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.

Rheological characterization of thermoresponsive semisolids for vaginal HIV vaccine delivery

Purpose. To manufacture and characterize, through oscillatory rheology, thermoresponsive rheologically structured vehicles
(RSV’s) capable of enhanced retention times within the vagina for the purposes of HIV vaccine delivery.
Methods. Pluronics F127, F108 and F68 were investigated and RSV’s were prepared by dissolving sorbic acid (0.1% w/w)
and mucoadhesive component (Gantrez SBF97 or Noveon AA1, 3% w/w) in the required amount of H2O and NaOH.
Pluronic (10% w/w) was added via mixing in an ice-bath followed by hydroxyethylcellulose (5%) and subsequently
poly(vinylpyrollidone) (4%w/w). Oscillatory temperature sweeps between 10-38°C were preformed within the linear
viscoelastic region of the formulations on an AR2000 rheometer (T.A. Instruments, Surrey, England) with a 2cm diameter
parallel plate geometry and a plate gap of 1000µm at 1Hz.

A novel continuous forward algorithm for RBF neural modelling

A continuous forward algorithm (CFA) is proposed for nonlinear modelling and identification using radial basis function (RBF) neural networks. The problem considered here is simultaneous network construction and parameter optimization, well-known to be a mixed integer hard one. The proposed algorithm performs these two tasks within an integrated analytic framework, and offers two important advantages. First, the model performance can be significantly improved through continuous parameter optimization. Secondly, the neural representation can be built without generating and storing all candidate regressors, leading to significantly reduced memory usage and computational complexity. Computational complexity analysis and simulation results confirm the effectiveness.

Constructing networks of continuous-time velocity-based models

A conventional local model (LM) network consists of a set of affine local models blended together using appropriate weighting functions. Such networks have poor interpretability since the dynamics of the blended network are only weakly related to the underlying local models. In contrast, velocity-based LM networks employ strictly linear local models to provide a transparent framework for nonlinear modelling in which the global dynamics are a simple linear combination of the local model dynamics. A novel approach for constructing continuous-time velocity-based networks from plant data is presented. Key issues including continuous-time parameter estimation, correct realisation of the velocity-based local models and avoidance of the input derivative are all addressed. Application results are reported for the highly nonlinear simulated continuous stirred tank reactor process.