Gauge Gravitational Field in a Fractal Space-Time

Considering the fractal structure of space-time, the scale relativity theory in the topological dimension DT = 2 is built. In such a conjecture, the geodesics of this space-time imply the hydrodynamic model of the quantum mechanics. Subsequently, the gauge gravitational field on a fractal space-time is given. Then, the gauge group, the gauge-covariant derivative, the strength tensor of the gauge field, the gauge-invariant Lagrangean, the field equations of the gauge potentials and the gauge energy-momentum tensor are determined. Finally, using this model, a Reissner- Nordstrom type metric is obtained.     

Computing Topological Entropy in a Space of Quartic Polynomials

This paper adds a computational approach to a previous theoretical result illustrating how the complexity of a simple dynamical system evolves under deformations. The algorithm targets topological entropy in the 2-dimensional family P ^Q of compositions of two logistic maps. Estimation of the topological entropy is made possible by the correspondence between P ^Q and a subfamily of sawtooth maps P ^T , and is based on the well-known fact that the kneading-data of a map determines its entropy. A complex search for kneading-data in P ^T turns out to be computationally fast and reliable, delivering good entropy estimates. Finally, the algorithm is used to produce a picture of the entropy level-sets in P ^Q , as illustration to theoretical results such as Hu (Ph.D. thesis, CUNY, 1995) and Radulescu (Discrete Cont. Dyn. Syst. 19(1):139–175, 2007).     

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.     

Three soliton contribution to the specific heat in sine-Gordon systems

The three soliton contribution to the specific heat of a classical easy-plane ferromagnet chain is calculated using asymptotic methods from the theory of differential equations depending on a large parameter.     

Transformation of 5-hydroxymethylene-5H-6,7-dihydrodibenzo[a,c]cyclohepten-6-one over Ru-containing BEA zeolites

Ru–BEA catalysts with 1.0–2.5 wt.% Ru were prepared by ion exchange. The acidic properties of these catalysts were investigated using deuterated acetonitrile, pyridine, and 2,6-di-tert-butyl-pyridine. The deposited Ru was studied by CO-FTIR spectroscopy. The materials were tested as catalysts in the hydrogenation of a conjugated cyclic keto–enol, namely, 5-hydroxymethylene-5H-6,7-dihydrodibenzo[a,c]cyclohepten-6-one. Beside hydrogenation, hydrogenolysis products were identified by GC–MS and ¹H NMR techniques. Relations were sought between the selectivity and some physicochemical properties of the catalyst.     

Chemogenetic protein engineering: an efficient tool for the optimization of artificial metalloenzymes

Artificial metalloenzymes, based on the incorporation of a catalytically active organometallic moiety within a host protein, lie at the interface between organometallic and enzymatic catalysis. In terms of activity, reaction repertoire, substrate range and operating conditions, they take advantage of the versatility of the organometallic chemistry. In contrast, the enantioselectivity is determined by the biomolecular scaffold, which provides a well defined second coordination sphere to the organometallic moiety, reminiscent of enzymes. The attractive feature of such systems is their optimization potential, which combines chemical and genetic methods (i.e. chemogenetic) to screen diversity space. This feature article describes the implementation of such an optimization protocol for artificial transfer hydrogenases, for which we have the most detailed understanding.     

Magnetic beads-based immunoassay as a sensitive alternative for atrazine analysis

A new immunoassay strategy for sensitive atrazine determination based on magnetic beads is reported. The immuno-method is a competitive solid-phase immunoassay where the anti-atrazine antibody is immobilized on the magnetic beads surface and fixed at the reaction cell bottom using a simple magnet, which generates a magnetic field. Analyte and HRP (horseradish peroxidase) tracer compete for active sites of antibody. After the immunointeractions antibody-analyte and antibody-tracer, atrazine quantification from the sample is performed by injection of the chemiluminescence substrate (luminol, hydrogen peroxide and p-iodophenol). Different antibodies (polyIgG anti-atrazine Ab I and affinity purified polyIgG anti-atrazine AbI) were tested in this configuration. Also, optimum concentration of antibody-covered magnetic beads was set up (8 mg/l Ab II). Finally, the performance of magnetic beads-based immunoassay for atrazine determination was evaluated demonstrating that the magnetic beads-based immunoassay is one of the most sensitive method for atrazine determination (LoD = 3 pg/l, IC₅₀ = 37 pg/l, DR = 10-1000 pg/l).     

Cyclometalated platinum(II) complexes of pyrazole-based, N=C=N-coordinating, terdentate ligands: the contrasting influence of pyrazolyl and pyridyl rings on luminescence

1,3-Bis(1-pyrazolyl)-5-methyl-benzene, HL(2), undergoes cyclometalation at the C(2) position upon reaction with K(2)PtCl(4), to generate an N=C=N-coordinated complex, PtL(2)Cl. This compound is luminescent in degassed solution at 298 K, emitting in the blue region of the spectrum on the microsecond time scale (lambda(max) = 453 nm, tau = 4.0 micros, Phi(lum) = 0.02, in CH(2)Cl(2)). Compared to the analogous complex Pt(dpyb)Cl that incorporates pyridyl rather than pyrazole rings {dpybH = 1,3-di(2-pyridyl)-benzene}, the excited state is displaced to higher energy by 1700 cm(-1). This effect is rationalized in terms of the poorer pi-acceptor nature of pyrazolyl compared to pyridyl rings, leading to destabilization of the lowest unoccupied molecular orbital, which is largely localized on the heteroaromatic rings in both cases. Cyclic voltammetry and density functional theory calculations reinforce this interpretation, and suggest that the lowest-energy excited state is probably best described as heavily mixed pi(L)/d(Pt)/p(Cl) --> pi*(L) (IL/MLCT/LLCT) in character. 5-Aryl-substituted analogues of HL(2) are accessible in three steps from 1,3,5-tribromobenzene by Pd-catalyzed cross-coupling with aryl boronic acids, followed by copper-catalyzed bromo-iodo exchange, and subsequent amination with pyrazole under relatively mild conditions also catalyzed by copper. The corresponding Pt(II) complexes display red-shifted and more intense luminescence compared to PtL(2)Cl. Ligands incorporating one pyrazole and one pyridyl ring are also accessible; for example, 1-(1-pyrazolyl)-3-(2-pyridyl)benzene, HL(6). Their complexes are highly luminescent in solution; for example, for PtL(6)Cl, lambda(max) = 487 nm, tau = 6.9 micros, Phi(lum) = 0.55, in dilute solution in CH(2)Cl(2). At elevated concentrations, PtL(6)Cl displays an additional excimeric emission band that is substantially blue-shifted compared to that displayed by Pt(dpyb)Cl (bands centered at 645 and 695 nm, respectively), indicating that the presence of the pyrazole ring destabilizes the excimer. The introduction of a methyl substituent into the central aryl ring of such complexes is sufficient to eliminate the excimer emission.