Why meshes lose material when joined?
Texture disappear on joining
Are there any disadvantages to always using nvarchar(MAX)? Given a fraction:  $$\frac{a}{b}$$  I now add a number $n$ to both numerator and denominator in the following fashion:  $$\frac{a+n}{b+n}$$  The basic property is that the second fraction is suppose to closer to $1$ than the first one. My question is how can we prove that?  What I have tried:  I know $\frac{n}{n} = 1$ so now adding numbers $a$ and $b$ to it would actually "move it away" from $1$. But I cannot understand why $\frac{a}{b}$ is actually farther away from $1$ than $\frac{a+n}{b+n}$.  Why is that? What does it mean to add a number to both the numerator and denominator? In Unity3D, how do I create an efficient scratch card effect? I want to create a scratch-card-like effect in new Unity UI's new Image tag.  I know it's possible with setPixels, but that's prohibitively expensive on mobile devices.  Something like this:    I'd like the user to be able to drag on any part of the image to "scratch off" the top layer and reveal the content underneath it.  How can I do this? This is an exercise in some textbooks.     Let $E$ be an algebraic extension of $F$. Suppose $R$ is ring that contains $F$ and is contained in $E$. Prove that $R$ is a field.   The trouble is really with the inverse of $r$, where $r\in R$. How to prove that $r^{-1}\in R$, in apparent lack of a characterization of $R$.  It occurred to me to use the smallest field containing $R$ ($R$ is easily shown to be an integral domain), that's the field of quotients, and proving that it's $R$ itself, but I don't really know how to proceed.  A not-too-weak, not-too-strong hint will be much appreciated.   Beware $ $ Readers seeking only hints should  beware that there is now a complete answer. Integration of $e^{ax}\cos bx$ and $e^{ax}\sin bx$ I am curious about the proof of these two integrations. It would be great if you could point me in the right direction : $ \int{e^{ax}\cos({bx})dx}= \dfrac{e^{ax}}{a^{2}+b^{2}}[a\cos(bx)+b\sin(bx)] + C $ &amp; $ \int{e^{ax}\sin({bx})dx}= \dfrac{e^{ax}}{a^{2}+b^{2}}[a\sin(bx)-b\cos(bx)] + C $ Suppose I have a node in the shape of a circle. How can I make its border thicker?   \node[circle, draw=blue!80, inner sep=0pt, minimum size=12pt] (1) at (0,0) {1}; "Goose"–"geese" vs. "moose"–"moose" Why is it that the plural of goose is geese but the plural of moose is moose? The same goes for mouse and house. Mouse becomes mice, yet house becomes houses. There is a classic problem:  Suppose that $X_1,\ldots,X_n$ form an i.i.d. sample from a uniform distribution on the interval $(0,\theta)$, where $\theta&gt;0$ is unknown. I would like to find the MLE of $\theta$.  The pdf of each observation will have the form: $$ f(x\mid\theta) =  \begin{cases} 1/\theta\quad&amp;\text{for }\, 0\leq x\leq \theta\\ 0 &amp;\text{otherwise}. \end{cases} $$ The likelihood function therefore has the form: $$ L(\theta) = \begin{cases} 1/\theta^n \quad&amp;\text{for }\; 0\leq x_i \leq \theta\;\; \text{for all }i,\\ 0 &amp;\text{otherwise}. \end{cases} $$ The general solution is usually that the MLE of theta must be a value of $\theta$ for which $\theta \geq x_i$ and which maximizes $1/\theta^n$ among all such values.   The reasoning is that since $1/\theta^n$ is a decreasing function of $\theta$, the estimate will be the smallest possible value of $\theta$ such that $\theta\geq x_i$.  Therefore, the mle of $\theta$, $\hat{\theta}$, is $\max(X_1,\ldots,X_n)$.  Here, I do not understand why we cannot just differentiate the likelihood function with respect to theta and then set it equal to $0$?  Thanks! Title says it all I looked for a proof on this site but couldn't find one.  Prove if $f$ is analytic on $D$ and $g$ is analytic on $\Omega$ containing the range of $f$ show $g(f(z))$ is analytic.  The statement seems obvious but I can't seem to be able to prove it. Editing old questions Identifying selected feature using PyQGIS? What is the name of the operation $v^T H v$? To find out how something is called is the one thing I don't know how to use Google for.  If I have a vector $v$ and a symmetric matrix $H$, then the operation $v^T H v$ gives me some sort of projection of the matrix $H$ on the vector $v$. For example if $H$ is the Hessian, the operation gives me the second derivative in the direction of $v$.  What is the name of this operation? Would I be scrutinized at the border for traveling to the US twice in a quick succession? I am a British citizen visiting the USA in early August for a two week vacation with friends. After the holiday I'm returning to my home in the UK for three weeks. After that I will return to the USA and will be working for my British employer under the Visa Waiver Program for a period of 80-85 days.  I have read already that there is technically no problems with this under ESTA rules, but should I limit this working period to a shorter time frame (e.g. 70 or so days) so that it does not negatively affect the decision made by the POE officer? Ideally I would love to be over in the states for the near-full 85 day period.  Any advice or previous experiences anyone can offer?  Some clarifications: As confirmed by the immigration attorney, as I am employed by my UK employer, it will be regarded as a business trip, the important part being that I will be working officially as a consultant for my UK employer just overseas for the allotted 85 or so days How to reset evolution settings to defaults? I have not used Evolution for long time now and I would like to reset all the settings and start from scratch. How would I be able to do this? Segmentation fault on large array sizes Deriving the conditional distributions of a multivariate normal distribution We have a multivariate normal vector ${\boldsymbol Y} \sim \mathcal{N}(\boldsymbol\mu, \Sigma)$. Consider partitioning $\boldsymbol\mu$ and ${\boldsymbol Y}$ into  $$\boldsymbol\mu = \begin{bmatrix}  \boldsymbol\mu_1 \\  \boldsymbol\mu_2 \end{bmatrix} $$ $${\boldsymbol Y}=\begin{bmatrix}{\boldsymbol y}_1 \\  {\boldsymbol y}_2 \end{bmatrix}$$  with a similar partition of $\Sigma$ into $$  \begin{bmatrix} \Sigma_{11} &amp; \Sigma_{12}\\ \Sigma_{21} &amp; \Sigma_{22} \end{bmatrix} $$ Then, $({\boldsymbol y}_1|{\boldsymbol y}_2={\boldsymbol a})$, the conditional distribution of the first partition given the second, is  $\mathcal{N}(\overline{\boldsymbol\mu},\overline{\Sigma})$, with mean $$ \overline{\boldsymbol\mu}=\boldsymbol\mu_1+\Sigma_{12}{\Sigma_{22}}^{-1}({\boldsymbol a}-\boldsymbol\mu_2) $$ and covariance matrix $$ \overline{\Sigma}=\Sigma_{11}-\Sigma_{12}{\Sigma_{22}}^{-1}\Sigma_{21}$$  Actually these results are provided in Wikipedia too, but I have no idea how the $\overline{\boldsymbol\mu}$ and $\overline{\Sigma}$ is derived. These results are crucial, since they are important statistical formula for deriving Kalman filters. Would anyone provide me a derivation steps of deriving $\overline{\boldsymbol\mu}$ and $\overline{\Sigma}$ ? Thank you very much! From a paper via Schneier on Security's  (emphasis mine):  In the case of AES-128, there is no known attack which is faster than the 2128 complexity of exhaustive search. However, AES-192 and AES-256 were recently shown to be breakable by attacks which require 2176 and 2119 time, respectively. While these complexities are much faster than exhaustive search, they are completely non-practical, and do not seem to pose any real threat to the security of AES-based systems. In this paper we describe several attacks which can break with practical complexity variants of AES-256 whose number of rounds are comparable to that of AES-128.  Is the implication here that AES-192 is stronger than AES-256? If so, in simple terms, how is that possible?  The attack exploits the fact that the key schedule for 256-bit version is pretty lousy -- something we pointed out in our 2000 paper -- but doesn't extend to AES with a 128-bit key.  Again, in simple terms, what does that mean? In practice, does this mean I should drop AES-256 in favor of its 128-bit counterpart, like Schneier recommends in the comments?  That being said, the key schedule for AES-256 is very poor. I would recommend that people use AES-128 and not AES-256. Is just after your PhD a good time to switch your research area? I am finishing my PhD soon. The area in which I pursued my PhD is very challenging as I was only able to publish couple of papers even after spending many years. I want to switch into other research are due these reasons   to attract more students  to be comfortable to do research (along with teaching, I should be able to do research)   Even though I like the research I am doing right now, I seem to be isolated in my university. If ten students join my university for a PhD, hardly one student takes this area. My research area is not like machine learning or deep learning etc, so researchers of my domain are also not that much interested in my work.   The thing is I can work different research area but: Is this the right time? I am heading to a post-doc and learning a new area will probably take several months. Although my switch is not 180 degree, I am still worried. I need to have a list of all available view modes for an entity type so I can use it as the #options in a select field.  Any ideas? Thanks What happens to waves when they hit smaller apertures than their wavelenghts? I was wondering this for quite a long time now. Let's say you have a water wave (like ripples, not the ones you see during tsunamis) with wavelength 10 m. Imagine you put a boundary with an opening of 1 m. Will diffraction be observed? According to my research, no. But, then, what would be seen?