Four different vector fields on (x,y)-plane A vector field on a sphere ♣ Curves. A smooth curve is a continuous curve (no gaps or discontinuities) with no corners (no abrupt changes in slope at a point such as you would get from the intersection of two lines). A continuous and differentiable produces a smooth function. A path C is called closed if its initial and final points are the same point...

If φ : L → L′ is a bijection from the set of lines of a linear space (P,L) onto the set of lines of a linear space (P ′,L′) (dim (P,L), dim (P ′,L′) ≥ 3), such that intersecting lines go over to intersecting lines in both directions, then φ is arising from a collineation of (P,L) onto (P ′,L′) or a collineation of (P,L) onto the dual linear space of (P ′,L′). However, the second possibility can...

A method of representing transformations of a finite set pictorially is described. These pictures of a function are used to count certain idempotent transformations, and interesting formulae for the Fibonacci numbers are obtained. No part of any string extends beyond the region ° : : ; z ::; 1, and if two strings intersect then they join together, from the point of intersection, to meet the sam...

We present an algorithm for ray–tetrahedron intersection. The algorithm uses Plücker coordinates to represent the ray and the edges of the tetrahedron and employs a robust and efficient test to determine the intersection. The algorithm is highly optimized and provides a significant performance increase over related algorithms.

Uncontrolled intersections are the intersections where there are no external signs or signals to control the movement of vehicles. In mixed traffic conditions priority rules are often violated by the road users. In All-way-stop-controlled intersections (AWSC), the vehicle should stop themselves before they enter the intersection and should check whether any vehicles are present in the other app...

Intersection crashes account for 1.72 million crashes per year in the United States. In 2004 stop-sign and traffic signal violations accounted for approximately 302,000 crashes resulting in 163,000 functional lifeyears lost and $7.9 billion of economic loss [1]. The objective of the Cooperative Intersection Collision Avoidance System for Violations (CICAS-V) project was to design, develop, and ...

In this paper, we introduce a new concept of volumes difference function of the projection and intersection bodies. Following this, we establish the Minkowski and Brunn-Minkowski inequalities for volumes difference function of the projection and intersection bodies.

We present an algorithm for determining if a ray intersects a triangle interior; and computing intersection point parameters as well as distance of intersection in response to the ray intersecting a triangle interior. Particularly a variation of a hybrid test having all benefits of Plücker and projected barycentric tests is proposed. The test is also vectorized using SIMD instructions for effic...

As a common generalization of matchings and matroid intersection, W.H. Cunningham and J.F. Geelen introduced the notion of path-matchings, then they introduced the more general notion of even factor in weakly symmetric digraphs. Here we give a min-max formula for the maximum cardinality of an even factor. Our proof is purely combinatorial. We also provide a Gallai-Edmonds-type structure theorem...