Generalized Evidence Theory

Conflict management is still an open issue in the application of Dempster Shafer evidence theory. A lot of works have been presented to address this issue. In this paper, a new theory, called as generalized evidence theory (GET), is proposed. Compared with existing methods, GET assumes that the general situation is in open world due to the uncertainty and incomplete knowledge. The conflicting evidence is handled under the framework of GET. It is shown that the new theory can explain and deal with the conflicting evidence in a more reasonable way.Comment: 39 pages, 5 figure

Enumerative properties of generalized associahedra

Some enumerative aspects of the fans, called generalized associahedra, introduced by S. Fomin and A. Zelevinsky in their theory of cluster algebras are considered, in relation with a bicomplex and its two spectral sequences. A precise enumerative relation with the lattices of generalized noncrossing partitions is conjectured and some evidence is given.Comment: 15 page

Nonlinear Generalized Functions: their origin, some developments and recent advances

We expose some simple facts at the interplay between mathematics and the real world, putting in evidence mathematical objects " nonlinear generalized functions" that are needed to model the real world, which appear to have been generally neglected up to now by mathematicians. Then we describe how a "nonlinear theory of generalized functions" was obtained inside the Leopoldo Nachbin group of infinite dimensional holomorphy between 1980 and 1985. This new theory permits to multiply arbitrary distributions and contains the above mathematical objects, which shows that the features of this theory are natural and unavoidable for a mathematical description of the real world. Finally we present direct applications of the theory such as existence-uniqueness for systems of PDEs without classical solutions and calculations of shock waves for systems in non-divergence form done between 1985 and 1995, for which we give three examples of different nature: elasticity, cosmology, multifluid flows.Comment: 42 pages, 4 figure

The effect of debt on corporate profitability : Evidence from French service sector

Current study aims to provide new empirical evidence on the impact of debt on corporate profitability. This impact can be explained by three essential theories: signaling theory, tax theory and the agency cost theory. Using panel data sample of 2240 French non listed companies of service sector during 1999-2006. By utilizing generalized method of moments (GMM) econometric technique on three measures of profitability ratio (PROF1, PROF2 and ROA), we show that debt ratio has no effect on corporate profitability, regardless of the size of company (VSEs, SMEs or LEs

Giant Goos–Hänchen shifts and radiation-induced trapping of Helmholtz solitons at nonlinear interfaces

Giant Goos–Hänchen shifts and radiation-induced trapping are studied at the planar boundary separating two focusing Kerr media within the framework of the Helmholtz theory. The analysis, valid for all angles of incidence, reveals that interfaces exhibiting linear external refraction can also accommodate both phenomena. Numerical evidence of these effects is provided, based on analytical predictions derived from a generalized Snell’s law