Infinite Product Identity for Hyperbolic Sine
Infinite Product $\prod\limits_{k=1}^\infty\left({1-\frac{x^2}{k^2\pi^2}}\right)$
What "time travel" story required the traveller to mentally reconstruct his world in order to return to it? Here's what I remember about it:   The protagonist is sent a relatively short distance into the future (maybe a year? I've forgotten). When he arrives in this "future" he finds himself in a completely different world, with non-human inhabitants. The inhabitants use a machine to teach him their torturous language. He tries to return home, and (eventually) finds himself in a realm of chaos/nothingness. He laboriously reconstructs in his mind everything he can remember about his home and finds himself back there somehow. The twist is      that in his "home" reality everyone speaks the language he was taught by the non-human inhabitants at his first stop. Should I file Form 1040 or Form 1040 NR? I am currently on H1 B (since October 1, 2017). Last year when on F1 OPT, I had filed Form 1040 NR for my taxes. Which form is advisable for 2017, considering I am on H1 B now. What options do I have? MySQL Great Circle Distance (Haversine formula) I've got a working PHP script that gets Longitude and Latitude values and then inputs them into a MySQL query. I'd like to make it solely MySQL. Here's my current PHP Code:  if ($distance != "Any" &amp;&amp; $customer_zip != "") { //get the great circle distance      //get the origin zip code info     $zip_sql = "SELECT * FROM zip_code WHERE zip_code = '$customer_zip'";     $result = mysql_query($zip_sql);     $row = mysql_fetch_array($result);     $origin_lat = $row['lat'];     $origin_lon = $row['lon'];      //get the range     $lat_range = $distance/69.172;     $lon_range = abs($distance/(cos($details[0]) * 69.172));     $min_lat = number_format($origin_lat - $lat_range, "4", ".", "");     $max_lat = number_format($origin_lat + $lat_range, "4", ".", "");     $min_lon = number_format($origin_lon - $lon_range, "4", ".", "");     $max_lon = number_format($origin_lon + $lon_range, "4", ".", "");     $sql .= "lat BETWEEN '$min_lat' AND '$max_lat' AND lon BETWEEN '$min_lon' AND '$max_lon' AND ";     }   Does anyone know how to make this entirely MySQL? I've browsed the Internet a bit but most of the literature on it is pretty confusing. Is it correct to say e.g. "I like your way of wearing" or "the way you wear looks perfect"?  Is it politely? Is it in use or not? May I use "the way you wear" referring to whole wearings including dress, scarf, hat, bracelet. jewellery, etc?  Thank you for your suggestions in advance. How does "virus been detected" on android pop up on chrome when visiting some sites? What is the cause of this chrome bug on android? The last site I went to was www.destructoid.com and all of a sudden it gets redirected to the following url. This happened previously awhile back, but I didn't document everything as I did today. I'm also on android chrome canary if that matters.   I took some screenshots before closing out of that tab. But my question is:   What chrome bug or malware is causing these random redirects? How can one detect if they have this vulnerability?   The url is: Does a photon in vacuum have a rest frame? Quite a few of the questions given on this site mention a photon in vacuum having a rest frame such as it having a zero mass in its rest frame. I find this contradictory since photons must travel at the speed of light in all frames according to special relativity.  Does a photon in vacuum have a rest frame? Homework - set theory infinite union A question from my homework I'm having trouble understanding. We are given:  $A(1) = \{\varnothing\}$, $A(n+1) = A(n)\cup (A(n)\times A(n))$  $A=A(1)\cup A(2)\cup A(3)\cup \cdots \cup A(n)\cup A(n+1) \cup \cdots$ to infinity  The questions are:  1) show that $A\times A \subseteq A$  2) Is $A \times A = A$?  Thank you for your help.  I've tried writing $A(2)$ but it gets really complicated and I'm having trouble understanding what the sets are. Let alone solve the question. Why is it true that "I before E, except after C"? bcmwl-kernel-source broken on kernel: 5.8.0-34-generic What make is my BMX frame? I have a BMX forsale, but I would like to know what make the frame is so I can determine how much it is worth. Does anyone recognise this symbol on the frame?  Thanks for your help Jon Bachelor thesis or Bachelor's thesis Old movie about aliens and a family; father briefly abducted About 15 or so years ago, I dimly recall watching a movie on TV about aliens, which really struck a chord, but I can't remember enough to google a name or anything more specific. The action takes place on Earth, perhaps in the USA. It was a live action movie, not animated.    It was about a family; the father (grandfather?) was an army pilot, and when he was flying, he was abducted by aliens (briefly, then returned, I think?). The (grand?)daughter is a little child, and her nanny is trying to teach her telekinetic abilities (perhaps a result of modifications done to the father?). I think I remember her also conjuring up a glowing orb between her hands. The nanny turned out to work for the aliens. There was also something about the government trying to chase/capture the family.   Any help will be appreciated! Will upgrading Windows 8 to 8.1 affect Ubuntu? It's a rather simple question (I hope). I currently have Windows 8 and I am dual booting it with Ubuntu 13.04.   If I were to install the latest update for Windows 8, that being 8.1, will it affect Ubuntu or will there be any conflicts between the two? Which singular names ending in “s” form possessives with only a bare apostrophe? I’ve run into a limitation in the cURL bindings for PHP. It appears there is no easy way to send the same multiple values for the same key for postfields. Most of the workarounds I have come across for this have involved creating the URL encoded post fields by hand tag=foo&amp;tag=bar&amp;tag=baz) instead of using the associative array version of CURLOPT_POSTFIELDS.  It seems like a pretty common thing to need to support so I feel like I must have missed something. Is this really the only way to handle multiple values for the same key?  While this workaround might be considered workable (if not really annoying), my main problem is that I need to be able to do multiple values for the same key and also support file upload. As far as I can tell, file upload more or less requires to use the associate arravy version of CURLOPT_POSTFIELDS. So I feel like I am stuck.  I have  about this problem in more detail on the cURL PHP mailing list in the hopes that someone there has some ideas about this.  Suggestions or hints on where I can look for more information on this are greatly appreciated! If rest mass does not change with $v$ then why is infinite energy required to accelerate an object to the speed of light? I know that as the velocity increases, the mass of the object also increases so it becomes tougher and tougher to move the object which ultimately leads to a requirement of infinite energy to accelerate an object to the speed of light. But I have a doubt.  As far as I know only the observable mass (Relativistic mass) increases but not the Proper Mass or Intrinsic Mass, right? The actual mass of the object will remain the same. So if the actual mass ($m_0)$ remains the same and only the observable mass increases, why is more and more energy required? I know that even if the object exceeds the speed of light, we will not be able to say that it is moving faster than the speed of light but is it possible to make it move faster than light?  If rest mass does not change with $v$ then why is infinite energy required to accelerate an object to the speed of light?  I quote Igor Ivanov (a stackexchange user from this question ) to give an insight into my question.     The mass (the true mass which physicists actually deal with when they calculate something concerning relativistic particles) does not change with velocity. The mass (the true mass!) is an intrinsic property of a body, and it does not depends on the observer's frame of reference. I strongly suggest to  popular article by Lev Okun, where he calls the concept of relativistic mass a "pedagogical virus".   EDIT  After reading the answers I have a doubt.  SO can I say that only the overall energy of the system increases while the mass remains constant? But then if mass remains constant, then why is more and more energy gradually required? I mean there should be a reason for that requirement of infinite energy. Inverse of sum of exponential random variables (mean and variance) Assume $X_1,X_2, \dots , X_n$ following the exponential distribution with mean $\theta &gt; 0 $ and the statistic: $$ T = \sum\limits_{i = 1}^n X_i $$  I know that the sum of exponential random variables follows the Gamma distribution, but I cannot infer anything about the inverse of the sum $\frac{1}{T}$. My guess would be that: $$ E\left[\frac{1}{T}\right] = \frac{1}{\theta} \quad \text{and} \quad V\left[ \frac{1}{T} \right] = \frac{1}{\theta^2} $$ but why? How does the Deposit-User work? Would a backpack or cargo rack be better for commuting? Right now I use a backpack to hold all of my supplies including spare tubes, pump, patch kits, tools, my change of clothes for work, etc.  This is the backpack I use:    It's about as comfortable as a backpack can get without getting into the hiking backpacks with frames. Altogether I would say it weighs no more than 10 lbs max. The muscles in my back get slightly irritated during my commute.  Would it be more comfortable to use a rear cargo rack on my bike instead? Will adding more weight to the bike change how the bike rides and feels?  EDIT: After doing some research I came across  that explains the different methods of carrying your gear on commutes and how it affects your body. It's worth a look.  EDIT #2: Having tried both for a couple of weeks now, I can say that (for me personally) the backpack is the better way to go given the relatively light weight I have to carry.  If you do use a backpack, make sure that the straps are tightened enough so that it's positioned higher up on your back and to the point to where there is little to no movement on your back. This makes a world of difference when it comes to comfort. Can't delete the filter called My Filter I'm unable to get rid of a filter that goes by the name of "My Filter".  This is the default name you get when you click on New Filter.  There's a clickable "Delete this filter", which leads to a confirmation question on whether you really want to delete it.  Clicking "Yes" leads you back to the "New Filter" Screen,  with a new filter named "My Filter".    I don't know whether this is the same filter I was just trying to get rid of,  or whether it got rid of the old one, and now is making a new one with the same old name.  Either way, I'm stuck.