We explicitly evaluate the Green function for the operator acting on the quadratic differentials on genus-2 hyperelliptic surfaces. As a consequence we express the second-order null vector equations for the conformal blocks of the minimal conformal models in terms of coordinates that naturally exist ...
There is another avatar of the propagator: it is a Green's function for the Klein-Gordon opera...
In this article, we study the Green function of the operator (⊕+m 2)k which is iterated k-times and is defined by where m is a positive real number and p+q=n is the dimension of the n-dimensional Euclidean space ℝn, x=(x 1, x 2, …, x n)∈ℝn and k is a non...
Summation formulas are obtained for products of associated Lagurre polynomials by means of the Green's functionKfor the HamiltonianH0=d2∕dx2+x2+Ax2(A>0).Kis constructed by an application of a Mercer-type theorem that arises in connection with integral equations. The approach introduced in thi...
Green's function of the Dirichlet problem for the differential operator on a star-shaped graph at m The paper gives an explicit representation of the Green's function of the Dirichlet boundary value problem for the polyharmonic equation in the unit ball. ... GHA Rasa,G Auzerkhan,MN Konyrkul...
I. INTRODUCTION differential operator ˆ In the present work we elaborate on the FEM for solv- L{r} = (∇{r} + f(r)) · (∇{r}) + g(r), (1) ing complex two-dimensional partial differential equa- tions (DE) using a Green function construction. Green’s acting on a...
摘要: The vector wave functions in a quasi-optical cavity are obtained with the paraxial approximation. The dyadic Green's functions in the quasi-optical cavity are developed using the eigenvector wave function expansion.<关键词: Green' s function methods electromagnetic field theory wave ...
This was how I was introduced to John, an operator from the US Forest Service, Following John’s instruction on the phone, I finally escaped from the woods. I breathed a sigh of relief. Then my phone rang, and it was John, making sure I was still going in the right direction. “By...
As an example, if the Green’s function is symmetric, i.e.,\(G(x,y)=G(y,x)\)for all\(x,y\in \Omega \), then the operator\(\mathcal {L}\)is self-adjoint. Another aspect of human interpretability is that the poles of the trained rational NN tend to cluster in a way that...
OperatorInternal OperatorPrivate OperatorProtected OperatorPublic OperatorSealed OperatorShortcut OptimizePivotTable OrderAscending OrderDescending OrderedList OrderedTest OrientPathNone OrientPathNormal OrthographicCamera OutGoingCodeReview OutlinedRectangle OutlinedRoundedRectangle 出力 OutputColumn OutputExcluded OutputParamet...