the operations of differentiating and integrating (using the unique symbol D ± m ) on the radius of the HC function.

If (lin Lambda_{omega}^{p}(mathcal{M})^), then there exists a unique operator (yin Lambda_{omega}^{p}(mathcal{M})^{prime}) such that (l(x)=tau yx)) for every (xinmathcal{M}) and (|l|geq|y|_{Lambda_{omega}^{p}(mathcal{M})^{prime}}).

Given a connection σ, there is a unique operator monotone function (f: mathbb {R}^ to mathbb {R}^) satisfying begin{aligned} f(x)I = I,sigma,(xI),quad x geqslant 0. end{aligned} Moreover, the map (sigmamapsto f) is a bijection.

Given an operator connection σ, there is a unique operator monotone function (f:[0,infty) to[0,infty)) such that f(A) = I mathbin {sigma }A, quad A geqslant 0. (5.4) In fact, the map (sigmamapsto f) is a bijection. In addition, σ is a mean if and only if (f(1)=1). Such a function f is called the representing function of σ.

Viral parameters such as HBeAg, antiHBe IgG and HBV plasma viral load from frozen samples were simultaneously measured by a unique operator to reduce intra and inter-assay variations.

Gleason's theorem can now be invoked to identify the states on A with the density operators on H: to each state ω in ω(AH) there corresponds a unique

Clearly, T ( 0 ) = { 0 } if and only if T can determine a unique linear operator from D ( T ) into X whose graph is T. Therefore, T is said to be an operator if T ( 0 ) = { 0 }.

It can easily be verified that T ( 0 ) = { 0 } if and only if T can determine a unique linear operator from D ( T ) into X whose graph is just T. For convenience, we will identify a linear operator in X with a subspace in X 2 via its graph.

Then (1.1) with f ≡ 0 has a unique resolvent operator.

Thus it associates to a unique symmetric operator mean, denoted by (diamondsuit_{r}).