We enumerate the number of surfaces degree $d$ in $P^3$ having a singular line order $k$, passing through $\delta$ generic points (where is dimension moduli space such surfaces).

Menger called a finitely-compact metric space in which any two distinct points are contained in exactly one set congruent to a euclidean straight line a straight-line space (S.L. space) [ l ] . 1 He observed that in such spaces a segment (or vector) addition can be defined in a very simple way (see §2 of the present paper) which satisfies all requirements for an abelian group except, in general...

In this paper, we present a factor 16 approximation algorithm for the following NP-hard distance fitting problem: given a finite set X and a distance d on X, find a Robinsonian distance dR on X minimizing the l∞-error ||d−dR||∞ = maxx,y∈X{|d(x, y)− dR(x, y)|}. A distance dR on a finite set X is Robinsonian if its matrix can be symmetrically permuted so that its elements do not decrease when mov...

In this paper, we present a factor 16 approximation algorithm for the following NP-hard distance fitting problem: given a finite set X and a distance d on X, find a Robinsonian distance dR on X minimizing the l∞-error ||d−dR||∞ = maxx,y∈X{|d(x, y)− dR(x, y)|}. A distance dR on a finite set X is Robinsonian if its matrix can be symmetrically permuted so that its elements do not decrease when mov...

Background: In intensity modulated radiation therapy, cone beam computed tomography (CT) has been used to evaluate patients prior to treatment. This study conducted a comparative evaluation of the image reconstruction ability of the clinically used half-fan bowtie filter and the full-fan bowtie filter. Materals and Methods: A CT simulation marker was inserted inside a human phantom, and the pel...