Is there a sequence $f_{n}:\mathbb{R} \to \mathbb{R}$ such that the series $\sum \limits_{k=1}^{\infty}f_{n}(x)$ converges uniformly to $f(x)$, but $\sum \limits_{k=1}^{\infty}|f_{n}(x)|$ converges only pointwise, for all $x\in \mathbb{R}$?  I tried limiting the domain to $(0,1)$ and using Dirichlet Eta function, but that approach failed. I know that the sequence $f_{n}$ cannot be strictly positive and can't be equibounded, otherwise  $\sum \limits_{k=1}^{\infty}|f_{n}(x)|$ would converge uniformly by Weierstrass M-test.
Find an example of a function sum $\sum_{n=1}^\infty u_n $ that converges   uniformly on $[a,b]$ and converges absolutely pointwise, but   $\sum_{n=1}^\infty |u_n| $ doesn't converge uniformly on $[a,b]$.   This seems pretty straightfoawrd but it's really hard to find an example. The choice of $u_n$ must be very specific. You can actually prove any power series wont work (due to Abel's theorem)  In addition, in order to prove the uniform convergence, $u_n$ must not satisfy Weierstrass' M-Test (because then $\sum |u_n|$ would converge uniformly aswell)
Does anyone know the name of travel posters from the 1930s? Disable white background of pasted text in PowerPoint When I paste text from another source with "Keep source formatting option" into PowerPoint 2010 I receive a white background, that I don't want.    How can I make this text background transparent, so there would be just red text on purple? Add field "tome" to biblatex entries I need to add a new field in the @book or @InProceedings entries: this field is "tome", for I have for instance the following title:  Francesco Bertolini, Società di trasmissione orale: mito e folclore, in Lo spazio letterario della Grecia antica, a cura di G. Cambiano, L. Canfora e D. Lanza, vol. I, tomo I, Salerno, Roma 1992, pp. 47--75.   So the following code is not enough:  @InProceedings{ bertolini:1992,   author                   = "Francesco Bertolini",   title                    = "Società di trasmissione orale: mito e folclore",   booktitle                = "Lo spazio letterario della Grecia antica",   editor                   = "G. Cambiano and L. Canfora and D. Lanza",   publisher                = "Salerno",   location                 = "Roma",   year                     = "1992",   volume                   = "1,   pages                    = "47--75", }   Using othes codes, I was able only to produce the "tome" field, but with a general trouble about the other fields:  \DeclareSourcemap{   \maps[datatype=bibtex]{     \map{       \step[fieldsource=tome,fieldtarget=usera]     }   } } \DeclareFieldFormat{usera}{tomo\space{#1}}   \DeclareBibliographyDriver{book}{%   \usebibmacro{author/editor}%   \setunit{\labelnamepunct}\newblock   \usebibmacro{title}%   \newunit\newblock   \usebibmacro{journal+issuetitle}%   \setunit{\bibpagespunct}%   \printfield{pages}%   \newunit\newblock   \printfield{usera}%   \usebibmacro{finentry}} \renewcommand*{\finentrypunct}{}   (useful for articles, but not for my case). By real, I'm not able to understand  which bibmascros I have to invocate...  I tried to write a biblatex-tome.dbx:  \ProvidesFile{biblatex-tome.dbx}   \DeclareDatamodelFields[type=field,datatype=literal,skipout=false]{tome}   \DeclareDatamodelEntryfields{tome}   Inside the main .tex file I put just this code:  \DeclareFieldFormat{tome}{\mkbibacro{tome}\addcolon\space #1} \newcommand*{\patchmoretome}[1]{   \xpatchbibdriver{#1}%     {\printfield{tome}}     {\printfield{tome}%           \newunit\newblock      \printfield{tome}}%     {\typeout{patching #1 to include more tome succeded}}%     {\typeout{patching #1 to include more tome failed}}% } % patch all drivers \patchmoretome{article} \patchmoretome{book} \patchmoretome{collection} \patchmoretome{inbook} \patchmoretome{incollection} \patchmoretome{inproceedings} \patchmoretome{manual} \patchmoretome{periodical} \patchmoretome{proceedings} \patchmoretome{report} \patchmoretome{thesis}   but it doesn't print the field in bibliographic entry. 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But when it wakes up, the only things on the screen are the icon bar at the left and the top bar with status icons on the right end. The rest of the screen is blue, not my normal lock screen image. The screen isn't locked, it doesn't prompt for a password, it's just...blue.  I can move the mouse pointer around the screen, the icons react if I click on one, I can bring up the popup with volume/brightness controls on the top bar. But if the pointer is on the blue background, neither left nor right button clicks do anything.  Now, if I press ctrl-alt-F1 from there, I get a lock screen where I can enter my password. Then I get the blue screen back, but if I press ctrl-alt-F2 I get my normal screen (with running applications) back.  ctrl-alt-F2 without going through the lock screen first does nothing.  I'm not finding anything while searching that matches either of these sets of symptoms. Suggestions? How can I iterate over an enum? Am I required to pay UK/ USA Visa fees if I have a German residence permit? Here is the situation. I am non-european but staying in Germany with a Residence permit. I can visit all Schengen listed countries with no issue. Assuming that I would want to travel to a non-Schengen country e.g. UK or USA, can I use my residence permit to travel there or am I required to apply as a citizen of my country? Assuming Germans are not required to pay Visa fees to that country, will I have to pay since I only have a residence permit? Third case, Europeans can fly directly to the airport of some countries and apply for a visa from there. In some other countries, you are required to book a Visa appointment at the embassy, which may be granted or not. Does that apply for one with a residence permit? 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It has several spots like this in the code:  if ($REMOTE_ADDR == "") $ip = "no ip"; else $ip = getHostByAddr($REMOTE_ADDR);  I have always thought brackets are needed to enclose what you want to do if the condition is true.  Is there some other alternative, such as if it is on the same line you don't?  There is also another line like this: if ($action != ""): mail("$adminaddress","Visitor Comment from YOUR SITE",  My instinct is to say this wouldn't work, but I also don't know if it is an outdated PHP file and it used to work? In his 1984 paper , Paul Holland raised one of the most fundamental questions in statistics:     What can a statistical model say about   causation?   This led to his motto:     NO CAUSATION WITHOUT MANIPULATION   which emphasized the importance of restrictions around experiments that consider causation.  Andrew Gelman makes :     "To find out what happens when you change something, it is necessary to change it."...There are things you learn from perturbing a system that you'll never find out from any amount of passive observation.   His ideas are summarized in .  What considerations should be made when making a causal inference from a statistical model? I have an excel spreadsheet with header and survey drill data. Header data contains hole ID, and location coordinates, and the survey data contains related downhole survey with Distance, Azimuth and Dip values.   Since I know the hole location and surface elevation, I would like to be able to convert the survey table to XYZ coordinates as well.  Does anyone has a function / procedure / example?  (VB &amp; ArcObjects)  Header Data:    Survey Data: A finite summation of double binomial coefficients I find the following identity and have checked on Mathematica, while I have no idea how to prove it:  $$\sum_{j=0}^n(-1)^{n-j}\binom{p+j}{j}\binom{n+\beta}{n-j}=\binom{p-\beta}{n}, \quad \beta&gt;-1, \quad p&gt;\beta-1.$$  It seems that proof by induction does not work and because of the gamma function, the transform technique does not work either. Why is the derivative of a circle's area its perimeter (and similarly for spheres)? When differentiated with respect to $r$, the derivative of $\pi r^2$ is $2 \pi r$, which is the circumference of a circle.  Similarly, when the formula for a sphere's volume $\frac{4}{3} \pi r^3$ is differentiated with respect to $r$, we get $4 \pi r^2$.  Is this just a coincidence, or is there some deep explanation for why we should expect this?