On certain surfaces in the Euclidean space E3{\mathbb{E}}^3

In the present paper we classify all surfaces in \E^3 with a canonical principal direction. Examples of these type of surfaces are constructed. We prove that the only minimal surface with a canonical principal direction in the Euclidean space ${\mathbb{E}}^3$ is the catenoid.Comment: 13 Latex page

Minimal translation surfaces in the Heisenberg group Nil3

A translation surface in the Heisenberg group $\mathrm{Nil}_3$ is a surface constructed by multiplying (using the group operation) two curves. We completely classify minimal translation surfaces in the Heisenberg group $\mathrm{Nil}_3$.Comment: 10 page

On weak r-Helix submanifolds

In this paper, we investigate special curves on a weak r-helix submanifold in Euclidean n-space E^{n}. Also, we give the important relations between weak r-helix submanifolds and the special curves such as line of curvature, asymptotic curve and helix line.Comment: arXiv admin note: text overlap with arXiv:1203.160

Surfaces in R4 with constant principal angles with respect to a plane

We study surfaces in R4 whose tangent spaces have constant principal angles with respect to a plane. Using a PDE we prove the existence of surfaces with arbitrary constant principal angles. The existence of such surfaces turns out to be equivalent to the existence of a special local symplectomorphism of $\R^2$. We classify all surfaces with one principal angle equal to $0$ and observe that they can be constructed as the union of normal holonomy tubes. We also classify the complete constant angles surfaces in R4 with respect to a plane. They turn out to be extrinsic products. We characterize which surfaces with constant principal angles are compositions in the sense of Dajczer-Do Carmo. Finally, we classify surfaces with constant principal angles contained in a sphere and those with parallel mean curvature vector fiel

Markers for tumor margin assessment through raman spectroscopy in comparative oncology

The occurrence of tumour diseases in both animals and humans is continuously increasing. Research in nanosciences and molecular biology has put lately an intense effort to identify the aetiology factors and seek for new ways of diagnostic and targeted therapies aimed at reducing mortality and increasing chances to healing. Extensive development of cancer tumours is frequently counteracted through surgery. Assessment of a clean surgical margin is vital and a precise and rapid diagnostic down to molecule level represents a technical challenge with important clinical implications. We present a new way of using surgery instruments and surface enhanced Raman spectroscopy for direct ex vivo (no freezing, no staining) and in vivo diagnostic of clean margins in mammary tumour surgery of pets (dogs and cats).Raman spectroscopy extracts chemical information with reported 100%sensitivity, 100% specificity and overall accuracy of 93% in identifying carcinomas. Our main result stays in identification of a set of molecular markers (carotenoids, lipids and intramolecular water) for Raman diagnostic in cat and dog mammary tumour surgery. Those markers have already been confirmed for human patients

Mechanical and tribological properties of poly(hydroxyethyl methacrylate) hydrogels as articular cartilage substitutes

Poly(hydroxyethyl methacrylate) (p(HEMA)) hydrogels have been proposed as promising biomaterials to replace damaged articular cartilage. A major obstacle to their use as replacement bearing tissue is their poor mechanical properties in comparison with healthy articular cartilage. The purpose of this study was to obtain p(HEMA) hydrogels with physicochemical and mechanical properties close to healthy articular cartilage, by introducing a hydrophilic monomer, namely acrylic acid (AA). Formulations of hydrogels with different amounts of hydrophilic monomer (acrylic acid, AA) were synthesized and tested: p(HEMA), p(HEMA-co-5%AA), p(HEMA-co-25%AA). The macro-mechanical tests were reproduced at nanoscale in order to verify if the superficial properties of the hydrogels are similar to the bulk ones