For what values of ''$a$'' , does this Improper Integral converges? For which values of  ''$a$'',   does the integral $$\int_{0}^{\infty} \frac{\sin x}{x^a}\;\mathrm dx$$ converges?  I have shown that  $$\left| \int_{0}^{\infty} \frac{\sin x}{x^a}\;\mathrm dx \right|\le \lim_{n\to\infty} \int_{0}^{n} \frac 1{x^a}\;\mathrm dx,$$ which converges if $a &gt; 1$. Are there other values of $a$ for which the integral converges?
For what values of $\alpha$, does this integral converge? For what values of $\alpha&gt;0$ this integral converges $$\int_0^{\infty} \frac {\sin x}{x^{\alpha}}dx $$
How many ways can the average of n dice be a? How to limit execution time of a function call? There is a socket related function call in my code, that function is from another module thus out of my control, the problem is that it blocks for hours occasionally, which is totally unacceptable, How can I limit the function execution time from my code? I guess the solution must utilize another thread. In Windows 7, How to query times, when the computer was locked? Is there a way to get a list of the following times:  whenever windows is locked (using windows+l combo)  whenever windows is unlocked in the past week?   I've tried poking in the event log, to no avail. Many thanks! In what order does WordPress load plugin files? In what order are plugins loaded in WordPress?   And within a particular plugin's folder, what order is followed for loading? Shrink the database only up to its initial size which is set after creating database In SQL server every database has a property Initial Size (MB) which can be seen in properties of database in SSMS. By default it will be 3 MB for mdf and 1 MB for ldf file.  So now if create a new database then it will be set to default size(i.e 3 MB for mdf and 1 mb for ldf file). But after creating the database  I change the initial size to some other value say For mdf 10 MB and ldf 5 MB.(In real-time some database administrator may want to change initial after creating database)  But now if shrink the database it will shrink beyond the initial size I have set after creation(consider that no data is there in database otherwise it will shrink to its actual content size). It will shrink till the initial size it had during creation of database(i.e 3mb for mdf and 1 mb for ldf). I was expecting to shrink till the initial size which I have set(i.e 10 mb for mdf and 5mb for ldf). Can it be possible to do? If possible then how?  In some article i saw like dbcc SHRINKFILE can be used to shrink beyond initial size and dbcc SHRINKDATABASE cannot shrink beyond initial size. But I want to shrink only till the initial size to which I have set.  Note: I know that shrink is bad and should not be done.But I want to know how it can be done? If sql server considers only the initial size set during creation of database then what is the use of setting the initial size after creating database?  EDIT:  From microsoft shrink related article: Using DBCC SHRINKDATABASE you can not shrink database below its initial size.  My question is Can I change the initial size of existing database itself?  EDIT:  I have about 5 sql server instance. All the database where created with default size of 3 mb for data and 1 mb for log(about 3 years back). Now all the databases are in the range of 100-1000 mb. I wont shrink the database normally as it is not good practice. But some database grow more than 10 GB(mdf file itself as i insert so much data in it). So when database is large I will shift unimportant and old contents from this database to another server as it is not required in that server for me. So that database size reduces from 10 GB to 1 GB. Now the remaining 9 Gb left unused. Now I  want to specify database size to be reduced to 2 GB so that i will get 1 GB free space(Also 2 Gb is the ideal size for this database), Which can be used to avoid autogrowth till next 1 Gb of data is filled. Also i have set 100 MB auto-growth for this kind of large database which has more writes. So instead of specifying size as 2 GB in shrinkfile command,if it was possible to change initial size to 2 GB (which shrink considers) then it would have been better. During this database creation there was no plan about size ,autogroth etc. As it was created about 3 years back. 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For example if my object has a Boolean modifier and an Array modifier, which both refer to an empty or another object (in the Array modifier there is for example an Object offset you can specify). Would it be possible to select all those object with one click? Thanks. Correct user names when tracking /etc/ in git repository and committing as root We use git to track changes in /etc/ on our servers.  Administrators work as root when changing files in /etc/, and thus their commits have author  root &lt;root@machinename&gt;   This is not very satisfying since you cannot see which admin actually did the change.  What can we do to get the real admin names in the git log? I don't think that keeping a local clone of the repository is feasible since we often change interatively until something works, and a change-commit-push-seeError-repeat cycle would not help here. Bounded sequence in a metric space I have an iMac, connected to the Internet via Ethernet, and an iPhone 4. 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(10k only) indicate that the top sites for the last 90 days are:   Superuser - 564 - 5% rejected ServerFault - 278 - 10% rejected Tex - 157 - 13% rejected DBA - 144 - 2% rejected Sharepoint - 127 - 1% rejected Programmers - 126 - 26% rejected CodeReview - 100 - 3% rejected Meta.SO - 81 - 18% rejected Wordpress - 75 - 14% rejected Webmasters - 58 - 8% rejected   All these migrations for sites out of the list required a flag and a moderator to process it.  This is just extra work for the mod team!  If we had the top 5 destinations by volume as the 5 options, we would have had a net savings of 160 flags to be processed.  I suspect we will actually see these numbers change quite a bit if it's easier for users to put questions in the appropriate spot without moderator intervention.  Can we have a review of the migration path list based on migration volume?  Think of the flags! How do I loop through a MySQL query via PDO in PHP? I'm slowly moving all of my LAMP websites from mysql_ functions to PDO functions and I've hit my first brick wall.  I don't know how to loop through results with a parameter.  I am fine with the following:  foreach ($database-&gt;query("SELECT * FROM widgets") as $results) {    echo $results["widget_name"]; }   However if I want to do something like this:  foreach ($database-&gt;query("SELECT * FROM widgets WHERE something='something else'") as $results) {    echo $results["widget_name"]; }   Obviously the 'something else' will be dynamic. Idiomatic batch processing of text in Emacs? Regex to get string between curly braces