Pilot-Wave Theory and Financial Option Pricing

This paper tries to argue why pilot-wave theory could be of use in financial economics. We introduce the notion of information wave. We consider a stochastic guidance equation and part of the drift term of that equation makes reference to the phase of the wave. In order to embed information in financial option pricing we could use such a drift. We also briefly argue how we could embed information in the pricing kernel of the option price. PACS: 03, 89.65.Gh.     

Huge fluctuations in weight measurements at the bottom of a two-dimensional vertical sheet of grains

Weight measurements at the bottom of a quasi-2D vertical sheet of static cohesionless grains are carried out. The grains are held between two coaxial cylinders. This peculiar setup allows us to set either periodic or fixed lateral boundary conditions. Huge relative fluctuations in weight measurements appear in case of fixed lateral walls. This may be related to some indetermination in the mobilization state of friction forces on lateral walls. This argument would hold for any piling, but would lead to huge fluctuations in 2D systems only, because of averaging effects in 3D.     

Measures on the Splitting Subspaces of an Inner Product Space

Let S be an inner product space and let E(S) (resp. F(S)) be the orthocomplemented poset of all splitting (resp. orthogonally closed) subspaces of S. In this article we study the possible states/charges that E(S) can admit. We first prove that when S is an incomplete inner product space such that dim S/S < , then E(S) admits at least one state with a finite range. This is very much in contrast to states on F(S). We then go on showing that two-valued states can exist on E(S) not only in the case when E(S) consists of the complete/cocomplete subspaces of S. Finally we show that the well known result which states that every regular state on L(H) is necessarily -additive cannot be directly generalized for charges and we conclude by giving a sufficient condition for a regular charge on L(H) to be -additive.     

Hydrodynamics within the electric double layer on slipping surfaces

We show, using extensive molecular dynamics simulations, that the dynamics of the electric double layer (EDL) is very much dependent on the wettability of the charged surface on which the EDL develops. For a wetting surface, the dynamics, characterized by the so-called zeta potential, is mainly controlled by the electric properties of the surface, and our work provides a clear interpretation for the traditionally introduced immobile Stern layer. In contrast, the immobile layer disappears for nonwetting surfaces, and the zeta potential deduced from electrokinetic effects is considerably amplified by the existence of a slippage at the solid substrate.     

A general method for the synthesis of bastaranes and isobastaranes: first total synthesis of bastadins 5, 10, 12, 16, 20, and 21

A general strategy for the synthesis of twenty naturally occurring bastadins (all but bastadin 3) is presented. A key retrosynthetic disconnection of the two amide bonds, common in all target molecules, bisects the macrocyclic core into two diaryl ether fragments, an alpha,omega-diamine (western part) and an alpha,omega-dicarboxylic acid (eastern part). Efficient preparation of the synthetically challenging o-mono or dibromo-substituted diaryl ether linkages was achieved employing the diaryl iodonium salt method. Regarding the western part, variations of the aliphatic chain were more efficiently secured by the preparation of two different alpha,omega-aminonitrile moieties. Cobalt boride mediated reduction of the nitrile functionality established the required diamines and, at the same time, provided the necessary variation of the aromatic-ring bromination pattern. Regarding the eastern part, two different dicarboxyl precursors had to be prepared in order to accommodate bromination-pattern variations. Coupling and subsequent macrolactamization of different combinations of these key intermediates may lead at will to any member of this family of marine natural products. Four bastaranes (bastadins 5, 10, 12 and 16) and two isobastaranes (bastadins 20 and 21) were synthesized as a demonstration of the flexibility and efficiency of the approach presented.     

Une Conjecture de Lebesgue

Let A > 0 be an integer. The equation x⁵–y⁵ = Az⁵ wasfirst studied by Dirichlet and Lebesgue. Lebesgue conjecturedin 1843 that if A has no prime divisors of the form 10k+1, theequation has no solutions except the visible ones. Partial resultswere obtained by Lebesgue and by Terjanian in 1987. The purposeof the paper is to prove Lebesgue's conjecture. The main toolused is the method known as the elliptic Chabauty method.     

Numerical predictions and experiments on the free-plate edge mode

In this paper, te edge mode variation is studied with three different methods: the reciprocal work method, already used by Torvik [J. Acoust. Soc. Am. 41 (1967) 346] to model this phenomenon, the S-parameter method and a finite element model that are applied for the first time to the study of the edge resonance. Moreover, laser probe measurements of the edge mode have also been performed and compared to the numerical predictions. The good agreement between the numerical predictions and the experimental data allows full understanding of the resonant phenomenon. The edge resonance is linked to the strong increase in amplitude of two complex Lamb waves, and the edge mode is proved to radiate into the plate as the first symmetrical Lamb mode S(0). Displacements at the edge and away from the edge have been computed and measured to evaluate the spatial and temporal behaviour of the edge mode. The dependence of the edge resonance frequency and amplitude on the Poisson coefficient has also been studied.     

On the characterization of disordered and heterogeneous carbonaceous materials by Raman spectroscopy

The applicability of Raman spectroscopy to characterize disordered and heterogeneous carbonaceous materials (CM) is discussed, by considering both natural and synthetic CM. First, different analytical mismatches during the measurement are discussed and technical indications are provided in order to eliminate them. Second, the accuracy and relevance of the different parameters obtained by the decomposition of spectra by conventional fitting procedure, is reviewed. Lastly, a new Raman technique (Raman area mode microspectroscopy) giving an homogeneous repartition of power within a large laser beam is presented, this technique being powerful to study strongly heterogeneous CM and/or photosensitive samples.