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.

Sulfur-tolerant NOx storage traps: an infrared and thermodynamic study of the reactions of alkali and alkaline-earth metal sulfates

The sulfur tolerance of a barium-containing NOx storage/reduction trap was investigated using infrared analysis. It was confirmed that barium carbonate could be replaced by barium sulfate by reaction with low concentrations of sulfur dioxide (50 ppm) in the presence of large concentrations of carbon dioxide (10%) at temperatures up to 700 degreesC. These sulfates could at least be partially removed by switching to hydrogen-rich conditions at elevated temperatures. Thermodynamic calculations were used to evaluate the effects of gas composition and temperature on the various reactions of barium sulfate and carbonate under oxidizing and reducing conditions. These calculations clearly showed that if, under a hydrogen-rich atmosphere, carbon dioxide is included as a reactant and barium carbonate as a product then barium sulfate can be removed by reaction with carbon dioxide at a much lower temperature than is possible by decomposition to barium oxide. It was also found that if hydrogen sulfide was included as a product of decomposition of barium sulfate instead of sulfur dioxide then the temperature of reaction could be significantly lowered. Similar calculations were conducted using a selection of other alkaline-earth and alkali metals. In this case calculations were simulated in a gas mixture containing carbon monoxide, hydrogen and carbon dioxide with partial pressures similar to those encountered in real exhausts during switches to rich conditions. The results indicated that there are metals such as lithium and strontium with less stable sulfates than barium, which may also possess sufficient NOx storage capacity to give sulfur-tolerant NOx traps.

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).