Local bifurcation and regularity for steady periodic capillary–gravity water waves with constant vorticity

We study periodic capillary–gravity waves at the free surface of water in a flow with constant vorticity over a flat bed. Using bifurcation theory the local existence of waves of small amplitude is proved even in the presence of stagnation points in the flow. We also derive the dispersion relation. Moreover, we prove a regularity result for the free surface.     

Structure and magnetism of a spin ladder system: (C5H9NH3)2CuBr4

The crystal structure of bis(cyclopentylammonium)tetrabromocuprate(II) has been determined at room temperature and at -70 degrees C. The room temperature structure is orthorhombic, space group Pn2(1)a, with a = 12.092(6) A, b = 8.134(4) A, and c = 18.698(10) A. The low temperature structure is also orthorhombic, space group Pna2(1), with a = 24.111(5) A, b = 8.089(2) A, and c = 18.448(4) A. DSC studies reveal the presence of a weak endotherm at -13 degrees C. The structures of the two phases are very similar, differing only in the relative orientations of the cyclopentyl rings of the organic cations and slight displacements of the anionic tetrahedra. The CuBr(4)(2)(-) anions in the low temperature phase are arranged to define a spin ladder system through Cu-Br.Br-Cu two-halide exchange pathways. Magnetic susceptibility data have been analyzed and yield antiferromagnetic exchange strengths 2J(rail)/k = -11.6 K and 2J(rung)/k = -5.5 K with a singlet-triplet gap energy Delta/k(B) = 2.3 K. This is the first report of a spin ladder with a stronger interaction along the axis of the ladder than along the rungs.     

Simultaneous Determination of Vitamins D3 (Calcitriol,Cholecalciferol) and K2 (Menaquinone-4 and Menaquinone-7) in Dietary Supplements by UHPLC

The content and composition of dietary supplements is of great interest due to their increasing consumption and variety of available brand offered in the market. Accurate determination of vitamins is important for the improvement of dietary supplement quality and nutrition assessments. In this regard, the simultaneous determination of vitamin D3 (calcitriol—CT and cholecalciferol—CHL) and K2 (menaquinone-4—MK-4 and menaquinone-7—MK-7) in dietary supplements was developed by using ultra-high-pressure liquid chromatography (UHPLC). The overall runtime per sample was above 35 min, with the retention times of 2.40, 6.59, 7.06, and 32.6 min for vitamin D3 (CT and CHL) and vitamin K2 (MK-4 and MK-7), respectively. The limits of detection and limits of quantification for the target nutritional compounds ranged between 0.04–0.05 µg/mL, respectively. The validation results indicated that the method had reasonable linearity (R² ≥ 0.9990), good recovery (>82%), satisfactory intra-day precision (≤1.9%) and inter-day precision (≤3.5%), and high selectivity and specificity. The validated UHPLC method was demonstrated to be precise, accurate, and robust for the simultaneous determination of vitamins D3 (CT and CHL) and K2 (MK-4 and MK-7) in dietary supplements.     

Application of Inductively Coupled Plasma Spectrometric Techniques and Multivariate Statistical Analysis in the Hydrogeochemical Profiling of Caves—Case Study Cloșani,Romania

The aim of the study was to develop the hydrogeochemical profiling of caves based on the elemental composition of water and silty soil samples and a multivariate statistical analysis. Major and trace elements, including rare earths, were determined in the water and soil samples. The general characteristics of water, anions content, inorganic and organic carbon fractions and nitrogen species (NO₃⁻ and NH₄⁺) were also considered. The ANOVA—principal component analysis (PCA) and two-way joining analysis were applied on samples collected from Cloșani Cave, Romania. The ANOVA-PCA revealed that the hydrogeochemical characteristics of Ca²⁺-HCO₃⁻ water facies were described by five factors, the strongest being associated with water-carbonate rock interactions and the occurrence of Ca, Mg and HCO₃⁻ (43.4%). Although organic carbon fractions have a lower influence (20.1%) than inorganic ones on water characteristics, they are involved in the chemical processes of nitrogen and of the elements involved in redox processes (Fe, Mn, Cr and Sn). The seasonal variability of water characteristics, especially during the spring, was observed. The variability of silty soil samples was described by four principal components, the strongest influence being attributed to rare earth elements (52.2%). The ANOVA-PCA provided deeper information compared to Gibbs and Piper diagrams and the correlation analysis.     

Characteristic Zero Loop Space Homology of Two-Cones

Given a principal ideal domain R of characteristic zero, containing1/2, and a two-cone X of appropriate connectedness and dimension,we present sufficient algebraic conditions for the Hopf algebraFH(X; R) to be isomorphic with the universal enveloping algebraof an R-free graded Lie algebra; here, F stands for free part(that is, quotient by the R-torsion), H for homology, and forthe Moore loop space functor. 2000 Mathematics Subject Classification55P35, 55P62, 57T05, 17B70, 17B35.     

A steady stratified purely azimuthal flow representing the Antarctic Circumpolar Current

We construct an explicit steady stratified purely azimuthal flow for the governing equations of geophysical fluid dynamics. These equations are considered in a setting that applies to the Antarctic Circumpolar Current, accounting for eddy viscosity and forcing terms.     

Minimal spaser threshold within electrodynamic framework: Shape,size and modes

It is known (yet often ignored) from quantum mechanical or energetic considerations, that the threshold gain of the quasi‐static spaser depends only on the dielectric functions of the metal and the gain material. Here, we derive this result from the purely classical electromagnetic scattering framework. This is of great importance, because electrodynamic modelling is far simpler than quantum mechanical one. The influence of the material dispersion and spaser geometry are clearly separated; the latter influences the threshold gain only indirectly, defining the resonant wavelength. We show that the threshold gain has a minimum as a function of wavelength. A variation of nanoparticle shape, composition, or spasing mode may shift the plasmonic resonance to this optimal wavelength, but it cannot overcome the material‐imposed minimal gain. Furthermore, retardation is included straightforwardly into our framework; and the global spectral gain minimum persists beyond the quasi‐static limit. We illustrate this with two examples of widely used geometries: Silver spheroids and spherical shells embedded in and filled with gain materials.