On solvability of linear differential equations in ${\Bbb R}^{\Bbb N}$

We construct $x^0$ in ${\Bbb R}^{\Bbb N}$ and a row-finite matrix $T=\{T_{i,j}(t)\}_{i,j\in\N}$ of polynomials of one real variable $t$ such that the Cauchy problem $\dot x(t)=T_tx(t)$, $x(0)=x^0$ in the Fr\'echet space $\R^\N$ has no solutions. We also construct a row-finite matrix $A=\{A_{i,j}(t)\}_{i,j\in\N}$ of $C^\infty(\R)$ functions such that the Cauchy problem $\dot x(t)=A_tx(t)$, $x(0)=x^0$ in ${\Bbb R}^{\Bbb N}$ has no solutions for any $x^0\in{\Bbb R}^{\Bbb N}\setminus\{0\}$. We provide some sufficient condition of solvability and of unique solvability for linear ordinary differential equations $\dot x(t)=T_tx(t)$ with matrix elements $T_{i,j}(t)$ analytically dependent on $t$.

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.

On the solvability of Hamilton's equations in Hilbert spaces

We construct a bounded function $H : l_2\times l_2 \to R$ with continuous Frechet derivative such that for any $q_0\in l_2$ the Cauchy problem $\dot p= - {\partial H\over\partial q}$, $\dot q={\partial H\over\partial p}$, $p(0) = 0$, q(0) = q_0$ has no solutions in any neighborhood of zero in R.

Some results on solvability of ordinary linear differential equations in locally convex spaces

Let $\Gamma$ be the class of sequentially complete locally convex spaces such that an existence theorem holds for the linear Cauchy problem $\dot x = Ax$, $x(0) = x_0$ with respect to functions $x: R\to E$. It is proved that if $E\in \Gamma$, then $E\times R^A$ is-an-element-of $\Gamma$ for an arbitrary set $A$. It is also proved that a topological product of infinitely many infinite-dimensional Frechet spaces, each not isomorphic to $\omega$, does not belong to $\Gamma$.

Genetic algorithms for local controller network construction

Local Controller Networks (LCNs) provide nonlinear control by interpolating between a set of locally valid, subcontrollers covering the operating range of the plant. Constructing such networks typically requires knowledge of valid local models. This paper describes a new genetic learning approach to the construction of LCNs directly from the dynamic equations of the plant, or from modelling data. The advantage is that a priori knowledge about valid local models is not needed. In addition to allowing simultaneous optimisation of both the controller and validation function parameters, the approach aids transparency by ensuring that each local controller acts independently of the rest at its operating point. It thus is valuable for simultaneous design of the LCNs and identification of the operating regimes of an unknown plant. Application results from a highly nonlinear pH neutralisation process and its associated neural network representation are utilised to illustrate these issues.

A surface plasmon resonance biosensor assay for the simultaneous determination of thiamphenicol, florefenicol, florefenicol amine and chloramphenicol residues in shrimps

A rapid and sensitive screening qualitative method using a surface plasmon resonance (SPR) biosensor was developed which can detect of all fenicol antibiotic residues in shrimps from a single sample extract. This method requires ethyl acetate extraction followed by a single wash with isooctane/chlorofonrm. Each sample extract is injected over the surfaces of two biosensor chip flow cells, one surface having the capability to detect florefenicol amine (FF amine), florefenicol (FF), and thiamphenicol (TAP) and the second surface for chloramphenicol (CAP) detection. The estimated detection capabilities (CC beta) were 0. 1, 0.2, 250, and 0.5 ppb for CAP, FF, FF amine, and TAP, respectively. This quick, simple test allowed the detection of CAP residues in shrimps at the minimum required performance limit (MRPL) of 0.1 mu g kg(-1) for this compound and of FF, FF amine, and TAP below their maximum residue limits (MRLs). (c) 2006 Elsevier B.V. All rights reserved.

The effect of simultaneous contractions of ipsilateral muscles on changes in corticospinal excitability induced by paired associative stimulation (PAS)

Consideration was given to means of increasing the reliability and muscle specificity of paired associative stimulation (PAS) by utilising the phenomenon of crossed-facilitation. Eight participants completed three separate sessions: isometric flexor contractions of the left wrist at 20% of maximum voluntary contraction (MVC) simultaneously with PAS (20s intervals; 14 min duration) delivered at the right median nerve and left primary motor cortex (MI); isometric contractions at 20% of MVC: and PAS only ( 14 min). Eight further participants completed two sessions of longer duration PAS (28 min): either alone or in conjunction with flexion contractions of the left wrist. Thirty motor potentials (MEPs) were evoked in the right flexor (rFCR) and extensor (rECR) carpi radialis muscles by magnetic stimulation of left M1 Prior to the interventions, immediately post-intervention, and 10 min post-intervention. Both 14 and 28 min of combined PAS and (left wrist flexion) contractions resulted in reliable increases in rFCR MEP amplitude, which were not present in rECR. In the PAS only conditions, 14 min of stimulation gave rise to unreliable increases in MEP amplitudes in rFCR and rECR, whereas 28 min of PAS induced small (unreliable) changes only for rFCR. These results support the conclusion that changes in the excitability of the corticospinal pathway induced by PAS interact with those associated with contraction of the muscles ipsilateral to the site of cortical stimulation. Furthermore, focal contractions applied by the opposite limb increase the extent and muscle specificity of the induced changes in excitability associated with PAS. (C) 2008 Elsevier Ireland Ltd. All rights reserved.

Development and validation of an HPLC method for the rapid and simultaneous determination of 6-mercaptopurine and four of its metabolites in plasma and red blood cells

An HPLC method has been developed and validated for the rapid determination of mercaptopurine and four of its metabolites; thioguanine, thiouric acid, thioxanthine and methylmercaptopurine in plasma and red blood cells. The method involves a simple treatment procedure based on deproteinisation by perchloric acid followed by acid hydrolysis and heating for 45 min at 100 degrees C. The developed method was linear over the concentration range studied with a correlation coefficient >0.994 for all compounds in both plasma and erythrocytes. The lower limits of quantification were 13, 14, 3, 2, 95 pmol/8 x 101 RBCs and 2, 5, 2, 3, 20 ng/ml plasma for thioguanine, thiouric acid, mercaptopurine, thioxanthine and methylmercaptopurine, respectively. The method described is selective and sensitive enough to analyse the different metabolites in a single run under isocratic conditions. Furthermore, it has been shown to be applicable for monitoring these metabolites in paediatric patients due to the low volume requirement (200 mu l of plasma or erythrocytes) and has been successfully applied for investigating population pharmacokinetics, pharmacogenetics and non-adherence to therapy in these patients. (C) 2008 Elsevier B.V. All rights reserved.