When I updated my iPhone 8 to 12.2 (16E227), it broke the WiFi and now apps like YouTube can't connect and often times I can't even load apple.com in Safari. When I restart the phone then it works for about a minute. When I turn airplane mode on and off, it works for about a minute.  However my iPad with iOS 9.3.5 works flawlessly. My Samsung laptop works flawlessly. Also when I turn WiFi off on my iPhone and use cell data, it also works.
I'm trying to downgrade my iPhone from the current iOS to an older one, as per .  But every time I try, I always receive this error:     The iPhone could not be restored. This device isn't eligible for the requested build.     I have tried many times with and without DFU mode. Any ideas regarding this?
I am using Log4Net with the AdoNetAppender to log messages from a simple systray application into a SQL Server 2005 database.  I want to log the machine name along with the log message because this application will be running on multiple machines and I need to know on which one the message originated.  But, I cannot find a way to expose this information via the log4net.Layout.PatternLayout that I am using with the appender.  Is there a way to log the machine name via log4net in this manner? Implications of parity violation for molecular biology In biology, the concept of parity emerges in the context of chiral molecules, where two molecules exist with the same structure but opposite parity. Interestingly, one enantiomer often strongly predominates over the other in natural biological systems (e.g. D-glucose is ubiquitous, L-glucose is rare in nature).  In physics, it has been established that weak interactions violate parity, which (if I understand correctly) implies a physical difference between left- and right-handed systems.  This suggests to me the following questions: Does parity violation in physics affect the physical or chemical properties of chiral molecules? And does this have any implications for our understanding of biological homochirality? How to count derangements? I was going through .Suppose that there are n persons who are numbered 1, 2, ..., n. Let there be n hats also numbered 1, 2, ..., n. We have to find the number of ways in which no one gets the hat having same number as his/her number. Let us assume that the first person takes hat i. There are n − 1 ways for the first person to make such a choice. There are now two possibilities, depending on whether or not person i takes hat 1 in return:  A) Person i does not take the hat 1. This case is equivalent to solving the problem with n − 1 persons and n − 1 hats: each of the remaining n − 1 people has precisely 1 forbidden choice from among the remaining n − 1 hats (i's forbidden choice is hat 1).  B) Person i takes the hat 1. Now the problem reduces to n − 2 persons and n − 2 hats.  From this, the following relation is derived: !n = (n - 1) (!(n-1) + !(n-2))  I have a hard time understanding point B and the equation derived. I was trying to understand with an example of 4 people named A, B, C and D and the corresponding hats A, B, C and D. Everyone of them are supposed to wear any hat except their own matching hat i.e. A can wear B, C or D.  If suppose A wears B hat so we will be left with only 3 people and 3 hats. So I can understand "(n-1)!(n-1)" part but what i didn't understand is part B(marked above). Can anyone help? I'm trying to install  in VirtualBox but the installation get stuck at Do you want to install boot loader GRUB    Some background:   The VM was created from the Ubuntu 32-bit (x86) VirtualBox template The VM has 1 core + 3096 MB RAM Video memory: 32 MB PAE/NX enabled Hardware virtualization: both VTx and nested pagination enabled Graphics acceleration: disabled (both 2D and 3D) Storage: 64 GB attached to IDE virtual controller (was SATA before: makes no difference)   I've already tried all the "standard" VirtualBox procedure (PAE yes/no; SATA/IDE; no soundcard; no USB; graphics accel. yes/no).  I also tried run the Live CD in VESA mode: like this it starts, but I'd still prefer to install it. getOnClickListener() in Android views Is an expanding map on a compact metric space continuous? I got inspired by this question  to think about the following problem: Suppose you have a compact metric space $(X,d)$ and an expanding map $T:X\rightarrow X$, i.e. $d(Tx,Ty)\geq d(x,y)$ for every $x,y\in X$. Is the map $T$ then continuous? Without assuming continuity we already know that $T^n(X)$ must be dense in $X$ for any $n\geq 1$, since given $z\in X$ the orbit of $z$ must accumulate upon $z$. But showing continuity has escaped me so far. If there are counter-examples using the Axiom of Choice that also interests me. With a macro such as:  \def\naive{na\"{\i}ve}   I find that the space which I would hope to follow it, is absent. So, with  the \naive approach   I get     the naïveapproach   in the output. How do I bring back the space? Average arc length of a uniformly distributed points Suppose I have $N$ points on a unit circle. I am aware that for a uniform distribution the average angle of one point is not defined, but I want to calculate the average arc length between nearest-neighbors. I disregard arc lengths larger than $\pi$.  For $N = 2$ I am formulating the problem as: \begin{equation} \langle \Delta x \rangle = \frac 1 {\pi^2}\int\limits_0^\pi \int\limits_0^\pi  dx_1 dx_2 \, |x_1-x_2| = \frac \pi 3. \end{equation}  This answer does not make sense to me. Did I make a mistake constructing this integral?  What would happen to $N = 3$, etc? how i evaluate this integral with integration by substitution $x=\frac{\pi}{2}-t$  $$\int _0^{\frac{\pi }{2}}\:\frac{\sqrt[3]{\sin^2\left(x\right)}}{\sqrt[3]{\sin^2\left(x\right)}+\sqrt[3]{\cos^2\left(x\right)}}dx$$ AlwaysOn AG: Current Host Server - Owner Node - Primary Instance Group presentation for discrete Heisenberg group One of the most common gauges in QED computations are the $R_{\xi}$ gauges obtained by adding a term  \begin{equation} -\frac{(\partial_\mu A^{\mu})^2}{2\xi} \end{equation} to the Lagrangian. Different choices of $\xi$ correspond to different gauges ($\xi=0$ is Landau, $\xi=1$ is Feynman etc.) The propagator for the gauge field is different depending on the choice of gauge. The choice of Landau gauge forces $\partial_\mu A^\mu=0$, but I have never seen a similiar statement for the other gauges. I would like to know what constraint on the gauge field is produced by the other covariant gauges. For instance, what is the constraint on $A_\mu$ when $\xi=1,2,3,...$ etc. Is it still $\partial_\mu A^\mu=0$ or something different (it seems like it should be different)? How exactly using VB6 can I can call any Windows shell command as you would from the command-line?  For example, something as trivial as:  echo foo Ramanujan log-trigonometric integrals I discovered the following conjectured identity numerically while studying a family of related integrals.  Let's set $$ R^{+}:=  \frac{2}{\pi}\int_{0}^{\pi/2}\sqrt[\normalsize{8}]{x^2 + \ln^2\!\cos x} \sqrt{ \frac{1}{2}+\frac{1}{2}\sqrt{ \frac{1}{2}+ \frac{1}{2}  \sqrt{ \frac{\ln^{2}\!\cos x}{ x^2 + \ln^2\! \cos x}}}}\,\mathrm{d}x, \tag1 $$ $$ R^{-}:=  \frac{2}{\pi}\int_{0}^{\pi/2}\frac{1}{\sqrt[\normalsize{8}]{x^2 + \ln^2\!\cos x}} \sqrt{ \frac{1}{2}+\frac{1}{2}\sqrt{ \frac{1}{2}+ \frac{1}{2} \sqrt{ \frac{\ln^{2}\!\cos x}{ x^2 + \ln^2\! \cos x}}}}\,\mathrm{d}x. \tag2 $$ We may numerically observe with at least 500 digits of precision that $$  \begin{align} &amp; R^{+}R^{-} \stackrel{?}{=}1 \tag 3 \\\\ &amp; R^{+} \stackrel{?}{=} \sqrt[\normalsize{4}]{\ln 2} \tag4 \\\\ &amp; R^{-} \stackrel{?}{=}\frac{1}{\sqrt[\normalsize{4}]{\ln 2}}. \tag5 \end{align} $$  How can we prove it?  A version of this has been sent to Eric Weisstein, these integrals are on Mathworld as . I cannot find these strings using Transifex:      (name hidden from user)       Regards,   {site name} Moderation Team          There is  and it seems like this string does not work ok (it is translated and approved, but, unfortunately, not rendered on the site).   All of the strings are taken from Moderator Private Messages interface.   Could you please fix it? Making an elastic waistband on clothing? How can I check the existence of an element in jQuery?  The current code that I have is this:  if ($(selector).length &gt; 0) {     // Do something }   Is there a more elegant way to approach this? Perhaps a plugin or a function? Solve the recurrence $T(n) = 2T(n-1) + n$ Solve the recurrence  $T(n) = 2T(n-1) + n$ where $T(1) = 1$ and $n\ge 2$.  The final answer is $2^{n+1}-n-2$  Can anyone arrive at the solution? Rank of a Matrix Sum I have $3\times3$ matrices such that S=A+B. I know there is an inequality connecting rank of the matrices A, B and its sum S. Could you write down that here? It will be a great help for me.  Means equation  or inequality connecting rank(S), rank(A) and rank(B). How to execute .sh file on Windows? When I am trying to execute a file(name.sh) in the command line by the command  ./name.sh  , I am getting the error that:     "." is not recognized as an internal   or external command, operable or batch   file   please help me execute the .sh file