Family of holomorphic functions on the unit disk with zeros at $1/4$ and $1/5$
Showing that $|f(z)| \leq \prod \limits_{k=1}^n \left|\frac{z-z_k}{1-\overline{z_k}z} \right|$
This is a general, community wiki  question to address non-specific "I need a CMS or Wiki that does x, y, and z..." questions.  If your question was closed as a duplicate of this question and you feel that the information provided here does not provide a sufficient answer, please open a discussion on .    I have a list of features that I want for my website's Content Management System (CMS) - where can I find a [free] script that includes all of them? Find three real orthogonal matrices of order $3$ having all integer entries.   I have no idea to solve the problem. I don't know how to start. If $A$ be such matrix then $AA^T=A^TA=I_3$. Please help me. How to get Intel Dual Band Wireless-AC 3168 work on Ubuntu 16.04? I searched many solutions on this site but most of them were referring to Broadcom Wifi drivers while mine has Intel one.   Output of lspci -knn | grep Net -A2  arijit@HP-AU134TX:~$ lspci -knn | grep Net -A2  05:00.0 Network controller [0280]: Intel Corporation Device [8086:24fb] (rev 10) DeviceName: Intel Dual BandWireless-AC 3168 802.11 ac 1x1 WiFi + BT 4.0 Combo Adapter Subsystem: Intel Corporation Device [8086:2110]   Output of rfkill list  arijit@HP-AU134TX:~$ rfkill list  arijit@HP-AU134TX:~$    i.e No Output  Output of uname -a; dmesg | grep iwl  arijit@HP-AU134TX:~$ uname -a; dmesg | grep iwl  Linux HP-AU134TX 4.4.0-31-generic #50-Ubuntu SMP Wed Jul 13 00:07:12 UTC 2016 x86_64 x86_64 x86_64 GNU/Linux Event binding on dynamically created elements? I have a bit of code where I am looping through all the select boxes on a page and binding a .hover event to them to do a bit of twiddling with their width on mouse on/off.  This happens on page ready and works just fine.  The problem I have is that any select boxes I add via Ajax or DOM after the initial loop won't have the event bound.  I have found this plugin (), but before I add another 5k to my pages with a plugin, I want to see if anyone knows a way to do this, either with jQuery directly or by another option. Sci-Fi book female fighter pilot All I remember about the book is that the protagonist was a human female fighter pilot, she has short hair, not sure if it was blond or auburn and she was involved in making peace with the alien race.  The alien race was invading Earth, but because of her they stopped, surrendered and because of her helped Earth improve its technology. I remember that she melded with something and was starting to sort of think like them and lose a bit of her humanity.  It was set in the not too distant future. I believe I read it in the 90s. Ubuntu App Development. Unable to install Ubuntu SDK and buggy Ubuntu emulator I am faced with the following problem: Servers get saturated since current load balancing strategy is based on client IP. Some corporate clients access our servers from behind large proxies so all clients appear with same IP to our load balancer. I think we are using some hardware load balancing device (can investigate further if necessary). We need to maintain session affinity (site is constructed in ASP), so all requests with same IP get routed to the same node.  Since all the communication goes over the HTTPS, no request data (like session Id) is available to balancer as a client discriminator. Is there a way to use some other data besides the IP to distinguish between clients and route the clients even when coming from same IP to different nodes?  Note: I need to maintain the traffic between the balancer and nodes safe (encrypted). What do bookcases do for enchanting? Why people think dark matter as a massive particle? Couldn't it be gravitational waves? Dark matter is said to be present in the galaxies which helped galaxies to exist in the first place forming the glue to attach all the matter in the galaxies.  Given that dark matter never been seen or detected and only effect of which could be felt why do we believe it would be a particle? We have universe (almost) equally distributed in all directions with dark matter forming the skeleton for all the matter that could be seen. Can the dark matter be a illusion of gravitational waves interfering with each other forming this uniform interference pattern of galaxies/matter that is seen by us?  That would also explain the repulsive dark energy which would be the troughs in the gravitational waves indicating desructive interference in the gravitational waves.  Can we hope to simulating the above to come to the possible conclusion of source(two or many) of these gravitational waves that could give rise to skeleton of dark matter and dark energy which may be present in some higher dimentions? Intuition behind the definition of linear transformation I have studied that given vector spaces $V_1$ and $V_2$, a function $T:V_1 \rightarrow V_2$ is called a linear transformation of $V_1$ into $V_2$, if following two properties are true for all $u, v \in V_1$ and scalar $c$:  $(1)$:  $T(u+v) = T(u) + T(v)$ and $(2):  T(cu) = c T(u) $.  My questions are   $1$: What is the geometrical interpretation of properties $1$ and $2$ which says that $T$ preserves additivity and scalar multiplication. I am not able to see this geometrically. What is the meaning of preserving additivity and scalar multiplication.  $2$: At some place I have studied that a linear transformation will be linear if it sends each line to line and planes to planes and so on. How can we interpret this based on these two properties.  I need help to understand this.   Thank you very much for your time.. What are the responsibilities of each Pseudo-Terminal (PTY) component (software, master side, slave side)? I am trying to figure out how a tty works1 (the work-flow and responsibilities of each elements). I have read several interesting articles about it, but there are still some blurry areas.  This is what I understand so far:   The emulated terminal makes different system calls to /dev/ptmx, the master part of the pseudo-terminal. The master part of the pseudo terminal allocates a file in /dev/pts/[0-N], corresponding to the obsolete serial port, and "attaches" a slave pseudo terminal to it. The slave pseudo terminal keeps information such as session Id, foreground job, screen size.   Here are my questions:   Has ptmx any purpose besides allocating the slave part? Does it provide some kind of "intelligence", or the emulated terminal (xterm for instance) has all the intelligence of behaving like a terminal? Why does xterm has to interact with the master part, as it only forwards the stdout and stdin of the slave part? Why can't it directly write and read from the pts file? Is a session ID always attached to one pts file and vice versa? Could I type a ps command and found 2 sessionId for the same /dev/pts/X? What other information does the pts store? Does Xterm update all fields by himself, or does the ptm add some "intelligence" on it?     1. I base my understanding on the , and the  posts, as on several other How do you run a Python script as a service in Windows? I am sketching the architecture for a set of programs that share various interrelated objects stored in a database. I want one of the programs to act as a service which provides a higher level interface for operations on these objects, and the other programs to access the objects through that service.  I am currently aiming for Python and the Django framework as the technologies to implement that service with. I'm pretty sure I figure how to daemonize the Python program in Linux. However, it is an optional spec item that the system should support Windows. I have little experience with Windows programming and no experience at all with Windows services.  Is it possible to run a Python programs as a Windows service (i. e. run it automatically without user login)? I won't necessarily have to implement this part, but I need a rough idea how it would be done in order to decide whether to design along these lines.  Edit: Thanks for all the answers so far, they are quite comprehensive. I would like to know one more thing: How is Windows aware of my service? Can I manage it with the native Windows utilities? What is the equivalent of putting a start/stop script in /etc/init.d? ... or should I offer them a separate formular/window where the user can fill the data to the related person?  Its about entering marks/grades of pupils for a certain subject. So sliding to the wrong line could be bad or good for the one or other pupil...  A separate Window could help, but the productivity is smaller.  What do you think? Finding matrix $B$ is not zero matrix where $AB= 0$ I created a Compute Engine VM (Ubuntu 18.04), and when I log into it using the SSH button in the VM instances list I'm logged in as user username.  After a while, I realised I needed to be able to use another SSH client as well. As per  I enabled OS Login by adding a key-value pair in metadata, where key is enable-oslogin and value is TRUE.  I then tried to add my existing SSH key:  gcloud compute os-login ssh-keys add --key-file path/to/key.pub --ttl 0  which was successful except one major problem: it has added the key for user username_gmail_com and will only allow me to ssh to my VM as that user:  ssh username_gmail_com@myinstance  And it has also created that user on my VM. From the web interface, I'm logged in to the VM with that new user as well (/home/username_gmail_com). Of course, I can still access the original user's data (/home/username). When I disable OS Login the web interface logs me in as username again and SSH from another client is disabled.   Why is the username different when enabling OS Login? Can I change the username with OS Login enabled?   Edit  There has been an addition to the docs explaining exactly this question. Check here:  and on  all the way at the bottom under "Expected login behaviors". Story with multiple 'third planet' races prove $\frac {ab}{a+b} \geq \sum ^n_{i=1} \frac{a_ib_i}{a_i+b_i}$ Index entries duplicated for captions In document class book, and package caption, creating index with makeidx. Index entries for the main text and for footnotes collate properly; but those for captions create their own entries.  Example: for the tag \index{New York!Custom House!\textit{Cartouche}}, text and footnotes collate properly; but used in a caption, a new entry is created at the third level, and is also out-of-alphabetic-sequence. Note: the top level, and first sub are correct; only the second sub is duplicated.  How to get the caption index entries under the same entry? Exploring $ \sum_{n=0}^\infty \frac{n^p}{n!} = B_pe$, particularly $p = 2$. I was exploring the fact that $$ \sum_{n=0}^\infty \frac{n^p}{n!} = B_pe,$$ where $B_n$ is the $n$th Bell number.   I found this result by exploring the series on wolframalpha and looking up the sequence of numbers generated. I have no experience with Bell numbers other than knowing that they represent the number of ways of partitioning a set.   What I tried  Looking at the base case we can verify $$\sum_{n=0}^\infty \frac{n}{n!} = \sum_{n=1}^\infty \frac{1}{(n-1)!} = e. $$  But then I realize that $n^2$ is going to be difficult.  Specifically what I want  I am doing this for fun, so I just want to glean some sort of lesson out of this. Resources that let me learn for myself are just as good!   An accepted answer will have any one of the following:   A proof that $\sum_{n = 0}^{\infty} \frac{n^2}{n!} = 2e$ (this interests me a lot) A description of why this series is related to Bell numbers and the number of partitions of a set A link to some resource that introduces Bell numbers and/or their connection to this series. link new object to scene with python in 2.8 In Python 2.8, I would like to create copies of the object 'CubeTemplate' but am having no luck.  I have reviewed every blender.stackexchange post on this subject (, ,  and ) but cannot get them to work - either they don't apply or the sample code throws errors (perhaps because it was pre 2.8).  The code below throws this error:       AttributeError: 'bpy_prop_collection' object has no attribute 'link'   for x in range(1, 3):     bpy.data.objects['CubeTemplate'].select_set(True)     bpy.context.view_layer.objects.active = bpy.data.objects['CubeTemplate']     me = bpy.context.object.data # use current object's data     me_copy = me.copy()     ob = bpy.data.objects.new('CubeCopy'+str(x), me_copy)     ob.location = (0, 0, x)     scene = bpy.context.scene     scene.objects.link(ob)     scene.update()