Lorentzian Isothermic Surfaces and Bonnet Pairs

Lorentzian surfaces in Lorentz three-space are studied using an indefinite version of the quaternions. A classification theorem for Bonnet pairs in Lorentz three-space is obtained

Lorentzian Isothermic Surfaces in R-j(n)

If a time-like surface in R-j(n) is isothermic then there is another, uniquely determined surface which is either anti-conformal or conformal and sign-reversing with the same Gauss map. The choice of mapping depends on whether the shape operator is diagonalizable over R or C

Shape Operators of Einstein Hypersurfaces in Indefinite Space Forms

The possible shape operators for an Einstein hypersurface in an indefinite space form are classified algebraically. If the shape operator A is not diagonalizable then either A2 = 0 or A2 = -b2Id

A note about isothermic surfaces in Rn−j,j

In this note we survey our results on the description of ti-melike isothermic surfaces in Rn-j,j using the Grassmannian systems or U/K-systems. We give the natural extensions of the definition of Ribaucour and Darboux transformations for timelike isothermic surfaces and review how those transformations correspond to dressing actions of suitable simple elements.      &nbsp

On the reduction of the degree of linear differential operators

Let L be a linear differential operator with coefficients in some differential field k of characteristic zero with algebraically closed field of constants. Let k^a be the algebraic closure of k. For a solution y, Ly=0, we determine the linear differential operator of minimal degree M and coefficients in k^a, such that My=0. This result is then applied to some Picard-Fuchs equations which appear in the study of perturbations of plane polynomial vector fields of Lotka-Volterra type

Sparse 3D Point-cloud Map Upsampling and Noise Removal as a vSLAM Post-processing Step: Experimental Evaluation

The monocular vision-based simultaneous localization and mapping (vSLAM) is one of the most challenging problem in mobile robotics and computer vision. In this work we study the post-processing techniques applied to sparse 3D point-cloud maps, obtained by feature-based vSLAM algorithms. Map post-processing is split into 2 major steps: 1) noise and outlier removal and 2) upsampling. We evaluate different combinations of known algorithms for outlier removing and upsampling on datasets of real indoor and outdoor environments and identify the most promising combination. We further use it to convert a point-cloud map, obtained by the real UAV performing indoor flight to 3D voxel grid (octo-map) potentially suitable for path planning.Comment: 10 pages, 4 figures, camera-ready version of paper for "The 3rd International Conference on Interactive Collaborative Robotics (ICR 2018)

Charge-remote fragmentation in a hybrid (BEqQ) mass spectrometer to determine isotopic purity in selectively polydeuterated surfactants

AbstractThe combination of fast atom bombardment with charge-remote fragmentation using a hybrid (BEqQ) mass spectrometer was used successfully to assess and localize the extent of selective deuterium isotope labeling of tetradecyltrimethylammonium bromdes. Spectral details reveal a new reaction that can give rise to ions isobaric with those formed by charge-remote fragmentation

Recovery of an Early Evidence of Castor Plant, Ricinus Communis L. from the Central Sudan and its Positioning within a World-wide Context

Evidence of castor plant R. communis, L. is recovered from the Early Holocene archaeological site of Kabbashi Haitah in the Central Sudan and dated to c. 7700 - 7200 bp. This evidence represents the earliest botanical evidence recovered –so far- from the Central Sudan and elsewhere in Eastern Tropical Africa and the World. No evidence is found in the material culture remains which might indicate the likelihood of its being imported. Most of the ancient and traditional utilizations of castor plant are strikingly similar despite their being practised at different times in different and far apart regions in the World. This modest contribution stands to show that the wide spread and utilizations of castor plant strongly accentuate its significant and indispensable role since ancient times. It also reflects that inedible plants, as seen in the case of castor plant, were (and still are) not less important than food plant, hence stresses the need for attending to their study in a fashion equal to that of studying foodplants since prehistoric and early historic times