Embedding Bold Small Caps
How to embed fonts at compile time with pdflatex
Suppose we have (some categories and some functors such that) $F_1$ is left adjoint to $G_1$, $G_1$ left adjoint to $F_2$, $F_2$ left adjoint to $G_2$. Will $F_1$ then be equal to $F_2$ (and $G_1$ to $G_2$)?  Or can there exist arbitrarily long 'chains' of adjoint functors that do not trivialize? How to rename multiple files sequentially from command line? How to rename file as below  AS1100801000002.RAW7AGS  AS1100801001008.RAW7AH4 AS1100801002001.RAW7AH9 AS1100801003002.RAW7AHE AS1100801004009.RAW7AHT AS1100801005002.RAW7AHY AS1100801010002.RAW7AJ3   to new name  AS1.txt AS2.txt AS3.txt AS4.txt AS5.txt AS6.txt AS7.txt In Visual Studio, How do I show all classes inherited from a base class?    For example, in ASP.NET MVC there are several '' types -- and they all inherit from / implement the base class ActionResult.    It looks like unless you just 'know' that View and Json are valid ActionResult types, there is no way you can easily find this information out.    Please prove me wrong.  Is there something in the object browser that makes this easy to find out?  I'm even up for suggestions of tools outside of Visual Studio to discover this information about various classes.  For example: is there something in Resharper that will help me out? Dual boot Ubuntu (14.04) with Windows 10 Hide a Subdomain from Google/Search Engine SEO Result? What kind of matter are black holes made of? Imagine a black hole originally formed from, for example, Rubidium atoms. On the other hand, one made from, for example, Helium atoms. Will it be there any difference between the two? Or perhaps once formed it all turns into the same type of matter?  Can the "composition" of the matter-energy in the black hole be inferred somehow?  Could one say that "black hole substance" is a distinct form or state of matter different from other forms or states of matter? How to reach local computer via machine name instead of IP? Developer here prototyping a mobile app, somewhat new to mobile:   I have a simple HTTP service running (currently) on my main laptop with machine name latitude. Another laptop named vaio sharing the same WiFi network can access that service via http://latitude:8080 -- in other words, it can easily resolve the (current) IP 192.168.x.y (or whatever dynamic IP it has at that moment) of latitude somehow. Now my HTC Android phones, connected to the same WiFi network, can reach the IP address of latitude so opening in its browser http://192.168.x.y:8080 works. But I'd like to use the machine name here, too, like when I access the HTTP service from vaio, simply by typing http://latitude:8080 and have the phone resolve the current dynamic IP of latitude. This doesn't work, only get the standard browser error page: "Webpage not available".   Is there some DNS setting in Android I need to tweak? Haven't found anything from playing around with Settings, and a question like this is notoriously hard to google, too...  The One V has Android 4.0, and the One M7 has Android 4.2 in case that makes a difference.  (Note, this should work even when the Android is not USB-connected to my computers and is not acting as a WiFi Hotspot -- obviously, since it's consuming my main WiFi network anyway). Why does the Stern–Gerlach quantum spin experiment conflict with classical mechanics? My understanding of the Stern–Gerlach experiment is that neutral (0 total charge) particles are sent through a non-homogeneous magnetic field, with the expectation that the field will push that particle's path higher or lower on a detector because of the collective spin of that particle. While the detector can detect particles in a two-dimensional surface, the results of the experiment are that particles appear in only two localized areas directly above the path of the particle stream, or directly below the path of the particle stream - spin up or spin down. The conclusions from these measurements are that the particle, when measured, will always have about the same magnitude.  Why does this not follow from classical mechanical theory related to magnetism? If you shot a magnet through a similar apparatus, I would expect the magnet to be rotated to align with the magnetic field in some way which, at high enough field strengths relative to the mass of the magnet, would cause us to measure basically the same magnitude as if the magnet entered the apparatus pre-aligned with the field.  How is my explanation incorrect? Let $\{a_n\}$ be defined as follows: $$a_1 = 2, a_{n+1}=\dfrac{1}{3-a_n}$$ $n \geq 1$.   Does $\{a_n\}$  converge?    Using the monotone convergence thereom, if the sequence is both bounded below and decreasing, $\forall n\in\mathbb{N}, n\geq 1$, then we can say the sequence converges.  I'm having trouble proving that the sequence is bounded below by induction.    Claim: The sequence is bounded below by $0$.  Base Case:  $n=1$  $a_1 = 2 \geq 0$, so this holds.  Induction Step  Suppose that $a_k \geq 0$, for some $k \in\mathbb{N}$. (IH)  Prove $a_k \geq 0\to a_{k+1} \geq 0$  I have some difficulty here.  $a_{k}=\dfrac{1}{3-a_{k-1}} \geq 0$  $a_{k+1}=\dfrac{1}{3-a_{k}}$, but we know $a_k \geq 0$, but we don't know how much bigger. It could be that $a_k = 4$, and then I have $a_{k+1}=\dfrac{1}{3-4}$, which is negative, and does not confirm with my claim of being bounded below by $0$. Have I gone somewhere wrong in my induction? Please Join Us in Welcoming Our New Meta Stack Exchange Moderators! Intuition behind logistic regression Recently I began studying machine learning, however I failed to grasp the intuition behind .   The following are the facts about logistic regression that I understand.   As the basis for hypothesis we use . I do understand why it's a correct choice, however why it's the only choice I don't understand. Hypothesis represents the probability that the appropriate output is $1$, therefore the domain of our function should be $[0,1]$, this is the only property of sigmoid function I found useful and appropriate here, however many functions satisfy this property. In addition, sigmoid function has a derivative in this form $f(x)(1-f(x))$, but I don't see the utility of this special form in logistic regression.   Question: what so special about sigmoid function, and why we cannot use any other function with domain $[0,1]$? The cost function consists of two parameters ${\rm Cost}(h_{\theta}(x),y)=-\log(h_{\theta}(x))$ if $y=1, {\rm Cost}(h_{\theta}(x),y)=-\log(1-h_{\theta}(x))$ if $y=0$. In the same was as above, I do understand why it's correct, however why is it the only form? For example, why couldn't $|h_{\theta(x)}-y|$ be a good choice for the cost function?  Question: what is so special about the above form of cost function; why cannot we use another form?   I would appreciate if you could share your understanding of logistic regression. How to clean an E: drive (new Recovery drive since Windows 10 1803) on HP laptop How to sanity check a date in Java I find it curious that the most obvious way to create Date objects in Java has been deprecated and appears to have been "substituted" with a not so obvious to use lenient calendar.  How do you check that a date, given as a combination of day, month, and year, is a valid date?  For instance, 2008-02-31 (as in yyyy-mm-dd) would be an invalid date. $A$ is normal and nilpotent, show $A=0$ Given a matrix $A \in R^{n \times n}$ which is normal ($AA^H=A^HA$ where $A^H$ is hermitian of $A$) and nilpotent ($A^k=0$ for some $k$). Now we need to show that $A=0$. (This is essentially exercise 5(b) in sec. 80 on p.162 of Paul R. Halmos' Finite-Dimensional Vector Spaces.) I tried to show in the following way, we know that, $AA^H=A^HA$ pre-multiply by $A^{k-1}\implies A^kA^H=A^{k-1}A^HA$ Now, we have $0 = A^{k-1}A^HA$, since $A$ nilpotent. I am not sure how to proceed from here to show $A=0$. Can someone help me in this problem? counting with max and min restrictions $$x_1 + x_2 + x_3 + x_4 = 10$$ But $x_1 \ge 1$ and $x_2 \ge2$.  Finally, $x_1&lt;6,  x_2&lt;6, x_3&lt;6$ and $x_4&lt;6$.  I started off by finding the total amount that you can get for the original equation. That would be $C (13, 3)$. Then i calculated for the cases of numbers being greater than or equal to 5. I dont know how to incorporate $x_1\ge1$ and $x_2\ge2$. Any help?  $x_1, x_2, x_3, x_4$ are all integers that could be >= 0(But $x_1$ and $x_2$ have their own restriction). update-initramfs missing /lib/modules/4.4.0-13-generic Should I remove non-significant variables from my regression model I have run a multiple linear regression using stepwise regression to select the best model, however the best model returned has a non-significant variable. When I remove this the AIC value goes up indicating the model without the significant variable is a worse fit. Should I remove the non-significant predictor or should I leave it in as it is a better model? I have an iPhone 4s with iOS7 and somehow I see iCloud music which I haven't downloaded yet on my iOS device. How can I get rid of these, I do not need to see them. Examples proving why the tensor product does not distribute over direct products. I recently read about the result that the tensor product distributes over direct sums. I was curious if it also distributes over direct products, but google tells me it doesn't.   What are some simple counterexamples to why this property isn't true? I know that there is a natural homomorphism  $$ \left(\prod M_i\right)\otimes N\to \prod (M_i\otimes N) $$ given by $(\prod m_i)\otimes n\mapsto \prod (m_i\otimes n)$ when $M$ and $N$ are modules over some commutative ring $R$. Are there standard examples where this homomorphism is not injective/surjective and hence not an isomorphism? Understanding the -exec option of `find`