Tab or Session Manager for Safari 12?
Safari Extension to Manage Tabs?
line segment joining two centers of circles is perpendicular to line segment joining two intersection point of the circles If $p\equiv1\mod{4}$, then $p=a^{2}+b^{2}$ where a and b are uniquely determined From Ireland,Rosen's Number Theory book, ex.8.12.  Let $p\equiv1\mod{4}$, then we can write $p=a^{2}+b^{2}$, where $a,b\in\mathbb{Z}$. Now, let $a$ be odd and $b$ be even and $a,b&gt;0$. How can we show that $a$ and $b$ are uniquely determined? The hint says to use the fact that $\mathbb{Z[i]}$ is a UFD and $p=a^{2}+b^{2}\implies a+bi$ is prime in $\mathbb{Z[i]}$ Our team is developing a new system and it has a Warehouse table that must have a hierarchical relationship between entries since a customer can have 1st, 2nd, 3rd and Nth degree warehouses.  We first thought that  was the best way to do it. By creating a Parent and a Child column on the table and then making Parent the FK to Child (on the same table) but friend DBA told us that there is a different way.  So, for instance, we had thought about making a table like this:  CREATE TABLE Warehouse( filterId INT PRIMARY KEY IDENTITY, parentId INT NOT NULL, active BOOL DEFAULT 1, warehouseName VARCHAR(30) NOT NULL, FOREIGN KEY parentId REFERENCES Warehouse(filterId)  | FILTERID   | PARENTID | ACTIVE | WAREHOUSENAME | -------------------------------------------------- |          1 |        0 |      1 | N WAREHOUSE 1 | |          2 |        1 |      1 | ROOM 1        | |          3 |        1 |      1 | ROOM 2        | |          4 |        1 |      1 | ROOM 3        | |          5 |        1 |      1 | ROOM 4        | |          6 |        2 |      1 | SHELF 1       | |          7 |        2 |      1 | SHELF 2       | |          8 |        2 |      1 | SHELF 3       | |          9 |        2 |      1 | SHELF 4       | |         10 |        2 |      1 | SHELF 5       | |         11 |        2 |      1 | SHELF 6       | |         12 |        2 |      0 | SHELF 7       | |         13 |        3 |      1 | BOX 1         | |         14 |        3 |      0 | BOX 2         | |         15 |        3 |      1 | BOX 3         | |         16 |        3 |      1 | BOX 4         | --------------------------------------------------   But this DBA said that we should work on something like this:  CREATE TABLE Warehouse( filterId VARCHAR(20) PRIMARY KEY, active BOOLEAN DEFAULT 1, warehouseName VARCHAR(30) NOT NULL)   | FILTERID   | ACTIVE | WAREHOUSENAME | --------------------------------------- | 1.00       |      1 | N WAREHOUSE 1 | | 1.01       |      1 | ROOM 1        | | 1.02       |      1 | ROOM 2        | | 1.03       |      1 | ROOM 3        | | 1.04       |      1 | ROOM 4        | | 1.01.01    |      1 | SHELF 1       | | 1.01.02    |      1 | SHELF 2       | | 1.01.03    |      1 | SHELF 3       | | 1.01.04    |      1 | SHELF 4       | | 1.01.05    |      1 | SHELF 5       | | 1.01.06    |      1 | SHELF 6       | | 1.01.07    |      0 | SHELF 7       | | 1.01.01.01 |      1 | BOX 1         | | 1.01.01.02 |      0 | BOX 2         | | 1.01.01.03 |      1 | BOX 3         | | 1.01.01.04 |      1 | BOX 4         | ---------------------------------------   Which way should we follow?   On one hand we have a relationship between parentId and filterId; on the other we do not have any relationship, but it is easy to understand where does the entry belong.  Not all the warehouses are of the same level - that's what I mean by degree. They should be ordered like: For Customer A, 1 is parent of 1.1 and 1.2, 2 is parent of 2.1, 3 is parent of 3.1 and 4 is parent of 4.1 and 4.2 - but 1, 2, 3 and 4 are of the same level (1st level), and 1.1, 1.2, 2.1, 3.1, 4.1 and 4.2 are also of the same level (2nd level) but not of the same parents. Quite simply (and similarly to my other questions about previous versions of this feat  and ) I want to know if this feat is balanced and if not then what should be done to improve it? Since the last iteration I have changed the wording as per David Coffron's answer, increased the time and monetary cost as well as added in the action requirement to activate the rune as per Ruse's answer and increased the costs as per linksassin's answer     Rune Caster      Prerequisites: ability to cast at least one spell of 1st level or higher      When you take this feat you can imbue your spells of 1st level or higher into a rune by casting the spell as a rune, this means that you must have the object you want to put the rune on within reach for the entire duration of the casting as well as any tools required to make the rune.      When casting a rune you add the time listed in the cost time table to the casting time and the cost listed in the cost time table to the components of the spell in accordance with the stored spell.      \begin{array}{|l|l|l|} \hline \text{Spell level} &amp; \text{Time (hrs)} &amp; \text{Cost (GP)}\\ \hline 1 &amp; 1 &amp; 50 \\ \hline 2 &amp; 2 &amp; 100\\ \hline 3 &amp; 4 &amp; 500\\ \hline 4 &amp; 6 &amp; 1,000\\ \hline 5 &amp; 8 &amp; 5,000\\ \hline 6 &amp; 12 &amp; 10,000\\ \hline 7 &amp; 16 &amp; 50,000\\ \hline 8 &amp; 18 &amp; 100,000\\ \hline 9 &amp; 24 &amp; 500,000\\ \hline \end{array}      When making a rune you choose a trigger which is touch and/or command word and can be specified to only a group of people/creatures or a body part. When defining creatures that can activate the rune you may be as specific or general as you want. The DM interprets the designated creatures as your character would have interpreted them when you made the rune.      When you store a spell in a rune some of the ranges are altered, a range of touch becomes a range of self, a range and target keeps the same range and the person who activates the rune designates the target and range with an aoe sets the origin to the center of the rune, lastly a range of self stays the same.      When a rune is activated the spell is released acting as if it had just been cast without requiring any components or concentration. The rune then disappears leaving no trace of its presence. To activate a rune you must complete the trigger, this means speaking any command words and physically touching the rune each if applicable, this requires the activator to use the object interaction action while within reach for touch runes and while within 60 ft for command words. If both triggers are used then they must both be fulfilled within the same turn. I'm trying to write an automated test of an application that basically translates a custom message format into an XML message and sends it out the other end.  I've got a good set of input/output message pairs so all I need to do is send the input messages in and listen for the XML message to come out the other end.  When it comes time to compare the actual output to the expected output I'm running into some problems.  My first thought was just to do string comparisons on the expected and actual messages.  This doens't work very well because the example data we have isn't always formatted consistently and there are often times different aliases used for the XML namespace (and sometimes namespaces aren't used at all.)  I know I can parse both strings and then walk through each element and compare them myself and this wouldn't be too difficult to do, but I get the feeling there's a better way or a library I could leverage.   So, boiled down, the question is:  Given two Java Strings which both contain valid XML how would you go about determining if they are semantically equivalent?  Bonus points if you have a way to determine what the differences are. Can Eigenvalues[] and Eigenvectors[] be assumed to return the same ordering? Can we define tension in a string as the reactive force produced in a string being pulled at both ends? In my textbook, the definition of tension was given that  is the reactive force which exists when string is being stretched at its both end. After it there was a case given that to calculate acceleration and tension produced in string while it's attached with different masses at both its ends and passed over a frictionless pulley. First body is being hung and second is placed over horizontal frictionless surface with relatively smaller mass. It is given in my book that there are three forces acting on the body placed on horizontal smooth surface viz., Weight of body, the reaction force to weight and tension in string pulling body towards pulley's wheel. How can there be tension in string according to the definition given my book however there is no acting force (pulling force) on the body that pulls it away from wheel.  There are different definitions for tension. The one in our book is creating problem however second one, that is, " tension describes the pulling force exerted by each end of a string, cable, chain, or similar one-dimensional continuous object " is al right.  Since acceleration is lowered due to Tension then acceleration produced in the body must be given by, $a=\frac{Net-Force}{m}$ $=&gt;$ $a=\frac{m_1g-T}{m_1}$ since $W_1$ $&gt;$ $T$.  If tension in string is the reactive force to the weights pulling the string apart then according to Sir Isaac Newton, $W_1=W_2=T$. In Rey's vision, whose voice says "These are your first steps"? Can I connect to a sandbox using JWT Flow and Prod connect app? I'm trying to connect to a sandbox using the sfdx cli and the JWT flow through force:auth:jwt:grant. According to , we can use the same connected app information from Production to connect to our Scratch Org.  Is it something that should work for sandbox too ? I'm getting a "Failed: Not approved" error.  Connected app in sandbox comes from the refresh but has a different consumer key. The Permission set is set correctly on my user.  Is there a way to connect to a recently refreshed sandbox using the JWT flow (without manually changing something like the consumer key) ? Monotonicity in argmin function I have the following equation $$f(a)=\text{argmin}_{t\in\mathbb{R}} \sum_{i=1}^n\frac{1}{2}(1-a)(b_i-t)^2+a| b_i-t |, a\in[0,1]$$  How does one prove that the function is monotone in a? a command to list all packagas installed on the system and their installed files, how? Implementing i18n string translation in a custom module? I have a custom module I've built which essentially acts as a repository of custom CTools keywords that users can arbitrarily define. The issue I'm facing is I need to be able to translate these user-defined strings, so I think I need to implement string translation using the i18n_string module.  I have never worked with translation or localization before, so I'm a bit lost with regards to going about how to implement this. I think I'm on the right path with i18n_string though. Can someone experienced with i18n provide examples that I can look at so I can learn the proper way to implement this? Windows 10 doesn't shut down properly Building where clause based upon parameters $f(z)=\frac1{2\pi i}\int_{\Gamma}\frac{f(\zeta)}{z-\zeta}d\zeta$ if $\lim_{z\to\infty}f(z)=0$ and $f$ is analytic in $|z|\ge1$ Let $f$ be analytic in $|z|\ge1$ and  $\lim_{z\to\infty}f(z)=0$. Then is $f(z)=\frac1{2\pi i}\int_{\Gamma}\frac{f(\zeta)}{z-\zeta}d\zeta$,$\forall |z|\ge2$, where $\Gamma$ is the circle of radius $2$ with centre at the origin.   I think yes, by the Cauchy integral formula. But, how do we ensure that the non analyticity of $f$ in $|z|&lt;1$ dosent affect the formula? Thanks beforehand. "In the Internet" vs. "on the Internet" When should I use "in the Internet" and when "on the Internet"? I was wondering if anybody knew a command that would allow me to open a Nautilus (if that's the right name for the Ubuntu graphic/window explorer) window from the command line at the current directory that the user is at.  So, if I open a command line, and type:  cd /home/myUser/some/long/path/to/a/directory   Then, I'd like to be able to issue some command:  nautilus open-sesame   And have a graphic window opened to /home/myUser/some/long/path/to/a/directory. Is this even possible? I updated some entries in the  at C:\WINDOWS\System32\drivers\etc.  As a test, I decided to make Google point to 127.0.0.1.  # Additionally, comments (such as these) may be inserted on individual # lines or following the machine name denoted by a '#' symbol. # # For example: # #      102.54.94.97     rhino.acme.com          # source server #       38.25.63.10     x.acme.com              # x client host  127.0.0.1       localhost ::1             localhost 127.0.0.1       google.com   This works fine on Windows Vista, but not on Widows 7. When I type google.com into my browser, it goes directly to Google's website.  I am not using a proxy server, and I think there might be some temporary DNS settings that need to be flushed, but I'm not sure.  Does anyone know how to fix this? The volume "filesystem root" has only 0 bytes disk space remaining? What is the physical significance of the imaginary part when plane waves are represented as $e^{i(kx-\omega t)}$? I've read that plane wave equations can be represented in various forms, like sine or cosine curves, etc. What is the part of the imaginary unit $i$ when plane waves are represented in the form $$f(x) = Ae^{i (kx - \omega t)},$$ using complex exponentials?