Sum of two vectors in spherical coordinates.
How to sum 2 vectors in spherical coordinate system
The particle number on my settings appear in gray, I don't think i'm able to change the number even thought i need it, how can i make it white again? How to deal with variable income in the budget We have a budget planned out for various categories, and in order to make ends meet we count on child support for my wife's child from a previous marriage.  However, lately we have not been receiving this amount.  How do we deal with this in the budget?    My wife has just been "borrowing" it from our savings, but I don't think that is reasonable given that I find it highly unlikely we will ever be able to recover it.  On the other hand, she doesn't think it reasonable to cut out of her budget and cutting it out of the budget for the kids (which is where it really should be going!) isn't reasonable either. Is there a convenient way to place a figure* at the end of the current page instead of taking up the entire next page in the twocolumn environment? Placement modifiers [Hb] do not work. Can you deliver it [when,after] it [is | will be] assembled? Why and how can you hear explosions in space in Star Wars? Considering that sound can't travel through vacuum. Help center still has the guidance about old Favorite tags Is there a difference between the original file and a hard link to it? I'd like to synchronise some configuration files via a file hoster like Dropbox. I could create a hard link in the software's configuration folder and let it point to my cloud storage directory.  When having done that, is there a difference between those two files? I read somewhere that both files are attributes of the file in the master file table and that there would be no difference at all.  On the other hand, on Windows, directory junctions via mklink can be found using dir /AL /S, so they somehow differ from real directories.  Is that correct? Given two input layers  The clip layer - an arbitrary layer (though in my case it's a float 1 band geotiff) The mask layer - a paletted raster in which every pixel is either NO DATA or a single &quot;color&quot; value, same for every pixel.  I want to create an output raster whose overall extent matches the extent of the mask layer and each pixel is either NO DATA if the corresponding pixel of the mask layer is NO DATA or the value of the corresponding pixel from the clip layer if the corresponding pixel of the mask layer is not NO DATA. I know I can mask the clip layer with a polygon, but the mask layer is a raster. Polygonizing the raster layer is possible in principle, but would result in a polygon with a lot of very short edges. Is there a direct way to do this in QGIS? I suppose there's probably a path that involves creating a new layer and using the raster calculator, but I'm hoping there's something more direct. Further complicating the matter is that the two rasters might not have the same resolution and origin. I believe this is equivalent to  in ArcMap. How to find the center of an ellipse? How to partition for Windows/Ubuntu dual boot on same SSD I have a 500GB SSD in which i would like to have both Windows and Ubuntu. My plan is to have something similar to this: Windows 8.1 and ubuntu 14.04 Uefi boot   an efi partition (created by windows installer) which will have Grub as bootloader 150GB ntfs for Windows 15GB ext4 for Ubuntu (root) 35GB ext4 for Ubuntu (home) ~8-16GB swap for Ubuntu (I have 16GB RAM) ~284-292GB ntfs for Data shared for both Windows and Ubuntu   My current setup is   200GB ntfs Windows 300GB ntfs for Data   I plan to shrink both the Windows and the data partiton in order to achieve my desired plan.  My questions:   Does the order of partitions matter? Does it matter if the ubuntu partitions are not at the end/beggining of the drive? Does the swap partition behaves better if its the last/first partition? Can I use the shared NTFS Data partition between windows and ubuntu without encountering problems? Do I have enough space for my ubuntu /home partition (thinking that I'll have access to the ntfs shared partition)?   Edit: Laptop, Asus N56jr, i7, 16Gb Ram, SSD samsung 850 evo 500gb  Windows 8.1 and Ubuntu 14.04 I have a few questions regarding Named Credentials. I need to perform a SOAP based call out to an external system from Sales Force. I used the wsdl2apex function to generate the class for the call out. When I started integrating this class into my process I got to thinking about securely storing the username and password for the call out, which led me to discover Named Credentials. Question is, can Named Credentials be used in the auto-generated apex class? If so, could you please provide an example?  Thanks in advance Electron flow and electric potential In the physics tutorial topic on current electricity it defines the positive terminal as the high potential terminal and the negative as the low potential. When talking about positive test charges this analogy makes sense, the charge moves from the +ve to the -ve where it loses potential till it has to be "topped" up by the cell.   What confuses me when they begin talking electrons. Using this analogy would mean that the electrons move from the -ve to the +ve but this means it would work against the electric field so the potential energy increases till it reaches the +ve terminal.   My question is how does this analogy, if it does, change to accommodate electrons? Does the electric field reverse so the -ve terminal is the high potential and the +ve the low potential? Quantifiers "most" vs. "most of" List or IList Can anyone explain to me why I would want to use IList over List in C#?  Related question: /testfor for item enchantment What I have now is:  /testfor @a {SelectedItemSlot:0,Inventory:[{Slot:0b,id:"diamond_pickaxe"}]}   How can I use the /testfor command to test a specific slot for a specific item that is enchanted? I'm trying to find a story for my father, from the 70s or earlier  Earth is at war with aliens (possibly Martians) and was unable to effectively fight back as the aliens had planetary (or at least city-protecting) force fields through which no bombardment was possible.  Earth eventually wins through invention of a device that allows them to teleport weapons (nukes?) under the force fields.  originally believed to be one of Harry Harrison's 'One step from earth' shorts, but this is not the case.  Thanks in advance for any help here! Print programs with its proper syntax Suppose that $f(z)$ is analytic function in the disk $|z|\le R$ and $A(r)=\max_{|z|=r}Re(z)$ then prove that $r&lt;R$  $$\max_{|z|=r}\left|\frac{f^n(z)}{n!}\right|\le \frac{2^{n+2}R}{(R-r)^{n+1}}\{A(r)+|f(0)|\}$$  MY attempt   Using Cauchy generalized integral formula   $f^{(n)}(z_0)=\frac{n!}{2\pi i}\int _c\frac{f(z)dz}{(z-z_0)^{n+1}}$  then $\max_{|z|=r}\left|\frac{f^n(z)}{n!}\right|=\left|\max_{|z|=r} \frac{1}{2\pi i}\int _c\frac{f(z)dz}{(z-z_0)^{n+1}}\right|$  and i think we can solve by using Borel caratheodory theorem  Let $f(z)$ be holomorphic function on $|z|\le R$ and let $M(r)=\max_{|z|=r}|f(z)|$ and $A(r)=\max_{|z|=r}Re f(z)$ then  for $0&lt;r&lt;R$  $$ M(r)\le \frac{2r}{R-r}A(R)+\frac{R+r}{R-r}|f(0)|$$  from here how to processed ? How do I drag and drop files into an application? Convergence of the arithmetic mean Let $(a_n)_{n \in \mathbb{N}}$ be a convergent sequence with limit $a \in \mathbb{R}$. Show that the arithmetic mean given by: $$s_n:= \frac{1}{n}\sum_{i=1}^n a_i \tag{A.M.} $$ also converges to $a$.  I have read:  but unfortunately the answers there don't help me much because I don't understand their substitutions and most of it all, why their substitutions seem to work.   What I know from the problem is that since $a_n$ is convergent and $\epsilon &gt;0$ is given, I can say that:   $$\exists N_1 \in \mathbb{N}, \forall n \geq N_1: |a_n-a|&lt;\epsilon_1 $$ I also know that since $a_n$ is convergent, it is bound, so $(a_n) &lt; M, \ \forall n \in \mathbb{N}$   I need to show that: $$\exists N_2 \in \mathbb{N}, \forall n \geq N_2: |s_n-a|&lt; \epsilon_2$$ I started as follows: $$ \left|s_n-a \right| = \left|\frac{1}{n}\sum_{i=1}^na_i -a\right|= \left|\frac{1}{n}\sum_{i=1}^m(a_i-a)+\frac{1}{n}\sum_{i=m+1}^n(a_i-a) \right| \\ \leq \frac{1}{n} \sum_{i=1}^m|(a_i-a)|+\frac{1}{n}\sum_{i=m+1}^n|a_i-a|$$ I believe to understand that the left sum after the $\leq$ is finite, bound and doesn't depend on the values that $n$ takes on. However, I don't understand where all the substitutions come from and make this proof so seemingly easy to complete.   Is there a general idea I can follow to complete such proofs? Because I know that the last step is to show that the given sum is smaller than $\epsilon$. I also know that I should bring the condition $a_n &lt; M$ into place somewhere, but I don't know where.  If I choose an $n \geq N: |a_n-a|&lt; \epsilon'$ what does that tell me about $|a_i-a|$? I know that they are seemingly the same just with a different index.