Does this integral converge when $p<0$?
Convergence of $\int_0^\infty $sin$ (x^p) dx$
Clicking leave closed shows the reopen pop-up Are there philosophers who examined the reasons for believing in the existence of other people? While I am familiar with Descartes and the oft-quoted idea, I think therefore I am, I am not familiar with any philosophy that actively sought to rationalize that anybody else exists.  Are there philosophers who analyzed this question? Or is it taken for granted that it is (im)possible for anybody to validate their own existence to somebody else? UK Visitor Visa: Required Time or Interval Between Visits? I am a US citizen and have recently visted the UK  with simply a passport which allowed me to vist for 6months I have heard rumors that I am obligated to stay in the US for a Equal amount of time that I have visited the UK before I am able to return, but I am struggling tour no any proof of this obligation .. Am I missing somthing or is it simply not true I have a windows 7 user who belongs to admin group. I want to execute sc command that requires admin privileges. I DON'T want to open an elevated cmd, want to be able to simply Win+R->Enter command, enter password and that's all. I tried the runas command, but it doesn't seem to work:  &gt;runas /user:me "cmd"   and it asks for a password, and then the command is executed with normal privileges. I know I could use /user:administrator but I don't know the admin pass and I think the admin user (me) should work. In the Avengers movie, why is Hulk's behaviour inconsistent? In the Avengers movie, when      Bruce Banner is on the helicarrier, he becomes angry and transforms into the Hulk. Black Widow happens to be next to him and even though both are on same team, he attacks her and then Thor.  He becomes hostile to everyone on the ship.  But later on, in the fight against Chitauri troops, Hulk is very comfortably self-controlled.    Why is that?    The only thing I could think of is that it has been many days (a year?) since the Hulk had gotten angry, so he couldn't control himself.    But that's lame to be so puny when Bruce Banner was compared to Stephen Hawking in intelligence. I was reading the CernCourier, my favorite source of message on Higgs and friends. I was rather shocked, when I saw this:     "The mechanism by which neutrino mass is generated is not known."   What? Not known?  says: In Higgs-based theories, the property of 'mass' is a manifestation of potential energy transferred to particles when they interact ("couple") with the Higgs field, which had contained that mass in the form of energy.  Does this mean that neutrinos don't couple to the Higgs field? MacBook [Pro] - how many displays, what resolution/frequency? Which balancing issues, if any, would arise from allowing PCs to spend actions on bonus action features? I understand that RAW, features/spells/etc. that require a bonus action (e.g. Bardic Inspiration or Healing Word) cannot be used with a regular action instead (see ).  However, what would be the long-term ramifications and effects on game balance if I were to instead allow PCs to use a regular action for bonus-action features/spells/etc.?  For the sake of narrowing this down a bit; I'm only asking about ramifications when allowing player characters to do this, no need to take NPCs or Monsters into account. I don't use the variant rule of feats either, so no need to consider those as well. How can I set default value in ActiveRecord?  I see a post from Pratik that describes an ugly, complicated chunk of code:   class Item &lt; ActiveRecord::Base     def initialize_with_defaults(attrs = nil, &amp;block)     initialize_without_defaults(attrs) do       setter = lambda { |key, value| self.send("#{key.to_s}=", value) unless         !attrs.nil? &amp;&amp; attrs.keys.map(&amp;:to_s).include?(key.to_s) }       setter.call('scheduler_type', 'hotseat')       yield self if block_given?     end   end   alias_method_chain :initialize, :defaults end   I have seen the following examples googling around:    def initialize      super     self.status = ACTIVE unless self.status   end   and    def after_initialize      return unless new_record?     self.status = ACTIVE   end   I've also seen people put it in their migration, but I'd rather see it defined in the model code.  Is there a canonical way to set default value for fields in ActiveRecord model? How can I derive effect sizes in lme4 and describe the magnitude of fixed effects? How do I change my Chrome language back to English? Need to get logfile smaller This might be a stupid question, but nonetheless, it has been bothering me.  If you take a photon, make it go through some atoms in a solid, liquid or whatever, then you have the chance of this photon being absorbed by an electron, and thereby exciting the electron. This requires the photon to have enough energy to actually excite the electron to another energy level.  My question is then: How does the photon know if it has enough energy or not? Do they interact very quickly to determine if it's okay or not, or is it just something it "knows?" I need to build a probabilistic cellular automaton for simulating land-use changes and am wondering how to implement this in a GIS. I understand that Markov chains are a way of doing this, and IDRISI has some sort of module for Markov chains, but I have no access to IDRISI.  that, with raster data, this can, in theory, be done with any GIS that can do raster algebra. Presumably this means that it can even be done in ArcGIS, and I think I've figured out how to build cellular automata in ModelBuilder (once I know with certainty how to make iteration work there).  Still, I can find next to no practical advice on this. Once I have two datasets, one showing the land use at a certain point in time (time A) and the other at a later time (time B), I imagine doing the following (correct me if I'm wrong):   If there are (for example) 3 types of land use, then there are 9 possible things that can happen to a cell from time A to time B; thus, reclassify each dataset such that each land use is represented by a different number (for example, 9, 11, and 14 at time A and 3, 4, and 5 at time B); Divide one raster by the other, obtaining a raster with 9 possible cell values. Determine the percentage of cells in the new raster that has each of the 9 values (I forgot, how does one do this in ArcGIS?); those will be the probabilities of each type of change (or lack thereof) in land use.   What I cannot figure out, though, is how to apply these probabilities during the next iteration. Finally, I wonder if there is a way of making an external factor (say, proximity to roads) influence the spatial distribution (not the overall likelihood) of change in my model.  Can anyone recommend where to find information on how to do this in ArcGIS? I'm attempting to build an LED bed lamp that will be powered by 240V mains. The LEDs are  which if I use with a 12V supply and have calculated correctly will draw 0.24W each. I plan to use 5 or 6 of them in the lamp so will consume a maximum of 1.5W.  Initially I thought I'd use a transformer and bridge rectifier to get the required 12V DC but the transformer weighs a ton and is too bulky. The next option was to use a  but I'm wondering is there is a better way?  I think it would be possible to power the LEDs directly from mains using only a rectifier without mains and stepping down the voltage but then it's not safe. Are there any smallish components that can both isolate the mains and supply a DC voltage? How to change the camera from Landscape to Portrait I need a way to render a picture that is longer heighth-wise than width-wise. Changing the scale of the camera does nothing. I've been told to look in the scene focus settings, and I didn't see anything. Is there a way to change the shape of the rendered image? Passing HTML to template using Flask/Jinja2 How do I merge two dictionaries in a single expression (taking union of dictionaries)? I want to put the section title in the left margin using titlesec. However, it results to a superfluous empty line when using list environment. How should I remove it without using vspace?  Minimal example:  \documentclass{article}  \usepackage{geometry} \geometry{   a4paper,   top=2cm,   bottom=2cm,   left=4.5cm,   right=1.5cm, }  \usepackage{titlesec} \titleformat{\section}[leftmargin]{\large\scshape\sffamily}{}{0cm}{} \titlespacing{\section}{2.5cm}{2ex}{0.5cm}  \usepackage{enumitem}  \usepackage{mwe}  \begin{document}  \section{Section A}  This line is aligned with the section title.  \blindtext  \section{Section B}  \begin{itemize}[nosep]   \item This line is not aligned with the section title. \end{itemize}  \end{document} Exercise 12 from SEC. 82 of Finite-Dimensional Vector Spaces - 2nd Edition by Paul R. Halmos.  If $A$ and $B$ are linear transformations on a finite-dimensional inner product space, and if $\textbf{0} \le A \leq B$, then $\det A \leq \det B$.  Notation: $0 \le A$ means that $A$ is positive.  If $\det B = 0$, choose $x \in \ker B$, then $0 \le ((B-A)x,x) = (Bx, x) - (Ax, x) = -(Ax, x) \le 0$. Therefore $\ker B \subseteq \ker A$ and $0 = det A \le det B = 0$. How to prove for the case when $B$ is invertible? Intuitively, I feel that since both $A$ and $B$ are positive their proper values are also positive and $B$'s proper values should be greater the $A$'s and same for determinants.