Theorem 8.17 , Chapter II, Hartshorne
Hartshorne Theorem 8.17
Missing whitespace in beta site statistics box How to simulate slow internet connections on the mac What's a good software solution to slow down internet connections on the mac for testing and simulations?  My primary need is when testing code in the iPhone / iOS simulator, so slowing down the connection for specific applications or processes would be great. How can I keep low resolution textures pixelated? I have a problem. I am going to make a minecraft animation in blender. But when I put a minecraft texture on a 3d cube that is 16x16x16 it is very low resolution is there a way to get the texture in a better resolution or is there a way to make blender make the texture better?  I hope you have an answer. Thanks in advance "Reality" of EM waves vs. wavefunction of individual photons - why not treat the wave function as equally "Real"? In thinking how to ask this question (somewhat) succinctly, I keep coming back to a Microwave Oven.  A Microwave Oven has a grid of holes over the window specifically designed to be smaller in diameter than the wavelength of the microwaves it produces, yet larger than the wavelengths of the visible light spectrum - this is so you can watch your food being heated without getting an eye full of microwaves.  The "realness" of electromagnetic waves seems indisputable - both from the microwave example above, and also because if I want to broadcast a radio wave with a certain wavelength, then I need to make sure I have an antenna of corresponding length to produce the wave I'm looking for.  Furthermore, we discuss and treat these waves as real, measurable "objects" that exist and can be manipulated.     Now, if I want to describe the behavior of my Microwave Oven in the framework of QM (let's pretend my oven is going to only produce 1 photon of energy corresponding to a wavelength of the microwave spectrum for simplicity) then I'll describe the behavior of that photon as a wavefunction that evolves over time and gives a probability distribution within my microwave that similarly does not allow the photon to pass through the safety grid and exit the oven cavity giving me a retinal burn.  The difference is, the wavefunction is never treated as something "real" in this description.  When the safety grid is described as working to protect you because it has holes smaller than the wavelength of the classical waves it's blocking, this is a useful description that seems to describe "real" objects/be-ables.  While it is possible to describe why an individual photon has low probability of passing through the same grid but extended physical properties such as wavelength (in space) are treated as non-real because we're dealing with a point particle and with behavior described by something we also treat as non-real (the wavefunction); it seems unclear to me why we insist this wave function which predicts behavior of physical measurements so well is somehow "non-real."    Put another way, if we have no problem treating EM waves as "Real," then why do we insist on treating the wavefunction that describes the same behavior as "unreal?"  I understand there is recent research (Eric Cavalcanti and his group for one) trying to argue this point, but as every respectable physics professor, I've ever encountered, has treated the wavefunction as an indisputably non-real mathematical tool, I needed to ask this community for an answer. Is it possible for an iPad to get a virus? How to sandbox applications? I want to run small untrusted programs, but restrict them from accessing any files outside of their folder, network access, and everything else that they don't really need. What is the simplest way to achieve this? Is there anything in RAW that supports spell level as a character concept, or alternatively that supports it as solely a player concept?  On the one hand, I see nothing that explicitly states that a character knows that there are spell levels. On the other hand, I don't see how a spellcaster could manage spell slots without knowing about spell levels. Pacf lag axe , is not an integer I'm trying to use ARIMA process to predict the behaviour of a time series, the probleme I face is that I can't get the order of each component of ARIMA, the lag is between 0 and 1, same goes for the acf. The time series has no tendency, and I guess no seasonality.     My question is : Does this mean that ARIMA orders are all 0s, and if so, is the HoltWinters a good (or the best) solution for modelling this kind of TS ? Do I have to pay taxes in the US if my online store sells to US customers even though I don't live in the US? I  own a website and I sell digital content. I'm a nonresident alien with the US. Most of my customers are US based so I was wondering will I have to pay any taxes to the US?  I have read that      For nonresidents, taxable income is separated into two categories:         Income that is effectively connected with a U.S. trade or business, after the deductions that are allowed, is subject to U.S. income tax   at graduated rates - the same rates that apply to U.S. citizens and   residents - or lower rates if the provisions of a tax treaty apply.   Income that is subject to U.S. income tax, for being U.S. source income, but that is not effectively connected with a U.S. trade or   business, is subject to a flat 30% tax      Is this true and do I belong to any of these categories?  If I form an LLC or C corp am I liable for this withholding tax?  My customers are based in the US and I believe all income is considered FDAP income according to the IRS:     Fixed, Determinable, Annual, or Periodical (FDAP) income is all   income, except:         Gains derived from the sale of real or personal property (including market discount and option premiums, but not including original issue   discount)   Items of income excluded from gross income, without regard to the U.S. or foreign status of the owner of the income, such as tax-exempt   municipal bond interest and qualified scholarship income      The thing is the IRS also says:     Effectively Connected Income, after allowable deductions, is taxed at   graduated rates. These are the same rates that apply to U.S. citizens   and residents. FDAP income generally consists of passive investment   income; however, in theory, it could consist of almost any sort of   income. FDAP income is taxed at a flat 30 percent (or lower treaty   rate) and no deductions are allowed against such income. Effectively   Connected Income should be reported on page one of Form 1040NR. FDAP   income should be reported on page four of Form 1040NR.   In the last quote, it’s like they say it only applies to passive income but if they feel like it, they can apply this to all income?? "'Hello', says he. 'Hello', says I" — is this correct? I'm reading a novel in which once in a while a character says something like "I are", "He do", and similar stuff. I understand the author is just reproducing the way people talk on the streets.  However I've found a piece of text of which I'm not sure if it's proper English. One of the characters, who almost always speaks proper English, is reproducing a conversation that happened many years ago using the present tense in the following manner:     I was with this guy and "Hi", says he, "how are you", says I...   and so on.  My question is if the "says I" is proper English (a special case in which "I" is treated as a third person because we are relating in present tense something that happened in the past) or it's just kind of slang.  I was also a bit surprised by how the usual order is switched ("says he" instead of "he says") but to me it's secondary to the "says I" issue. In Iron Man 3,      When the real villain kidnapped the President of the United States,   it is never explained why none of the other Avengers came to help, or why Tony didn't call them. The only explanation so far is: "it was an Iron Man movie...", but an in universe answer would be good. Let $(a,b)$ and $(c,d)$ be intervals in $\Bbb R$, and find an injective and surjective function from $(a,b)$ to $(c,d)$ So here is this question I got stuck on:  Let $(a,b)$, $(c,d)$ be intervals (not sure if that's the correct term) on $\Bbb R$, so that $a&lt;b$, $c&lt;d$. Find an injective and surjective function $f:(a,b)\rightarrow(c,d)$.   Thanks in advance!   P.S. I get these question a lot. Is that some way of thinking, or some general method I should follow to make these question easier for me to solve? Strange floating-point behaviour in a Java program In my program I have one array with 25 double values 0.04 When I try to sum these values in a loop I get following results:  0.0 + 0.04 = 0.04 0.04 + 0.04 = 0.08 0.08 + 0.04 = 0.12 0.12 + 0.04 = 0.16 0.16 + 0.04 = 0.2 0.2 + 0.04 = 0.24000000000000002 0.24000000000000002 + 0.04 = 0.28 0.28 + 0.04 = 0.32 0.32 + 0.04 = 0.36 0.36 + 0.04 = 0.39999999999999997 0.39999999999999997 + 0.04 = 0.43999999999999995 0.43999999999999995 + 0.04 = 0.4799999999999999 0.4799999999999999 + 0.04 = 0.5199999999999999 0.5199999999999999 + 0.04 = 0.5599999999999999 0.5599999999999999 + 0.04 = 0.6 0.6 + 0.04 = 0.64 0.64 + 0.04 = 0.68 0.68 + 0.04 = 0.7200000000000001 0.7200000000000001 + 0.04 = 0.7600000000000001 0.7600000000000001 + 0.04 = 0.8000000000000002 0.8000000000000002 + 0.04 = 0.8400000000000002 0.8400000000000002 + 0.04 = 0.8800000000000002 0.8800000000000002 + 0.04 = 0.9200000000000003 0.9200000000000003 + 0.04 = 0.9600000000000003   Why on earth could that happen?! The only solutions that I know of till now are $(x,y) = (1,1) \space , (19,7)$. We can note that: $$x^2-x+1 = y^3 \implies (2x-1)^2 = 4y^3-3$$ Thus, if odd prime $p \mid y$, then $(2x-1)^2 \equiv -3 \pmod{p}$ and thus, $-3$ is a quadratic residue. This implies that $p \equiv 1 \pmod{6}$ .  How can we further proceed into this problem?  Note: As mentioned in one of the links in the comments, if we instead replace $x$ by $x+1$, we get $x^2+x+1 = y^3$. Thus, the solutions for this is $(x,y) = (0,1) \space, (18,7)$. Entity Query field condition for Webform submissions I'm trying to query webform submissions based on a field value. The field is called "ticket_for". Somethings I tried and do not work:      -&gt;condition('ticket_for',$adnummer)     -&gt;condition('webform_submission_data:ticket_for',$adnummer,'CONTAINS') ...   What kind of condition should I be using in a query like this?  $query = \Drupal::entityQuery('webform_submission') -&gt;condition('webform_id', 'ticket') -&gt;condition('entity_id', $eventID) -&gt;condition('webform_submission_data:ticket_for',$adnummer,'CONTAINS'); hard self collision: make particles occupy space $f\geq 0$, continuous and $\int_a^b f=0$ implies $f=0$ everywhere on $[a,b]$ Since the version of the word "that" might matter to the correct answer, I'll provide the actual title in question:  Title:  Existing Solutions that Didn't Work  If someone could explain the why of the answer, I would be appreciative.  EDIT:  It has been suggested that this is a duplicate, and that may be, in a sense.  However, the after reading the suggested prior question, I'm no closer to my answer.  I think it may have to do with my use of the word "that."  Perhaps it is incorrect?  Using these definitions of the word "that:" I'm having trouble figuring out which definition of that matches my title.  Am I even using it correctly?  Perhaps I should use which instead:  Possible Title:  Existing Solutions which Didn't Work  If my original usage is incorrect, and I should use which, then the answer is simple since which is always a pronoun or adjective, and those are both capitalized in a title.  However, I'm having difficulty understanding which part of speech that is in my original title. Suppose you cut a five year old's hair, save it for 10 years, and then use it for a Polyjuice transformation. What age do you turn into: The toddler or the teenager? Full List of inventory items After beating the game, I still have several empty inventory spots.  I most likely missed several items in my addicted frenzy to finish the game.  What are all the items that can be found in the game? And where can they found?