Global Definition and 430 Threads

Hey! :o Let $a_1, a_2, \ldots , a_k\in \mathbb{R}^n$ and $f:\mathbb{R}^n\rightarrow \mathbb{R}$ defined by $\displaystyle{f(x)=\sum_{j=1}^k\|x-a_j\|^2}$ with the euclidean norm $\|\cdot \|$. Show that f has an uniquely defined global minimum and calculate it. I have done the following...

This article describes how total carbon in organisms is distributed among different groups. Science news article here. Original PNAS article here. Plants win, not surprisingly (primary producers). Bacteria are next (Archaea which are similar to bacteria in many ways have much less carbon)...

Hi, this question is related to global and local SU(n) gauge theories. First of all, some notation: ##A## will be the gauge field of the theory (i.e: the 'vector potential' in the case of electromagnetic interactions) also known as 'connection form'. In components: ##A_\mu## can be expanded in...

In conducting research into historical accounts of Earths magnetic field, I consistently come across proposals of stable planetary magnetic grid systems; many of these theories which have apparently been developed through much time and effort. While I am unaware of any theory that cannot be...

Interesting Article in Nature and looks like better news (as opposed to doom and gloom) things may not be as bad as previously predicted. It will be interesting to follow further research as we gain more data and produce more accurate climate predictions. Unfortunately, the article itself is...

In general relativity, a vector parallel along a curve on a manifold M with a connection field Γ can be expressed: ∂v+Γv=0 We know that if the curvature corresponding to Γ is non-zero, which means if we parallel transport a vector along different paths between two points, we will get different...

Elon Musk says we can terraform Mars by converting its CO2 and H2O into CH4 and O2 using solar power, the latter two compounds being quite useful. Can't we use his idea to reduce the CO2 in our atmosphere and reverse global warming?

Consider the transformation from Poincare-AdS##_3## geometry to global AdS##_3## geometry: $$ds^{2} = \frac{dr^{2}}{r^{2}} + r^{2}g_{\alpha\beta}dx^{\alpha}dx^{\beta}, \qquad \text{Poincare-AdS$_3$}$$ $$ds^{2} = \frac{dr^{2}}{r^{2}} + r^{2}\left(-dt^{2}+r^{2}d\phi^{2}\right), \qquad...

Breaking of a local symmetry is impossible. It is often said that therefore the role of the Higgs mechanism in the standard model is a different one. Namely, Once a gauge is fixed, however, to remove the redundant degrees of freedom, the remaining (discrete!) global symmetry may undergo...

In the class our prof said, Sun changes its magnetic poles in every 11 year.And when changes the black spots on the sun increases Is this true ? Also she said Sun's cosmic radiation waves destroyes the upper atmosphere of earth.It was something like this.I don't quite remember.Actually thata...

I have been reading Thomas Hartman's lecture notes (http://www.hartmanhep.net/topics2015/) on Quantum Gravity and Black Holes. -------------------------------------------------------------------------------------------------------------------------------- In page 97, he derives (9.4), which is...

Is there a universal criteria to determine if a coordinate system is global? I think that it is sufficient for the determinant of the metric to be non-zero in order for a coordinate system to be global. Is this so? For example, take the metric ##ds^{2} = \ell^{2}(-\cosh^{2}\rho\ dt^{2} +...

Hey! :o I am looking at the following: The differentiable and so also continuous function $f:[a,b]\rightarrow \mathbb{R}$ gets its global maximum at a point $x^{\star}$. Show that the following holds $$f'(x^{\star})=\left\{\begin{matrix} =0\\ \leq 0\\ \geq 0 \end{matrix}\right. , \ \text{...

The mantra in theoretical physics is that global gauge transformations are physical symmetries of a theory, whereas local gauge transformations are simply redundancies (representing redundant degrees of freedom (dof)) of a theory. My question is, what distinguishes them (other than being...

Homework Statement Let γ : I → Rn be a regular smooth curve. Show that the map γ is locally injective, that is for all t0 ∈ I there is some ε > 0 so that γ is injective when restricted to (t0 − ε , t0 + ε ) ∩ I. Homework Equations The Attempt at a Solution [/B] So I know a function (or a...

Hey! :o I have show that the function $y=f(x)=x-\frac{5}{2}+\frac{4}{x}=\frac{2x^2-5x+8}{2x}$ has a local minimum at $x=22$ and a local maximum at $x=-2$. How ca we check if they are also global extrema? (Wondering) The same at the function $f(x)=10e^{-x}(x-1)^2$, at $x=1$ the function has a...

This is for a fictional project, but the tools I need will more likely be found here in Earth forum, I think. Move to fiction if necessary. I want to render a map of Earth with the "poles" of the grid in a different place. Say, the South "pole" of the grid is at Tierra del Fuego (ish) in S...

Hi I have a simple question about global warming. The percentage of carbon dioxide in the Earth atmosphere is about 0.04% . My question is how is such a small percentage of this gas able to have such a powerful affect on global warming? Thanks

I would imagine that most here believe in global warming. My question is what effect does the sun have on global warming because the heat increases as it's fuel is consumed.

According to this author, http://www.math.uic.edu/undergraduate/mathclub/talks/Weeks_AMM2001.pdf, a locally Minkowski spacetime with a nontrivial global topology may have a preferred inertial frame, in the sense that hypersurfaces of constant time can only be defined using particular time...

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...

1.5 C vs 2 C global warming: New study shows why half a degree matters Global warming is scary. It makes me wonder why people don't take it too seriously. Though I have read somewhere that the energy consumption of the US actually went down by a bit last year so maybe people are taking baby...

Just like it says on the tin. Looking for recent statistics on global traffic by various (preferably application layer) protocols (i.e., DNS, HTTP, SMTP, etc.). Closest I can find are some regional and national breakdowns, but mostly from a lay reader's point of view.

Hi all, I saw some figures about potential (contour) plot in some articles that has some beautiful gradient lines. The shape is quite weird but you can see clearly there are some strong concentration of potential at some places. For example, if you have 300x300 grids, there shows strong...

Under SR, we can talk about inertial frames that apply globally. However apparently, under GR, this concept only applies locally, because it breaks down on larger scales. Can anyone provide an explanation as to why this is? Is this due to the fact that space-time is warped in GR?

When I was taking my introduction to C class, our professor heavily stressed that we were supposed to use local variables except when indicated otherwise. When we used C for microcontrollers with the same professor, he had the same requirement. Does this reflect a standard among computer...

Hello, I hope this kind of plea is allowed here, if not, please just let me know. I'm new here :-) I have this story idea that seems to be taking up permanent residence in my head and it will be set around 200 years in the future...and here comes the catch: I need that future to be without...

Okay so to start, this is just about the most random inapplicable proposal ever, so bear with me. Its just a cool question to consider. So, here goes: What would happen, (again, this is highly theoretical) in the instance that an enormous screen - much like the ones that rests behind most...

It's awesome because I am able to be outside imaging during January. No snow on the ground and not unreasonably cold. This is the first year I've been able to consistently image Orion- here's a full-frame and 100% crop of Orion Nebula, 21m total exposure, 800/5.6 ISO varied from 640-2000, 6s...

I obtained the black hole solution whose the metric function f(r) and scalar function ##\varphi(r)## are ; ##f(r)=\frac{1}{4}+\left(\frac{Z^{2}}{2r^{2}}\right)^{2}-\frac{1}{3}\Lambda r^{2}## ##\varphi(r)=\pm\left(\frac{1}{\sqrt{2}l}\right)r## where ##Z##, ##\Lambda## and ##l## are just...

Ok, I got a story for you. It's 1993 and I meet this girl at a college party. I take a liking to her and she "shares my bed." So now we're a couple. About 8 months later a friend of mine provides me with evidence that my girlfriend had advertisements in the local Santa Rosa newspaper as well...

Back home, the average depths of the world's oceans--and the Mediterranean Sea--are as follows: Atlantic--3926 meters Pacific--4028 meters Indian--3963 meters Arctic--1205 meters Southern--4500 meters Mediterranean--1500 meters In this alternate Earth, the average depths are as follows...

I'm so tiredd of hearing Obama and his global warming ilk use the 'seas will rise' because of melting polar ice argument. There are two kinds of ice on the planet, the ice that is free floating such as much of the northern pole area, and ice that is not floating such as Antarctica and glaciers...

Hi, Where can I find a research or statics about the contribution of cellulars or general mobile devices (tablets, PDAs) to the global warming? But I am looking for specifically cellular phones for a project. Thanks a lot!

In another thread I was arguing that leaving aside reasonable physical conditions that are added independently from the math of GR, [wich I consider basically the EFE, the EP, general covariance and the metric and curvature tensors in the neighbourhood of points that solve the EFE in the context...

Urs Schreiber submitted a new PF Insights post Higher Prequantum Geometry III: The Global Action Functional - Cohomologically Continue reading the Original PF Insights Post.

Greetings, I want to ask if there is any subroutine for computing a global spherical harmonic reference field. I read journal and they say it exists, I hope we can share information regarding this subject. Thank you in advance.

At least according to NASA's interpretation. Both measurements of the gravitational field and of the rotation rate of the surface agree on that. If the surface is not connected to the core, its libration is stronger, and apparently the observed magnitude is not compatible with a solid...

A group of scientists used geology models and data about nuclear reactors together with results from two neutrino detectors to produce a worldwide map of antineutrino emission. Man-made reactors are contributing 1% to the total emission, but the production is so localized it is clearly visible...

the global hawk have the raytheon electronic systems ISS with a E-O and IR sensors plus a SYthetic Aperture radar (SAR). this are the Performance E-O/IR field of view : visible 5.1 x 5.2 mrad MWIR 5.4x7.3 mrad...

Why is ##\bar{\psi}=e^{i\theta}\psi##, where ##\theta## is a real number, used as the global gauge transformation? Why ##e^{i \theta}##; what's the physical significance or benefit? Why is ##\bar{\psi} = e^{i \theta(x)} \psi## the local gauge transformation? What does ##\theta## being a...

I am working on proving that an equilibrium point of a two-dimensional dynamical system is globally asymptotically stable. The background and justifications are below. I have gotten to the final steps (in bold), but cannot justify it. It seems right intuitively. Can someone navigate the argument...

For the moment, ignoring whether or not we can change the global climate, completely ignoring the CO2 and anthropogenic warming argument, what would be a good global temperature? Russian President Putin once said that global warming was a good thing because then they could grow crops in...

I am a retired climatologist, not a physicist. I am seeking the help of physicists to resolve a matter that has always puzzled me. I shall try to list my reasoning in what appears to me to be a logical order. I will number my statements so that you may isolate my errors more easily. 1. When...

http://www.wsj.com/articles/switzerland-scraps-currency-cap-1421320531 http://www.bloomberg.com/news/2015-01-15/new-zealand-currency-broker-closes-on-losses-after-swiss-shock.html A news report about the NZ based dealer going out of business is available -...

Complete the function to replace any period by an exclamation point. Ex: "Hello. I'm Miley. Nice to meet you." becomes: "Hello! I'm Miley! Nice to meet you!" Sample program: #include <iostream> #include <string> using namespace std; void MakeSentenceExcited(string& sentenceText) { <STUDENT...

Homework Statement I need to confirm if I correct in saying the following: If f(x) is a function having the domain [a,b) as shown in the figure, then f(x) has several local maxima but none of them is global maximum, and f(x) does not have a global maximum. Homework Equations and...

Japan Slides Into Recession as Tax Hike Takes Toll http://abcnews.go.com/International/wireStory/japan-slides-recession-tax-hike-takes-toll-26960189 EU seems somewhat optimistic, at least about EU and US. http://ec.europa.eu/economy_finance/publications/european_economy/2014/pdf/ee2_en.pdf...

Hey guys, I'm doubting some of my answers and I'd appreciate some help. I'm only asking about 2abc, ignore 1ab please: For 1a, I simply took the derivative (as I did with all three of these questions) and calculated global and local extrema and critical points. Ultimately, I found that...

Homework Statement find the global extrema on the disc x^2 + y^2 \le 1 given the function f(x,y)=xy+5y The Attempt at a Solution For the interior of the disc \nabla f = <y,x+5> the critical point is (0,-5) for the boundary of the disc using lagrange multipliers...