Explicit minimal Scherk saddle towers of arbitrary even genera in R3\R^3

Starting from works by Scherk (1835) and by Enneper-Weierstra\ss \ (1863), new minimal surfaces with Scherk ends were found only in 1988 by Karcher (see \cite{Karcher1,Karcher}). In the singly periodic case, Karcher's examples of positive genera had been unique until Traizet obtained new ones in 1996 (see \cite{Traizet}). However, Traizet's construction is implicit and excludes {\it towers}, namely the desingularisation of more than two concurrent planes. Then, new explicit towers were found only in 2006 by Martin and Ramos Batista (see \cite{Martin}), all of them with genus one. For genus two, the first such towers were constructed in 2010 (see \cite{Valerio2}). Back to 2009, implicit towers of arbitrary genera were found in \cite{HMM}. In our present work we obtain {\it explicit} minimal Scherk saddle towers, for any given genus $2k$, $k\ge3$

Hierarchical Mean-Field Theories in Quantum Statistical Mechanics

We present a theoretical framework and a calculational scheme to study the coexistence and competition of thermodynamic phases in quantum statistical mechanics. The crux of the method is the realization that the microscopic Hamiltonian, modeling the system, can always be written in a hierarchical operator language that unveils all symmetry generators of the problem and, thus, possible thermodynamic phases. In general one cannot compute the thermodynamic or zero-temperature properties exactly and an approximate scheme named ``hierarchical mean-field approach'' is introduced. This approach treats all possible competing orders on an equal footing. We illustrate the methodology by determining the phase diagram and quantum critical point of a bosonic lattice model which displays coexistence and competition between antiferromagnetism and superfluidity.Comment: 4 pages, 2 psfigures. submitted Phys. Rev.

A laser-scanning confocal microscopy study of carrageenan in red algae from seaweed farms near the Caribbean entrance of the Panama Canal

Kappaphycus alvarezii (Doty) Doty ex P.C. Silva, a red macroalga, is a commercial source of carrageenan, a widely used polysaccharide compound important in the food and pharmaceutical industries, in nanotechnology, and in pharmacological applications. Carrageenan is found mainly in the cell wall and in the intercellular matrix. This is the first study to propose the characterization of carrageenans in vitro, using the auto-fluorescence properties of the alga treated with different polyamines: putrescine, spermidine, and spermine. This study suggests a four-phase cultivation sequence for seaweed farmers to enhance and assess the potential carrageenan yield of their crops. In phase 1, seedlings were treated with each of the polyamines. Explants were subsequently transferred through two additional culture phases before being planted on the sea farms in phase 4 and then harvested after 60 days for analysis. Images from transverse sections of 11 representative cultured K. alvarezii samples were obtained at 561 nm excitation wavelength for both the cell center and the cell wall of each sample. Spectral data were also analyzed using the spectral phasor algorithm of SimFCS developed at the Laboratory for Fluorescence Dynamics (www.lfd.uci.edu). We report on the identification of several spectral fluorescence emission fingerprints from different auto-fluorescence compounds spatially mapped using this technique. These fingerprints have the potential to improve strain selection of explants for enhanced carrageenan yield in seaweed farming operations as well as to enable wholesale pricing to correspond with crop quality