Map Definition and 403 Threads

Hi guys, I have read a lot about car's MAP sensor and it's function but there are some areas that are not completely understood yet! Let me put it this way: My car's MAP sensor reads 337 mbar (millibar) @ idle (800 RPM). When i open the throttle, the reading DROPS (for example at 2500 RPM it...

Hello, I am watching a video about spherical harmonics, and I am at the point where the color map is being shown for various values of ##l## and ##m## My question is, what am I supposed to make of these plots? Pretty colors yes, but what do these things mean?

In my book its says let i: U →M (but with a curved arrow) and calls it an inclusion map. What exactly is an inclusion map? Doesn't the curve arrow mean its 1-1? So are inclusion maps always 1-1?

Let $f:\mathbf R^n\to\mathbf R^m$ be a smooth function of constant rank $r$. Let $\mathbf a\in \mathbf R^n$ be such that $f(\mathbf a)=\mathbf 0$. Then $f^{-1}(\mathbf 0)$ is a manifold of dimension $n-r$ in $\mathbf R^n$. We imitate the proof of Lemma 1 on pg 11 in Topology From A...

My question is as it says in the title really. I've been reading Nakahara's book on geometry and topology in physics and I'm slightly stuck on a part concerning adjoint mappings between vector spaces. It is as follows: Let W=W(n,\mathbb{R}) be a vector space with a basis...

Homework Statement Hi all. For some reason I have been having a lot of difficulty with this problem in Peter Petersen's text. The problem is Prove: ##d(exp_p(tv), exp_p(tw)) = |t||v-w| + O(t^2 )## Homework Equations The exponential map is the usual geodesic exponential map. And ##d(p,q)## is...

Hi all, I was wondering what the relationship between the Riemannian Geometry exponential map and the regular manifold exponential map and for the reason behind the name.

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1/ Prove that the set-valued map F defined by F : [0, 2π] ⇒ R2 as F(α) := {λ(cos α, sin α) : λ ≥ 0}. is continuous, but not upper semicontinuous at any α ∈ [0, 2π]. 2/ What is the fact that " F is continuous if it is both u.s.c. and l.s.c". I would like illustrate that and thank you.

Hello, I have to create the CMB multipole map from a Planck Data Map with Healpix routines on IDL, and I just don't got a clue of how it must be done! Can anybody help me?Thanks! physfed

Homework Statement Hello, i have the following task in my homework: When doing an X-ray crystallography experiment to determine the structure of biomolecules (protein/DNA), why do consider interpreting an electron-density map (EDM) instead of directly using the diffraction data? 2. The...

How would I get a Listing or a Map of All the Constellation Boundaries in Right Ascension and Declination.

Do you think we will ever be able to create a simplified computer simulation of the universe using the cosmic microwave background as the initial state that would generate the true locations of galaxies or at least galaxy clusters, and then be able to find our own galaxy or galaxy cluster within...

Is there a way to map time-like curves in Minkowski space to curves in a Euclidean space such that the length of the curve in the Euclidean space is equal to the proper time of the curve in Minkowski space?

Can you guys give me a concrete example of a completely positive map from M_m → M_n?

f^-1 (E^c) = (f^-1(E))^c where f is map from X to Y and E is in Y. Prove equality is true.

Hi, this question seem to fall somewhere between Analysis and Algebra; I just choose this section; sorry if it is the wrong one. I would appreciate any suggestions, refs., etc. I'm basically trying to see if the different definitions of adjoint maps can be unified into a single...

Homework Statement Let p: E \rightarrow B be a covering map. If B is compact andp^{-1}(b) is finite for each b in B, then E compact. Note: This is a problem from Munkres pg 341, question 6b in section 54. The Attempt at a Solution I begin with a cover of E denote it \{U_\alpha\}. I...

I am reading munkres topolgy and I am struggling with understanding the following sentence: "We say that a subset C of X is saturated (with respect to the surjective map p:X→Y) if C contains every set p-1({y}) that it intersects" if you have the second edition its in chapter 2 section 22...

I am given this function $f(x)=\langle (1/9) \cos(x_1+ \sin(x_2)) , (1/6) \arctan(x_1+ x_2) \rangle$ where $x_1= \langle 0,-1 \rangle$. may I please get hints on how to prove that this function is a contraction map

Hi, i've just installed Healpix on IDL, and I'm starting to try all the subroutines. First of all, i learned how to make a dipole map with random numbers (it works!:) ). Now i'd like to plot a map using real data. The .txt file is organized like this: DEC(°) AR(°)...

http://imageshack.com/a/img824/2641/1cpe.png The black curve I drew there represents the load curve in 5th gear. Why is it that at 5500 rpm(160kph), I have a lesser fuel consumption(270g/kWh) than at 4000 rpm(280g/kWh)? Intuitively,if I produce more power at 180kph(ie 5500rpm),I should...

if you given a function f from R^2 to R^2 f(x)=<f_1(x),f_2(x)>, x in R^2 with f_1 and f_2 from R^2 to R being differentiable on R. if there is contants K_1 and K_2 greater than or equal to 0 so the 2-norm of (gradient f_1(x)) is less than or equal to K_1 and 2-norm of (gradient f_2(x)) is...

Homework Statement Find numerically the r values for the first 2 bifurcations. Homework Equations xi+1 = f(xi), f(x) = rx(1 − x) The Attempt at a Solution To find the values of r, first I set rx(1−x)=0 to find x and then used the x values to find r=0 and r=1. But, I am still...

Homework Statement Using the properties of the exponential map, construct a one to one mapping of the strip S to the sector C: S=\{-\sqrt{2}x-t<y<-\sqrt{2}x\} , C=\{-\frac{\pi}{6}<arg(w)<\frac{\pi}{3}\}, where t is a fixed positive real number. Here we let z=x+iy. Homework Equations...

I am reading Dummit and Foote, Section 10.4: Tensor Products of Modules. I am currently studying Example 3 on page 369 (see attachment). Example 3 on page 369 reads as follows: (see attachment) ------------------------------------------------------------------------------- In general, $$...

I am a bit confused, so this question may not make much sense. A unitary operator from one vector space to another is one whose inverse and Hermitian transpose are identical. It can be proved that unitary operators are norm preserving and inner product preserving. Which raises the question...

Hi all, I have made a BSFC plot in MATLAB with engine data tested on an eddie current dyno, The code I used for it is: >> NP=40; >> [RP TP]=meshgrid(linspace(min(RPM),max(RPM),NP),linspace(min(Torque),max(Torque),NP)); >> BSFC_IT=griddata(RPM,Torque,BSFC,RP,TP); >> NC=12; >>...

Homework Statement For a group G consider the map i:G\rightarrow G , i(g)=g^{-1} For a subgroup H\subset G show that i(gH)=Hg^{-1} and i(Hg)=g^{-1}H Homework Equations The Attempt at a Solution I know that for g_1,g_2 \in G we have i(g_1g_2)=(g_1g_2)^{-1}=g_2^{-1}g_1^{-1} Then...

Hello! I have hard to understand this input for this linear map $$T:P_3(R)->P_2(R)$$ $$T(p(x))=P'(1-x)$$ so they get this value when they put in which I have hard understanding I don't understand how they get those, I am totally missing something basic...! The only logical explain is that in...

I was given a C++ program (a hefty one at that) and asked to create a map of it. He added some more details (something about functions), and I left his office thinking I understood what he requested but now I realize I don't. I'll approach him and ask for more details but before I do that...

Just for some observation, is there any good "maps" of the universe? like nothing detailed but shows the hemispheres. Also is there any website which show totals of matter in the universe, and how it changes when you go to different parts of the universe?

Hi everyone, :) Trying hard to do a problem recently, I encountered the following question. Hope you can shed some light on it. :) Suppose we have a continuous mapping between two metric spaces; \(f:\, X\rightarrow Y\). Let \(A\) be a subspace of \(X\). Is it true that, \[f(A')=[f(A)]'\]...

This question broadly relates to principle component analysis (PCA) Say you have some data vector X, and a linear transformation K that maps X to some new data vector Z: K*X → Z Now say you have another linear transformation P that maps Z to a new data vector Y: P*Z → Y is there...

Write out the minimal Sum of Products(SOP) equation given the following Karnaugh Map. YZ|WX 00 01 11 10 00 d 1 1 1 01 1 1 0 0 11 0 0 d 1 10 0 0 0 0 Need someone to check my answer. My answer: $$yzw + \bar{y}\bar{z} + \bar{y}\bar{w}$$

Please check my road to Physics I am a new member,been to this forum before but was never a registered user (?) Before hitting on the topic, I think it is necessary to describe my background. So here it is: I live in India! I am currently enrolled in BSc MATHEMATICS at IGNOU (INDIRA GANDHI...

Hi everyone, I have this linear map $$A:R^3 \rightarrow R^3$$ I have that $$A(v)=v-2(v\dot ô)ô); v,ô\in R^3 ;||ô||=1$$ I know that $$A(A(v))=v$$ this telling me that A is it's own inverse. From there, how can I find the eigenvalue of A? Thanks

Suppose that H, K are Hilbert spaces, and A : H -> K is a bounded linear operator and an isomorphism. If X is a dense set in H, then is A(X) a dense set in K? Any references to texts would also be helpful.

Awesome thanks.. Mind checking this as well? Minimize Sum of Products equation given the following K map. My Answer: $$\bar{y} \bar{w} + wx + y\bar{z}w + yw\bar{x} $$

Please refer to the attached image. Ok, I'm in a bit of strife here. I like to give in my own feedback and thoughts on particular questions so I can have one of you experts tell me where I am going wrong/right and help me, however I have absolutely no idea with these two questions. Could I...

how is the logistic function characterized by the differential equation df(x)/dx = f(x)(1-f(x)) [with solution f(x)=1/(1+e-x), but this is irrelevant to the question] the continuous version of the logistic map, given by the recursive function: xn+1 = xn(1-xn)? It would seem to me that...

Meissner et al just posted a paper where they see those circles in the high res. microwave sky of Planck. Who knows if this is real, or what it would mean if it were confirmed? Meissner has a followup paper in preparation with Penrose and others. Either way I think it's pretty interesting...

while it has been extensively proven that any 2D map can be colored with at most 4 colors, has any hypothesized why that is (outside the computer programmed brute force method)?

Homework Statement Let ##L: R^{2} → R^{2}## be a linear map such that ##L ≠ O## but## L^{2} = L \circ L = O.## Show that there exists a basis {##A##, ##B##} of ##R^{2}## such that: ##L(A) = B## and ##L(B) = O.## The Attempt at a Solution Here's the...

I was curious if anyone is aware of anything resembling a mathematical map, or learning tree. By this I mean a diagram that illustrates the sequence in which one must learn particular topics. I ask because I find myself encountering topics (today it was finite element method) and clicking the...

In Quantum Computation we define a map that takes on density matrix to another. It is represented by some kraus matrices. I do not know why it has to be completely positive.

Hi, Is there a concept map that actually shows all the concepts of math, and how they relate to each other? Kind like this one but more complete. I alreaady searched the web and didn't find anything, that's why I'm here so, Please Help. Thanks.

Homework Statement Find an interval [a, b] for which the Contraction Mapping Theorem guarantees convergence to the positive fixed point or verify that there is no such interval. Homework Equations x = g(x) = \frac{14}{13} - \frac{x^{3}}{13} The Attempt at a Solution I know...

I wasn't quite sure where to put this, so here goes: I am trying to find out some facts about the group SO(2,1). Specifically; Is the exponential map onto? If so, can the Haar measure be written in terms of the Lebesgue integral over a suitable subset of the Lie algebra? What is that subset...

Hi! Let's say in mathematica I declare this function t[x_,y_]:= (x'[s]+y'[s])^2 Now I can call it with $$L=1;$$ t[(#^2)+L &, (#^3)+L &] if I call it this way it will remplace the # with s and evalute the derivative. Now let's say I wana do this for for every L from 1 to 10. so i got...