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We propose a verified approach to the formal verification of timed properties using model-checking techniques. We focus on properties commonly found during the analysis of reactive systems, expressed using real-time specification patterns. We use observers in order to transform the verification of these timed patterns into the verification of simpler LTL formulas. While the use of observers for model-checking is quite common, our contribution is original in several ways. First, we define a formal framework to verify that observers are correct and non-intrusive. Second, we define different classes of observers for each pattern and use a pragmatic approach in order to select the most efficient candidate in practice. This approach is implemented in an integrated verification tool chain for the Fiacre language.

Here T1and T2*relaxation time measurements by low-field NMR have been used to quantify the state of oil and water in frozen emulsions. Water-in-oil and oil-in-water emulsions have been studied. A discrete method (NLREG program) and a continuous method (CONTIN program) have been used to analyze the FID and inversion-recovery relaxation curves. The FID signal (T2*) analysis allowed us to calculate the global solid–intermediate–liquid ratio, and the state of the solid and liquid phases was determined by the T1values. Thus we have been able to show that the major part of water (∼99%) is in a solid state in such emulsions (average droplet diameter of about 1.5 μm). This result was confirmed by the study of a solid paraffin–Span 80–water emulsion and a heavy water–caseinate–triolein emulsion. These first results have shown the interest of this new method for the study of the state of water and oil in frozen emulsions.

Abstract: The solid-to-liquid ratio is an important parameter in the study of fats. Many methods can be used: dilatometry, differential scanning calorimetry (DSC), and nuclear magnetic resonance (NMR). However, below approximately 20C, NMR gives much lower solid-to-liquid values than DSC. This difference can be attributed to the presence of a semisolid state, whose T2 value would be of the order of 50–200 s, and which should give an NMR signal of 14 to 88.5% of the total signal of this phase at a time when the signal of the liquid phase is measured. Thus, such a state is seen partially as a liquid by NMR. In a previous study using time domain NMR, we have shown that in milk fat samples an intermediate component state clearly exists between the solid and liquid phases, constituting only about 6% of an aged milk fat. The T2* distribution of these components in this intermediate state shows two peaks at about 60 and 170 s. We have shown from the T2* resolved T1 distribution of the peak, corresponding to a T2* of approximately 60 s, that there is in the continuity in the crystalline phase. This first intermediate component state does not exist in pure triglyceride or in cocoa butter, and is scarcely present in a tristearin crystal/soy oil suspension. We have attributed this first intermediate component to fatty acid residue extremities that protrude from the crystalline phase and/or to chain ends at the edges of holes created by short chains.

The purpose of this study was to elucidate the molecular mechanism involved in the behavioural changes observed at macroscopic level in a starch-sorbitol-water system. At a low sorbitol content (<27%), maximum stress decreased and the yield at break was quite constant at around 5%. This behaviour was compared with antiplasticisation, a well-known phenomenon occurring with synthetic polymers. The study of storage loss modulus by dynamic thermal mechanical analysis (DTMA) confirmed antiplasticisation. Sorbitol at high content (>27%) acts as a plasticiser. The two relaxations observed with DTMA, α associated with glass transition (occurring at high temperature, >30 °C) and two occurring at low temperatures (<10 °C), were involved in behavioural changes. System mobility as a function of sorbitol content was determined by time domain nuclear magnetic resonance. Much of this study was performed by replacing H2O with deuterium oxide to mask the signal from water and therefore analyse only the starch and sorbitol signals. The results show the existence of two competitive effects: one associated with a decrease in mobility and the other with the enhanced mobility of the system. The relative importance of these two effects seems to be reversed, depending on sorbitol content, which could account for the changes observed at the macroscopic level.

This study evaluated the oxygen permeability (O.P.) of starch‐sorbitol‐water films produced by casting. With a sorbitol content <20%, O.P. (0.15 10−16cm2/s.Pa for 8.8% sorbitol) was lower than for other polymers classically used as oxygen barriers. With a sorbitol content >20%, O.P. (1.6 10−16cm2/s.Pa for 24.9% sorbitol) was higher than for starch films without a plasticizer. These results were correlated with molecular mobility as determined by time‐domain NMR. Low and high O.P. corresponded respectively to a decrease and an increase of molecular mobility relative to sorbitol content.

The solid-to-liquid ratio is an important parameter in the study of fats. Many methods can be used: dilatometry, differential scanning calorimetry (DSC), and nuclear magnetic resonance (NMR). However, below approximately 20°C, NMR gives much lower solid-to-liquid values than DSC. This difference can be attributed to the presence of a semisolid state, whose T2value would be of the order of 50–200 µs, and which should give an NMR signal of 14 to 88.5% of the total signal of this phase at a time when the signal of the liquid phase is measured. Thus, such a state is seen partially as a liquid by NMR. In a previous study using time domain NMR, we have shown that in milk fat samples an intermediate component state clearly exists between the solid and liquid phases, constituting only about 6% of an aged milk fat. The T2* distribution of these components in this intermediate state shows two peaks at about 60 and 170 µs. We have shown from the T2* resolved T1distribution of the peak, corresponding to a T2* of approximately 60 µs, that there is in the continuity in the crystalline phase. This first intermediate component state does not exist in pure triglyceride or in cocoa butter, and is scarcely present in a tristearin crystal/soy oil suspension. We have attributed this first intermediate component to fatty acid residue extremities that protrude from the crystalline phase and/or to chain ends at the edges of holes created by short chains.

The aim of this work is to show that a low resolution NMR spectrometer in combination with a pulsed field gradient unit can be used for the determination of the water droplet size distributions of water-in-oil emulsions. To improve the treatment of NMR measurements, we added an unrestricted diffusion component to the restricted one used up to now. The purpose of this second term is either (i) to improve the fitting of the experimental values to take into account that the distribution of the droplet sizes is not perfectly lognormal, or (ii) to show a significant unrestricted diffusion component due to poor emulsification of the sample. The NMR results are compared with those of laser diffraction. These results are the first step in a study of "solid" water-in-oil emulsions such as butter or margarine.

Diels‐Alder reaction of the acrylate (II) with the heterodiene (I) yields the thiazine (III).