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.