Finite automata for testing uniqueness of Eulerian trails

We investigate the condition under which the Eulerian trail of a digraph is unique, and design a finite automaton to examine it. The algorithm is effective, for if the condition is violated, it will be noticed immediately without the need to trace through the whole trail

A seasonal circulation index for the ocean and its application to the South China Sea

Ocean circulation is crucial in redistributing mass and energy on Earth. However, it varies significantly on a seasonal time scale due to external forcing. To quantify the seasonality of ocean circulation, we propose a seasonal circulation index (SCI). This index is defined as the normalized maximum deviation from the velocity vector, whose magnitude is the largest in one period. We have substantiated the efficiency of this index using the monsoon wind in the South China Sea (SCS). By utilizing this index, we have obtained the 3D structure of the seasonality of ocean circulation in the SCS. The SCI and the seasonal circulation amplitude (SCA) exhibit large values over 0.9 and 0.8 m s-1 in the western boundary current. Alternating southwest-northeastward bands of SCI with high and low values are distributed from the north shelf to the south, especially in the eastern basin. Although SCA decreases significantly with depth, SCI exhibits values higher than 0.7 in both the middle and deep layers, indicating a noteworthy seasonality and middle-layer enhancement in the abyssal basin of the SCS