Mapping Definition and 364 Threads

Homework Statement I don't know if this has ties to linear algebra, so sorry in advance if I'm posting in a wrong section. We have an n*n matrix A, n is an odd number, and "the matrix's sides are 0" meaning: we'll call non-zero elements as 1's for now.1st line 1111...1111 2nd line 0111...1110...

Homework Statement Let f be a function defined on all of R and assume there is a constant c such that 0<c<1 and |f(x)-f(y)<c|c-y| a) Show f is continuous on all of R b)Pick some point y1 in R and construct the sequence (y1,f(y1),f(f(y1)),...) In general if y_(n+1)=f(yn) show that the...

Let D = {x \in R : -3\leq x \leq 5 and x \neq0} and define g(x) = [cos(x) - 1]/x + sqrt(x+3)(5-x) Find G: R ->R such that G is continuous everywhere and g(x)=G(x) when x\inD I'm not really sure how to start this and I've been looking at it for quite a while now. I might just need a push...

Homework Statement So I'm going through baby Rudin. Problem 15 in chapter 4 has us trying to prove that every continuous open mapping is monotonic. I'm trying to see how this is the case. So, I'm considering f(x) = sin(x). Let V = (Pi/3, 7*Pi/12) be an open set. Then, f(V) = (\sqrt{3}/2, (1...

Assume you're given a circle with the line AB containing its center O, such that A and B are on the circle (OA=OB=radius). A tangent t is drawn on the point A, and I should calculate the mapping of certain points (a,b,c,d...) of the circle to the points on the tangent (at, bt, ct, dt, ...) such...

Homework Statement Let {p_n}n>0 be the ordered sequence of primes. Show that there exists a unique element f in the ring R such that f(p_n) = p_n+1 for every n>0 and determine the family I_f of left inverses of f. Homework Equations The ring R is defined to be: The ring of all maps...

Homework Statement relation from R^2-->R^2 ( R is real line) (y1) [0 1] (x1) (y2) =[-1 1] (x2) is this left invertible? if so what is the left inverse? y1,y2 are element in a 2by 1 matrix, same with x1, x2. the elemenst 0,1,-1,1 are in a 2x2 matrix. I did no know how to...

Homework Statement Let (a1, a2, ...) and (b1, b2, ...) be sequences of real numbers, where ai > 0, for every i. Let the map h : Rω --> Rω be defined with h((x1, x2, ...)) = (a1x1 + b1, a2x2 + b2, ...). One needs to investigate under what conditions on the numbers ai and bi h is continuous...

I have recently been extremely bothered by the fact that we can construct a bijection from [0,1] onto the entire two-dimensional plane which itself contains [0,1]. Similarly, I have been bothered by the fact that we can construct a bijection from (0,1) to all real numbers. Indeed we do so...

Homework Statement The recombination frequency between gene “Q” and gene “Z” is found to be 23.5%. The recombination frequency between “Q” and a third gene “R” is 10%. The frequency of recombination between “Z” and “R” is 13.5%. Which one of the following is NOT true concerning these three...

Homework Statement Two homozygous plants are crossed and all offspring (F1) are yellow with long stems. A cross of the offspring (F1)produces the following phenotypes in the F2 generation: 1,263 yellow, long stem 1,196 white, short stem 205 yellow, short stem 195 white, long stem...

We define isometric mapping so that its tangent mapping preserves the scalar product of vectors from tangent space (the definition doesn't refer explicite to notion of distance in the manifold). Distance between two points of manifold is the length of geodesics which joins them. I wonder...

Homework Statement Consider the function g : [0,∞) → R defined by g(x) = x + e−2x. Given |g(x2) − g(x1)| < |x2 − x1| for all x1, x2 ∈ [0,∞) with x1 ≠ x2. Is g a contraction on [0,∞)? Why? Homework Equations I think we are intended to use the given equation and the CMT CMT states that...

Homework Statement Suppose X = [0,1] x [0,1] and d is the metric on X induced from the Euclidean metric on R^2. Suppose also that Y = R^2 and d' is the Euclidean metric. Is the mapping T: [0,1] x [0,1] \rightarrow R^2, T(x,y) = (xy, e^(x.y)) uniformly continuous? Explain your answer...

Homework Statement map the function \begin{equation}w = \Big(\frac{z-1}{z+1}\Big)^{2} \end{equation} on some domain which contains z=e^{i\theta}. \theta between 0 and \pi Hint: Map the semicircular arc bounding the top of the disc by putting $z=e^{i\theta}$ in the above formula. The...

Can an element of a quotient group G/N in an isomorphism f:G/N--H map back onto itself if it does not have a corresponding element in H? The example I am looking at is the quotient group of the group of symmetries of an n-gon, G, where n is an even number and N equal to the normal subgroup...

We know that a linear operator T:X\rightarrowY between two Banach Spaces X and Y is an open mapping if T is surjective. Here open mapping means that T sends open subsets of X to open subsets of Y. Prove that if T is an open mapping between two Banach Spaces then it is not necessarily a closed...

Let p,q : \mathbb{C} \to \mathbb{C} be defined by \begin{align*} p(z) =& z^7 + z^3 - 9z - i, \\ q(z) =& \frac{z^7 + z^3 - i}{9} \end{align*} 1. Prove that p has a zero at z_0 if and only if z_0 is a fixed point for q. If z_0 is a fixed point for q then \begin{align*} q(z_0) =...

I would like you to share mapping of Physics for high school. Please help me .:smile:

how do we describe the biholomorphic self maps of the multiply puncture plane onto itself? I mean C\{pi,p2,p3..pn} Plane with n points taken away. I wanted to generailze the result for the conformal self maps of the punctured plane, but I do feel these are quite different animals. I...

According to Einstein, the Big Bang theory did not make sense because he said if you mapped the paths of the galaxies and stars back in time they would not collide at a singularity at the center of the universe, they would miss each other. Since many people accept the Big Bang theory, has it...

i been trying to understand this and basically the answer i got was it makes it easier to solve for product of sums...is this close to being correct? could you explain how it is applied. thank you.

Homework Statement let T(V)=V be a linear map, where V is a finite-dimensional vector space. Then T^2 is defined to be the composite TT of T with itself, and similarly T^(i+1) = TT^i for all i >=1. Suppose Rank (T) = Rank (T^2) Homework Equations a) prove that Im(T) = Im(T^2) b) for...

Homework Statement I know that the Mobius transformation: g(z) = \frac{z-z_1}{z-z_3}\frac{z_2-z_3}{z_2-z_1} maps a circle (with points z_1, z_2, z_3 somewhere on the circumference) onto a line. But, i want a general formula for f(z) that maps a circle (z_1,z_2,z_3) ontp a circle...

A complex function f\left(z\right)=\sqrt{z} can be splitted into two branches: 1. Principal branch: f_{1}\left(z\right)=\sqrt{r} e^{i \left(\theta/2\right)} 2. Second branch: f_{2}\left(z\right)=\sqrt{r} e^{i \left[\left(\theta+2\pi\right) /2\right]} My question is, is there a way to...

Define the mapping torus of a homeomorphism \phi:X \rightarrow X to be the identification space T(\phi)= X \times I / \{ (x,0) \sim (\phi(x),1) | x \in X \} I have to identify T(\phi) with a standard space and prove that it is homotopy equivalent to S^1 by constructing explicit maps f:S^1...

Homework Statement Hi all. We are asked to transform the shaded area in below figure to between two concentric circles, an annulus. Where these circles' center will be is not important, just transform the area to between any two concentric circles. As you see in figure, shaded area is whole...

1. Homework Statement Find all \mathcal{C}^1 functions f(\mathbf{x}) in \mathbb{R}^3 such that the mapping \psi : \mathbb{R}^3 \to \mathbb{R}^3 also preserves volumes, where \begin{equation*} \psi(\mathbf{x}) = \left( \begin{array}{c} x_1 \\ x_1^2 + x_2 \\ f(\mathbf{x})...

Homework Statement Let B be the outside of the unit ball centered at the origin, and let c be a non-zero constant. Consider the mapping where k=1,2,3. Find the image of the set B under the mapping. (Hint: consider the norm of (y1, y2, y3)) Homework Equations The unit ball would be 2...

Given: G is the group of matrices of the form: 1 n 0 1 Where n is an element of Z, and G is a group under matrix multiplication. I must show that G is isomorphic to the group of integers Z. I do not know how to do this, since all examples we covered gave us the specific mapping...

Homework Statement I'm trying to find a function that map the exterior of a circle |z|>1 into the interior of a regular hexagon. Homework Equations The Attempt at a Solution I have tried mapping the exterior to the interior circle. Then mapping interior circle to the upper plane which then I...

Hi My book defines one-to-one mapping as A mapping T is one-to-one on D* if for (u,v) and (u',v') ∈ D*, T(u,v) = T(u', v') implies that u = u' and v = v' I don't really understand what they are trying to say, because right now what I'm getting from this information is that only...

Here's an interesting article on the first 'skylight' - opening to a possible underground lava tube or cavern - discovered on the Moon: http://www.newscientist.com/article/dn18030-found-first-skylight-on-the-moon.html I'm wondering how it might be possible to map out underground caverns and...

Hi, my question is what mapping to use for the problem in the picture attached. I need to be able to find the potential distribution etc by mapping from the x-y plane (as pictured) to a straight lines plane capacitor, which would be pretty straightforward, but I can't find this map in any...

Hey guys, new to the forum but hoping you can help. How do you prove that vector spaces V and U have a linear injective map given V is finite dimensional. I got the linear part but cannot really figure out the injectivity part, although I am thinking that it has to do with the kernel...

Hello, so i was looking up the defintion of linear mapping and mapping in general and i have seen the technical defintion a few times but i was wondering if someone would mind explaining it to me in more general english. How would you explain it instead of just pointing out the definition...

Homework Statement Find the Mobieus mapping that maps { z e C, |z| <= 1 } to a disk {z e C, |z - 1| <= 1} in a real axis. The Attempt at a Solution I have had an idea that Mobieus mapping is from C to C such that it is a homeomorfism and it has an inverse mapping. I am not sure how...

Homework Statement We're supposed to find a bijective mapping from the open unit disk \{z : |z| < 1\} to the sector \{z: z = re^{i \theta}, r > 0, -\pi/4 < \theta < \pi/4 \}.Homework Equations The Attempt at a Solution This is confusing me. I tried to find a function that would map [0,1), which...

Homework Statement I need to find a unitary operator that can map two (two-dimensional) pure states |+\rangle, |-\rangle as follows: |+\rangle \to \cos\theta |+\rangle + \sin\theta |-\rangle |-\rangle \to \sin\theta |+\rangle + \cos\theta |- \rangle For an arbitrary angle 0 \leq...

Homework Statement If i have a sketch of field lines, and equipotential lines which i completed in a lab, and i know the voltage,V, of points located at intervals ,L, how do i find the electric field for the whole plane? Homework Equations lEl = DeltaV/DeltaL The Attempt at a...

Let B={s|s is a function mapping the set of natural numbers to {0,1}}. Is B a countable set-that is, is it possible to find a function \Phi() mapping the set of natural numbers onto B-? I know that it has to do with infinite binary sequences, but the countability part confuses me. Can...

For an infinitesimal mapping with u = 1,2,3,4: x ^u \rightarrow x^u + \xi^u(x) Now suppose we introduce a new set of variables: x^{'u} = x^{'u}(x) I would have thought the infinitesimal mapping in terms of the new variables should be written as: \xi^{'u}(x^{'}) = \frac{\partial...

Hey! I have a really easy question here, but I still can't figure it out. I have a range of values from 182 to 455. I need a function that gives me back values from 1-50. IE, f(318) = 25. The numbers aren't critical, but I'd love a general equation to use for this kinda stuff. Can anybody...

Homework Statement Hello. :smile: I was hoping I could get some help with a homework question. "Draw the graph of f. State whether f is One to One and also whether it is Onto." Homework Equations Equation 1 : f(x) = 1/x^2 if x≤-1 Equation 2 : f(x) = (x+3)/2 if -1≤x≤1 Equation...

In order to build a QE measurement system, I want to confirm the following issues: (1) Is collimated light required for QE characterization of the entire solar cell? How "bad" it could be if having Gaussian beam? (2) It seems LBIC is most common for QE mapping. Is it possible to use...

Homework Statement Let T: R2 -> R1 be given by T(x,y) = (y^2)x + (x^2)y. Is T linear? justify your answer Homework Equations The Attempt at a Solution Yes it is a linear mapping because both points map onto one point.

Homework Statement Hi all. I have seen a conformal mapping of z = x+iy in MAPLE, and it consists of horizontal and vertical lines in the Argand diagram (i.e. the (x,y)-plane). On the Web I have read that a conformal map is a mapping, which preserves angles. My question is how this...

If I take F(x)=\sqrt{1+x^2}, then the derivative is always less than one so this is a contraction mapping from R to R, right? But there is no fixed point where F(x)=x, where the contraction mapping theorem says there should be. So where have I gone wrong? Cheers

mapping a: S --> T be so that any x ε S has one and only one y &# What makes it necessary for any mapping a: S --> T be so that any x ε S has one and only one y ε T?

Let L:=\{z:|z-1|<1\} \cap \{z:|z-i|<1\}. Find a Mobius transformation that maps L onto the sector \{z: 0< arg(z) < \alpha \}. What is the angle \alpha? no idea of how about to set up the problem The intersection of the two circles forms a lens shaped region L with boundary curves, let's...