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.

Improving neural network training solutions using regularisation

This paper describes the application of regularisation to the training of feedforward neural networks, as a means of improving the quality of solutions obtained. The basic principles of regularisation theory are outlined for both linear and nonlinear training and then extended to cover a new hybrid training algorithm for feedforward neural networks recently proposed by the authors. The concept of functional regularisation is also introduced and discussed in relation to MLP and RBF networks. The tendency for the hybrid training algorithm and many linear optimisation strategies to generate large magnitude weight solutions when applied to ill-conditioned neural paradigms is illustrated graphically and reasoned analytically. While such weight solutions do not generally result in poor fits, it is argued that they could be subject to numerical instability and are therefore undesirable. Using an illustrative example it is shown that, as well as being beneficial from a generalisation perspective, regularisation also provides a means for controlling the magnitude of solutions. (C) 2001 Elsevier Science B.V. All rights reserved.

Nutrient regulation of pancreatic beta-cell function in diabetes: problems and potential solutions

increasing prevalence of obesity combined with longevity will produce an epidemic of Type 2 (non-insulin-dependent) diabetes in the next 20 years. This. disease is associated with defects in insulin secretion, specifically abnormalities of insulin secretory kinetics and pancreatic beta-cell glucose responsiveness. Mechanisms underlying beta-cell dysfunction include glucose toxicity, lipotoxicity and beta-cell hyperactivity. Defects at various sites in beta-cell signal transduction pathways contribute, but no single lesion can account for the common form of Type 2 diabetes. Recent studies highlight diverse beta-cell actions of GLP-1 (glucagon-like peptide-1) and GIP (glucose-dependent insulinotropic polypeptide). These intestinal hormones target the beta-cell to stimulate glucose-dependent insulin secretion through activation of protein kinase A and associated pathways. Both increase gene expression and proinsulin biosynthesis, protect against apoptosis and stimulate replication/neogenesis of beta-cells. Incretin hormones therefore represent an exciting future multi-action solution to correct beta-cell defect in Type 2 diabetes.

Interaction of Room Temperature Ionic Liquid Solutions with a Cholesterol Bilayer

Water solutions of representative (IC(4)mim][Cl] and [C(4)mim][Tf2N] room temperature ionic liquids (ILs) in contact with a neutral lipid bilayer made of cholesterol molecules has been investigated by molecular dynamics simulations based on an empirical force field model. The results show that both ILs display selective adsorption at the water-cholesterol interface, with partial inclusion of ions into the bilayer. In the case Of [C(4)mim][Cl], the adsorption of ions at the water-cholesterol interface is limited by a sizable bulk solubility of the IL, driven by the high water affinity of [Cl](-). The relatively low Solubility Of [C(4)mim][Tf2N], instead, gives rise to a nearly complete segregation of the IL component on the bilayer, altering its volume, compressibility, and electrostatic environment. The computational results display important similarities to the results of recent experimental measurements for ILs in contact with phospholipid model membranes (see Evans, K. O. Int. J. Mol. Sci. 2008, 9, 498-511 and references therein).

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.

Assessment of Self-Compacting Concrete Immersed in Acidic Solutions

Ettringite and thaumasite can be found among the deterioration products of cementitious materials exposed to sulfate and hydrochloric attack. The results of a test program to investigate the acid resistance of self-compacting concrete (SCC) and conventional concrete (CC), immersed up to 18 weeks at 20°C in sulfuric and hydrochloric acid solutions, are described. The SCC was prepared with 47% carboniferous limestone powder, as a replacement for cement, and an ordinary portland cement. The CC was prepared with portland cement only. The water-binder ratios of the SCC and CC were 0.36 and 0.46, respectively. The parameter investigated was the time, in weeks, taken to cause 10% mass loss of fully immersed concrete specimens in a 1% solution of sulfuric acid and the same amount of loss in a 1% solution of hydrochloric acid. The investigation indicated that the SCC performed better than the CC in sulfuric solution but was slightly more vulnerable to hydrochloric acid attack compared to CC. The mode of attack between the two solutions was different.

Extraction of cesium ions from aqueous solutions using calix[4]arene-bis(tert-octylbenzo-crown-6) in ionic liquids

Solvent extraction of cesium ions from aqueous solution to hydrophobic ionic liquids without the introduction of an organophilic anion in the aqueous phase was demonstrated using calix[4]arene-bis(tert-octylbenzo-crown-6) (BOBCalixC6) as an extractant. The selectivity of this extraction process toward cesium ions and the use of a sacrificial cation exchanger (NaBPh4) to control loss of imidazolium cation to the aqueous solutions by ion exchange have been investigated.