Mapping Definition and 364 Threads

What is set associated mapping and What are the difference between direct and set associated mapping

Homework Statement Find function that maps area between ##|z|=2## and ##|z+1|=1## on area between two parallel lines. Homework Equations The Attempt at a Solution I don't know how to check if my solution works for this problem? I used Möbious transformation...

Homework Statement Find a conformal mapping of the strip ##D=\{z:|\Re(z)|<\frac{\pi}{2}\}## onto itself that transforms the real interval ##(-\frac{\pi}{2},\frac{\pi}{2})## to the full imaginary axis.The Attempt at a Solution I tried to map the strip to a unit circle and then map it back to the...

what is the map of the area bound by y=5x and y=-3x in the upper half plane, under w=1/z we have the lines : $ z(t) = t + 5t i $ , and the line $z(t) = t - 3ti $ Fist line $\displaystyle w_1 = \dfrac{1}{t+5ti} = \dfrac{1}{26t} - \dfrac{5i}{26t} $ Second $\displaystyle w_2 = \dfrac{1}{t -...

Let say i have two sets of numbers A and B. and I want to assigne to each number from A two slosest numbers from B. What i would do is to pick an elements from A and then go through the entire B set and find two closest. now if i go the other way arround in orderd to achieve the same result i...

I am looking for a way to map gases over a city, what are some ways I could do that? This is a theoretical experiment so cost is not an issue. Thanks in advance

Hello I've been doing a mind map of Abstract Algebra. A mind map is a visual representation of a subject, like algebra, organic chemistry, etc. , in a way that makes the subject structured in a more intuitive way, without losing the logical component. It's a map of the subject that make the...

Prove the Contraction Mapping Theorem. Let ##(X,d)## be a complete metric space and ##g : X \rightarrow X## be a map such that ##\forall x,y \in X, d(g(x), g(y)) \le \lambda d(x,y)## for some ##0<\lambda < 1##.Then ##g## has a unique fixed point ##x^* \in X ##, and it attracts everything, i.e...

For an upcoming lab I will be mapping out the equipotential lines in an electric field with an isolated conductor in it. The conductor is a hollow cylinder. I have attached a crude paint drawing of the apparatus. The lab asks some qualitative questions that I would like to knock out before hand...

Hi I uploaded the question and its answer first of all I am not good at all in mapping I don't understand it that much like here we want the output of the function under that specific domain that's what we want to see. I understand until PI < alpha < 5/2 * PI but I don't understand how did he...

Hi, Homework Statement I'd like to show that the mapping w=u+iv=1/z tranforms the line x=b in the z plane into a circle with radius 1/2b and center at u=1/2bHomework Equations The Attempt at a Solution z*w=1=(b+iy)(u+iv) → 1=|(bu-yv)+i(bv+yu)| → u2+v2=1/(b2+y2) Now, a circle with radius 1/2b...

Hi. This is a homework question, so I can't ask or give out too much info. SO, there is a linear mapping F, and it is given that F=F^2. Can I assume that everything about F, i.e. dimension, kernel, image, etc, is exactly the same for F^2? Or does it just mean that given a vector v, F(v) =...

Assume that $$ f: E \to Y \,\,\, , E \subset X$$ then can we say that $$f(E^c)=f(E)^c$$ what about the inverse mapping $$f^{-1}: V \to X \,\,\, , V\subset Y$$ do we have to have some restrictions on f and its inverse ? My immediate answer is that we have to have a bijection in order to conclude...

This occur when two phonons interact and the sum of their momenta add to a new wavevector outside the new Brillioun zone. The resulting wavevector is then mapped back into the Brillioun zone by subtraction of a suitable reciprocal lattice vector. I don't think I understand the physics in all of...

Hi, This is a little different from most questions in that it's not something I want to solve, but rather hoping I could get a little clearer explanation on what mapping is and why/when we use it? I'm soon to go over conformal maps, but I don't think i understand anything to do with mapping as...

The overall phylogeny of eukaryotes has long been a difficult and contentious subject, almost as bad as the phylogeny of prokaryotes. One could recognize some well-defined groups, but that was about it. But as biologists learned out to sequence proteins, and then nucleic acids, they got a...

The identity map on the direct sum of V1 and V2 would be i1 composed with p1 + i2 composed with p2. Would such an identity map exist for an infinite direct sum? And an analogous mapping for a direct product?

I am somewhat puzzled after reading that polynomials can be vectors, this concept confuses me. For instance, they can say that a basis for polynomials P_2 can be. B=\{1+t^{2},t+t^{2},1+2t+t^{2}\} In this case will the mapping [1+t^{2}]_{B} be [1,0,0] or [1,0,1]?

Let $f$ be a continuous mapping of a compact metric space $X$ into a metric space $Y$ then $f$ is uniformly continuous on $X$. I have seen a proof in the Rudin's book but I don't quite get it , can anybody establish another proof but with more details ?

Let ##L## be a linear operator ::##L(A)= Tr(A)## where ##Tr(A)## is the trace of a square matrix Find a basis of the kernel of L. Any help would be really appreciated . thanks in advance

Homework Statement Let L: V →V be a linear mapping such that L^2+2L+I=0, show that L is invertible (I is the identity mapping) I have no idea how to solve this problem or how to start,I mean this problem is different from the ones I solved before, the answer is "The inverse of L is -L-2 "...

So I have been trying to figure out some orientation data that I gather from a triaxial gyroscope, and figure out my orientation using only initial conditions and angular velocity from the gyroscope's current axes. The data is all relative to the current orientation, so if I rotate the device...

When we map the algebraic function, w(z), to a Riemann surface we essentially create a new "Riemann" coordinate system over a surface that is called the "algebraic function's Riemann surface". This mapping allows one to create single-valued functions, f(z,w), of the coordinate points over...

Hi... first post here! Sorry if not in the right place. I am trying to decode the parameters for an xml file format and I would appreciate help in interpreting some parameters. I know the thing specified is a "transition curve" or clothoid curve, as the transition between a straight path and...

Hello All: I am working on a function given as f(x) = 10/x + (1/20)x^2 for x such that 0≤x≤10. What can be said about the contraction mapping property of f(x)=x? If it is not a contraction map, is there any way to make modifications on the function or the interval and prove a contraction mapping...

Homework Statement I wasn't sure where to post this in particular, so I apologize if this is in the wrong section. I've been getting interested in the topic of problem mapping lately. I came across this problem while reading and I'm not quite sure if I have the right idea or not. The...

Here is a link to the question: Prove that a contraction T on a metric space is a continuous mapping? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Hello, I'm trying to construct an explicit map that takes the 4D torus to the 4-sphere such that the wrapping is non-trivial (i.e. homotopically, i.e. you can't shrink it continuously to zero). More concretely, I'm looking for \phi: T^4 \to S^4: (\alpha,\beta,\gamma,\delta) \mapsto (...

Homework Statement Find the kernel and range of the following linear mapping. b) The mapping T from P^{R} to P^{R}_{2} defined by T(p(x)) = p(2) + p(1)x + p(0)x^{2} The Attempt at a Solution I'm not sure how to go about this one. Normally I would use the formula T(x) = A * v...

Homework Statement Let G be a group and let Aut(G) be the group of automorphisms of G. (a) For any g \in G, define \phi_{g}(x) = g^{-1}xg. Check that \phi_{g}(x) is an automorphism. (b) Consider the map: \Phi:G \rightarrow Aut(G) g \mapsto \phi_{g} Check that \Phi is a...

Homework Statement Show that the following linear transformation matrix is a contraction mapping. \begin{bmatrix} 0.5 & 0 & -1 \\ 0 & 0.5 & 1 \\ 0 & 0 & 1 \end{bmatrix} I don't know how to make that into a matrix, but it is a 3x3 matrix. The first row is [.5 0 -1] the second row is [0...

I'm studying Landau's Electordynamics of continuous media and, although I like how succinct it is, sometimes it is too succinct! I'm having trouble with a particular passage, so I'll just try to summarize the section up until the part I don't understand. The topic at hand is electrostatic field...

W= z+2 /z-2 drawing mapping find image in w plane line Re(z)constant and im(z)=constant find fixed point from mapping In my textbook have just W = z-1 / z+1 . Thank a lot for your help.

Let f: R -> R be a local diffeomorphism (diffeomrophism in a neighborhood of each point). Show that the image of R under f is an open interval. Furthermore show that f is a diffeomorphism of R on to f(R). Ok, here is what I am thinking.. that since we are dealing with a "diffeomorphism" we...

What's the trick to convert changes in current to some voltage equivalent? 50% increase in current --> 50% increase in voltage Can it be done? What I'm doing is trying to take a photoresistor and have it act as an analog input on a ADC however the ADC is voltage based. :-\

Let f(x) be a function which is defined in the open unit disk (|z| < 1) and is analytic there. f(z) maps the unit disk onto itself k times, meaning |f(z)| < 1 for all |z| < 1 and every point in the unit disk has k preimages under f(z). Prove that f(z) must be a rational function. Furthermore...

Hi, Given that the flow normal to a thin disk or radius r is given by \phi = -\frac{2rU}{\pi}\sqrt{1-\frac{x^2+y^2}{r^2}} where U is the speed of the flow normal to the disk, find the flow normal to an ellipse of major axis a and minor axis b. I can only find the answer in the...

I googled this but couldn't find a clear answer. Is every invertible mapping an isomorphism b/w 2 grps or does it have to be linear?

When I am editing German Latex files in vim using a us keyboard, I would like to map "a to a-umlaut etc. I added corresponding imap commands in my vimrc and they work in principle. However I have to type "a" after """ at a certain speed, if not, the cursor jumps from before """ to after it...

I'm trying to plot positions of earthquakes on a map. The primary goal is to make Matlab plot a map so I can put the positions of earthquakes on it. I've read through the help section for Matlab's Toolbox but to be honest I'm still confused about it. Has anyone used Mapping Toolbox to know...

Suppose that we have rigged Gilbert space Ω\subsetH\subsetΩ\times (H is infinite-dimensional and separable). Is the Ω a separable space? Is the Ω\times a separable space? Consider the complete set of commuting observables (CSCO) which contain both bounded and unbounded operators...

Let y=Ax. A is a matrix n by m and m>n. Also, x gets its values from a finite alphabet. How can i show if the mapping from x to y is injective for given A and alphabet (beside a search method)? For example, let A and the alphabet be [1 0 1/sqrt2 1/sqrt2] [0 1 1/sqrt2 -1/sqrt2] and...

f:[1,infinity)->[1,infinity) $f(x)=x^{0.5}+x^{-0.5}$ I thought about using MVT but it doesn't work and I've tried showing it conventially but i can't reduce it to k|x-y|

So just had this question as extra credit on a final: Let D be an integral domain, and suppose f is a non-constant map from D to the non-negative integers, with f(xy) = f(x)f(y). Show that if a has an inverse in D, f(a) = 1. Couldn't figure it out in time. I was thinking the way to go...

Homework Statement I have the double integral, ∫∫sqrt(x^2+y^2) dxdy, and the area D:((x,y);(x^2+y^2)≤ x) Homework Equations The Attempt at a Solution By completing the squares in D we get that D is a circle with origo at (1/2,0), and radius 1/2. Then I tried changing...

Homework Statement We have the conformal map w = f(z) = z + K/z. Prove this mapping is indeed conformal. Homework Equations z = x + iy A map w = f(z) is conformal if it is analytic and df/dz is nonzero. f(z) = u(x,y) + iv(x,y) The Attempt at a Solution df/dz = 1 - Kz^-2 =/= 0 for finite...

Homework Statement Take the unit circle in the x-y plane with center at (0, 0), bisected by the x-axis. Take two maps, the first MS from the circle minus the south pole S to the x-axis that take a point P on the circle to the intersection of the line from the south pole (0, −1) through P with...

Hi, All: I'm trying to show that the Mapping torus of a manifold X is a manifold, and I'm trying to see what happens when X has a non-empty boundary B. Remember that the mapping torus M(h) of a space X by the map h is constructed like this: We start with a homeomorphism h:X-->X (we...

Homework Statement i recently saw a question about complex number, and its answer about the center of a circle is 1/2*(1+i). what does that mean? Homework Equations f:ℂ → ℝ^2 The Attempt at a Solution since we define z=x+yi is an element of ℂ, so by the mapping above, we can say...

So I want to clarify if what I'm thinking is correct. Suppose we have a mapping f : A → B and we have a in A and b in B. If f is an injective map, then f(a) = f(b) implies that a = b or conversely a≠b implies f(a)≠f(b). If f is a surjective map, then for b in B, there exists an a in A such...