Map Definition and 403 Threads

Homework Statement Let p : X --> Y be a closed, continuous and surjective map. Show that if X is normal, so is Y. The Attempt at a Solution I used the following lemma: X is normal iff given a closed set A and open set U containing A, there is an open set V containing A and whose...

I often look up at the sky and wonder how far away this or that star/object is. I know that most discernible stars are in our neighborhood, but I have a hard time figuring out just how close they are. Is there a map/graphic that would map all the objects we can see with a naked eye in our...

Homework Statement I have posted this problem on another website (mathhelpforum) but have received no replies. I don't know whether this is because no one knows what I am talking about or if it's just that no one can find a fault with my reasoning. Please please please could you post a reply...

http://blogs.nationalgeographic.com/blogs/news/breakingorbit/2010/11/new-dark-matter-map-hubble.html?source=link_tw20101112hubble" i found this article interesting , so shared here

Make a circuit to multiply two 2-bit numbers AB and CD together to produce a 4-bit output. (a) construct a truth table to represent all states of the inputs and the corresponding outputs. (b) make a Karnaugh map for each output bit. Write down the Boolean algebraic expressions that describe...

I don not know whether I was right or not, please give me a hint. (R3,+) can be considered a Lie group. and its TG in 0 is still R3. suppose X as a infinitesimal generater, it can give a left-invariant vector field and also an one-parameter subgroup. but i think, this one-parameter...

I want a projection of Earth where distances are undistorted. i.e. 10 degrees of latitude at the equator is exactly the same map distance as 10 degrees of latitude at the Arctic Circle. As a disqualified example, the Mercator Projection has map distance increasing with increasing latitude...

urgent homomophim and cannoical map assignement due in 13 hours due now

Homework Statement Let V={a cosx + b sinx | a,b \in R} (a) Show that V is a subspace of the R-vector space of all maps from R to R. (b) Show that V is isomorphic to R^2, under the map f: V\rightarrowR^2 a cosx + b sinx \rightleftharpoons [ a over b ] (this is...

Homework Statement Let f:V\rightarrow V be a linear map and let v\inV be such that f^n(v)\neq0 and f^(n+1)(v)=0. Show that v,f(v),...,f^(n-1)(v) are linearly independent. The Attempt at a Solution I'm really stuck with this one. I know the definition of linear independence and...

Homework Statement the question here said is L, linear transformation/mapping is singular? i'm still googling the definition singular linear map, can anyone give me the definition please T_T p/s; i thought it L maybe the matrix representation, but the question L : R^m -> R^n...

Now F:S^2->R^4 is a map of the following form: F(x,y)=(x^2-y^2,xy,xz,yz) now using the smooth covering map p:S^2->RP^2, p is the composition of inclusion map i:S^2->R^3 and the quotient map q:R^3\{0}->RP^2. show that F descends to a smooth embedding of RP^2 into R^4. Is the problem asked to...

Suppose M and N are smooth manifold with M connected, and F:M->N is a smooth map and its pushforward is zero map for each p in M. Show that F is a constant map. I just remember from topology, the only continuous functions from connected space to {0,1} are constant functions. With this be...

Homework Statement Let T: \mathbb{R}^3 \to \mathbb{R}^3 be the linear map represented by the matrix \begin{pmatrix} 4 & -1 & 0 \\ 6& 3 & -2\\ 12& 6 & -4\end{pmatrix} What is the image under T of the plane 2x - 5y + 2z = -5? Homework Equations None The Attempt at a Solution I...

Vector Help! Homework Statement The treasure map in the figure gives the following directions to the buried treasure: "Start at the old oak tree, walk due north for 490 paces, then due east for 150 paces. Dig." But when you arrive, you find an angry dragon just north of the tree. To avoid the...

Homework Statement Let F be the set of all functions f mapping R into R that have derivatives of all orders. Determine whether p is an isomorphism of the first binary structure with the second. 1. <F, +> with <R, +> where p(f) = f'(0) 2. <F, +> with <F, +> where p(f)(x) = \int^{x}_{0}...

In all map, we always see the north on top, why's that? when was this way first used? Anybody know? Thanks

Homework Statement T(2,1)---> (5,2) and T(1,2)--->(7,10) is a linear map on R^2. Determine the matrix T with respect to the basis B= {(3,3),(1,-1)} Homework Equations The Attempt at a Solution matrix = 5 7 2 10 ?

The terms "function" and "map". I have noticed that the term "map" is used more often than "function" when a map/function is defined using the "mapsto" arrow, as in "the map x\mapsto x^2 ". It has occurred to me that when a function is defined this way, it's usually not clear what the codomain...

Why do Karnaugh map work? I don't understand how they work. If I follow the rules I get a minimized expression easily enough...it just seems like magic.

I'm trying to show an inverse map composed with its noninverse results in the identity in terms of the set map f:X-->Y between topological spaces when f is one to one function. If I define the inverse map of a set as the disjoint union of the inverse map of each point in the set in Y, then...

It's easy to construct maps of even degree from the three-sphere to real projective three-space. Do there exist maps of odd degree?

it is easy to construct a map from S^2 to S^2, with covering time being unity but how to do the similar task on the projected manifold RP^2=S^2/Z_2? i tried to use the stereographical trick the points on the lower half semisphere are projected onto the plane the problem is that the...

Homework Statement Let A = 1 3 2 2 1 1 0 -2 0 1 1 2 Viewing A as a linear map from M_(4x1) to M_(3x1) find a basis for the kernal of A and verify directly that these basis vectors are indeed linearly independant. The Attempt at a...

Hello everyone, I would like to ask what's the purpose of identity map? Recently I came across something that apparently use this to find the inverse image of a function F(x) in the form of F(x) = ( f(x) , x ) . Thanks. Wayne

Can anyone help me with this problem?? Let M be a surface in R^3 oriented by a unit normal vector field U=g1U1+g2U2+g3U3 Then the Gauss map G:M\rightarrow\Sigma of M sends each point p of M to the point (g1(p),g2(p),g3(p)) of the unit sphere \Sigma. Show that the shape operator of M is...

This gave me a chuckle. http://www.economist.com/world/europe/displayStory.cfm?story_id=16003661&source=most_commented Some folks have had http://en.wikipedia.org/wiki/File:Jesusland_map.svg" , too.

Hello all, I am using 2008 C++ Express edition on a Windows XP machine and I have the following question regarding use of a map. How would you use a map to do the following: The user enters a pipe size, say 1/8" NPS, now there are three possible schedules for that pipe size. They are...

Hi, everyone: I am confused about the result that every map from a contractible space X into any topological space Y is contractible. I think the caveat here is that the homotopy between any f:X-->Y and c:X-->Y with c(X)={pt.} is that the homotopy is free, i.e., the...

For the theorem: " If v1,...,vr are eigenvectors of a linear map T going from vector space V to V, with respect to distinct eigenvalues λ1,...,λr, then they are linearly independent eigenvectors". Are the λ-eigenspaces all dimension 1. for each λ1,...,λr.? Is the dimension of V, r? ie...

D is be a bounded domain in the complex plane. Suppose f : D -->D is a holomorphic automorphism (conformal bijection). Now define f_n(z) = f(f(f(f ..(z) (composed n times ). Trying (and failing) to show: (i) the sequence {f_n} has a subsequence that converges either to a constant or to an...

to my local meridian at various times of the year. An object's declination will be fixed - relatively speaking - but its altitude on my local horizon varies from season to season because of Earth's movement, doesn't it? Also, if I'm at a lat. 47.3 N shouldn't celestial objects w/dec. of -{90 -...

Is it be possible to produce from the Intensity return of reflective IR laser the true color of the object causing the reflection of the laser? My though is that surfaces of the same material, but of different colors would cause slight changes in wave length of the laser light. These changes...

I have the following mapping (generalized geometric mean): y(i)=exp\left[{\sum_j p(j|i)\log x(j)}\right]\\ ,\ i,j=1..N where p(j|i) is a normalized conditional probability. my question is - is this a contraction mapping? in other words, does the following equation have a unique...

Homework Statement My book states as follows: --- If u and v have the coordinate vectors X and Y respectively in a given orthonormal basis, and the symmetric, linear map \Gamma has the matrix A in the same basis, then \Gamma(u) and \Gamma(v) have the coordinates AX and AY, respectively. This...

Homework Statement Consider the map L from the space of 2x2-matrices to R given by: L([a b]) = a+ d ([c d]) For clarity, that's L(2x2 matrix) = a + d The Attempt at a Solution Im confused how any function of a matrix could possibly equal addition of two scalars, and thus have no...

help me about karnaugh maps

help me please

What is a "phase map"? I am doing some reading on Structured Light 3D Scanners using digital fringe projection, where a projector shines light (e.g. sinusoidal patterns) onto an object, a camera takes some pictures, and some software uses them to extract a 3D model of the object. The papers...

I'm doing the movement part of the wumpus game. I'm sure many of you are familiar with it, but if not; basically the player starts out in room 1 and s allowed to move into any adjacent room, then from that room into any adjacent room and so on . The map files that are organized as such: 1...

Field of modulo p equiv classes, how injective linear map --> surjectivity Homework Statement Let Fp be the field of modulo p equivalence classes on Z. Recall that |Fp| = p. Let L: Fpn-->Fpn be a linear map. Prove that L is injective if and only if L is surjective. Homework Equations...

Homework Statement This problem is from Schaum's Outline, chapter 7 #38 i believe. Let f: (0, inf) -> [-1,1] be given as f(x) = sin(1/x), where R is given the usual euclidean metric topology and (0,inf) and [-1,1] are given the relative subspace topology. Show that f is not an open map...

How do I write u''+u*e^x = 0 as a planar system?

If p is prime, prove that for every function f: Fp -> Fp there exists a polynomial Q (depending on f) of degree at most p-1 such that f(x) = Q(x) for each x in Fp.

Homework Statement The group G acts transitively from the left on the set X. Let G_x be the little group of the element x \epsilon X. Show that the map i:G/G_x, i(gG_x)=gx is well defined and bijective. Homework Equations transitive action:for any two x, y in X there exists a g in G such...

Here is the press conference. https://www.youtube.com/watch?v=<object width="425" height="344"><param name="movie" value="http://www.youtube.com/v/mTnwjd8CF1c&color1=0xb1b1b1&color2=0xcfcfcf&hl=en&feature=player_embedded&fs=1"></param><param name="allowFullScreen" value="true"></param><param...

Here is a small segment that was dumped after an error in a program has occurred - that does a lot of memory allocation.b7ee6000-b7ee7000 rw-p 00157000 08:02 72280 /lib/libc-2.9.so b7ee7000-b7eea000 rw-p b7ee7000 00:00 0 b7eea000-b7ef7000...

Hi, Say F:A->A where A is a metric space and F is onto. I think it should be true that this implies that F is also one to one. Is there a way to formally prove this? Thanks.

Smooth transition map (easy!?) Homework Statement Check the transition map http://img132.imageshack.us/img132/4341/18142532.png is smooth in the set for which their images intersect The Attempt at a Solution I have thought of two ways to show this. (1) Show that Φ is a composition...

I am trying to prove that the bth projection map Pb:\PiXa --> Xb is both continuous and open. I have already done the problem but I would like to check it. 1) Continuity: Consider an open set Ub in Xb, then Pb-1(Ub) is an element of the base for the Tychonoff topology on \PiXa. Thus, Pb is...