Sequentially continuous non-linear fundamental systems of solutions of affine equations in locally convex spaces

According to the Mickael's selection theorem any surjective continuous linear operator from one Fr\'echet space onto another has a continuous (not necessarily linear) right inverse. Using this theorem Herzog and Lemmert proved that if $E$ is a Fr\'echet space and $T:E\to E$ is a continuous linear operator such that the Cauchy problem $\dot x=Tx$, $x(0)=x_0$ is solvable in $[0,1]$ for any $x_0\in E$, then for any $f\in C([0,1],E)$, there exists a continuos map $S:[0,1]\times E\to E$, $(t,x)\mapsto S_tx$ such that for any $x_0\in E$, the function $x(t)=S_tx_0$ is a solution of the Cauchy problem $\dot x(t)=Tx(t)+f(t)$, $x(0)=x_0$ (they call $S$ a fundamental system of solutions of the equation $\dot x=Tx+f$). We prove the same theorem, replacing "continuous" by "sequentially continuous" for locally convex spaces from a class which contains strict inductive limits of Fr\'echet spaces and strong duals of Fr\'echet--Schwarz spaces and is closed with respect to finite products and sequentially closed subspaces. The key-point of the proof is an extension of the theorem on existence of a sequentially continuous right inverse of any surjective sequentially continuous linear operator to some class of non-metrizable locally convex spaces.

Characterization of T-type calcium current and its contribution to electrical activity in rabbit urethra.

Rabbit urethral smooth muscle cells were studied at 37 degrees C by using the amphotericin B perforated-patch configuration of the patch-clamp technique, using Cs(+)-rich pipette solutions. Two components of current, with electrophysiological and pharmacological properties typical of T- and L-type Ca(2+) currents, were recorded. Fitting steady-state inactivation curves for the L current with a Boltzmann equation yielded a V(1/2) of -41 +/- 3 mV. In contrast, the T current inactivated with a V(1/2) of -76 +/- 2 mV. The L currents were reduced by nifedipine (IC(50) = 225 +/- 84 nM), Ni(2+) (IC(50) = 324 +/- 74 microM), and mibefradil (IC(50) = 2.6 +/- 1.1 microM) but were enhanced when external Ca(2+) was substituted with Ba(2+). The T current was little affected by nifedipine at concentrations

Liquid-liquid miscibility and volumetric properties of aqueous solutions of ionic liquids as a function of temperature

The volumetric properties of seven {water + ionic liquid} binary mixtures have been studied as a function of temperature from (293 to 343) K. The phase behaviour of the systems was first investigated using a nephelometric method and excess molar volumes were calculated from densities measured using an Anton Paar densimeter and fitted using a Redlich-Kister type equation. Two ionic liquids fully miscible with water (1-butyl-3-methylimidazolium tetrafluoroborate ([CCIm][BF]) and 1-ethyl-3-methylimidazolium ethylsulfate ([CCIm][EtSO])) and five ionic liquids only partially miscible with water (1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([CCIm][NTf]), 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([CCIm][NTf]), 1-butyl-3-methylimidazolium hexafluorophosphate ([CCIm][PF]), 1-butyl-3-methylpyrrolidinium bis(trifluoromethylsulfonyl)imide ([CCPyrro][NTf]), and butyltrimethylammonium bis(trifluoromethylsulfonyl)imide ([N][NTf])) were chosen. Small excess volumes (less than 0.5 cm · mol at 298 K) are obtained compared with the molar volumes of the pure components (less than 0.3% of the molar volume of the pure ionic liquid). For all the considered systems, except for {[CCIm][EtSO] + water}, positive excess molar volumes were calculated. Finally, an increase of the non-ideality character is observed for all the systems as temperature increases. © 2009 Elsevier Ltd. All rights reserved.

An Investigation into the Dissolution Properties of Celecoxib Melt Extrudates: Understanding the Role of Polymer Type and Concentration in Stabilizing Supersaturated Drug Concentrations

In this study, the dissolution properties of celecoxib (CX) solid dispersions manufactured from Eudragit 4155F and polyvinylpyrrolidone (PVP) were evaluated. Hot-melt extrusion (HME) technology was used to prepare amorphous solid dispersions of drug/polymer binary systems at different mass ratios. The drug concentrations achieved from the dissolution of PVP and Eudragit 4155F solid dispersions in phosphate buffer, pH 7.4 (PBS 7.4) were significantly greater than the equilibrium solubility of CX (1.58 µg/mL). The degree of supersaturation increased significantly as the polymer concentration within the solid dispersion increased. The maximum drug concentration achieved by PVP solid dispersions did not significantly exceed the apparent solubility of amorphous CX. The predominant mechanism for achieving supersaturated CX concentrations in PBS 7.4 was attributed to stabilization of amorphous CX during dissolution. Conversely, Eudragit 4155F solid dispersions showed significantly greater supersaturated drug solutions particularly at high polymer concentrations. For example, at a drug/polymer ratio of 1:9, a concentration of 100 µg/mL was achieved after 60 min that was stable (no evidence of drug recrystallization) for up to 72 h. This clearly identifies the potential of Eudragit 4155F to act as a solubilizing agent for CX. These findings were in good agreement with the results from solubility performed using PBS 7.4 in which Eudragit 4155F had been predissolved. In these tests, Eudragit 4155F significantly increased the equilibrium solubility of CX. Solution 1H NMR spectra were used to identify drug/polymer interactions. Deshielding of CX aromatic protons (H-1a and H-1b) containing the sulfonamide group occurred as a result of dissolution of Eudragit 4155F solid dispersions, whereas deshielding of H-1a protons and shielding of H-1b protons occurred as a result of the dissolution of PVP solid dispersions. In principle, it is reasonable to suggest that the different drug/polymer interactions observed give rise to the variation in dissolution observed for the two polymer/drug systems.

The birth place of the type Ic supernova 2007gr

We report our attempts to locate the progenitor of the peculiar Type Ic SN 2007gr in Hubble Space Telescope (HST) preexplosion images of the host galaxy, NGC 1058. Aligning adaptive optics Altair/NIRI imaging of SN 2007gr from the Gemini ( North) Telescope with the preexplosion HST WFPC2 images, we identify the supernova (SN) position on the HST frames with an accuracy of 20 mas. Although nothing is detected at the SN position, we show that it lies on the edge of a bright source 134 +/- 23 mas (6.9 pc) from its nominal center. On the basis of its luminosity, we suggest that this object is possibly an unresolved, compact, and coeval cluster and that the SN progenitor was a cluster member, although we note that model profile fitting favors a single bright star. We find two solutions for the age of this assumed cluster: 7 -/+ 0.5 Myr and 20 - 30 Myr, with turnoff masses of 28 +/- M-circle dot and 12 - 9 M-circle dot, respectively. Preexplosion ground-based K- band images marginally favor the younger cluster 4 age/higher turnoff mass. Assuming the SN progenitor was a cluster member, the turnoff mass provides the best estimate for its initial mass. More detailed observations, after the SN has faded, should determine whether the progenitor was indeed part of a cluster and, if so, allow an age estimate to within similar to 2 Myr, thereby favoring either a high-mass single star or lower-mass interacting binary progenitor.

Note on the single-shock solutions of the Korteweg-de Vries-Burgers equation

The well-known shock solutions of the Korteweg-de Vries-Burgers equation are revisited, together with their limitations in the context of plasma (astro)physical applications. Although available in the literature for a long time, it seems to have been forgotten in recent papers that such shocks are monotonic and unique, for a given plasma configuration, and cannot show oscillatory or bell-shaped features. This uniqueness is contrasted to solitary wave solutions of the two parent equations (Korteweg-de Vries and Burgers), which form a family of curves parameterized by the excess velocity over the linear phase speed.

Combinatorial Frequency Generation in Quasi-Periodic Stacks of Nonlinear Dielectric Layers

Three-wave mixing in quasi-periodic structures (QPSs) composed of nonlinear anisotropic dielectric layers, stacked in Fibonacci and Thue-Morse sequences, has been explored at illumination by a pair of pump waves with dissimilar frequencies and incidence angles. A new formulation of the nonlinear scattering problem has enabled the QPS analysis as a perturbed periodic structure with defects. The obtained solutions have revealed the effects of stack composition and constituent layer parameters, including losses, on the properties of combinatorial frequency generation (CFG). The CFG features illustrated by the simulation results are discussed. It is demonstrated that quasi-periodic stacks can achieve a higher efficiency of CFG than regular periodic multilayers.

Effect of carbohydrate type and concentration on polyhydroxy alcohol and trehalose content of conidia of three entomopathogenic fungi

The entomopathogenic fungi Beauveria bassiana, Metarhizium anisopliae and Paecilomyces farinosus were cultured on solid agar media containing different carbohydrate components (glycerol, glucose, trehalose or starch) at concentrations of ≤ 142.7 g added carbon 1-1 for 30 d at 25°C. The water activity (a(w)) of the media ranged from 0.925 to 0.998. Growth of M. anisopliae and P. farinosus was stimulated between 0.975 and 0.995 a(w) on glucose media and that of P. farinosus at 0. 975 a(w) on glycerol media. At < 0.970 a(w), growth of each fungal species was significantly reduced (P < 0.05). Polyhydroxy alcohols (polyols) and trehalose were extracted from conidia produced on different media and quantified using HPLC. Total polyol content of conidia produced on glucose media varied between 5.2 and 52.2 mg g-1 for B. bassiana, 77.3 and 90.3 mg g-1 for M. anisopliae, and 26.7 and 76.1 mg g-1 for P. farinosus. The amounts of specific polyols in conidia varied significantly from media of different glucose concentrations. Mannitol was the predominant polyol in conidia of all three species, with conidia of M. anisopliae, for example, containing as much as 75.2 mg mannitol g-1 when cultured on glucose media. The amount of the lower molecular mass polyols glycerol and erythritol was greater in conidia produced on glucose media with > 50.0 g added carbon 1-1 than that in conidia produced at lower glucose concentrations. Conidia contained between 10.8 and 20.8 mg glycerol plus erythritol g-1 on glucose media with 142.7 g added carbon 1-1, depending on species. Conversely, conidia of B. bassiana and P. farinosus contained maximum amounts of trehalose ( ≤ 23.5 mg g-1) when produced on glucose media with < 50.0 g added carbon l-1, and trehalose content was considerably less at higher glucose concentrations. There were accumulations of glycerol and erythritol in conidia of all three species when grown on glycerol media with > 25.0 g added carbon 1-1; conidia of B. bassiana contained up to 154.0 mg glycerol plus erythritol g-1. hen B. bassiana and P. farinosus were grown on trehalose media, conidia contained up to 222.1 mg trehalose g-1. By contrast, conidia of M. anisopliae contained < 17.0 mg trehalose g-1 under all conditions tested. The water availability of solutions of different polyols is discussed in relation to their potential to act in osmotic adjustment during germination. The ability to manipulate polyol and trehalose content of fungal propagules may be critical in enhancing the storage life and efficacy of biological control agents.

Solutions of fourth-order parabolic equation modeling thin film growth

In this paper we study the well-posedness for a fourth-order parabolic equation modeling epitaxial thin film growth. Using Kato's Method [1], [2] and [3] we establish existence, uniqueness and regularity of the solution to the model, in suitable spaces, namelyC⁰([0,T];L^p(Ω)) where  with 1<α<2, n∈N and n≥2. We also show the global existence solution to the nonlinear parabolic equations for small initial data. Our main tools are L_p–L_q-estimates, regularization property of the linear part of e^−tΔ2 and successive approximations. Furthermore, we illustrate the qualitative behavior of the approximate solution through some numerical simulations. The approximate solutions exhibit some favorable absorption properties of the model, which highlight the stabilizing effect of our specific formulation of the source term associated with the upward hopping of atoms. Consequently, the solutions describe well some experimentally observed phenomena, which characterize the growth of thin film such as grain coarsening, island formation and thickness growth.

Symmetries and exact solutions of KP equation with an arbitrary nonlinear term

The generalized KP (GKP) equations with an arbitrary nonlinear term model and characterize many nonlinear physical phenomena. The symmetries of GKP equation with an arbitrary nonlinear term are obtained. The condition that must satisfy for existence the symmetries group of GKP is derived and also the obtained symmetries are classified according to different forms of the nonlinear term. The resulting similarity reductions are studied by performing the bifurcation and the phase portrait of GKP and also the corresponding solitary wave solutions of GKP
equation are constructed.

Influence of plasticizer type and storage conditions on properties of poly(methyl vinyl ether-co-maleic anhydride) bioadhesive films

Poly(methyl vinyl ether-co-maleic anhydride) formed films from aqueous formulations with characteristics that are ideal as a basis for producing a drug-containing bioadhesive delivery system when plasticized with a monohydroxyl functionalized plasticizer. Hence, films containing a novel plasticizer, tripropylene glycol methyl ether (TPME), maintained their adhesive strength and tensile properties when packaged in aluminized foil for extended periods of time. Films plasticized with commonly used polyhydric alcohols, such as the glycerol in this study, underwent an esterification reaction that led to polymer crosslinking, as shown in NMR studies. These revealed the presence of peaks in the ester/carbonyl region, suggesting that glyceride residue formation had been initiated. Given the polyfunctional nature of glycerol, progressive esterification would result in a polyester network and an accompanying profound alteration in the physical characteristics. Indeed, films became brittle over time with a loss of both the aqueous solubility and bioadhesion to porcine skin. In addition, a swelling index was measurable after 7 days, a property not seen with those films containing TPME. This change in bioadhesive strength and pliability was independent of the packaging conditions, rendering the films that contain glycerol as unsuitable as a basis for topical bioadhesive delivery of drug substances. Consequently, films containing TPME have potential as an alternative formulation strategy.

Rapid Early Growth is Associated With Increased Risk of Childhood Type 1 Diabetes in Various European Populations

OBJECTIVE: To confirm that early growth is associated with type 1 diabetes risk in European children and elucidate any role of infant feeding. RESEARCH DESIGN AND METHODS: Five centers participated, each with a population-based register of type 1 diabetes diagnosed at