By defining the valid digits and the standard fraction form of a terminating decimal, this paper makes an investigation on the number of digits in the fractional part of addition, subtraction, and multiplication of two terminating decimals. It is proved that the number of the val...
Open access
Research Article10.9734/arjom/2023/v19i7678
This paper derives an interesting property of the rectangular hyperbola. On the branch of the first quadrant, the slope of a chord starting from the vertex of the hyperbola has an opposite sign with the slope of the line segment from the coordinate origin to the peak of the chord...
Open access
Research Article10.9734/jamcs/2022/v37i121724
By means of constructing on the hyperbola xy = N a triangle whose shape is changed under the rule that one vertex is fixed at the vertex of the hyperbola, one vertex is moving on the hyperbola and the two laterals with respect to the fixed and the moving vertices respectively kee...
Open access
Research Article10.9734/jamcs/2022/v37i530450
The paper makes an extensive study on the symmetric brothers of a node in a perfect binary tree. Through proving several new properties of the symmetric brothers of a node, it reveals how the symmetric brothers and the symmetric ancestors distribute on the tree and how they are b...
Open access
Research Article10.9734/arjom/2021/v17i630305
This paper continues investigating connections on a valuated binary tree. By defining three types of new connections, the paper derives several new properties for the new connections, and proves that odd integers matching to the new cases can be easily and rapidly factorized. Pro...
Open access
Research Article10.9734/arjom/2021/v17i530297
This paper makes an investigation on geometric relationships among nodes of the valuated binary trees, including parallelism, connection and penetration. By defining central lines and distance from a node to a line, some intrinsic connections are discovered to connect nodes betwe...
Open access
Research Article10.9734/arjom/2021/v17i330287
Based on cubic non-uniform B-spline curve constrained with tolerance band, a tool path smoothing approach is proposed for the purpose to achieve high-speed and high-precision machining of consecutive short line segments. According to a given tolerance band, the approach calculate...
Open access
Research Article10.9734/jerr/2023/v25i121041