I encountered the following version of \mathcal{H} and like it a lot:    This is slightly different from the usual one from Computer Modern font:     I have done some search and tried different fonts, e.g., mtpro2, mathptmx, and mathpazo etc., but could not find the first \mathcal{H}.  Here is my question: Is there a way that I could get the first one? Is it some sort of "old \mathcal symbols"?  Any help would be highly appreciated.  PS: I have found an example for the source of the first \mathcal{H} .  I downloaded the *.tex file of that pdf, and here are all the packages used there:  \documentclass[11pt]{article}   \usepackage{xcolor}   \definecolor{labelkey}{rgb}{0,0.08,0.45}   \definecolor{refkey}{rgb}{0,0.6,0.0}   \definecolor{Brown}{rgb}{0.45,0.0,0.05}   \definecolor{dgreen}{rgb}{0.00,0.40,0.00}   \definecolor{dblue}{rgb}{0,0.08,0.45}    \usepackage{amsmath}   \usepackage{amssymb}   \usepackage{theorem}   Of course, typing \mathcal{H} in this setting yields the second one, but somehow the \mathcal{H} in the link looks like this:     So I guess there must be something "weird" going on here.  PS:  I often see the first one in papers published by Springer, e.g.,  (it appears right in the title)   I also saw the first one \mathcal{H} in this question .
Why, with Springer's  svmono template, do the letters written with the \mathcal font change? It seems that \mathcal becomes \mathscr.  Edit: Look at this image:    With the svmono template \mathcal returns the first alphabet and not the (classical) latter.  Here the packages I use in my document:  \documentclass[envcountsame,envcountchap]{svmono}  \usepackage{subfiles} \usepackage[utf8]{inputenc}  \usepackage{mathptmx} \usepackage[bottom]{footmisc} \usepackage{microtype} \usepackage{stmaryrd}    \usepackage{amsmath} \usepackage{courier} \usepackage{mathrsfs}  \usepackage{amssymb}  \usepackage[all,cmtip]{xy} \usepackage{faktor} \usepackage{graphicx} \usepackage{mathdots} \usepackage[colorlinks={true},linkcolor={blue},citecolor={blue}]{hyperref} \usepackage[frame,width=15truecm,height=23.5truecm,center]{crop}   With this settings I have the above strange behavior of \mathcal.
I was skimming through  by Cosma Shalizi (in particular, section 2.1.1 of the ), and was reminded that you can get very low $R^2$ even when you have a completely linear model.  To paraphrase Shalizi's example: suppose you have a model $Y = aX + \epsilon$, where $a$ is known. Then $\newcommand{\Var}{\mathrm{Var}}\Var[Y] = a^2 \Var[x] + \Var[\epsilon]$ and the amount of explained variance is $a^2 \Var[X]$, so $R^2 = \frac{a^2 \Var[x]}{a^2 \Var[X] + \Var[\epsilon]}$. This goes to 0 as $\Var[X] \rightarrow 0$ and to 1 as $\Var[X] \rightarrow \infty$.  Conversely, you can get high $R^2$ even when your model is noticeably non-linear. (Anyone have a good example offhand?)  So when is $R^2$ a useful statistic, and when should it be ignored? I block everything Google, including Google APIs, as I don't like to to have Google tracking all of my usage on the Internet. Is there any way to use Stack Exchange without Google APIs?  I usually am browsing with Windows 7 and Firefox, but of course not Firefox with StackExchange. A weaker Axiom of Infinity? For realism should I use the maximum number of Subsurf levels? I was wondering if I always need to use the maximum value of the options from the elements of "Add Modifier". For example, do I need to use the view 6 in Subdivision surface? I know it depends of what we are trying to achieve, but we all want the same. Make something look the most believable. So do you always use the maximum value Blender offers? I often need to select a number of rows from each group in a result set.  For example, I might want to list the 'n' highest or lowest recent order values per customer.  In more complex cases, the number of rows to list might vary per group (defined by an attribute of the grouping/parent record). This part is definitely optional/for extra credit and not intended to dissuade people from answering.  What are the main options for solving these types of problems in SQL Server 2005 and later? What are the main advantages and disadvantages of each method?  AdventureWorks examples (for clarity, optional)   List the five most recent recent transaction dates and IDs from the TransactionHistory table, for each product that starts with a letter from M to R inclusive. Same again, but with n history lines per product, where n is five times the DaysToManufacture Product attribute. Same, for the special case where exactly one history line per product is required (the single most recent entry by TransactionDate, tie-break on TransactionID. Get specific GPS location somehow on windows 8 How do I "parent" objects? Showing that $f_0 (x_1, \ldots, x_m) \mathrm tr A =\displaystyle{ \sum_{i=1}^n} f_0(x_1, \ldots, Ax_i,\ldots, x_m)$ Question:  Consider $f: (-\epsilon, \epsilon) \to \mathbb R^{m^2}$ a differentiable path of matrices $m \times m$ such that $f(0) = I_m$ and the function $g: I \to \mathbb R$ is defined by $$g(t) = \det f(t)$$  Show that $g'(0) = \mathrm{tr} \,a $ (trace of the matrix $a$), where $a = f'(0)$.   Attempt:  First we use that $\det f(t) = \det (f_1(t), \ldots, f_m(t)) $, where $f_i$ is the $i$-th row of the matrix $f(t)$ $m \times m$. Considering the operator $': \mathbb R^m \to \mathbb R^m$, $f(t) \mapsto f'(t)$  With this in mind $$\begin{align}g'(t) = \det'f(t) &amp;= \sum_{i=1}^{m} \det (f_1(t),\ldots,f'_i(t),\ldots, f_m(t)) \\&amp;\underbrace{=}_{(*)}\det(f_1(t), \ldots, f_m(t))\, \mathrm tr f'(t) \end{align}$$  For $t = 0$ we have   $$\begin{align}g'(0) &amp;=\det(e_1, \ldots, e_m) \,\mathrm tr f'(0) \\&amp;= 1 \dot\, \mathrm tr \,a \\&amp; = \mathrm tr \, a\end{align}$$  I'm trying to come up with a proof using the fact that $\det$ is a $m$-linear form.   In order to prove $(*)$ I need the following equality, which according to this  holds.   If $A: V \to V$ is a linear operator and $f_0$ is a alternated $m$-linear form, such that $f_0 (e_1, \ldots, e_m) = 1$ then   $$f_0 (x_1, \ldots, x_m) \mathrm tr A = \sum_{i=1}^m f_0(x_1, \ldots, Ax_i,\ldots, x_m) $$  Could someone give a proof to this? I'm usually running many different StackExchange sites in Firefox using tabs (using ReloadEvery to update every 5 minutes).  Right now to check for activity, I have to manually click on the tab to see if the envelope is lighted.  How about making the icon on the tab i.e. the title text change in some way, denoting that you have activity on the page?  We already add a message count for the chat tabs, so this shouldn't be very complicated.  Possible Example: I have been wondering about the differences between model paramters and model hyperparameters, as well as what their categorization means for a learning problem.  Is the distinction between model parameters and hyperparameters only about reducing the complexity of the problem or are there implications for the 'model quality' to be considered?  Let's consider an example from (1, Eq. 2.43), a linear expansion of basis functions   $$f_\theta(x) = \sum_{m=1}^{M} \theta_m h_m(x), $$  where $h_m\:\forall m=1,...,M$ is some function of $x$, $\theta=[\theta_1,...,\theta_M]^\intercal$ is a vector of the parameters of the model and $M$ is the number of basis functions.   In my understanding, we would consider $\theta$ to contain the parameters of the model, while $M$ is a .  To quote the Wikipedia article of hyperparameter that I linked above:     In machine learning, a hyperparameter is a parameter whose value is   set before the learning process begins. By contrast, the values of   other parameters are derived via training.   It makes sense treating the values in $\theta$ as parameters that should be learned from the data, similar to the coefficients in a linear model - it is surely far more reliable  and  specifying them manually would be quite annoying, although it's not impossible. But what about $M$? It surely is easier to pick some integer value for it. But would it really be terrible to determine $M$ based on the data, too? Probably not, as that is what we would do if we search a grid of possible values for the best performing one.   Let's consider the above basis expansion model and choose Gaussian kernel functions to serve as basis functions. As the Kernel itself has parameters too  this makes the problem a bit more complicated.  $$f_\theta(x) = \sum_{m=1}^{M}\theta_m K_{\lambda_m}(\mu_m,x), $$ with $\mu_1,...,\mu_m$ being the location of the kernels and $\lambda_1,...,\lambda_m$ their scales/bandwidths.  Friedman et al. write in (1, p. 36)        "In general we would like the data to dictate them as well. Including   these as parameters changes the regression problem from a   straightforward linear problem to a combinatorially hard nonlinear   problem. In practice, shortcuts such as greedy algorithms or two stage processes are used."   I see that if we were to treat $M$, $\theta_1 ... \theta_M$, $\mu_1 ... \mu_M$ and $\lambda_1 ... \lambda_M$, as model parameters, this problem would be really complex, especially with the choice of $M$ determining the number of the other parameters. But what if we simplify the model definition - let us for example use the same scale/bandwidth for each kernel, that gives us only one parameter $\lambda$. Furthermore, let's say we specify $\mu_1 ... \mu_M$ based on some heuristic, which would mean we treat it as a hyperparameter.  This gives us   $$f_{\theta,\lambda}(x) = \sum_{m=1}^{M}\theta_m K_\lambda(\mu_m,x), $$  Besides increased complexity of the involved optimization problem, does treating $\lambda$ as a parameter rather than a hyperparameter have other negative or undesired effects?      (1) Friedman, Jerome, Trevor Hastie, and Robert Tibshirani. The   elements of statistical learning. Vol. 1. No. 10. New York: Springer   series in statistics, 2001. I made a simple FM transmitter following  and it worked! Now I need some help to understand how.  My coil is made of 1 mm copper wire has 6 turns and 8 mm wire diameter. According to this online calculator:  this means that: L = 3.9e-7 H  I did not have any 5 pF trim capacitor so I used a 3 pF capacitor instead.  Am I correct in assuming that the frequency this will transmit on can be found by looking at the L1 C2 as a LC oscillator and using the frequency formulae:  fR = 1/(2*pi*sqrt(LC))  ?  If so I should get fR = 147 MHz. Which is strange since I received the signal on 91.5 MHz on my radio.  In a LC circuit I understand that the signal decays exponentially over time. That is hopefully not happening here. Why? Because of C4 maybe?  Also what is the purpose of C1?  If I want to increase the range of this FM transmitter somewhat can I do this by simply replacing R2 with a 470 Ohm resistor?  Are there free simulator programs that let me see the resulting spectrum at the antenna? Taking the second derivative of a parametric curve Ubuntu 13.04 on Mac Mini 6,2 ethernet port Broadcom NetXtreme BCM57766 not detected The said network adapter is not recognized in 13.04. In 12.04 and 12.10 I had used the driver proposed from broadcom download site, configured as dkms package it was always updated.  On the 3.8.x kernels this provided kernel driver from broadcom does not compile anymore - and the distribution provided tg3 drivers does not recognize the ethernet adapter - even though it is a newer version.  ~$ modinfo /lib/modules/3.8.0-19 generic/kernel/drivers/net/ethernet/broadcom/tg3.ko | grep -i version version:        3.128 srcversion:     D737202366709FE01964BF0 vermagic:       3.8.0-19-generic SMP mod_unload modversions    Here the working version on kernel 3.5.x using dkms  ~$ modinfo /lib/modules/3.5.0-25-generic/updates/dkms/tg3.ko | grep version version:        3.124c srcversion:     D01ED9A7BF2C3956E212A63 vermagic:       3.5.0-25-generic SMP mod_unload modversions    The Network card:  ~$ lspci -nn | grep 0200 01:00.0 Ethernet controller [0200]: Broadcom Corporation NetXtreme BCM57766 Gigabit Ethernet PCIe [14e4:1686] (rev 01)   As found on the i7 Mac Mini 6,2.  Anyone knows where I can get a kernel that recognizes that ethernet device ? That chip is supported somehow ... And - the 3.8.x kernel is way better on the HD4000 chip - reason I use it.  Note - to get the WiFi working, just make sure you load the b43 driver at boot (/etc/modules). At least then you have Network connectivity. I am a graduate student of math right now but I was not able to get a topology subject in my undergrad... I just would like to know if you guys know the best one.. Problem regarding radius of convergence of $\sum n!x^{n^2}$. $$\sum_{n=0}^\infty n!x^{n^2}$$   Can anyone tell me what will be the radius of convergence for this power series. According to me it is $0$.   If you can please show me how to go about it if I am wrong. What are the strengths and weaknesses of each follower? I am not experienced in Number Theory but what I know is that some results of this filed are applicable in other areas, e.g. algebra. For sure FLT made (and makes) people be interested in Number Theory leading to the development of new methods which can be themselves applied not only for the proof of FLT (like financial problems motivated somehow development of stochastic analysis). I am interested - if there are applications or implications of FLT itself?  More precisely: if the fact "for each $n\geq3$ there are no integer solutions of $a^n+b^n=c^n$" leads to solutions of problems which are not in the field of Number Theory?   I would specify that I wonder about some problems which are already formulated: since FLT is known for more then 300 years I am pretty sure that there were formulated hypothesis which follow from FLT directly (if there are such hypothesis not in the field of Number Theory). Run a script as root from apache Is "a total of 10 payments" singular or plural? A total of 10 payments were made.   OR     A total of 10 payments was made.   Which is correct? Or can both be correct? 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.