Félix's or Félix'?
Which singular names ending in “s” form possessives with only a bare apostrophe?
When is the past perfect exactly needed? Combinations of sets raised to the power of a prime modulus: $\binom{p^{\alpha}-1}k \equiv (-1)^k \pmod p$ What happens if a Rainbow Servant takes levels in Mystic Theurge? When a Rainbow Servant hits level 10 they gain access to all nondomain Cleric spells. All spells that do not appear on any other spell list they have are cast as Divine spells. This means that, if they have the skills and have learned 2nd level spells, they qualify for the Mystic Theurge Prestige Class.  But what happens when you actually start to take levels in it? The text says:     When a new mystic theurge level is gained, the character gains new spells per day as if he had also gained a level in any one arcane spellcasting class he belonged to before he added the prestige class and any one divine spellcasting class he belonged to previously.   What it does not say however, here or elsewhere, that these classes have to be different classes. Do you get one level in Wizard/Warmage/whaever for being an Arcane caster, then ANOTHER level for being a Divine caster as well? The text for the Rainbow Servant says the following:     Such spells are cast as divine spells if they don’t appear on the sorcerer/wizard or bard spell lists.   So it comes down to these questions:   Does being able to cast Divine spells qualify you as a Divine Caster, or is there more to it than that? If it is, what happens when you take levels in Mystic Theurge like this? Do you go up one level or two? What happens if this means you go over 20th caster level? Do you keep gaining spell slots like a level 20+ character, or does something else happen? SSL certificate for a public IP address? I just tried buying a Comodo Positive SSL but it was rejected due to not supporting a public IP address, but instead they only support a domain name.  Does anyone know any SSL certificate provider that supports public IP address instead of a domain name?  My company has a dedicated server hosted with a web hosting company, which is used for running a bugtracker for multiple projects (for multiple clients). Since it's only used for a bugtracker, we don't need a domain name (our clients access it by typing the public IP in their browser). Trig sum: $\tan ^21^\circ+\tan ^22^\circ+\cdots+\tan^2 89^\circ = \text{?}$ As the title suggests, I'm trying to find the sum $$\tan^21^\circ+\tan^2 2^\circ+\cdots+\tan^2 89^\circ$$ I'm looking for a solution that doesn't involve complex numbers, or any other advanced branch in maths. The solution can involve techniques such as induction, telecoping, etc, but preferably only ideas from precalculus, e.g. trig identities, polynomials, etc.  EDIT: I know that the sum is a rational number. Significance contradiction in linear regression: significant t-test for a coefficient vs non-significant overall F-statistic OK, I've been having weird problems for the last 1/2 hour trying to  on StackOverflow, and I keep getting this result (on Firefox 3.6)     The connection was reset      The connection to the server was reset while the page was loading.         The site could be temporarily unavailable or too busy. Try again in a few        moments.   If you are unable to load any pages, check your computer's network        connection.   If your computer or network is protected by a firewall or proxy, make sure        that Firefox is permitted to access the Web.      The problem seems to occur when I try to post some code with 'd--- table' in it, where 'd---' is replaced by the word drop.  I cannot post the following 3 lines, in either SO or this site, if they include the well-known SQL statements DROP.  stat.executeUpdate('d--- table if exists people;'); stat.executeUpdate('create table people (name, occupation);'); prep = conn.prepareStatement(...     'insert into people values (?, ?);');   test again:  'dro* table' 'drop ball' drop the table drop fable drop    t*ble droptable   drop a table  The evil words for me are "drop" and "table"... how come you guys can post? :(  edit: Could someone please suggest another online site that is not stackoverflow that is a quick way to try out a POST request of a text field?  UPDATE: Never mind. I don't know what the answer is, but the same problem occurs on Google's website. So it's not stackoverflow. Now to go to my IT Dept... What is the formula for percent of frame filled at a specific distance and focal length? How can I access and process nested objects, arrays or JSON? Is there any actual written dialog for the astromech droids? When R2-D2 and BB-8 converse in The Force Awakens for example, is there any written record of what the two characters were saying to each other?  I mean actual dialog, if it exists, and not something like ”BB-8 beeps excitedly”. How should one interpret the comparison of means from different sample sizes? Take the case of book ratings on a website. Book A is rated by 10,000 people with an average rating of 4.25 and the variance $\sigma = 0.5$. Similarly Book B is rated by 100 people and has a rating of 4.5 with $\sigma = 0.25$.   Now because of the large sample size of Book A the 'mean stabilized' to 4.25. Now for 100 people, it may be that if more people read Book B the mean rating may fall to 4 or 4.25.   how should one interpret the comparison of means from different samples and what are the best conclusions one can/should draw?    For example - can we really say Book B is better than Book A. I want to change my thesis topic (to the extent that the ethos is still in tact) but my advisor does not agree. What can I do? I am doing a phd where my aim is to solve a problem A which is very interesting. My supervisor has got a lot of connections in a technology B and he claims to be an expert in B. I came to this group because of these accomplishments. But soon I realized that B is not really a great technology for A.   So in my phd proposal I proposed a method which encompasses B but is more general (say R). Now I realize that I do not want to use B at all because my preliminary results are not encouraging. In fact, I am inclined to use E as a base technique which does not have any impact on R.  But my supervisor, who is interested in only publishing in B  and frowns upon everything else (it was a nightmare to convince him to let me work on R) is dead against it. He says that he is an expert in B and his vision of the group is not inclined with me trying other things.  There are other professors in my university who have worked in E and could collaborate but my supervisor won't collaborate with people from outside his kingdom. I also know professors from outside my university who could help me if needed. I could knock the doors of school committee in order to  help me but that would create a lot of problems as my supervisor wields a lot of power and influence everywhere.    Another query is, is it ethical to collaborate with people outside the university (of course after letting my supervisor know) for my PhD work. My Masters supervisor would be happy to help me out.  Edit: After looking at comments, I am thinking that after all, it is MY PhD. Yes, I have spent 1.5 years, but 1.5 years is left. Why should I spend any moment of my life on something I find to be not exciting, particularly less exciting because it is forced on me. And in those 1.5 years I learnt to write well and also learnt 'A' which is important. Its not total waste. My supervisor has his agenda, and why should I give up mine to make him happy? His vision is fine, but he does not have the right to force his vision on me. How to directly prove that $M$ is maximal ideal of $A$ iff $A/M$ is a field? An ideal $M$ of a commutative ring $A$ (with unity) is maximal iff $A/M$ is a field.  This is easy with the correspondence of ideals of $A/I$ with ideals of $A$ containing $I$, but how can you prove it directly?  Take $x + M \in A/M$.  How can you construct $y + M \in A/M$ such that $xy - 1 \in M$?  All I can deduce from the maximality of $M$ is that $(M,x) = A$. Equals(=) vs. LIKE When using SQL, are there any benefits of using = in a WHERE clause instead of LIKE?  Without any special operators, LIKE and = are the same, right? Setting controller variables not reliable from apex:commandButton I'm trying to set a variable inside my controller via an actionFunction, which is called by some Javascript, which is initially called by either by an actionPanel (with styleClass='btn') or a commandButton.  If the caller is the actionPanel then the variable updates reliably. However with the commandButton I can see the updated value flash briefly before reverting to its previous value. Maybe one out of every six clicks of the button actually causes the new value to stick. Sometimes it can take a dozen or more tries, regardless of click frequency.  Can someone please explain what's going on here?  PAGE  &lt;apex:page controller="MyController"&gt;     &lt;apex:form &gt;         &lt;apex:outputPanel id="panel"&gt;             &lt;apex:outputText value="MyString = {!MyString}"/&gt;             &lt;apex:actionFunction name="SetString" rerender="panel"&gt;                 &lt;apex:param name="param1" value="" assignTo="{!MyString}"/&gt;             &lt;/apex:actionFunction&gt;             &lt;script&gt;                 function JSetString() {                     SetString('{!MyString}' + '.');                 }             &lt;/script&gt;             &lt;apex:outputPanel onclick="JSetString()" styleClass="btn"&gt;                 Grow {!MyString} (works)             &lt;/apex:outputPanel&gt;             &lt;apex:commandButton onclick="JSetString()" value="Grow {!MyString} (unreliable)" rerender="panel"/&gt;         &lt;/apex:outputPanel&gt;     &lt;/apex:form&gt; &lt;/apex:page&gt;   CONTROLLER  global class MyController {      public MyController() { MyString = 'hello'; }      public String MyString {get;set;} } I see a lot of questions comparing full frame (e.g EF for Canon, FX for Nikon) and crop lenses (e.g. EF-S for Canon, DX for Nikon) but I can't find the answer to what would be the differences between the photos taken with say a 50mm f/1.4 EF and EF-S lenses both used with   same APS-C sensor sized camera same ISO same f/1.4 f-stop same focal length same shutter speed   What would be the resulting differences in the photos? Which one would   be brighter than the other due the EF-S lens concentrating the light more? no that's wrong. Both put the same amount of light from the same FoV on the sensor. have greater depth-of-field? neither less problems towards the edges? generally the full frame more lens flare? generally the full frame lens unless there is, or you provide more shading anything else? not really, unless you start down the road of which one is typically of better build quality.   Edit: Added the answers from what seems to be the general consensus from the multiple answers and comments.  Results: My desire to buy a fast medium-high quality lens compatible with both full frame and crop camera's doesn't have to be hampered by the APS-C sensor size of my current camera.  This means I'm willing to part with more money to get a higher performance/quality lens as the performance/quality will be useful now and when I upgrade my camera.  Though reading reviews of some full frame lenses with short focal lengths, look out, as some are really only made to perform well on crop cameras even though they fit on a full frame camera and will give you a full frame picture, the edge quality is very bad. No continuous function switches $\mathbb{Q}$ and the irrationals I can’t for the life of me figure out where to use a and where to use the — and where there is no article at all. Is there a simple rule of thumb to memorize?   The standard rule you always hear:     “If a person knows which item you are talking about then use "the"   . . . doesn’t clear things up for me, as I have no idea whether or not they know. How much Valyrian steel is there that is unused for link making and why aren't people making weapons out of it? Conjugacy Class in a matrix group with columns of standard basis I want to find the conjugacy classes of this group: $$G=\{(a_1,a_2,a_3):a_i=\pm e_j\}\subset GL_3(\mathbb C)$$ I know that $S_3$ is one of the subgroups of this group, so I can check which elements of $S_3$ continues to be conjugate in our group, I know that in $Z(G)$ there is two elements $I,-I$. I know that I have to check the diagonal matrices on which ones are conjugate, but I don't know how to finish and find the others conjugacy class of this group, and I don't Know how to find the number of the elements of the conjugacy class. I'll be thankful for help