A Note on Modular Partitions and Necklaces

Musical Scales, Integer Partitions, Necklaces, and Polygons

A musical scale can be viewed as a subsequence of notes taken from a chromatic sequence. Given integers (N,K) N > K we use particular integer partitions of N into K parts to construct distinguished scales. We show that a natural geometric realization of these scales results in maximal polygons.

A note on modular hyperconvex space

k-Efficient partitions of graphs

A set $S = {u_1,u_2, ldots, u_t}$ of vertices of $G$ is an efficientdominating set if every vertex of $G$ is dominated exactly once by thevertices of $S$. Letting $U_i$ denote the set of vertices dominated by $u_i$%, we note that ${U_1, U_2, ldots U_t}$ is a partition of the vertex setof $G$ and that each $U_i$ contains the vertex $u_i$ and all the vertices atdistance~1 from it in $G$. In this ...

Designing a High Resistant, High-torque Downhole Drilling Motor (RESEARCH NOTE)

Downhole drilling motors or mud motors are frequently used during the oil and gas well construction, especially for construction of directional and horizontal segments. However, low operation life of the down hole drilling motors and high rate of wear in their working elements may constrain their application due to technical and economical disadvantageousness. In this work, a high-torque modula...

Design patterns of kids’ spaces Focusing on enhancing their creativity

As recent researches show, creativity is very important in art, technology, science, education, management and etc. Also, preschool ages are a golden time for developing motor creativity. So, it‘s necessary to enhance creativity of preschoolers. Many scholars have studied cognitional-emotional aspects of creativity. Some, have focused on the creativity process and creativity techniques. B...