In this study, highly accurate measurements of density and dynamic viscosities of a recombined live oil and its mixture with additional CO2 were performed. The experiments were carried out under pressure and temperature gradients found in Brazilian Pre-salt reservoirs, that is, in the pressure range from (27.6 to 68.9) MPa and at (333.15 and 353.15) K. The assumption of volume change on mixing is evaluated from the experimental results, and the influence of pressure and temperature on the volume change upon mixing is assessed. The densities of mixtures are calculated considering (i) the excess volume approach, and (ii) no volume change. The densities are better correlated using the excess volume approach with Average Absolute Deviations (AAD) of 0.03%. Thirteen mixing rules of viscosity are examined by comparing the predicted values with the experimental viscosity of the recombined live oil + CO2 mixture. The performance of some rules using compositional fractions (molar, volume and weight) is also evaluated. Thus, a total of 28 different ways to calculate the mixture viscosities were tested in this study. The worst result was obtained with Bingham’s method, leading to 148.6% AAD. The best result was obtained from Lederer’s method with 2% AAD and a maximum deviation of 5.8% using volume fractions and the fitting parameter α. In addition, deviations presented by the predictive methods of Chevron, Double log, and Kendall did not exceed 9% AAD, using weight fractions (Chevron and Double log) and molar fractions (Kendall and Monroe).

Handwritten mathematical expression recognition (HMER) is a challenging task due to factors such as ambiguity, variety of writing styles, and complexity of two-dimensional writing. In this paper, we identify challenges in HMER applications through experiments that simulate real scenarios that go far beyond the usual cases found in literature: variations on luminance; different stroke width, inclination and color; different background pattern; and partially shaded images. The results of state-of-the-art methods (as TAP and Dense-WAP) and a commercial tool (MathPix) are analyzed, using the CROHME 2016 database. We proved that, although the area has had a lot of improvement in recent years, there are still issues to overcome.

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Treatment of N‐aryl‐ or N‐alkyl‐5‐amino‐4‐(cyanoformimidoyl)‐1H‐imidazoles 1 with benzoyl or ethoxycarbonyl isocyanates resulted in the formation of 5‐amino‐4‐[N‐benzoyl‐ or N‐(ethoxycarbonyl)carbamoylcyanoformimidoyl]‐1H‐imidazoles 2. In the presence of catalytic amounts of DBU (1,8‐diazabicyclo[5.4.0]undec‐7‐ene), these compounds cyclized to give the 5′‐amino‐5‐imino‐4,4′‐bi‐1H‐imidazol‐2(5H)‐ones 3. Compounds 3 efficiently rearrange to yield 6‐amidino‐2‐oxopurines 5 in ethanol or DMF solution. The formation of purines 5 both from imidazoles 2 and from bi‐imidazoles 3 was followed by 1H NMR, allowing a deeper understanding of the reaction mechanism. The rearrangements are acid‐catalysed (trifluoroacetic acid), but the use of one equivalent of acid produced different products, identified as the bi‐imidazoles 8.(© Wiley‐VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2007)

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