UK visa refusal because of my economic ties in the Philippines
UK visa refusal on V 4.2 a + c (and sometimes 'e')
How can I make a directory on the desktop?  I tried cd /desktop command but it gives an error  no such file or directory.  What's the correct command? Prove that $d(n)\leq 2\sqrt{n}$ In Waclaw Sierpinski's book Elementary Theory of Numbers on page 168 there is the following exercise:  "Exercises. 1. Prove that for natural numbers $n$ we have $d(n) \leq 2\sqrt{n}$," where $d(n)$ is the number of divisors of n.  As a hint right below is given: "The proof follows from the fact that of two complementary divisors of a natural number $n$ one is always not greater than $\sqrt{n}$.  I understand the hint but I don't know how it can be used to prove $d(n)\leq 2\sqrt{n}$.  Complementary divisors are pairs of divisors that when multiplied gives the number that is to be divided. For example the number $120$ has the complementary divisors: \begin{align*} &amp; 1, 120 \\ &amp; 2, 60 \\ &amp; 3, 40 \\ &amp; 4, 30 \\ &amp; 5, 24 \\ &amp; 6, 20 \\ &amp; 8, 15 \\ &amp; 10, 12 \\ \end{align*} How do you prove that $d(n) \leq 2\sqrt{n}$? Should we write “allow” or ”allows” in “require that the class allow[s]”? Can you explain to me whether I should or should not use ‑s at the end of the  verb allow in this sentence?     This function requires that the container class allow[s] random access   The sentence in the book I read wrote allow without ‑s. However, the container class is a third-person singular, so the ‑s must be required. Is that right? Does $\sum \limits_{n=1}^\infty\frac{\sin n}{n}(1+\frac{1}{2}+\cdots+\frac{1}{n})$ converge (absolutely)? I've had no luck with this one. None of the convergence tests pop into mind.  I tried looking at it in this form $\sum \sin n\frac{1+\frac{1}{2}+\cdots+\frac{1}{n}}{n}$ and apply Dirichlets test. I know that $\frac{1+\frac{1}{2}+\cdots+\frac{1}{n}}{n} \to 0$ but not sure if it's decreasing.  Regarding absolute convergence, I tried:  $$|\sin n\frac{1+\frac{1}{2}+\cdots+\frac{1}{n}}{n}|\geq \sin^2 n\frac{1+\frac{1}{2}+\cdots+\frac{1}{n}}{n}=$$  $$=\frac{1}{2}\frac{1+\frac{1}{2}+\cdots+\frac{1}{n}}{n}-\frac{1}{2}\cos 2n\frac{1+\frac{1}{2}+\cdots+\frac{1}{n}}{n}$$  But again I'm stuck with $\cos 2n\frac{1+\frac{1}{2}+\cdots+\frac{1}{n}}{n}$. Assuming it converges then I've shown that $\sum \sin n\frac{1+\frac{1}{2}+\cdots+\frac{1}{n}}{n}$ doesn't converge absolutely. Minimize the sum of distances between two point and a circle Let's $A$,$B$ and $O$ be random point in a plane, such that they are not colinear. Let's $c$ be a circle centered on $O$, such that points $A$ and $B$ are outside of it. Find a point $X$ that lies on the circle $c$ and the sum $AX + BX$ is minimal.  First I tried to minimize the function:  $$f(x,y) = \sqrt{(A.x - x)^2 + (A.y - y)^2} + \sqrt{(B.x - x)^2 + (B.y - y)^2}$$ with  constraint $$g(x,y) = x^2 + y^2 - r^2 = 0$$  By moving $O$ to $(0,0)$ and do the same with $A$,$B$ so the relative distance will not change.  But these works when we know the coordinates of $A$,$B$ and the radius of the circle. Yet this isn't the right way because the problem is to construct that point.  Later I tried to approach using geometry.  The smallest distance from the point $A$ to the circle is the intersection of the circle $c$ and the ray $OA$, this is the same for $B$. Then we construct circles centered on $A$ and $B$ that are tangent to $c$. If the two circle intersect we'll get a common point for the both $A$ and $B$ and the distance will be minimal. Using computer I find the point X should be somewhere around the intercetion of the circle $c$ and the ray from $O$ to the new point.   Sometimes the optimal point differs just a bit and also this method fails when the two circles do not intersect each other I (as a middle-school student) was wondering how virtual particles even conserve energy of the entire system? I don't mean just the particle's energy, but conservation with respect to the surroundings?  Let me explain more, Einstein proved that $E = mc^2$ and equivalently, we can say $m = \frac{E}{c^2}$ . We however know mass causes curvature in space-time (gravity well). Now that statement being completely valid we can use Quantum Fluctuation, implying energy and time can be related by the relation:  $\Delta{E}\Delta{t}\approx\frac{\hbar}{2}$ and by that simple relation we can make the following points:   As the energy increases, the time allowed to be "borrowed" decreases, before it gives it back to the universe. As time increases, the energy allowed to be "borrowed" decreases.    These are completely satisfactory points I've made, I believe.  Now, I have read that the vacuum is filled with constantly bubbling virtual particles that get created from the energy "borrowed" by the above relation and is destroyed again, which satisfies the energy conservation laws.   This seems to imply that  in the short time the virtual particle exists, they must have a very small mass which is: $m_{1} = \frac{\Delta{E}}{c^2}$ and using basic classical mechanics rather than GR (for sake of simplicity) we calculate that the gravitational force mediated by this short-lived virtual particle;  $F_{g}= G\frac{m_1 * m_x}{r^2}$   where $m_x$ is an particle\mass in question. Nevertheless since we know the force set upon an object moves the object in a direction, we can say it would increase its kinetic energy by this factor: $F_g = \frac{1}{2}mv^2$ which is equal to $G\frac{m_1 * m_x}{r^2} = \frac{1}{2}mv^2$.  Surely, this implies that every time quantum fluctuations happen, energy of real-particles\masses increases and therefore violates energy conservation, but what prevents this violation from taking place?  If virtual particles are not really present and interact with objects like I thought, how can Hawking radiation (currently a large concept in black hole physics) then be accepted in physics community? AutoScroll on chat exchange doesn't work in chrome 61 I updated the chrome to version 61, and the auto-scroll stopped working, it is necessary to scroll down the page manually. The problem does not occur in the previous version or in firefox.  Also, the reply icon no longer working when the message replied to is not in the current chat page. (Middle click still works and opens the link in new tab.) Terminal returns not found for most commands Mac OSX How can I create a Windows bootable USB stick using Ubuntu? I'd like to create a Windows bootable USB stick, but I don't have a Windows machine with me at the moment to do so. How could I achieve the same using Ubuntu? I was wondering how to list all the hardware info in my computer?   Both terminal and GUI solutions please. Is there a single utility to monitor most hardware's working status? Just like some software in Windows?   Thanks and regards! Prove that $f(x)$ is irreducible iff its reciprocal polynomial $f^*(x)$ is irreducible. This is what I'm trying to prove:     Let $f(x)\in\mathbb{Q}[x]$ and $\deg(f(x))&gt;1$. Prove that $f(x)$ is irreducible in $\mathbb{Q}[x]$ iff its reciprocal polynomial $f^*(x)$ is irreducible in $\mathbb{Q}[x]$.    Note: The reciprocal polynomial $f^*(x)=x^nf(1/x) \in \mathbb{Q}[x]$, where $n=\deg f$.   So my thoughts are to prove the contrapositive, i.e. $f^*(x)$ is reducible iff $f(x)$ is reducible.   So to prove the ($\Rightarrow$) direction I assume that $f^*(x)=g(x)h(x)$, so I get that $g(x)h(x)=x^nf(1/x)$ which implies $f(1/x)=(1/x^n)g(x)h(x)$. I want to say this somehow makes $f(x)$ reducible but I am unable to proceed as $f(1/x)\notin \mathbb{Q}[x] $. I thought about substituting $y=1/x$, which gives $f(y)=y^ng(1/y)h(1/y)$, but I am unable to show that this is irreducible in $\mathbb{Q}[y]$. If I could, then it would be irreducible in $\mathbb{Q}[x]$ since $\mathbb{Q}[y]\cong \mathbb{Q}[x]$   Any suggestions or hints will be appreciated. Difference between staticmethod and classmethod We are developing a C# application for a web-service client. This will run on Windows XP PC's.  One of the fields returned by the web service is a DateTime field. The server returns a field in GMT format i.e. with a "Z" at the end.  However, we found that .NET seems to do some kind of implicit conversion and the time was always 12 hours out.  The following code sample resolves this to some extent in that the 12 hour difference has gone but it makes no allowance for NZ daylight saving.  CultureInfo ci = new CultureInfo("en-NZ"); string date = "Web service date".ToString("R", ci); DateTime convertedDate = DateTime.Parse(date);               As per :     UTC/GMT Offset       Standard time zone: UTC/GMT +12 hours   Daylight saving time: +1 hour   Current time zone offset: UTC/GMT +13 hours     How do we adjust for the extra hour? Can this be done programmatically or is this some kind of setting on the PC's? Let $X$ be a metric space. Prove that if every continuous function $f: X \rightarrow \mathbb{R}$ is bounded, then $X$ is compact.  This has been asked before, but all the answers I have seen prove the contrapositive. Realistically, this may be the way to go, but is there way to exhibit an unbounded continuous function (under the assumption $X$ is not compact) without appealing to results beyond introductory real analysis (e.g., the solution I've seen involves the Tietze Extension theorem)?  Because we're working with metric spaces, it's clear that the assumption that $X$ is noncompact (towards proving contrapositive) will lead us to extract a sequence of points in the space with no convergent subsequences. But how can we infer the existence of an unbounded continuous on the space knowing only about some sequence of points in this space (without using anything too advanced)? Is it correct to use that/which in the relative clause when it is referring to the place as an object pronoun? Help, I cannot get my test code coverage higher than 75%! Code below 12.04 GPU lockup I was able to install Ubuntu 12.04 using the alternative version of the image, (64 bit) but when I start the system it tells me the GPU  locked up, and instead presents a text only screen.  I understand that this site is not for bug reports, but at the same time, I know that there are some versions of the installer than have to be compatible with my graphics card (Nvidia GTS 360M).  I assumed that the mere fact that the alternative installer ran was an indication that I could get some sort of graphical interface running after the install.  Is there some way of getting some type of graphical interface running on my machine? Even better would be is there a way to get the rest of the system running as normal (i.e. GPU up and running)?  If an internet connection is required to download driver support or something similar, directions for how to configure a wireless connection with WPA2-Personal protection from the text-only interface (bash).  Any help would be appreciated.  Note: I was able to find  which tells me that the card is supported.  Note 2: In the install software stage of the install, I was unable to install anything (no internet connection)  Update: The exact error message is [8.591394] [drm] 0000:01:00.0: GPU Lockup - switching to software fbcon  Update 2: If I try to install with the regular version of Ubuntu, the screen goes staticy. This also happens if I install with Wubi (distasteful I know) and then try to use Ubuntu.  Update 3: I've tried xforcevesa, nomodeset and xforcevesa nomodeset as my wubi boot options.  Update 4: Thanks to jokerdino, I can now connect to the internet, so internet tools would now be a possibility. One post with multiple questions or multiple posts? I want to ask several questions about the same problem domain but each question is independent from the others. Should I put all the questions in a single post or should I split them and send multiple posts? WinForms DataGridView font size How do I change font size on the DataGridView? We are small team which working on car racing game but we don't know about licensing process for branded cars like Nissan, Lamborghini, Chevrolet and etc.   Do we need to buy any licence for using real car brand names, models, logos,... or we can use them for free?  Second option we think about using not real brand with real models is it possible? If someone have experience with that, fell free to share it.  Any information about that is welcome.