Exponential distance-based fuzzy clustering for interval-valued data

In several real life and research situations data are collected in the form of intervals, the so called interval-valued data. In this paper a fuzzy clustering method to analyse interval-valued data is presented. In particular, we address the problem of interval-valued data corrupted by outliers and noise. In order to cope with the presence of outliers we propose to employ a robust metric based on the exponential distance in the framework of the Fuzzy C-medoids clustering mode, the Fuzzy C-medoids clustering model for interval-valued data with exponential distance. The exponential distance assigns small weights to outliers and larger weights to those points that are more compact in the data set, thus neutralizing the effect of the presence of anomalous interval-valued data. Simulation results pertaining to the behaviour of the proposed approach as well as two empirical applications are provided in order to illustrate the practical usefulness of the proposed method.     

On the existence and profile of nodal solutions for a two-dimensional elliptic problem with large exponent in nonlinearity

We study the existence of nodal solutions to the boundary valueproblem – u = |u|^{p – 1}u in a bounded, smooth domain in ², with homogeneous Dirichlet boundary condition, when pis a large exponent. We prove that, for p large enough, thereexist at least two pairs of solutions which change sign exactlyonce and whose nodal lines intersect the boundary of .     

Formation of share market prices under heterogeneous beliefs and common knowledge

Financial economic models often assume that investors know (or agree on) the fundamental value of the shares of the firm, easing the passage from the individual to the collective dimension of the financial system generated by the Share Exchange over time. Our model relaxes that heroic assumption of one unique “true value” and deals with the formation of share market prices through the dynamic formation of individual and social opinions (or beliefs) based upon a fundamental signal of economic performance and position of the firm, the forecast revision by heterogeneous individual investors, and their social mood or sentiment about the ongoing state of the market pricing process. Market clearing price formation is then featured by individual and group dynamics that make its collective dimension irreducible to its individual level. This dynamic holistic approach can be applied to better understand the market exuberance generated by the Share Exchange over time.     

Non-simple blow-up solutions for the Neumann two-dimensional sinh-Gordon equation

For the Neumann sinh-Gordon equation on the unit ball

Heat problems for a starlike shaped plate

The Fourier solution of the heat problem for a circular plate is generalized to a starlike shaped plate. We show that the classical solution can be used even in this more general case, provided that a suitable change of variables in the polar co-ordinate system is performed.     

Drawing parameters optimization for birefringence reduction in optical fibers

The impact of the drawing process on the stress-induced birefringence in optical fiber is experimentally analyzed. By means of the photoelastic tomographic technique, residual internal stresses are measured in fiber samples drawn under different conditions of temperature, drawing tension and speed. From measured residual stress distributions, the stress-induced birefringence and beatlength are mathematically derived and compared, proving that an effective birefringence reduction can be obtained by a proper choice of drawing parameters.     

A quasi-Newton method for solving fixed point problems in Hilbert spaces

Summary We study the convergence properties of a projective variant of Newton's method for the approximation of fixed points of completely continuous operators in Hilbert spaces. We then discuss applications to nonlinear integral equations and we produce some numerical examples.     

Non-steroidal antiinflammatory agents. VI. Synthesis of 10-oxo-5H-pyrrolo[1,2-b]isoquinoline-3-acetic Acid,a conformationally restricted analogue of tolmetin

The synthesis of 10-oxo-5H-pyrrolo[1,2-b]isoquinoline-3-acetic acid 4 , a tricyclic analogue of tolmetin which might show significant analgesic-antiinflammatory activity, has been accomplished in four steps. Alkylation of ethyl 2-pyrrolylglyoxylate ( 15 ) with 2-cyanobenzyl bromide afforded derivative 16 , which was transformed by the Huang-Minion reaction into the dicarboxylic acid 6 . Cyclization of this key intermediate to 17 , followed by alkaline hydrolysis, afforded 10-oxo-5H-pyrrolo[1,2–6]isoquinoline-3-acetic acid ( 4 ). Various attempted syntheses of 6 are also discussed.