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.     

Third-Order Phase Transition: Random Matrices and Screened Coulomb Gas with Hard Walls

Journal of Statistical Physics - Consider the free energy of a d-dimensional gas in canonical equilibrium under pairwise repulsive interaction and global confinement, in presence of a volume...     

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.     

Equilibrium strategy and population-size effects in lowest unique bid auctions

In lowest unique bid auctions, N players bid for an item. The winner is whoever places the lowest bid, provided that it is also unique. We use a grand canonical approach to derive an analytical expression for the equilibrium distribution of strategies. We then study the properties of the solution as a function of the mean number of players, and compare them with a large data set of internet auctions. The theory agrees with the data with striking accuracy for small population-size N, while for larger N a qualitatively different distribution is observed. We interpret this result as the emergence of two different regimes, one in which adaptation is feasible and one in which it is not. Our results question the actual possibility of a large population to adapt and find the optimal strategy when participating in a collective game.