منابع مشابه
On the degree of the polynomial defining a planar algebraic curves of constant width
In this paper, we consider a family of closed planar algebraic curves C which are given in parametrization form via a trigonometric polynomial p. When C is the boundary of a compact convex set, the polynomial p represents the support function of this set. Our aim is to examine properties of the degree of the defining polynomial of this family of curves in terms of the degree of p. Thanks to the...
متن کاملOn constant products of elements in skew polynomial rings
Let $R$ be a reversible ring which is $alpha$-compatible for an endomorphism $alpha$ of $R$ and $f(X)=a_0+a_1X+cdots+a_nX^n$ be a nonzero skew polynomial in $R[X;alpha]$. It is proved that if there exists a nonzero skew polynomial $g(X)=b_0+b_1X+cdots+b_mX^m$ in $R[X;alpha]$ such that $g(X)f(X)=c$ is a constant in $R$, then $b_0a_0=c$ and there exist nonzero elements $a$ and $r$ in $R$ such tha...
متن کاملFigures of Constant Width on a Chessboard
Every row and column of the board has only two occupied squares. But if we also consider the diagonals with slope +1 or −1, we see that each of them contains either zero or two squares of the figure. We say that Figure 1 has constant width three by rows and columns, and that Figure 2 has constant width two by rows, columns, and diagonals. The first figure is easy to generalize in the sense that...
متن کاملConvex sets of constant width
A bounded convex set has constant width d iff any two parallel (and nonidentical) tangent planes to it have identical distance d from each other. Clearly balls have this property, but there are also other sets of constant width. This lecture was originally designed for a general audience as part of a series of lectures during the German “Year of Mathematics” 2008. It starts by presenting eviden...
متن کاملWidth and dual width of subsets in polynomial association schemes
The width of a subset C of the vertices of a distance-regular graph is the maximum distance which occurs between elements of C. Dually, the dual width of a subset in a cometric association scheme is the index of the “last” eigenspace in the Q-polynomial ordering to which the characteristic vector of C is not orthogonal. Elementary bounds are derived on these two new parameters. We show that any...
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ژورنال
عنوان ژورنال: Missouri Journal of Mathematical Sciences
سال: 1997
ISSN: 0899-6180
DOI: 10.35834/1997/0901023