Helicoidal surfaces satisfying {\Delta ^{II}\mathbf{G}=f(\mathbf{G}+C)}

In this paper, we study helicoidal surfaces without parabolic points in Euclidean 3-space \({\mathbb{R} ^{3}}\), satisfying the condition \({\Delta ^{II}\mathbf{G}=f(\mathbf{G}+C)}\), where \({\Delta ^{II}}\) is the Laplace operator with respect to the second fundamental form, f is a smooth function on the surface and C is a constant vector. Our main results state that helicoidal surfaces without parabolic points in \({ \mathbb{R} ^{3}}\) which satisfy the condition \({\Delta ^{II} \mathbf{G}=f(\mathbf{G}+C)}\), coincide with helicoidal surfaces with non-zero constant Gaussian curvature.     

Investigation of plasmas produced by laser ablation using single and double pulses for food analysis demonstrated by probing potato skins

We report on investigations of plasmas produced by laser ablation of fresh potatoes using infrared nanosecond laser radiation. A twin laser system consisting of two Nd:YAG oscillators was used to generate single or double pulses of adjustable interpulse delay. The potatoes were irradiated under ambient air with moderate pulse energies of about 10 mJ. The expansion dynamics of the ablation plume was characterized using fast imaging with a gated camera. In addition, time-resolved optical emission spectroscopy was applied to study the spectral line emission of the various plasma species. The electron density was deduced from Stark broadening, and the plasma temperature was inferred from the relative emission intensities of spectral lines. The relative concentrations of metals were estimated from the comparison of the measured emission spectra to the spectral radiance computed for a plasma in local thermal equilibrium. It is shown that the plasma produced by double pulses has a larger volume and a lower density. These properties lead to an increase of the signal-to-noise ratio by a factor of 2 and thus to an improved measurement sensitivity.     

Helicoidal surfaces in the three-dimensional Lorentz�CMinkowski space satisfying �� II r i ?=?�� i r i

In this paper, we study helicoidal surfaces without parabolic points in the 3-dimensional Lorentz?CMinkowski space under the condition ?? ^II r _i ?=??? _i r _i where ?? ^II is the Laplace operator with respect to the second fundamental form and ?? _i is a real number. We prove that there are no helicoidal surfaces without parabolic points in the 3-dimensional Lorentz?CMinkowski space satisfying that condition.