Standard Graded Algebra over a field
Standard graded algebra
I am having trouble understanding the estimation of an AR process. In some textbooks, the AR(1) process is defined as follows: $y_{t}=\theta y_{t-1}+ϵ_t$ (which does not contain a constant). So the OLS estimator is biased. I am confused about the cause of the bias. It is explained that $y_{t-1}$ is dependent on $ϵ_{t-1}$ although it is independent of $ϵ_t$. However in linear regression, if the equation does not contain a constant, we cannot make sure the expectation of disturbance is zero. So the OLS estimator is bias without a constant. Does it mean that the OLS estimator is unbiased if I add a constant in AR process? How do the tens­es and as­pects in English cor­re­spond tem­po­ral­ly to one an­oth­er? How do I detect orientation on app launch for splash screen animation on iPad! How many Naruto Shippuden dubbed episodes are there? I am watching Naruto and I am currently on episode 164. How many episodes of Shippuden do they have dubbed, and are they still dubbing it? I have a ListBox DataTemplate in WPF. I want one item to be tight against the left side of the ListBox and another item to be tight against the right side, but I can't figure out how to do this.  So far I have a Grid with three columns, the left and right ones have content and the center is a placeholder with it's width set to "*". Where am I going wrong?  Here is the code:  &lt;DataTemplate x:Key="SmallCustomerListItem"&gt;     &lt;Grid HorizontalAlignment="Stretch"&gt;         &lt;Grid.RowDefinitions&gt;             &lt;RowDefinition/&gt;         &lt;/Grid.RowDefinitions&gt;         &lt;Grid.ColumnDefinitions&gt;             &lt;ColumnDefinition/&gt;             &lt;ColumnDefinition Width="*"/&gt;             &lt;ColumnDefinition/&gt;         &lt;/Grid.ColumnDefinitions&gt;         &lt;WrapPanel HorizontalAlignment="Stretch" Margin="0"&gt;             &lt;!--Some content here--&gt;             &lt;TextBlock Text="{Binding Path=LastName}" TextWrapping="Wrap" FontSize="24"/&gt;             &lt;TextBlock Text=", " TextWrapping="Wrap" FontSize="24"/&gt;             &lt;TextBlock Text="{Binding Path=FirstName}" TextWrapping="Wrap" FontSize="24"/&gt;          &lt;/WrapPanel&gt;         &lt;ListBox ItemsSource="{Binding Path=PhoneNumbers}" Grid.Column="2" d:DesignWidth="100" d:DesignHeight="50"      Margin="8,0" Background="Transparent" BorderBrush="Transparent" IsHitTestVisible="False" HorizontalAlignment="Stretch"/&gt;     &lt;/Grid&gt; &lt;/DataTemplate&gt; Commenting out multiple lines of code, specified by line numbers, using vi or vim I have learned from  that it is possible to use vi/vim to comment out a specified range of line numbers.  For example, suppose I have the following bash script:  #!/bin/bash  This is my very very great script   Now suppose that I want to comment out line numbers 6 through 8 (which contain the words very, very, and great) using the # comment character.  In vi/vim, I can simply type :6,8s/^/# to obtain the following:  #!/bin/bash  This is my #very #very #great script   which comments out lines 6 through 8.  My question is, is it possible to type a similar one liner that will remove the # comment character from lines 6 through 8 (but not any other commented lines in the file)?  Having said this, I realize that there is some debate about whether I am actually using vi or vim.  In practice, I open a file script.sh with the command vi script.sh.  Also, when I type the command which vi, I obtain /usr/bin/vi.  Nevertheless, when I simply type vi and press Enter, I obtain this:  ~                              VIM - Vi IMproved ~ ~                               version 7.2.330 ~                           by Bram Moolenaar et al. ~                 Vim is open source and freely distributable ~ ~                           Sponsor Vim development! ~                type  :help sponsor&lt;Enter&gt;    for information ~ ~                type  :q&lt;Enter&gt;               to exit ~                type  :help&lt;Enter&gt;  or  &lt;F1&gt;  for on-line help ~                type  :help version7&lt;Enter&gt;   for version info   which seems to suggest that I'm actually using vim.  I am accessing a remote Ubuntu Linux cluster using SSH from my PC.  I am not using a Ubuntu Linux GUI. I can get goosebumps at will, regardless of the environment. Its mostly visible on my arms, and I can feel it on my head. It requires some level of concentration to achieve this.  My questions are : what biological mechanisms are involved in doing this ? Is it common ? Is it useful ? If nonnegative $f: [0,1] \rightarrow \mathbb{R}$ has a continuous $f''$, then $\int_0^1 \Big| \frac{f''(x)}{f(x)} \Big| \,dx >4$ Some areas of the mesh are dark (Shadow artefacts) I've been modeling a hermit crab and I don't know why but some areas of the mesh are really dark on some spots, like the legs and the claws.   I hope you can help me fix it. Is linear algebra more “fully understood” than other maths disciplines? In , it was discussed how LA is a foundation to other branches of mathematics, be they pure or applied. One answer argued that linear problems are fully understood, and hence a natural target to reduce pretty much anything to.   Now, it's evident enough that such a linearisation, if possible, tends to make hard things easier. Find a Hilbert space hidden in your domain, obtain an orthonormal basis, and bam, any point/state can be described as a mere sequence of numbers, any mapping boils down to a matrix; we have some good theorems for existence of inverses / eigenvectors/exponential objects / etc..  So, LA sure is convenient.  OTOH, it seems unlikely that any nontrivial mathematical system could ever be said to be thoroughly understood. Can't we always find new questions within any such framework that haven't been answered yet? I'm not firm enough with G&ouml;del's incompleteness theorems to judge whether they are relevant here. The first incompleteness theorem says that discrete disciplines like number theory can't be both complete and consistent. Surely this is all the more true for e.g. topology.  Is LA for some reason exempt from such arguments, or does it for some other reason deserve to be called the best understood branch of mathematics? How to delete entry in Auto Complete in Microsoft Edge How do I delete an unwanted entry in AutoComplete in Microsoft Edge?  I have tried everything including highlighting with the down arrows and nothing works. How to reset evolution settings to defaults? I have not used Evolution for long time now and I would like to reset all the settings and start from scratch. How would I be able to do this? Initialize parameter of method with default value If $n = p_1^{a_1} ... p_r^{a_r}$ the set of nilpotents of $\mathbb{Z}_n$ is $(p_1 p_2 ... p_{r-1} p_r)\Bbb Z_n$ Text in Ubuntu Software Center is unreadable When I do a search in the software center this is what the results look like.    I can only see the text if I select one of them.  I tried changing themes but that didn't fix it. Remove empty directory from CVS? I'm not quite sure how this happened, but somehow a completely empty hierarchy of directories has ended up in my repository:  com/ com/companyname/ com/companyname/blah/ com/sun/ com/sun/java/ com/sun/java/jax_rpc_ri/   I think what happened was that these directories did have files in them, but then a developer realized he/she shouldn't have checked them in in the first place since these are by-products of the build process, so he/she removed the files but somehow the empty directories are left in the repository as ancient relics.  How can I remove this from CVS? The only results I seem to be able to find on google say that there shouldn't be a need to remove empty directories as CVS won't keep them around in the first place, and that the -P (prune) options to cvs update should remove them from the working directory  - which is zero help if you actually have empty directories in your repository.  A cvs remove and cvs commit doesn't seem to take care of this situation:  $ cvs remove -Rf com cvs remove: Removing com cvs remove: Removing com/companyname cvs remove: Removing com/companyname/blah cvs remove: Removing com/sun cvs remove: Removing com/sun/java cvs remove: Removing com/sun/java/jax_rpc_ri $ cvs commit com cvs commit: Examining com cvs commit: Examining com/companyname cvs commit: Examining com/companyname/blah cvs commit: Examining com/sun cvs commit: Examining com/sun/java cvs commit: Examining com/sun/java/jax_rpc_ri $ ls -l com total 24 drwxrwxr-x  2 matt matt 4096 Oct 15 14:38 CVS drwxrwxr-x  9 matt matt 4096 Oct 15 14:38 companyname drwxrwxr-x  4 matt matt 4096 Oct 15 14:38 sun   It's still there!  Does SVN have this weird behavior too? Google Cloud frequently doesn't have enough resources Vertical text (not in table) What's wrong with this demonstration?:  $$A \iff 1 = 1^1$$ $$A \implies 1 = 1^\frac{2}{2}$$ $$A \implies 1 = (1^2)^\frac{1}{2}$$ $$A \implies 1 = ((-1)^2)^\frac{1}{2}$$ $$A \implies 1 = (-1)^\frac{2}{2}$$ $$A \implies 1 = (-1)^1 = -1$$  So finaly we get  $$1 = -1$$ Does going outside of range or line of sight after casting a spell have any effect?