What is Map: Definition and 441 Discussions

A map is a symbolic depiction emphasizing relationships between elements of some space, such as objects, regions, or themes.
Many maps are static, fixed to paper or some other durable medium, while others are dynamic or interactive. Although most commonly used to depict geography, maps may represent any space, real or fictional, without regard to context or scale, such as in brain mapping, DNA mapping, or computer network topology mapping. The space being mapped may be two dimensional, such as the surface of the earth, three dimensional, such as the interior of the earth, or even more abstract spaces of any dimension, such as arise in modeling phenomena having many independent variables.
Although the earliest maps known are of the heavens, geographic maps of territory have a very long tradition and exist from ancient times. The word "map" comes from the medieval Latin Mappa mundi, wherein mappa meant napkin or cloth and mundi the world. Thus, "map" became a shortened term referring to a two-dimensional representation of the surface of the world.

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  1. mfb

    Global Antineutrino Map: Measuring Nuclear Reactor Emissions Worldwide

    A group of scientists used geology models and data about nuclear reactors together with results from two neutrino detectors to produce a worldwide map of antineutrino emission. Man-made reactors are contributing 1% to the total emission, but the production is so localized it is clearly visible...
  2. Borg

    Exploring the Map of Physics - 1932 Edition

    This is an interesting visualization of the historical outline of physics (as of 1932). Enjoy. http://scimaps.org/maps/map/being_a_map_of_physi_171/detail
  3. J

    Cosmic acoustics -- why no intermediate waves on CMB map

    I fully understand the representation of the set of waves that are either at full compression or full rarefaction at recombination, thus, yielding a CMB map. But at this time are there no waves that are intermediate, e.g. 50% of the way to full compression or full rarefaction. Why don't these...
  4. O

    MHB What is the relationship between $f$ and $X$?

    let f:X to X be and f(X) C X...then f is invariant..if f is invariant, then f is self map on X ? is it true ?
  5. caffeinemachine

    MHB Kernel of the Symmetrizing Map

    Let $V$ be a finite dimensional vector space over a field of characteristic $0$ and let $sym:\bigotimes^k V\to \bigotimes^k V$ be the map defined as $$ sym(\alpha)=\frac{1}{r!}\sum_{\sigma\in S_k}{^\sigma}\alpha $$ where $S_k$ is the permutation group on $k$ letters and ${^\sigma}\alpha$...
  6. D

    Differential map between tangent spaces

    I've been struggling since starting to study differential geometry to justify the definition of a one-form as a differential of a function and how this is equal to a tangent vector acting on this function, i.e. given f:M\rightarrow\mathbb{R} we can define the differential map...
  7. P

    K Map Help: Finding Minterms for Reordered Expression F(C,B,A,D)

    1. The original expression is: F(A,B,C,D) = Σm(0,1,2,5,8,9,10) If I changed the order of ABCD to: F(C,B,A,D) What would be the minterms now?2. Use the truth table for 0 to 15The Attempt at a Solution I used the truth table in the regular order ABCD and for CBAD.ABCD | F 0000 | 1 0001 | 1...
  8. K

    Understanding MAP Sensor Reading on Peugeot Cars

    Hi guys, I have read a lot about car's MAP sensor and it's function but there are some areas that are not completely understood yet! Let me put it this way: My car's MAP sensor reads 337 mbar (millibar) @ idle (800 RPM). When i open the throttle, the reading DROPS (for example at 2500 RPM it...
  9. gfd43tg

    What do the color maps in spherical harmonics represent?

    Hello, I am watching a video about spherical harmonics, and I am at the point where the color map is being shown for various values of ##l## and ##m## My question is, what am I supposed to make of these plots? Pretty colors yes, but what do these things mean?
  10. F

    What is an inclusion map? (manifolds)

    In my book its says let i: U →M (but with a curved arrow) and calls it an inclusion map. What exactly is an inclusion map? Doesn't the curve arrow mean its 1-1? So are inclusion maps always 1-1?
  11. caffeinemachine

    MHB To Prove that The Level Set Of A Constant Rank Map is a Manifold

    Let $f:\mathbf R^n\to\mathbf R^m$ be a smooth function of constant rank $r$. Let $\mathbf a\in \mathbf R^n$ be such that $f(\mathbf a)=\mathbf 0$. Then $f^{-1}(\mathbf 0)$ is a manifold of dimension $n-r$ in $\mathbf R^n$. We imitate the proof of Lemma 1 on pg 11 in Topology From A...
  12. D

    Adjoint of an adjoint of a linear map

    My question is as it says in the title really. I've been reading Nakahara's book on geometry and topology in physics and I'm slightly stuck on a part concerning adjoint mappings between vector spaces. It is as follows: Let W=W(n,\mathbb{R}) be a vector space with a basis...
  13. I

    Geodesic exponential map distance

    Homework Statement Hi all. For some reason I have been having a lot of difficulty with this problem in Peter Petersen's text. The problem is Prove: ##d(exp_p(tv), exp_p(tw)) = |t||v-w| + O(t^2 )## Homework Equations The exponential map is the usual geodesic exponential map. And ##d(p,q)## is...
  14. I

    Riemannian Geometry exponential map and distance

    Hi all, I was wondering what the relationship between the Riemannian Geometry exponential map and the regular manifold exponential map and for the reason behind the name.
  15. M

    How Can Set-Valued Maps Be Integrated in Measurable Spaces?

    laTex
  16. M

    Is F continuous if it is both upper and lower semicontinuous?

    1/ Prove that the set-valued map F defined by F : [0, 2π] ⇒ R2 as F(α) := {λ(cos α, sin α) : λ ≥ 0}. is continuous, but not upper semicontinuous at any α ∈ [0, 2π]. 2/ What is the fact that " F is continuous if it is both u.s.c. and l.s.c". I would like illustrate that and thank you.
  17. P

    Multipole Map with Healpix routines

    Hello, I have to create the CMB multipole map from a Planck Data Map with Healpix routines on IDL, and I just don't got a clue of how it must be done! Can anybody help me?Thanks! physfed
  18. T

    X-ray crystallography - Electron-density map

    Homework Statement Hello, i have the following task in my homework: When doing an X-ray crystallography experiment to determine the structure of biomolecules (protein/DNA), why do consider interpreting an electron-density map (EDM) instead of directly using the diffraction data? 2. The...
  19. Philosophaie

    Map or a Listing of All the Constellation Boundaries in Right Ascensio

    How would I get a Listing or a Map of All the Constellation Boundaries in Right Ascension and Declination.
  20. D

    True map of universe from computer simulation with CMB initial state

    Do you think we will ever be able to create a simplified computer simulation of the universe using the cosmic microwave background as the initial state that would generate the true locations of galaxies or at least galaxy clusters, and then be able to find our own galaxy or galaxy cluster within...
  21. P

    Map Taking Proper Time to Euclidean Length

    Is there a way to map time-like curves in Minkowski space to curves in a Euclidean space such that the length of the curve in the Euclidean space is equal to the proper time of the curve in Minkowski space?
  22. G

    Example of Completely positive map from M_n to M_m

    Can you guys give me a concrete example of a completely positive map from M_m → M_n?
  23. C

    MHB Inverse map is closed under complementation

    f^-1 (E^c) = (f^-1(E))^c where f is map from X to Y and E is in Y. Prove equality is true.
  24. W

    Unifying Different Definitions of Adjoint Map

    Hi, this question seem to fall somewhere between Analysis and Algebra; I just choose this section; sorry if it is the wrong one. I would appreciate any suggestions, refs., etc. I'm basically trying to see if the different definitions of adjoint maps can be unified into a single...
  25. E

    If p is a covering map with B compact and fiber of b finite, E compact

    Homework Statement Let p: E \rightarrow B be a covering map. If B is compact andp^{-1}(b) is finite for each b in B, then E compact. Note: This is a problem from Munkres pg 341, question 6b in section 54. The Attempt at a Solution I begin with a cover of E denote it \{U_\alpha\}. I...
  26. hideelo

    Understanding Saturated Sets in Quotient Maps

    I am reading munkres topolgy and I am struggling with understanding the following sentence: "We say that a subset C of X is saturated (with respect to the surjective map p:X→Y) if C contains every set p-1({y}) that it intersects" if you have the second edition its in chapter 2 section 22...
  27. S

    MHB Is This Function a Contraction Map?

    how do i prove that this function is a contraction map? f(x)=⟨(1/9)cos(x1+sin(x2)),(1/6)arctan(x1+x2)⟩; x1=⟨0,−1⟩.i wantd to use the matrix form of the jacobian i said x(1)' = -1÷9sin(x_1 +sinx_2) ∙ (x'_1 + cos_2) x(2)' = 1÷(6(1+ (x_1 + x_2)^2) ∙ x'_1 + x'_2 I don't know how to put this...
  28. O

    MHB Contraction Map: Proving $f(x)$ is a Contraction

    I am given this function $f(x)=\langle (1/9) \cos(x_1+ \sin(x_2)) , (1/6) \arctan(x_1+ x_2) \rangle$ where $x_1= \langle 0,-1 \rangle$. may I please get hints on how to prove that this function is a contraction map
  29. F

    Help Healpix: from data to map

    Hi, i've just installed Healpix on IDL, and I'm starting to try all the subroutines. First of all, i learned how to make a dipole map with random numbers (it works!:) ). Now i'd like to plot a map using real data. The .txt file is organized like this: DEC(°) AR(°)...
  30. marellasunny

    Engine map with load curve in 5th gear:fuel consumption varies weirdly

    http://imageshack.com/a/img824/2641/1cpe.png The black curve I drew there represents the load curve in 5th gear. Why is it that at 5500 rpm(160kph), I have a lesser fuel consumption(270g/kWh) than at 4000 rpm(280g/kWh)? Intuitively,if I produce more power at 180kph(ie 5500rpm),I should...
  31. S

    MHB Working on lipschitz function and contraction map

    if you given a function f from R^2 to R^2 f(x)=<f_1(x),f_2(x)>, x in R^2 with f_1 and f_2 from R^2 to R being differentiable on R. if there is contants K_1 and K_2 greater than or equal to 0 so the 2-norm of (gradient f_1(x)) is less than or equal to K_1 and 2-norm of (gradient f_2(x)) is...
  32. S

    Bifurcation values for logistic map

    Homework Statement Find numerically the r values for the first 2 bifurcations. Homework Equations xi+1 = f(xi), f(x) = rx(1 − x) The Attempt at a Solution To find the values of r, first I set rx(1−x)=0 to find x and then used the x values to find r=0 and r=1. But, I am still...
  33. J

    Mapping a Strip to a Sector Using the Exponential Map

    Homework Statement Using the properties of the exponential map, construct a one to one mapping of the strip S to the sector C: S=\{-\sqrt{2}x-t<y<-\sqrt{2}x\} , C=\{-\frac{\pi}{6}<arg(w)<\frac{\pi}{3}\}, where t is a fixed positive real number. Here we let z=x+iy. Homework Equations...
  34. Math Amateur

    MHB Tensor Products - D&F page 369 Example 3 - The map phi

    I am reading Dummit and Foote, Section 10.4: Tensor Products of Modules. I am currently studying Example 3 on page 369 (see attachment). Example 3 on page 369 reads as follows: (see attachment) ------------------------------------------------------------------------------- In general...
  35. B

    Is every norm preserved under a unitary map?

    I am a bit confused, so this question may not make much sense. A unitary operator from one vector space to another is one whose inverse and Hermitian transpose are identical. It can be proved that unitary operators are norm preserving and inner product preserving. Which raises the question...
  36. A

    MATLAB MATLAB Filter command for BSFC map

    Hi all, I have made a BSFC plot in MATLAB with engine data tested on an eddie current dyno, The code I used for it is: >> NP=40; >> [RP TP]=meshgrid(linspace(min(RPM),max(RPM),NP),linspace(min(Torque),max(Torque),NP)); >> BSFC_IT=griddata(RPM,Torque,BSFC,RP,TP); >> NC=12; >>...
  37. J

    Exploring Subgroup Inverse Maps in Group Theory

    Homework Statement For a group G consider the map i:G\rightarrow G , i(g)=g^{-1} For a subgroup H\subset G show that i(gH)=Hg^{-1} and i(Hg)=g^{-1}H Homework Equations The Attempt at a Solution I know that for g_1,g_2 \in G we have i(g_1g_2)=(g_1g_2)^{-1}=g_2^{-1}g_1^{-1} Then...
  38. Petrus

    MHB Linear Map Input: Solving P'(1-x) | \pi\rangle

    Hello! I have hard to understand this input for this linear map T:P_3(R)->P_2(R) T(p(x))=P'(1-x) so they get this value when they put in which I have hard understanding I don't understand how they get those, I am totally missing something basic...! The only logical explain is that in p'(x)=3x^2...
  39. D

    When someone asks for a map of a program, what do they mean?

    I was given a C++ program (a hefty one at that) and asked to create a map of it. He added some more details (something about functions), and I left his office thinking I understood what he requested but now I realize I don't. I'll approach him and ask for more details but before I do that...
  40. N

    Website For Universe map, and Matter Totals

    Just for some observation, is there any good "maps" of the universe? like nothing detailed but shows the hemispheres. Also is there any website which show totals of matter in the universe, and how it changes when you go to different parts of the universe?
  41. Math Amateur

    MHB Affine Algebraic Sets - D&F Chapter 15, Section 15.1 - Properties of the map I

    I am reading Dummit and Foote Ch 15, Commutative Rings and Algebraic Geometry. In Section 15.1 Noetherian Rings and Affine Algebraic Sets, the set \mathcal{I} (A) is defined in the following text on page 660: (see attachment)...
  42. Sudharaka

    MHB Is the continuous map property preserved under taking limit points?

    Hi everyone, :) Trying hard to do a problem recently, I encountered the following question. Hope you can shed some light on it. :) Suppose we have a continuous mapping between two metric spaces; \(f:\, X\rightarrow Y\). Let \(A\) be a subspace of \(X\). Is it true that, \[f(A')=[f(A)]'\]...
  43. T

    Is There a Linear Transformation to Map Data Set X to Y in PCA?

    This question broadly relates to principle component analysis (PCA) Say you have some data vector X, and a linear transformation K that maps X to some new data vector Z: K*X → Z Now say you have another linear transformation P that maps Z to a new data vector Y: P*Z → Y is there...
  44. S

    MHB Sum of Products with Karnaugh Map

    Write out the minimal Sum of Products(SOP) equation given the following Karnaugh Map. YZ|WX 00 01 11 10 00 d 1 1 1 01 1 1 0 0 11 0 0 d 1 10 0 0 0 0 Need someone to check my answer. My answer: yzw + \bar{y}\bar{z} + \bar{y}\bar{w}
  45. F

    Please check my road map for becoming a theoretical physicist

    Please check my road to Physics I am a new member,been to this forum before but was never a registered user (?) Before hitting on the topic, I think it is necessary to describe my background. So here it is: I live in India! I am currently enrolled in BSc MATHEMATICS at IGNOU (INDIRA GANDHI...
  46. Barioth

    MHB Find the eigenvalue of a linear map

    Hi everyone, I have this linear map A:R^3 \rightarrow R^3 I have that A(v)=v-2(v\dot ô)ô); v,ô\in R^3 ;||ô||=1 I know that A(A(v))=v this telling me that A is it's own inverse. From there, how can I find the eigenvalue of A? Thanks
  47. L

    Do Hilbert Space Isomorphism Map Dense Sets to Dense Sets?

    Suppose that H, K are Hilbert spaces, and A : H -> K is a bounded linear operator and an isomorphism. If X is a dense set in H, then is A(X) a dense set in K? Any references to texts would also be helpful.
  48. S

    MHB Given a K map, minimize the Product of Sums

    Awesome thanks.. Mind checking this as well? Minimize Sum of Products equation given the following K map. My Answer: \bar{y} \bar{w} + wx + y\bar{z}w + yw\bar{x}
  49. N

    MHB Find Conformal Map to Remove Semidisk | Solutions & Explanations

    Please refer to the attached image. Ok, I'm in a bit of strife here. I like to give in my own feedback and thoughts on particular questions so I can have one of you experts tell me where I am going wrong/right and help me, however I have absolutely no idea with these two questions. Could I...
  50. nomadreid

    Recursive logistic map vs continuous logistic function

    how is the logistic function characterized by the differential equation df(x)/dx = f(x)(1-f(x)) [with solution f(x)=1/(1+e-x), but this is irrelevant to the question] the continuous version of the logistic map, given by the recursive function: xn+1 = xn(1-xn)? It would seem to me that...
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