Existence and uniqueness of best proximity points in geodesic metric spaces

A mapping T:A∪B→A∪B such that T(A)⊆B and T(B)⊆A is called a cyclic mapping. A best proximity point x for such a mapping T is a point such that d(x,Tx)= dist(A,B). In this work we provide different existence and uniqueness results of best proximity points in both Banach and geodesic metric spaces. We improve and extend some results on this recent theory and give an affirmative partial answer to a recently posed question by Eldred and Veeramani in [A.A. Eldred, P. Veeramani Existence and convergence of best proximity points, J. Math. Anal. Appl. 323 (2) (2006) 1001-1006].     

Leucoxol,a new diterpenoid from acacia leucophloea. X-ray structure determination

From $\text{Acacia leucophloea}$ (Roxb.) Willd. (Mimosaceae) the new diterpenoid 11α, 16-epoxy-1β, 15$\text{R}$-dihydroxy-isopimar-8(14)-ene (leucoxol) has been isolated. Its structure was determined by X-ray diffraction analysis.     

Photoprotective properties of a hydrophilic extract of the fern Polypodium leucotomos on human skin cells

The effect of a hydrophilic extract of the fern Polypodium leucotomos (PLE) has been investigated in terms of photoprotection against UV-induced cell damage. PLE efficiently preserved human fibroblast survival and restored their proliferative capability when the cells were exposed to UVA light. This effect was specific and dose-dependent. Photoprotection was not restricted to fibroblasts, as demonstrated by its effect on survival and proliferation of the human keratinocyte cell line HaCat. Finally, treatment of the cells with PLE prevented UV-induced morphological changes in human fibroblasts, namely disorganisation of F-actin-based cytoskeletal structures, coalescence of the tubulin cytoskeleton and mislocalization of adhesion molecules such as cadherins and integrins. Our in vitro results demonstrate the photoprotective effect of PLE on human cells and support its use in the preventive treatment of sunburning and skin pathologies associated with UV-mediated damage.     

Density and wave function analysis of actinide complexes: what can fuzzy atom, atoms-in-molecules, Mulliken, Lowdin, and natural population analysis tell us?

Recent advances in computational methods have made it possible to calculate the wave functions for a wide variety of simple actinide complexes. Equally important is the ability to analyze the information contained therein and produce a chemically meaningful understanding of the electronic structure. Yet the performance of the most common wave function analyses for the calculation of atomic charge and bond order has not been thoroughly investigated for actinide systems. This is particularly relevant because the calculation of charge and bond order even in transition metal complexes is known to be fraught with difficulty. Here we use Mulliken, Lowdin, natural population analysis, atoms-in-molecules (AIM), and fuzzy atom techniques to determine the charges and bond orders of UO(2)(2+), PuO(2)(2+), UO(2), UO(2)Cl(4)(2-), UO(2)(CO)(5)(2+), UO(2)(CO)(4)(2+), UO(2)(CN)(5)(3-), UO(2)(CN)(4)(2-), UO(2)(OH)(5)(3-), and UO(2)(OH)(4)(2-). This series exhibits a clear experimental and computational trend in bond lengths and vibrational frequencies. The results indicate that Mulliken and Lowdin populations and bond orders are unreliable for the actinyls. Natural population analysis performs well after modification of the partitioning of atomic orbitals to include the 6d in the valence space. The AIM topological partitioning is insensitive to the electron donating ability of the equatorial ligands and the relative atomic volume of the formally U(VI) center is counterintuitively larger than that of O(2-) in the UO(2)(2+) core. Lastly, the calibrated fuzzy atom method yields reasonable bond orders for the actinyls at significantly reduced computational cost relative to the AIM analysis.     

Interaction of epothilone analogs with the paclitaxel binding site: relationship between binding affinity, microtubule stabilization, and cytotoxicity

The interactions of epothilone analogs with the paclitaxel binding site of microtubules were studied. The influence of chemical modifications in the C15 side chain and in C12 on binding affinity and microtubule elongation was characterized. Modifications favorable for binding affinity are (1). a thiomethyl group at C21 of the thiazole side chain, (2). a methyl group at C12 in S configuration, (3). a pyridine side chain with C15 in S configuration, and (4). a cyclopropyl moiety between C12 and C13. The same modification in different ligands has similar effect on affinity, allowing good structure-affinity characterization. The correlation between binding, microtubule stabilization, and cytotoxicity of the compounds has been determined, showing differential effects of the modifications. The binding constants correlate well with IC(50) values, demonstrating that affinity measurements are a useful tool for drug design.     

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.     

Model Systems for Evidencing the Mediator Role of Riboflavin in the UVA Cross-Linking Treatment of Keratoconus

Riboflavin under UVA radiation generates reactive oxygen species (ROS) that can induce various changes in biological systems. Under controlled conditions, these processes can be used in some treatments for ocular or dermal diseases. For instance, corneal cross-linking (CXL) treatment of keratoconus involves UVA irradiation combined with riboflavin aiming to induce the formation of new collagen fibrils in cornea. To reduce the damaging effect of ROS formed in the presence of riboflavin and UVA, the CXL treatment is performed with the addition of polysaccharides (dextran). Hyaluronic acid is a polysaccharide that can be found in the aqueous layer of the tear film. In many cases, keratoconus patients also present dry eye syndrome that can be reduced by the application of topical solutions containing hyaluronic acid. This study presents physico-chemical evidence on the effect of riboflavin on collagen fibril formation revealed by the following methods: differential scanning microcalorimetry, rheology, and STEM images. The collagen used was extracted from calf skin that contains type I collagen similar to that found in the eye. Spin trapping experiments on collagen/hyaluronic acid/riboflavin solutions evidenced the formation of ROS species by electron paramagnetic resonance measurements.     

Adsorption of procaine at the mercury/electrolyte solution interface

The adsorption of the local anaesthetic procaine hydrochloride at the mercury/electrolyte interface solution is followed using capacitance measurements. The adsorption is studied at various procaine concentrations, in potassium chloride, potassium bromide or potassium fluoride used as supporting electrolytes, and at various pH values and temperatures. Procaine has basic properties with two acidity constants K. The results indicate the way the procaine molecules orientate at the interface. In all cases studied no hemimicelles or condensed film are observed.