Global Optimization: On Pathlengths in Min-Max Graphs

Let f be a smooth nondegenerate real valued function on a finite dimensional, compact and connected Riemannian manifold. The bipartite min-max graph is defined as follows. Its nodes are formed by the set of local minima and the set of local maxima. Two nodes (a local minimum and a local maximum) are connected in by means of an edge if some trajectory of the corresponding gradient flow connects them. Given a natural number k, we construct a function f such that the length of the shortest path in between two specific local minima exceeds k. The latter construction is independent of the underlying Riemannian metric.     

Fourier transform infrared spectrum of carbon disulphide in the 4ν2 + ν3 band region near 3100 cm−1

Fourier transform spectra have been recorded for carbon disulphide CS₂ in the region of the 4ν₂ + ν₃ band near 3100 cm^?1. The data analysis has determined new molecular constants. Bands were also observed for the isotopomer ¹²C³²S³⁴S.     

Spectra of carbon disulphide in the 3400–4400 cm−1 region by Fourier transform spectroscopy

Fourier transform spectra have been recorded for carbon disulphide (CS₂) in the region between 3400 cm^?1 and 4400 cm^?1. A data analysis has determined new molecular constants: 14 bands were observed for the main isotopic form ¹²C³²S₂, two bands for the isotopomer ¹²C³²S³⁴S and one each for ¹²C³²S³³S and ¹³C³²S₂.