A method for solving two-point boundary-value problems of difference equations

The paper proposes an iterative solution method for discrete-time, nonlinear, two-point boundary-value problems (TPBVP) of the form: $$\begin{gathered} x(k) - x(k - 1) = f(k, x(k - 1), p(k)), \hfill \\ p(k) - p(k - 1) = g(k, x(k - 1), p(k)), \hfill \\ \end{gathered} $$ subject to $$h(x(0), p(0)) = 0,e(x(N), p(N)) = 0.$$ It is a counterpart of a method recently proposed by the authors for similar continuous-time TPBVPs with ordinary differential equations. The method, based on invariant imbedding and a generalized Riccati transformation, reduces the TPBVP to a pair of approximate initial-value problems with ordinary difference equations. Numerical tests are run on two examples originating in optimal control problems.     

Back-and-forth shooting method for solving two-point boundary-value problems

The paper proposes a special iterative method for a nonlinear TPBVP of the form (t)=f(t, x(t),p(t)), (t)=g(t, x(t),p(t)), subject toh(x(0),p(0))=0,e(x(T),p(T))=0. Certain stability properties of the above differential equations are taken into consideration in the method, so that the integration directions associated with these equations respectively are opposite to each other, in contrast with the conventional shooting methods. Via an embedding and a Riccati-type transformation, the TPBVP is reduced to consecutive initial-value problems of ordinary differential equations. A preliminary numerical test is given by a simple example originating in an optimal control problem.     

Method development for mono- and disaccharides monitoring in cell culture medium by capillary and microchip electrophoresis

The rapidly growing, competitive biopharmaceutical market requires tight bioprocess monitoring. An integrated, automated platform for the routine online/at-line monitoring of key factors in the cell culture medium could greatly improve process monitoring. Mono- and disaccharides, as the main energy and carbon source, are one of these key factors. A CE-LIF method was developed for the analysis of several mono- and disaccharides, considering requirements and restrictions for analysis in an integrated, automated monitoring platform, such as the possibility for miniaturization to microchip electrophoresis. Analysis was performed after fluorescent derivatization with 8-aminopyrene-1,3,6-trisulfonic acid. The derivatisation reaction and the separation BGE were optimized using design of experiments. The developed method is applicable to the complex matrix of cell culture medium and proved transferable to microchip electrophoresis.     

Carboxylate Catalyzed Isomerization of β,γ-Unsaturated N-Acetylcysteamine Thioesters**

We demonstrate herein the capacity of simple carboxylate salts – tetrametylammonium and tetramethylguanidinium pivalate – to act as catalysts in the isomerization of β,γ-unsaturated thioesters to α,β-unsaturated thioesters. The carboxylate catalysts gave reaction rates comparable to those obtained with DBU, but with fewer side reactions. The reaction exhibits a normal secondary kinetic isotope effect (k_1H/k_1D=1.065±0.026) with a β,γ-deuterated substrate. Computational analysis of the mechanism provides a similar value (k_1H/k_1D=1.05) with a mechanism where γ-reprotonation of the enolate intermediate is rate determining.     

Interval length continuation method for solving two-point boundary-value problems

We consider the solution of the following two-point boundary-value problem: $$\begin{gathered} \dot x(t) = f(t,x(t),p(t)), \dot p(t) = g(t,x(t),p(t)), t \in [0,T], \hfill \\ h(x(0),p(0)) = 0, p(T) = q. \hfill \\ \end{gathered} $$ We propose a combination technique consisting of the interval length continuation method and the back-and-forth shooting method. Certain alternative ways of employing continuation are discussed, and some of them are well suited for the problem under consideration. As a test for the method, a numerical example of a problem originating in optimal control is given.     

Analysis of amino acids in cell culture supernatant using capillary electrophoresis with contactless conductivity detection

CE-C⁴D methods for the analysis of amino acids (AAs) are presented. Combining the results from two methods with acetic acid and cyclodextrin-based BGEs, 20 proteinogenic AAs could be analyzed using CE. CE-C⁴D was also, for the first time, applied to analyze free AAs in samples of mammalian cell culture supernatant. After dilution as only sample preparation, combining the results of the two CE methods allowed monitoring the concentration changes of 17 AAs in samples taken during the cultivation of CHO cells.     

A four-element phased array coil for high resolution and parallel MR imaging of the knee

A four-element phased array coil for MR imaging of the knee was designed, built and tested for clinical use at 1.5 Tesla. In routine imaging, it provides over twofold increase in signal-to-noise (SNR) compared to two commercially available knee coils, and supports higher spatial image resolution. The phased array knee coil was also tested for its compatibility with parallel MR imaging that reduces imaging time by several folds over conventional MR technique. Results obtained using SiMultaneous Acquisition of Spatial Harmonics (SMASH) technique shows that our phased array knee coil can be used with parallel MR imaging. These improvements may enhance knee diagnosis with higher image quality and reduced scan time.