On geodesic completeness for Riemannian metrics on smooth probability densities

The geometric approach to optimal transport and information theory has triggered the interpretation of probability densities as an infinite-dimensional Riemannian manifold. The most studied Riemannian structures are the Otto metric, yielding the \(L^2\)-Wasserstein distance of optimal mass transport, and the Fisher–Rao metric, predominant in the theory of information geometry. On the space of smooth probability densities, none of these Riemannian metrics are geodesically complete—a property desirable for example in imaging applications. That is, the existence interval for solutions to the geodesic flow equations cannot be extended to the whole real line. Here we study a class of Hamilton–Jacobi-like partial differential equations arising as geodesic flow equations for higher-order Sobolev type metrics on the space of smooth probability densities. We give order conditions for global existence and uniqueness, thereby providing geodesic completeness. The system we study is an interesting example of a flow equation with loss of derivatives, which is well-posed in the smooth category, yet non-parabolic and fully non-linear. On a more general note, the paper establishes a link between geometric analysis on the space of probability densities and analysis of Euler–Arnold equations in topological hydrodynamics.     

Further Validation of the Quartic Concentration Profile Approximation for Describing Intraparticle Transport in Cyclic Adsorption Processes

Models developed previously by the authors that describe nonlinear adsorption, and simultaneous pore and surface diffusion in a single particle, that are based on intraparticle quartic and parabolic concentration profile approximations, and that utilize the summation of the gas and adsorbed phases approach in the material balance formulations, were further validated under more diverse, yet more realistic, cycling conditions. Periodic square, sinusoidal and triangular wave functions were used to more accurately represent the periodic boundary conditions that the external surface of an adsorbent particle may be exposed to during repeated adsorption and desorption cycles in a fixed bed adsorber. Analytical solutions that describe the periodic uptake and release of the adsorbate by the adsorbent were obtained for all three periodic wave functions, and for both the quartic and parabolic profile approximations. By comparing the predictions obtained from both models with the exact numerical solution, the superiority of the quartic model over the parabolic model was clearly demonstrated for all wave functions, and for a wide range of adsorbate-adsorbent systems and bulk concentrations. Excellent agreement between the quartic and exact models was obtained in most cases. In general, the predictions improved as the wave function changed more gradually with time (triangular more gradual than sinusoidal and sinusoidal more gradual than square), as the degree of mathematical linearity of the adsorbate-adsorbent system increased, and as the maximum external surface concentration decreased (an isotherm nonlinearity effect). Subtle differences in the predictive ability of the new approximate models, stemming from the use of the different wave functions, were exposed. Overall, these results exemplify the importance of comparing the predictive ability of new approximate models that describe intraparticle transport under more diverse cycling conditions than are typically utilized in the literature, which has been dominated by the square wave function.     

Quantification of Eugenol in Cinnamomum tamala Nees and Eberm. Leaf Powder by High-Performance Thin-Layer Chromatography

JPC – Journal of Planar Chromatography – Modern TLC - Eugenol is used as a flavor in the food industry, has a variety of biological activity, and can serve as a biomarker. Because...     

ON THE ORIGIN OF GLOW PEAKS IN EUGLENA CELLS, SPINACH CHLOROPLASTS AND SUBCHLOROPLAST FRAGMENTS ENRICHED IN SYSTEM I OR II

Abstract— The origin of glow peaks (thermoluminescence) was investigated in isolated spinach chloroplasts and Euglena cells by pretreatment with various concentrations of 3-(3,4 dichlorophenyl)-1,1-dimethylurea (DCMU)?, different light intensities, and after mild heating at various temperatures. Experiments are also reported on subchloroplast fractions enriched in pigment systems I (PSI) or II (PSII) (prepared under conditions to reduce destruction of membranes by excessive detergent contact). These results provide the following, most likely, suggestion for the origin of glow peaks: (1) Z peak originates in metastable states; it is insensitive to DCMU, temperature (320–328 K), and appears only when other peaks are saturated (10 Wm^-2). (2) Peak I involves the use of a reducing entity A (plastoquinone) beyond Q (the primary electron acceptor of pigment system II, PSII), or, of a high “S” state (charge accumulator) of oxygen evolving system; its intensity is dramatically reduced by low concentrations (1 μM) of DCMU, and, there is more of it in PSII than in PSI particles. (3) Peak II is due to reaction of Q^- with the “S” states of the oxygen evolving system; its intensity increases upon the addition of low concentrations of DCMU, at the expense of peak I; it is most sensitive to mild heating, and there is more of it in PSII than in PSI particles. (4) Peak III was not studied here as it was not resolved in most of our preparations. (5) Peak IV is from both pigment system I and II; it is sensitive to heating (>50°C), is somewhat sensitive to DCMU, and is present in both PSI and PSII particles. (6) Peak V is from PSI; it is least sensitive to mild heating, and it is enriched in PSI particles. The present studies have extended our knowledge regarding the origin of glow peaks in spinach chloroplasts and Euglena cells; in particular, the involvement of the charge accumulating “S” states of oxygen evolution (for peaks I and II) and of system I (for peak V) are emphasized in this paper.     

Capillary Electrophoretic Determination of Gatifloxacin from Pharmaceutical Preparation

Capillary zone electrophoresis has been used for the determination of gatifloxacin from its pharmaceutical preparation (tablets), using fused silica capillary. Separation was performed after hydrodynamic injection; the separation was achieved by applying 21 Kv voltage. Phosphate buffer solution (pH 9.5) was used as separation electrolyte. Detection was at 280 nm using a UV- detector. Under these experimental conditions the analysis takes 8 min. A linearity range for gatifloxacin was between 20.0 g mL^–1 to 60.0 g mL^–1. The method was validated and was found to be specific, precise, accurate, reproducible and robust and can be applied for the routine analysis of gatifloxacin from formulation and bulk drug.     

Simultaneous RP-LC Determination of Losartan Potassium, Ramipril, and Hydrochlorothiazide in Pharmaceutical Preparations

A simple, rapid, and precise reversed-phase high-performance liquid chromatographic method has been developed for simultaneous determination of losartan potassium, ramipril, and hydrochlorothiazide. The three drugs were separated on a 150 mm × 4.6 mm i.d., 5 μm particle, Cosmosil C₁₈ column. The mobile phase was 0.025 m sodium perchlorate–acetonitrile, 62:38 (v/v), containing 0.1% heptanesulphonic acid, pH adjusted to 2.85 with orthophosphoric acid, at a flow rate of 1.0 mL min⁻¹. UV detection was performed at 215 nm. The method was validated for linearity, accuracy, precision, and limit of quantitation. Linearity, accuracy, and precision were acceptable in the ranges 35–65 μg mL⁻¹ for losartan, 1.75–3.25 μg mL⁻¹ for ramipril, and 8.75–16.25 μg mL⁻¹ for hydrochlorothiazide.     

Acetic acid effects on enhancement of growth rate and reduction of amorphous carbon deposition on CNT arrays along a growth window in a floating catalyst reactor

The mm-long carbon nanotube (CNT) arrays were grown in a floating catalyst reactor, using xylene-ferrocene and a small amount of acetic acid as the feed. The CNT arrays deposited on a quartz substrate at several positions along the reactor were extensively characterized using Raman spectroscopy, scanning electron microscopy, X-ray diffraction, high-resolution transmission electron microscopy, and optical microscopy. Various characterization methods consistently reveal that the acetic acid additive to the feed alleviates deposition of amorphous carbon layer, which gradually thickens CNTs along the reactor. The acetic acid also resulted in a higher growth rate along the so-called growth window, where CNT arrays are deposited on the quartz substrate. High-performance liquid chromatography of extracted byproducts (PAHs) confirmed the presence of some polycyclic aromatic hydrocarbons. The solid weight of PAHs decreased upon addition of ferrocene as the catalyst precursor, as well as of acetic acid to xylene feed. The results suggest that primary light products of xylene pyrolysis can be competitive reactants for both catalytic and subsequent pyrolytic reactions. They may also be more efficient feeds for CNT growth than xylene itself.     

High-Performance Thin-Layer Chromatographic Determination of Idebenone in Pharmaceutical Preparations

JPC – Journal of Planar Chromatography – Modern TLC - A high performance thin layer chromatographic method has been developed for the determination of idebenone in pharmaceutical...