Stability and linear oscillations of liquid bridges with varied boundary conditions under zero gravity

This article deals with stability and small linear oscillations of liquid bridges between fixed solid surfaces (parallel plates, spheres, ...) under zero gravity. A general investigation method for any kind of axisymmetric liquid bridge is exposed but the author focus his work on the spherical liquid bridge cases. In particular, he exposes a full theoretical study of spherical liquid bridges between two spheres, plates and cones.     

Errata: “Universality in Orthogonal and Symplectic Invariant Matrix Models with Quartic Potential”

The errata concern mainly the last computations for the universality of the local statistics of eigenvalues at the edge of the spectrum in parts (iii) of Theorems 2.3 and 2.4.     

Refraction holodiagrams and Snell's law

The refraction holodiagram RHD is analyzed here with respect to the law of refraction. Particularly, we study the surface that exactly conjugates by refraction a virtual point source with a real image or conversely. By using the total optical path as a parameter we build a diagram that consists in a family of Descartes ovals of the apple type that contains the Pascal's limaçon as a particular extreme case and the spherical surface with the Weierstrass points as another. These representations permit the straightforward application of Fermat's principle in the case of arbitrary refracting surfaces and show the shape of generalized Fresnel's zones in the intersections with any surface. Snell's law is applied to rays incident on the apple type surfaces to find out the conditions for exact conjugation. Sensitivity to optical path variations is also discussed. The RHD curves family can be represented in a Cartesian way where the ovals appear as equally spaced straight lines.     

Equilibrium States in the Quadruple–Kerr Solution

The extended quadruple–Kerr metric is used to consider equilibrium states of four collinear Kerr particles. We explain our previous failure to solve numerically the full set of the balance equations, and we derive a self–consistent system of the axis conditions leading to the equilibrium of all four constituents which can be black holes or hyperextreme objects. The equilibrium configurations obtained in this paper exhibit similar features with those occurring in the systems of two Kerr particles, for instance, the balance of four Kerr black holes with positive masses does not seem possible. Equilibrium states of two identical compound Kerr objects are also discussed.     

Interaction of indigo carmine dye with silica modified with humic acids at solid/liquid interface

Two distinct humic acids, one extracted from Brazilian peat soil, HA_PS, and another one obtained from commercial source, HA_FL, were attachment onto silica gel modified with aminopropyltrimethoxysilane, producing two material named SiHA_PS and SiHA_FL, respectively. The ability of these materials in removing indigo carmine dye from aqueous solution was followed through series of adsorption isotherms adjusted to modified Langmuir equation. The maximum number of moles adsorbed gave 6.82 ± 0.12 × 10⁻⁴ and 2.15 ± 0.17 × 10⁻⁴ mol g⁻¹ for SiHA_PS and SiHA_FL, respectively. Same interactions were calorimetrically followed and the thermodynamic data showed endothermic enthalpic values: 12.31 ± 0.55 and 24.69 ± 1.05 kJ mol⁻¹ for SiHA_PS and SiHA_FL surfaces, respectively. Gibbs free energies for two adsorption processes of indigo carmine dye presented negative values, reflecting dye/surface interactions must be accompanied by an increased in entropy values, which are 65 ± 3 and 98 ± 5 J mol⁻¹ K⁻¹ for SiHA_PS and SiHA_FL materials, respectively. The adsorption processes for both materials were spontaneous in nature although they presented an endothermic enthalpy for the interaction, resulting in an entropically favored process.     

Synthesis and applications of chiral bis-THF in asymmetric synthesis

The synthesis of enantiopure bis-THF is described, starting from d-mannitol. Bis-THF is used as chiral ligand for organolithium reagents in four different reactions. The enantioselectivity provided by this ligand is moderate, and the asymmetric induction is in line with the expected model.     

Mapping Properties of a Projection Related to the Helmholtz Equation

We study the continuity properties of a projection derived from a recent characterization of Herglotz Wave Functions in the plane. Herglotz Wave Functions are the entire solutions of the Helmholtz equation which have L²-Far-Field-Pattern. The behavior of this projection is reminiscent of the Disc Multiplier Operator on both L^p and mixed L^p-normed spaces. In particular a Kakeya type set plays a central role in our analysis. As a consequence we answer a question posed by Alvarez, Folch-Gabayet and Pérez-Esteva.     

An easy and fast way to determine the enantiomeric purity of substituted cyclanones

The determination of the enantiomeric purity of 2 or 3-substituted cyclanones, particularly cyclohexanones, is conveniently achieved by derivatisation into cyclic aminals with commercially available (R, R)-1,2-diphenylethylenediamine. The derivatisation procedure is directly done into the NMR tube, instantaneously, and ¹³C NMR allows an accurate measure of the ee.