For each integer $k \in [0,9]$, we count the number of plane cubic curves defined over a finite field $\mathbb{F}_q$ that do not share common component and intersect in exactly $k\ \mathbb{F}_q$-rational points. We set this up as problem about weight enumerator certain projective Reed-Muller code. The main inputs to proof include counting pairs component, configurations points fail impose indep...

Surface/plane intersection problem is a special case of surface/surface intersection, and is an active area of research across many disciplines in computer-aided geometric design. This paper presents, in general the setting of derivational continuities, (i.e. C, C, and C), a surface/plane intersection algorithm for parametric Bézier triangular surface over triangular domain. The present algorit...

A number of operational and geometric factors impact the safety of at-grade intersections. Examples include the type of traffic control, the existence of left-turn lanes, and adequate sight distance. Determining whether an intersection of particular geometric design has unusual crash patterns could help identify those locations that need additional safety evaluation. During the last two years, ...

In this paper we prove an explicit formula for the arithmetic intersection number (CM(K).G1)` on the Siegel moduli space of abelian surfaces, generalizing the work of Bruinier-Yang and Yang. These intersection numbers allow one to compute the denominators of Igusa class polynomials, which has important applications to the construction of genus 2 curves for use in cryptography. Bruinier and Yang...

We study the arithmetic self-intersection number of the dualizing sheaf on arithmetic surfaces with respect to morphisms of a particular kind. We obtain upper bounds for the arithmetic self-intersection number of the dualizing sheaf on minimal regular models of the modular curves associated with congruence subgroups Γ0(N) with square free level, as well as for the modular curves X(N) and the Fe...

when the degree of saturation at intersection approaches one, webster’s optimum cycle length equation becomes inapplicable, because the cycle length will becomes very big when the degree of saturation approaches one and will be fully unrealistic when the degree of saturation becomes greater than one. this is not a problem for hcm2000 method. but optimum cycle length calculation in this method h...

information retrieval can be achieved through computerized processes by generating a list of relevant responses to a query. the document processor, matching function and query analyzer are the main components of an information retrieval system. document retrieval system is fundamentally based on: boolean, vector-space, probabilistic, and language models. in this paper, a new methodology for mat...

Constructions and bounds are given for the largest clique that can be represented as an intersection graph of intervals on the real line with bounded depth and multiplicity. Also, for the graph defined on the subsets of a set by putting vertices adjacent if and only if the corresponding subsets intersect, the interval number and boxicity are examined. Ke ywords: intersection graph, interval num...

We caution that # Fix(ψ) has to be interpreted with some care: it really denotes a fixed point count with multiplicities. A better way to phrase it as follows. Inside M ×M we have two submanifolds: the diagonal ∆ and the graph Γψ. We can then try to take # Fix(ψ) := ∆ · Γψ = “intersection number of ∆ and Γψ”. When ∆ and Γψ intersect transversely this intersection number coincides with the naïve...

This note conjectures that if two surface patches intersect with G continuity along an entire curve, the probability is one that the curve is rational. This idea has significance for surface intersection algorithms. Surface intersection algorithms are typically designed to deal with G intersections, in which the normal vectors of the two surfaces are parallel at only a small number (typically z...