Which one is correct to speak? Why?   I will call you. I would call you.   What is the difference between the two? Thanks.
What is the difference between would and will in the following examples?        How would you use this word in a sentence?     How will you use this word in a sentence?
Evidence for quantum gravity from gravitational waves The rumor spreads that .  I am far from being an experimentalist, but I want to know if there is any chance that the mentioned observations will reveal any experimental evidence for quantum gravity.  Personally, I feel like this is merely impossible as gravitational waves should propagate in agreement with classical General Relativity. But I might very well not see pitfalls if there are any.  UPDATE: by "evidence for quantum gravity" I mean experimental results which don't agree with predictions of General Relativity or its classical generalizations. They might be coming from string theory or loop gravity or from a completely different approach which we haven't discovered yet. I want to understand what are the chances that new physics will show up during the upcoming  gravitational wave observations.  Also, I expect gravitational waves to be in a highly coherent state, thus making the individual gravitons unobservable. Is this true? Hardware issue on iMac, flashing question mark I have an iMac 2008/2009 issue and recently the computer would not boot and I would get a flashing question mark. Ran through all the usual steps, try boot in safe mode, flash RAM,  try single user for fdisk, put in OS disk and boot from CD, etc... No dice.   Replaced the hard drive and put the OS disc in the system, press and hold option. (holding C didn't work) I can see the OS disk but when I click on it the system will act like it is going to run and then freeze. The best I got was the OS X disc that changed the screen to dark grey and told be the system had to restart.  Purchased a usb mount for an external hard drive. Was able to mount the old hard drive to a laptop and run disk utility. Everything checked out.  At this point I am pretty sure it isn't the hard drive.   Any other hard ware items this can point too? My iMAC can also "see" the hard drive (and the recovery partition) when connected via the USB and I hold "option" on start up. But it crashes when trying to boot from either.  I am going to take out and re-install the RAM for giggles but I am not sure what else to do.   Ideas are welcome. How to enable multiple logon remote desktop in Windows 7 What is the meaning of the "expansion of space"? When we say that "the space between galaxies is expanding," what do we really mean? For instance, if I think of space as being a Cartesian grid, then when space expands should I think of it as adding more grid-points or as making the distance between the grid-points larger? Or is this a flawed picture of space-time even when far from significant mass densities?  It seems to me that it must be the case that we are "adding more grid-points" because otherwise we would not observe the expansion since anything that occupied that part of the grid (e.g. light, my hand, etc.) would also expand by a corresponding amount (otherwise, after a sufficient amount of expansion, we would be able to observe sub-atomic scale processes as being macroscopic in scale). But if it is the case that we are adding more grid-points, then the "expansion" of space seems like a misnomer: shouldn't it be called the "creation" of space?  That being said, either case (adding grid-points or stretching distances) could conceivably be the same process depending on the nature of space-time (i.e. if it were discrete but dense - like the Rationals - rather than either strictly discrete (Integers) or strictly continuous (Reals)... I hope that analogy makes sense).   So what is really going on in intergalactic space? What is the meaning of its expansion? Does it correspond to creating more space, stretching the space that's already there, or something more subtle? I need to build a function which parses the domain from a URL.  So, with   http://google.com/dhasjkdas/sadsdds/sdda/sdads.html   or  http://www.google.com/dhasjkdas/sadsdds/sdda/sdads.html  it should return google.com  with   http://google.co.uk/dhasjkdas/sadsdds/sdda/sdads.html  it should return google.co.uk. I created a test MVC sharepoint app succesfully in a solution. Now I need to integrate this into a main solution project.   But when I added a SharePoint MVC App into the solution and hit F5, I am getting following error:  Error occurred in deployment step 'Install app for SharePoint':  Failed to install app for SharePoint. Please see the output window for details.   Detailed stack trace:  CorrelationId: 50583239-71cb-4b07-8bcb-4bbc51a22631      ErrorDetail: There was a problem with activating the app web definition.      ErrorType: App      ErrorTypeName: App Related      ExceptionMessage: Microsoft.SharePoint.SPException: Exception from HRESULT: 0x81070964 ---&gt; System.Runtime.InteropServices.COMException: Exception from HRESULT: 0x81070964 at Microsoft.SharePoint.Library.SPRequestInternalClass.EnableModuleFromXml(String bstrSetupDirectory, String bstrFeatureDirectory, String bstrUrl, String bstrXML, Boolean fForceUnghost, ISPEnableModuleCallback pModuleContext) at Microsoft.SharePoint.Library.SPRequest.EnableModuleFromXml(String bstrSetupDirectory, String bstrFeatureDirectory, String bstrUrl, String bstrXML, Boolean fForceUnghost, ISPEnableModuleCallback pModuleContext) --- End of inner exception stack trace --- at Microsoft.SharePoint.Administration.SPElementDefinitionCollection.ProvisionModules(SPFeaturePropertyCollection props, SPSite site, SPWeb web, SPFeatureActivateFlags activateFlags, Boolean fForce) at Microsoft.SharePoint.Administration.SPElementDefinitionCollection.ProvisionElements(SPFeaturePropertyCollection props, SPWebApplication webapp, SPSite site, SPWeb web, SPFeatureActivateFlags activateFlags, Boolean fForce) at Microsoft.SharePoint.SPFeature.Activate(SPSite siteParent, SPWeb webParent, SPFeaturePropertyCollection props, SPFeatureActivateFlags activateFlags, Boolean fForce) at Microsoft.SharePoint.SPFeatureCollection.AddInternal(SPFeatureDefinition featdef, Version version, SPFeaturePropertyCollection properties, SPFeatureActivateFlags activateFlags, Boolean force, Boolean fMarkOnly) at Microsoft.SharePoint.SPFeatureCollection.AddInternalWithName(Guid featureId, Int32 compatibilityLevel, String featureName, Version version, SPFeaturePropertyCollection properties, SPFeatureActivateFlags activateFlags, Boolean force, Boolean fMarkOnly, SPFeatureDefinitionScope featdefScope) at Microsoft.SharePoint.SPFeatureCollection.AddInternal(Guid featureId, Version version, SPFeaturePropertyCollection properties, Boolean force, Boolean fMarkOnly, SPFeatureDefinitionScope featdefScope) at Microsoft.SharePoint.SPFeatureCollection.Add(Guid featureId, Boolean force, SPFeatureDefinitionScope featdefScope) at Microsoft.SharePoint.SPUserSolutionCollection.EnsureWebFeaturesActivated(SPUserSolution solution) at Microsoft.SharePoint.Packaging.SPUserCodeSolutionDeploymentGroup.ActivateSolution(SPWeb web, SPUserSolution solution) at Microsoft.SharePoint.Packaging.SPUserCodeSolutionDeploymentGroup.Deploy() at Microsoft.SharePoint.Administration.SPAppTask.DeployOperation() at Microsoft.SharePoint.Lifecycle.MonitoredTaskExecution.DoTask()      Source: AppWeb      SourceName: App Web Deployment   Can somebody shed a light on this issue? :) Ubuntu Software (Software Center) Crash - Ubuntu 16.04 Books on Number Theory for Layman : So how many named special cases of each modal verb are there, in toto? There's   1. subjunctive should, and   2. mandative should, and   3. , at least;   and I s[up]pose 4. Should we? is suggestive should, and   5. Shouldn't we? is tag **should**, and I can think of a lot more.    I ask about only operative uses of this modal verb including literary and formal usage,  but please omit anything obsolete. I'm trying to classify them and learn the formal terms describing each. Are there any apt others in addition to the ones above? (I added the enumeration below)  1. What's 'subjunctive should'?  Whenever should is conjugated in the subjunctive mood? 5. What's a tag **should** ? 6. Where does  should/would  feature? What's it called? This should is detailed in   or  or . Integer solutions to combinations of floating point numbers Imagine two kids each sitting in the center of their own tilt-a whirl®, each holding steady a flashlight (or laser) whose beam is parallel to the deck.  Each machine rotates and precesses (we'll leave out nutation) at different, real, rates.  How do we determine the least number of rotations to alignment, for each kid. If you prefer another analogy: Saturn and Jupiter orbit with different (real) periods.  How many orbits for each until conjunction in precisely the same position in space?  Simplify by assuming circular, observer-centric, orbits. specifically solutions to: aC1 + bC2 = N where a, b, N are positive integers of your own choosing and C1, C2 are constant, unique, positive, non-integer(real) numbers where C1 &lt; C2. I am hoping to avoid rigorous computational methods involving modulus tests. Hope I clarified the ambiguities. Thanks, @DonThousand the Bezout identity looks interesting. Integrating Knowledge into an existing website Below, the  of second-order logic is used.    My question is about a second-order analogue of $ZFC$ other than the usual "second-order $ZFC$." Rather than define the latter, I'll just state that its (set-sized) models are exactly the $V_\kappa$s with $\kappa$ strongly inaccessible (or if you prefer, the uncountable Grothendieck universes).  Specifically, I'm interested in the second-order theory consisting of the usual (first-order) axioms of Pairing, Extensionality, Union, Choice, Infinity, and Powerset, and the Separation and Replacement schemes ranging over second-order formulas. I'll call this "$ZFC_2^{scheme}$."    Specifically, for each formula $\varphi(x, y_1,...,y_k)$ of second-order logic with only the displayed variables, each of which is first-order, we have a corresponding Separation and Replacement instance. We do not allow second-order parameters here, so formulas with second-order free variables don't yield Separation/Replacement instances.   The passage from $ZFC$ to $ZFC_2^{scheme}$ has a nice uniformity: it's an example of a more general operation $\mathcal{ZFC}$ which spits out a $ZFC$-analogue given a logic at least as strong as first-order logic.    This is the reason for the parameter restriction above: I want $ZFC_2^{scheme}$ to look just like $\mathcal{ZFC}(\mathcal{L})$ for any other logic $\mathcal{L}$, and not take into account the particular feature that we now have a new kind of variable at our disposal - and in particular, take as "syntax-free" an approach to logics as we can get away with. (This is a choice of arguable value, but it's the one I'm making for now.)   It's easy to show that every model of $ZFC_2^{scheme}$ is well-founded, so to understand its models we only need to look at transitive sets. A natural hope at this point is that $ZFC_2^{scheme}$ is just second-order $ZFC$ in disguise, that is, that for a transitive set $M$ we have $M\models ZFC_2^{scheme}$ iff $M=V_\kappa$ for some strongly inaccessible $\kappa$. However, this isn't at all obvious to me (although it is easy to show the right-to-left direction).     Question. What are the (set-sized) models of $ZFC_2^{scheme}$?   (Note by contrast that the "arithmetic analogues" $PA_2^{scheme}$ and second-order $PA$ are equivalent since each pins down $\mathbb{N}$ up to isomorphism - although that leads to .)  (I'm happy to drop Choice if that would help.)  EDIT: As Hanul Jeon pointed out below,  shows that consistently $ZFC_2^{scheme}$ (there called "$ZFC_2^{def}$") has countable models, so we have a partial answer. However, I don't see at the moment a way to get an outright $ZFC$ proof that $ZFC_2^{scheme}$ is strictly weaker than second-order $ZFC$. Can markdown mini replace an en dash with a normal hyphen in URLs? Low-RAM Linux Distro Specifically for serving static sites I'm looking for a near-zero-configuration linux distro that is designed specifically for serving static web sites and nothing else on a low-RAM machine (I'm planning on 128MB, but the option of less would be nice).  Any ideas of a linux distro specifically tuned for serving static sites in a small footprint? Trigger to use HTTP callout and update record with the results I have been trying to integrate Google Shortener API into my salesforce org. I wrote a class to make the call out, but am having difficulty bringing the value back into the record. I have a custom object called "referral_advocate__c" with a field called "Short_URL__c". Anytime the field "unique_ID__c" has a value, I am wanting to send this value with a static URL to google shortener and then save the response value to "referral_advocate__c.short_URL__c" on the record. This is the class to make the call out:  public class URLshort {  final string urls = 'https://www.myurl.com'; referral_advocate__c adv = new referral_advocate__c();  @future(callout = true) public static void URLshortner() {      HttpRequest req = new HttpRequest();     HttpResponse res = new HttpResponse();     Http http = new Http();      req.setEndpoint('https://www.googleapis.com/urlshortener/v1/url?key=myapikey');     req.setMethod('POST');     req.setHeader('Content-Type','application/json');            req.setBody('{"longUrl":+urls + adv.unique_reference_number_c}');       try {         res = http.send(req);         System.debug(res.getBody());     } catch(System.CalloutException e) {         System.debug('Callout error: '+ e);         System.debug(res.toString());     }   }  }   The after insert trigger on "referral_advocate__c" I wrote is not firing correctly. How do I return the results from this class and update the field "short_URL__C" with the returned value from a trigger? Why is there a peeking duck in my profile pic? In , you may see something odd: a peeking duck.    I've just recently uploaded this new profile picture of mine. I checked it after the upload and everything's fine. After a few hours, I opened my profile and there it is, the duck has somehow become afraid of the people viewing it.  Is this a bug, a feature, or is it just the duck?  I am about to re-upload my profile pic, but I've decided to drop first this topic to meta.  And if you're curious,  is the original picture.    ADDITIONAL: I've used the non-gravatar way to upload the picture.  ADDITIONAL 2: The problem only shows in the profile view. No problem in chat, less info profile view, and in the questions and answers.  UPDATE: Re-uploaded picture. Status normal (for now, at least). The residue at $\infty$ I am stuck on the following problem :      $\,\,\,\,$*Problem*$\quad$The residue of an entire function at $\infty$ is $0$.      Solution: True. This follows from the definition of the residue at $\infty$ together with the Cauchy-Goursat Theorem. Another way to see this is to take the Taylor expansion for $f$ at $0$ $\displaystyle f(z)=\sum_{n=0}^\infty a_nz^n$ and replace $z$ with $1/z$ to get the Laurent expansion for $f(1/z)$ at $0$: $\displaystyle f(z)=\sum_{n=-\infty}^0a_{-n}z^n.$ Then we have that the residue at $\infty$ is given by the negative coefficient of the $1/z$ term of    $$ \dfrac1{z^2}f\left(\dfrac1z\right)=\sum_{n=-\infty}^{-2}a_{-n-2}z^n, $$   which is clearly $0$.   I am having trouble to understand the last few lines (in italic) in the given solution. Can someone give lucid explanation? Thanks and regards to all. Evans PDE Problem 5.15: Poincaré inequality for functions with large zero set I have trouble proving the following problem (Evans PDE textbook 5.10. #15). Could anyone kindly help me solving the problem? I know that I should somehow use Poincaré inequality but I still cannot solve it.   Fix $\alpha&gt;0$ and let $U=B^0(0,1)\subset \mathbb{R}^n$. Show there exists a constant $C$ depending only on $n$ and $\alpha$ such that $$ \int_U u^2 dx \le C\int_U|Du|^2 dx,  $$ provided that $u\in W^{1,2}(U)$ satisfies $|\{x\in U\ |\ u(x)=0\}|&gt;\alpha$. Why can't a single ReLU learn a ReLU? As a follow-up to  I simplified even more and tried to train a single ReLU (with random weight) to a single ReLU.  This is the simplest network there is, and yet half the time it fails to converge.  If the initial guess is in the same orientation as the target, it learns quickly and converges to the correct weight of 1:      If the initial guess is "backwards", it gets stuck at a weight of zero and never goes through it to the region of lower loss:        I don't understand why.  Shouldn't gradient descent easily follow the loss curve to the global minima?  Example code:  from tensorflow.keras.models import Sequential from tensorflow.keras.layers import Dense, ReLU from tensorflow import keras import numpy as np import matplotlib.pyplot as plt  batch = 1000   def tests():     while True:         test = np.random.randn(batch)          # Generate ReLU test case         X = test         Y = test.copy()         Y[Y &lt; 0] = 0          yield X, Y   model = Sequential([Dense(1, input_dim=1, activation=None, use_bias=False)]) model.add(ReLU()) model.set_weights([[[-10]]])  model.compile(loss='mean_squared_error', optimizer='sgd')   class LossHistory(keras.callbacks.Callback):     def on_train_begin(self, logs={}):         self.losses = []         self.weights = []         self.n = 0         self.n += 1      def on_epoch_end(self, batch, logs={}):         self.losses.append(logs.get('loss'))         w = model.get_weights()         self.weights.append([x.flatten()[0] for x in w])         self.n += 1   history = LossHistory()  model.fit_generator(tests(), steps_per_epoch=100, epochs=20,                     callbacks=[history])  fig, (ax1, ax2) = plt.subplots(2, 1, True, num='Learning')  ax1.set_title('ReLU learning ReLU') ax1.semilogy(history.losses) ax1.set_ylabel('Loss') ax1.grid(True, which="both") ax1.margins(0, 0.05)  ax2.plot(history.weights) ax2.set_ylabel('Weight') ax2.set_xlabel('Epoch') ax2.grid(True, which="both") ax2.margins(0, 0.05)  plt.tight_layout() plt.show()     Similar things happen if I add bias: 2D loss function is smooth and simple, but if the relu starts upside down, it circles around and gets stuck (red starting points), and doesn't follow the gradient down to the minimum (like it does for blue starting points):    Similar things happen if I add output weight and bias, too.  (It will flip left-to-right, or down-to-up, but not both.) How to tell if mains voltage is on with microcontroller? I want to be able to tell if the mains voltage is on or off with an Arduino.   How could I do this safely with minimal components (or components from Radio Shack)?