Charts Definition and 57 Threads

Given the definition of a smooth map as follows: A continuous map ##f : X → Y## is smooth if for any pair of charts ##\phi : U →R^m, \psi:V →R^n## with ##U ⊂ X, V ⊂Y##, the map ##\phi(U ∩f^{-1}(V)) → R^n## given by the composition $$\psi ◦ f ◦ \phi^{-1}$$ is smooth. Claim: A map ##f : X → Y##...

I found this as problem 3/42 from here (copied below for viewing convenience). I'm a little confused about Instruction 2. The way I interpret it, upon the first loop, no evaluation is occurring, but instruction 1 now becomes "increase Box 2 by 2". So now the three instructions are 1) increase...

[Moderator's note: Spun off from previous thread due to topic shift.] I believe this is only possible if the set of timelike curves forms a congruence that is both geodesic and hypersurface orthogonal. (The congruence of worldlines at rest in a global inertial frame in Minkowski spacetime of...

Hello:) i need some help trying to find some formulas that i can retrive the material index from at the end of simplification to use with an ashby chart to select materials. here is an example of deflection equation from a sphere used for a spherical cap and what material index we used to find...

From Zorich, Mathematical Analysis II, 1st ed., pag.163: where the referred mapping (12.1) is a map ##\varphi:I_k\to U_S(x_0)##, in which: 1. ##I_k\subset\mathbb{R}^n## is the k-dimensional unit cube, 2. ##x_0## is a generic point on the surface ##S## and ##U_S(x_0)## is a neighborhood of...

[Ref. 'Core Principles of Special and General Relativity by Luscombe] Let ##\gamma:\mathbb{R}\supset I\to M## be a curve that we'll parameterize using ##t##, i.e. ##\gamma(t)\in M##. It's stated that: Immediately after there's an example: if ##X=x\partial_x+y\partial_y##, then ##dx/dt=x## and...

Hi, starting from this (old) thread I'm a bit confused about the following: the transition function ##ϕ_{12}(b)## is defined just on the intersection ##U_1\cap U_2## and as said in that thread it actually amounts to the 'instructions' to glue together the two charts to obtain the Möbius...

Working 1. a (i) 1/4=×5% (ii)120/360×100=33.3% (b) newspaper=£9000 Leaf=£6500 Transport=£19000 55000-34500=£20500 Tv=16.7% 0.167×55000=£9185 ( answer) (c) Tv=16.7% News=25% Leaf=15.3% Other=9.72% Trans=33.3%(answer) Note: they were rounded to (3sf)

I was reading about differentiable manifolds on wikipedia, and in the definition it never specifies that the differentiable manifold has a metric on it. I understand that you can set up limits of functions in topological spaces without a metric being defined, but my understanding of derivatives...

<< Mentor Note -- Thread moved from the technical forums, so no Homework Template is shown >> I was looking into process control and capability of general manufacturing company. e.g one that constructs bolts There process was was within tolerance and in control producing screws within...

Homework Statement Uploaded as image 1 I will show my workings for 2 if 1 are in the right direction I also don't understand what is meant as I/O Designation charts (nowhere in my study notes) Homework Equations None The Attempt at a Solution Uploaded as image 2 is my attempt.

Recently I was playing around with the idea of graphs of projectile motion and I started wondering what it would look like if someone were to graph every parabolic trajectory of a single initial velocity over all angles between o and 90 degrees above the horizontal. I decided to find out so in...

My question unfortunately does not fit in the Homework template, so I hope this is okay. I attached a question below which involves multiple parts using the concepts related to energy, work, impulse, and momentum. Under the "Simplify and Diagram" section (you will notice it is in bold text), I...

Homework Statement Homework Equations Smith Charts TL equations The Attempt at a Solution So I am having a hard time understanding how smith charts work. for this problem in part a, I know we have to find the Normalized impedance first which is: .5 + j0 And then we have to go to our...

I would simply like to know: Given a lossless transmission line with a certain characteristic impedance Z terminated in a load L. How can I go about computing the fraction of the time average incident power arriving that is dissipated in the load? Is this possible without knowing the voltage or...

Im drawing a system using control systems engineering. It changes over time and many factors affect each other. So far I've been using draw.io for drawing program architecture and it works great but I am looking for something more directed at flowcharts/control systems. Requirements: >Layers...

I feel embarrassed to ask this, but I may have a misunderstanding in my understanding of some basics. I was told that ##\psi: U \rightarrow \psi(U)##, where ##U = (0, \infty) \times (0, \pi) \times (-\pi, \pi)## and ##\psi(\rho, \varphi, \theta) = (\rho\cos\theta\sin\varphi...

Homework Statement I am having a bit of trouble interpreting flow charts given in my biology question sets. Given the following stimulus: The question is : In which of the following options does each substance play two different roles in the series of events from plaque ruprture to MI? ADP...

I am confused about the procedure for finding the transition functions given an atlas. I understand the theory; it's applying it to real life examples where I have my problem. So for example, take S1 (the circle). I want to use 2 charts given by: U1 = {α: 0 < α < 2π} φ1 = (cos α, sin α) U2...

I'm fairly new to differential geometry (learning with a view to understanding general relativity at a deeper level) and hoping I can clear up some questions I have about coordinate charts on manifolds. Is the reason why one can't construct global coordinate charts on manifolds in general...

Suppose we have an n-dimensional manifold Mn and take a coordinate neighborhood U with associated coordinate map φ: U → V where V is an open subset of ℝn. So far I'm clear on this. However, where I become confused is when some books say that φ-1 is called a parameterization of U and basically...

Hi everyone, I am looking for basic elements resistivity vs. temperature laboratory measurements charts. Anyone has ideas where to look for? Regards

I am reading John M. Lee's book: Introduction to Smooth Manifolds ... I am focused on Chapter 1: Smooth Manifolds ... I need some help in fully understanding Example 1.3: Projective Spaces ... ... Example 1.3 reads as follows:My questions are as follows:Question 1In the above example, we...

I am reading "An Introduction to Differential Topology" by Dennis Barden and Charles Thomas ... I am focussed on Chapter 1: Differential Manifolds and Differentiable Maps ... I need some help and clarification on an apparently simple notational issue regarding the definition of a chart...

Jorrie submitted a new PF Insights post LightCone7Combo Tutorial Part II - Charts Continue reading the Original PF Insights Post.

I am studying differential geometry and I stumbled on something that I don't understand. When we have a m- dim differential manifold, with U_i and U_j open subsets of M with their corresponding coordinate function phi. As can be seen in the figure. If I understand it correctly phi_j of a...

I have recently had a lengthy discussion on this forum about coordinate charts which has started to clear up some issues in my understanding of manifolds. I have since been reading a few sets of notes (in particular referring to John Lee's "Introduction to Smooth Manifolds") and several of them...

So I know that this involves using the chain rule, but is the following attempt at a proof correct. Let M be an n-dimensional manifold and let (U,\phi) and (V,\psi) be two overlapping coordinate charts (i.e. U\cap V\neq\emptyset), with U,V\subset M, covering a neighbourhood of p\in M, such that...

I've decided to work on some topics about supersymmetry for my undergraduate thesis. My background is that I have had a one-semester course in differentiable manifolds, plus typical undergrad math courses, real analysis and module theory (graduate algebra). So, I went to the library and found a...

Comet Lovejoy is well placed in the sky for the next week or so... it has just gone past peak magnitude of M4.2 around 4 days ago ( 9th Jan). But it is still a bright and easy object particularly with binoculars Visually ( from a dark site) or in binoculars, its a bright fuzzy blob ... sort of...

When you have a general coordinate chart on spacetime you have a lot of freedom to pick your coordinates, but you are always going to have 4 coordinates and each 4-tuple uniquely (in that chart) identifies one event in the manifold. When you are choosing generalized coordinates for a...

I am trying to understand my superchargers isentropic chart. For an example case where a supercharger outputs 10m3/hr but the engine only takes 6.57m3/hr in capacity, I get a volume ratio (VR) of 1.52 - easy... I can then work out a pressure ratio by VR^k = 2.0^1.4 = 1.8 The theoretical...

Hi, What software could you recommend for making complex physics and chemistry charts (for better overview) like the following 3 examples? Exapmple of SI. Units in physics http://physics.nist.gov/cuu/Units/i/SubwayDiagram.gif Chemistry chart...

As far as I have understood it submersions play the analogous role in manifold theory to quotient spaces in topology. Now is that suppose that we have submersion ##\pi: M \to N## with ##M## having a certain differential structure, then how is the differential structure of ##N## related to that...

I have a (probably trivial) question about coordinate charts. I've been studying Sean Carroll's lecture notes on General Relativity. I'm on my second re-read and I'm trying to make sure I understand the basics properly. I hope the terminology is correct - this is my first use. Carroll cites...

My textbook says that "a chart or coordinate system consists of a subset U of a set M, along with a one-to-one map \phi :U\rightarrow\mathbf{R}^n, such that the image \phi(U) is open in \mathbf{R}^n." What's the motivation for demanding that the image of U under \phi be open?

I've been reading on differential topology, and all the examples they give me are very abstract . They speak of arbitrary charts (V,ψ), and (U,φ), which map pieces of the m-manifold onto ℝm, which is fine, I understand the concepts, but how does one describe the functions for real, certainly you...

Ok, so this relates to my homework, but I really can't find an answer anywhere, so this is more of a general question. First off, what does a "chart" of a manifold look like? Is it a set, a function, a drawing, a table, what?! I have found so many things about charts, but nothing shows what...

Homework Statement Charts on the torus T. Let S1 be the unit circle, and for each value 0 ≤ θ < 2π, let P(θ) be the point on the circle at angle θ. Let S1×S1 be the Cartesian product of two circles. The elements of S1×S1 are P(φ), P(θ), where 0 ≤ φ, θ < 2π.Let P(φ, θ) be the point on the...

Ok first of all I'd like to mention that I've searched the forum and didn't find anything similar, so hopefully this thread is not unwelcome... Now as the title suggests, I am interested in a parallelization of the two concepts. Personally I like to introduce the idea of submanifolds prior to...

One of my family member's trades the markets and wants to see that the indicator she has written in JavaScript for esignal can be converted to run on sierra charts?can this be done?

Can anyone help me with impedance matching WITHOUT using smith charts. I am trying to develop a mathcad template to calculate imput impedances for normal power line systems as well as parallel and series impedance matching. I was not very good at using smith charts and never really got the...

Have some problems concerning these questions relating to the Smith Chart: A 300 ohm transmission line is terminated with an antenna with a (450Ω - j600Ω) load impedance. (1) What is the normalized load admittance? (2) How far from the load should a short circuit stub be placed to match the...

Hi everyone, I'm wondering if given a particular load impedance (Zl) and some general information such as length of the transmission line, characteristic impedance (Zo) and wavelength λ how would you be able to determine shortest distance from the load to the location on the line where the...

Hi all I'm having a bit of trouble trying to calculate the Upper and Lower Control Limit on R chart. The file "QualityIndex1180" contains the information from which I'm doing my calculations. Ob1, Ob2, and Ob3 are basically 3 samples that have been taken the first of 15 batches on some...

Hey, you've already guessed that I'm looking into the Lake Michigan/Southern Lake Huron Firestorms of October 8th-9th, 1871. I need to get the synoptic charts for this region for the period 7 October through 12 October 1871. Can anyone tell me how to get these materials?

I'm new to manifolds, so please forgive me if this sounds ignorant. I was just wondering whether the charts of a smooth manifold (within some atlas) always "overlap". If I'm not mistaken they map to open subsets of R^n, and being homeomorphisms should have the inverse image as open. But I'm not...

What is the least number of charts needed to specify a given smooth manifold, for simplicity of dimension 2? For instance the minimum number of charts to cover a torus, or a 2-sphere or a 2D 1-sheet hyperboloid? I would think it goes with the definition of manifold that in any case you need at...

I've been programming a lot for my thesis in Matlab. I've to include a technical description for my job without being too specific about the code used. So my intention is to use nice flowcharts to describe what my scripts are doing. What kind of software do you suggest me for drawing...

Does anyone know where I could find a good chart listing the thermal and electrical conductivities of metals? The chart doesn't need to be terribly accurate, I only need to know general values for comparison to other metals on the chart. All I need is one basic value for each metal. If anyone...