Math 5587 – Lecture 21
نویسنده
چکیده
Consider the problem of automatic maze navigation. Our maze in a two dimensional maze constructed on the plane R2. We have a starting point x0 ∈ R2, and a target set Γ ⊂ R2, which should be thought of as the ‘end’ of the maze. Our maze is defined by a speed function c(x) for x ∈ R2, which is the speed the robot can move at location x. Objects the robot cannot move through, i.e., walls, are modeled by setting c(x) = 0 in these regions. This also allows us to model the possibility that the robot may be able to move faster through some regions of the maze than others. A path is a continuous function
منابع مشابه
Math 140a: Foundations of Real Analysis I
1. Ordered Sets, Ordered Fields, and Completeness 1 1.1. Lecture 1: January 5, 2016 1 1.2. Lecture 2: January 7, 2016 4 1.3. Lecture 3: January 11, 2016 7 1.4. Lecture 4: January 14, 2014 9 2. Sequences and Limits 13 2.1. Lecture 5: January 19, 2016 13 2.2. Lecture 6: January 21, 2016 15 2.3. Lecture 7: January 26, 2016 18 2.4. Lecture 8: January 28, 2016 21 3. Extensions of R: the Extended Rea...
متن کاملMath 5587 – Lecture 15 Jeff Calder
1.1 Topology Let us first recall some basic Euclidean topology. For x0 = (x0, y0, z0) ∈ R3 and r > 0 we define the open ball of radius r > 0 centered at x0 to be B(x0, r) = {x ∈ R | ‖x− x0‖ < r}. Recall that ‖x‖ = √ x2 + y2 + z2 is the Euclidean norm, or length, of the vector x. Definition 1 (Open set). We say a set D ⊂ R3 is open if for every x0 ∈ D, there exists a radius r > 0 such that B(x0,...
متن کاملLecture Notes in Computer Science 5587
The Asprox infection weaves a complex chain of dependencies involving bots that perform SQL injections on vulnerable web servers, and visitors whose machines get compromised simply by visiting infected websites. Using real-world data sets, we study Asprox bots, infected web servers, and the malicious infrastructure behind Asprox propagation. We find that themalware-propagation infrastructure in...
متن کاملMath 117 Lecture Notes
This is the set of lecture notes for Math 117 during Fall quarter of 2017 at UC Santa Barbara. The lectures follow closely the textbook [1].
متن کامل