Window Rendering Problem
Colored borders around windows after update
Let $l \in\mathbb{R} $ and $ f:(0,\infty) \to \Bbb R $ be a function such that $ \lim_{x\to \infty} xf(x)=l $ .  Prove that  $ \lim_{x\to \infty} f(x)=0 $.  Any help would be appreciated - I found this difficult to prove Where can I find examples of good Mathematica programming practice? I feel uncomfortable saying sentences like the following:    "I've a car" instead of "I have a car" "They've a great time" instead of "They have a great time" "He's a pen" instead of "He has a pen" etc   I ask this because I read this sort of thing in a book.  Are they correct? And what is the rule? Can you use such forms in a formal setting? Is it possible to learn a neural networks for a constant target? I saw a paper () where they learn L based on the following cost function: $$(D_1L(q(k-1), q(k)) + D_2L(q(k),q(k+1)))² = 0$$ Here $D$ is the derivative with respect to ith argument of L. This can be obtained via automatic differentiation and it is fully compatible with backpropagation. So the target is always zero independently of the input of L but how does the optimization method knows the real values of L for a given input? I mean as long as the cost function is satisfied with a zero value the model is learning but it can be learning wrong values for L. For instance, if the real value of $D_1L(q(k-1), q(k))$ is 10 then the real value of $D_2L(q(k),q(k+1))$ has to be -10. However the neural network may be learning wrong values for L as long as they are symmetric, for example -3 and 3. This is an ill posed problem due to the infinite possible solutions. Am I missing something or the method in that paper simply doesn't make any sense? Is it possible to learn a neural network in regression task with constant target? Edit: The goal is not to predict always that value. The goal is to learn L by predicting always zero (see the cost function). The question here is in order to learn L in such a way that it respects the cost function, there are infinite possible solutions, for instance if $D1L(q(k−1),q(k))$ = x then D2L(q(k),q(k+1))=-x and its sum gives 0 respecting the cost function. But as you can see x can assume any value as long as the cost function is respected, when in reality the goal is to learn a specific L. But the optimization doesn't know a priori value for L so I guess it should just assume a random value for x. In the paper they don't mention the ill posedness of the problem, either they solved it or not. I would like to know if what I'm thinking makes sense or if I'm just missing something. Mathematical operators, such as function names, should be set in roman type, not italics. Latex already has commands for some operators, including \max, \min, and \log.  How can I define additional such commands? Error when clipping raster in QGIS: "'ascii' codec can't encode character"? I have done it many times (clipping a raster with a polygon layer or by extension) but today I got an error for the first time and I don't know how to solve it. I am always using the same type of raster layers. When running the clipping tool I got the following message:  gdal_translate -of GTiff -ot Byte -projwin 410282.185971 4694950.41162 410783.882475 4694524.96815 -co COMPRESS=DEFLATE -co PREDICTOR=1 -co ZLEVEL=6 -co TFW=YES "C:/Users/FERRAN ALA/Desktop/Justificació Fontanals/QGIS/Topo 1_5000/bt5mv20sd0f283077st1r031.sid" "C:/Users/FERRAN ALA/Desktop/Justificació Fontanals/QGIS/background/image.tif"   GDAL command output:     'ascii' codec can't encode character u'\xf3' in position 201: ordinal not in range(128) See log for more details   Does anybody know what that is? We've tried this a few times. First time we used an old ceramic container and it started sheding on the inside and ruined it. Next time we used a new metal garbage can with one of those super sized 10 gallon zip lock bags as a liner. It went rank very quickly. This could have been due to our packing though. Before we get into this again, what is you recommendation for a good container? I hate the thought of plastics but it seems it might just be the best choice as long as it's made for food storage. Showing that $\Bbb R[x] / \langle x^2 + 1 \rangle$ is isomorphic to $\Bbb C$ question I'm new to regular expressions and would appreciate your help.  I'm trying to put together an expression that will split the example string using all spaces that are not surrounded by single or double quotes. My last attempt looks like this: (?!") and isn't quite working. It's splitting on the space before the quote.  Example input:   This is a string that "will be" highlighted when your 'regular expression' matches something.   Desired output:  This is a string that will be highlighted when your regular expression matches something.   Note that "will be" and 'regular expression' retain the space between the words. We have a situation: someone saw the boy break the window. Can I make this passive sentence?     The boy was seen to break the window.   I use Murphy's Grammar and this structure is never discussed. ng-options with simple array init Mutineers force captain to record instructions to spaceship's computer but he leaves out "please" The crew mutinies on a spaceship whose captain controls it with verbal orders. They test whether they can control the ship with recordings of the captain's voice with an order to increase orbital speed (currently orbiting a planet). It works, so they force the captain to record all the possible orders they may need, and execute him. Only then do they realize that the ship obeys only orders couched in polite language, and only the test recording was like this, but the other recordings are not. They will die once the ship's faster orbit somehow causes it to run out of fuel, or something like that. I seem to remember the ship's &quot;computer&quot; following the captain around on robotic legs. I read the story circa 1980, but it might have been published much earlier. Ubuntu 12.04 software upgrade does not show 12.10 upgrade What is the difference between ref and out parameters in .NET? What are the situations where one can be more useful than the other? What would be a code snippet where one can be used and another can't? US and Canada border crossing and computer privacy: What do I need to know? I've read stories about border officials searching laptops when crossing the border in one direction or the other. Does this really happen, typically speaking?  As a US citizen, can I be forced to give them my laptop's password for any/no reason? I don't believe they are allowed to deny entry to the US to a US citizen? ....but who knows these days?  Canada can deny me entry for any reason, so that's fine. But in practice, does this even happen in either crossing direction?  EDIT - I've now made the trip. They didn't so much as glance in the direction of my laptop. My biggest issue turned out to be lack of international wireless data service! Prove that $f$ continuous and $\int_a^\infty |f(x)|\;dx$ finite imply $\lim\limits_{ x \to \infty } f(x)=0$ Benevolent aliens who (initially) refuse to show themselves This is a sci-fi book where aliens arrive on Earth and push Earth towards world peace, but refuse to reveal themselves physically. When the aliens finally do show themselves, we find that they       look like .   I recall that the aliens seemed benevolent, but that humanity did not like the direction they were being told to go. I cannot remember the ending or if the aliens turned out to be truly benevolent. The topic which haunted me for two years until I gave up on it. But now I am doing engineering and this topic suddenly popped out of my textbook from nowhere. I seriously need to understand this topic because I wasn't able to do so in the past. I have read many book on 'energy' and it came to nothing. Maybe just because the many books I have read all said 'energy' is something which doesn't 'exist'! It is 'abstract'! It is just a number which represents the state or orientation of a system. But then I see so many examples that 'uses' energy to do 'work'. But the question here is that if anything doesn't exist in this universe, then how can the same thing be used to do something that exist?  My problem is that I didn't understood the topic 'energy' and all the other topics related to it (work, power etc.) Why isn't the symmetric twin paradox a paradox? Two twin sisters synchronize their watches and simultaneously (from the earth frame) depart earth in different directions. Following a predetermined flight plan, each sister accelerates identically to 99.9%c and then returns home at the same time (again in the earth frame). The observers on earth see each twin as having aged identically, as the symmetry of the problem dictates. Each twin however should see the other as having aged... What gives? How to Implement Page Object and Page Factory Pattern in Selenium Webdriver?