In vivo SPECTROPHOTOMETRIC EVALUATION OF NEOPLASTIC AND NON-NEOPLASTIC SKIN PIGMENTED LESIONS–I. REFLECTANCE MEASUREMENTS

Reflectance spectrophotometry from 400 to 800 nm on different cutaneous pigmented lesions, including primary and metastatic malignant melanoma, pigmented nevi, lentigo and seborrhoeic keratosis, has been performed by using an external integrating sphere coupled to a spectrophotometer. Measurements show that reflectance spectra of the different lesions manifest dissimilar patterns, particularly in the near IR region. Comparison of reflectance of nevi with that of malignant melanomas results in a highly significant difference (P less than 10(-6)) between the two samples. Though interpretation of the spectra remains difficult as a result of the complexity of the optical processes of scattering and absorption, our results suggest that a detailed analysis of the reflectance spectrum may give clinically useful information, and could be utilized as an aid in clinical diagnosis of cutaneous pigmented lesions, especially where malignant melanoma is concerned.     

The large deformation of nonlinearly elastic rings in a two-dimensional compressible flow

The nonlinear nonlocal system of the equilibrium equations ofan elastic ring under the action of an external two-dimensionaluniformly subsonic potential barotropic steady-state gas flowis considered. The configurations of the elastic ring are identifiedby a pair of functions (, ). The simple curve represents theshape of the ring and the real-valued function identifies theorientation of the material sections of the ring. The pressurefield on the ring depends nonlocally on , and on two parametersU and P which represent the pressure and the velocity at infinity.The system is shown to be equivalent to a fixed-point problem,which is then treated with continuation methods. It is shownthat the solution branch ensuing from certain equilibrium states((₀, ₀), 0, P₀) in the solution-parameter space of ((₀, ₀),0, P₀) either approaches the boundary of the admissible ((,), U,p)'s in a well-defined sense, or is unbounded, or is homotopicallynontrivial in the sense that there exists a continuous map from the branch to a two-dimensional sphere which is not homotopicin the sphere to a constant, while restricted to the branchminus ((₀, ₀), 0, P₀) is homotopic to a constant in the sphere.Furthermore, by fixing the pressure parameter at P₀ and by consideringthe one-parameter problem in ((, ), U), the following holds.Every hyperplane in the solution-parameter space of the ((,), U)'s which contains the equilibrium state ((₀, ₀), 0) anddoes not include a welldetermined one-dimensional subspace intersectsthe solution branch above at a point different from ((₀, ₀),0).