Map Definition and 441 Threads

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. H

    Calculating Moment Map of 2-Torus Action on C^3

    Homework Statement Given a 2-torus action on C^3 can be defined by (a,b).(x,y,z)= (abx, a^-1by, bz). What is the moment map? Homework Equations The Attempt at a Solution Here the Lie algebra is isomorphic to the dual Lie algebra which is dual to R^2. I was trying to...
  2. J

    Find basis for the kernel of linear map

    I need help. For this problem, you have to use the Gram-Schmidt process to make it orthogonal. My trouble is finding the bais for the kernel of the linear map L: R4 -> R1 defined by L([a,b,c,d)]=a-b-2c+d I know the dimension of the kernel is 3, but how? I have tried setting it...
  3. T

    Science Map: 800,000 Papers Sorted into 776 Paradigms

    http://img61.imageshack.us/img61/9930/scimapgx8.jpg This map was constructed by sorting roughly 800,000 published papers into 776 different scientific paradigms (shown as pale circular nodes) based on how often the papers were cited together by authors of other papers. Links (curved black...
  4. marcus

    Fairbairn-Livine map spinfoam developments

    In trying to get some perspective on the papers that appeared first quarter 2007, I've come to the opinion that this is potentially one of the more productive ones. It is not just about 3D quantum gravity-and-matter. It has also things to say about 4D gravity-and-matter...
  5. robphy

    Mathematicians Map [ the exceptional Lie group ] E8

    https://www.physicsforums.com/showthread.php?p=1277407 (main thread in Linear & Abstract Algebra) http://science.slashdot.org/science/07/03/19/117259.shtml
  6. P

    Matrix Representation of a Linear Map

    Homework Statement Consider the linear map A : R3 ----> R3 given by A(x1, x2, x3) = (x1 − x2,−x1 + x2, x3). (a) Find the adjoint map A^*. (b) Obtain the matrix representations of A and A* with respect to the canonical basis f_1 = [1, 2, 1], f_2 = [1, 3, 2], f_3 = [0, 1, 2]...
  7. T

    Quotient map on a product space

    suppose q:M -> M/R is a quotient map. i've asked my dad what is the quotient map from MxM to (M/R)x(M/R)? he told me it is qxq: MxM -> (M/R)x(M/R) defined by (qxq)(x,y) = (q(x), q(y)), but there are some conditions to be met, but he could not remember what those conditions are. i...
  8. C

    Does Hubble's Dark Matter Map Challenge MOND Theory?

    Dark Matter Mapped by Hubble (space.com article): http://www.space.com/scienceastronomy/070108_mm_darkmatter_map.html This is a very interesting article on Dark Matter and there are nice pics showing its clumpiness at varying distances from Earth. According to the last paragraph of the...
  9. N

    First 3D Map of Dark Matter in the Universe

    http://www.esa.int/esaCP/SEMZ6GSVYVE_index_0.html Go read it while I try to comprehend how they managed to map the dark matter in the universe by studying a relatively tiny part of the sky.
  10. A

    Contour map and Intersection points

    Homework Statement (i) Drawing a contour map for the function h(x.y) = -12-4x^2+16x-y^2-8y (ii) (Continuing from i) at the point (1,-1,7) which direction to move to have the maximum increase in height? (iii) Find the point closest to the origin on the curve of intersection of the...
  11. I

    C/C++ Opening a bit map in Visual C++

    Could someone recommend a way to open and edit a bitmap file in Visual C++?
  12. marcus

    New map of the galaxy (Levine Blitz Heiles)

    http://physicsweb.org/articles/news/10/6/3/1?rss=2.0 ===sample quote=== Levine and colleagues took previously obtained data from the hydrogen "21-cm emission lines" and applied a technique called unsharp masking to increase the contrast between high and low signal regions. They found that the...
  13. O

    What is the Boolean Equation for This Karnaugh Map?

    Hi, this should be simple but it's really giving me difficulty. Does anybody know what the Boolean Equation would be for this Karnaugh Map? Thanks in advance, Oliver
  14. H

    Contour: Constructing a Contour Map from h(x,y) = x^2 + y

    Hello, I have a sum: ------- make a contour map from a height field h(x,y) = x^2 + y on the domain: [-3<_ x <_3 ; 0<_ y <_9]. Make an east-western cross section (paralell to x-axis) through the field h in the northern, middle and southern part of the domain and draw all three height...
  15. J

    One-form is a linear map from a vector to a real number

    I'm trying to understand what one-forms are. The book I'm reading says a one-form is a linear map from a vector to a real number. It uses the gradient as an example but isn't the gradient a map from a function to a vector?
  16. C

    Drawing a genetic map (recombination)

    We discovered that in the fungus Sordaria fimicola, a gene caused the fungus to produce normal black or mutant tan colored ascospores. Observations of crosses between normal and mutant fungi showed that 56% of the asci produced by these hybrid fungi are recombinant. This translated to a 28%...
  17. T

    Can Quotient Spaces Show Chaotic Behavior?

    The logistic equation; x(n+1) = rx(n)(1-x(n)) shows chaotic behavior under some values of r. It is a discrete chaotic system. Is it possible to translate it to continuous chaotic system? I tried it in the following site; http://geocities.com/tontokohirorin/mathematics/moduloid/moduloid2.htm
  18. A

    Surface Ocean Currents: Temperature Map

    I have to list the temperature (cold or warm, the black ones "are the same temperature as the current leading into it") of the following currents: North Atlantic Labrador (Newfoundland) Oyashio (Japan) Alaska California Gulf Stream Canary (NWAfrica) Kuroshio (Taiwan) Peru...
  19. T

    "next state" eqn from the karnaugh map of a present state?

    does anyone knows how to find out the "next state" eqn from the karnaugh map of a present state?? pls help...
  20. Astronuc

    Oldest map in Europe from 500 BC

    Archaeologists find western world's oldest map By Hilary Clarke in Rome http://www.telegraph.co.uk/news/main.jhtml?xml=/news/2005/11/18/wmap18.xml&sSheet=/news/2005/11/18/ixworld.html Hopefully there is more.
  21. A

    How to Make a Chemistry Concept Map in Microsoft Word

    I have to make a concept map in Microsoft Word (Not necessarily but that's the only thing I know how to use.) but I can't figure out how. I've done it before so I can't figure out why it isn't working now...:confused: Anyone have any suggestions for making a concept map?:smile:
  22. JamesU

    HTML/CSS Troubleshooting HTML Image Area Map Issues

    I'm trying to create an area mep for an image, but it's not working right. any help? <html> <head> <title>Enter through the door</title> </head> <body> <map name="amap"> <area shape="rect" coords="474,202,541,358" href="../leveltwo.htm"> </map> <center><img...
  23. Pengwuino

    Map Out Where You Live: Find Friends Near You

    Oh wow this is friggen awesome! http://www.risingconcepts.com/frapper/physicsforums You just type in your screen name and zip code and you're put on the map! Now we can see where everyone lives :)
  24. V

    Conformal map for regular polygon in circle.

    Hi All, I'm looking for the conformal mapping (using complex functions) that maps the unit circle (or the upper half plane) into a REGULAR polygon with n vertices. I know the Schwarz-Christoffel transformation for an ARBITRARY polygon, but that doesn't help me because the expression is way...
  25. marcus

    What impact on QG if the CMB map is revised?

    A paper just came out this month that makes it more certain that the Cosmic Microwave map will have to be revised, with even less quadrupole and octopole power. http://www.arxiv.org/abs/astro-ph/0508047/ On the large-angle anomalies of the microwave sky I opened a thread on this paper in...
  26. C

    Transpose of Matrix as Linear Map

    What are the relations between a matrix H and its transpose H^T? I am not asking about the relations between the coefficients, I am asking the relations as linear maps (H: F^m->F^n; H^T: F^n->F^m). I am not sure exactly how I should pose the question actually, but I am thinking there is some...
  27. marcus

    Why CDT changes the map of quantum gravity

    I happen to think it does. I will try to say why in this thread. Other people may very likely disagree, so it is possible to have discussion about this. you can get most of CDT out of two basic papers "Dynamically..." and "Reconstructing..." the links are in my signature. I will copy them...
  28. M

    Is the Sky Disc of Nebra a genuine ancient artifact or a modern forgery?

    Source; The Guardian - London, UK http://www.guardian.co.uk/arts/news/story/0,11711,1427600,00.html 03-01-05 Ancient Sky Map Or Fake? German Experts Row Over Star Disc Luke Harding in Berlin The Guardian quote:"One of Germany's most acclaimed archaeological finds - a 3,600-...
  29. hitssquad

    Global national-IQ map posted at Children of Millennium

    Children of Millennium has posted a rather impressive-looking global map of national IQs. Here is the map: http://www.childrenofmillennium.org/eugenics/pages/articles/IQmap.gif It is linked from this article on national IQs: http://www.childrenofmillennium.org/science.htm
  30. T

    How Can I Map Cassini's Oval to the Unit Disk?

    Okay, so I'm having problems figuring out how exactly i can map the interior of Cassini's oval (|z^2-a^2|<r^2 , 0<a<r) onto the unit disk (|w|<1), so that the axis of symmetry are preserved. Anyone know how to do this? :confused: (In this case, the cassini oval is a peanut shaped domain, i think)
  31. S

    What are the properties of open sets in X x Y for a continuous projection map?

    I'm trying to prove some stuff that involves the projection map, say p:X x Y ->X. But I need to know if it's continuous. If a map is continuous, then the preimage of a open/closed set is open/closed. The problem is, what do open sets in X x Y look like? I know what the basis elements are...
  32. P

    Calculating Position of Summit on a Map

    Sorry to have posted this twice, but I didn't realize there is a special homework help section until after I'd posted in another part of the board. Anyway, any guidance in how to draw the diagram for the following problem would be greatly appreciated. I'm not sure about the position of the Z...
  33. J

    Plane Maps and Planar Graphs: A Mutual Relationship?

    Plane Map <=> Planar Graph ?? Hi, Wondering if anyone can help me to find some kind of proof that all Plane Maps can be represented by planar graphs and vice versa... for all Planar Graphs exists a Plane Map? I did a quick search without much luck. Thanks
  34. M

    Looking for a *3D navigable* star map.

    What I DO NOT NEED OR WANT! Star maps that show the locations of stars from any point of view on Earth. (I don't need to see views from Earth, already got plenty of resources for that. I need to be able to see what surrounding stars would look like if you were at or near OTHER stars.) I do...
  35. enigma

    Looking for a Lunar altitude map

    Hi all, I'm trying to locate a map with a lunar "sea-level" and colors (or similar) which change based on relative altitudes. I'm striking out online in my quick 15 minute search. Does anyone know of where I should be looking? Thanks,
  36. Nibles

    How do scientists create a map of the sky using cosmic background radiation?

    I was reading some article about some scientists who were able to 'read' some sort of cosmic background radiation and determine the size, shape, and age of the universe or whatever. How do they take these radiation readings and create an 'image' or understanding of the universe?
  37. chroot

    What Is the Logarithmic Map of the Universe?

    Way cool. http://www.astro.princeton.edu/~mjuric/universe/ - Warren
  38. Raavin

    Physics Equation Map: Solve Problems Easily

    Physics equation map? Does anyone know if there is some sort of 'map' or flowchart available whereby you can use the information you have and trace your way through directions to get another result eg. start at distance/time ==Differentiate=> velocity =differentiate=>...
  39. Ivan Seeking

    How Do Gravity Anomalies Affect Earth's Shape?

    "These gravity anomalies, as they are known, are imperceptible to the human senses, and so the scientists have wrapped the data on to a sphere and exaggerated the highs and lows." http://news.bbc.co.uk/2/hi/science/nature/3093927.stm
  40. S

    News Is Israel's Sacrifice of Territory for Ceasefire a Triumph for Terrorism?

    Recently, Israel has sacrificed the town of http://story.news.yahoo.com/news?tmpl=story&cid=540&ncid=736&e=1&u=/ap/20030701/ap_on_re_mi_ea/israel_palestinians on the west bank to Palestinians, in exchange for a cease fire that was broken by the Palestinians. Fleeing Israelis destroyed their...
  41. marcus

    Question about irred rep of SU(2) that factor by the covering map

    Let &phi; SU(2) ---> SO(3) be the double covering Any irreducible representation of SO(3) pulls back by &phi; to provide an irreducible representation of SU(2) on the same finite dimensional Hilbert space. this seems clear, almost not worth saying: the pullback is obviously irred. and...
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