DC to AC inverter calculations
How to Calculate the time of Charging and Discharging of battery?
Showing equality of sequence of holomorphic functions to limit function if converges uniformly locally I do not know how to proof following question:  Let $D$ be a domain in $C$.  ${{f}_{n}}$ be a sequence of holomorphic functions on $D$ that converges uniformly locally to a function non-constant $f$. Show that for each $z\in D$, there is a sequence ${{z}_{n}}\to z$ as ${{f}_{n}}({{z}_{n}})=f(z)$ for all sufficiently large $n$.  Actually, I know that I should use an assumption such as: ${{f}_{n}}({{z}_{n}})\ne f(z)$  Therefore, there is compact set    that  $\left\| {{f}_{{{n}_{k}}}}({{z}_{{{n}_{k}}}})-f(z) \right\|&gt;\varepsilon $  Then I think I have to use Montel theorem, but I do not know how to show the contradiction. I am trying to find all the Sylow 2 subgroups of S4 using Sylow’s theorems. Now, I know that a Sylow 2 subgroup of S4 has size 8, and that there are either 1 or 3 of them (as the number of of Sylow 2-subgroups has form 1+2k and divides 3, the index).  Now my lecturer states “stabilisers of the 3 different bisections of {1,2,3,4} yield 3 distinct Sylow 2 subgroups”  Now my questions are:  1) What does it mean by stabilisers of 3 different bijections of {1,2,3,4}? Is that to say the elements of S4 which send {1,2} and {3,4} to {1,2},{3,4} i.e. by (12)(34)?  2) How does he know that there are 8 elements of this set? Perhaps this will become clearer after the 1st question is answered.  Many thanks, group theory is hard. When you first add a cylinder, you have the option to change the number of vertices, etc, but once you do anything else in blender, it seems you no longer can edit those parameters.   Is there a setting anywhere or an add-on that allows these parameters to be edited later on? If not, how easy would such an addon/feature be to create for anyone reading this? Is there an efficient way to enumerate the unique subgroups of the symmetric group? Naïvely, for the symmetric group $S_n$ of order $\left | S_n \right | = n!$, there are $2^{n!}$ subsets of the group members that could potentially form a subgroup. In addition, many of these subgroups are going to be isomorphic to each other. I feel that the question has an easy answer in terms of the conjugacy classes, but I don't see how. If the answer generalizes to all finite groups, please elaborate! Suppose I have 30 numbers that vary between 0 and 1.0 and which sum to 1.0.  The mean is obviously 0.033.  A client wants these scaled to lie between 0 and 1.0 but to have a mean of 0.5.  By the way, I'll probably have to do this for any set of numbers (positive, negative, outside the range 0 - 1) so that they lie in the range 0 - 1 and have a mean 0.5.  Any suggestions? Where can I find out when the next kernel version will be released for my distro version? I checked the , , and  wiki pages but still cannot seem to find a complete answer to this.  When using an LTS release like 18.04, is there somewhere public that can be checked to determine what kernel versions are being tested and when they are anticipated to be released for it? I would like to use 4.19, for example, but would like to know how to check this for any anticipated kernel release.  I know I could potentially just install the 4.19 kernel myself but I would rather know when it (and future kernel releases) were in the release pipeline. Is there somewhere on Launchpad that I could check? Somewhere else? Where are the Ubuntu kernel package maintainers doing their work? Activate Field Service Lightning feature in a Salesforce DX scratch org? I am struggling to figure out how to -- or if it's even possible to -- create a DX scratch org with the "Field Service Lightning" (FSL) feature installed. Based on the feature list  I'm guessing the answer is no and I'll just have to wait. But I'm not sure I'm interpreting that source correctly or missing something entirely since I'm just wrapping my head around DX.   Background: we have a production org with FSL installed and active, along with it's accompanying managed packages. I can create sandboxes from it and do development using standard Metadata API tools, but I was hoping to start a new project using DX. But I'm stuck configuring a scratch org with the proper features. How do I protect Python code from being read by users? Replacements for switch statement in Python? Prove that neither $A$ nor $B$ is divisible by $5$ Let the sum   $$ {1+ \frac12 + \frac13 + \frac 14+ \dots +\frac1{99} + \frac 1{100}}$$  be written as $\frac AB$, where $A$ and $B$ are positive integers with no common factors. Show that neither $A$ nor $B$ is divisible by $5$.    Using Mathematica, I found the sum is $$\frac AB=\frac {14466636279520351160221518043104131447711}{278881500918849908658135235741249214‌2272}$$ Show that $$\sum_{k=0}^n(-1)^k\binom nk=0$$ So for odd $n$ we have an even number of terms. So $\binom nk=\binom n{n-k}$ which have opposite signs. Thus the sum is 0.  For even $n$ we have that $$\sum_{k=0}^n(-1)^k\binom nk= \binom n0+\sum_{k=1}^{n-1}(-1)^k\binom nk+\binom nn$$ Now $$\sum_{k=1}^{n-1}(-1)^k\binom nk= \sum_{k=1}^{n-1}(-1)^k\left[\binom{n-1}k+\binom{n-1}{k-1}\right]$$ What would that sum be in the square brackets? Rational solutions of $y^2 = x^3 - x$ Why does cold metal seem colder than cold air? (I apologize for this elementary question. I don't know much about physics.)  Let's say that I put a metal pot in the refrigerator for several hours.  At this point, I guess, the pot and the air (in the refrigerator) have the same temperature.  Now, I touch this pot. It feels very cold. But when I "touch" the air (that is inside the fridge) it doesn't "feel" as cold. I don't feel the same "ouch!" that I feel when I touch the pot.  Why is that? Why does the metal seem colder than air although they both have the same temperature?  (I know that gas has less particles in it in one unit of volume compared to solids and liquids, but since "temperature" means "the average kinetic energy", these fewer air particles are supposed to hit my hand in a velocity that's going to compensate for their lower number, aren't they?)  A related question, for clarification:  If I use a thermometer to measure the temperature of the pot &amp; air (let's assume it's a thermometer that has a probe that can touch objects), will it show the same reading for both? If so, what makes the thermometer different than my hand? I mean, my hand is sort of a thermometer, so why would it fail whereas a non-human thermometer would work? It is generally believed and claimed that quantum computers can outperform classical devices in at least some tasks.  One of the most commonly cited examples of a problem in which quantum computers would outperform classical devices is $\text{Factoring}$, but then again, it is also not known whether $\text{Factoring}$ is also efficiently solvable with a classical computer (that is, whether $\text{Factoring}\in \text{P}$).  For other commonly cited problems in which quantum computers are known to provide an advantage, such as database search, the speedup is only polynomial.  Are there known instances of problems in which it can be shown (either proved or proved under strong computational complexity assumptions) that quantum computers would provide an exponential advantage? I have the following table:     \documentclass[a4paper,preprint,aps,                    unsortedaddress]{revtex4}     \usepackage[top=2.5cm,bottom=2.5cm,                 left=3.5cm,right=2.5cm]{geometry}     \usepackage{longtable,array,booktabs}      \ifdefined\mc        \renewcommand{\mc}{\multicolumn}     \else        \newcommand{\mc}{\multicolumn}     \fi      \begin{document}           \setlength\LTleft{-3.0cm}         \setlength\LTright{-2.0cm}          \scriptsize      \begin{longtable}{ l r @{--} p{1.3cm} &gt;{\centering}p{2.6cm}                         *{4}{p{1.25cm}} p{2.1cm}}                    %% headers and footers      \caption{Table} \\      \hline\hline     \endfirsthead      \mc{9}{c}{\tablename\ \thetable\ -- \emph{Continued from previous page}} \\      \hline     aaaaaaaaaaaaaaaaaaaaaaaa &amp; \mc{2}{c}{bbb--ccc} &amp; ddd &amp; eee &amp; fff &amp; ggg &amp; hhh &amp; iii \\     \hline     \endhead      \hline     \mc{9}{r}{\emph{Continued on next page}} \\     \endfoot      \hline\hline     \endlastfoot      %% body of table          aaaaaaaaaaaaaaaaaaaaaaaa &amp; \mc{2}{c}{bbb--ccc} &amp; ddd &amp; eee &amp; fff &amp; ggg &amp; hhh &amp; iii \\     aaaaaaaaaaaaaaaaaaaaaaaa &amp; bbb &amp; ccc &amp; ddd &amp; eee &amp; fff &amp; ggg &amp; hhh &amp; iii \\     aaaaaaaaaaaaaaaaaaaaaaaa &amp; bbb &amp; ccc &amp; ddd &amp; eee &amp; fff &amp; ggg &amp; hhh &amp; iii \\     aaaaaaaaaaaaaaaaaaaaaaaa &amp; bbb &amp; ccc &amp; ddd &amp; eee &amp; fff &amp; ggg &amp; hhh &amp; iii \\      \end{longtable}     \end{document}   which I would like to shift to the left by setting \setlength\LTleft{-3.0cm}  and \setlength\LTright{-2.0cm}. Furthermore, I have to apply \scriptsize for the table. However, none of these commands are working with revtex4. Could you please provide a solution to this problem? (This question is the same as in , but I cannot sign up with that username.)  If it is not possible, an alternative solution would also be useful for me. For this case, I attached the first page of my real table. A new Victorian-set British novel begins sentences containing h-dropping with lower-case e's, as in " 'e took my money, 'e did." This seems incorrect but I'm at a loss to find the rule. SQL to generate a list of numbers from 1 to 100 Unable to install Cisco Packet Tracer 7.3 on Ubuntu 20.04 I am trying to install Packet Tracer 7.3 (latest version) on Ubuntu 20.04 but do not succeed to so so because of two dependencies which are not installable ("libdouble-conversion1" and "qt-at-spi").  However I successfully installed the previous version (7.2.2) which was available in an Ubuntu installer format (.run file) but I nothing happens when I run it from my gnome desktop.  I am quite a newbie in Linux so I appologies if answers are obvious...  Thanks in advance ;-)  Denis Integrating trigonometric function problem $\int \frac{3\sin x+2\cos x}{2\sin x+3\cos x}dx$ \begin{eqnarray*} \int \frac{3\sin x+2\cos x}{2\sin x+3\cos x}dx &amp;=&amp;  \int \frac{(3\sin x+2\cos x)/\cos x}{(2\sin x+3\cos x)/\cos x}dx\\ \\ &amp;=&amp; \int \frac{3\tan x +2}{2\tan x +3} dx\\ &amp;&amp; u = \tan x \text{ and } du = \sec^2 x \ dx  \end{eqnarray*} Am I going in the right direction with this one? It seems like not. Custom one-key keyboard shortcuts in Outlook 2010 or 2013?