We consider global attractors Af of dissipative parabolic equations ut = uxx + f(x, u, ux) on the unit interval 0 ≤ x ≤ 1 with Neumann boundary conditions. A permutation πf is defined by the two orderings of the set of (hyperbolic) equilibrium solutions ut ≡ 0 according to their respective values at the two boundary points x = 0 and x = 1. We prove that two global attractors, Af and Ag, are glo...

Thirteen bands for the B(1)Δg-A(1)Πu system and eleven bands for the B'(1)Σg(+)-A(1)Πu system of C2 were identified in the Fourier transform infrared emission spectra of hydrocarbon discharges. The B'(1)Σg(+)v = 4 and the B(1)Δg v = 6, 7, and 8 vibrational levels involved in nine bands were studied for the first time. A direct global analysis with Dunham parameters was carried out satisfactoril...

In der Arbeit von Schrijver [3] wird die folgende Formulierung von Maders Satz aus [2] bewiesen (siehe Satz 1). Wir werden skizzieren wie man aus diesem Satz die Formulierung von Maders Satz über kreuzungsfreie H-Wege (siehe Korollar 2) herleiten kann. Eine Menge P von Wegen in einem Graphen G = (V,E) ist kreuzungsfrei, wenn die Schnittmenge der Eckenmengen zweier unterschiedlicher Wege aus P e...

The process of fast gas heating in air in the near afterglow of a pulsed nanosecond spatially uniform discharge has been investigated experimentally and numerically at moderate (3−9 mbar) pressures and high (200−400 Td) reduced electric fields. The temporal behavior of discharge current, deposited energy, electric field and temperature were measured. The role of processes with participation of ...

We describe how closed geodesics lying in a prescribed homology class on a negatively curved manifold split when lifted to a finite cover. This generalizes a result of Zelditch in the case of compact hyperbolic surfaces. 0. Introduction Given a compact manifold of negative curvature, there are geometric analogues of the Chebotarev Theorem in algebraic number theory due to Sunada [13] (cf. also ...

The global potential energy surfaces of the first six singlet electronic states of CO2, 1-3(1)A', and 1-3(1)A" are constructed using high level ab initio calculations. In linear molecule, they correspond to X̃(1)Σg (+), 1(1)Δu, 1(1)Σu (-), and 1(1)Πg. The calculations accurately reproduce the known benchmarks for all states and establish missing benchmarks for future calculations. The calculated...

Hence, we see the existence of π ∈ Sym(I) with α(g) = πg for all g ∈ G. (⇐) Assume π ∈ Sym(I) exists such that α(g)(i) = (π ◦ g ◦ π−1)(i).† By definition of the symmetric group, π : I → I, i → π(i) is a bijection. Let g ∈ G and i ∈ I. Observe π(g ¦ρ i) = π(g(i)) = (π ◦ g) ◦ (π−1 ◦ π)(i) = (π ◦ g ◦ π−1) ◦ π(i) = α(g) ◦ π(i)† = g ¦ρ◦α π(i) Hence, by definition 2.10.13(a), π is G-equivariant. We a...

Absorption of radiation from the sodium dimer molecular states correlating to Na(3s)-Na(3s) is investigated theoretically. Vibrational bound and continuum transitions from the singlet X Σg state to the first excited A Σu and B Πu states and from the triplet a Σu state to the first excited b Σg and c Πg states are studied quantum-mechanically. Theoretical and experimental data are used to charac...

We consider a system in which a classical oscillator is interacting with a purely quantum mechanical oscillator, described by the Lagrangian L = 12 ẋ 2 + 12 Ȧ 2 − 1 2(m 2 + e2A2)x2 , where A is a classical variable and x is a quantum operator. With 〈x(t)〉 = 0, the relevant variable for the quantum oscillator is 〈x(t)x(t)〉 = G(t). The classical Hamiltonian dynamics governing the variables A(t), ...

Absorption of radiation from the sodium dimer molecular states correlating to Na(3s)-Na(3s) is investigated theoretically. Vibrational bound and continuum transitions from the singlet X Σg state to the first excited A Σu and B Πu states and from the triplet a Σu state to the first excited b Σg and c Πg states are studied quantum-mechanically. Theoretical and experimental data are used to charac...