Presentation of SL$(2,\mathbb{Z}_p)$
Presentation of SL$(n,\mathbb{Z}_p)$
Problems in Creating InfoWindow on each individual circle with mouseover using Google Map API T-SQL: How to update just date part of datetime field? Do professors care about their rating on websites such as RateMyProfessor or Koofers? I am wondering if a professor is already an Associate Professor, do they still care about their reputation in the eyes of the department considering tenureship is already granted? In convex optimization, the feasible region is convex if equality constraints $h(x)$ are linear or affine, and inequality constraints $g(x) \leq 0$ are convex. Does this mean that if $h(x)$ is nonlinear, then the optimization problem is non-convex? Is there any special case where $h(x)$ is nonlinear and the feasible region is still convex? How to make a water vortex I'm fairly new to LaTeX and I want to know how to change the way sections are numbered by default. I use LyX, and there it is relatively simple to change the way an enumeration is numbered, i.e.  1 foo  a bar    i baz   But I want to know if there is a way to do this by default for sections and subsections. Can the Telekinesis spell be used to manipulate liquids? Maximal ideals of polynomial rings in infinitely many variables Let $k$ be an algebraically closed field. Nullstellensatz states that the maximal ideals of the polynomial ring $R=k[X_1,\dots,X_n]$ are precisely those of the form $\langle X_1-a_1,\dots,X_n-a_n\rangle$, with $(a_1,\dots,a_n)\in k^n$.     What if we are working with infinitely many variables, say $\{X_i\}_{i\in I}$, being $I$ an infinite set? Again, the ideals of the form $\bigl\langle\{X_i-a_i: i\in I\}\bigr\rangle$, with $(a_i)_{i\in I}\subseteq k$ are maximal (even if $k$ is not algebraically closed), but what about the converse? I would like to ask if MS Access database supports working in networks &amp; multi-user access? What is the meaning of the term "thread-safe"? Does it mean that two threads can't change the underlying data simultaneously? Or does it mean that the given code segment will run with predictable results when multiple threads are executing that code segment? C# object references and Action types What are the characteristics of a flip card in my library? Truncated 200GB table but disk space not released Why is this command not working: "ps aux | grep xscreensaver" I didn't see any hits about this on google, so I'm asking you:  I just tried to run this command in an ssh session, local is Debian Wheezy KDE, remote is Fedora 21 Gnome:  ps aux | grep xscreensaver   and this is the output:  bash:  grep: command not found...   I never seen this before, what is the cause?  I just few hours before updated the system, but didn't see any packages marked for removal. There are only two users on the system, and only me installs or removes software on it.  EDIT #1  Here is the commands and output copied,notice that the space is not there the second time:  [root@Hostname ~]# ps aux |  grep xscreensaver bash:  : command not found... [root@Hostname ~]# ps aux | grep xscreensaver bash:  grep: command not found... Redirect automatically when selecting an item from a select drop-down list This page does it the way I want it to:   But I want to find a better way using jQuery, can anyone point me to a good script that uses jQuery to accomplish this? Gravitational wave solutions to the Einstein field equations It is well known that general relativity predicts gravitational waves, but I would like to know how. What solution(s) to the Einstein field equations yield something which can be interpreted as a wave(-like) phenomenon? Effect of elementary row operations on determinant? Why is it disadvantageous in graduate admissions to have a higher degree? indicates that holders of a master’s degree are held to higher standards when it comes to graduate admissions. The stated requirements for some graduate programs () also outright exclude applicants with doctoral degrees. These seem to be saying that holding a higher degree prior to application is a disadvantage (a fatal one in the case of a PhD). This also applies to private universities: Stanford  (at least in computer science); .  I don't understand why:   If there are two applicants, Alice and Bob, who have achieved largely similar things, it seems logical that both should have a roughly equal chance of being admitted. However, based on JeffE's answer, if Alice has a Masters degree while Bob does not, it's Bob that gets admitted instead of Alice. JeffE's answer even indicates that if Alice has achieved slightly more than Bob, it's still Bob that gets admitted.  If graduate admissions is looking for students that are capable of succeeding in its program, then Alice should be more likely to succeed than Bob since she's already had some experience of graduate study. This should be even more the case if Alice already has a PhD – if she can do it once, she should be able to do it again.    JeffE's answer indicates that since Alice has had more opportunities than Bob, she should also be held to higher standard. However it should also be true that Alice has already achieved what Bob has yet to and in fact might not be able to achieve. Further, JeffE's answer seems to be saying that Alice should do the academic equivalent of financial engineering and pass her graduate-level courses &amp; thesis without getting a master’s degree even if she qualifies for it, which sounds silly.  As for applicants with PhD degrees, my first guess would be that this is because , and the university is acting in the applicant's best interests. However if this is the case, then this is effectively telling the applicant "I know what you want better than you do", which also sounds silly. UC Berkeley's requirements also seem to be saying that if someone with a CV worthy of a tenured position were to apply for a PhD student position, the university will say "no" even though it's clearly better in their best interests (in terms of research output) to say "yes".   Presumably I'm misunderstanding something because if this behavior were irrational, it would already have been changed. What am I missing?  EDIT: I wonder if things are different in programs where the student is involved in research directly without spending time on coursework? Retrieving n rows per group I often need to select a number of rows from each group in a result set.  For example, I might want to list the 'n' highest or lowest recent order values per customer.  In more complex cases, the number of rows to list might vary per group (defined by an attribute of the grouping/parent record). This part is definitely optional/for extra credit and not intended to dissuade people from answering.  What are the main options for solving these types of problems in SQL Server 2005 and later? What are the main advantages and disadvantages of each method?  AdventureWorks examples (for clarity, optional)   List the five most recent recent transaction dates and IDs from the TransactionHistory table, for each product that starts with a letter from M to R inclusive. Same again, but with n history lines per product, where n is five times the DaysToManufacture Product attribute. Same, for the special case where exactly one history line per product is required (the single most recent entry by TransactionDate, tie-break on TransactionID. Show that if $ R $ is an integral domain then a polynomial in $ R[X] $ of degree $ d $ can have at most $ d $ roots Show that if $ R $ is an integral domain then a polynomial in $ R[X] $ of degree $ d $ can have at most $ d  $ roots.  Thoughts so far:  I feel like I might be missing something here. If $ R $ is an integral domain, then so is $ R[X] $. The factor theorem gives a correspondence between roots and factors. Clearly (is this clear?) a polynomial of degree $ d $ can't have more than $ d $ irreducible factors.