Regularity of solutions to a fractional elliptic problem with mixed Dirichlet-Neumann boundary data

In this work we study regularity properties of solutions to fractional elliptic problems with mixed Dirichlet-Neumann boundary data when dealing with the Spectral Fractional Laplacian

The valuation of clean spread options: linking electricity, emissions and fuels

The purpose of the paper is to present a new pricing method for clean spread options, and to illustrate its main features on a set of numerical examples produced by a dedicated computer code. The novelty of the approach is embedded in the use of a structural model as opposed to reduced-form models which fail to capture properly the fundamental dependencies between the economic factors entering the production process

Invariants of Combinatorial Line Arrangements and Rybnikov's Example

Following the general strategy proposed by G.Rybnikov, we present a proof of his well-known result, that is, the existence of two arrangements of lines having the same combinatorial type, but non-isomorphic fundamental groups. To do so, the Alexander Invariant and certain invariants of combinatorial line arrangements are presented and developed for combinatorics with only double and triple points. This is part of a more general project to better understand the relationship between topology and combinatorics of line arrangements.Comment: 27 pages, 2 eps figure

Matter-antimatter asymmetry without departure from thermal equilibrium

We explore the possibility of baryogenesis without departure from thermal equilibrium. A possible scenario is found, though it contains strong constraints on the size of the $CPT$ violation ($CPTV$) effects and on the role of the $B$ (baryon number) nonconserving interactions which are needed for it.Comment: Revtex, 4page

Characterization of periodic cavitation in an optical tweezer

Microscopic vapor explosions or cavitation bubbles can be generated periodically in an optical tweezer with a microparticle that partially absorbs at the trapping laser wavelength. In this work we measure the size distribution and the production rate of cavitation bubbles for microparticles with a diameter of 3 $\mu$m using high speed video recording and a fast photodiode. We find that there is a lower bound for the maximum bubble radius $R_{max}\sim 2~\mu$m which can be explained in terms of the microparticle size. More than $94 \%$ of the measured $R_{max}$ are in the range between 2 and 6 $\mu$m, while the same percentage of the measured individual frequencies $f_i$ or production rates are between 10 and 200 Hz. The photodiode signal yields an upper bound for the lifetime of the bubbles, which is at most twice the value predicted by the Rayleigh equation. We also report empirical relations between $R_{max}$, $f_i$ and the bubble lifetimes.Comment: 5 pages, 3 figure