Sentence examples for nice function from inspiring English sources

Since the denominator in (2.6) tends to zero exponentially as | ξ | → ∞, b is a "nice" function only under very stringent assumptions on a and hence on h ( t ).

Nevertheless, if f is a sufficiently nice function, we can define (f({mathscr {L}}_A,{mathscr {R}}_B)), in which case the functions f(A, B) defined by (3.1.1) coincide with (f({mathscr {L}}_A,{mathscr {R}}_B I).

Actually, their approach allows to prove the existence of a finite real signed Borel measure (nu ) such that begin{aligned} {text {trace}}(f(A -f B))=int _{mathbb R}f'(s),dnu (s),quad hbox {and}quad Vert nu Vert le Vert TVert _{{varvec{S}}_1} end{aligned} (1.6.3 for sufficiently nice functions f.

They discovered the following formula that expresses the derivative in terms of double operator integrals: begin{aligned} frac{d}{dt}(f(A+tK))|_{t=0}= iint limits _{{mathbb R}times {mathbb R}}frac{f(x -f y)}{x -f yE_A(x)K,dE_A(y) end{aligned}for sufficiently nice functions f.

In the paper [24] Daletskii and Krein proved that in the case when the self-adjoint operator A is bounded for nice functions f the map (tmapsto f(A+tK)) has m-th derivative and it can be expressed in terms a multiple operator integral whose integrand is a higher order divided difference of f.

And this nice simple function is f.

The main difficulty arises from finding a nice diffusion function.

I had some luck with the Barcelona Web site guia.bcn.cat, which has an English version and a nice filtering function.

Storytellers are increasingly important in this space, as the tools become easier to use (at least on the surface – I can only imagine the complexities that are in play behind the scenes that make everything look nice and function well).

We obtain Taylor approximations for functionals V↦Tr(f(H0+V)) defined on the bounded self-adjoint operators, where H0 is a self-adjoint operator with compact resolvent and f is a sufficiently nice scalar function, relaxing assumptions on the operators made in [17], and derive estimates and representations for the remainders of these approximations.

As you can see above, there's a nice embed function.