QUATERNION-TYPE REPRESENTATION FOR MEASURING THE RENNET COAGULATION TIME OF MILK BY COLOR IMAGE SEQUENCES PROCESSING

The determination of the rennet coagulation time of milk by image sequences processing was performed using a computer vision system (CVS), consisting of a computer coupled with a transmitted light microscope equipped with a digital camera. Algorithms implemented with Matlab 2014 encoded the color image as a quaternion, computed and analyzed the histogram peak. The evolution of this last parameter was monitored as a function of the milk coagulation time, for different concentrations of calcium chloride (0.01–0.03 M) and for coagulation temperatures varying between 30 and 36°C. No statistically significant difference was observed in the measurements of the rennet coagulation time, neither by the Berridge method nor by the analysis of the image sequences, except for those at 36°C. The association of the optical microscopic method and the analysis of image sequences by a quaternion-type representation, made it possible to identify optical changes during gel formation and to accurately determine the rennet coagulation time of milk.

Külshammer ideals of algebras of quaternion type

For a symmetric algebra [Formula: see text] over a field [Formula: see text] of characteristic [Formula: see text] Külshammer constructed a descending sequence of ideals of the center of [Formula: see text]. If [Formula: see text] is perfect, this sequence was shown to be an invariant under derived equivalence and for algebraically closed [Formula: see text] the dimensions of their image in the stable center were shown to be invariant under stable equivalence of Morita type. Erdmann classified algebras of tame representation type which may be blocks of group algebras, and Holm classified Erdmann’s list up to derived equivalence. In both classifications, certain parameters occur in the classification, and it was unclear if different parameters lead to different algebras. Erdmann’s algebras fall into three classes, namely of dihedral, semidihedral and of quaternion type. In previous joint work with Holm, we used Külshammer ideals to distinguish classes with respect to these parameters in case of algebras of dihedral and semidihedral type. In the present paper, we determine the Külshammer ideals for algebras of quaternion type and distinguish again algebras with respect to certain parameters.