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A new modification of the Homotopy Analysis Method (HAM) is presented for highly nonlinear ODEs on a semi-infinite domain. The main advantage of the modified HAM is that the number of terms in the series solution can be greatly reduced; meanwhile the accuracy of the solution can be well retained. In this way, much less CPU is needed. Two typical examples are used to illustrate the efficiency of the proposed approach.
5-Alkenyl-2,2-butylidene-1,3-dioxane-4,6-diones were synthesized by the Knoevenagel condensation reaction of aromatic aldehydes with 2,2-butylidene-1,3-dioxane-4,6-dione using o-phthalimide-N-sulfonic acid as catalyst, without solvent under ultrasonic irradiation. The present method has some notable advantages such as mild reaction conditions, short reaction times, less catalyst dosage and high yields with the green aspects by avoiding toxic catalysts and solvents. Further, the catalyst can be reused for five times without any noticeable decrease in the catalytic activity.
In this research, we have concentrated on trajectory
extraction based on image segmentation and data association in order to provide
an economic and complete solution for rapid microfluidic cell migration
experiments. We applied region scalable active contour model to segment the
individual cells and then employed the ellipse fitting technique to process
touching cells. Subsequently, we have also introduced a topology based
technique to associate the cells between consecutive frames. This scheme
achieves satisfactory segmentation and tracking results on the datasets
acquired by our microfluidic platform.