Smooth and Toothed Core Armatures

Smooth biproximity spaces and P-smooth quasi-proximity spaces

The notion of smooth biproximity space  where $delta_1,delta_2$ are gradation proximities defined by Ghanim et al. [10]. In this paper, we show every smooth biproximity space $(X,delta_1,delta_2)$ induces a supra smooth proximity space $delta_{12}$ finer than $delta_1$ and $delta_2$. We study the relationship between $(X,delta_{12})$ and the $FP^*$-separation axioms which had been introduced by...

Tagging and Playback Studies to Toothed Whales

While atypical mass strandings of beaked whales have been linked to naval exercises using midfrequency sonar, the causal chain of events from sound exposure to stranding has not been elucidated. We now know that beaked whales react strongly to sonar, killer whale calls, and bandlimited noise by ceasing echolocation and completing an unusually slow, directional ascent, in many cases leaving the ...

Functional Convergence in Bat and Toothed Whale

The rook problem on saw-toothed chessboards

A saw-toothed chessboard, or STC for short, is a kind of chessboard whose boundary forms two staircases from left down to right without any hole inside it. A rook at square (i, j) can dominate the squares in row i and in column j . The rook problem of an STC is to determine the minimum number of rooks that can dominate all squares of the STC. In this paper, we model an STC by two particular gra...

Innovative Design and Performance Evaluation of Bionic Imprinting Toothed Wheel

A highly efficient soil-burrowing dung beetle possesses an intricate outer contour curve on its foreleg end-tooth. This study was carried out based on evidence that this special outer contour curve has the potential of reducing soil penetration resistance and could enhance soil-burrowing efficiency. A toothed wheel is a typical agricultural implement for soil imprinting, to increase its working...