Map Definition and 441 Threads

Meissner et al just posted a paper where they see those circles in the high res. microwave sky of Planck. Who knows if this is real, or what it would mean if it were confirmed? Meissner has a followup paper in preparation with Penrose and others. Either way I think it's pretty interesting...

while it has been extensively proven that any 2D map can be colored with at most 4 colors, has any hypothesized why that is (outside the computer programmed brute force method)?

Homework Statement Let ##L: R^{2} → R^{2}## be a linear map such that ##L ≠ O## but## L^{2} = L \circ L = O.## Show that there exists a basis {##A##, ##B##} of ##R^{2}## such that: ##L(A) = B## and ##L(B) = O.## The Attempt at a Solution Here's the...

OK, this is one where I am having trouble starting because I am not sure I am reading the question correctly to begin with. So start with: M_{m×n}(K) denotes the set of all matrices with m rows and n columns with entries in the field K. Let β⊂V and β′⊂W be bases of vector spaces V and W...

I was curious if anyone is aware of anything resembling a mathematical map, or learning tree. By this I mean a diagram that illustrates the sequence in which one must learn particular topics. I ask because I find myself encountering topics (today it was finite element method) and clicking the...

In Quantum Computation we define a map that takes on density matrix to another. It is represented by some kraus matrices. I do not know why it has to be completely positive.

Hi, Is there a concept map that actually shows all the concepts of math, and how they relate to each other? Kind like this one but more complete. I alreaady searched the web and didn't find anything, that's why I'm here so, Please Help. Thanks.

Homework Statement Find an interval [a, b] for which the Contraction Mapping Theorem guarantees convergence to the positive fixed point or verify that there is no such interval. Homework Equations x = g(x) = \frac{14}{13} - \frac{x^{3}}{13} The Attempt at a Solution I know...

I wasn't quite sure where to put this, so here goes: I am trying to find out some facts about the group SO(2,1). Specifically; Is the exponential map onto? If so, can the Haar measure be written in terms of the Lebesgue integral over a suitable subset of the Lie algebra? What is that subset...

Hi! Let's say in mathematica I declare this function t[x_,y_]:= (x'[s]+y'[s])^2 Now I can call it with L=1; t[(#^2)+L &, (#^3)+L &] if I call it this way it will remplace the # with s and evalute the derivative. Now let's say I wana do this for for every L from 1 to 10. so i got...

Not sure if this is the right category but i need help. On a map of a school, 3 inches represents 9 feet. How many inches would represent 1 foot 6 inches?

Homework Statement Let R be an arbitrary ring, B and B' be left R-modules, and i: B' \to B be an R-module morphism. Show that if the induced map i^*: \operatorname{Hom}_R(B,M) \to \operatorname{Hom}(B',M) is surjective for every R-module M, then i: B' \to B is injective. The...

Homework Statement Draw a contour map for T(x,t)=10e^{-\lambda x}\sin(\omega t-\lambda x) 0\leq\lambda x\leq2\Pi and 0\leq\omega t\leq2\Pi Homework Equations The Attempt at a Solution Because those two variables are within that given range I'm not sure how to do this...

Here is the question: Here is a link to the question: Linear Algebra Problem *Help Please*? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement Consider the field Q(\sqrt{2}), viewed as a vector space of dimension 2 over Q. Let r + s\sqrt{2} \in Q(\sqrt{2}), and define the multiplication map M_{r+s\sqrt{2}}: Q(\sqrt{2}) → Q(\sqrt{2}) by M_{r+s\sqrt{2}}(\alpha)= (r+s\sqrt{2})*\alpha In other words...

I am working on a Bachelors thesis and need to make a grid on a map over a entire floor. Can someone show me how to do this in matlab?

I've two routes in google map: i) A ---> B ii) C ---> D How can I determine if these routes overlap or not?

My textbook says that "a chart or coordinate system consists of a subset U of a set M, along with a one-to-one map \phi :U\rightarrow\mathbf{R}^n, such that the image \phi(U) is open in \mathbf{R}^n." What's the motivation for demanding that the image of U under \phi be open?

Hi, I'm trying to figure out a few questions on a practice exam that I'm working on for my Intro to Logic Systems class and could use some help. One of the questions (and the others are similar) says: Determine the minimized realization in the sum-of-produicts form using literals of the...

Hi! I was wondering why it is possible to write any proper orthochronous Lorentz transformation as an exponential of an element of its Lie-Algebra, i.e., \Lambda = \exp(X), where \Lambda \in SO^{+}(1,3) and X is an element of the Lie Algebra. I know that in case for compact...

Can you help me to construct a 1-1 mapping from real numbers onto non-integers? thanks

I have what I hope to be just a simple notation/definition question I can't seem to find an answer to. I'm not going to post my homework question, just a piece of it so I can figure out what the question is actually asking. I have a function i:A --> X I also have a continuous function g: A...

I quote an unsolved question from MHF posted by user jackGee on February 3rd, 2013. P.S. Of course, I meant in the title and instead of an.

I quote an unsolved problem from MHF (Linear map problem) posted by user jdm900712

Homework Statement Let V be a vector space over the field F. and T \in L(V, V) be a linear map. Show that the following are equivalent: a) I am T \cap Ker T = {0} b) If T^{2}(v) = 0 -> T(v) = 0, v\in V Homework Equations The Attempt at a Solution Using p -> (q -> r) <->...

So I have to implement a 4 input 1 output circuit. I am given the Karnaugh map (obviously a 4by4) and have to build the circuit. I have already determined the essential prime implicants for my map and three possible permutations of nonessential prime implicants. So let's say I pick a...

Whether a continuous and locally one-to-one map must be a (globally) one-to-one map? If the answer is not. Might you please give a counter-example? Thank in advance.

I've been poking around, learning a little about homology theory. I had a question about the boundary operator. Namely, how it's defined. There's two definitions I've seen floating around. The first is at: http://en.wikipedia.org/wiki/Simplicial_homology The second, at...

Commutative ring, map R / ( I /\ J) -> ( R/I ) x ( R/J ) I quote an unsolved question posted in MHF (November 25th, 2012) by user needhelp2. P.S. Communicative note: Of course I meant in the title, commutative instead of communitative.

We are just looking for an example of a quotient map that is not open nor closed. Let π: ℝxℝ -> ℝ be a projection onto the first coordinate. Let A be the subspace of ℝxℝ consisting of all points (x,y) such that x≥0 or y=0 or both. Let q:A -> ℝ be a restriction of π. ( Note: assume that q was...

This is not actual "homework." I am building a POV globe and I want to get as accurate of a projection as possible. The images I will upload into the globe will be a simple 2 dimensional image projected onto a 3 dimensional plane. I have researched and it appears that a Mercator type map is the...

Homework Statement The Attempt at a Solution set x(t)=1+∫2cos(s(f^2(s)))ds(from 0 to t) then check x(0)=1+∫2cos(s(f^2(s)))ds(from 0 to 0)=1 then the initial condition hold, by FTC, we have dx(t)/dt=2cos(tx^(t)), then solutions can be found as fixed points of the map but for...

Homework Statement Find the eigenvectors and eigenvalues of the differentiation map C1(R) -> C1(R) from the vector space of differentiable functions to itself. Homework Equations The Attempt at a Solution Hi, I'm not entirely sure how to go about this, because would the...

Homework Statement Suppose H is an infinite cyclic subgroup of Z. Show that H and Z are isomorphic. Homework Equations We know that any infinite cyclic group H isomorphic to Z. H = <a> ≠ <0> |a| = ∞ The Attempt at a Solution Define f : Z → H | f(k) = ak for all k in Z. We...

Suppose T belongs to L(V,V) where L(A,W) denotes the set of linear mappings from Vector spaces A to W, is such that every subspace of V with dimension dim V - 1 is invariant under T. Prove that T is a scalar multiple of the identity operator. My attempt : Let U be one of the sub spaces of V...

How bad is my statistics knowledge based on the following mind map? Any concepts which aren't bold are the concepts that I know; the bold ones are the ones I'm currently learning. The mind map in question: http://i.imgur.com/4He3f.png What should I learn next based on my current...

Homework Statement As in title. Homework Equations Described in my attempt. The Attempt at a Solution Where do I go from here? I need to show that those 2 unioned sets are open in A. I'm not seeing it

Homework Statement let a be the vector [2,3,1] in R3 and let T:R3-->R3 be the map given by T(x) =(ax)a State with reasons, the rank and nullity of THomework Equations The Attempt at a Solution Im having trouble understanding this... I know how to do this with a matrix ie row reduce and no. of...

Homework Statement Show that B = {x2 −1,2x2 +x−3,3x2 +x} is a basis for P2(R). Show that the differentiation map D : P2(R) → P2(R) is a linear transformation. Finally, find the following matrix representations of D: DSt←St, DSt←B and DB←B. Homework Equations The Attempt at a...

Hi there, I'm reading a report about the efficiency of the drive train of an electric car. The author recorded the speed and acceleration of the car over a period of time and created the graph below to illustrate the efficiency. Could anybody tell me what the relationship is between the...

Homework Statement Let D be a division ring, C its center and let S be a division subring of D which is stabilized by every map x -> dxd-1, d≠0 in D. Show that either S = D or S is a subset of C. 2. The attempt at a solution I haven't actually started working on it yet because I am not...

Hi all, I need help with a paragraph of my book that I don't understand. It says: "the map sending all of ℝ^n into a single point of ℝ^m is an example showing that a continuous map need not send open sets into open sets". My confusion arising because I can't figure out how this map can be...

In the recommended format :) Homework Statement First we say that f:S→T is a map. If Y ⊆ T and we define f-1(Y) to be the largest subset of S which f maps to Y: f-1(Y) = {x:x ∈ S and f(x) ∈ Y} I must prove that f[f-1(Y)] = Y for every subset Y of T if, and only if, T = f(S). Homework...

The definition of a homomorphism is that it must preserve some algebraic structure, so if I transform a vector space using homomorphism between vector spaces (linear map), the result must be a vector space too, correct? Now, if "v" and "w" are two vectors in a vector space V, than "(v + w)"...

A nice animation of sky map containing about 400,000 galaxies. http://www.youtube.com/watch?v=FUAu9ulnwRw

Hi all. I am new here and I am having difficulty figuring out what exactly is required of me in this question. If someone could be so kind as to explain. For this part of the project we will consider the evolution of a discrete dynamical system given by a logistic map. We will consider a...

Hi! I'm trying to understand a proof for the fact that the isometry group of a symmetric space is a Lie group. The proof uses a lemma and I don't see how the lemma works. Here is the statement in question: (Let me give you the definition for \tau_v: Let M be a symmetric space and c:\mathbb R...

Hi! Suppose we have a topological space X, a point x\in X and a homomorphism \rho:\pi(X,x) \rightarrow S_n with transitive image. Consider the subgroup H of \pi(X,x) consisting of those homotopy classes [\gamma] such that \rho([\gamma]) fixes the index 1\in \{1,\ldots,n\}. I know that H...

Homework Statement If the set \Z of integers is equipped with the relative topology inherited from ℝ, and κ:\Z→\Z_n (where κ is a canonical map and \Z_n is the residue class modulo n) what topology/topologies on \Z_n will render κ globally continuous? Homework Equations The Attempt...

Hello All, I am a Masters student in Microelectronics and stuck at something very trivial. In implementing Pass transistors using K Map, i am facing some probs. For eg. consider the function bc(bar) now if you draw a k map the left downward 4 blocks will be filled with 1s. I don't understand...