Can someone could help me write the mathematical/backshift equation for the seasonal ARIMA (0,0,1) x (2,1,2) with 12 periods? I'm confused with how to go about this. I would prefer an equation involving $B$, $Y_{t}$, $e_{t}$, $\phi$, $\Phi$, $\theta$, and $\Theta$.  This is different from other models that have previously been answered and I don’t understand the explanation in FPP2.
I would appreciate if someone could help me write the mathematical equation for the seasonal ARIMA (2,1,0) x (0,2,2) period 12. I'm a little confused with how to go about this. I would prefer an equation involving $Y_t , e_t, θ$ and $Θ$.
Combinatorial Proof Question: Vandermonde convolution identity I'm really iffy on combinatorial proofs in general and now that there is a sum, it's just confused me even more. Can someone try and walk me through this proof?  $$ \binom{m + n}{r} = \sum_{k=0}^r \binom{m}{k}\binom{n}{r - k} $$ Power Off button is gone on Ubuntu 20.04 LTS I recently installed Ubuntu 20.04 LTS on my laptop and I noticed that I no longer have the Power Off button but rather a menu that I need to click on and then I need to click on Power Off... and then Power Off. Is there a way to get the button back? WCF - Faults / Exceptions versus Messages We're currently having a debate whether it's better to throw faults over a WCF channel, versus passing a message indicating the status or the response from a service.  Faults come with built-in support from WCF where by you can use the built-in error handlers and react accordingly. This, however, carries overhead as throwing exceptions in .NET can be quite costly.  Messages can contain the necessary information to determine what happened with your service call without the overhead of throwing an exception. It does however need several lines of repetitive code to analyze the message and determine actions following its contents.  We took a stab at creating a generic message object we could utilize in our services, and this is what we came up with:  public class ReturnItemDTO&lt;T&gt; {     [DataMember]     public bool Success { get; set; }      [DataMember]     public string ErrorMessage { get; set; }      [DataMember]     public T Item { get; set; } }   If all my service calls return this item, I can consistently check the "Success" property to determine if all went well. I then have an error message string in the event indicating something went wrong, and a generic item containing a Dto if needed.  The exception information will have to be logged away to a central logging service and not passed back from the service.  Thoughts? Comments? Ideas? Suggestions?  Some further clarification on my question  An issue I'm having with fault contracts is communicating business rules.  Like, if someone logs in, and their account is locked, how do I communicate that? Their login obviously fails, but it fails due to the reason "Account Locked".  So do I:  A) use a boolean, throw Fault with message account locked  B) return AuthenticatedDTO with relevant information Let $f:S^{2n} \rightarrow S^{2n}$ be a continuous map. Show that          there exists $x \in S^{2n}$, such that $f(x) =x$ or $f(x) = -x$;   any continous map $g: \mathbb R P^{2n} \rightarrow \mathbb RP^{2n}$ has a fixed point;      I think 1 implies 2. So, how can I find an $x$ in 1?  Thanks for the help. How to copy all files of a certain type into a folder from command prompt? I want to copy all files of a certain type (like .docx, .pdf, etc) on my PC into a folder. How can I do that? Xcode - How to fix 'NSUnknownKeyException', reason: … this class is not key value coding-compliant for the key X" error? Is a black hole singularity a single point? General relativity is expressed in terms of differential geometry, which allows you to do interesting things with the coordinates: multiple coordinates may refer to a single point, eg. the  has whole lines at the top and the bottom that correspond to the North and South poles, respectively; or a single coordinate may refer to multiple points, for example by using inverse geometry the origin refers to all the points infinitely far away.  So, is the singularity just a single point in the curved spacetime, or can it be a more extended object, described by a single coordinate? What do I need in a camera to take non-blurry photos of a fast-moving child? Find the value of $P(1)$ Let $P (x) = x^2 + bx + c$, where $b$ and $c$ are integer.       If $P(x)$ is a factor of both $x^4 + 6x^2 + 25$ and $3x^4 + 4x^2 + 28x  + 5$, find the value of $P(1)$.   I am not being able to solve this.Some hints/suggestions?  Tell me if I can edit to improve this question.I could'nt try much.Got stuck. How to deal with variable income in the budget We have a budget planned out for various categories, and in order to make ends meet we count on child support for my wife's child from a previous marriage.  However, lately we have not been receiving this amount.  How do we deal with this in the budget?    My wife has just been "borrowing" it from our savings, but I don't think that is reasonable given that I find it highly unlikely we will ever be able to recover it.  On the other hand, she doesn't think it reasonable to cut out of her budget and cutting it out of the budget for the kids (which is where it really should be going!) isn't reasonable either. What is the monomorphism restriction? I've just made a set of armor by using a male body mesh model I downloaded and selecting certain faces from the model and duplicating them to create viable armor pieces.   Since the pieces are just duplicated from the same mesh male model, then it's still part of the same object.   How do I separate the armor piece from the model to make the pieces separate? Cannot select vertices from different object while in edit mode Whenever I enter edit mode, with 2 separate meshes (cubes), I can only select vertices/edges/faces of 1 mesh.  Example (the screen shot did not include the mouse cursor):    Also, when I enter edit mode with both meshes selected, one of the meshes has a red border and cannot be selected (it also has this border in Object mode): MySQL Hashing Function Implementation I know that php has md5(), sha1(), and the hash() functions, but I want to create a hash using the MySQL PASSWORD() function.  So far, the only way I can think of is to just query the server, but I want a function (preferably in php or Perl) that will do the same thing without querying MySQL at all.  For example:  MySQL hash -> 464bb2cb3cf18b66  MySQL5 hash -> *01D01F5CA7CA8BA771E03F4AC55EC73C11EFA229  Thanks! We have a SQL Server 2012 instance that contains a database with data for many product lines.   We are looking for a way to take subsets of this data into another database on the same instance.  This doesn't have to be continuous as we are looking for ways to make it easy to export backups of the subsets that we can send out to vendors (we have a company that loads this data into their own sql server to produce a product we sell, naturally its huge and we want to trim it down to just the product lines they work with on a regular enough basis) or use to load SQLite DB's for use with offline applications.  ProductDB - the superset of all product line data.  ProductLine1DB - A subset identical in structure to ProductDB, but with data only relevant to product line 1.  ProductLine2DB - A subset identical in structure to ProductDB, but with data only relevant to product line 2.  This can be done nightly, weekly, as often as we need to but not a continuous replication.  We don't want to add in distributor servers or even extra subscriber servers. We would like the replication to happen on the same server with the subscriber databases being on the same server.  Is this a good candidate for transactional replication?  Why or why not?  We obviously have other options to load this data, but it seems like this might be a good case to use something like transactional replication. I've heard its powerful but prone to issues when not setup optimally.  Note: I am not a DBA, simply a developer, but we are currently looking for a new DBA and some of us are taking over duties like this temporarily. How can I get the current date and time in UTC or GMT in Java? When I create a new Date object, it is initialized to the current time but in the local timezone. How can I get the current date and time in GMT? Upgrade High-Trust Addin/App from 2013 to 2016 I have a SharePoint 2013 environment with several High-Trust Addins. This must now be upgraded to SharePoint 2016.  My Questions:   I was unable to find any documentation on the required steps. Links are welcome. Do i have to migrate App-Management Service and Subscription Settings Service?  don't even mention them.   say yes, but linked background is no longer available.  , i had to create a New-SPTrustedSecurityTokenIssuer. In this step, a RegisteredIssuerName had to be specified. This IssuerName consists of the Realm and the .   I think IssuerID can and should be migrated to SharePoint 2016, as it it also defined inside the High-Trust app. What about the Realm? This is by default the same value as FarmID. If i migrate this value, i have to change the Realm in SharePoint 2016. Or should i create the TST with a new Realm and existing IssuerID? I have installed Ubuntu alongside Windows 8.1. But the wifi is not working in Ubuntu (perhaps the drivers are not present), which worked fine in windows. Also I cant connect with Ethernet since my laptop does not have an Ethernet port. So is there any way for me to connect to the internet in ubuntu? Edit: Output of the terminal command  lspci -knn | grep Net -A2:  vikram@vikram-Inspiron-11-3148:~$ lspci -knn | grep Net -A2 01:00.0 Network controller [0280]: Broadcom Corporation BCM43142 802.11b/g/n [14e4:4365] (rev 01)     Subsystem: Dell Device [1028:0018]     Kernel driver in use: bcma-pci-bridge vikram@vikram-Inspiron-11-3148:~$    I did what Pilot6 suggested. Here is the output:    vikram@vikram-Inspiron-11-3148:~$ sudo dpkg -i *.deb [sudo] password for vikram:  Selecting previously unselected package bcmwl-kernel-source. (Reading database ... 163804 files and directories currently installed.) Preparing to unpack bcmwl-kernel-source_6.30.223.141+bdcom-0ubuntu2_amd64.deb ... Unpacking bcmwl-kernel-source (6.30.223.141+bdcom-0ubuntu2) ... Selecting previously unselected package dkms. Preparing to unpack dkms_2.2.0.3-1.1ubuntu5.14.04_all.deb ... Unpacking dkms (2.2.0.3-1.1ubuntu5.14.04) ... Setting up dkms (2.2.0.3-1.1ubuntu5.14.04) ... Setting up bcmwl-kernel-source (6.30.223.141+bdcom-0ubuntu2) ... Loading new bcmwl-6.30.223.141+bdcom DKMS files... First Installation: checking all kernels... Building only for 3.16.0-30-generic Building for architecture x86_64 Building initial module for 3.16.0-30-generic ERROR (dkms apport): kernel package linux-headers-3.16.0-30-generic is not supported Error! Bad return status for module build on kernel: 3.16.0-30-generic (x86_64) Consult /var/lib/dkms/bcmwl/6.30.223.141+bdcom/build/make.log for more information. modprobe: FATAL: Module wl not found. update-initramfs: deferring update (trigger activated) Processing triggers for man-db (2.6.7.1-1ubuntu1) ... Processing triggers for initramfs-tools (0.103ubuntu4.2) ... update-initramfs: Generating /boot/initrd.img-3.16.0-30-generic vikram@vikram-Inspiron-11-3148:~$ Is it safe to put hot food in the fridge? I heard that putting really warm food in the fridge right after cooking it is not the right thing to do. It might cause bacterial growth? Is this true? Why does an argument similiar to 0.999...=1 show 999...=-1? I accept that two numbers can have the same supremum depending on how you generate a decimal representation. So $2.4999\ldots = 2.5$ etc. Can anyone point me to resources that would explain what the below argument that shows $999\ldots = -1$ is about? Here is the most usual proof I see that $0.999\ldots = 1$:  $x=0.999\ldots$ $10x=9.999\ldots$ $10x - x = 9$ $x=1$  Using this same argument template I can show $999\ldots=-1$:  $x= \ldots9999.0 $ $0.1x= \ldots9999.9$ $0.1x - x = 0.9$ $x=-1$  What might this mean? Edit from one of the comments: $$\sum_{k=0}^{\infty}{9 \cdot 10^k}=-1$$