Working With Reducer class in hadoop
How do I compare strings in Java?
Basically the &quot;updates page&quot; loads in a non rich html format, and if theres an update it's missing the tabs on the update page as well.  I can't figure out if this is just because apple may have stopped supporting El Capitan or if I have something else going on.  Any help would be appreciated.  I've trashed the caches in library and the user profile. But this page is the only one that still loads like this (see pic below) on my app store. When I'm going through a whole bunch of shots to determine which to delete and which to flag, it's fastest for me to just keep both hands on the keyboard.  However, if I want to zoom in to 100% on a picture and then pan to a specific area, it seems I can only get halfway there -- 'Z' to zoom, but then I'm stuck having to pick up the mouse to pan around.  I was excited to find page-up/page-down/home/end can be used, but they seem to exist to provide an exhaustive, linear scrolling of the image, panning top-to-bottom then left-to-right, without unconstrained 2d movement.  Is there some way to toggle the arrow keys so they can pan instead of navigate to the next/prev photo?  Something else?  Or am I out of luck? Is the empty set a group? I know that a set G with a binary operation $*$ is a group, if:   $a*b\in G$, for all $a, b \in G$. $*$ is associative:   $$(a*b)*c=a*(b*c) \\ \text{for all }a, b, c\in G.$$   An identity element $e \in G$ exists, such that   $$a*e = e*a = a\\ \text{for all }a\in G.$$   For all elements $a \in G$, there exists an $a^{-1} \in G$, such that:   $$a*a^{-1} = a^{-1}*a=e.$$  Can I use that to show that the empty set is a group? 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. Prove that $ m_{a} \geq m_{g} \geq m_{h} $ using strict inequalities unless $ a = b $. $ m_{a} = \frac{1}{2} (a + b) $   $ m_{g} =  \sqrt{ab} $   $ \frac{1}{m_{h}} = \frac{1}{2}(\frac{1}{a} + \frac{1}{b})$   Attempted Solution:  I believe I have shown the first step, which is $ m_{a} \geq m_{g} $ but i'm stuck on showing $ m_{g} \geq m_{h} $  $ \frac{a + b}{2} &gt; \sqrt{ab} $  $ (\frac{a + b}{2})^2 &gt; (\sqrt{ab})^2 $  $\frac{a^2 + 2ab + b^2}{4} &gt; ab$  $a^2 + 2ab + b^2 &gt; 4ab $  $a^2 -2ab + b^2 &gt; 0 $  $(a - b)^2 &gt; 0 $   so if $a = b$ we have $(a -b)^2 \geq 0$  Therefore, $m_{a} \geq m_{g} $  Now, i'm not sure if that is correct or not, if not can you please guide me to the complete solution or if I am correct on this part, provide a solution for $m_{g} \geq m_{h} $ How to remove \n from a list element? In The Matrix Reloaded, the Architect reveals to Neo that Trinity is about to die. I can't help but wonder if Neo would still choose the left door if the Architect had withheld that information.  The Architect could have designed a better choice mechanism so as to trick Neo into making a choice in the machine's favor rather than a highly risky one.   Did I miss anything important in the movie? Gauss's Lemma for polynomials claims that a non-constant polynomial in $\mathbb{Z}[X]$ is irreducible in $\mathbb{Z}[X]$ if and only if it is both irreducible in $\mathbb{Q}[X]$ and primitive in $\mathbb{Z}[X]$.   I wonder if this holds for multivariable case.      Is it true that a non-constant polynomial in $\mathbb{Z}[X_1,\dots,X_n]$ is irreducible in $\mathbb{Z}[X_1,\dots,X_n]$ if and only if it is both irreducible in $\mathbb{Q}[X_1,\dots,X_n]$ and primitive in $\mathbb{Z}[X_1,\dots,X_n]$?    Thank you for your help. What's the meaning of the transpose? Would approaching a distant star at near the speed of light unfold its entire history in "fast-forward"? Which are the safety recommendations for soldering? In the previous version the logout button is under your username, which it can be found by clicking the down arrow. However, in the new version, after a couple minutes of searching, it is under the "site-switcher" button:        This is really illogical since the logout button is usually under your username, including Google and Yahoo! services.  I suggest bringing back the  which will definitely benefit new users and even old users. I am currently studying  answer on the Moore-Penrose pseudoinverse and the Euclidean norm by the user &quot;Etienne dM&quot;. The first point of their answer proceeds as follows:  Let $x$ be $A^+y$.  Let me begin by the second point. For all $z$, we have: \begin{align} \lVert Az-b \rVert_2^2 &amp;= \lVert Ax-b \rVert_2^2 + \lVert A(z-x) \rVert_2^2 + 2 (z-x)^TA^T(Ax-b)\\ &amp; \geq  \lVert Ax-b \rVert_2^2 + 2 (z-x)^TA^T(Ax-b) \end{align} Moreover, because $(AA^+)^T = AA^+$, $$ A^T(Ax-b) = ((AA^+)A)^Tb - A^Tb = 0$$ Thus, we prove that for all $z$, $\rVert Az-b \lVert_2^2 \geq\rVert Ax-b \lVert_2^2$, that is to say $A^+b$ is as close as possible to $y$ in term of the Euclidian norm $\lVert Ax-b\rVert_2$.   I realise that $x = A^+ y$, but I don't understand how any of this implies that &quot;$A^+ b$ is as close as possible to $y$ in terms of the Euclidean norm $\lVert Ax-b\rVert_2$&quot;. I would greatly appreciate it if people would please take the time to explain this to me. Hair particles render not same as 3dView(Eevee) Hair particle renders are not same as in 3dView(Eevee). Hair is using Principle Bsdf shader and  camera is set to Orthographic. Force and turbulence fields are applied to it. How to resolve this? How can a file be copied? Google Sheets Customize View Using Create Custom Menu and Hiding/Showing Specifc Columns Trying to determine a way that I can use a custom menu (.createMenu) with views that will allow me to show / hide specific columns.  I need the capability to pick specific multiple columns and not ranges.  In the example below how can you pick a custom view from the menu (say "Customer Info") that will only show columns A, B, C, and H?  Maybe another view could show "Financial". How do I get the SQLSRV extension to work with PHP, since MSSQL is deprecated? How to change css property using javascript Primes dividing $11, 111, 1111, ...$ Adding coordinate system to layout in QGIS composer? I would like to know if there is a way to add a dynamic coordinate system field into a QGIS composer layout.  I can use an expression to add many items such as document name, file path, etc but I can;t seem to figure out how to add the coordinate system?