Diophantine geometry over groups I: Makanin-Razborov diagrams

Manucsrit re?u le 4 janvier 2000.     

Dominant strategies, superior information, and winner's curse in second-price auctions

In a general model of common-value second-price auctions with differential information, we show equivalence between the following characteristics of a bidder: (i) having a dominant strategy; (ii) possessing superior information; (iii) being immune from winner's curse. When a dominant strategy exists, it is given by the conditional expectation of the common value with respect to bidder's information field; if the dominant strategy is used, other bidders cannot make a profit. Final version November 2001     

Diophantine geometry over groups III: Rigid and solid solutions

This paper is the third in a series on the structure of sets of solutions to systems of equations in a free group, projections of such sets, and the structure of elementary sets defined over a free group. In the third paper we analyze exceptional families of solutions to a parametric system of equations. The structure of the exceptional solutions, and the global bound on the number of families of exceptional solutions we obtain, play an essential role in our approach towards quantifier elimination in the elementary theory of a free group presented in the next papers of this series. The argument used for proving the global bound is a key in proving the termination of the quantifier elimination procedure presented in the sixth paper of the series. Partially supported by an Israel Academy of Sciences Fellowship.     

Two-channel Kondo physics in two-impurity Kondo models

We consider the non-Fermi-liquid quantum critical state of the spin-S two-impurity Kondo model and its potential realization in a quantum dot device. Using conformal field theory and the numerical renormalization group, we show the critical point to be identical to that of the two-channel Kondo model with additional potential scattering, for any spin S. Distinct conductance signatures are shown to arise as a function of device asymmetry, with the square-root behavior commonly believed to arise at low-energies dominant only in certain regimes.     

Dehn fillings that reduce Thurston norm

We construct examples for which more than one Dehn filling reduces the Thurston norm of (distinct) second homology classes of Φ _P -atoroidal 3-manifolds. We bound the number of these Dehn fillings by the number of faces of the Thurston Ball. This work is part of a thesis under the supervision of Eliahu Rips at the Hebrew University of Jerusalem. Sponsored in part by the Landau Center for Mathematical Research.     

Structure and rigidity in hyperbolic groups I

We introduce certain classes of hyperbolic groups according to their possible actions on real trees. Using these classes and results from the theory of (small) group actions on real trees, we study the structure of hyperbolic groups and their automorphism group.The second author was partially supported by an NSF grant.     

Newly designed polysiloxane-graft-poly (oxyethylene) copolymeric surfactants: preparation,surface activity and emulsification properties

Two sets of comb-grafted polymeric surfactants based on poly-(methylhydrogen siloxane) (PHMS) and/or poly(dimethylsiloxane) (PHMS-PDMS) were prepared by sililation of the active Si-H group with an active omega-vinyl group of specially designed undecenoic-polyethyleneglycol esters (UPEG) to form newly-designed polysiloxane-grafted-polyethyleneglycol comb-copolymeric surfactants.The hydrophilic moieties are hooked to the hydrophobic backbone through a spacer (undecenoic acid). The variations in the surfactants' structures were in the length and density of the grafted hydrophilic moieties, the chain length (DP) and nature of the hydrophobic backbone.The first 12 different polymeric surfactants (set 1), termed PHMS-UPEG, were found to be ineffective emulsifiers with limited ability to stabilize oil-in-water emulsions. The second set of surfactants, named PHMS-PDMS-UPEG comb-grafted copolymers, significantly reduced the oil-water interfacial tension and effectively stabilized several types of oil-in-water emulsions. The best emulsifier of this set (PHMS-PDMS-52-UPEG-45), seems to be the one whose anchor backbone (PHMS-PDMS) dissolves (rather than spreads) in the oil phase, and whose stabilizing moieties are sufficiently long (45 EO units) and hooked to the silicone backbone at high density (52% substitution).     

Diophantine geometry over groups IV: An iterative procedure for validation of a sentence

This paper is the fourth in a series on the structure of sets of solutions to systems of equations in a free group, projections of such sets, and the structure of elementary sets defined over a free group. In the fourth paper we present an iterative procedure that validates the correctness of anAE sentence defined over a free group. The terminating procedure presented in this paper is the basis for our analysis of elementary sets defined over a free group presented in the next papers in the series. Partially supported by an Israel Academy of Sciences Fellowship.     

Can Special Relativity Be Derived from Galilean Mechanics Alone?

Special relativity is based on the apparent contradiction between two postulates, namely, Galilean vs. c-invariance. We show that anomalies ensue by holding the former postulate alone. In order for Galilean invariance to be consistent, it must hold not only for bodies’ motions, but also for the signals and forces they exchange. If the latter ones do not obey the Galilean version of the Velocities Addition Law, invariance is violated. If, however, they do, causal anomalies, information loss and conservation laws’ violations are bound to occur. These anomalies are largely remedied by introducing waves and fields that disobey Galilean invariance. Therefore, from these inconsistencies within classical mechanics, electromagnetism could be predicted before experiment proved its existence. Special relativity, it might be argued, would then follow naturally, either as a resolution of the resulting conflict or as an extrapolation of the path between the theories. We conclude with a review of earlier attempts to base SR on a single postulate, and point out the originality of the present work.