I have index i need to get the element of this index from list – prolog

Can anyone tell me how to get the element from spifiec index ? Say for example I need to get the element in the index 5 in my list

list manipulation – Using coding to calculate my average for functions defined on countable sets?

Suppose we have a function $f:Atomathbb{R}$ where $Asubseteq(a,b)$, $a,binmathbb{R}$ and $Ssubseteq A$.

Now suppose $f$ is

$$f(x)=begin{cases}
x^2+1 & xin S_1\
x & xin S_2\
end{cases}$$

Where $S_1$ and $S_2$ are pairwise disjoint subsets of $A=S_1cup S_2$ where $S_1=left{frac{1}{c}+frac{sqrt{2}}{2}:cinmathbb{Z}right}cap(0,1)$, $S_2=left{frac{1}{2^{(d_1)}}+frac{1}{2^{(d_2)}}:d_1,d_2inmathbb{Z}right}cap(0,1)$ and $(a,b)=(0,1)$ where $a=0$ and $b=1$.

Suppose we divide $(0,1)$ into $r$ sub-intervals $left{(x_{i-1},x_i)right}_{i=1}^{r}$, where $a=x_0le x_1 le …le x_i le …le x_{r-1}le x_r=b$; and, if $f$ is defined in that sub-interval we take a point from that sub-interval; (however, if $f$ is not defined, we set $f=0$) and multiply it by measures $mu(S_1cap(x_{i-1},x_i),A)$, for $f(S_1)$, and $mu(S_2cap(x_{i-1},x_i),A)$, for $f(S_2)$,

We define $mu(S_1,A)$ and $mu(S_2,A)$ as the following:

In each sub-interval $(x_{i-1},x_i)$, we cover $S_1cap (x_{i-1},x_i)$ by $m_1$ sub-intervals, of each of the sub-intervals in $left(I_{i}right)_{i=1}^{r}=left{(x_{i-1},x_i)right}_{i=1}^{r}$. We define this as $left(I_{i_1,k}right)_{k=1}^{m_1}$, where $1 le m_1 le maxleft{|S_1|,1right}$. Then cover $S_2cap(x_{i-1},x_i)$ by $m_2$ sub-intervals of each of the sub-intervals in $left(I_{i}right)_{i=1}^{r}=left{(x_{i-1},x_i)right}_{i=1}^{r}$, which we define as $left(I_{i_2,k}right)_{k=1}^{m_2}$, where $1 le m_2 le maxleft{|S_2|,Aright}$. Last, cover $A=S_1cup S_2$ by $n$ sub-intervals of $J=(a,b)$, which we define as $left(J_{k}right)_{k=1}^{n}$ where $1 le n le maxleft{|A|,1right}$. All these sub-intervals have the same length which we define as $cinmathbb{R}^{+}$.

We wish to minimize (or find the infimum) of the total sum of the lengths of the $m_1$ sub-intervals covering $S_1cap(x_{i-1},x_i)$, where the infimum depends on $c$. This means we must set $c$ to specific values before taking the infimum. This would give us $m_1$ divided by $n$. The same is applied with $m_2$ sub-intervals covering $S_2cap (x_{i-1},x_i)$ and the $n$ sub-intervals covering $Acap (x_{i-1},x_i)$. This would give us $m_2$ divided by $n$.

Next we want want to find the infimum of $m_1$ divided by $n$ over $c$, (both $m_1$ and $n$ depends on $c$). We want the same with the infimum of $m_2$ divided by $n$ over $c$. This gives us $mu(S_1cap(x_{i-1},x_i),A)$ and $mu(S_2cap(x_{i-1},x_i),A)$.

To get our average one must take

$$sum_{i=1}^{r}(x_i^2+1)mu(S_1cap(x_{i-1},x_i),A)+sum_{i=1}^{r}(x_i)mu(S_2cap(x_{i-1},x_i),A)$$

Questions

  1. How would we do this on Mathematica?
  2. How would we generalize this to any piece-wise function defined on a countable set?

My Attempt

Subscript(S, 1)(c_Integer, r_) := 
 Select(Union@
   Flatten(Table(
     1/2^(Subscript(d, 1)) + 1/2^(Subscript(d, 2)), {Subscript(d, 1), 
      1, c}, {Subscript(d, 2), Subscript(d, 1), c})), 
  Between(#, 
    r) &) 

This lists all elements in $S_1$ as c$toinfty$ and groups them into $r$ sub-intervals of $(0,1)$

Subscript(S, 2)(c_Integer, q_) := 
 Select(Union@
   Flatten(Table(
     1/Subscript(u, 1) + Sqrt(2)/2, {Subscript(u, 1), 1, c})), 
  Between(#, 
    q) &) 

This lists all elements of Set $S_2$ as and groups them into $r$ sub-intervals of $(0,1)$

Subscript(f, 1)(x_) := 
 x^2 

This is the function $f=f_1$ on $xin S_1$

Subscript(f, 1, 1)(c_Integer, r_) := 
 Subscript(f, 
  1) /@ (Subscript(S, 1)(c, #) & /@ Partition(Subdivide(r), 2, 1)) 

Groups $S_1$ into $r$ sub-intervals

Subscript(f, 1, 1, 1)(c_Integer, r_) := 
 Subscript(f, 1, 1)(c, r) /. {} -> {0}

Converts null sets to zero

Subscript(f, 1, 1, 1)(30, 100);

Subscript(f, 2)(
  x_) := x 

This is the function $f=f_2$ on $xin S_2$

Subscript(f, 2, 2)(c_Integer, r_) := 
 Subscript(f, 
  2) /@ (Subscript(S, 2)(c, #) & /@ 
    Partition(Subdivide(r), 2, 
     1)) (* Groups Subscript(S, 2) into r sub-intervals *)
Subscript(f, 2, 2, 2)(c_Integer, r_) := 
 Subscript(f, 2, 2)(c, r) /. {} -> {0} 

Converts null sets to zero

In(205):= 
Subscript(I, 1)(r_) := 
 Block({m = 10^16}, 
   With({k = Ceiling@Log2@N@m + 2}, 
    Total(#) + 1 - Last(#) &@
     Unitize@BinCounts(
       Total(Tuples(2^Range(-k, -1), 2), {2}), {Min(#1) &, Max(#1) &, 
        1/m}))) /@ Partition(Subdivide(r), 2, 1) 

This is supposed to give $m_1$ from where the total sum of the length of all $m_1$ sub-intervals, of each of the $r$ sub-intervals, covering the intersection of $S_1$ and the $r$ sub-intervals are as small as possible.

In(206):= Subscript(I, 1)(10)

During evaluation of In(206):= BinCounts::bins: The bin specification {Min(#1)&,Max(#1)&,1/10000000000000000} is not a list of 2 or 3 real values.

Out(206)= If(29155653097335068495 === $SessionID, 
Out(206), Message(
MessageName(Syntax, "noinfoker")); Missing("NotAvailable"); Null)

Unfortunately, there is something wrong with this function.

Subscript(I, 2)(r_) := 
 Block({m = 10^16}, 
   With({k = Ceiling@N@m + 2}, 
    Total(#) + 1 - Last(#) &@
     Unitize@BinCounts(
       Total(Tuples(Range(-k, -1), 1), {2}), {Min(#1) &, Max(#1) &, 
        1/m}))) /@ 
  Partition(Subdivide(r), 2, 
   1) 

This is supposed to give $m_2$ from where the total sum of the length of all $m_2$ sub-intervals, of each of the r sub-intervals, covering the intersection of $S_2$ and the $r$ sub-intervals are as small as possible

Subscript(I, 2)(10)
J(r_) := Sum(
  Subscript(I, 1)(i) + Subscript(I, 2)(i), {i, 1, 
   r}) 

This is supposed to give $n$ from where the total sum of the length of all $n$ sub-intervals, of each of the $r$ sub-intervals, covering the intersection of $A$ and the $r$ sub-intervals are as small as possible

Subscript(Avg, 1)(r_) := 
 Sum(Subscript(f, 1, 1, 1)(30, i)((i, 1))*
   Subscript(I, 1)(r)((i))/J(r), {i, 1, 
   r}) (* Subscript(I, 1)(r)((i))/A(r) is mu(Subscript(S, 1),A) as m
(Rule) Infinity, the whole sum is supposed to give the average over 
Subscript(f, 1) *)
Subscript(Avg, 2)(r_) := 
 Sum(Subscript(f, 2, 2, 2)(30, i)((i, 1))*
   Subscript(I, 2)(r)((i))/J(r), {i, 1, 
   r}) (* Subscript(I, 1)(r)((i))/A(r) is mu(Subscript(S, 2),A) as m
(Rule)Infinity, the whole sum is supposed to give the average over 
Subscript(f, 2) *)
Subscript(Avg, 1)(10000) + 
 Subscript(Avg, 1)(10000) (* This is the combined total sum *)

During evaluation of In(217):= General::nomem: The current computation was aborted because there was insufficient memory available to complete the computation.

During evaluation of In(217):= Throw::sysexc: Uncaught SystemException returned to top level. Can be caught with Catch((Ellipsis), _SystemException).

Out(218)= SystemException("MemoryAllocationFailure")

During evaluation of In(217):= BinCounts::bins: The bin specification {Min(#1)&,Max(#1)&,1/10000000000000000} is not a list of 2 or 3 real values.

During evaluation of In(217):= BinCounts::bins: The bin specification {Min(#1)&,Max(#1)&,1/10000000000000000} is not a list of 2 or 3 real values.

During evaluation of In(217):= General::nomem: The current computation was aborted because there was insufficient memory available to complete the computation.

During evaluation of In(217):= Throw::sysexc: Uncaught SystemException returned to top level. Can be caught with Catch((Ellipsis), _SystemException).

Out(222)= SystemException("MemoryAllocationFailure")

Unfortunately, as you see here I am not getting any results.

How do we fix the errors in my code? Is my attempt correct?

Sort Sharepoint Online List views alphabetically

I have multiple Sharepoint Online lists each with more than 100+ views created.
The problem is that these views are listed in the order of creation and not alphabetically .
To navigate to a particular view it is getting very cumbersome to scroll through the long list.

I would like to know if it is possible to sort them out easily without renaming.

google – Dynamically loading list of links with JavaScript (SEO)

An item belongs to a potentially infinite number of categories (usually most of them are spam).

After the item page loads, it shows one category link with the highest score (and thus probably non-spam) of all categories the item belongs to. There is More... button that loads with JavaScript 10 more categories (or less if the list of categories is exceeded). If More... is pressed twice, 20 categories would be loaded, etc.

How to make this page behave well in SEO perspective?

  1. How to make Google understand that More... leads to more links?

  2. How to make Google understand that the lower the link is in the list, the more likely it’s spam?

How to add a removed element to the associated sublist after manipulating a list

I have the attached point list and use the following script to cluster the points. The clustering should just be applied to the first three-member of each sublist so I removed the fourth element from each sublist. However, after clustering the fourth member should be added to the associated sublist. How I can do that.
https://pastebin.com/SKvFEEQD

A11 = Drop[dataDCMp, None, {4}];
nng = NearestNeighborGraph[A11, 4];
ccmp = ConnectedComponents[nng];

Submitting to SP List, Input string was not in correct format error JavaScript

I am getting the error, “Input list was not in correct format error”

My sharepoint list has single text fields so i cannot see the problem

function savingsdatick(varid) {
//Get Current Tabs before submission
var allTicksForSave = {};
$(“.thischeck”).each(function () {
allTicksForSave($(this).attr(“id”)) = $(this).is(“:Checked”)
});
console.log(“So…”)
console.log(allTicksForSave)

var Tickbox1 = “Tickbox1”;
var Tickbox2 = “Tickbox2”;
var Tickbox3 = “Tickbox3”;
var Tickbox4 = “Tickbox4”;
var Tickbox5 = “Tickbox5”;
var Tickbox6 = “Tickbox6”;
var Tickbox7 = “Tickbox7”;
var Tickbox8 = “Tickbox8”;
var Tickbox9 = “Tickbox9”;
var Tickbox10 = “Tickbox10”
var Tickbox11 = “Tickbox11”;
var Tickbox12 = “Tickbox12”;
var Tickbox13 = “Tickbox13”;
var Tickbox14 = “Tickbox14”;
var Tickbox15 = “Tickbox15”;
var Tickbox16 = “Tickbox16”;
var Tickbox17 = “Tickbox17”;
var Tickbox18 = “Tickbox18”;
var Tickbox19 = “Tickbox19”;
var Tickbox20 = “Tickbox20”;
var Tickbox21 = “Tickbox21”;
var Tickbox22 = “Tickbox22”;
var Tickbox23 = “Tickbox23”;
var Tickbox24 = “Tickbox24”;
var Tickbox25 = “Tickbox25”;
var Tickbox26 = “Tickbox26”;
var Tickbox27 = “Tickbox27”;
var Tickbox28 = “Tickbox28”;
var Tickbox29 = “Tickbox29”;
var Tickbox30 = “Tickbox30”;

  var varid = localStorage.getItem("projectnewTitle");
  var currentStorm = document.getElementById("dale3").innerHTML;
  var siteUrl = _spPageContextInfo.webServerRelativeUrl;
  var clientContext =  SP.ClientContext.get_current();
  var oList = clientContext.get_web().get_lists().getByTitle('SecurityDesignAssuranceLeft');
  this.oListItem = oList.getItemById(currentStorm)
    if(allTicksForSave.SDALEFTBOX0) oListItem.set_item('Tickbox1', 'True');
    if(allTicksForSave.SDALEFTBOX1) oListItem.set_item('Tickbox2', 'True');
    // if(allTicksForSave.SDALEFTBOX2) oListItem.set_item(Tickbox3, "True")
    // if(allTicksForSave.SDALEFTBOX3) oListItem.set_item(Tickbox4, "True")
    // if(allTicksForSave.SDALEFTBOX4) oListItem.set_item(Tickbox5, "True")
    // if(allTicksForSave.SDALEFTBOX5) oListItem.set_item(Tickbox6, "True")
    // if(allTicksForSave.SDALEFTBOX6) oListItem.set_item(Tickbox7, "True")
    // if(allTicksForSave.SDALEFTBOX7) oListItem.set_item(Tickbox8, "True")
    // if(allTicksForSave.SDALEFTBOX8) oListItem.set_item(Tickbox9, "True")
    // if(allTicksForSave.SDALEFTBOX9) oListItem.set_item(Tickbox10, "True")
    // if(allTicksForSave.SDALEFTBOX10) oListItem.set_item(Tickbox11, "True")
    oListItem.update();
clientContext.executeQueryAsync(Function.createDelegate(this, this.onQuerySucceeded4), Function.createDelegate(this, this.onQueryFailed4));
function onQuerySucceeded4() {
alert("Hi")

}

function onQueryFailed4(sender, args) {
alert(“Failed” + args.get_message())
}
}

google sheets – Using REGEXMATCH with list input

I’m trying to see if a COL A contains anything from a specified list. (if it does, I put say a ‘1’ in COL B, or ‘0’ if not.

I’m currently doing it this slow, insane way. (putting this formula into col B – replace ‘I20’ with A20 for example).

Is there a better way?

=if(REGEXMATCH(I20,"SOUTHERN"),1,0) + if(REGEXMATCH(I20,"GLASS"),1,0) + if(REGEXMATCH(I20,"HOME"),1,0) + if(REGEXMATCH(I20,"JOHN"),1,0) + if(REGEXMATCH(I20,"ENTERPRISE"),1,0) + if(REGEXMATCH(I20,"BRITISH A"),1,0) + if(REGEXMATCH(I20,"WSELECTRICAL"),1,0) + if(REGEXMATCH(I20,"VIKING"),1,0) + if(REGEXMATCH(I20,"TASCHEN"),1,0) + if(REGEXMATCH(I20,"FRANCY"),1,0) + if(REGEXMATCH(I20,"MODELSHOP"),1,0) + if(REGEXMATCH(I20,"APPLE"),1,0) + if(REGEXMATCH(I20,"CURRYS"),1,0) + if(REGEXMATCH(I20,"WATFORD"),1,0) + if(REGEXMATCH(I20,"WICKES"),1,0) + if(REGEXMATCH(I20,"LEYLAND"),1,0) + if(REGEXMATCH(I20,"IKEA"),1,0)

enter image description here

c# – Refresh the List box with new rooms from the server every 3 seconds

So i have a server which I send a Request to and it sends me back a list of rooms,Now i made a window for joining rooms and I’m trying to refresh it every 3 seconds but when i use the Timer thread to refresh the list it doesn’t work if I use the normal refresh method with the Timer it works just fine.
Here’s some code:

private void AutoRefresh()
{
   System.Timers.Timer timer = new System.Timers.Timer(TimeSpan.FromMilliseconds(3000).TotalMilliseconds);
   timer.AutoReset = true;
   timer.Elapsed += new System.Timers.ElapsedEventHandler(this.Refresh);
   timer.Start();
  }

private void Refresh(object sender, System.Timers.ElapsedEventArgs elapsedEventArg)
{
    GetRoomsResponse response;
    response = SendAndRecv();
    Button temp;
    foreach (RoomData room in response.rooms)
    {
        temp = new Button { Content = room };
        temp.Click += (sender, e) =>
    {
        JoinRoomClick(sender, e);
    };
        temp.Content = room.Name;
        buttons.Add(temp);
    }
ListBoxRooms.ItemsSource = buttons;
}

If I call refresh from the main it works perfectly if I call AutoRefresh it doesn’t I think it gets stuck on the for each loop no error’s just doesn’t do it’s job

list manipulation – How to partition $[0,1]$ into $m$ equal sub-intervals and count the number of sub-intervals that intersect with my cantor set?

Suppose I define my cantor set as

 cantor = {a_, 
    b_} :> {{a, a + (b - a)*1/7}, {a + (b - a)*2/7, 
     a + (b - a)*3/7}, {a + (b - a)*4/7, 
     a + (b - a)*5/7}, {a + (b - a)*6/7, b}};
CantorRegion(c_Integer?NonNegative) := 
 Module({ints}, 
  ints = Flatten(
    Nest(Flatten(Map(Function(s, s /. cantor), #), 1) &, {{0, 1}}, c)))
ListPlot(Table({CantorRegion(3)((c)), 0}, {c, 1, 
   Length(CantorRegion(3))}))
generateA(n_Integer) := CantorRegion(n)

enter image description here

How do we divide $(0,1)$ into $m$ sub-intervals of equal length and count the number of sub-intervals that intersect with my cantor set?

My attempt:

In(11):= partition(a_List, s_) := Module({f, r}, f({}, x_) := {x};
  f(l_List, x_) := If(x - l((1)) < s, Append(l, x), Sow(l); {x});
  r = Reap(Fold(f, {}, a));
  Append(r((2, 1)), r((1))))
partition({0, 1, 2, 7, 10, 11, 12}, 5)
(*{{0,1,2},{7,10,11},{12}}*)

Out(12)= {{0, 1, 2}, {7, 10, 11}, {12}}

Unfortunately for my cantor set

partition(Flatten(generateA(5)), 5)

I get the following:

Part::partw: Part 1 of {} does not exist.

Part::pkspec1: The expression {0,1/16807,2/16807,3/16807,4/16807,5/16807,6/16807,1/2401,2/2401,15/16807,16/16807,17/16807,18/16807,19/16807,20/16807,3/2401,4/2401,29/16807,30/16807,31/16807,32/16807,33/16807,34/16807,5/2401,6/2401,43/16807,44/16807,45/16807,46/16807,47/16807,48/16807,1/343,2/343,99/16807,100/16807,101/16807,102/16807,103/16807,104/16807,15/2401,16/2401,113/16807,114/16807,115/16807,116/16807,117/16807,118/16807,17/2401,18/2401,127/16807,<<1998>>} cannot be used as a part specification.

How do we fix my code? Is there a better solution?

Auto Upload verified list to hoster

hi..
my server just got hacked via bitcoin locker (ransomware) everything is lost (project.ser+verified list)
im wondering it would be cool if GSA has this feature ( upload current project or verified list txt ) to our hoster ,at least ftp them
just a suggestion