Energy conservation in Hubble Expansion
Redshifting of Light and the expansion of the universe
E.g.: If your Gmail ID is abc.xyz@gmail.com, it considers this the same as abcxyz@gmail.com.  Why is this so? Rollback Committed transaction in SQL Server Is it possible to rollback a committed transaction?  I have deleted all the data in a table. The delete statement is inside Begin Transaction and I have committed the transaction with a commit transaction command. Now is it possible to rollback and get the data back? Significant figures vs. absolute error On , $N_A = 6.022\;141\;29 \times 10^{23} \text{ mol}^{-1}$ has 9 significant figures and a standard uncertainty of $0.000\;000\;27 \times 10^{23} \text{ mol}^{-1}$.  First, can it be written as the following?  $$ N_A = 6.022\;141\;29 \times 10^{23} \pm 0.000\;000\;27 \times 10^{23} \text{ mol}^{-1} $$ If yes, consider the following quote from  (emphasis added):     Whenever you make a measurement, the number of meaningful digits that you write down implies the error in the measurement. For example if you say that the length of an object is 0.428 m, you imply an uncertainty of about 0.001 m. To record this measurement as either 0.4 or 0.42819667 would imply that you only know it to 0.1 m in the first case or to 0.00000001 m in the second. You should only report as many significant figures as are consistent with the estimated error. The quantity 0.428 m is said to have three significant figures, that is, three digits that make sense in terms of the measurement. Notice that this has nothing to do with the "number of decimal places". The same measurement in centimeters would be 42.8 cm and still be a three significant figure number. The accepted convention is that only one uncertain digit is to be reported for a measurement. In the example if the estimated error is 0.02 m you would report a result of 0.43 ± 0.02 m, not 0.428 ± 0.02 m.   and the following quote from  (emphasis added):     The absolute error places bounds telling you that the actual value is expected to fall between x - D x and x + D x. The absolute error is an easy way to report the error and makes it easy to check that you are not reporting too many significant figures. For example, suppose you had a measurement that was reported to be 10.02 ± 0.3 m. Because the reported value is uncertain in the tenths place, it is wrong to report it to the hundredths place. It should be reported to the same decimal place as the absolute error: 10.0 ± 0.3 m. Another point is that the absolute error and the reported value must have the same units.   If there is such a convention (cf. Rice's lab guide) and it is wrong to report more significant figures than is warranted by the absolute error (cf. the joint project's guidelines), and NIST should have adhered to such convention and striven to be correct, is it true that NIST adheres and is correct because the standard uncertainty has two least significant digits (i.e., $27$)?  Had the standard uncertainty been $0.000\;000\;2\text{ mol}^{-1}$, would NIST have reported Avogadro's Number as $N_A = 6.022\;141\;3\times 10^{23}$ with 8 significant figures? It is asked to solve the PDE  $$u_x + u_y + u = e^{x+2y}$$  My attempt: We have that $$\frac{dx}{1}=\frac{dy}{1}=\frac{du}{e^{x+2y}-u} $$  $\Rightarrow \frac{dy}{dx}=1 \Rightarrow y=x+C_1 \iff C_1=y-x$  $\Rightarrow \frac{du}{dx}= e^{x+2y}-u \iff \dot{u}+u=e^{x+2y} \iff \\ \frac{d}{dx}(e^x u) = e^{2x+2y} \iff u = e^{-x} ( \frac{1}{2}e^{2x+2y} + C_2)$  As $u$ is constant along its characteristics:  $$u(x,y)=\frac{e^{-x}}{2}(e^{2x+2y} + 2C_2(y-x))$$  where $C_2$ is any function of one variable. But wolfram gave the following answer  $$u(x,y)=\frac{e^{-x}}{4}(e^{2x+2y} + 4C_2(y-x))$$  as you can check   What am I doing wrong? Prove the summation:  $$\sum_{i=1}^n i! \cdot i = (n+1)! - 1$$ using induction.   base case:  $n=1$: \begin{align*} \sum_{i=1}^1 i! \cdot i &amp;= (1+1)! - 1 \\ 1 &amp;= 2 - 1 \\ 1 &amp;= 1 \end{align*}   This is a question from my test review packet, currently have the base case completed and I am a bit lost on where to go from there. Any help/hints are appreciated. I'm having a really hard time trying to understand what the differences between a desktop environment and a window manager are?  EDIT: From this :  There are basically three layers that can be included in the Linux desktop: X Windows – This is the foundation that allows for graphic elements to be drawn on the display.  builds the primitive framework that allows moving of windows, interactions with keyboard and mouse, and draws windows. This is required for any graphical desktop. Window Manager – The Window Manager is the piece of the puzzle that controls the placement and appearance of windows. Window Managers include: , , , , , etc. Requires X Windows but not a desktop environment. Desktop Environment – This is where it begins to get a little fuzzy for some. A Desktop Environment includes a Window Manager but builds upon it. The Desktop Environment typically is a far more fully integrated system than a Window Manager. Requires both X Windows and a Window Manager.  Examples of desktop environments are , , ,  among others) No Dropbox top panel icon since update to 18.04 How do I clone a single branch in Git? If $m$ divides $n$, find a free resolution of $\mathbb{Z}/m$ as a $\mathbb{Z}/n$-module. If $m$ divides $n$, find a free resolution of $\mathbb{Z}/m$ as a $\mathbb{Z}/n$-module.   I have tried this one and got $0 \leftarrow \mathbb{Z}/m \leftarrow \mathbb{Z}/n \leftarrow \mathbb{Z}/n$.  The map $\mathbb{Z}/n \to \mathbb{Z}/n$ is multiplication by $m$, but I couldn't go further. Please help me. I've discovered a new pattern.  Is this pattern well known or what is the opinion about it?  Basically, I have a hard time scrubbing up and down source files to figure out what module imports are available and so forth, so now, instead of  import foo from bar.baz import quux  def myFunction():     foo.this.that(quux)   I move all my imports into the function where they're actually used., like this:  def myFunction():     import foo     from bar.baz import quux      foo.this.that(quux)   This does a few things.  First, I rarely accidentally pollute my modules with the contents of other modules.  I could set the __all__ variable for the module, but then I'd have to update it as the module evolves, and that doesn't help the namespace pollution for code that actually lives in the module.  Second, I rarely end up with a litany of imports at the top of my modules, half or more of which I no longer need because I've refactored it.  Finally, I find this pattern MUCH easier to read, since every referenced name is right there in the function body. Do you recommend using semicolons after every statement in JavaScript? In many situations, JavaScript parsers will insert semicolons for you if you leave them out. My question is, do you leave them out?  If you're unfamiliar with the rules, there's a description of semicolon insertion on the . Here's the key point:     If the first through the nth tokens of a JavaScript program form are grammatically valid but the first through the n+1st tokens are not and there is a line break between the nth tokens and the n+1st tokens, then the parser tries to parse the program again after inserting a virtual semicolon token between the nth and the n+1st tokens.   That description may be incomplete, because it doesn't explain @Dreas's example. Anybody have a link to the complete rules, or see why the example gets a semicolon? (I tried it in JScript.NET.)   is related, but only talks about a specific scenario. The context for my question might be a bit strange.   I have stuttering and therefore I have some difficulties pronouncing some words starting with particular phonetics. And I've found that if a sentence starts with a /th/ sound, it makes me feel uncomfortable.  Especially in the word is "thanks" or "thank you".  So I want to know if there's a popular alternative for "thank you" that may not seem strange and that unnatural. I've searched the website and I know there are alternatives like "I appreciate your help." but that sounds a bit overly formal for me. (Or is it? correct me if I'm mistaken.) Defaulting to the sign-up form? Recently I've noticed more and more sign-in / sign-up workflows defaulting to the sign-up option first and providing a minimal "Sign-In / Login" action somewhere else on the page. What's the reason behind this practice?  Examples where I've seen this recently: I am currently trying to establish a clear picture of pure/mixed/entangled/separable/superposed states. In the following I will always assume a basis of $|1\rangle$ and $|0\rangle$ for my quantum systems. This is what I have so far:   superposed: A superposition of two states which a system $A$ can occupy, so $\frac{1}{\sqrt{2}}(|0\rangle_A+|1\rangle_A)$ seperable: $|1\rangle_A|0\rangle_B$ A state is called separable, if its an element of the (tensor)product basis of system $A$ and $B$ (for all possible choices of bases) entangled: $\frac{1}{\sqrt{2}}(|0\rangle_A|1\rangle_B+|1\rangle_A|0\rangle_B)$ is not a state within the product basis (again for all possible bases). mixed state: Is a statistical mixture, so for instance $|1\rangle$ with probability $1/2$ and $|0\rangle$ with probability $1/2$ pure state: Not a mixed state, no statistical mixture   I hope that the above examples and classifications are correct. If not it would be great if you could correct me. Or add further cases, if this list is incomplete.   On wikipedia I read about      Another way to say this is that while the von Neumann entropy of the whole state is zero (as it is for any pure state), the entropy of the subsystems is greater than zero.   which is perfectly fine. However I also read on wikipedia a criterion for :     Another, equivalent, criterion is that the von Neumann entropy is 0 for a pure state, and strictly positive for a mixed state.   So does this imply that if I look at the subsystems of an entangled state, that they are in a mixed state? Sounds strange... What would be the statistical mixture in that case?  Moreover I also wanted to ask, whether you had further illustrative examples for the different states I tried to describe above. Or any dangerous cases, where one might think a state of one kind to be the other? What did Hegel mean by 'world spirit'? I understand that Hegel intends to justify the history of mankind by stating that every town and society that has existed has been a test indirectly arranged by the 'world spirit' in order to eventually create a town in which people would live ethically, and that this process has been done in order for the 'world spirit' to become aware of its freedom. But what exactly is this 'world spirit'?   In the last quiz of a course I'm taking (I´ve taken this year a philosophy course at college), I wrote that the 'world spirit' was some kind of parasitic entity which inhabits every human being that has existed and is going to exist. Does this seem right? "Yesterday" time specification shown when it was actually the day before yesterday Square of a function with an essential singularity Let $a$ be a point on the complex plane such that the function $f$ has an essential singularity. I am trying to prove that the square of that function also has an essential singularity.  I suppose that it does not have an essential singularity. Then $\exists ;k$ such that $(z-z_0)^{2k}f^2(z)$ differentiable. Then if I could take the square root and preserve the differentiability I would have finised. Can I do that? As of today, a  has been found affecting versions 1.0.1 through 1.0.1f (inclusive) and 1.0.2-beta.  Since Ubuntu 12.04, we are all vulnerable to this bug. In order to patch this vulnerability, affected users should update to OpenSSL 1.0.1g.  How can every affected user apply this update now? grep: memory exhausted Why Java needs Serializable interface? We work heavily with serialization and having to specify Serializable tag on every object we use is kind of a burden. Especially when it's a 3rd-party class that we can't really change.  The question is: since Serializable is an empty interface and Java provides robust serialization once you add  implements Serializable - why didn't they make everything serializable and that's it?    What am I missing?