Peter von Jülich – De modo mensurandi vasa. Ein Traktat zur Fassmessung aus dem frühen 15. Jahrhundert. Herausgegeben, übersetzt und kommentiert von Menso Folkerts und Martin Hellmann

Mathematische Semesterberichte -     

Benchtop NMR analysis of piperazine-based drugs hyperpolarised by SABRE

Piperazine-based drugs, such as N-benzylpiperazine (BZP), became attractive in the 2000s due to possessing effects similar to amphetamines. Herein, BZP, in addition to its pyridyl analogues, 2-, 3-, and 4-pyridylmethylpiperidine (2-PMP, 3-PMP, and 4-PMP respectively) was subjected to the hyperpolarisation technique Signal Amplification By Reversible Exchange (SABRE) in order to demonstrate the use of this technique to detect these piperazine-based drugs. Although BZP was not hyperpolarised via SABRE, 2-PMP, 3-PMP, and 4-PMP were, with the ortho- and meta-pyridyl protons of 4-PMP showing the largest enhancement of 313-fold and 267-fold, respectively, in a 1.4-T detection field, following polarisation transfer at Earth's magnetic field. In addition to the freebase, 4-PMP.3HCl was also appraised by SABRE and was found not to polarise, however, the addition of increasing equivalents of triethylamine (TEA) produced the freebase, with a maximum enhancement observed upon the addition of 3 equivalents of TEA. Further addition of TEA led to a reduction in the observed enhancement. SABRE was also employed to polarise 4-PMP.3HCl (~20% w/w) in a simulated tablet to demonstrate the forensic application of the technique (138-fold enhancement for the ortho-pyridyl protons). The amount of 4-PMP.3HCl present in the simulated tablet was quantified via NMR using D₂O as a solvent and compared well to complimentary gas chromatography–mass spectrometry data. Exchanging D₂O for CD₃OD as the solvent utilised for analysis resulted in a significantly lower amount of 4-PMP.3HCl being determined, thus highlighting safeguarding issues linked to drug abuse in relation to determining the amount of active pharmaceutical ingredient present.     

Effect of Sulfation Route and Subsequent Oxidation on Derivatization Degree and Biocompatibility of Cellulose Sulfates

Sulfated cellulose (CS) represents an interesting biopolymer due to bioactivity comparable to heparin. However, use of CS for making surface coatings or hydrogels requires the presence of reactive groups for covalent reactions. Here, an approach is presented to oxidize cellulose sulfates for subsequent cross‐linking reactions with amino groups to form imine bonds. Cellulose is sulfated by direct sulfation or acetosulfation, followed by a M alaprade oxidation. The CS obtained is characterized by elemental analysis and ¹³C‐NMR spectroscopy. The resulting oxidized cellulose sulfates (oxCS) have different degrees of sulfation ranging from 0.79 to 1.13 and oxidation degrees from 0.18 to 0.34, but also different mass average molecular mass (M_W). Toxicity studies are carried out with mouse 3T3 fibroblasts exposed to aqueous solutions of oxCS. The results show that all oxCS are non‐toxic at lower concentrations (0.5 mg mL^?1), but with both increasing degree of oxidation and concentrations, toxic effects are observed particularly for acetosulfated and lesser for direct sulfated oxCS, which is related to a decrease in the M_W of the products. It is concluded that oxCS obtained by direct sulfation with M_W above 70 kDa may represent a biocompatible material for the applications suggested above.     

Perturbation theory for the effective interaction in nuclei

Starting from a decomposition of the Hamiltonian H(x) of the nuclear many-body problem in the form H(x) = H₀ + xV, where H₀ is a shell-model Hamiltonian, V the residual interaction, and x a strength parameter, we introduce a general effective interaction W(x) describing the interaction of nucleons within a shell, and the associated effective operators $\text{A}\text{?}\text{(x)}$. We display some properties of these operators. From a particular choice of W(x) we obtain the expressions introduced earlier by several authors. The convergence of the expansions for W(x) and $\text{A}\text{?}\text{(x)}$ in powers of x is investigated. It is shown that W(x) and $\text{A}\text{?}\text{(x)}$ are holomorphic in a domain of the complex x-plane including the point x = 0. With the help of a generalization of the von Neumann-Wigner noncrossing rule, we exhibit the nature of the common singularity of W(x) and $\text{A}\text{?}\text{(x)}$ which is closest to the origin and thus defines the radius r₀ of convergence of the expansions of W and $\text{A}\text{?}$. It is shown that r₀ is unaffected by the cancellation of unlinked diagrams. A criterion of consistency is established, which shows that most of the practical calculations of W lead to results which are inconsistent with the definition of W.     

Wireless retrospective gating: Application to cine cardiac imaging

A new “wireless” method of cardiac imaging is introduced, which, unlike ECG triggering, allows imaging the heart at end-diastole, and greatly reduces smearing artifacts in the phase-encoding direction. It is an improvement over ECG-driven retrospective gating, in that patients with poor ECGs can be imaged. This method extends the applicability of cardiac imaging, and since it requires no physiological monitoring hardware, can be implemented easily on any MR imager. The images produced by this method are superior to those from ECG triggering, especially when viewed in a “cine” loop. The technique described herein is, furthermore, extendable to any area where periodic or quasi-periodic motion is a problem.     

Bifurcation and stability of dynamical structures at a current instability

We investigate bifurcation and stability of nonuniform current states at a voltage-controlled current instability. We consider a model which exhibits bulk negative differential conductivity due to Bragg scattering of hot electrons. The system is described by balance equations for momentum and energy densities of the carriers. These transport fields are coupled to Maxwell's equations. The uniform stationary current state is unstable against long-wavelength dielectric relaxation modes at a critical field. We find that the softening of these modes gives rise to a family of periodic travelling waves and to a solitary solution (dipole domain). We show that the periodic travelling waves are unstable, wheras the dipole domain can be stabilized by coupling the sample to a suitable external circuit, if the static impedance of the sample in the domain state is negative. The model describes therefore a discontinuous nonequilibrium transition to a large amplitude domain state.Work Supported by the Swiss National Science Foundation