On existence of cone-maximal points in real topological linear spaces

A sufficient condition for a convex coneC in a Hausdorff topological linear space is given in order to ensure the existence of cone-maximal points. The condition becomes a necessary one in a topological linear space with a countable local base, that is, if the space is pseudometrizable. The paper extends known results to infinite dimensions and we answer Corley’s question in the affirmative with the exception of a pathological case.     

Resonantly Interacting Weakly Nonlinear Hyperbolic Waves. I. A Single Space Variable

We present a systematic asymptotic theory for resonantly interacting weakly nonlinear hyperbolic waves in a single space variable. This theory includes as a special case the theory of nonresonant interacting waves for general hyperbolic systems developed recently by J. Hunter and J. B. Keller, when specialized to a single space variable. However, we are also able to treat the general situation when resonances occur in the hyperbolic system. Such resonances are the typical case when the hyperbolic system has at least three equations and when, for example, small-amplitude periodic initial data are prescribed. In the important physical example of the 3 × 3 system describing compressible fluid flow in a single space variable, the resonant asymptotic theory developed by the authors yields, as limit equations, a pair of inviscid Burgers equations coupled through a linear integral operator with known kernel defined through the initial data for the entropy wave. (In the general case we give many new conditions guaranteeing nonresonance for a given hyperbolic system with prescribed initial data, as well as other new structural conditions which imply that resonance occurs.) A method for treating resonantly interacting waves in several space variables, together with applications, will be developed by the authors elsewhere.     

Closure Approximations for Passive Scalar Turbulence: A Comparative Study on an Exactly Solvable Model with Complex Features

Some standard closure approximations used in turbulence theory are analyzed by examining systematically the predictions these approximations produce for a passive scalar advection model consisting of a shear flow with a fluctuating cross sweep. This model has a general geometric structure of a jet flow with transverse disturbances, which occur in a number of contexts, and it encompasses a wide variety of possible spatio-temporal statistical structures for the velocity field, including strong long-range correlations. Even though the Eulerian and Lagrangian velocity statistics are not equal and the passive scalar statistics exhibit broader-than-Gaussian intermittency, this model is nevertheless simple enough so that many passive scalar statistics can be computed exactly and compared systematically with the predictions of the closure approximations. Our comparative study illustrates the strength and weaknesses of the closure approximations and points out the physical phenomena that these approximations are able or not able to describe properly. In particular it is shown that the direct interaction approximation (DIA), one of the most sophisticated closure approximations available, fails to reproduce adequately the statistical features of the scalar and may even lead to absdurd predictions, even though the equations it produces are rather complicated and difficult to analyze. Two alternative closure approximations, the Modified DIA (MDIA) and the Renormalized Lagrangian Approximation (RLA), with different levels of sophistication, both are simpler to use than the DIA and perform better. In particular, it is shown that both closure approximations always reproduce exactly the second order statistics for the scalar and that the MDIA is even able to capture intermittency effects.     

Direct structural identification of polysaccharides from red algae by FTIR microspectrometry I: Localization of agar inGracilaria verrucosa sections

Unlike carrageenans, agars have not been studied very extensively by infrared spectroscopy, in so far as the structures of this kind of polygalactanes are not as well defined as carrageenans. However, in a previous work we have carried out a vibrational analysis of both carrageenans and agars and some important assignments of the main absorptions have been made. Consequently, the present work has been undertaken in order to identify agars without any extraction directly in various seaweeds using the infrared microspectrometry method. The main advantage of this method is that the sample consists only of a dehydrated algal section. The red algaeGradlaria verrucosa has been the subject of the present study. In the first place, spectra of extracted agars were recorded, as they can help us to confirm the nature of the compound identified by this technique. In a second stage, spectra of different parts of the sections have been carried out. The comparison between the resulting spectra with those of the extracted polysaccharides, has demonstrated, firstly that the best results are obtained from the cortical area, because, as expected, the agar is mainly located in the cell wall of this area of the algae. Indeed, the feature bands of agars are all observed, especially the intense ones between 1000 and 1100 cm^–1 and the more characteristic absorptions in the wavenumbers range below 1000 cm^–1 so as the ones at 988, 965, 930, 890, 870, 771 and 741 cm^–1. Secondly, it may be also identified in smaller amounts in the medullar area, the cells are greater than in the cortical area and the cytoplasm is preponderent. However, in the latter case a coexisting polysaccharide, present in a considerable quantity and called floridean starch (Its structure is not very well known, as it varies from one algae to another), masks the spectra of agar, as its spectrum is very similar to those of polygalactanes.     

The Effect of Mean Flows on Enhanced Diffusivity in Transport by Incompressible Periodic Velocity Fields

Avellaneda and one of the authors ([1], [3]) have recently established that an upper bound for the enhanced diffusivity in the large scale, long time advection-diffusion with periodic steady incompressible velocity fields has the form where Pe is the Peclet number and is the reciprocal of the Prandtl number. In this paper, flow fields with maximal and minimal enhanced diffusion are studied. Maximal enhanced diffusion requires that in some directions the enhanced diffusion tensor also has the lower bound . For minimal enhanced diffusion, the effect of the velocity field is to boost the enhanced diffusivity by a negligible amount that is bounded by a fixed constant times the bare diffusivity regardless of Peclet number. Stieltjes measure formulas are used to develop a simple, necessary, and sufficient condition for maximal enhanced diffusion and also to characterize minimal enhanced diffusion. It is established here that constant mean flows can have a dramatic effect on maximal and minimal enhanced diffusion. In particular, for flows in two space dimensions, an explicit criterion is developed that guarantees the surprising fact that mean flows with rational ratios typically generate maximal enhanced diffusion through interaction with an arbitrary steady periodic incompressible flow with zero mean. In contrast, a simple criterion for flows without stagnation points is developed here that guarantees that the effect of mean flows with irrational ratios on advection-diffusion in two dimensions creates minimal enhanced diffusion. The theory for the phenomena mentioned above is elementary yet mathematically rigorous. Examples are emphasized throughout this work including a discussion of enhanced diffusivity for a class of flows recently introduced by Childress and Soward [8]. The theory developed here is also supplemented by a series of numerical experiments that both verify the theoretical predictions and display interesting crossover phenomena at rather large but finite Peclet numbers.     

A novel method for screening the glutathione transferase inhibitors

Background  

Glutathione transferases (GSTs) belong to the family of Phase II detoxification enzymes. GSTs catalyze the conjugation of glutathione to different endogenous and exogenous electrophilic compounds. Over-expression of GSTs was demonstrated in a number of different human cancer cells. It has been found that the resistance to many anticancer chemotherapeutics is directly correlated with the over-expression of GSTs. Therefore, it appears to be important to find new GST inhibitors to prevent the resistance of cells to anticancer drugs. In order to search for glutathione transferase (GST) inhibitors, a novel method was designed.     

(Co)polymers of oligo(ethylene glycol) methacrylates—temperature‐induced aggregation in aqueous solution

The synthesis and aggregation behavior of well‐defined thermosensitive (co)polymers of oligo(ethylene glycol) methacrylates (POEGMA) in aqueous solutions were investigated. The cloud points of the POEGMAs solutions were determined by turbidimetry and dynamic light scattering. For POEGMA (co)polymers the cloud point temperature (T_CP) increased linearly with increasing content of more hydrophilic comonomer. The mesoglobules formed by POEGMAs in dilute aqueous solutions above T_CP were studied by light scattering. The size of mesoglobules depended on the concentration and the heating procedures. The aggregates became smaller with decreasing initial concentration of polymer and increasing rates of temperature change. By selecting the proper heating and dilution procedures, the influence of the (co)polymer structure on the size of the mesoglobules could be determined. The size of the mesoglobules decreased with the length of the OEG side chains and increased with increasing content of more hydrophilic comonomer. The light scattering parameters of the mesoglobules—A₂ values and shape factors ${R_{\rm g}\over R_{\rm h}}$ —suggested that the hydrophilic OEG side chains placed at the periphery of the mesoglobules in direct contact with the surrounding water controlled the size of mesoglobules and their stability. Shape factors for all POEGMA mesoglobules indicated that the mesoglobules remained highly hydrated after formation. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

An Approach to Transfer Methods from HPLC to UHPLC Techniques in Some Carbapenems

Stability-indicating LC methods were developed and validated for the quantitative determination of doripenem, meropenem and tebipenem in the presence of their degradation products formed during forced degradation studies. Isocratic HPLC and UHPLC separations were performed with a core–shell Kinetex 1.7, 2.6 and 5 µm, all C18, 100A, 100 × 2.1 mm columns and the mobile phase composed of acetonitrile and 12 mmol L^?1 ammonium acetate in different ratios. The flow rates of the mobile phase were: 0.5 mL min^?1 for 1.7 µm column, and 1.0 mL min^?1 for 2.6 and 5 µm ones. Detection wavelength was 298 nm and temperature was set at 30 °C. All analysed drugs were exposed to stress conditions which caused their hydrolysis and thermal degradation. The methods were validated by evaluation of linearity, accuracy, precision, selectivity and robustness. Proposed methods were successfully applied for the determination of investigated antibiotics during kinetic studies in aqueous solutions and in the solid state. The advantages of chromatographic procedures which are based on the use of C18 stationary phases with different particle sizes in the analysis of selected carbapenems were discussed.