Latex what symbol looks like letter I, Greek letter Iota, but is neither?
How to look up a symbol or identify a letter from a math alphabet or other character?
Changing text applied when duplicating file in Finder When duplicating files in the finder, OS X attaches a space followed by 'copy' to the file name. This can lead to some file alphabetizing problems and the copies may appear out of order (not directly subsequent to the original). Is there a way to change the appended text? I would prefer that it says '_1' or _copy. Thanks. Select groups based on number of unique / distinct values Solving recurrence relation. Recurrence How does one solve the matrix equation $AX+XB=C$ for $X$? It doesn't seem too difficult. I tried many times but failed.  I'm an adult student... I am now vexed about Gilbert Strang - An Introduction to Linear Algebra. I don't even understand a single word in Wikipedia: . If you have ever use some nice workable materials or lecture notes? You can generously upload and share the links of the lecture notes and assignments. Different subjects/ topics are welcome, as long as you deem they are nice and workable.   The problem origins from a system of diff equation, using undetermined coefficients (matrix) to find the particular solution. Try $y_p=X\begin{pmatrix}   e^{\alpha t} \\ e^{\beta t} \end{pmatrix}$  $\dot{y}+Ay=C\begin{pmatrix} e^{\alpha t} \\ e^{\beta t}\end{pmatrix}$   $\dot{y_p}=X\begin{pmatrix} \alpha &amp; 0 \\ 0 &amp; \beta \end{pmatrix} \begin{pmatrix}e^{\alpha t} \\ e^{\beta t}\end{pmatrix}$  substitute $\dot{y_p}$ and $y_p$ into the original differential equation..  $X\begin{pmatrix} \alpha &amp; 0 \\ 0 &amp; \beta \end{pmatrix}+AX=C$ Luggage, connecting flights and customs question for USA I'm flying to the USA, from Australia, through LAX and catching a connecting flight 6 hours later, think it's the same ticket, booked all at once. I've never traveled before, and I'm wondering what happens with customs.   Do I collect my bags at LAX so they can be checked? Do I have to check in at every airport or is it all done when I catch the first flight? There are 4 flights on my itinerary. Functional Equation (no. of solutions): $f(x+y) + f(x-y) = 2f(x) + 2f(y)$ Find all the functions $f\colon\mathbb{Q} \to \mathbb{Q}$ such that $f(x+y) + f(x-y) = 2f(x) + 2f(y)$, for all rationals $x,y$. Is "there're" (similar to "there's") a correct contraction? Q: "Do you have any juice?"   A: "Yes, there's some in the fridge."   Sounds perfectly fine to me, but:     Q: "Do you have any towels?"   A: "Yes, there's some in the closet."   Does not.  I asked for towels - plural - so wouldn't "Yes, there're some in the closet," in which there are is turned into a contraction be the correct way to say it?  Spellcheck, however, doesn't like "there're", and I think I'm the only person I've ever heard use the word "there're".  Even folks who I know say "there are" shorten it to "there's" when possible.  Am I saying it wrong, or are both forms acceptable? How does entropy depend on location and scale? The entropy of a continuous distribution with density function $f$ is defined to be the negative of the expectation of $\log(f),$ and therefore equals  $$H_f = -\int_{-\infty}^{\infty} \log(f(x)) f(x)\mathrm{d}x.$$  We also say that any random variable $X$ whose distribution has density $f$ has entropy $H_f.$  (This integral is well-defined even when $f$ has zeros, because $\log(f(x))f(x)$ can be taken to equal zero at such values.)  When $X$ and $Y$ are random variables for which $Y = X+\mu$ ($\mu$ is a constant), $Y$ is said to be a version of $X$ shifted by $\mu.$  Similarly, when $Y = X\sigma$ ($\sigma$ is a positive constant), $Y$ is said to be a version of $X$ scaled by $\sigma.$ Combining a scale with a shift gives $Y=X\sigma + \mu.$  These relations occur frequently.  For instance, changing the units of measurement of $X$ shifts and scales it.  How is the entropy of $Y = X\sigma + \mu$ related to that of $X?$ Let $a,b,c\in \Bbb R^+$ such that $(1+a+b+c)(1+\frac{1}{a}+\frac{1}{b}+\frac{1}{c})=16$. Find $(a+b+c)$ Will the silhouette formula change depending on the distance metric? I am using Silhouette width to compute the best value for k in k-means. As I am performing document clustering, I am calculating the values of a and b as follows in Python:  a = distance(data[index], centroids[clusters[index]], metric=metric, p=p) b = min([distance(data[index], c) for i,c in enumerate(centroids) if i != currentindex]) score = float(b - a) / max(a, b) if max(a, b) &gt; 0 else 0.0   The original formula from the  is the following:    I am using a cosine similarity measure to compute the distances and was wondering if this formula needs to be changed or it can be left as is. In the above snippet of code, the function distance computes the cosine similarity metric. I just finished a test as part of a job interview, and one question stumped me, even using Google for reference. I'd like to see what the StackOverflow crew can do with it:  The memset_16aligned function requires a 16-byte aligned pointer passed to it, or it will crash. a) How would you allocate 1024 bytes of memory, and align it to a 16 byte boundary? b) Free the memory after the memset_16aligned has executed.  {        void *mem;    void *ptr;     // answer a) here     memset_16aligned(ptr, 0, 1024);     // answer b) here     } Why does mathematical convention deal so ineptly with multisets? What is the name of the depiction of concentration with raised eyebrow called? What is the importance of eigenvalues/eigenvectors? (Revised) Prove that $\phi$ is a group homomorphism and find the kernel. Quoting " Let $\phi : \Bbb Z \rightarrow \Bbb Z$ be given by $\phi(n) = 7n$. Prove that $\phi$ is a group homomorphism. Find the kernel, and the image of $\phi$."   My understanding:  Part 1:   Given $n,m \in \Bbb Z$, let's check that $\phi(n+m) =\phi(n)+\phi(m)$  $$\phi(n+m) = 7(n+m) = 7n + 7m = \phi(n)+\phi(m)$$  Therefore as the group operation in $\phi$ is preserved, $\phi$ is a group homomorphism.  Part 2 (revised):   $\phi$ is one-to-one as:  $\space \space \phi (n) = \phi(m) \Rightarrow 7n =7m \Rightarrow n=m  $. We also know that $\phi(e)=e$ by the property of homomorphism. Therefore, no other object than $0$ in the domain can map to $0$ in the codomain. It follows that: $$\ker(\phi)=\{ x \in \Bbb Z : \phi(x)=e\}=\{e\}$$   Part 3 (revised):  I claim that the only possible image-elements of $\phi$ are the multiples of $7$ in $\mathbb Z$ denoted $7\mathbb Z$.   To prove this I have to show that Im$(\phi) \subset 7 \Bbb Z$ and that $ 7 \Bbb Z \subset $ Im$(\phi)$.  Proving Im$(\phi) \subset 7 \Bbb Z$ :      $\forall y \in $ Im$(\phi)$ such that $  y =\phi(x)$ where $x \in 7 \Bbb Z$. It follows that $y \in 7 \Bbb Z$, therefore Im$(\phi) \subset 7 \Bbb Z$   Proving $ 7 \Bbb Z \subset $ Im$(\phi)$:   $\forall y \in  7\Bbb Z$ such that $  y =7x$ where $x \in \phi(x)$. It follows that $y \in \phi(x)$, therefore $ 7 \Bbb Z \subset $ Im$(\phi)$.   Any input to my understanding is much appreciated. How can one have a mini table of contents for the current chapter appear just after the chapter name listing all sections of that chapter? Is it possible to programmatically change connectedApp settings in production? Background: I have a requirement to make it so that an SFDC connected app defaults/is super easy to set to Admin Users are Pre-authorized instead of All users may self-authorize. This setting is important to make this app work and we have historically have had problems with admins not configuring this setting correctly.  Here is a quick history on what I have tried to do to get the isAdminApproved set to "true":   Directly, via xml definition (doesn't get honored) Directly via apex code (doesn't get honored)  (ended up being more pain than what it was worth and was told that it wouldn't work in prod because of security restrictions) Indirectly via a connected-app connected service to make a metadata API call: works in a scratch org but not in prod, which I assume is because it is a managed package. This would occur when an Admin clicks on a button, not from a post-install script.   Details on what I mean by it isn't working in prod: When I try to do a readMetadata call on my connectedApp objects that are in my managed package, the response comes back as [{\n    'fullName': None\n}] instead of with the metadata configuration of my connected app.  Here is a sequence diagram of what I am trying to do in #4 right now:    My question is this: Am I on a fool's errand, where this is impossible to do? ...Or is there a way to set a connected app (in a managed package that I publish) to Admin Users are Pre-authorized without making the admin just do it themselves directly in the settings? A set with a finite integral of measure zero? Stein's lemma condition (Apologies if I break some conventions, this is my first time posting!)  I am working on proving Stein's characterization of the Normal distribution: for Z $\sim N(0,1)$ and some differentiable function $f$ with $E[|f'(Z)|] &lt; \infty$, $$E[Zf(Z)] = E[f'(Z)]$$ Writing the LHS expression in integral form and integrating by parts, I eventually obtain: $$E[Zf(Z)] = \frac{1}{\sqrt{2\pi}} \left[ -f(z) \cdot \exp \left\{ \frac{-z^2}{2} \right\} \right] \Bigg|_{-\infty}^{\infty} + E[f'(Z)]$$ Now I need to show that the first expression on the right hand size is zero. Intuitively, this seems clear because of the exponential term, but I am having trouble explicitly applying the condition on $f'$ to prove this rigorously. Any ideas? Why do I get "Required key not available" when install 3rd party kernel modules or after a kernel upgrade?