That was thw refusal letter i got .. been traveling to the uk since 2011 and all through my travel history have never stayed this long.. i own my company an i stayed dis long cause of marital issues.. came bach home as soon as everything was ok. pls house kindly advice on what to do. thanks in anticipation
I plan to attach my 2014 and 2015 annual leave letters to prove I was on leave, and a letter from my sales manager who was in charge of the business during my vacation.  I intend to explain all my sources of income in additional letter because the ECO calculations of my income were different from mine.   How else can I improve my new application?
Pausing a long running program in the terminal? Is there a keyboard key combination that I can use to pause a program running in the terminal? In case it matters, I don't intend to run anything else inside that terminal while the program is paused. I just want to pause the program execution, and resume it later. How can I do this? Method overloading in Objective-C? Bevel is not symmetrical Torque direction meaning I apologize if this question is dumb, but I've looked all over for a straightforward answer, and either I can't find one or either the terms are too complex for me to understand. I have only a rudimentary knowledge of Mechanics, but I do understand basic Linear Algebra. So torque, mathematically, is the cross product of the radial distance vector and a force vector. This cross-product gives another vector that is orthogonal to both vectors and it points either outside or towards the &quot;page&quot; (in the context of a two-dimensional diagram). Assuming this is correct, I do not understand what it pointing in or out means. Does it even have a physical, intuitive meaning? The best answer I've been able to come up with is that it's just a mathematical convention with no actual physical meaning, meant to provide a framework within which operations between torque vectors, such as addition and subtraction, make sense. Am I correct or way off the mark here? Help proving the primitive roots of unity are dense in the unit circle. I'm having difficulty understanding how to prove that the primitive roots of unity are in fact dense on the unit circle. I have the following so far:  The unit circle can be written $D=\{x\in\mathbb{C}:|x|=1\}$. The set of primitive $m$-th roots of unity is $A_m=\{\zeta_k:\zeta_k^m=1,\zeta_k\text{ is primitive}\}$.  Hence, the set of all primitive roots $A$ is given by the union of $A_m$ over $m=1,2,3,\ldots$. But I can't seem to get started on how to prove that $A$ is dense in $D$. pure code formatting, to enhance a question, is impossible (without 2k rep) Just ran the latest batch of updates on 20.04 (Xubuntu), and now I'm getting a GRUB error: symbol 'grub_calloc' not found  I'm dropped into the 'grub rescue' shell, but have no idea what to do there that might be useful. To me, 'symbol not found' implies some sort of build error with the grub package, but I don't really know how grub works. I noticed that this update also included 'firmware', not sure if that could be related. Is my best bet just to boot from a live CD and see if I can roll back the update to grub somehow? Edited to add: OK, thanks to lots of people ! Here's what I think I now understand.  On 'non-UEFI' systems, grub is installed in two separate parts. The first, most basic, part is the part that is started on bootup. But for most of it's functionality, it needs the second part. These parts must be aligned - neither part must require any functionality from the other part which is not actually there. The visible, run-time problem occurs when these parts are not aligned, and the function grub_calloc is not supplied. It's not 100% clear to me if grub_calloc belongs in the second, larger part or the first. I would have expected the second, but the grub build system is a work of considerable art, so I don't know :).  The root cause of the problem is that the grub update has not ensured that both parts have been updated. Ideally, failure to do this should cause grub installation to fail, and the system should be reverted to a safe state. This does not happen. This is actually still a bit of a mystery to me. All that the update needs to do by default is put each part where the current parts are, because obviously that worked. If the install locations/drives are configuration - driven, and one of these locations can't be reached, then somehow a mismatch has arisen between that configuration data and reality. This might not show up as a problem as long as no new dependency was introduced between the parts.   All flavours of solution involve reinstalling grub to ensure that the two parts are aligned. It's not actually necessary to go back to the previous version ( although that will work ), because it's not the grub runtime per se that is broken. There are numerous ways to achieve this, depending on your environment, but running the Boot-repair live disk worked for me. It may be useful, for the purpose of avoiding such a misalignment in future, to ensure that the grub installer on your system is configured to install to the correct devices. This update resolves some important bugs (). If you have reverted grub to resolve this problem, be aware that you are exposed to these issues. I use ${\dot \hat E}$ to put a hat and dot on top of an E simultaneously. However, an error occurs. Get display resolution from the command line for Linux Desktop I'm looking for a method of reporting display resolution. I want to set up scripts to launch rdesktop, and I want to launch it on several machines with different resolutions, so I want a way to dynamically determine it. I normally write using the American English forms, but for some particular words, I tend to naturally write it in the British manner (like with the word favourite rather than favorite).  Is it wrong to mix both styles? If not *wrong*, does it looks weird? When do I use the PHP constant "PHP_EOL"? When is it a good idea to use ?  I sometimes see this in code samples of PHP. Does this handle DOS/Mac/Unix endline issues? Where was this picture taken (screensaver on LG Oled TV)? Can someone please tell me where this picture was taken? Recursive bash script to collect information about each file in a directory structure How do I work recursively through a directory tree and execute a specific command on each file, and output the path, filename, extension, filesize and some other specific text to a single file in bash. How to prove that the radial basis function is a kernel? How to prove that the radial basis function $k(x, y) = \exp(-\frac{||x-y||^2)}{2\sigma^2})$ is a kernel? As far as I understand, in order to prove this we have to prove either of the following:   For any set of vectors $x_1, x_2, ..., x_n$ matrix $K(x_1, x_2, ..., x_n)$ = $(k(x_i, x_j))_{n \times n}$ is positive semidefinite. A mapping $\Phi$ can be presented such as $k(x, y)$ = $\langle\Phi(x), \Phi(y)\rangle$.   Any help? How to prove that eigenvectors from different eigenvalues are linearly independent How can I prove that if I have $n$ eigenvectors from different eigenvalues, they are all linearly independent? I need to prove that the language $\mathscr L=\{0^n \big|\text{n is the square of a natural number}\}$ is non regular using the pumping lemma   My try:  $\mathscr L=\{\overbrace{\epsilon}^{0^2},\overbrace{0}^{1^2},\overbrace{0000}^{2^2},\overbrace{000000000}^{3^2},\overbrace{0000000000000000}^{4^2},\dots\}$  Suppose that $\mathscr L$ is regular so $\exists$ a word '$x$' with length of at least $n$   $|x|\geq n $ such that  $(1)\,\,\,|uv|\leq n$  $(2)\,\,\,|v|\geq 1$  $(3)\,\,\,uv^iw \in \mathscr L$  Now, let as choose the word $\color{blue}{x=0^{n^2}}$  $|x|\geq n$ so we can use $(1)-(3)$  $x=\underbrace{000000\dots}_{n^2\text{ times}}$  $x=uv0^kw=\underbrace{uv0^k}_{\text{n zeros   }}\overbrace{w}^{n^2-n\text{ zeros }}$  Let as choose $\color{blue}{i=??}$      I'm difficult choosing the word '$\color{blue}x$' and choosing  $\color{blue}i$ to come to contradiction with the lemma multiplicative group of infinite fields Book recommendation on the history of PDE/ODE? Java Generics: List, List, List Can someone explained, as detailed as possible, the differences between the following types?  List List&lt;Object&gt; List&lt;?&gt;   Let me make this more specific. When would I want to use  // 1  public void CanYouGiveMeAnAnswer(List l) { }  // 2 public void CanYouGiveMeAnAnswer(List&lt;Object&gt; l) { }  // 3 public void CanYouGiveMeAnAnswer(List&lt;?&gt; l) { } This question is related to a couple of other questions ( and ) relating to some material that I teach in sampling theory.  Consider the critical points of the  defined as follows.  The value $t_{n-1, \alpha/2}$ is a function of $n$ defined by the implicit equation: $$\frac{\alpha}{2} = \frac{1}{\sqrt{(n-1) \pi}} \cdot \frac{\Gamma(\tfrac{n}{2})}{\Gamma(\tfrac{n-1}{2})} \int \limits_{t_{n-1, \alpha/2}}^\infty \Big( 1+ \frac{r^2}{n-1} \Big)^{-n/2} dr.$$ Normally we treat the input $n&gt;1$ as an integer, but it is possible to extend the treatment to consider it a real value (since the T-distribution is well-defined for non-integer degrees-of-freedom).  I'm trying to come up with a (relatively simple) proof that this critical point value is decreasing in $n$, but I seem to be making quite a mess.  Differentiation using Leibniz rule gets part way, but it quickly becomes a bit of a mess.  Consequently, I would like to solicit proofs of this result --- this simpler the better. Question: How do you prove that this critical point is strictly decreasing in $n$?