Portable single-sided NMR measurements at variable temperatures: Implementation of a thermo-controlled device and application to the heating of bread dough

A temperature control unit was implemented to vary the temperature of samples studied on a commercial Mobile Universal Surface Explorer nuclear magnetic resonance (MOUSE-NMR) apparatus. The device was miniaturized to fit the maximum MOUSE sampling depth (25 mm). It was constituted by a sample holder sandwiched between two heat exchangers placed below and above the sample. Air was chosen as the fluid to control the temperature at the bottom of the sample, at the interface between the NMR probe and the sample holder, in order to gain space. The upper surface of the sample was regulated by the circulation of water inside a second heat exchanger placed above the sample holder. The feasibility of using such a device was demonstrated first on pure water and then on several samples of bread dough with different water contents. For this, T1 relaxation times were measured at various temperatures and depths and were then compared with those acquired with a conventional compact closed-magnet spectrometer. Discussion of results was based on biochemical transformations in bread dough (starch gelatinization and gluten heat denaturation). It was demonstrated that, within a certain water level range, and because of the low magnetic field strength of the MOUSE, a linear relationship could be established between T1 relaxation times and the local temperature in the dough sample.     

Three-term polynomial progressions in subsets of finite fields

We prove that the group of diffeomorphisms of the interval [0, 1] contains surface groups whose action on (0, 1) has no global fix point and such that only countably many points of the interval (0, 1) have non-trivial stabiliser.     

Simple, expedient methods for the determination of water and electrolyte contents of cellulose solvent systems

The concentrations of water, W, and electrolytes present in solutions of LiCl in N,N-dimethylacetamide, LiCl/DMAc, and of tetrabutylammonium fluoride. x-hydrate in DMSO, TBAF.xW/DMSO can be accurately and expediently determined by three independent methods, UV–vis, FTIR and EMF measurement. The first relies on the use of solvatochromic probes whose spectra are sensitive to solution composition. It is applicable to W/LiCl/DMAc solutions but not to TBAF.xW/DMSO, because the charge-transfer complex bands of the probes are suppressed by strong interactions with the latter electrolyte. Integration of ν_OH band of water may be employed in order to determine [W], hence [electrolyte] by weight difference. EMF measurement uses ion-selective electrodes in order to determine [electrolyte], hence [W] by weight difference. Results of the latter method were in excellent agreement with those of FTIR. The reason for the failure of Karl Fischer titration is addressed, and the relevance of the results obtained to functionalization of cellulose under homogenous solution conditions is briefly commented on.     

Molecular dynamics and information on possible sites of interaction of intramyocellular metabolites in vivo from resolved dipolar couplings in localized H NMR spectra

Proton NMR resonances of the endogenous metabolites creatine and phosphocreatine ((P)Cr), taurine (Tau), and carnosine (Cs, β-alanyl-l-histidine) were studied with regard to residual dipolar couplings and molecular mobility. We present an analysis of the direct ¹H–¹H interaction that provides information on motional reorientation of subgroups in these molecules in vivo. For this purpose, localized ¹H NMR experiments were performed on m. gastrocnemius of healthy volunteers using a 1.5-T clinical whole-body MR scanner. We evaluated the observable dipolar coupling strength SD₀ (S = order parameter) of the (P)Cr-methyl triplet and the Tau-methylene doublet by means of the apparent line splitting. These were compared to the dipolar coupling strength of the (P)Cr-methylene doublet. In contrast to the aliphatic protons of (P)Cr and Tau, the aromatic H2 (δ = 8 ppm) and H4 (δ = 7 ppm) protons of the imidazole ring of Cs exhibit second-order spectra at 1.5 T. This effect is the consequence of incomplete transition from Zeeman to Paschen-Back regime and allows a determination of SD₀ from H2 and H4 of Cs as an alternative to evaluating the multiplet splitting which can be measured directly in high-resolution ¹H NMR spectra. Experimental data showed striking differences in the mobility of the metabolites when the dipolar coupling constant D₀ (calculated with the internuclear distance known from molecular geometry in the case of complete absence of molecular dynamics and motion) is used for comparison. The aliphatic signals involve very small order parameters S ≈ (1.4 − 3) × 10⁻⁴ indicating rapid reorientation of the corresponding subgroups in these metabolites. In contrast, analysis of the Cs resonances yielded S ≈ (113 − 137) × 10⁻⁴. Thus, the immobilization of the Cs imidazole ring owing to an anisotropic cellular substructure in human m. gastrocnemius is much more effective than for (P)Cr and Tau subgroups. Furthermore, ¹H NMR experiments on aqueous model solutions of histidine and N-acetyl-l-aspartate (NAA) enabled the assignment of an additional signal component at δ = 8 ppm of Cs in vivo to the amide group at the peptide bond. The visibility of this proton could result from hydrogen bonding which would agree with the anticipated stronger motional restriction of Cs. Referring to the observation that all dipolar-coupled multiplets resolved in localized in vivo ¹H NMR spectra of human m. gastrocnemius collapse simultaneously when the fibre structure is tilted towards the magic angle (θ ≈ 55°), a common model for molecular confinement in muscle tissue is proposed on the basis of an interaction of the studied metabolites with myocellular membrane phospholipids.     

Phase modulation in dipolar-coupled A2 spin systems: effect of maximum state mixing in H NMR in vivo

Coupling constants of nuclear spin systems can be determined from phase modulation of multiplet resonances. Strongly coupled systems such as citrate in prostatic tissue exhibit a more complex modulation than AX connectivities, because of substantial mixing of quantum states. An extreme limit is the coupling of n isochronous spins (A_n system). It is observable only for directly connected spins like the methylene protons of creatine and phosphocreatine which experience residual dipolar coupling in intact muscle tissue in vivo. We will demonstrate that phase modulation of this “pseudo-strong” system is quite simple compared to those of AB systems. Theory predicts that the spin-echo experiment yields conditions as in the case of weak interactions, in particular, the phase modulation depends linearly on the line splitting and the echo time.     

Piecewise Deterministic Markov Control Processes with Feedback Controls and Unbounded Costs

The control of piecewise-deterministic processes is studied where only local boundedness of the data is assumed. Moreover the discount rate may be zero. The value function is shown to be solution to the Bellman equation in a weak sense; however the solution concept is strong enough to generate optimal policies. Continuity and compactness conditions are given for the existence of nonrelaxed optimal feedback controls.     

Kinetics of the bromate–bromide reaction at high bromide concentrations

At bromide concentrations higher than 0.1 M, a second term must be added to the classical rate law of the bromate–bromide reaction that becomes ?d[BrO₃^?]/dt = [BrO₃^?][H⁺]²(k₁[Br^?] + k₂[Br^?]²). In perchloric solutions at 25°C, k₁ = 2.18 dm³ mol^?3 s^?1 and k₂ = 0.65 dm⁴ mol^?4 s^?1 at 1 M ionic strength and k₁ = 2.60 dm³ mol³ s^?1and k₂ = 1.05 dm⁴ mol^?4 s^?1 at 2 M ionic strength. A mechanism explaining this rate law, with Br₂O₂ as key intermediate species, is proposed. Errors that may occur when using the Guggenheim method are discussed. © 2006 Wiley Periodicals, Inc. Int J Chem Kinet 39: 17–21, 2007     

The minimum span of L(2,1)-labelings of certain generalized Petersen graphs

In the classical channel assignment problem, transmitters that are sufficiently close together are assigned transmission frequencies that differ by prescribed amounts, with the goal of minimizing the span of frequencies required. This problem can be modeled through the use of an L(2,1)-labeling, which is a function f from the vertex set of a graph G to the non-negative integers such that |f(x)-f(y)|? 2 if xand y are adjacent vertices and |f(x)-f(y)|?1 if xand y are at distance two. The goal is to determine the λ-number of G, which is defined as the minimum span over all L(2,1)-labelings of G, or equivalently, the smallest number k such that G has an L(2,1)-labeling using integers from {0,1,…,k}. Recent work has focused on determining the λ-number of generalized Petersen graphs (GPGs) of order n. This paper provides exact values for the λ-numbers of GPGs of orders 5, 7, and 8, closing all remaining open cases for orders at most 8. It is also shown that there are no GPGs of order 4, 5, 8, or 11 with λ-number exactly equal to the known lower bound of 5, however, a construction is provided to obtain examples of GPGs with λ-number 5 for all other orders. This paper also provides an upper bound for the number of distinct isomorphism classes for GPGs of any given order. Finally, the exact values for the λ-number of n-stars, a subclass of the GPGs inspired by the classical Petersen graph, are also determined. These generalized stars have a useful representation on Möebius strips, which is fundamental in verifying our results.