Mapping Definition and 364 Threads

Homework Statement Hi all. I am given the following discrete mapping: x_{n+1}=f(x_n)=x_n+r-x_n^2 for r>0. Objective: Find the r, where a period doubling takes occurs. Attempt: First I find the fixed points: These are x=-\sqrt{r} (which is unstable for all r) and x=\sqrt{r} (which is...

can i know how to map a vector to a vector by preserving the operation if addition and mutiplication ..pls dun use f(x+y)=f(x)+f(y).. i wan to know how to use in abstract ... if i do the mapping wat will happens?

Homework Statement graph |z-1|=1 and then graph z^2 Homework Equations z=x+iy The Attempt at a Solution well, |z-1|=1 => |(x-1)+iy|=1, squaring both sides. we get, (x-1)^2+y^2=1. This is a circle. But how am i supposed to get z^2 from this? I don't know what to do with...

hi if P and Q are 2 permutations of X, their product, P.Q, is the permutation of X (X=1,2,3,4,5), obtained by following the mapping Q with the mapping P. if Q=2 3 4 1 5, and P is 1 2 5 3 4, then how do i find P.Q and Q.P ? i have tried a few mappings but can never get the same answer as in...

Hi, I'm trying to write a score function. The score function is applied to each cell of a grid and because the grid has many cells ( 400x600 or 800x600 ) If I want to experiment with different score functions to see which one is best I'd have to see some kind of visual results. I thought...

If V is a vector space with an inner space <.,.>. V1 is an non empty subset of V. Vector x is contained in V is said to be orthogonal to v1 if <x,y>=0 for all y contained in V1. 1) if v is contained in V and define the mapping f(x)=<x,v>v. Show f is a linear transformation and describe its...

A mapping from [0,1) to Reals?? A cont. onto mapping from [0,1) to Reals? I cannot find it. Could somebody throw a hint at me please?

We have a continuous bijection f:X-->Y. Prove that if f is open, then f inverse is continuous. I can't figure it out. "Proof". For V open in Y, there exists W open in X such that f[W] \subseteq V. Where does the f is open definition apply?

Hi, everyone: I have been trying to show this using the following: Given f: Y-->X IF S^n ~ Y_f(x) , then S^n deformation-retracts to Y , and ( not sure of this) also is homeomorphic to Y (I know Y_f(x) is homotopic to Y ) . But ( so I am branching out into more...

f(x) is a bijection if and only if f(x) is both a surjection and a bijection. Now a surjection is when every element of B has at least one mapping, and an injection is when all of the elements have a unique mapping from A, and therefore a bijection is a one-to-one mapping. Let's say that...

If S is a finite set having m > 0 elements, how many mappings are there of s into itelf? I believe there would be however many mappings there are elements> Any suggestions?

Homework Statement For X= NxN, Y=N, define the mapping phi: X-->Y as phi(x,y)=x+y. Find the inverse image of phi-inverse (5) of the singleton set {5}. If n: X-->Y is the product operation n(x,y)=xy, find n-inverse (4). The Attempt at a Solution I'm not even really sure what the question...

Hi, I'm having some difficulty with this problem. I need to project a point in R2 to the line x2 = x1 (sqrt(3)) and then rotate it 30 degrees clockwise. I believe the 2x2 matrix to map it is just sqrt(3) 0 0 1 and to rotate a vector clockwise as opposed to counter clockwise...

Hi everyone, (I hope I'm posting it in the right place, please feel free to move this thread to the appropriate place) My high school graduation project is about the application of the theory of complex variables in physics. Specifically, I am learning about the complex potential, its...

i have a english (uk) keyboard but my computer has the keyboard mapping set to english (us). does anyone know how i can change it to english (uk)?

Hi guys I hope I'm in the right subforum. I was thinking of a way to map a house or outside area with radar or some other method, and then using that info to create a map for a game. So my question is, what are the different methods available for sensing the surrounding area and creating a...

Could anybody help me check whether my judgements ture or false? (MJ = My Judgement) Suppose f maps A into B, and g maps B into C 1. If f and g are injective, then g\circf is injective; (MJ)but that when g\circ f is injective, the injectivity of f and g are unsure. 2. If f and g are...

I'd like to map the open unit circle to the open ellipse x/A^2 + y/B^2 = 1. How would I go about doing this? I really have no idea how to go about doing these mappings. I'm working with the text Complex Var. and Applications by Ward and Churchill which has a table of mappings in the back...

Hello, I have a general question about isomorphisms of vector spaces. I understand the concepts of mappings being one to one, and onto, but how do I go about SHOWING that a mapping is either one to one, onto, one or the other or both? For example, the mapping R^2-->R^2 defined by f(x,y) =...

Homework Statement This is an example in Advanced Engineering Mathematics by Erwin Kreyszig p.675 which I don't understand. If you map w=z^2 using Cartesian Co-ordinates, w is defined as w=u(x,y)+iv(x,y), therefore, u=Re(z^2)=x^2-y^2 and v=Im(z^2)=2xy. The function is graphed using u and v...

I heard that one can solve 2D problem with conformal mapping of complex numbers. Is it possible to use this method for 3D axial-rotationally symmetric problems (which are effectively 2D with a new term in the differential equation)?

I'm trying to map out how certain mathematical subjects depend on each other, i.e. which subjects could be described as prerequesites for which other subjects, in the sense that the former define needed or helpful concepts for the latter. In a crude ascii diagram, which might look messed up...

A quick question this time... Example: Let (u,v)=f(x,y)=(x-2y, 2x-y). Find the region in the xy-plane that is mapped to the triangle with vertices (0,0),(-1,2),(2,1) in the uv-plane. Solution: (0,0)=f(0,0), (-1,2) = f(5/3,4/3), and (2,1)=f(0,-1), the region is the triangle with...

[Related concepts: Inverse mapping theorem, transformations and coordinate systems] 1) For each of the following transformations (u,v) = f(x,y), (i) compute det Df, (ii) find formulas for the local inverses of f when they exist. a) u=x^2, v=y/x b) u=(e^x) cos y, v=(e^x) sin y I got...

Homework Statement "Study the infinitesimal behavior of f at the point c. (In other words, use the conformal mapping theorem to describe what is happening to the tangent vector of a smooth curve passing through c.)" f(z) = 1/(z-1), c=i Homework Equations |f'(c)| and arg f'(c)...

When trying to solve one problem (my own, not an exercise), I encountered the need for a conformal mapping between a square [0,1]^2 and a triangle (0,0)-(1,1)-(2,0), so that the side (0,0)-(0,1) of the square gets mapped into a point (0,0), and the three other sides become the sides of the...

Hi All I have one final question that's related to flow problems with obstacles. Any help would be greatly appreciated as I am finding fluid flows extremely difficult. "Examinations are formidable even to the best prepared, for the greatest fool may ask more than the wisest man...

Hello, I'm working on some questions and I need some further explanation; First I must Consider the open interval (0,1), and let S be the set of point in the open unit square; that's is, S={(x,y):0<x,y<1}. Question (a) says Find a 1-1 function that maps (0,1) into, but not necessarily onto, S...

During learning linear algebra, I have met at least three items (kind of action in my own word): function, mapping and transformation. What are the relation and difference among them? e.g. Given y=f(x), we can say f map x to y, f transform x to y and the function of x is y. In saying the...

I have got a begginner's course in computer organisation this semester. The course consists of the basic stuff like types of memories and memory hierarchy with the detailed description of each etc etc. Now, what i really don't get is memmory mapping and how exactly data is read and written on...

Does anybody know of free 3-D EM software so that I can model a transformer? In particular, I'm interested in mapping Poynting vectors. Thanks.

When you reach out to grab something that is hot, or you receive an unexpected electrical shock, the normal human reaction to withdrawal the limb is reflexive, or so I understand. As such, no signal reaches the brain before the reflex begins - if this is incorrect, let me know. However, given...

Homework Statement If I was to map elements in R/A to R/B via the function p. So p:R/A -> R/B Can I assume there are no elements in R/B before the mapping? Or is it more there are elements in R/B already before the mapping. However during the mapping, I highlight each element in R/B...

Homework Statement Can there be a mapping that may not map any elements from one domain to another? The reason is that the mapping has a condition. For example, it will only map elements if the one in the domain are related in some way to the element they are mapped to (i.e congruence via a...

Homework Statement How do you define a mapping f:K->N with K={0} N is the integers. that maps the element 0 to every single single element in N? ie. 0->-n, ... , -2, -1, 0, 1, 2, ... , nIs that even possible? The mapping Z->Z by multiplying each element in Z by 0 is a legitamate mapping...

Here is the question from our book: ------- Let (X,d) be a complete metric space, and let f:X\to X and g:X\to X be two strict contractions on X with contraction coefficients c and c' respectively. From the Contraction Mapping Theorem we know that f has some fixed point x_0, and g has some fixed...

Does anyone know what the conformal mapping of an aerofoil at incidence is? Does it use the Joukowski transformation? Or something else.. Thanks

Equipotential Lines! I recently did a lab in class that dealt with electric field mapping (very similar to http://physics.nku.edu/GeneralLab/211%20Elect%20Pot.%20&%20Field%20Map.html) and i have to write a lab report now.. I don't understand why the equipotential lines are always perpendicular...

Homework Statement K = {x C S7 | 2x=2, {1,4}x={1,4}, {1,5,7}x={1,5,7}}. Draw Lattice Diagram for K.2. The attempt at a solution I've looked at this for about 30 minutes and came to the conclusion that there are 140 unique solutions to this mapping, and I know for a fact that the professor...

w = 1/(z+2j): w = u + jv, z = x+jy Its not hard to express this in terms of z... z = 1/w - 2j But how can i go about expressing x and y and terms of u and v Substitution of those above terms gets you x + jy = 1/(u + jv) - 2j I am not clear on the next steps Any help is much...

I have the linear mapping Pw(x). How can I prove that: ||P_w(x)||^2 = \Sigma (<x, x_i>)^2 Where the sum is from i = 1 to k x is any vector which is an element of R^n I have tried expanding ||P_w(x)||^2 but it doesn't seem to give me the right side of the equation. Is there any other...

This issue of infinity (undefined?) keeps coming up in the following problems. For example, the following question: Computer the image of the sector 0 \leq r \leq 1, 0 \leq \theta \leq \pi, under the map ln(z). ------------- So I first graphed this thing in the x,y (z-plane) and obviously...

Prove that there is a mapping from a set to itself that is one-to one but not onto iff there is a mapping from the set to itself that is onto but not one-to -one. Since this is a 'iff' proof, so I must prove the statementlike two 'if' statements. Let g:S ---> S. Assume that g is 1-1...

There are 2 parts to this question: How many functions are there from a set S with n elements to a set T with m elements? Assume n<=m, how many one-to-one functions are there from S to T? I am pretty sure that the answer to the first part is mn. So if there are 3 elements in the first...

Is it possible to transform an ellipse x^2/a^2 + y^2/b^2 = 1 ("a" minor or major semiaxis) Into a rectangle? If so, how can I do it? I am not very familiar so please explain all the details. I know the transformation from a circle to an airfoil, but not this one.

so i know what it is (i think lol) ... but what are its applications?

Hi there. I've recently come across the Implicit Mapping Theorm in my studies and noticed that there is a condition that the rank of the image must be the maximum possible. I'm not directly seeing why this condition is needed, so I was wondering if anyone could provide me with an example of why...

Hey, so in 2003, it was announced that the human genome was more or less mapped. The difference between individual humans is about 0.2 percent of the 3 000 000 000 genes we have. So somehow, this percentage should account for all of the human variations that aren't dependent on environment...

If two oppositely charged point charges are separated, with a fairly large circular (spherical) conductor between them, then the equipotential surfaces will kind of wrap around the contour of the conductor, correct? And the electric field would look like it does for a normal dipole, with the...

Does the history of wave packets translate exactly onto infinite phase space, or is phase space incompletely (or redundantly) covered by quantum mechanics?