Most plants require carbon dioxide for their photosynthesis, which Mars has in overabundance.   Would atmosphere composition (let's ignore temperatures for the purpose of this question) of Mars allow vegetation to grow?
Do we know of any living forms on Earth that could continue to live on Mars?
My motherboard currently supports both SATA II and III (3 Gb/s and 6Gb/s respectively), but after reading some online, it seems as though connecting a HDD to the 6 Gb/s is pretty much pointless. If this is the case I'm going to leave my two SATA III ports open for something that can actually use it (which at this point I'm not really sure what can).  This is part of an article I read:     In terms of everything else, we saw basically no difference from the same single drive being plugged into a SATA 6Gb/s or SATA 3Gb/s port. All of this is obviously due to the hard drive not being able to actually take advantage of the 6Gb/s bus.   from . Proving replacement theorem? I want to see if I am understanding the proof of the replacement theorem correctly.   Let $V$ be a vector space that is spanned by a set $G$ containing $n$ vectors.  Let $L \subseteq V$ be a linearly independent subset containing $m$ vectors.  Then $m\leq n$ and there exists a subset H of G containing exactly $n-m$ vectors s.t. $L \cup H$ generates $V$.   The proof in the book says to start with $m=0$. In that case $L=\varnothing$, the empty set.        Let's assume this theorem is true for some integer $m \geq 0$.   Let $L = \{v_j\}_{j=1}^{m+1}$ and define it as a linearly independent subset of $V$ consisting of $m+1$ vectors.  Since any subset of a linearly independent set is linearly independent as well ($S_1 \subseteq S_2 \subseteq V$), then $\{v_j\}_{j=1}^m$ is linearly independent also.   It then says to use the induction hypothesis to say that $m \geq n$. Well, ok, but that seems sort of pulled out of nowhere to me. The next step is to say that there is therefore another subset, $\{u_k\}_{k=1}^{n-m}$ of G such that $\{v_j\}_{j=1}^m \cup \{u_k\}_{k=1}^{n-m}$ spans $V$.   That being the case there are scalars $(a_j)_{j=1}^m$ and $(b_k)_{k=1}^{n-m}$ which you can multiply by the vectors $v_j$ and $u_k$. You can then add the two sets of vectors, yielding $$\sum_{j=1}^m a_j v_j + \sum_{k=1}^{n-m} b_k u_k = v_{m+1}$$  At this point I am not sure I understand things. Because we are assuming $n-m&gt;0$ -- otherwise $v_{m+1}$ is linearly dependent. But then it says not only is $n&gt;m $ but $n&gt;m+1$, and that is where I am losing the plot to get to the next step. How to find the inverse modulo $m$? For example: $$7x \equiv 1 \pmod{31} $$ In this example, the modular inverse of $7$ with respect to $31$ is $9$. How can we find out that $9$? What are the steps that I need to do? Update If I have a general modulo equation: $$5x + 1 \equiv 2 \pmod{6}$$ What is the fastest way to solve it? My initial thought was: $$5x + 1 \equiv 2 \pmod{6}$$ $$\Leftrightarrow 5x + 1 - 1\equiv 2 - 1 \pmod{6}$$ $$\Leftrightarrow 5x \equiv 1 \pmod{6}$$ Then solve for the inverse of $5$ modulo 6. Is it a right approach? Thanks. Zip a file without including the parent directory An excited electron loses energy in the form of radiation. The radiation constitutes photons which move at a speed $c$. But is the process of conversion of the energy of the electron into the kinetic energy of the photon instantaneous? Is there a a simple way to visualize this process rather than math? It may be something that will happen to the person who is having the feeling but it may also be to several persons, as might occur with a highly destructive earthquake, for instance.   The word or phrase would be used in the following sentence:      “I’m no spiritualist but I have a feeling of ___. I hope it’s just a feeling."   EDIT - The phrase I'm looking for conveys a much stronger feeling than "I have a bad hunch". It is about something catastrophic which the person feels is "going to happen in a few minutes". What makes someone deserving of a Ph.D.? Few days back while attending a thesis defense, one Professor was asking the defender why does he think, he deserves the degree. I was wondering since then, is there really any general answer for that? or the answer should be given describing my own work and then emphasis them how it is important for research field?  I asked the question here to know your opinion about it and to list down what could be the possible answers to this question. Formula field is too big to execute (5,480 characters) I got an error when i am trying to add fomrula in formula field.  Error: Compiled formula is too big to execute (5,480 characters). Maximum size is 5,000 characters  My formula is   (ED__c+Service_Tax__c+Total_Site_Work_Price1__c+Total_Selling_Price_Based_on1__c )*WCTper__c   In this formula ED__c, Total_Site_Work_Price1__c, Total_Selling_Price_Based_on1__c are also Formula fields. And these formulas are also contain fomrula fields.  How can i calculate the formula..? I am trying to work through Hartshorne's book and while working through one of the exercises, I need to show the following:  Let $k$ be an algebraically closed field. Let $Y \subseteq A^3$ be the set $Y=\{(t,t^2,t^3)\;|\;t \in k\}$. Show that $Y$ is an affine variety.  The rest of the problem I have completed. I'm just not sure how to show that this set is closed and irreducible. I assume that they intend for $A^3$ to have the Zariski topology. Evaluating $\sum_{n=1}^\infty \frac{2^{2n-1}}{5^{n+1}}$ How can I test the fairness of a d20? Are there any disadvantages to always using nvarchar(MAX)? Short version: In what circumstances is dd safe to use for copying data, safe meaning that there is no risk of corruption due to a partial read or write?  Long version — preamble: dd is often used to copy data, especially from or to a device (). It's sometimes attributed mystical properties of being able to access devices at a lower level than other tools (when in fact it's the device file that's doing the magic) — yet dd if=/dev/sda is the same thing as cat /dev/sda. dd is sometimes thought to be faster, but . Nonetheless, .  Problem: dd if=foo of=bar is not, in fact, the same as cat &lt;foo &gt;bar. On most unices¹, dd makes a single call to . (I find  fuzzy on what constitutes “reading an input block” in dd.) If read() returns a partial result (which, according to POSIX and other reference documents, it's allowed to unless the implementation documentation says otherwise), a partial block is copied. Exactly the same issue exists for write().  Observations: In practice, I've found that dd can cope with block devices and regular files, but that may just be that I haven't exercised it much. When it comes to pipes, it's not difficult to put dd at fault; for example try :  yes | dd of=out bs=1024k count=10   and check the size of the out file (it's likely to be well under 10MB).  Question: In what circumstances is dd safe to use for copying data? In other words, what conditions on the block sizes, on the implementation, on the file types, etc, can ensure that dd will copy all the data?  ( has a fullblock flag to tell it to call read() or write() in a loop so as to transfer a full block. So dd iflag=fullblock is always safe. My question is about the case when these flags (which don't exist on other implementations) are not used.)  ¹  I've checked on OpenBSD, GNU coreutils and BusyBox. Limit $ a_{n+1} = \frac{1}{3}(2a_n + \frac{5}{a_n^{2}}), a_1 > 0 $ Let $ a_{n+1} = \frac{1}{3}(2a_n + \frac{5}{a_n^{2}}), a_1 &gt; 0 $. Show the sequence converge and find it's limit.    I did the following:  We see that $a_n$ is positive for every n obviously (considering $a_1 &gt; 0$). Then:  $$ a_{n+1} - a_n = \frac{2a_n^{3} + 5}{3a_n^{2}} - a_n = \frac{5 - a_n^{3}}{3a_n^{2}}$$  We see that for each $a_n &gt; ^3\sqrt{5}$ the sequence is decreasing. That means the proof collapses to prove  $a_n &gt; ^3\sqrt{5}$ in order for $a_n$ to be decreasing. Suppose $ a_n &gt; ^3\sqrt{5}$ then obviously $a_{n+1} = \frac{2a_n^{3} + 5}{3a_n^{2}} &gt; \frac{2(\sqrt[3]{5})^{3} + 5}{3(\sqrt[3]{5})^{2}} = \sqrt[3]{5}$ so we deduced $a_{n+1} &gt; ^\sqrt[3]{5} $.  (It's important to note $a_1$ might be less then $\sqrt[3]{5}$, hence the sequence will decrease from the second element.) So we observed $a_n$ is always positive and decreasig hence it's bounded below so it's bounded. As for it's limit:   $$\begin{align} L = \lim_{n \to \infty} a_{n+1} = \lim_{n \to \infty} \frac{1}{3}(2a_n + \frac{5}{a_n^{2}}) = \frac{1}{3}(2L + \frac{5}{L^{2}}) =  \sqrt[3]{5}\end{align}$$  I'm not sure as of the correctness of the solution. I'm aware that it's not a contradiction because it only implies it's in the epsilon-environment of $\sqrt[3]{5}$, or rather in this case $(\sqrt[3]{5}, \sqrt[3]{5}+\epsilon)$.  Is it correct?  EDIT: If anyone encounter a question in the likes, to sum it up you obviously should show the sequence is montonic and bounded. In this case for example we can show it using AM-GM inequality to see the sequence is bounded by $\sqrt[3]{5}$ and then in the difference of two consequective elements we see the difference is negative due to every element being greater then the third root of 5. From here we know the sequence is bounded below and decreasing hence it's bounded. If we plug in the limit of the sequence to itself we will see it's the third root of five. And that's it. How to make child process die after parent exits? Suppose I have a process which spawns exactly one child process. Now when the parent process exits for whatever reason (normally or abnormally, by kill, ^C, assert failure or anything else) I want the child process to die. How to do that correctly?    Some similar question on stackoverflow:   (asked earlier)  (asked later)      Some similar question on stackoverflow for Windows: What wand was used by Mr Graves at the time of Fantastic Beasts? We know that the movie Fantastic Beasts is set in 1926. From the movie, we learn that at this time, Dumbledore is a teacher at Hogwarts and Grindelwald is lose after escaping a previous arrest. In the movie we learn that      Mr Graves is in fact Grindelwald in disguise. Grindelwald is shown to be at least in his forties, maybe fifties so he should already be the owner of the wand since he stole it from Gregorovitch as a teen.   We know that Dumbledore won the wand from Grindelwald after defeating him in their historic duel. That duel is always described as being “the end of the dark wizard Grindelwald” so I’m assuming that it didn’t happen prior to the movie and that he didn’t escape after that duel, please correct me if you have cannon evidence stating the contrary.      In the movie, we see Graves’ wand a few time and it isn’t the (very recognizable) one used in DH as the Elder Wand. This could of course be a prop error but since David Yates was also the director on DH and a lot of the visuals are similar I’m assuming it wasn’t. Graves could of course be using another wand in the fear that someone could recognize it but he would still be the rightful master of the Elder Wand. At the end of the movie, Newt is the one that disarms Graves/Grindelwald.   In all logic, he should have been made the new owner of the wand, whether Grindelwald was actually using it or not. That would have made it impossible for Dumbledore to win it from Grindelwald later.  So my question is: What wand is that character using at that specific time? Is he already the owner of the Elder Wand?      And if so, why wasn’t Newt made the new owner of the wand? Show that $\lim_{n\to\infty} \sqrt[n]{a^{n} + b^{n}} = \max(a, b)$ Prove that:  $$\lim_{n\to\infty} \sqrt[n]{a^{n} + b^{n}} = \max(a, b)$$  I don't have a clue even how to start the proof here. Any hint is appreciated! I noticed a peculiar behavior of my Ubuntu 13.04 (although possibly it's also present in previous versions): when my system freezes completely (I do not ask for troubleshooting this) so that even X does not respond to Ctrl+Alt+FX keys, the CapsLock toggle diode on my keyboard blinks (with frequency of ~1Hz), although the system is completely unresponsive.   What is the cause of this phenomena? Is it caused by some internal kernel mechanisms? Is this specific to Ubuntu (is it caused some custom Ubuntu additional software)? Does it has anything to do with HAL? What is the purpose of it? Can I customize this behavior on Ubuntu? Why do physicists think that the electron is an elementary particle? Default constructor with empty brackets