KdV‐invariant polynomial functionals

1987 ◽  
Vol 28 (8) ◽  
pp. 1886-1900
Author(s):  
Toru Tsujishita
Keyword(s):  
Invariant Polynomial ◽  
Polynomial Functionals

An accurate full-dimensional potential energy surface for the reaction OH + SO → H + SO2

2021 ◽  
Vol 23 (1) ◽  
pp. 487-497
Author(s):  
Jie Qin ◽  
Jun Li
Keyword(s):  
Neural Network ◽  
Potential Energy ◽  
Potential Energy Surface ◽  
Energy Surface ◽  
Invariant Polynomial ◽  
Network Approach ◽  
Neural Network Approach ◽  
Polynomial Neural Network

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

scholarly journals The Discretization for a Special Class of Ideal Projectors

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Zhe Li ◽  
Shugong Zhang ◽  
Tian Dong
Keyword(s):  
Special Class ◽  
Invariant Polynomial ◽  
Classical Type ◽  
Matrix Computation ◽  
New Class

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.

scholarly journals The algebra of Wick polynomials of a scalar field on a Riemannian manifold

2020 ◽  
Vol 32 (08) ◽  
pp. 2050023 ◽  
Author(s):  
Claudio Dappiaggi ◽  
Nicolò Drago ◽  
Paolo Rinaldi
Keyword(s):  
Riemannian Manifold ◽  
Scalar Field ◽  
Partial Differential Operator ◽  
Algebra Structure ◽  
Functional Formalism ◽  
Algebraic Quantum ◽  
Globally Hyperbolic Spacetimes ◽  
Hyperbolic Spacetimes ◽  
Møller Operator ◽  
Polynomial Functionals

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.

scholarly journals On the convergence of the zeta function for certain prehomogeneous vector spaces

1995 ◽  
Vol 140 ◽  
pp. 1-31 ◽  
Author(s):  
Akihiko Yukie
Keyword(s):  
Invariant Measure ◽  
Zeta Function ◽  
Complex Variable ◽  
Vector Spaces ◽  
Invariant Polynomial ◽  
Connected Component ◽  
Relative Invariant ◽  
Prehomogeneous Vector Space ◽  
Prehomogeneous Vector Spaces ◽  
Rational Character

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.

Inelastic vibrational dynamics of CS in collision with H2 using a full-dimensional potential energy surface

2018 ◽  
Vol 20 (45) ◽  
pp. 28425-28434 ◽  
Author(s):  
Benhui Yang ◽  
P. Zhang ◽  
C. Qu ◽  
P. C. Stancil ◽  
J. M. Bowman ◽  
...  
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Ab Initio ◽  
Energy Surface ◽  
Invariant Polynomial ◽  
Polynomial Method ◽  
Vibrational Dynamics ◽  
Close Coupling ◽  
High Level

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.

Calculations of the active mode and energetic barrier to electron attachment to CF3 and comparison with kinetic modeling of experimental results

2016 ◽  
Vol 18 (45) ◽  
pp. 31064-31071 ◽  
Author(s):  
Huixian Han ◽  
Benjamin Alday ◽  
Nicholas S. Shuman ◽  
Justin P. Wiens ◽  
Jürgen Troe ◽  
...  
Keyword(s):  
Neural Network ◽  
Potential Energy ◽  
Ab Initio ◽  
Kinetic Modeling ◽  
Potential Energy Surfaces ◽  
Electron Attachment ◽  
Invariant Polynomial ◽  
Active Mode ◽  
Polynomial Neural Network ◽  
Energy Surfaces

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.

An accurate full-dimensional permutationally invariant potential energy surface for the interaction between H2O and CO

2019 ◽  
Vol 21 (43) ◽  
pp. 24101-24111 ◽  
Author(s):  
Yang Liu ◽  
Jun Li
Keyword(s):  
Neural Network ◽  
Potential Energy ◽  
Potential Energy Surface ◽  
Energy Surface ◽  
Invariant Polynomial ◽  
Polynomial Neural Network ◽  
Invariant Potential

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.

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