I have the below python code:  x = range(3) x.append(x) x[3][3][3][3][0] = 5   The value of x after this is [5, 1, 2, [...]]. But, I dont understand how the parameter is passed in the above context. Can anyone please help me understand?
So I was writing up a simple binary tree in Python and came across [...]  I don't believe this to be related to the Ellipsis object, more it seems to have something to do with an infinity loop (due to Python's shallow copy?). The source of this infinity loop and why it doesn't get expanded while expanding when accessed is something I'm completely lost to, however   &gt;&gt;&gt; a [[[[[], [], 8, 3], [[], [], 3, 2], 6, 3], [], 1, 4], [[], [], -4, 2], 0, 0] &gt;&gt;&gt; Keys(a)#With a+b [0, 1, 6, 8, 3, -4] &gt;&gt;&gt; Keys(a)#With [a,b] [8, [...], [...], 3, [...], [...], 6, [...], [...], 1, [...], [...], -4, [...], [...], 0, [...], [...]] &gt;&gt;&gt; Keys(a)[1]#?? [8, [...], [...], 3, [...], [...], 6, [...], [...], 1, [...], [...], -4, [...], [...], 0, [...], [...], 8, [...], [...], 3, [...], [...], 6, [...], [...], 1, [...], [...], -4, [...], [...], 0, [...], [...]]     Version using a+b  def Keys(x,y=[]):     if len(x):y+=[x[2]]+Keys(x[0],y)+Keys(x[1],y)#Though it seems I was using y=y[:]+, this actually outputs an ugly mess     return y   version using [a,b]  def Keys(x,y=[]):     if len(x):y+=[x[2],Keys(x[0],y),Keys(x[1],y)]     return y   So what exactly is [...]?
I was trying to install Lightworks 11.5.1 (amd64) on Ubuntu 14.04(amd64) but there's a notice: Dependency is not satisfiable: libtiff4. Is there anyway to solve this dependency issue?  Thanks in advance. How do I get a Realtek RTL8723BE wireless card to work? I have installed Ubuntu 15.04 on my laptop with RTL8723BE Wi-fi card. But it is always disconnecting from network. I have tried echo "options rtl8723be fwlps=N ips=N" | sudo tee /etc/modprobe.d/rtl8723be.conf but that didn't helped. What can I do to prevent the wifi from disconnecting? If I upgrade to kernel 4.X, will it help?  ~$ lspci -knn | grep Net -A2  09:00.0 Network controller [0280]: Realtek Semiconductor Co., Ltd. RTL8723BE PCIe Wireless Network Adapter [10ec:b723]     Subsystem: Hewlett-Packard Company Device [103c:2231]     Kernel driver in use: rtl8723be   ~$ rfkill list 0: hci0: Bluetooth     Soft blocked: yes     Hard blocked: no 1: phy0: Wireless LAN     Soft blocked: no     Hard blocked: no   ~$ ifconfig &amp;&amp; iwconfig &amp;&amp; route -n &amp;&amp; ping -c 1 google.com eth0      Link encap:Ethernet  HWaddr 38:63:bb:cd:4a:7e             UP BROADCAST MULTICAST  MTU:1500  Metric:1           RX packets:3 errors:0 dropped:0 overruns:0 frame:0           TX packets:53 errors:0 dropped:0 overruns:0 carrier:0           collisions:0 txqueuelen:1000            RX bytes:752 (752.0 B)  TX bytes:8445 (8.4 KB)  lo        Link encap:Local Loopback             inet addr:127.0.0.1  Mask:255.0.0.0           inet6 addr: ::1/128 Scope:Host           UP LOOPBACK RUNNING  MTU:65536  Metric:1           RX packets:3870 errors:0 dropped:0 overruns:0 frame:0           TX packets:3870 errors:0 dropped:0 overruns:0 carrier:0           collisions:0 txqueuelen:0            RX bytes:314613 (314.6 KB)  TX bytes:314613 (314.6 KB)  wlan0     Link encap:Ethernet  HWaddr c0:38:96:6d:c4:83             inet addr:192.168.1.205  Bcast:192.168.1.255  Mask:255.255.255.0           inet6 addr: fe80::c238:96ff:fe6d:c483/64 Scope:Link           UP BROADCAST RUNNING MULTICAST  MTU:1500  Metric:1           RX packets:15240 errors:0 dropped:0 overruns:0 frame:0           TX packets:14627 errors:0 dropped:0 overruns:0 carrier:0           collisions:0 txqueuelen:1000            RX bytes:14410285 (14.4 MB)  TX bytes:2192744 (2.1 MB)  eth0      no wireless extensions.  wlan0     IEEE 802.11bgn  ESSID:"DIR-615"             Mode:Managed  Frequency:2.437 GHz  Access Point: 00:90:4C:08:00:0D              Bit Rate=150 Mb/s   Tx-Power=20 dBm              Retry short limit:7   RTS thr=2347 B   Fragment thr:off           Power Management:off           Link Quality=70/70  Signal level=-22 dBm             Rx invalid nwid:0  Rx invalid crypt:0  Rx invalid frag:0           Tx excessive retries:0  Invalid misc:186   Missed beacon:0  lo        no wireless extensions.  Kernel IP routing table Destination     Gateway         Genmask         Flags Metric Ref    Use Iface 0.0.0.0         192.168.1.1     0.0.0.0         UG    400    0        0 wlan0 169.254.0.0     0.0.0.0         255.255.0.0     U     1000   0        0 wlan0 192.168.1.0     0.0.0.0         255.255.255.0   U     0      0        0 wlan0 PING google.com.Dlink (172.26.136.19) 56(84) bytes of data. 64 bytes from 19.136.26.172.in-addr.arpa (172.26.136.19): icmp_seq=1 ttl=249 time=102 ms  --- google.com.Dlink ping statistics --- 1 packets transmitted, 1 received, 0% packet loss, time 0ms rtt min/avg/max/mdev = 102.547/102.547/102.547/0.000 ms A real nxn matrix always has a real eigenvalue when n is odd what do it mean by "A real nxn matrix always has a real eigenvalue when n is odd?" Shouldnt it be that regardless of odd or even there will always have a real root?  hope to hear from you guys soon:) Why does the kinetic energy of a particle moving in circular motion increase when the turn radius decreases and no torque is acting? Why does the kinetic energy of a particle moving in circular motion increase when the turn radius decreases and there is no torque acting? E.g. if a planet is rotating about its axis and it shrinks to half of its radius then according to conservation of angular momentum velocity will doubled, i.e. its kinetic energy will increase. Does this mean that without any external force the kinetic energy of any thing can be increased? Please explain! Is it safe to format msftres, msftdata and hidden partitions? Layover at Narita, Japan. Do I need a transit visa? I will be transferring between two international flights at Tokyo Narita airport. I'm scheduled to depart the same day I arrive. I am planning to stay within the airport during the layover. Does anyone know if I will require a transit visa at Narita? Let $A$ be a $m \times n$ matrix with entries from some field $F$. Define the determinant rank of $A$ to be the largest possible size of a nonzero minor, i.e. the size of the largest invertible square submatrix of $A$. It is true that the determinant rank is equal to the rank of a matrix, which we define to be the dimension of the row/column space.  It's not difficult to see that $\text{rank} \geq \text{determinant rank}$. If some submatrix of $A$ is invertible, then its columns/rows are linearly indepedent, which implies that the corresponding rows/columns of $A$ are also linearly indepedent.  Is there a nice proof for the converse? How to add spacing between columns? Proving a vector space is infinite-dimensional Let $S$ be a vector space. Suppose that for any positive integer $n$, there exists a linearly independent subset $S_n ⊆ V$ of size $n$.   How do you show that $S$ is not finite dimensional but infinite-dimensional.  I understand that to be finite dimensional then it must have a finite then  there exists a finite set that such at $\operatorname{Span}(T)=S$. So would it be right to prove by contradiction that there is not a finite spanning set that satisfies $\operatorname{Span}(T)=S$, and hence I could argue that the vector space $S$ is infinite dimensional.  How would I show that $S$ does not have a spanning set $T$, such that $\operatorname{Span}(T)=S$? Is the $ L^{p}$$[0,1]$ norm continuous in p? I ran into the following problem when I was doing my homework, and I have no thoughts on where I should start with:  (1) If $f\in L^{2}$, show that $\displaystyle \lim_{p \rightarrow 1^{+}}\int_{[0,1]}|f|^{p}=\int_{[0,1]}|f|$  (2) If $0&lt;p$, show that $\displaystyle \lim_{q\rightarrow p^{-}}||f||_{q}=||f||_{p}$  My first thought was Generalized LDCT, but it didn't seem to work. I also made some other attempts but none of them were successful... Can anybody give me some hints on how I should look at this question?  Also, I know if $p\rightarrow\infty$ then $||f||_{p}\rightarrow||f||_{\infty}$ on $[0,1]$, but does similar continuity in p holds for other $L^{p}[0,1]$ norms in general?  Thank you!  Edit:   Sorry if I did not make it clear enough in the question. All $L^{p}$ refers to $L^p[0,1]$.  The first question is found  (thanks to t.b.), but the second question remains, mainly because $f$ is not guaranteed to be in any $L^{p}$. Did this character lose a limb in “The Force Awakens?” Inspired by  which states limb loss as a recurring theme, I started thinking about the final lightsaber battle. After watching The Force Awakens the second time, I was not sure if      Kylo Ren   lost a limb or just lost his lightsaber. We definitely see      Rey slash at Ren’s right hand.   So knowing that context:      Did Kylo Ren actually lose his arm/hand? I hope to receive my PhD in Mathematics in May of 2015, so I am currently applying for jobs.  Due to life circumstances, I'm fairly certain that I will only be staying at my next position for about 2 years.  Does this mean I shouldn't even try to apply for tenure-track positions?  Will a hiring committee not even consider me for the position if I'm not willing to commit to staying with them for a certain amount of time?  I would love to get a teaching/lecturing position at any institute of higher education (4-year research university, liberal arts school, community college), but as I look for openings, a lot of them are tenure-track assistant professor positions.  Should I go through the effort of sending in an application, or will that be a waste of my, and the committee's, time?  Thanks for any advice you have!  Edit (to address Nate's comment):  My wife is currently applying for 2 year graduate degree programs in various cities in the US, so I'm applying for jobs in the same cities.  When she finishes her program, we plan to move outside of the US (Africa or Southeast Asia), where I do hope to remain in academia, teaching mathematics to college-aged students. How can I clip an image via a bezier-path? How to change permissions of multiple files found with find command? In thinking about Sturm-Liouville theory a bit I see I have no actual idea what is going on.  The first issue I have is that my book began with the statement that given  $$L[y] = a(x)y'' + b(x)y' + c(x)y = f(x)$$  the problem $L[y] \ = \ f$ can be re-cast in the form $L[y] \ = \ \lambda y$.  Now it could be a typo on their part but I see no justification for the way you can just do that!  More importantly though is the motivation for Sturm-Liouville theory in the first place. The story as I know it is as follows:  Given a linear second order ode   $$F(x,y,y',y'') = L[y] = a(x)y'' + b(x)y' + c(x)y = f(x)$$  it is an exact equation if it is derivable from a differential equation of one order lower, i.e.  $$F(x,y,y',y'') = \frac{d}{dx}g(x,y,y').$$  The equation is exact iff  $$a''(x) - b'(x) + c(x) = 0. $$  If $F$ is not exact it can be made exact on multiplication by a suitable integrating factor $\alpha(x)$.  This equation is exact iff  $$(\alpha(x)a(x))'' - (\alpha(x)b(x))' + \alpha(x)c(x) = 0 $$  If you expand this out you get the Adjoint operator  $$L^*[\alpha(x)] \ = \ (\alpha(x)a(x))'' \ - \ (\alpha(x)b(x))' \ + \ \alpha(x)c(x) \ = 0 $$  If you expand $L^*$ you see that we can satisfy $L \ = \ L^*$ if $a'(x) \ = \ b(x)$ &amp; $a''(x) \ = \ b'(x)$ which then turns $L[y]$ into something of the form  $$L[y] \ = \ \frac{d}{dx}[a(x)y'] \ + \ c(x)y \ = \ f(x).$$  Thus we seek an integratiing factor $\alpha(x)$ so that we can satisfy this &amp; the condition this will hold is that $\alpha(x) \ = \ \frac{1}{a(x)}e^{\int\frac{b(x)}{a(x)}dx}$  Then we're dealing with:  $$\frac{d}{dx}[\alpha(x)a(x)y'] \ + \ \alpha(x)c(x)y \ = \ \alpha(x)f(x)$$  But again, by what my book said they magically re-cast this problem as  $$\frac{d}{dx}[\alpha(x)a(x)y'] \ + \ \alpha(x)c(x)y \ = \ \lambda \alpha(x) y(x)$$  Then calling  $$\frac{d}{dx}[\alpha(x)a(x)y'] \ + \ ( \alpha(x)c(x)y \ - \ \lambda \alpha(x) )y(x) \ = \ 0$$  a Sturm-Liouville problem.  My question is, how can I make sense of everything I wrote above? How can I clean it up &amp; interpret it, like at one stage I thought we were turning our 2nd order ode into something so that it reduces to the derivative of a first order ode so we can easily find first integrals then the next moment we're pulling out eigenvalues &amp; finding full solutions - what's going on? I want to be able to look at $a(x)y'' \ + \ b(x)y' \ + \ c(x)y \ = \ f(x)$ &amp; know how &amp; why we're turning this into a Sturm-Liouville problem in a way that makes sense of exactness &amp; integrating factors, thanks for reading! Proof of an inequality by induction: $(1 + x_1)(1 + x_2)...(1 + x_n) \ge 1 + x_1 + x_2 + ... + x_n$ Let $n \in \mathbb N^+$. Show that if $x_1, x_2, ... , x_n$ are $n$ real numbers such that $-1 \le x_i \le 0$ for each $1 \le i \le n$, then $$(1 + x_1)(1 + x_2)...(1 + x_n) \ge 1 + x_1 + x_2 + ... + x_n$$  I am using a proof by induction, but I am unable to complete it. I would appreciate any tips on how I could finish the proof.   Incomplete Proof Let $P(n)$ be the proposition that $(1 + x_1)(1 + x_2)...(1 + x_n) \ge 1 + \sum_{i = 1} ^ n x_i$. When $n = 1$, LHS = RHS = $1 + x_i$. Clearly $1 + x_i \ge 1 + x_i$ and so $P(1)$ is true. Assume that $P(k)$ is true, i.e. $(1 + x_1)(1 + x_2)...(1 + x_k) \ge 1 + \sum_{i=1}^k x_i$. Case 1 Suppose $x_{k + 1}  = -1$. Then $1 + x_{k + 1} = 0$, hence LHS = $(1 + x_1)(1 + x_2)...(1 + x_k)(1 + x_{k+1}) = 0$. RHS = $1 + x_1 + x_2 + ... + x_k - 1 = x_1 + x_2 + ... + x_k$ which is always nonpositive since each $x_i$ is nonpositive. Hence RHS $\le 0$ and so LHS $\ge$ RHS. Case 2 Suppose $x_{k+1} = 0$. Then $1 + x_{k+1} = 1$, hence multiplying it to LHS does not change anything. Also, adding $x_{k+1}$ to RHS does not change anything. Therefore, LHS $\ge$ RHS still holds. Case 3 Suppose $-1 &lt; x_{k+1} &lt; 0$. Then $0 &lt; 1 + x_{k+1} &lt; 1$. Adding $x_{k+1}$ to RHS makes the RHS smaller since $x_{k+1}$ is negative. If LHS $= 0$, then multiplying $1 + x_{k+1}$ to LHS does not change anything, and so LHS $\ge$ RHS holds. If LHS > $0$, then multiplying $1 + x_{k+1}$ to LHS makes the LHS smaller since $0 &lt; 1 + x_{k+1} &lt; 1$. In this case LHS $\ge$ RHS does not necessarily hold? ... I am looking for a clean and fast method to force GNOME in Ubuntu 14.04 to switch between active apps only on the current workspace when pressing the shortcut alt + tab. I am trying to align some text to left/center/right in the same line. For example, I want to put my phone number on the left, my name in the center, and my email on the right, how do I do that? What advantages does using (function(window, document, undefined) { ... })(window, document) confer? How to limit current of an AC signal For my project, I'm trying to work with the principle of electrovibration. This principle is about simulating textures using low current electricity on an insulated conductive surface ().  In order to do this, I will be experimenting with generated AC signals of 80 to 160 Vpp at 60Hz to 400Hz. I will do this by using an DC - AC converter, usually used for EL lamp applications.  My only concern is how to limit the current coming from the converter. Are the techniques for limiting AC current the same as DC, by using a simple resistor? Or is it, as I expect, more complex?  I need to limit the current to 0.5mA, for safety reasons.