Consider a $C^k$, $k\ge 2$, Lorentzian manifold $(M,g)$ and let $\Box$ be the usual wave operator $\nabla^a\nabla_a$. Given $p\in M$, $s\in\Bbb R,$ and $v\in T_pM$, can we find a neighborhood $U$ of $p$ and $u\in C^k(U)$ such that $\Box u=0$, $u(p)=s$ and $\mathrm{grad}\, u(p)=v$?
@Blue z is of type char so print it using printf("%c", z) or just putchar(c). You are treating it like a string so you're getting whatever happens to follow the variable z in memory.
@JohnRennie I'm going to sleep but I need you to remind me that I want to use some sort of Cauchy problem to split the derivatives and get the prescribed derivative that way
It was excellent! I am half tempted to give it another read for I might understand even more of it than I did now but it is quite dense, the book, even though it is only 150 pages long.
@JohnRennie I am finishing it now and I kid you not, it tastes great, if I say so myself!
@Kaumudi.H well yesterday was the third to last day of my stay, so I'm a day ahead of schedule :-) I'll (try and) eat sensibly today. Fish pie for dinner tonight!!
I'm not any better either, really; I am making the best use of my time with my mum! ...by eating all the food that she cooks, down to the very last morsel.
It's just that while macaroni cheese is nice it can be a little bland. Adding some coarsely chopped fresh chilli gives it a bit of crunch and of course some spicy zing!
For texture you might also consider adding some chick peas.
I find tomatoes tend to go soggy in things like macaroni cheese. And I don't think the tomato flavour works well with a cheese sauce. Just my personal view though.
I cook the macaroni, then make the cheese sauce. Chop and add the chillis then mix everything together, sprinkle grated cheese on top and put the whole lot under the grill to toast the cheese topping.
etymology: noun: from the Latin "etus" ("eaten"), the root "mal" ("bad"), and "logy" ("study of"). It means "the study of things that are hard to swallow."
The tog is a measure of thermal resistance of a unit area, also known as thermal insulance. It is commonly used in the textile industry and often seen quoted on, for example, duvets and carpet underlay.
The Shirley Institute in Manchester, England developed the tog as an easy-to-follow alternative to the SI unit of m2K/W. The name comes from the informal word "togs" for clothing which itself was probably derived from the word toga, a Roman garment.
The basic unit of insulation coefficient is the RSI, (1 m2K/W). 1 tog = 0.1 RSI. There is also a clo clothing unit equivalent to 0.155 RSI or 1.55 tog...
The stone or stone weight (abbreviation: st.) is an English and imperial unit of mass now equal to 14 pounds (6.35029318 kg).
England and other Germanic-speaking countries of northern Europe formerly used various standardised "stones" for trade, with their values ranging from about 5 to 40 local pounds (roughly 3 to 15 kg) depending on the location and objects weighed. The United Kingdom's imperial system adopted the wool stone of 14 pounds in 1835. With the advent of metrication, Europe's various "stones" were superseded by or adapted to the kilogram from the mid-19th century on. The stone continues...
Can you tell me why this question deserves to be negative?
I tried to find faults and I couldn't: I did some research, I did all the calculations I could, and I think it is clear enough . I had deleted it and was going to abandon the site but then I decided to learn what is wrong and see if I ca...
I am a bit confused in classical physics's angular momentum. For a orbital motion of a point mass: if we pick a new coordinate (that doesn't move w.r.t. the old coordinate), angular momentum should be still conserved, right? (I calculated a quite absurd result - it is no longer conserved (an additional term that varies with time )
in new coordinnate: $\vec {L'}=\vec{r'} \times \vec{p'}$
$=(\vec{R}+\vec{r}) \times \vec{p}$
$=\vec{R} \times \vec{p} + \vec L$
where the 1st term varies with time. (where R is the shift of coordinate, since R is constant, and p sort of rotating.)
would anyone kind enough to shed some light on this for me?
@JohnRennie I'm going to sleep but I need you to remind me that I want to use some sort of Cauchy problem to split the derivatives and get the prescribed derivative that way
From what we discussed, your literary taste seems to be classical/conventional in nature. That book is inherently unconventional in nature; it's not supposed to be read as a novel, it's supposed to be read as an encyclopedia
Hey! Could anyone help me with the "think why?" part of the explanation given in the solution? I can't interpret the reason for their having equal velocities.
@BalarkaSen Dare I say it, my literary taste continues to change as I have kept on reading :-)
One book that I finished reading today, The Sense of An Ending (different from the movie with the same title) is far from anything I would've been able to read, even, two years ago, but I absolutely loved it.
Got it. Yeah I have definitely seen that attitude towards a lot of books
Have you read Murakami? Strikes me as something you might like (you're onto mystery thrillers aren't you? Murakami incorporates mystery thriller elements with abstract surrealism)
@BalarkaSen Lol, I s'pose that's true. While I will struggle to put in words what sort of books I like, it's definitely not mystery thrillers! They're alright, but I'm not a fan.
Although, I must say, while we're on the topic of mystery thrillers, that I did like Gone Girl very, very much, in that it sort of blew my mind, the plot.
I've just started watching the Fall - it seems good so far (after 1 episode)... I'm with @JohnRennie on the Sherlock Holmes books and would add that the most recent TV episodes were appalling. I've been told to read Agatha Christy but haven't got round to it yet
fiction? read this this summer, given to me by friend, nice read, liked it, can relate various ways, recommend it, charles martin :) charlesmartinbooks.com/books/long-way-gone
?Is it possible to make a time machine ever? Please give an easy answer,a simple one A simple answer, but a possibly wrong one, is to say that a time machine is not possible. Currently, we don't have either the technology to build one, nor a definite, proven (or generally accepted) idea of how we could build one. — Countto1047 secs ago
@vzn if it's a romantic novel, which it looks like, it's probably not for me - I'm getting to be more and more fussy about books and have a ridiculously long list to read as it is. I'm going to counter that one by suggesting Ann Leckie's Ancillary Justice series
Although if you like epic fantasy, Malazan book of the Fallen is fantastic
re zeitgeist/ understanding Brexit/ Trump/ economics influencing politics trends, ran across this recently, recommend it, New Class War by Lind americanaffairsjournal.org/2017/05/new-class-war
@Mithrandir24601 lol it has some love story but its written by a guy so cant be a romantic novel... besides what decent stories dont involve love interests anyway :P ... was just reading his blog, they are gonna do a movie of one of his books with kate winslet, cant beat that right? :P variety.com/2016/film/news/…
@vzn about a third of the description screams 'romance' at me and telling me that they're going to make a film involving Kate Winslet isn't doing much to convince me that it's not a romance :P
@Mithrandir24601 lol its not the same book cited by me. so youre averse to romance? yikes, that removes wide swathes of "literature"... or maybe not :P o_O
@vzn "he falls in love with Daley Cross, an angelic voice in need of a song." I think that counts :P It's not that I don't like it, it's just that authors very rarely do anywhere near a decent job of it. If it's a major part of the plot, it's often either eyeroll worthy and cringy or boring and predictable with OK writing. A notable exception is Stephen Erikson
@Mithrandir24601 I struggled with the Malazan books, but I really like the Bauchelain & Korbal Broach novellas. If you haven't read them I think they they display a wonderful dark humour.
@vzn depends exactly what you mean by 'love story component', but often yeah... It's not always so bad in sci-fi and fantasy where it's not in the focus so much and just evolves in a reasonable, if predictable way with the storyline, although it depends on what you read (e.g. Brent Weeks, Brandon Sanderson). Of course Patrick Rothfuss completely inverts this trope :) and Lev Grossman is a study on how to do character development and totally destroys typical romance plots
It seems a bit harsh to have exams so soon after the holiday, but I guess the holiday comes smack in the middle of a term so the college didn't have much choice.
@heather it appears that the CM is looking at the QC proposal. I feel that this is good as it feels like it's getting closer to happening, but bad as some of the questions are now closed...
I say was because those pictures display exorbitant amounts of food; not unlike the sort of meals you are having now, hmm...so that would make it an ongoing project!
That is what it says on your Fb page :-) I like to browse through all those pictures of food sometimes, especially since I haven't looked through them all.
@JohnRennie Right, right :-)
I'm going to read for a bit before drifting off to sleep. Byebye!
@Slereah The idea is to pick some spacelike hypersurface $\Sigma$ containing $p$. Now specifying $u(p)$ is trivial because the wave equation is invariant under constant perturbations. So that's whatever. But I can specify $\nabla u(p)|\Sigma$ by specifying $u(\cdot, 0)$ and differentiate along the surface. For the Cauchy theorems I can also specify $u_t(\cdot,0)$.
Now take the neigborhood to be $\approx (-\epsilon,\epsilon)\times\Sigma$ and then split the metric like $-dt^2+h$
Do forwards and backwards Cauchy solutions, then check that the derivatives match on the interface $\{0\}\times\Sigma$
... wondering if PSE is the appropriate place to discuss this topic: https://physics.stackexchange.com/questions/356196/would-it-be-safe-to-hide-in-a-stairwell-during-a-hurricane
Why is it that you can only cool down a substance so far before the energy goes into changing it's state? I assume it has something to do with the distance between molecules meaning that intermolecular interactions have less energy in them than making the distance between them even smaller, but why does it create these bonds instead of making the distance smaller / just reducing the temperature more?
@Phase I think one thing to consider is that the molecules slow down allowing them to form instantaneous dipole-induced dipole bonds
Essentially at any point the electron cloud could have a higher electron density say - at the bottom and when molecules are moving slowly past each other this can form partial charges between them
So the dipole has been induced by the other atom attracting them to each otheer
Thanks @CooperCape but this leads me another question I forgot ages ago
If you have an electron cloud, is the electric field from that electron just some sort of averaged field from some centre of amplitude or is it a superposition of fields each coming from some point in the cloud?
Assuming that it doesn't cause collapse from the fact that peturbation theory exists with a weak field, im just confused about how you'd actually express the electric field of the electron
?
That doesn't really answer my question as far as I could gather