KdV‐invariant polynomial functionals

1987 ◽  
Vol 28 (8) ◽  
pp. 1886-1900
Author(s):  
Toru Tsujishita
2021 ◽  
Vol 23 (1) ◽  
pp. 487-497
Author(s):  
Jie Qin ◽  
Jun Li

An accurate full-dimensional PES for the OH + SO ↔ H + SO2 reaction is developed by the permutation invariant polynomial-neural network approach.


2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Zhe Li ◽  
Shugong Zhang ◽  
Tian Dong

We focus on a special class of ideal projectors, subspaces, which possesses two classes of D-invariant polynomial subspaces. The first is a classical type, while the second is a new class. With matrix computation, we discretize this class of ideal projectors into a sequence of Lagrange projectors.


2020 ◽  
Vol 32 (08) ◽  
pp. 2050023 ◽  
Author(s):  
Claudio Dappiaggi ◽  
Nicolò Drago ◽  
Paolo Rinaldi

On a connected, oriented, smooth Riemannian manifold without boundary we consider a real scalar field whose dynamics is ruled by [Formula: see text], a second-order elliptic partial differential operator of Laplace type. Using the functional formalism and working within the framework of algebraic quantum field theory and of the principle of general local covariance, first we construct the algebra of locally covariant observables in terms of equivariant sections of a bundle of smooth, regular polynomial functionals over the affine space of the parametrices associated to [Formula: see text]. Subsequently, adapting to the case in hand a strategy first introduced by Hollands and Wald in a Lorentzian setting, we prove the existence of Wick powers of the underlying field, extending the procedure to smooth, local and polynomial functionals and discussing in the process the regularization ambiguities of such procedure. Subsequently we endow the space of Wick powers with an algebra structure, dubbed E-product, which plays in a Riemannian setting the same role of the time-ordered product for field theories on globally hyperbolic spacetimes. In particular, we prove the existence of the E-product and we discuss both its properties and the renormalization ambiguities in the underlying procedure. As the last step, we extend the whole analysis to observables admitting derivatives of the field configurations and we discuss the quantum Møller operator which is used to investigate interacting models at a perturbative level.


1995 ◽  
Vol 140 ◽  
pp. 1-31 ◽  
Author(s):  
Akihiko Yukie

Let (G, V) be an irreducible prehomogeneous vector space defined over a number field k, P ∈ k[V] a relative invariant polynomial, and χ a rational character of G such that . For , let Gx be the stabilizer of x, and the connected component of 1 of Gx. We define L0 to be the set of such that does not have a non-trivial rational character. Then we define the zeta function for (G, Y) by the following integralwhere Φ is a Schwartz-Bruhat function, s is a complex variable, and dg” is an invariant measure.


2018 ◽  
Vol 20 (45) ◽  
pp. 28425-28434 ◽  
Author(s):  
Benhui Yang ◽  
P. Zhang ◽  
C. Qu ◽  
P. C. Stancil ◽  
J. M. Bowman ◽  
...  

A six-dimensional potential energy surface for the CS–H2 system was computed using high-level ab initio theory and fitted using a hybrid invariant polynomial method. Quantum close-coupling scattering calculations have been carried out for rovibrational quenching transitions of CS induced by H2.


2016 ◽  
Vol 18 (45) ◽  
pp. 31064-31071 ◽  
Author(s):  
Huixian Han ◽  
Benjamin Alday ◽  
Nicholas S. Shuman ◽  
Justin P. Wiens ◽  
Jürgen Troe ◽  
...  

Six-dimensional potential energy surfaces of both CF3 and CF3− were developed by fitting ∼3000 ab initio points using the permutation invariant polynomial-neural network (PIP-NN) approach.


2019 ◽  
Vol 21 (43) ◽  
pp. 24101-24111 ◽  
Author(s):  
Yang Liu ◽  
Jun Li

The first full-dimensional accurate potential energy surface was developed for the CO + H2O system based on ca. 102 000 points calculated at the CCSD(T)-F12a/AVTZ level using a permutation invariant polynomial-neural network (PIP-NN) method.


Sign in / Sign up

Export Citation Format

Share Document