I had applied for UK visa recently and it got refused
UK visa refusal on V 4.2 a + c (and sometimes 'e')
What is the size of a boolean variable in Java? Can any one tell the bit size of boolean in Java? Clear up confusion about the meaning of entropy So I though, and was told, that entropy is the amount of disorder in a system. Specifically the example of heat flow and it flows to maximize entropy. To me this seemed odd. This seemed more ordered to me, from two things (hot and cold) to one thing (lukewarm).   So as I have read today on wikipedia        In recent years the long-standing use of term "disorder" to discuss   entropy has met with some criticism.[20][21][22]      When considered at a microscopic level, the term disorder may quite   correctly suggest an increased range of accessible possibilities; but   this may result in confusion because, at the macroscopic level of   everyday perception, a higher entropy state may appear more homogenous   (more even, or more smoothly mixed) apparently in diametric opposition   to its description as being "more disordered". Thus for example there   may be dissonance at equilibrium being equated with "perfect internal   disorder"; or the mixing of milk in coffee being described as a   transition from an ordered state to a disordered state.      It has to be stressed, therefore, that "disorder", as used in a   thermodynamic sense, relates to a full microscopic description of the   system, rather than its apparent macroscopic properties. Many popular   chemistry textbooks in recent editions increasingly have tended to   instead present entropy through the idea of energy dispersal, which is   a dominant contribution to entropy in most everyday situations.    So what this is saying basically many people mistake the macroscopic outcome of entropy in the same manner as I have above. Seemingly two dissimilar things combining and becoming one.   They say to understand it microscopically. But this still is odd to me, take for example the particles in a box, when they come to thermal equilibrium they are said to have the most entropy they can within their system (from wiki again)     Entropy – in thermodynamics, a parameter representing the state of   disorder of a system at the atomic, ionic, or molecular level; the   greater the disorder the higher the entropy.[7]   What is disorder in the molecular sense I guess is my question. When the particles all come to thermal equilibrium they all seem to be uniform, which I equate with ordering.  I feel disorder in the molecular sense would be fast moving particles, making a mind boggling amount of interactions with each other. Such as in a hot gas, hot gas seems super disordered, but put cold gas in thermal contact with it, let them come to thermal equilibrium, and now they are more ordered!? What does *~ mean? At the end of a makefile I saw   rm -f *~ *.class   I understand the *.class, but what's *~? Can anyone provide me with (or point me to) real life gravitational lensing data that I can plug in to the first equation on this page (the standard lensing equation):   together with the luminous mass and distance to the galaxy(s).  I've looked for papers online and have not found any simple data that can be readily plugged in to the equation (I am not familiar with the details of how exactly the lensing is measured and have gotten lost in the mountains of data in the papers).  Thanks Cancelled UK visa on entry Implementing a PIVOT query How can I pivot the following SELECT statement:           SELECT sc.CID,                 sc.CodeName     as OverviewText,                 scRAG.CodeName  as RAGStatusText             FROM StatusCode      sc LEFT OUTER JOIN ProjectOverview po               ON sc.CID          = po.ProjectOverviewCID              AND po.ProjectId    = 180 LEFT OUTER JOIN StatusCode      scRAG               ON po.RAGStatusCID = scRAG.CID           WHERE sc.SCID         = 18   Such statement yields the result set that follows:  CID OverviewText    RAGStatusText --- ------------    ------------- 153 Cost            Green 154 Requirements    Yellow 155 Schedule        NULL 156 Technical       NULL 157 Testing         NULL   But, I want it to return one single row with 10 values, as shown bellow:   ----------------------------------------------------------------------------------------------  | Cost | Green | Requirements | Yellow | Schedule | NULL | Technical | NULL | Testing | NULL |  ----------------------------------------------------------------------------------------------   Can I pivot on CID? Display bare HTML from hook_menu() What would be the cleanest way to route URLs to functions and return only the HTML output from those functions (a.k.a. the menu callback)?  If I use hook_menu() the string that's returned will be the HTML within the rest of the site. I want the page to display only the string returned from the menu callback.  Should I use drupal_set_header() in the same way drupal_json() does? Is this not inefficient having fully bootstrapped Drupal, and then changing the header at the last minute?  I want the fastest code path possible since this is going to be for widgets on external sites.  I could start with a standalone .php file and bootstrap what I need but the hook_menu routing is nice.    How should you do this? Is there a quicker way to turn on WiFi Hotspot? is there a way to automate (or at least reduce the number of steps) to turn on or turn off the WiFi hotspot on my Galaxy 3.  I have to    unlock  press the menu button  press settings press More Settings Tethering and portable hotspot Slide portable hotspot on. Let $(X,\mathcal{M},\mu)$ be a measure space and $\{f\}$ be a sequence of functions on $X$, each of which is integrable over $X$. Show that $\{f_n\}$ is uniformly integrable if and only if for each $\varepsilon \gt 0$, there is a $\delta \gt 0$ such that for any natural number $n$ and measurable subset $E$ of $X$, if $\mu(E) \lt \delta$, $$ \left|\int_E f_n~d\mu\right| \lt \epsilon.$$     I think one direction $(\Rightarrow)$ is clear. Since $f_n$ being uniformly integrable imply that for every $\varepsilon\gt 0,~\exists \delta \gt 0$ such that for any $E\in \mathcal{M},~\mu(E)\lt \delta$, $\int_E |f_n|~d\mu$ for every natural $n$. But then   $$ \left|\int_E f_n~d\mu\right|\le \int_E|f_n|~d\mu \lt \varepsilon.$$    Any suggestions for the other direction?   Edit:  Following Davide's suggestions, I have   $$ \begin{align*} \int_E |f_n|~d\mu &amp; \le \int_{E\cap [f_n \ge 0]} f_n~d\mu + \int_{E\cap [f_n \lt 0]} (-f_n)~d\mu\\ &amp; = \left| \int_{E\cap [f_n \ge 0]} f_n~d\mu \right| + \left| \int_{E\cap [f_n \lt 0]}f_n~d\mu \right| \\ &amp; \lt \varepsilon + \varepsilon = 2\varepsilon. \end{align*} $$ Is it possible to use a spell scroll with a spell that requires a bonus action to cast? The DMG contains spell scrolls (on page 200), with the following rule:     If the spell is on your class's spell list, you can use an action to read the scroll and cast its spell without having to provide any of the spell's components.   This is all well and good for spells with a casting time of 1 action (which admittedly is most of them), but for spells with a bonus action casting time, how is it supposed to work?  Does it require:   Both an action and a bonus action?  Just an action? Just a bonus action? Something else I haven't thought of?   In case it needs saying, I'm not interested in speculation here - only RAW-based answers or explicit statements of developer intent should apply. Why is a Hyperplane called a "Hyper"plane? I just had this curious question. In other fields, the word "hyper" is actually used to refer to something which is "over; beyond; above" as defined by Google. An example of such terms would be Hyperglycaemia, defined by Wikipedia as:     a condition in which an excessive amount of glucose circulates in the blood plasma.   Or Hypersonic, defined by Google as:     relating to speeds of more than five times the speed of sound.   So, my question is, what would be the motive to give a Hyperplane such a name when it is defined as :     a subspace of one dimension less than its ambient space I need a little hint in a proof on convergence of a sequence. The problem I have is: Suppose $(x_n)$ is a monotone decreasing sequence of real numbers such that $\sum x_n$ converges, prove that:  $$\lim_{n \to \infty} nx_n=0$$  My idea is: proving this fact aims to prove that given $\epsilon &gt;0$ there's some natural $n_0 \in \mathbb{N}$ such that if $n &gt;n_0$ we have $|nx_n|&lt;\epsilon$.  Now, I know that $\sum x_n$ converges, so that given $\epsilon'&gt;0$ there's some $k_0 \in \mathbb{N}$ such that if $k &gt; k_0$ we have:  $$\left|\sum_{i=1}^{k}x_i - S\right|&lt;\epsilon'$$  Where $S = \sum x_n$. Now, since $(x_n)$ is monotone decreasing we know that we must have $x_1 &gt; \cdots &gt; x_k$ so that the sum of all $x_i$ should be less or equal to $k x_k$. So I know that I have:  $$\left|\sum_{i=1}^{k}x_i - S\right|\leq\left|\sum_{i=1}^{k}x_i\right|+|S|\leq|kx_k|+|S|$$  I feel that the proof will come from this, however I'm stuck at this point. Can someone give just a little hint on how to proceed from here?  Thanks very much in advance for your help. My task is to write a precise mathematical statement that "the sequence $(a_n)$ does not converge to a number $\mathscr l$"  So, I have my definition of a convergent sequence: "$\forall\varepsilon&gt;0$ $\exists N\in\Bbb R$ such that $|x_n -\mathscr l|&lt;\varepsilon$ $\forall n \in \Bbb N$ with $n&gt;N$"  Would the correct negation of this be "$\forall\varepsilon&gt;0$ $\exists N\in\Bbb R$ such that $|x_n -\mathscr l|&gt;\varepsilon$ $\forall n \in \Bbb N$ with $n&gt;N$"?  It doesn't seem that this is the answer as the next part of my task is to prove that a sequence is divergent using my formed proof, but it'd be difficult to do since it's a general proof of divergence and not just a proof that $(a_n)$ doesn't converge a specific number $\mathscr l$  Perhaps I should find a prove that $(a_n)$ tends to $\pm\infty$? This is more simple but it does not include monotone sequences such as $x_n:=(-1)^n$.  Can someone assist me with this task? All comments and answers are appreciated. Array with labeling columns Why can't I suggest edits on SE meta sites? When you click &quot;edit&quot; on a meta site as a non-edit-privileged user, the error message appears:  Suggested edits are not allowed on non-tag-wiki posts on meta sites.  Right as I was going to post this as a possible bug, I finally found  which says that per-site Metas don't have suggested edits by-design because it's &quot;not needed&quot;. However, I've been participating a lot over at  where there is a lot still to be figured out in terms of site guidelines.  The Meta is one of the most active I've seen and a lot of the questions are really trying to gather community-built suggestions.  So maybe more of those need to be Community Wiki, but it still brings me to ask why don't per-site-metas &quot;need&quot; suggested edits? Adding bounty: The more betas I participate in, the more I don't get this. What gifts would be welcome for a Swedish host family? Facebook: Ways to preserve image quality of uploaded images? Prove that $p \in \mathbb{R}[x]$ can be represented as a sum of squares of polynomials from $\mathbb{R}[x]$ Holomorphic function has at most countably zeros Let $f$ be holomorphic in a domain $U$, then $f$ has at most countably zeros.  How can I prove this statement? I have seen it in Sheng Gong  explicitly, but without any indications. How to copy files into /usr/local/? (permission denied) I'm still a little new to Ubuntu and was wondering how I can copy files, in this case Aptana Studio, to /usr/local/ without being denied.   Is there a way to do it in terminal? Or a way to allow myself permission?  I should add that I am using 10.10 Desktop edition, not server.