Mapping Definition and 364 Threads

Homework Statement Find the images of the following region in the z-plane onto the w-plane under the linear fractional transformations The first quadrant ##x > 0, y > 0## where ##T(z) = \frac { z -i } { z + i }## Homework EquationsThe Attempt at a Solution [/B] So for this, I looked at the...

I know the concepts of conformal mapping and complex mapping but I didn’t see none explanation about how apply this ideia and formula for convert a curve, or a function, between different maps. Look this illustration… In the Cartesian map, I basically drew a liner function f(x) = ax+b...

Homework Statement The question: Scientists need to take precautions when they carry out restriction mapping. They need to make sure that the enzyme they have used has completely digested the DNA. One check they may carry out is to add the sizes of the fragments together. How could scientists...

Often, in the study of algebraic objects certain things (like tensor products) are often defined primarily in terms of an universal mapping property. When one is used to "concrete objects" one can calculate with, this often comes as a shock to the system. One feels as if one is spinning...

hey all - ive built an big amp DC electric kart, and want to add a gas motor for secondary drive. not going serial hybrid - I want both to be drive motors. I've written controller code (can link to it if anyone wants) - but the problem is not the code - its how to map the transition of...

The second postulate of SR is telling us that light always travels at C in a vacuum(absent of gravity) measured by any observer independent of the source or inertial frame the observer is measuring the light from. However, light is made up of photons which do not travel like ping pong balls in...

Homework Statement [/B] Hello all, thank you in advance for your help. Please let me know if this is the wrong forum. My problem: Let x= a + b√2 and let y= the 2 x 2 matrix {a 2b}{b a}. Show that x maps to y. Homework Equations [/B] As I see it, for multiplication, this is pretty...

I have a toy quantum circuit simulator that I work on. I want to visually represent operations in multiple ways: as a Hamiltonian, as a unitary matrix, and as a Bloch sphere rotation. I want to double-check that I haven't flipped anything. I'll focus a concrete example: is this animation...

Hi, I've been trying to find one symmetric "injective" N²->N function, but could not find any. The quotes are there because the function I'm trying to find is not really injective, as I need that the two arguments be interchangeable and the value remains the same. In other words, the tuple (a...

Homework Statement Linear algebra:[/B] Find all x in R4 space that are mapped into the zero vector for the given matrix A A= | 1 -4 7 -5 | | 0 1 -4 3| | 2 -6 6 -4|Homework Equations None... it's linear algebra. Don't ban me. The Attempt at a Solution I tried RREF on this after...

Hello Physics Forum patrons! I am currently in search for some software and maybe hardware to analyze and map vibration/stability for rotating cutting tools (CNC milling). Being primarily a machine programmer and product designer, I have a very minimal understanding of vibration from a physics...

Homework Statement The bane of all physicists... 'Proof' questions... So we have the mapping, Δ : P3→P3 Δ[P(x)] = (x2-1) d2P/dx2 + x dP/dx And I need to prove that this is a linear mapping Homework Equations Linear maps must satisfy: Δ[P(x+y)] = Δ[P(x)] + Δ[P(y)] and Δ[P(αx)] - αΔ[P(x)]...

Homework Statement Let L be a mapping such that L(A) = A^t, the transpose mapping. Find a matrix representing L with respect to the standard basis [1,1,1,1] Homework EquationsThe Attempt at a Solution So should I end up getting a 4x4 matrix here? I got 1,0,0,0 for the first column, 0,0,1,0 for...

Homework Statement Let P be the vector space of one variable polynomials with complex coefficients. if D: P-->P is the derivative mapping, show that the linear mapping D^2+2D+I is invertible. Homework Equations show that D^2+2D+I is both injective and surjective The Attempt at a Solution...

"Definition: A map ƒ: A ⊂ ℂ→ ℂ is called conformal at z0, if there exists an angle θ ∈[0,2Pi) and an r > 0 such that for any curve γ(t) that is differentiable at t=0, for which γ(t)∈ A and γ(0)= z0, and that satisfies γ ' ≠0, the curve σ(t) = ƒ(γ(t)) is differentiable at t=0 and, setting u =...

Say you have a cross section of an electric field, and you want to make a visualization, not just of the magnitude, but showing each 3 components (negative and positive). What kind of colour transfer function scheme would you think is best in order to show the information that a physicist would...

Hello everybody, I am working on a project that require to have map of an MRI machine fringe field in 3d space. I basic idea is to measur it in one plane parallel to radius of machine and then by assuming that field is axissymetric make my map. does anybody have any idea on doing that or on my work?

Definition of Kannan Mapping Let (X,d) be a complete metric space...İf for each $x,y\in X$ following condition holds, then $T:X\to X$ is Kannan mapping $d(Tx,Ty)\le\alpha\left[d\left(x,Tx\right),d(\left(y,Ty\right)\right)]$ $\alpha\in[0,\frac{1}{2})$ Definition of Quasi-Nonexpansive...

Say I will make the transformation from the ##z## plane to the ##w## plane. Moreover, I'll transform a region ##R## with boundary ##C## in the ##z## plane to something in the ##w## plane. Why is it that if I know the equations for ##C## then I can transform these and immediately know that ##R##...

Let $T$ be a continuous mapping of a complete metric space $X$ into itself such that ${T}^{k}$ is a contraction mapping of $X$ for some positive integer $k$. Then $T$ has a unique fixed point in $X$. Proof: ${T}^{k}$ has a unique fixed point $u$ in $X$ and...

Please can you prove that $f\left(x\right)={e}^{{-e}^{-x}}$ is contraction mapping on R...Thank you for your attention...

Homework Statement Homework Equations RF = (#Recombinants)/(Total offspring) x 100 The Attempt at a Solution How do I know that b is unlinked? I know that unlinked genes have a recombination frequency of 50% or higher, but how do I calculate RF for the genes here?

Let $(X,d)$ be a complete metric space, and suppose that $f:X \to X$ satisfies the condition: for each $\epsilon >0$, there exists $\delta > 0$ such that for all $x,y \in X$ $$ \epsilon \le d(x,y) < \epsilon+\delta \implies d(f(x),f(y)) < \epsilon.$$Clearly, this condition...

Homework Statement Find the image of the rectangle with four vertices A=0, B= pi*i, C= -1+pi*i, D = -1 under the function f(z)=e^x 2. The attempt at a solution So, the graph of the original points is obvious. Now I have to map them to the new function. Seems easy enough, but I am not getting...

I want to see if we can map the space that is computable programs. You wouldn't consider complex problems, once you mapped the simplest problems into a space of points you can get a distribution. You may see that these clump. Seeing as several of the variables are proportional to the history of...

Hi, I need to sketche ach of the following regions: R = {z :|z| < √2, 7π/16 < Argz<9π/16}, R1 = {z :|z| < 16, Rez>0} and write down a one-one conformal mapping f1 from R onto R1. Here is my sketch https://onedrive.live.com/redir?resid=4cdf33ffa97631ef%2110238 But I'm finding hard to find the...

Homework Statement In each case, state whether the assertion is true or false, and justify your answer with a proof or counterexample. (a) Let ##f## be holomorphic on an open connected set ##O\subseteq \mathcal{C}##. Let ##a\in O##. Let ##\{z_k\}## and ##\{\zeta_k\}## be two sequences...

I have an Integral that is convergent over the range (-inf, Lambda) where 0< Lambda < 1. I need to change variables to move this to (0.1, 0.9) in such a way that I do not introduce any poor behavior, such as asymptotes or discontinuities as it needs to be well behaved. Is there a standard...

If you were to have clones of genes you wished to use for FISH in the form of a plasmid, cosmid, BAC and YAC, which would be best for gene mapping? I'm unsure as to what the distinction would be between these types particularly for use in FISH. Which is most commonly used and why? Thanks

What's a good textbook to learn conformal mapping in electrodynamics?

Homework Statement Let * and = be defined by a*b means a - b is an element of the integers and a = b means that a - b is an element of the rationals. Suppose there is a mapping P: (* equivalence classes over the real numbers) --> (= equivalence classes over the real numbers). show that this...

My book denotes by σ:Δk→X for some suitable topological space X a standard k-simplex of X. It then describes the free abelian group generated by such σ's as the group of k-chains on X. It is not clear to me what is meant by a chain for a map σ. I understand a chain in Rn to be sums of integer...

Homework Statement R = all real numbers F(x) = { y in R : sin(y) = x} 1. Is F a mapping from R to R 2. Describe the three sets F(5), F(0), F(1). 3.Can F be represtented as a function from R to R 4. Give two different choices of X and Y (take both X and Y to be subsets of ?) so that F can...

can anyone suggest any good reading material on operator state mapping in conformal field theory? I know only elementary field theory... So it might be helpful ifsomeone suggest a book where it is done in little detailed way..

I am looking for a conformal map from a "polygon" to eg the upper half plane, which consists of circle segments instead of lines. So for example, it could be a quadrilateral ABCD, but where AB is a circle segment. The closest I can find is the Schwarz-Christoffel mapping. Anyone has any tips?

Homework Statement 2. Find the formulae as in (3.4.1) for each of the following: (a) the rotation of angle π/2 about the point i ; Homework Equations The equation 3.4.1 is given below. ## f(z) → z*a + b ## where a, b and z are all complex numbersThe Attempt at a Solution I have attached my...

Homework Statement Suppose that ##\phi : \mathbb{Z}_n \rightarrow \mathbb{Z}_n##, where the rule is ##\phi([a]_n) = [ka]_n##. Formulate and prove a conjecture that gives necessary and sufficient conditions on the positive integers ##k## and ##n## which would guarantee that ##\phi## is an...

Suppose that we do not have any way to measure distance, but do have clocks. There are N observers, who can all see the distant events, say spaceships taking off and landing on far away planets. The question is: assuming the speed of light is constant, can we deduce the distance to the events...

Hi, I'm building a fluid model and using the method of characteristics to solve it. I'll not go into the details as they aren't necessary. Basically I have two points $(-\epsilon,70)$ and $(\epsilon, 0)$ and need to create an exponential curve between them. Could someone please tell me of a way...

Can someone please look at the diagram below and tell me how u1 is obtained. If it is through the use of m3 please explain how the gradient m3 is obtained.

Is there a conformal mapping that transforms regular polygons (e.g. triangle and square) to circle?

Homework Statement With The map f(z) = -(1-z)/(1+z) where z=x+iy, and f(z) maps z onto w = u + iv plane. show for which points of the z plane this map is conformal. Homework Equations The Attempt at a Solution I have read a lot about this subject, and I think I...

I am reading Chapter 2: Vector Spaces over $$\mathbb{Q}, \mathbb{R} \text{ and } \mathbb{C}$$ of Anthony W. Knapp's book, Basic Algebra. I need some help with some issues regarding the Universal Mapping Property of direct sums of vector spaces as dealt with by Knapp of pages 60-61. I am not...

During the course of working with inertial measurement units (IMU) I have run into a problem. The issue is that an IMU reports accelerations relative to the IMU's orientation rather than it's initial orientation. The IMU's initial orientation is the identity quaternion (1,0,0,0). All changes...

Homework Statement Prove that if G is a cyclic group with more than two elements, then there always exists an isomorphism: ψ: G--> G that is not the identity mapping. Homework Equations The Attempt at a Solution So if G is a cyclic group of prime order with n>2, then by Euler's...

Hi all, Isn't the mapping class group of a contractible space trivial (or, if we consider isotopy, {+/-Id})? Since every map from a contractible space is (homotopically)trivial.

Hello, Given the complex linear mapping: T(z) = Az + B where A is real and B is complex. However trying to show that T(a * z1 + z2) = a * T(z1) + T(z2) does not work which implies the mapping is not linear? Why does not this rule apply here? Thanks.

Hello, first of all, sorry if my question is either trivial or imprecise, I'm from the engineering domain :) I need to know how many different values the following pair can take: \left(a\cdot i + b\cdot j\right) \bmod n_1 \left(c\cdot i + d\cdot j\right) \bmod n_2 as (i,j) spans \mathbb{Z}^2...

I am reading Dummit and Foote, Section 10.5 : Exact Sequences - Projective, Injective and Flat Modules. I am studying Proposition 28 (D&F pages 387 - 388) In the latter stages of the proof of Proposition 28 we find the following statement (top of page 388): "In general, Hom_R (R, X) \cong X...

I am reading Dummit and Foote, Section 10.5 : Exact Sequences - Projective, Injective and Flat Modules. I am studying Proposition 28 (D&F pages 387 - 388) In the latter stages of the proof of Proposition 28 we find the following statement (top of page 388): "In general, $$ Hom_R (R, X) \cong...