$\sum_{n=1}^{\infty} a_n$ converges absolutely and $\sum _{n=1}^\infty a_{kn}=0 ,\forall k \ge 1 $ ; then $a_n=0 , \forall n \in \mathbb N $?
Prove that $a_{n}=0$ for all $n$, if $\sum a_{kn}=0$ for all $k\geq 1$
Conditional Rendering inside Visualforce pages Process Builder - Breaking Production Deployments? I have a Process Builder flow set up and I am running some tests around the InvocableMethod Apex code. The tests pass fine in my staging and production environments. Yet, when I try to deploy to production, I get a strange error.  CANNOT_EXECUTE_FLOW_TRIGGER, The record couldn’t be saved because it failed to trigger a flow.  Thankfully I received a somewhat more informative error email.  UPSERT FAILED ---  ERRORS :  (CANNOT_EXECUTE_FLOW_TRIGGER) The record couldn’t be saved because it failed to trigger a flow. common.exception.AssertionException: ORA-20070: Cannot read from apex_class and apex_trigger while running tests ---  for SFDC record with ID : null,  Unfortunately, the deployment has nothing to do with the flow and it is unclear why it is failing. What is the root cause of this error and how can I fix it? EDIT: I found out this is a . The other claimed workaround is to deploy via the Metadata API. UPDATE: Because I was subscribed to the Known Issue, I received the following confirmation this issue is resolved.  We are pleased to notify you that the following Known Issue has been resolved: Executing an InvocableMethod during an apex test run from a change set can cause Errors. Thank you for being patient while we worked to address this issue. Please feel free to reach out to Customer Support if you have further questions. Sincerely, Salesforce Success Team Logitech SetPoint software button remapping My Logitech G5 Laser mouse has 9 buttons but it's SetPoint software only allows 5 of them to be used as "mouse buttons" and the remaining 4 can only be assigned special windows functions (Forward, Back, Cruise Up, etc) or Keystroke Assignments.  Many of the games I play will take up to 10 "MOUSE BUTTON" inputs for in-game actions but wont recognize the remaining 4 buttons even when assigned keystroke assignments.  Is there a way to make these last 4 buttons "Generic Buttons" as well as buttons 3,4,and 5? (1 is left click and 2 is right click).  My other question is if the above is not possible, maybe I can use AutoHotkey to remap keystrokes as assigned by my SetPoint software to mouse button commands?  If so how? Evaluate the infinite product $$\lim_{ n\rightarrow\infty }\prod_{k=2}^{n}\left ( 1-\frac{1}{k^2} \right ).$$  I can't see anything in this limit , so help me please. For a while now I've noticed that if I take a cup of hot tea and pour it into two cups and leave it then both cups will cool faster than the single cup.  How is it that nature cools two cups of tea in parallel more quickly? It's still the same amount of tea but it gets cooled quicker if I have two cups. Is FFmpeg missing from the official repositories in 14.04? Can we prevent titles with an unnecessary tag in them? How can I add text in a non-english language? How can I add text with non Latin characters? I'd like to get text in other languages like Arabic, Russin (Cyrilic), Japanese, Chinese, Malayalam among others, but I get rectangles instead of Arabic letters. Where were the capital ships and bombers? Why is everybody so concerned about etc/passwd? Here is the content of my vagrant machine of this particular file:  root:x:0:0:root:/root:/bin/bash daemon:x:1:1:daemon:/usr/sbin:/usr/sbin/nologin bin:x:2:2:bin:/bin:/usr/sbin/nologin sys:x:3:3:sys:/dev:/usr/sbin/nologin sync:x:4:65534:sync:/bin:/bin/sync games:x:5:60:games:/usr/games:/usr/sbin/nologin man:x:6:12:man:/var/cache/man:/usr/sbin/nologin lp:x:7:7:lp:/var/spool/lpd:/usr/sbin/nologin mail:x:8:8:mail:/var/mail:/usr/sbin/nologin news:x:9:9:news:/var/spool/news:/usr/sbin/nologin uucp:x:10:10:uucp:/var/spool/uucp:/usr/sbin/nologin proxy:x:13:13:proxy:/bin:/usr/sbin/nologin www-data:x:33:33:www-data:/var/www:/usr/sbin/nologin backup:x:34:34:backup:/var/backups:/usr/sbin/nologin list:x:38:38:Mailing List Manager:/var/list:/usr/sbin/nologin irc:x:39:39:ircd:/var/run/ircd:/usr/sbin/nologin gnats:x:41:41:Gnats Bug-Reporting System (admin):/var/lib/gnats:/us$ nobody:x:65534:65534:nobody:/nonexistent:/usr/sbin/nologin syslog:x:100:103::/home/syslog:/bin/false   Could anybody explain me why it is bad if some evil guy could get this file of my production server? I discovered that you can start your variable name with a '@' character in C#.  In my C# project I was using a web service (I added a web reference to my project) that was written in Java. One of the interface objects defined in the WSDL had a member variable with the name "params". Obviously this is a reserved word in C# so you can't have a class with a member variable with the name "params". The proxy object that was generated contained a property that looked like this:  public ArrayList @params {     get { return this.paramsField; }     set { this.paramsField = value; } }   I searched through the VS 2008 c# documentation but couldn't find anything about it. Also searching Google didn't give me any useful answers. So what is the exact meaning or use of the '@' character in a variable/property name? My PC has a build-in VT1828S chip. The connection between PC and monitor (which has built-in speakers) is through an HDMI cable.  Audio preferences shows 2 devices for audio output: analog stereo and RS880 Audio Device [Radeon HD 4200] digital stereo (HDMI).  When I plug a headphone in the rear jack and I choose the former device, everything works. When I choose the latter device, instead, no sound is heard, and video playback is too fast. It is as if video frames want to synchronise with the audio timing, but the audio timing information is wrong.  HDMI audio worked perfectly with Ubuntu 11.04, but stopped after 11.10 upgrade. Grep: unexpected results when searching for words in heading from man page I'm running into weird behavior when trying to grep a man page on macOS. For example, the Bash man page clearly has an occurrence of the string NAME:  $ man bash | head -5 | tail -1 NAME   And if I grep for name I do get results, but if I grep for NAME I don't:  $ man bash | grep 'NAME' $ man bash | grep NAME   I've tried other uppercase words that I know are in there, and searching for SHELL yields nothing whereas searching for BASH yields results.  What's going on here?  Update: Thanks for all the answers! I thought it worth adding the context in which I ran into this. I wanted to write a bash function to wrap man and in cases where I've tried to look up the man page for a shell builtin, jump to the relevant section of the Bash man page. There might be a better way, but here's what I've got currently:  man () {   case "$(type -t "$1")" in     builtin)       local pattern="^ *$1"        if bashdoc_match "$pattern \+[-[]"; then         command man bash | less --pattern="$pattern +[-[]"       elif bashdoc_match "$pattern\b"; then         command man bash | less --pattern="$pattern[[:&gt;:]]"       else         command man bash       fi       ;;     keyword)       command man bash | less --hilite-search --pattern='^SHELL GRAMMAR$'       ;;     *)       command man "$@"       ;;   esac }  bashdoc_match() {   command man bash | col -b | grep -l "$1" &gt; /dev/null } L1 & L2 Regularization in Light GBM This question pertains to L1 &amp; L2 regularization parameters in Light GBM. As per official documentation:  reg_alpha (float, optional (default=0.)) – L1 regularization term on weights.  reg_lambda (float, optional (default=0.)) – L2 regularization term on weights  I have seen data scientists using both of these parameters at the same time, ideally either you use L1 or L2 not both together.   While reading about tuning LGBM parameters I cam across one such case: Kaggle official GBDT Specification and Optimization Workshop in Paris where Instructors are ML experts. And these experts have used positive values of both L1 &amp; L2 params in LGBM model. Link below (Ctrl+F 'search_spaces' to directly reach parameter grid in this long kernel)      I have seen same in XGBoost implementations.  My question is why use both at the same time in LGBM/XGBoost.  Thanks. I am trying to understand what mathematics is really built up of. I thought mathematical logic was the foundation of everything. But from reading a book in mathematical logic, they use "="(equals-sign), functions and relations.  Now is the "=" taken as undefined? I have seen it been defined in terms of the identity relation.  But in order to talk about functions and relations you need set theory.  However,  seems to be a part of mathematical logic.  Does this mean that (naive) set theory comes before sentential and predicate logic? Is (naive)set-theory at the absolute bottom, where we can define relations and functions and the eqality relation. And then comes sentential logic, and then predicate logic?  I am a little confused because when I took an introductory course, we had a little logic before set-theory. But now I see in another book on introduction to proofs that set-theory is in a chapter before logic. So what is at the bottom/start of mathematics, logic or set theory?, or is it circular at the bottom?  Can this be how it is at the bottom?  naive set-theory $\rightarrow$ sentential logic $\rightarrow $ predicate logic $\rightarrow$ axiomatic set-theory(ZFC) $\rightarrow$ mathematics  (But the problem with this explanation is that it seems that some naive-set theory proofs use logic...)  (The arrows are of course not "logical" arrows.)  simple explanation of the problem:  a book on logic uses at the start: functions, relations, sets, ordered pairs, "="  a book on set theory uses at the start: logical deductions like this: "$B \subseteq A$", means every element in B is in A, so if $C \subseteq B, B \subseteq A$, a proof can be "since every element in C is in B, and every element in B is in A, every element of C is in A: $C \subseteq A$". But this is first order logic? ($(c \rightarrow b \wedge b \rightarrow a)\rightarrow (c\rightarrow a)$).  Hence, both started from each other? I have been struggling for one hour with this simple problem (QGIS 1.8.0-Lisboa, Windows 7) :  I have a raster layer. I would like to display the label and not only the band value when I use the Identify Features button. Is it possible? How to get instance variables in Python? I am trying to run the following model:         I(week^2):mutation_status +         (week + I(week^2) | subject_id) ,          data = sim_dat)  This is the output I get from this model. The correlation between week and I(week)^2 is rather high (-0.95) and I was curious to know how I can change my data simulation code to lower that value. I am also having issues with convergence and would love to get thoughts on how to avoid issues regarding convergence. Thank you! Linear mixed model fit by REML. t-tests use Satterthwaite's method [lmerModLmerTest]  Formula: fetal_weight ~ week + mutation_status + week:mutation_status + I(week^2) +  I(week^2):mutation_status + (week + I(week^2) | subject_id) Data: sim_dat  REML criterion at convergence: 114  Scaled residuals:      Min      1Q  Median      3Q     Max  -1.9343 -0.3980 -0.0075  0.4168  1.9928   Random effects:  Groups     Name        Variance  Std.Dev. Corr         subject_id (Intercept)   1.51524  1.2309                          week         61.01832  7.8114   0.16                   I(week^2)   496.20236 22.2756  -0.19 -0.95  Residual                 0.05892  0.2427              Number of obs: 100, groups:  subject_id, 20  Fixed effects:                            Estimate Std. Error       df t value       Pr(&gt;|t|)     (Intercept)                  3.1331     0.4226  17.9961   7.413 0.000000713699 *** week                        -1.2465     3.5210  18.0053  -0.354          0.727     mutation_statusY             0.5061     0.5977  17.9961   0.847          0.408     I(week^2)                   34.5706    10.8146  18.0084   3.197          0.005 **  week:mutation_statusY       -1.0697     4.9795  18.0053  -0.215          0.832     mutation_statusY:I(week^2) 202.5521    15.2942  18.0084  13.244 0.000000000101 *** --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1  Correlation of Fixed Effects:             (Intr) week   mttn_Y I(w^2) wk:m_Y week        -0.160                             muttn_sttsY -0.707  0.113                      I(week^2)    0.145 -0.966 -0.103               wk:mttn_stY  0.113 -0.707 -0.160  0.683        mtt_Y:I(^2) -0.103  0.683  0.145 -0.707 -0.966  Code for data simulation: set.seed(123)  # set the seed J &lt;- 20  # number of individuals (clusters) cs &lt;- 5  # number of time points (cluster size) gam &lt;- c(0, 0.75, 1.34)  # fixed effects G &lt;- matrix(c(1.75, 0, 0,               0, 0.0125, 0,               0,0,0.0625),              nrow = 3)  # random effect variances (G-matrix) sigma2 &lt;- 0.08  mutation_status &lt;- rep(0:1, each = 5) mutation_status &lt;- rep(mutation_status, times = 10)  X &lt;- cbind(1, seq_len(cs),             (seq_len(cs))^2)  # for each individual X &lt;- X[rep(seq_len(cs), J), ]  X &lt;- X[rep(seq_len(cs), J), ]  X[,2] &lt;- X[,2]*0.05 X[,3] &lt;- X[,3]*0.05  # repeat each row cs times pid &lt;- seq_len(J)  # individual id pid &lt;- rep(pid, each = cs)   # Generate person-level (lv-2) random effects uj &lt;- lmf::rmnorm(J, mean = rep(0, 2), varcov = G)  # Generate repeated-measure-level (lv-1) error term eij &lt;- rnorm(J * cs, sd = sqrt(sigma2))  # Compute beta_j's betaj &lt;- matrix(gam, nrow = J, ncol = 3, byrow = TRUE) + uj  # Compute outcome: y &lt;- rowSums(X * betaj[pid, ]) + eij + mutation_status*X[ , 3]*10 + 3  # Form a data frame sim_dat &lt;- tibble(y, time = X[ , 2], pid, mutation_status) sim_dat &lt;- sim_dat[,c(3,2,4,1)] colnames(sim_dat) &lt;- c(&quot;subject_id&quot;, &quot;week&quot;, &quot;mutation_status&quot;, &quot;fetal_weight&quot;) sim_dat$week_2 &lt;-sim_dat$week*5 + 15  sim_dat$mutation_status &lt;- as.factor(ifelse(sim_dat$mutation_status == 0, &quot;N&quot;, &quot;Y&quot;)) sim_dat$subject_id &lt;- as.factor(sim_dat$subject_id ) #Model Building How can I solve the folowing Diophantine equation with two unknowns? Find one integer solution to the following Diophantine equation:   \begin{equation*} \\\forall \,x,y \in \mathbb{Z}\\ 6xy + x - y = 274 \end{equation*}   The resultat ist $x = 9$, $y = 5$ (Obtained with  )  I need to know a method that allows me to reach such a result. How can I calculate the value of these two variables in a Diophantine equation? For example: 6xy + x - y = 458 top x% in [tag] : rules for the tag to be taken into account?