Map Definition and 441 Threads

Homework Statement I'm trying to show that a distance preserving map is 1:1 and onto. The 1:1 part was easy, but I'm stuck on proving it's onto... Homework Equations X is compact T(X)\subseteqX THere's a hint saying to consider a point y in X\T(X) and consider the minimum distance...

I have a GPS track I'd like to plop on top of a map. The region of the track is very small, no bigger than the area of a city. I also have a bunch of shape files to build up a map of the city with all the buildings, roads, etc. in separate shp files. Although the shape files actually contain...

I don't understand the proof of this theorem: There is no continuous antipode-preserving map g: S2→S1. The proof is like this: Suppose g: S2→S1 is continuous and antipode-preserving. Take S1 to be the equator of S2. Then the restriction of g to S1 is a continuous antipode-preserving map h of...

I need help calculating the exponential map of a general vector. Definition of the exponential map For a Lie group G with Lie algebra \mathfrak{g}, and a vector X \in \mathfrak{g} \equiv T_eG, let \hat{X} be the corresponding left-invariant vector field. Then let \gamma_X(t) be the maximal...

Homework Statement Does anyone know the process for finding the differential of of f:S→S' where S,S' are surfaces. My textbook explains how to do this when f is a vector valued function but in the problem that I am working on I have something like f(x,y)=(g(x),h(x),j(y)) rather than something...

Homework Statement Prove that the identity map \mathrm{id}_{S^{2k+1}} and the antipodal map -\mathrm{id}_{S^{2k+1}} are smoothly homotopic. Homework Equations N/A The Attempt at a Solution My attempt: Fix k \in \mathbb{Z}_{\geq 0} and let \{e_i\}_{i=1}^{2k+2} be the standard basis for...

Homework Statement Evaluate the matrix elements x_{nn'} = \left<n\left|x\right|n'\right> and p_{nn'} = \left<n\left|p\right|n'\right> and map the energy eigenstates \left|n\right> to Cartesian unit vectors. Homework Equations x = \sqrt{\frac{\hbar}{2m...

consider we have a map. what condition should have our map that it has inverse?

Top down visual of near live wind trails in the US. Really neat! http://hint.fm/wind/ Now we just need it overlayed on google maps!

Hi everybody, sorry for the inconvenience. I try to plot the poincarè map of the restricted three body problem. I find in this forum the follow script that do this for the Lorenz system: mysol = NDSolve[{x'[t] == -3 (x[t] - y[t]), y'[t] == -x[t] z[t] + 26.5 x[t] - y[t], z'[t] ==...

1. Let G be any group and x∈G. Let σ be the map σ:y→xyx⁻¹. Prove that this map is bijective. It seems to be written strangely, since it never really says anywhere that y is in G, but I guess that must be an assumption.2. bijective=injective+surjective. in order to prove injective, we need to...

Homework Statement The Attempt at a Solution For part ii) I wrote it out as a matrix, getting \begin{array}{ccccccc} 0 & 0 & 0 & 0 & ... & 0 \\ 0 & 0 & 2 & 0 & ... & 0 \\ 0 & 0 & 0 & 6 & ... & 0 \\ . & . & . & . & . & . \\ 0 & 0 & 0 & 0 & ... & N(N-2) \end{array} So...

I want to make a m-file that show the behavior of the logistic map for dierent values of r using the bifurcation diagram. This is what i currently have, but i don't know why it is wrong. Can anyone help me? c=0; hold on while c < 4 y=0.5; for i=1:100; y =...

I found some Matlab code that works. However, I am not sure how to alter it for my needs. How can I make the code work for this:##N_{t+1} = \frac{(1+r)N_t}{1+rN_t}##What needs to be changed? %%% MAKES A COBWEB PLOT FOR A LOGISTIC MAP % compute trajectory a=3.0; % parameter x0=0.2...

Suppose you've got a linear map U between two Hilbert spaces H1 and H2. If U preserves the inner product - that is, (Ux,Uy)_2 = (x,y)_1 for all x and y in H1 - is it necessarily unitary? Or are there inner product-preserving linear mappings that aren't one-to-one or onto?

I'm looking at Munkres: Topology Problems 1.2.4(c), 1.2.4(e), and 1.2.5(a). Problem 1.2.4(c) asks, "If g\circ f is injective, what can you say about the injectivity of f and g?" Problem 1.2.4(e) asks, "If g\circ f is surjective, what can you say about the surjectivity of f and g?" I concluded...

Hey guys, I've often seen in the definition of a Fiber bundle a projection map \pi: E\rightarrow B where E is the fiber bundle and B is the base manifold. This projection is used to project each individual fiber to its base point on the base manifold. I then see a lot of references to...

Google France Sued by Bottin Cartographes for Providing Free Map Services... So this is an interesting story... Unfortunately all the articles I have seen seem to be based on the same AFP article and the AFP article is rather lacking in information. Add to that my lack of french and I am...

I'm interested in the proper way to give a mathematical definition of a certain geometric property exhibited by certain maps from points to sets. Consider mappings from a n-dimensional space of real numbers P into subsets of an m-dimensional space S of real numbers. For a practical...

It's used in a certain proof that I'm reading. A is a linear map from a vectorspace V onto itself. They say they can rewrite the vector space as \mathcal V = \bigoplus_\mu \mathbb C^{m_\mu} \otimes \mathcal V^\mu and I understand this, but they then claim one can (always, as any linear map)...

We were taught both methods to minimize gates. I frankly just want to pick one method all the time and become an expert in it, rather then try them both. So, according to your experience, which method do I better pick?

first i hope is the correct forum to ask this kind of question. so i asked to find the minimum SOP function from the Karnaugh map (given in the picture). so i started to solve it as you can see in the picture. and this what i got:fsop=AB+BC+ACD'X' till here i think is ok. now this is...

Homework Statement Let X and Y be ordered sets in the order topology. I want to show that a function f:X→Y is injective. We are given that f is surjective and preserves order. Homework Equations Definition of an order preserving map: If x≤y implies f(x)≤f(y) The Attempt at a...

Hi, All: I saw this question somewhere else: we are given any two topological spaces (X,T), (X',T'), and we want to see if there is always at least one continuous map between the two. The idea to say yes is this: we only need to find f so that f-1(U)=V , for every U in T', and some V in T. So...

Is there a C^infty map that is one to one from R^n to R? Thanks.

Throughout most of the discussions I have had about science, philosophy, physics, math, and life in general over the past 35 years (since beginning my first undergraduate class in philosophy) there is one element of every discussion that returns. It has to do with the statement "the map is not...

http://www.ted.com/talks/allan_jones_a_map_of_the_brain.html?utm_source=newsletter_weekly_2011-11-11&utm_campaign=newsletter_weekly&utm_medium=email" http://www.ted.com/speakers/allan_jones.html" http://human.brain-map.org/explorer.html" Lots of explore and research here, cheers Paul...

I have a 3D shape described by a triangulation map i.e. a map between the vertices to the faces of the shape which are all triangles. I then sliced the shape by a plane and computed the intersections of the plane and the triangle faces. Each triangle face that intersects the plane, will have...

I live less than a mile from the SAFZ near Frazier Park, and would like to identify related surface features like escarpments, tuff outcrops, etc. After much Googling, I have found no maps that would help me locate the identified fault line locations within even 1000ft. None. Has anyone here...

I have been exploring an algebraic structure with a map (_)* such that (x)*** = (x)* but in general it is not an involution. Also, the set of elements e such that e** = e do not form a substructure because they are not closed to addition. Has anyone seen such maps before, or know/can...

Chemistry: "Road map" question. Borax can be converted to pure boron through the series of chemical reactions shown below: Pure boron is isolated in the final step of this reaction series. The starting material Y, is a non-polar gas with terminal chlorine atoms. Compound Y (2 mol) is heated...

Homework Statement Find a bijective map : χωxχω\rightarrowχω Homework Equations An omega tuple is a function x:N\rightarrowχ, where χ is a set. χω is the set of all omega tuples of elements of χ. A bijective function is both injective and surjective. The Attempt at a...

Why, hello there. I'm doing Karnaugh maps. I'm using them to device gates to express the numbers 0, 1, 2, 3, 4 in a seven segmented digital display. Our teacher has provided us with predrawn Karnaugh maps, where we simply fill in the 1's and 0's. However, he's decided to invert the...

Let G have a transitive left action on a set X and set H = G_x to be the stabilizer of any point x. Show that the map defined by f: G/H \rightarrow X where f(gH) = gx is well defined, one to one, and onto. i think i know how to show well defined. letting g1 H = g2 H, if i multiply on the...

Homework Statement Verify that any square matrix is a linear operator when considered as a linear transformation. Homework Equations The Attempt at a Solution If a square matrix A\inℂ^{n,n} is a linear operator on the vector space C^{n}, where n ≥ 1, then the square matrix A is...

I have no programming experience and trying to get mathematica to do what I need it to do is frustrating. I have the following functions that I need to iterate. For notational purposes, k[t+1] is the value of K in the next period. w is a parameter. k[t+1] = -x[t] - y[t] + w x[t+1] =...

Don't know whether this belongs in chemistry or Earth science but there has been discussion about salinity here. http://www.bbc.co.uk/news/science-environment-15033532

I have the following question: Let $\mathbb{D}$ denote the unit disk. Let $f:X_1 \longrightarrow X_2$ be a continuous mapping between Riemann Surfaces. Let $ \pi_1 : \mathbb{D} \longrightarrow X_1$ , and $ \pi_2 : \mathbb{D} \longrightarrow X_2$ be the universal covering spaces of $X_1$ and...

Hi: More on Prelims: We have a map f: S^3 -->S^3 ; S^3 is the 3-sphere , given by: (x1,x2,x3,x4)-->(-x2,-x3,-x4,-x1). We're asked to find its degree, and to determine if f is homotopic to the identity. I computed that f^4 ( i.e., fofofof ) is the identity, and we have that...

Hi, Algebraists: The modN reduction map r(N) from a matrix group (any group in which the elements are matrices over Z-integers) over the integers, in which r is defined by r(N) : (a_ij)-->(a_ij mod N) is not always commutative, e.g.: r(6) :Gl(2,Z) --Gl(2,Z/N) is not...

Hi All, I am trying to draw a map, the raw data I have is Speed and G_Force (Lat and Acce). I have attached a XLS of the RAW data I have. Its from a race track, (I had to trim the file to 100kb, so it might or might not loop). I don't have a GPS, but I have seen software draw maps based on...

Homework Statement I have to find a conformal map from \Omega = \{ z \in \mathbb C | -1 < \textrm{Re}(z) < 1 \} to the unit disk D(0,1) Homework Equations an analytical function f is conformal in each point where the derivative is non-vanishing specifically, we can think of linear...

Homework Statement "Show that there is no conformal map from D(0,1) to \mathbb C" and D(0,1) means the (open) unit disk Homework Equations Conformal maps preserve angles The Attempt at a Solution I don't have a clue. I thought the clou might be that D(0,1) has a boundary, and C...

Has anyone ever drawn a gravity map of the Earth? i mean one that looks at mountain ranges, Vallie's, oceans, and shows the gravity (topology), or the shape of the deformation from a perfect sphere. edit, may be this should go in the Earth forum but i think it is more, gp.

Homework Statement This problem is an already solved one in Marsden and Hoffman's Basic Complex Analysis, but I can't seem to work out the last step. Here's the problem: Suppose a,b,c,d are real and ad-bc>0. Then show that T(z) = \frac{az+b}{cz+d} leaves the upper half plane invariant. Show...

Hello, I was wondering if there were alternative definitions to a "function" ( alternative to the standard f is a subset of A X B if f : A -> B ). I was introduced to the "general" definition of a cartesian product ( with respect to an indexing set H ) , it is weird to me because the general...

Novice question :blushing: I've been reading Brian Greene's "The Hidden Reality". It occurred to me that spacetime across the 2D analog of the U could be much like an isometric weather map. Could it be that the U isn't expanding, but that our region, like a High on a weather map is rushing...

Homework Statement Let b > a > 0. Consider the map F : [0, 1] X [0, 1] -> R3 defined by F(s, t) = ((b+a cos(2PIt)) cos(2PIs), (b+a cos(2PIt)) sin(2PIs), a sin(2PIt)). This is the parametrization of a Torus. Show F is a quotient map onto it's image. Homework Equations Proving that any subset...

Homework Statement Find the Linear Fractional Transformation that maps the line Re\left(z\right) = \frac{1}{2} to the circle |w-4i| = 4. Homework Equations For a transform L\left(z\right), T\left(z\right)=\frac{z-z_{1}}{z-z_{3}}\frac{z_{2}-z_{3}}{z_{2}-z_{1}}...

Hello, I am working with python's Image Library (PIL), Sympy, and Matlab. I have a topographical map of the earth, ( see 3d warehouse from google ). I am wondering if with an rgb matrix from a jpeg heightmap is traditionally the value of black and white ignored, because it seems that the...