Frothing milk more quietly?
"Screaming" noise while steaming milk?
I've got a Windows 10 Computer (home edition), which has 4GB of Ram and an i5 processor. I need to run an old 32 bit accounting programme. The vendor said it won't release a 64 bit version (although a 64bit version exists, it's missing key features from the older version).  The programme installs fine, but when I click on the programme icon, it says the programme won't work on a 64 bit system.   What options do I have?    I've done a fair bit of research, but it seems to run up dead ends.   1) WoW64     Apparently, this is supposed to let you run 32 bits on 64 bit Windows. However, I am not sure how to install it. I think it's for web servers only. However,  says it can work on Windows 7, but doesn't explain how to set it up (or if it will work on Windows 10).  2) XP mode     A 32bit Windows XP emulator. However, it seems to be for Windows 7 only. Also according to this , you need Windows Professional.   3) Virtual Box Machine    Let's you emulate Windows. Seems overkill for my purposes. Plus I would need to buy a 32 bit Windows license. I think it would run slowly with 4GB of Ram.  4) Partition drive into 32bit and 64 bit versions Apparently, you can use the free tool  to split the drive into two and then install separate 32bit and 64 bit versions.   Again, seems overkill and it looks like I would need buy a 32 bit Windows 10 license.   Are these my only options?     Images  Installation    First run (From the error message I guess it's a 16-bit program)   Clicking on programme Closed form solution for slope coefficients in bivariate regression In a univariate regression, $Y=a+bX+e$, the solution for slope b is given by $COV(X,Y)/VAR(X)$.  Is there a similar expression for a bivariate regression $Y=a+bX+cZ+e$. What is the closed form solution for b and c in this case? Is there a tool in Ubuntu to automatically merge two images having a common strip? I need to scan a large image, which will not fit at once in the scanner. I was thinking about scanning it in two parts and hand-editing the result in Gimp to join them. But probably an automatic tool can do the same more quickly and better.  EDIT I think I may have not made my point clear. My difficulty is not aligning two images. My problem is that one has to compensate for the rotation or distortion introduced by the manual process of putting the sheet into the scanner, and an automatic tool should obtain more precise results at analyzing common patterns in the two images to rotate and align them seamlessly. How do I run wireshark, with root-privileges? A standard installation of Wireshark doesn't give the program permission to access the network interface.   I suppose I have to run the program with sudo, but do not know how to add it to the icon - if that's the way to do it. Calculating optimal number of bins in a histogram I'm interested in finding as optimal of a method as I can for determining how many bins I should use in a histogram. My data should range from 30 to 350 objects at most, and in particular I'm trying to apply thresholding (like Otsu's method) where "good" objects, which I should have fewer of and should be more spread out, are separated from "bad" objects, which should be more dense in value. A concrete value would have a score of 1-10 for each object. I'd had 5-10 objects with scores 6-10, and 20-25 objects with scores 1-4. I'd like to find a histogram binning pattern that generally allows something like Otsu's method to threshold off the low scoring objects. However, in the implementation of Otsu's I've seen, the bin size was 256, and often I have many fewer data points that 256, which to me suggests that 256 is not a good bin number. With so few data, what approaches should I take to calculating the number of bins to use? Going into a directory linked by a link When I cd a link, my current path is prefixed with the link's path, rather than the path of the directory the link links to.  E.g.  ~/dirlinks/maths$ ls -l logic lrwxrwxrwx 1 tim tim 71 Jul 27 10:24 logic -&gt; /windows-d/academic discipline/study objects/areas/formal systems/logic  ~/dirlinks/maths$ cd logic ~/dirlinks/maths/logic$ pwd /home/tim/dirlinks/maths/logic  ~/dirlinks/maths/logic$ cd .. ~/dirlinks/maths$   I would like to have my current path changed to the path of the linked dir, so that I can work with the parent dirs of the linked dir as well. Besides ls the link to find out the linked dir, and then cd into it, what are some simpler ways to accomplish that? For example, after cd into a link, how do you change your current path to the path of the linked dir? I have a scrbook document with an openright option, i.e. every once in a while a blank left page appears in the document. Not that I really want to do this, but how could I include the infamous "This page has been intentionally left blank" in those blank pages cleanly, i.e. without too many hacks?  Bonus points for including a different famous quote on each blank page instead of the dull default ;) To flag or not to flag question that don't show own effort? I am a little confused about what do with questions that are just asking      "I want this and that (...) and I want it to look exactly like that   (...) please help"   without showning ANY own effort?  According to  those kind of answers are not welcome  also the  says those questions should not be asked:     Don't ask about...   Questions you haven't tried to find an answer for (show your work!)   But does this mean that I should flag those kind of "helpdesk" questions or not? And if yes as what? low quality ? flag for moderator attention ? Or is just adding a kind comment asking for the asker's own attempts enough? When is $f=\left(\frac{\sqrt{p+4}}{1-p}-1\right)x^5-3x+\ln5$ decreasing $\forall\; x$? When is $$f=\left(\frac{\sqrt{p+4}}{1-p}-1\right)x^5-3x+\ln5$$ decreasing $\forall\; x$?    Diffrentiating: $$f'=5\left(\frac{\sqrt{p+4}}{1-p}-1\right)x^4-3$$ If $f$ is decreasing, $f'&lt;0$: $$5\left(\frac{\sqrt{p+4}}{1-p}-1\right)x^4-3&lt;0\implies x^4&lt;\frac3{5\left(\frac{\sqrt{p+4}}{1-p}-1\right)}$$ Since if $\left(\frac{\sqrt{p+4}}{1-p}-1\right)\to0^+\implies x^4&lt;+\infty$, which holds forallx, So:$$p=\frac{3\pm\sqrt{21}}2$$which doesn't ply with textbook-answer, since it mentions an domain for p. How many numbers are in the Fibonacci sequence below a given threshold? Assuming I'm asked to generate Fibonacci numbers up to N, how many numbers will I generate? I'm looking for the count of Fibonacci numbers up to N, not the Nth number.  So, as an example, if I generate Fibonacci numbers up to 25, I will generate:   1, 1, 2, 3, 5, 8, 13, 21 that's 8 numbers   How do I calculate this mathematically for an arbitrary "n"? I am writing my thesis,  and i am in restructuring phase - sorting theorems where they should belong thematically. And it would be helpful to have all the proofs hidden so i am not laden with the additional information.  Is it possible to add something like hideproof to documentclass options to omit them when compiling the latex file. General trigger bulkification - best practices A general question asked from time to time on stack exchange is question of trigger bulkification.  Therefore I have 2 questions:   Which best practices are you using? What is the best way to handle updates of more than 200 records? (In case of more than 200 records the trigger is executed more than once.) Finding limit of a sequence in product form \begin{equation} \prod_{n=2}^{\infty} \left (1-\frac{2}{n(n+1)}  \right )^2 \end{equation}  I need to find limit for the following product..answer is $\frac{1}{9}$.  I have tried cancelling out but can't figure out.  Its a monotonically decreasing sequence so will converge to its infimum.. how to find the infimum? I want to create posters for my poster presentation on a conference. What tools or LaTeX classes are available for preparing posters ? Windows 8 skype is terrible.  They've removed many buttons, most of the preferences, and have in general made it impossibly oversimplified and difficult to use.  Old Skype was fine when I had windows 7.  Is there any way to get it back on Windows 8? How do you remove the axis multiplier? iOS 10 remember to "not trust this computer" Compactness of $\operatorname{Spec}(A)$ In an exercise in Atiyah-Macdonald it asks to prove that the prime spectrum $\operatorname{Spec}(A)$ of a commutative ring $A$ as a topological space $X$ (with the Zariski Topology) is compact.   Now because the basic open sets $X_f = \{\mathfrak{p} \in \operatorname{Spec} (A) : \{f\} \not\subseteq \mathfrak{p} \}$ form a basis for the Zariski Topology it suffices to consider the case when   $$X = \bigcup_{i \in I} X_{f_i}$$   where $I$ is some index set. Then taking the complement on both sides we get that   $$\emptyset = \bigcap_{i \in I} X_{f_i}^c$$  so there is no prime ideal $\mathfrak{p}$ of $A$ such that all the $f_i$'s are in $\mathfrak{p}$. Now from here I am able to show that the ideal generated by the $f_i$'s is the whole ring as follows. Since there is no prime ideal $\mathfrak{p}$ such that all the $f_i \in \mathfrak{p}$, it is clear that there is no $\mathfrak{p}$ such that $(f_i) \subseteq \mathfrak{p}$ for all $i \in I.$ Taking a sum over all the $i$ then gives $$\sum_{i \in I} (f_i) = (1).$$  Now here's the problem:          How do I show from here that there is an equation of the form $1 = \sum_{i \in J} f_ig_i,$ where $g_i \in A$ and $J$ some finite subset of $I$?       This part has been giving me a headache. I am not sure if the finiteness bit has to do with algebra, topology or the fact that we are dealing with prime ideals.  This is not a homework problem but rather for self-study.  $\textbf{Edit:}$ I have posted my answer below after the discussion with Dylan and Pierre. What desktop environments can group window icons in the taskbar like Windows 7? I find it much faster to identify a window in the taskbar (window list) by its icon,    rather than by its text:    The problem with most graphical interfaces I've  is that they don't group windows, and if you have more terminals or file managers, they'll just clutter the taskbar and you won't know which is which. Windows 7 offers a relatively elegant solution to this by grouping similar window icons together.  Question: What Linux  have this functionality? If addons exist that provide it, that's alright.  For reference, a Cinnamon applet that sort of does this is . I'd like to know how many downloads of a given package in a PPA there have been since it was first published.  I remember there was  about it about getting these metrics on the web UI, but as far as I know, it never got implemented.  But I think the number of downloads can nevertheless be obtained via the  if I'm the owner of that PPA. Any pointers?