Sentence examples for regularized formula from inspiring English sources

Second, by further combining the PCRF with the manifold regularization, the precise manifold and pairwise constraint jointly regularized formula (MPCJRF) is achieved.

In [19], Qian has introduced the following regularized sampling formula.

Finally, based on these results, a regularized trace formula for the eigenvalues is obtained.

In this work, a regularized trace formula for a differential operator of fourth order with bounded operator coefficient is found.

We must notice that the result of this paper is a starting point in calculating the regularized trace formula and solving the inverse scattering problem, which will be investigated later on.

In this work, we find the following regularized trace formula for a self-adjoint differential operator L of fourth order with bounded operator coefficient: sum_{m=0}^{infty} Biggl[sum _{n=1}^{infty} biggl(lambda _{mn}-biggl(m+ frac{1}{2}biggr -frac{1}{pi}frac{1}{pi} int _{0}^{pi }operatorname{tr}Q(x),dx biggr -frac{1}{pi} bint[operatorname{tr}Q(pi)-operatorname{tr}Q(0) bigr].

Investigations into the regularized trace formulas of scalar differential operators started with the work [1] firstly.

After that work, regularized trace formulas for several differential operators have been studied in some works as [2, 3] and [4].

In the article, spectrum of operator generated by differential operator expression given on semi axis is investigated and proved formula for regularized trace of this operator.

The regularized solution is calculated by formula (40) and Theorem 5 with parameter β = ϵ 1 2. Computational results are shown in Tables 3 and 4 (the relative error) and in Figure 3 (section cut graphs).

In particular, we prove Breit Wigner formulae for the regularized scattering phases, for semiclassical Schrödinger operators with long-range potentials.