text:
# Visualize an Array

Given an array of any depth, draw its contents with borders of +-| around each subarray. Those are the ASCII characters for plus, minus, and vertical pipe.

For example, if the array is [1, 2, 3], draw

+-----+
|1 2 3|
+-----+

For a nested array such as [[1, 2, 3], [4, 5], [6, 7, 8]], draw

+-----------------+
|+-----+---+-----+|
||1 2 3|4 5|6 7 8||
|+-----+---+-----+|
+-----------------+

For a ragged array such as [[[1, 2, 3], [4, 5]], [6, 7, 8]], draw

+-------------------+
|+-----------+-----+|
||+-----+---+|6 7 8||
|||1 2 3|4 5||     ||
||+-----+---+|     ||
|+-----------+-----+|
+-------------------+

Notice that there is more space after drawing [6, 7, 8]. You may either draw the contents on the top-most, center, or bottom-most line, but whichever you choose, you must remain consistent.

This challenge was inspired by the box verb < from J.

## Rules

• This is so the shortest code wins.
• Builtins that solve this are not allowed.
• The input array will contain only nonnegative integer values or arrays. Each array will be homogenous, meaning that its elements will either by only arrays or only integers, but never a mix of both.
• Each subarray may be nested to any depth.
• The output may either by as a string or as an array of strings where each string is a line of output.

## Test Cases

[]
++
||
++

[[], []]
+---+
|+++|
|||||
|+++|
+---+

[[], [1], [], [2], [], [3], []]
+-----------+
|++-++-++-++|
|||1||2||3|||
|++-++-++-++|
+-----------+

[[[[[0]]]]]
+---------+
|+-------+|
||+-----+||
|||+---+|||
||||+-+||||
|||||0|||||
||||+-+||||
|||+---+|||
||+-----+||
|+-------+|
+---------+

[[[[[4, 3, 2, 1]]]], [[[3, 2, 1]]], [[2, 1]], [1]]
+---------------------------------+
|+-------------+---------+-----+-+|
||+-----------+|+-------+|+---+|1||
|||+---------+|||+-----+|||2 1|| ||
||||+-------+|||||3 2 1|||+---+| ||
|||||4 3 2 1|||||+-----+||     | ||
||||+-------+|||+-------+|     | ||
|||+---------+||         |     | ||
||+-----------+|         |     | ||
|+-------------+---------+-----+-+|
+---------------------------------+

• If my language has no nested arrays, can I disregard the definition of the data type? – ThreeFx Oct 22 '16 at 19:40
• @ThreeFx You could also take the input as a string representing the nested array – miles Oct 22 '16 at 19:44
• That is REALLY inefficient (in Haskell). I'd have to parse numbers manually and so on. In that case it would be shorter to define and use the datatype. – ThreeFx Oct 22 '16 at 19:45
• @ThreeFx Or you could pad the array with sentinel values such as -1 since I also limited the integers to be non-negative. Then would just have to clean the output for those invalid values. – miles Oct 22 '16 at 19:47
• @MitchSchwartz Sure, take the input in a nested tuple or whatever format is native to your language. Your output is fine as long as you remain consistent. Integers can be drawn at the top, center, or bottom, and the boxes can be at the top, center, bottom, or stretched to fill out their space like in your example. – miles Nov 1 '16 at 2:54

# Dyalog APL, 56 bytes

Thanks to ngn for helping removing about a third of the bytes.

{⍵≡∊⍵:⍉⍪⍉⍕⍵⋄(⊢,⊣/)⊃,/(1⊖('++','|'⍴⍨≢),'-'⍪⍣2↑)¨↓↑↓¨∇¨⍵}⊂

### TryAPL

Define the function, then run each test case and compare to the built-in ]Display utility.
[1, 2, 3]
[[1, 2, 3], [4, 5], [6, 7, 8]]
[[[1, 2, 3], [4, 5]], [6, 7, 8]]
[]
[[], []]
[[], [1], [], [2], [], [3], []]
[[[[[0]]]]]
[[[[[4, 3, 2, 1]]]], [[[3, 2, 1]]], [[2, 1]], [1]]

# Explanation

Overall, this is an anonymous function {...} atop an enclose ⊂. The latter just adds another level of nesting prompting the former to add an outer frame.

The anonymous function with white-space (⋄ is the statement separator):

{
⍵ ≡ ∊⍵: ⍉ ⍪ ⍉ ⍕ ⍵
(⊢ , ⊣/) ⊃ ,/ (1 ⊖ ('++' , '|' ⍴⍨ ≢) , '-' ⍪⍣2 ↑)¨ ↓ ↑ ↓¨ ∇¨ ⍵
}

Here it is again, but with separated utility functions:

CloseBox ← ⊢ , ⊣/
CreateVertical ← '++' , '|' ⍴⍨ ≢
AddHorizontals ← 1 ⊖ CreateVertical , '-' ⍪⍣2 ↑
{
⍵ ≡ ∊⍵: ⍉ ⍪ ⍉ ⍕ ⍵
CloseBox ⊃ ,/ AddHorizontals¨ ↓ ↑ ↓¨ ∇¨ ⍵
}

Now let me explain each function:

CloseBox takes a table and returns the same table, but with the table's first column appended on the right of the table. Thus, given the 1-by-3 table XYZ, this function returns the 1-by-4 table XYZX, as follows:
⊢ the argument (lit. what is on the right)
, prepended to
⊣/ the leftmost column (lit. the left-reduction of each row)

CreateVertical takes a table and returns the a string consisting of the characters which would fit |s on the sides of the table, but with two +s prepended to match two rows of -. Eventually the table will be cyclically rotated one row to get a single +---... row above and below. Thus, given any three row table, this function returns ++|||, as follows:
'++' , two pluses prepended to
'|' ⍴⍨ a stile reshaped by
≢ the (rows') tally of the argument

AddHorizontals takes a list-of-lists, makes it into a table, adds two rows of -s on top, adds the corresponding left edge characters on the left, then rotates one row to the bottom, so that the table has a border on the top, left, and bottom. As follows:
1 ⊖ rotate one row (the top row goes to the bottom) of
CreateVertical , the string ++|||... prepended (as a column) to
'-' ⍪⍣2 minus added twice to the top of
↑ the argument transformed from list-of-lists to table

{The anonymous function}: If the argument is a simple (not nested) list, make it into a character table (thus, given the 3-element list 1 2 3, this function returns the visually identical 1-by-five character table 1 2 3). If the argument is not a simple list, ensure the elements are simple character tables; pad them to equal height; frame each on their top, bottom, and left; combine them; and finally take the very first column and add it on the right. As follows:
{ begin the definition of an anonymous function
⍵ ≡ ∊⍵: if the argument is identical to the flattened argument (i.e. it is a simple list), then:
⍉ transpose the
⍪ columnized
⍉ transposed
⍕ ⍵ stringified argument; else:
CloseBox Add the leftmost column to the right of
⊃ ,/ the disclosed (because reduction encloses) concatenated-across
AddHorizontals¨ add -s on top and bottom of each of
↓ ↑ ↓¨ the padded-to-equal-height* of
∇¨ ⍵  this anonymous function applied to each of the arguments
} end the definition of the anonymous function
* Lit. make each table into a list-of-lists, combine the lists-of-lists (padding with empty strings to fill short rows) into a table, then split the table into a list of lists-of-lists

f=(a,g=a=>a[0].map?<${a.map(g).join|}>:a.join ,s=g([a]),r=[s],t=s.replace(/<[ -9|]*>|[ -9]/g,s=>s[1]?s.replace(/./g,c=>c>9?+:-): ))=>t<+?r.join\n.replace(/<|>/g,|):f(a,g,t,[t,...r,t])  Port of @MitchSchwartz's Ruby solution. Previous version which worked by recursively wrapping the arrays (and therefore worked for arbitrary content, not just integers): f=(...a)=>a[0]&&a[0].map?[s=+${(a=a.map(a=>f(...a))).map(a=>a[0].replace(/./g,-)).join+}+,...[...Array(Math.max(...a.map(a=>a.length)))].map((_,i)=>|${a.map(a=>a[i]||a[0].replace(/./g, )).join|}|),s]:[a.join ]  Note: Although I'm using the spread operator in my argument list, to obtain the desired output, provide a single parameter of the original array rather then trying to spread the array; this has the effect of wrapping the output in the desired outer box. Sadly the outer box costs me 18 bytes, and space-separating the integers costs me 8 bytes, otherwise the following alternative visualisation would suffice for 197 bytes: f=a=>a.map?[s=+${(a=a.map(f)).map(a=>a[0].replace(/./g,-)).join+}+,...[...Array(Math.max(0,...a.map(a=>a.length)))].map((_,i)=>|${a.map(a=>a[i]||a[0].replace(/./g, )).join|}|),s]:[+a]  • Does this handle empty arrays? I receive an error Cannot read property 'map' of undefined for empty arrays such as []. For [1,2,[]], the last subarray isn't displayed for me. – miles Oct 24 '16 at 10:50 • @miles Sorry, I'd forgotten to check out the test cases, and those now all work. You haven't specified the output for [1,2,[]] because your examples only show arrays containing either integers or arrays but not both. – Neil Oct 24 '16 at 11:02 • Great. Also never mind that one, I didn't cover it in the test cases and the problem will be simpler (since yours is the only working entry so far) if each array is homogenous. – miles Oct 24 '16 at 11:13 # Ruby, 104 bytes ->s{r=s=s.gsub'}{',?| r=[s,r,s]*$/while s=s.tr('!-9',' ').gsub!(/{[ |]*}/){$&.tr' -}','-+'} r.tr'{}',?|}  Anonymous function that expects a string. For example, {{{{{4 3 2 1}}}}{{{3 2 1}}}{{2 1}}{1}} produces +---------------------------------+ |+-------------+---------+-----+-+| ||+-----------+| | | || |||+---------+||+-------+| | || ||||+-------+||||+-----+||+---+| || |||||4 3 2 1||||||3 2 1||||2 1||1|| ||||+-------+||||+-----+||+---+| || |||+---------+||+-------+| | || ||+-----------+| | | || |+-------------+---------+-----+-+| +---------------------------------+  You can use this code for testing: f=->s{r=s=s.gsub'}{',?| r=[s,r,s]*$/while s=s.tr('!-9',' ').gsub!(/{[ |]*}/){$&.tr' -}','-+'} r.tr'{}',?|} a=[] a<<'[1, 2, 3]' a<<'[[1, 2, 3], [4, 5], [6, 7, 8]]' a<<'[[[1, 2, 3], [4, 5]], [6, 7, 8]]' a<<'[]' a<<'[[], []]' a<<'[[], [1], [], [2], [], [3], []]' a<<'[[[[[0]]]]]' a<<'[[[[[4, 3, 2, 1]]]], [[[3, 2, 1]]], [[2, 1]], [1]]' a.map{|s|s.gsub! '], [','}{' s.tr! '[]','{}' s.gsub! ',','' puts s puts f[s],''}  This starts from the middle row and works outwards. First, instances of }{ are replaced with |. Then, while there are still braces, all innermost {...} strings are transformed into the appropriate +- sequences while characters other than |{} are turned into spaces. At the end, the intermediate braces are turned into pipes. • I took some liberties with the apparently lenient input formatting requirements. The code can be easily modified to handle a different input format, if required. – Mitch Schwartz Nov 1 '16 at 23:06 • Receiving poorly thought out comments is one of the great joys of participating on this site. – Mitch Schwartz Nov 8 '16 at 2:02 ## Brainfuck, 423 bytes ->>+>>,[[>+>+<<-]+++++[>--------<-]>[<+>-[[-]<-]]>[[-]<<[>>>>+<<<<<<-<[>-<-]>>>- ]<<<[-<<<<<<-<]>+>>>]<<<[>>+>>>>>+<<<<<<<-]>>>>>>>>>,]<<+[<<,++>[-[>++<,<+[--<<< <<<<+]>]]<[-<+]->>>>[<++<<[>>>>>>>+<<<<<<<-]>>>-[<++>-[>>>>+<<<<<++<]<[<<]>]<[>> +<<<<]>>>+>+>[<<<-<]<[<<]>>>>->+>[-[<-<-[-[<]<[<++<<]>]<[<++++<<]>]<[>+<-[.<<<,< ]<[<<]]>]<[-<<<<<]>>[-[<+>---[<<++>>+[--[-[<+++++++<++>>,]]]]]<+++[<+++++++++++> -]<-.,>>]>>>>+>>>>]<<-]  Formatted with some comments: ->>+>>, [ [>+>+<<-] +++++[>--------<-] > [ not open paren <+>- [ not paren [-]<- ] ] > [ paren [-] << [ close paren >>>>+<<<< <<-<[>-<-]>>> - ] <<< [ open paren directly after close paren -<<<<<<-< ] >+>>> ] <<<[>>+>>>>>+<<<<<<<-]>>> >>>>>>, ] <<+ [ <<,++> [ - [ >++< ,<+[--<<<<<<<+] > ] ] <[-<+] ->>>> [ <++<<[>>>>>>>+<<<<<<<-]>>>- [ at or before border <++>- [ before border >>>>+<<<< <++< ] <[<<] > ] < [ after border >>+<< << ] >>>+>+> [ column with digit or space <<<-< ] <[<<] >>>>->+> [ middle or bottom - [ bottom <-<- [ at or before border - [ before border < ] < [ at border <++<< ] > ] < [ after border <++++<< ] > ] < [ middle >+< -[.<<<,<] <[<<] ] > ] <[-<<<<<] >> [ border char or space - [ not space <+>--- [ not plus <<++>> + [ -- [ - [ pipe <+++++++<++>>, ] ] ] ] ] <+++[<+++++++++++>-]<-.,>> ] > >>>+>>>> ] <<- ]  Try it online. Expects input formatted like (((((4 3 2 1))))(((3 2 1)))((2 1))(1)) with a trailing newline, and produces output of the form: +---------------------------------+ |+-------------+---------+-----+-+| ||+-----------+|+-------+|+---+| || |||+---------+|||+-----+||| || || ||||+-------+||||| |||| || || |||||4 3 2 1||||||3 2 1||||2 1||1|| ||||+-------+||||| |||| || || |||+---------+|||+-----+||| || || ||+-----------+|+-------+|+---+| || |+-------------+---------+-----+-+| +---------------------------------+  The basic idea is to calculate which character to print based on the depth of nesting. The output format is such that the row index of a box's top border is equal to the corresponding array's depth, with symmetry across the middle row. The tape is divided into 7-cell nodes, with each node representing a column in the output. The first loop consumes the input and initializes the nodes, keeping track of depth and whether the column corresponds to a parenthesis (i.e., whether the column contains a vertical border), and collapsing occurrences of )( into single nodes. The next loop outputs one row per iteration. Within this loop, another loop traverses the nodes and prints one character per iteration; this is where most of the work takes place. During the initialization loop, the memory layout of a node at the beginning of an iteration is x d 0 c 0 0 0 where x is a boolean flag for whether the previous char was a closing parenthesis, d is depth (plus one), and c is the current character. During the character printing loop, the memory layout of a node at the beginning of an iteration is 0 0 d1 d2 c p y where d1 indicates depth compared with row index for top half; d2 is similar to d1 but for bottom half; c is the input character for that column if digit or space, otherwise zero; p indicates phase, i.e. top half, middle, or bottom half; and y is a flag that gets propagated from left to right, keeping track of whether we have reached the middle row yet. Note that since y becomes zero after processing a node, we can use the y cell of the previous node to gain more working space. This setup allows us to avoid explicitly calculating the max depth during the initialization phase; the y flag is back-propagated to update the p cells accordingly. There is a -1 cell to the left of the nodes to facilitate navigation, and there is a cell to the right of the nodes that keeps track of whether we have printed the last row yet. # PHP+HTML, not competing (170141135 130 bytes) saved 29 bytes inspired by SteeveDroz <?function p($a){foreach($a as$e)$r.=(is_array($e)?p($e):"$e");return"r";}  not competing because it´s no ascii output and because I let the browser do all the interesting work • You can make  tags instead of
 and you don't need to specify the color of the border. (Saving 9 bytes) – SteeveDroz Oct 31 '16 at 15:30 • You don't need to put a <tag> at all, just display the output as plain text, that will save a lot of bytes (80 bytes for the whole code after HTML removing) – ClementNerma Nov 1 '16 at 9:35 • @SteeveDroz With , I can also remove the white-space attribute, saving another 19 bytes. great! And I can replace padding with margin – Titus Nov 1 '16 at 10:05 # JavaScript (ES6), 221 A non recursive function returning an array of strings (still using a recursive subfunction inside) a=>[...(R=(a,l)=>a[r[l]='',0]&&a[0].map?'O'+a.map(v=>R(v,l+1))+'C':a.join )([a],l=-1,r=[],m='')].map(c=>r=r.map(x=>x+v[(k<0)*2+!k--],k=l,1/c?v='-- ':(v='-+|',c>'C'?k=++l:c>','&&--l,c='|'),m+=c))&&[...r,m,...r.reverse()]  This works in 2 steps. Step 1: recursively build a string representation of the nested input array. Example: [[[1, 2, 3], [],[4, 5]], [6, 7, 8]] -> "OOO1 2 3,,4 5C,6 7 8CC" O and C mark open and close subarray. Simple numeric subarrays are rendered with the elements separated by space, while if array members are subarrays they are separated by commas. This string keeps track of the multilevel structure of the input array, while I can get the middle row of the output just replacing OC, with |. While recursively building this temp string, I also find the max depth level and initialize an array of empty strings that will contain the half top part of the output. Note: the outer box is tricky, I nest the input inside another outer array, then I have drop the first row of output that is not needed Step 2: scan the temp string and build the output Now I have an array of empty strings, one for each level. I scan the temp string, keeping track of the current level, that increases for each O and decreases for each C. I visualize this like that: [[[1, 2, 3], [],[4, 5]], [6, 7, 8]] OOO1 2 3,,4 5C,6 7 8CC + + + + + + ++ + |||1 2 3||4 5||6 7 8||  The plus the goes up and down follow the current level For each char, I add a character to every row of output, following the rules: - if digit or space, put a '-' at the current level and below, put a space above - else, put a '+' at the current level, put a '-' if below and put a '|' if above OOO1 2 3,,4 5C,6 7 8CC +--------------------+ |+------------+-----+| ||+-----++---+| || |||1 2 3||4 5||6 7 8||  During the temp scan, I also build the middle row replacing OC, with | At the end of this step, I have the top half and the middle row, I only have to mirror the top to get the bottom half and I'm done Less golfed, commented code a=>{ r = []; // output array R = ( // recursive scan function a, // current subarray l // current level ) => ( r[l] = '', // element of r at level r, init to "" a[0] && a[0].map // check if it is a flat (maybe empty) array or an array of arrays ? 'O'+a.map(v=>R(v,l+1))+'C' // mark Open and Close, recurse : a.join  // just put the elements space separated ); T = R([a],-1)]; // build temp string // pass the input nested in another array // and start with level -1 , so that the first row of r will not be visible to .map // prepare the final output m = '' // middle row, built upon the chars in T l = -1 // starting level [...T].map(c => // scan the temp string { k = l; // current level 1/c // check if numeric or space ? v = '-- ' // use '-','-',' ' : ( v = '-+|', // use '-','+','|' c > 'C' ? k=++l // if c=='O', increment level and assign to k : c>'A'&&--l, // if c=='C', decrement level (but k is not changed) c='|' // any of O,C,comma must be mapped to '|' ); m += c; // add to middle row r = r.map( (x,i) => // update each output row // based on comparation between row index and level // but in golfed code I don't use the i index // and decrement l at each step x + v[(k[...(R=(a,l)=>a[r[l]='',0]&&a[0].map?'O'+a.map(v=>R(v,l+1))+'C':a.join )([a],l=-1,r=[],m='')].map(c=>r=r.map(x=>x+v[(k<0)*2+!k--],k=l,1/c?v='-- ':(v='-+|',c>'C'?k=++l:c>','&&--l,c='|'),m+=c))&&[...r,m,...r.reverse()] out=x=>O.textContent = x+'\n'+O.textContent ;[[1,2,3] ,[[[1, 2, 3], [4, 5]], [6, 7, 8]] ,[] ,[[], []] ,[[], [1], [], [2], [], [3], []] ,[[[[[0]]]]] ,[[[[[4, 3, 2, 1]]]], [[[3, 2, 1]]], [[2, 1]], [1]] ].forEach(t=> out(JSON.stringify(t)+'\n'+F(t).join\n+'\n') ) function update() { var i=eval(I.value) out(JSON.stringify(i)+'\n'+F(i).join\n+'\n') } update() #I { width:90%} <input id=I value='[[[1, 2, 3], [],[4, 5]], [6, 7, 8]]' oninput='update()'>

 # Ruby, 245 241 bytes The overhead needed to wrap everything in boxes as well as align everything is pretty heavy... Outputs arrays of strings, with one string per line, as per the spec. Bottom-aligned instead of the top-aligned sample test cases because it saves 1 byte. Try it online! V=->a{a==[*a]?(k=a.map(&V);k[0]==[*k[0]]?[h=?++?-*((k.map!{|z|z[1,0]=[' '*~-z[0].size+?|]*(k.map(&:size).max-z.size);z};f=k.shift.zip(*k).map{|b|?|+b.reduce{|r,e|r+e[1..-1]}+?|})[0].size-2)+?+,*f,h]:[h="+#{?-*(f=k*' ').size}+",?|+f+?|,h]):a}  • @Adám it's fixed now. Will try my best to optimize further later... – Value Ink Oct 31 '16 at 21:12 • Nice.First answer with bottom alignment. :-) – Adám Oct 31 '16 at 22:05 # PHP, 404 Bytes All solutions works with maximum depth of the array lesser then 10. for greater values the depth must store in an array and not in a string. <?foreach(str_split(json_encode(_GET[a]))as$j){$j!="]"?:$c--;$r=($j==",")?($l=="]"?"":" "):$j;$r=$r=="]"?"|":$r;$r=$r=="["?($v=="]"?"":"|"):$r;if($r!=""){$n.=$r;$d.=+$c;}$v=$l;$l=$j;$j!="["?:$c++;$m>=$c?:$m=$c;}for($x=0;$x<strlen($n);$x++)for($y=0;$y<$m;$y++)$z[$y].=$y==$d[$x]&&$n[$x]=="|"?"+":($y<$d[$x]?"-":($y>$d[$x]&&$n[$x]=="|"?"|":" "));echo join("\n",$z),"\n$n\n".(join("\n",array_reverse($z)));  Expanded foreach(str_split(json_encode($_GET[a]))as$j){ # split JSON representation of the array$j!="]"?:$c--;$r=($j==",")?($l=="]"?"":" "):$j;$r=$r=="]"?"|":$r;
$r=$r=="["?($v=="]"?"":"|"):$r;
if($r!=""){$n.=$r; # concanate middle string$d.=+$c; # concanate depth position }$v=$l;$l=$j;$j!="["?:$c++;$m>=$c?:$m=$c; # maximum depth of the array } for($x=0;$x<strlen($n);$x++)for($y=0;$y<$m;$y++)$z[$y].=$y==$d[$x]&&$n[$x]=="|"?"+":($y<$d[$x]?"-":($y>$d[$x]&&$n[$x]=="|"?"|":" "));
# Build the strings before the middle string dependent of value middle string and depth
echo join("\n",$z),"\n$n\n".(join("\n",array_reverse($z))); #Output  ## for 425 Bytes we can make this with REGEX <?$n=($p=preg_filter)("#\]|$#","|",r=p("#$,$#","|",p("#,(\d)#"," 1",json_encode(_GET[a]))));preg_match_all("#.#",r,e,256);foreach(e[0] asf){f[0]!="]"&&f[0]!="|"?:c--;d.=+c;f[0]!="|"&&f[0]!="["?:c++;m>=c?:m=c;}for(x=0;x<strlen(n);x++)for(y=0;y<m;y++)z[y].=y==d[x]&&n[x]=="|"?"+":(y<d[x]?"-":(y>d[x]&&n[x]=="|"?"|":" "));echo join("\n",z),"\nn\n".(join("\n",array_reverse(z)));  Expanded r=preg_filter("#$,$#","|",preg_filter("#,(\d)#"," 1",json_encode(_GET[a]))); preg_match_all("#.#",r,e,256); n=preg_filter("#$|\[#","|",$r); # concanate middle string
foreach($e[0] as$f){
$f[0]!="]"&&$f[0]!="|"?:$c--;$d.=+$c; concanate depth position$f[0]!="|"&&$f[0]!="["?:$c++;
$m>=$c?:$m=$c; # maximum depth of the array
}
# similar to the other ways
for($x=0;$x<strlen($n);$x++)
for($y=0;$y<$m;$y++)
$z[$y].=$y==$d[$x]&&$n[$x]=="|"?"+":($y<$d[$x]?"-":($y>$d[$x]&&$n[$x]=="|"?"|":" ")); echo join("\n",$z),"\n$n\n".(join("\n",array_reverse($z)));

## 455 Bytes for a recursive solution

<?function v($x,$t=0,$l=1){global$d;$d.=$t;$s="|";$c=count($x);foreach($x as$k=>$v){if(is_array($v))$e=v($v,$t+1,$k+1==$c);else{$e=$v." "[$k+1==$c];$d.=str_pad("",strlen($e),$t+1);}$s.=$e;}$d.=$l?$t:"";$s.=$l?"|":"";return$s;}$n=v($_GET[a]);$m=max(str_split($d));for($x=0;$x<strlen($n);$x++)for($y=0;$y<$m;$y++)$z[$y].=$y==$d[$x]&&$n[$x]=="|"?"+":($y<$d[$x]?"-":($y>$d[$x]&&$n[$x]=="|"?"|":" "));echo join("\n",$z),"\n$n\n".(join("\n",array_reverse($z)));  Expanded function v($x,$t=0,$l=1){
global$d; # concanate depth position$d.=$t;$s="|";
$c=count($x);
foreach($x as$k=>$v){ if(is_array($v)){$e=v($v,$t+1,$k+1==$c);} else{$e=$v." "[$k+1==$c];$d.=str_pad("",strlen($e),$t+1);}
$s.=$e;
}
$d.=$l?$t:"";$s.=$l?"|":""; return$s;
}
$n=v($_GET[a]); # concanate middle string
$m=max(str_split($d)); # maximum depth of the array
# similar to the other ways
for($x=0;$x<strlen($n);$x++)
for($y=0;$y<$m;$y++)
$z[$y].=$y==$d[$x]&&$n[$x]=="|"?"+":($y<$d[$x]?"-":($y>$d[$x]&&$n[$x]=="|"?"|":" ")); echo join("\n",$z),"\n$n\n".(join("\n",array_reverse($z)));

• 1) $j!="]"?:$c--; -> $c-=$j=="]"; (-2). 2) ($l=="]"?"":" ") -> " "[$l==$j] (-5). Most probably similar substitutions in the second loop. 3) if($r!=""){$n.=$r;$d.=+$c;} -> $n.=$r;if($r>"")$d.=+$c; (-3). 4) $l=$j;$j!="["?:$c++; -> $c+="["==$l=$j; (-5). 5) $x=0 is not needed (-4). 6) for($y=0;$y<$m;$y++) -> for($y=$m;$y--;) (-4). 7) join("\n",$z),"\n$n\n".(join("\n",array_reverse($z))); -> join("\n",array_merge($z,[$n],array_reverse($z))); (-4) 8) unnecessary whitespace: foreach($e[0]as$f) (-1) – Titus Nov 3 '16 at 10:16
• 9) unecessary parentheses at ($j==",") (-2). 10) if($r>"")$d.=+$c; -> $d.=$r>""?+$c:""; (-0) – Titus Nov 3 '16 at 10:22 • recursive version: 1) $d.=$l?$t; is obsolete (-10) 2) $s.=$l?"|":"";return$s; -> return$s."|"[$l]; (-6). 3) obsolete braces {$e=v($v,$t+1,$k+1==$c);} (-2). 4) {$e=$v." "[$k+1==$c];$d.=str_pad("",strlen($e),$t+1);} -> $d.=str_pad("",strlen($e=$v." "[$k+1==$c]),\$t+1); (-5). – Titus Nov 3 '16 at 10:47


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News: There is a new Ehell Kindness Project!  Check it out in the "Extending the Hand of Kindness" folder or here: http://www.etiquettehell.com/smf/index.php?topic=139832.msg3372084#msg3372084

• July 23, 2016, 02:46:20 PM

### Author Topic: General Magazine Nuttiness  (Read 31886 times)

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#### Kimblee

• I look good in white....
• Member
• Posts: 7113
• "Hugs don't go Boom." "They don't? Since when?"
##### Re: General Magazine Nuttiness
« Reply #60 on: November 04, 2013, 09:25:10 AM »
My mil subscribes to a couple of mags that she was sold to...and gives them to me.

Anyway, last month has a suggestion under, "help, I am out of lipstick and going out with the girls in an hour.  What to do??"

And the advice was to go to the Kitchen for a can of beets and to stain your lips with beet juice.

I quit reading the mag.

Seriously, if I am that desperate, beets are not the answer.

I'm completely fascinate by this suggestion.

Do that many people have cans of beets?  How do you run out of lipstick( I mean you can get a good 20 more application when they are worn own with a brush or even your finger.  Who has one tube of lipstick? *if its so important to you that cant go out without , to the point of putting beet juice on your lips wouldn't you notice a month before your one and only tube ran out? and how many people just can't take 3 minutes to buy one at the start of the evening or on their way out?  and I don't think beet juice would look good on everyone. Wouldn't it be messy , wouldn't purple strain all around your mouth look worse then no lipstick, I can put lipstick on without going "coloring outside the lines"  but beetjuice applied perfectly maybe a challange.... I know the point was that it was silly but it doesn't make sense on any level.

Also I have a jar of beets so am going to try it.  I think I'll end up with purple over half my chin

Plus, if you're going to take something from your kitchen, why not grab a q tip and the red food coloring? It'll last longer and you won't smell like beets!

#### Thipu1

• Member
• Posts: 7895
##### Re: General Magazine Nuttiness
« Reply #61 on: November 04, 2013, 10:06:44 AM »
MIL and her friends subscribe to a number of health newsletters.  Some of these are of more va
Ue than others. She frequently sends us tips on what we should be drinking.

In the last month, we've been told that we should ---

Drink cocoa instead of coffee for breakfast (good for the memory)

Drink a large glass of grape juice with every meal (good for the memory)

Drink a hot beverage after every meal (dissolves all the fat in the food you eat.  )

Of course, we should be drinking at least a gallon of water a day and at least ten cups of green tea.

Good grief!  With all that liquid, I'd be lucky if I ever got out of the bathroom.

#### Elfmama

• Member
• Posts: 7005
• Derailing threads since 2001!
##### Re: General Magazine Nuttiness
« Reply #62 on: November 04, 2013, 01:41:10 PM »
MIL and her friends subscribe to a number of health newsletters.  Some of these are of more va
Ue than others. She frequently sends us tips on what we should be drinking.

In the last month, we've been told that we should ---

Drink cocoa instead of coffee for breakfast (good for the memory)

Drink a large glass of grape juice with every meal (good for the memory)

Drink a hot beverage after every meal (dissolves all the fat in the food you eat.  )

Of course, we should be drinking at least a gallon of water a day and at least ten cups of green tea.

Good grief!  With all that liquid, I'd be lucky if I ever got out of the bathroom.
Some time ago, there were a series of ads in women's magazines for a fat-buster product.  Not to consume, mind you, but to put into your hot bath water.  It was supposed to somehow dissolve the fat, which then went down the drain.

This raised a number of questions in my mind, like "How dumb do these people think women are?"

And even more about "But what if it really worked?"
• Wouldn't the fat float to the top of the water?  Ewww, bathing in grease-coated water, my favorite thing in the world.  And think about having to clean the bathtub!
• If the fat does go down the drain, wouldn't it cause clogs?
• How long does it take to work?  If you sit in the tub, wouldn't it dissolve only the fat below the water-line? Or to even things out, do you have to sink down into the water and slowly rotate, like a chicken on a rotisserie?
~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~
Common sense is not a gift, but a curse.  Because then
you have to deal with all the people who don't have it.
~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~

#### cwm

• Member
• Posts: 2427
##### Re: General Magazine Nuttiness
« Reply #63 on: November 04, 2013, 01:49:18 PM »
MIL and her friends subscribe to a number of health newsletters.  Some of these are of more va
Ue than others. She frequently sends us tips on what we should be drinking.

In the last month, we've been told that we should ---

Drink cocoa instead of coffee for breakfast (good for the memory)

Drink a large glass of grape juice with every meal (good for the memory)

Drink a hot beverage after every meal (dissolves all the fat in the food you eat.  )

Of course, we should be drinking at least a gallon of water a day and at least ten cups of green tea.

Good grief!  With all that liquid, I'd be lucky if I ever got out of the bathroom.
Some time ago, there were a series of ads in women's magazines for a fat-buster product.  Not to consume, mind you, but to put into your hot bath water.  It was supposed to somehow dissolve the fat, which then went down the drain.

This raised a number of questions in my mind, like "How dumb do these people think women are?"

And even more about "But what if it really worked?"
• Wouldn't the fat float to the top of the water?  Ewww, bathing in grease-coated water, my favorite thing in the world.  And think about having to clean the bathtub!
• If the fat does go down the drain, wouldn't it cause clogs?
• How long does it take to work?  If you sit in the tub, wouldn't it dissolve only the fat below the water-line? Or to even things out, do you have to sink down into the water and slowly rotate, like a chicken on a rotisserie?

Okay, now you're making me laugh out loud at work, and while it's fun, I'm getting weird looks!

Maybe we should all just get some Adipose pills? The fat just walks away, or so I've been told...

#### Redwing

• Member
• Posts: 358
##### Re: General Magazine Nuttiness
« Reply #64 on: November 04, 2013, 01:57:00 PM »
I can't think of any outrageous things I've seen in the magazines in the 35 years I've been keeping my own house.  I pretty much stopped reading them years ago when I realized each issue of almost every magazine was causing me to feel badly about myself.  Everything in them was be a better homemaker, be a better mother, be a better scrabble player, be a better daughter, sister, aunt, drone.  It never ended.

After a long hiatus, I will buy them occasionally, mostly because I love magazines of almost any type.  But let's face it, everything they've got in them of value, like recipes, is available on the internet.

#### magicdomino

• Member
• Posts: 6033
##### Re: General Magazine Nuttiness
« Reply #65 on: November 04, 2013, 02:08:03 PM »
I "loved" the articles on How to Organize Your Small Closet.  Yeah, Smart Decorator Person? Let's see you stuff that stuff into my 24" by 36" closet.  Their small closets were easily twice the size of mine.

#### lowspark

• Member
• Posts: 5134
##### Re: General Magazine Nuttiness
« Reply #66 on: November 04, 2013, 02:52:49 PM »
I like to add up how much money was spent on an outfit when they list all the prices. It's amazing how many times it's upwards of $1000. And I'm just talking top, pants, shoes and purse or maybe a pair of earrings. I think they get sent a ton of free stuff from companies who hope they will promote their product. What happens to all that free stuff? I guess staff takes it home, right? After a few months of that, you probably get immune to the cost of things and how we in the real world actually have to shell out real money. My challenge: I defy you to find a woman's magazine that does NOT have a picture of some kind of make up which has been removed from its container and crushed, smeared or poured into an artistic mass. Something like this: http://www.pixibeauty.com/media/wysiwyg/Family_Circle_Pixi_March_2013.jpg Every single issue of every single woman's magazine I've ever opened up has some version of this page. Houston Texas USA #### TootsNYC • Member • Posts: 34453 ##### Re: General Magazine Nuttiness « Reply #67 on: November 04, 2013, 02:55:22 PM » well, they have to photograph makeup every month, and they want something semi-artistic. And I'll say that I've always had the urge to do that with makeup in the package. #### jedikaiti • Swiss Army Nerd • Member • Posts: 3543 • A pie in the hand is worth two in the mail. ##### Re: General Magazine Nuttiness « Reply #68 on: November 04, 2013, 02:59:28 PM » The lists of holiday suggestions that they've trotted out for the last 75 years, without changing so much as a period. "Wet the string when you tie up packages for mailing, and it won't come untied!" And the US Postal Service will refuse to accept it, and has so refused for decades. String would get caught in their machinery -- and we have adhesive tapes now MADE for sealing packages. "Use a flashlight instead of a candle in the pumpkin that your child carries around on Halloween." I'm 58 years old, and I have NEVER seen a child carrying a pumpkin around ToTing. WHY would someone do such a silly thing? They're too heavy and awkward for a small child, and kids can't carry a decent bag or bucket for the candy that way! I bet they mean those plastic pumpkins kids carry to collect candy. My dad did this for me. ] I can't imagine putting a candle in a candy bucket anyway, though. And it seems like the flashlight would just get buried and the light blocked, anyway. What part of v_e = \sqrt{\frac{2GM}{r}} don't you understand? It's only rocket science! "The problem with re-examining your brilliant ideas is that more often than not, you discover they are the intellectual equivalent of saying, 'Hold my beer and watch this!'" - Cindy Couture #### lowspark • Member • Posts: 5134 ##### Re: General Magazine Nuttiness « Reply #69 on: November 04, 2013, 03:00:18 PM » Yeah, I agree, it looks like it would be fun to crunch up the make up like that. I'm just sick to death of seeing it every single time. Houston Texas USA #### GlitterIsMyDrug • Member • Posts: 1120 ##### Re: General Magazine Nuttiness « Reply #70 on: November 04, 2013, 03:00:44 PM » well, they have to photograph makeup every month, and they want something semi-artistic. And I'll say that I've always had the urge to do that with makeup in the package. I'm not alone! Actually I've done that with make-up, but much cheaper make-up then what they use in magazines I'm sure. I find it fun. #### jedikaiti • Swiss Army Nerd • Member • Posts: 3543 • A pie in the hand is worth two in the mail. ##### Re: General Magazine Nuttiness « Reply #71 on: November 04, 2013, 03:25:19 PM » MIL and her friends subscribe to a number of health newsletters. Some of these are of more va Ue than others. She frequently sends us tips on what we should be drinking. In the last month, we've been told that we should --- Drink cocoa instead of coffee for breakfast (good for the memory) Drink a large glass of grape juice with every meal (good for the memory) Drink a hot beverage after every meal (dissolves all the fat in the food you eat. ) Of course, we should be drinking at least a gallon of water a day and at least ten cups of green tea. Good grief! With all that liquid, I'd be lucky if I ever got out of the bathroom. Some time ago, there were a series of ads in women's magazines for a fat-buster product. Not to consume, mind you, but to put into your hot bath water. It was supposed to somehow dissolve the fat, which then went down the drain. This raised a number of questions in my mind, like "How dumb do these people think women are?" And even more about "But what if it really worked?" • Wouldn't the fat float to the top of the water? Ewww, bathing in grease-coated water, my favorite thing in the world. And think about having to clean the bathtub! • If the fat does go down the drain, wouldn't it cause clogs? • How long does it take to work? If you sit in the tub, wouldn't it dissolve only the fat below the water-line? Or to even things out, do you have to sink down into the water and slowly rotate, like a chicken on a rotisserie? Okay, now you're making me laugh out loud at work, and while it's fun, I'm getting weird looks! Maybe we should all just get some Adipose pills? The fat just walks away, or so I've been told... Why that would be a secret thing, is beyond me. Just ask - there's thousands of people on Earth who'd happily help an alien race procreate in exchange for miraculous fat loss! What part of v_e = \sqrt{\frac{2GM}{r}} don't you understand? It's only rocket science! "The problem with re-examining your brilliant ideas is that more often than not, you discover they are the intellectual equivalent of saying, 'Hold my beer and watch this!'" - Cindy Couture #### Paper Roses • Member • Posts: 4858 ##### Re: General Magazine Nuttiness « Reply #72 on: November 04, 2013, 06:13:10 PM » In the last month, we've been told that we should --- Drink cocoa instead of coffee for breakfast (good for the memory) Drink a large glass of grape juice with every meal (good for the memory) I doubt I'd ever remember to do all that . . . No, you can't, because you wishpishabonnyfish. #### baglady • Member • Posts: 5010 • A big lass and a bonny lass and she loves her beer ##### Re: General Magazine Nuttiness « Reply #73 on: November 04, 2013, 06:21:21 PM » Have you seen http://Catalogliving.net and Magazine Living: http://curbed.com Wonderful snarky comments based on the assumption that people actually decorate their houses that way. The "save a bunch of money by giving up your daily Starbucks latte" tips crack me up. I don't do Starbucks, and if I did, I'd be buying plain old black coffee (do they sell such a thing?). I will buy the occasional$1.20 cup of coffee at the convenience store instead of, or in addition to, making my own at home. I guess I'm just not in their demographic. I'm definitely not in the "wear your panties as a Scrunchie" demographic -- they obviously haven't seen my plus-size cotton Hanes skivvies.
My photography is on Redbubble! Come see: http://www.redbubble.com/people/baglady

#### hobish

• Member
• Posts: 18187
• Release the gelfling!
##### Re: General Magazine Nuttiness
« Reply #74 on: November 04, 2013, 06:58:20 PM »
Have you seen http://Catalogliving.net and Magazine Living: http://curbed.com

Wonderful snarky comments based on the assumption that people actually decorate their houses that way.

The "save a bunch of money by giving up your daily Starbucks latte" tips crack me up. I don't do Starbucks, and if I did, I'd be buying plain old black coffee (do they sell such a thing?). I will buy the occasional \$1.20 cup of coffee at the convenience store instead of, or in addition to, making my own at home. I guess I'm just not in their demographic. I'm definitely not in the "wear your panties as a Scrunchie" demographic -- they obviously haven't seen my plus-size cotton Hanes skivvies.

OMGoodness, thank you. "Wars on Kinkade" on Curbed is killing me. I love it.
It's alright, man. I'm only bleeding, man. Stay hungry, stay free, and do the best you can.
~Gaslight Anthem


text:
# Impetus Reasoning Question

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NOTE: This section is not present in this company's placement process. If you still want to practise, some questions are provided below.
DIRECTIONS for the question 1-4: Read the information given below and answer the questions given below that accordingly.
During a certain week a sales representative must call on five customers - J, K, L, M and N.
She will call on each customer only once, and Monday through Friday, according to the following restrictions:
She cannot call on L on Monday.
She must call on J before she calls on M.
She must call on K before she calls on N.

# Complete Test Series for Wipro Bag your Dream Job Today Comprehensive Online Tests Inclusive Prep for All Placement Exams Acquire Essential Domain Skills

1. Which of the following is an acceptable schedule for the sales representative's calls?
1. J, M, L, K, N
2. K, M, J, N, L
3. L, K, N, J, M
4. L, M, J, K, N
5. N, L, K, J, M

As per conditions : (1) L - Mon X (2) J-M (3) K-N
Only choice A satisfy all conditions.
2. Which of the following two calls CANNOT be scheduled after L?
1. J and K
2. J and N
3. K and M
4. K and N
5. M and N

As per conditions : (1) L - Mon X (2) J-M (3) K-N
As per (1) L can be on Tue and then we are left with only 3 days so can't adjust 4 people.
3. If the sales representative calls on L earlier than J. which of the following must be true of her schedule?
1. K is first
2. L is second
3. J is third
4. N is second
5. M is fifth

As per conditions : (1) L - Mon X (2) J-M (3) K-N
If L is before J then we are left with only 3 days so can't adjust 4 people.
4. If L, K and N are scheduled on consecutive days, in that order, then M could be scheduled for which day?
1. Either Monday or Tuesday
2. Either Monday or Wednesday
3. Either Tuesday or Friday
4. Either Wednesday or Thursday
5. Either Thursday or Friday

As per conditions : (1) L - Mon X (2) J-M (3) K-N If L,K,N are consecutive they have to be Tue onwards. So day left is Fri. But if L is on Wed then day left is Tue as per 3rd condition.
DIRECTIONS for the question 5-7: Study the following letter-symbol-number sequence carefully and answer the questions given below. H U 8 * C P 1 T L Q @ M B 2 • £ X K 6 Δ G 3 $V F A 7 Z N D 1 β R 5. Four of the following five are alike in respect to their position in the above sequence and hence form a group. Which one does not belong to the group?. 1. M• 6G 2. PLB• 3. XΔ$A
4. Δ$7Z 5. H*TQ Answer: Option C. The pattern is +2, +3,+1,which is not followed in C. It should have been V instead of$.
6. If every alternate element starting from your left (H is dropped first) is dropped from the above sequence, which of the following will indicate numbers of symbols, letters and numbers, respectively which will remain in the sequence?
1. 4, 10, 3
2. 3, 10, 4
3. 5, 8, 4
4. 4, 7, 6
5. None of these

Just drop every alternate element from H, only (U*PTQM2£K∆3VAN1R) are left.
7. What is the total number of the "symbol immediately preceded by letter" and the "letter immediately preceded by symbol" together in the above sequence?
1. Four
2. Five
3. Six
4. Seven
5. None of these

H U 8 * C P 1 T L Q @ M B 2 • £ X K 6 ∆ G 3 \$ V F A 7 Z N D 1 β R Check out all letter-symbol and symbol-letter combinations. They are 8.
8. REPORT is related to UGSQUV in the same way as LONGER is related to
1. OQPIHT
2. OQQFGS
3. OQQIHT
4. QPQHIT
5. None of these

The pattern is +3 +2 +3 +2 and so on .
9. Four of the following five are similar in relation to their position in the English alphabet and hence form a group. Which one does not belong to the group?
1. BDHN
2. FHLR
3. QTYC
4. JLPV
5. NPTZ

The pattern is +2 +4 +6 for all options except C.
DIRECTIONS for the question 10: Study the following information carefully and answer the questions given below:
P + Q means P is the daughter of Q    P - Q means P is the husband of Q
P x Q means P is the brother of Q    P ÷ Q means P is the sister of Q
10. If A + B - C ÷ D, which of the following is true?
1. C is the mother of A
2. D is the father of A
3. A is the brother of C
4. A is the uncle of C
5. None of these


text:
# Existence of Derivative for an Integral

Let $f$ be a Riemann integrable function defined on $[-2,2]$. Define a function $F \colon (-1,1) \to \mathbb{R}$ by $$F(h)=\int_0^1 h | f(x+h)-f(x)|\, dx.$$ Show that the derivative $F'(0)$ exists.

I started form $\lim_{h\to 0}$ $\frac{F(h)-F(0)}{h}$

By definition, $F(0)=0$ since it $F(0)$ becomes a definite integral of zero.


text:
# Publications by Felix Parra Diaz

## Collisionality scaling of the electron heat flux in ETG turbulence

Plasma Physics and Controlled Fusion IOP Publishing: Hybrid Open Access (0)

GJ Colyer, AA Schekochihin, FI Parra, CM Roach, MA Barnes, Y-C Ghim, W Dorland

In electrostatic simulations of MAST plasma at electron-gyroradius scales, using the local flux-tube gyrokinetic code GS2 with adiabatic ions, we find that the long-time saturated electron heat flux (the level most relevant to energy transport) decreases as the electron collisionality decreases. At early simulation times, the heat flux "quasi-saturates" without any strong dependence on collisionality, and with the turbulence dominated by streamer-like radially elongated structures. However, the zonal fluctuation component continues to grow slowly until much later times, eventually leading to a new saturated state dominated by zonal modes and with the heat flux proportional to the collision rate, in approximate agreement with the experimentally observed collisionality scaling of the energy confinement in MAST. We outline an explanation of this effect based on a model of ETG turbulence dominated by zonal-nonzonal interactions and on an analytically derived scaling of the zonal-mode damping rate with the electron-ion collisionality. Improved energy confinement with decreasing collisionality is favourable towards the performance of future, hotter devices.

## Radially global $δf$ computation of neoclassical phenomena in a tokamak pedestal

ArXiv (0)

M Landreman, FI Parra, PJ Catto, DR Ernst, I Pusztai

Conventional radially-local neoclassical calculations become inadequate if the radial gradient scale lengths of the H-mode pedestal become as small as the poloidal ion gyroradius. Here, we describe a radially global $\delta f$ continuum code that generalizes neoclassical calculations to allow stronger gradients. As with conventional neoclassical calculations, the formulation is time-independent and requires only the solution of a single sparse linear system. We demonstrate precise agreement with an asymptotic analytic solution of the radially global kinetic equation in the appropriate limits of aspect ratio and collisionality. This agreement depends crucially on accurate treatment of finite orbit width effects.

## Experimental Signatures of Critically Balanced Turbulence in MAST

ArXiv (0)

Y-C Ghim, AA Schekochihin, AR Field, IG Abel, M Barnes, G Colyer, SC Cowley, FI Parra, D Dunai, S Zoletnik, TMAST Team

Beam Emission Spectroscopy (BES) measurements of ion-scale density fluctuations in the MAST tokamak are used to show that the turbulence correlation time, the drift time associated with ion temperature or density gradients, the particle (ion) streaming time along the magnetic field and the magnetic drift time are consistently comparable, suggesting a "critically balanced" turbulence determined by the local equilibrium. The resulting scalings of the poloidal and radial correlation lengths are derived and tested. The nonlinear time inferred from the density fluctuations is longer than the other times; its ratio to the correlation time scales as $\nu_{*i}^{-0.8\pm0.1}$, where $\nu_{*i}=$ ion collision rate/streaming rate. This is consistent with turbulent decorrelation being controlled by a zonal component, invisible to the BES, with an amplitude exceeding the drift waves' by $\sim \nu_{*i}^{-0.8}$.

## Intrinsic rotation with gyrokinetic models

ArXiv (0)

FI Parra, M Barnes, I Calvo, PJ Catto

The generation of intrinsic rotation by turbulence and neoclassical effects in tokamaks is considered. To obtain the complex dependences observed in experiments, it is necessary to have a model of the radial flux of momentum that redistributes the momentum within the tokamak in the absence of a preexisting velocity. When the lowest order gyrokinetic formulation is used, a symmetry of the model precludes this possibility, making small effects in the gyroradius over scale length expansion necessary. These effects that are usually small become important for momentum transport because the symmetry of the lowest order gyrokinetic formulation leads to the cancellation of the lowest order momentum flux. The accuracy to which the gyrokinetic equation needs to be obtained to retain all the physically relevant effects is discussed.

## Transport Bifurcation Induced by Sheared Toroidal Flow in Tokamak Plasmas

ArXiv (0)

EG Highcock, M Barnes, FI Parra, AA Schekochihin, CM Roach, SC Cowley

First-principles numerical simulations are used to describe a transport bifurcation in a differentially rotating tokamak plasma. Such a bifurcation is more probable in a region of zero magnetic shear than one of finite magnetic shear because in the former case the component of the sheared toroidal flow that is perpendicular to the magnetic field has the strongest suppressing effect on the turbulence. In the zero-magnetic-shear regime, there are no growing linear eigenmodes at any finite value of flow shear. However, subcritical turbulence can be sustained, owing to the transient growth of modes driven by the ion temperature gradient (ITG) and the parallel velocity gradient (PVG). Nonetheless, in a parameter space containing a wide range of temperature gradients and velocity shears, there is a sizeable window where all turbulence is suppressed. Combined with the relatively low transport of momentum by collisional (neoclassical) mechanisms, this produces the conditions for a bifurcation from low to high temperature and velocity gradients. The path of this bifurcation is mapped out using interpolation from a large number of simulations. Numerical simulations are also used to construct a parametric model which accurately describes the combined effect of the temperature gradient and the flow gradient over a wide range of their values. Using this parametric model, it is shown that in this reduced-transport state, heat is transported almost neoclassically, while momentum transport is dominated by subcritical PVG turbulence. It is further shown that for any given input of torque, there is an optimum input of heat which maximises the temperature gradient. The parametric model describes both the behaviour of the subcritical turbulence and the complicated effect of the flow shear on the transport stiffness. It may prove useful for transport modelling of tokamaks with sheared flows.


text:
### Who is online

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## Problem with Equation Reference

Add tags Information and discussion about LaTeX's math and science related features (e.g. formulas, graphs).

### Problem with Equation Reference

I tried to use the following commands
Code: Select all  •  Open in writeLaTeX
\begin{equation}\label{xx} 3+4=7 \end{equation}Referring to the equation \eqref{xx}

or

Code: Select all  •  Open in writeLaTeX
\begin{equation}3+4=7 \label{xx}\end{equation}Referring to the equation \eqref{xx}

but it did not work...
it worked just if instead of \eqref{xx} I wrote \ref{xx}. Why is it so? Should I use a particular package? N.B I am using Texniccenter and Mixtek as a compiler
beth87

Posts: 6
Joined: Sat Jun 11th, 2011

### Re: Problem with Equation Reference

"It doesn't work" is an error description that is as good as useless. What is the exact error message from the log? As a random shot I would guess that you forgot to load the amsmath package.

Thorsten
LaTeX Community Moderator

¹ System: openSUSE 13.1 (Linux 3.11.10), TeX Live 2013 (vanilla), TeXworks 0.5 (r1351)
² Posting stopped indefinitely due to offenses

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Posts: 9219
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Abstract : We study stringy modifications of T^3 -fibered manifolds, where the fiber undergoes a monodromy in the T-duality group. We determine the fibration data defining such T-folds from a geometric model, by using a map between the duality group and the group of large diffeomorphisms of a four-torus. We describe the monodromies induced around duality defects where such fibrations degenerate and we argue… ▽ More We study stringy modifications of T^3 -fibered manifolds, where the fiber undergoes a monodromy in the T-duality group. We determine the fibration data defining such T-folds from a geometric model, by using a map between the duality group and the group of large diffeomorphisms of a four-torus. We describe the monodromies induced around duality defects where such fibrations degenerate and we argue that local solutions receive corrections from the winding sector, dual to the symmetry-breaking modes that correct semi-flat metrics. △ Less

Submitted 1 March, 2018; originally announced March 2018.

Report number: LMU-ASC 06/18, MPP-2018-24

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Electron-impact excitation of diatomic hydride cations II: OH ^+ and SH ^+

Abstract : R-matrix calculations combined with the adiabatic-nuclei-rotation and Coulomb-Born approximations are used to compute electron-impact rotational rate coefficients for two open-shell diatomic cations of astrophysical interest: the hydoxyl and sulphanyl ions, OH ^+ and SH ^+ . Hyperfine resolved rate coefficients are deduced using the infinite-order-sudden approximation. The propensity rule… ▽ More R-matrix calculations combined with the adiabatic-nuclei-rotation and Coulomb-Born approximations are used to compute electron-impact rotational rate coefficients for two open-shell diatomic cations of astrophysical interest: the hydoxyl and sulphanyl ions, OH ^+ and SH ^+ . Hyperfine resolved rate coefficients are deduced using the infinite-order-sudden approximation. The propensity rule ΔF=Δj=ΔN=\pm 1 is observed, as is expected for cations with a large dipole moment. A model for OH ^+ excitation in the Orion Bar photon-dominated region (PDR) is presented which nicely reproduces Herschel observations for an electron fraction x_e=10^{-4} and an OH ^+ column density of 3\times 10^{13} ~cm ^{-2} . Electron impact electronic excitation cross sections and rate coefficients for the ions are also presented. △ Less

When fewer indices are provided than the number of axes, the missing indices are considered complete slices  :

The expression within brackets in  b[i]  is treated as an  i  followed by as many instances of  :  as needed to represent the remaining axes. NumPy also allows you to write this using dots as  b[i,...]  .

The dots (  ...  ) represent as many colons as needed to produce a complete indexing tuple. For example, if  x  is an array with 5 axes, then

Iterating over multidimensional arrays is done with respect to the first axis:

Iterating

However, if one wants to perform an operation on each element in the array, one can use the  flat  attribute which is an iterator over all the elements of the array:

An array has a shape given by the number of elements along each axis:

The shape of an array can be changed with various commands. Note that the following three commands all return a modified array, but do not change the original array:

The order of the elements in the array resulting from ravel() is normally “C-style”, that is, the rightmost index “changes the fastest”, so the element after a[0,0] is a[0,1]. If the array is reshaped to some other shape, again the array is treated as “C-style”. NumPy normally creates arrays stored in this order, so ravel() will usually not need to copy its argument, but if the array was made by taking slices of another array or created with unusual options, it may need to be copied. The functions ravel() and reshape() can also be instructed, using an optional argument, to use FORTRAN-style arrays, in which the leftmost index changes the fastest.

The  reshape  function returns its argument with a modified shape, whereas the Cheap Price Store Hush Puppies Rainmaker Black Mens Slipon Dress Shoes Discount Supply Sale Lowest Price Popular Online Great Deals For Sale rkp3Ps3Pj
method modifies the array itself:

If a dimension is given as -1 in a reshaping operation, the other dimensions are automatically calculated:

Several arrays can be stacked together along different axes:

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I have since put a small LED in my DX7 and then in my JR X9503 when I got it to provide an easy to see visual aid that the radio is turned on when I am too far away to see if the display is on. The Spektrum DX8 already has that simple little "power on" LED installed and using it to light up the patented Spektrum bar graph symbol is a nice touch.

Final Thoughts...

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# If f={(-3,4),(-1,5),(-2,6),(2,4),(0,3)} and g={(4,3),(5,7),(3,0),(6,0)} then find set of ordered pair of gof and fog and represent in arrow diagram.?

May 29, 2018

$g \setminus \boldsymbol{o} \setminus f = \left\{\begin{matrix}- 3 & 3 \\ - 1 & 7 \\ - 2 & 0 - \\ 2 & 3 \\ 0 & 0\end{matrix}\right\}$

$f \setminus \boldsymbol{o} \setminus g = \left\{\begin{matrix}3 & 3 \\ 6 & 3\end{matrix}\right\}$

#### Explanation:

Given the specified ordered pairs, we can write the functions $f$ and $g$ by the mappings:

 f = { (-3, |-> 4), (-1, |-> 5), (-2, |-> 6), (2, |-> 4), (0, |-> 3) :} \ \ \ , and  g = { (4, |-> 3), (5, |-> 7), (3, |-> 0), (6, |-> 0) :}

We can construct:

$g \setminus \boldsymbol{o} \setminus f = g \left(f\right)$

 g \ bb(o) \ f = { (gf(-3)), (gf(-1)), (gf(-2)), (gf(2)), (gf(0)) :} = { (g(4)), (g(5)), (g(6)), (g(4)), (g(3)) :} = { (3), (7), (0), (3), (0) :}

Thus using an ordered pair representation, we have:

$g \setminus \boldsymbol{o} \setminus f = \left\{\begin{matrix}- 3 & 3 \\ - 1 & 7 \\ - 2 & 0 - \\ 2 & 3 \\ 0 & 0\end{matrix}\right\}$

However, We have a restricted domain for

$g \setminus \boldsymbol{o} \setminus f = g \left(f\right)$

We get:

 f \ bb(o) \ g = { (fg(4)), (fg(5)), (fg(3)), (fg(6)) :} = { (f(3)), (f(7)), (f(0)), (f(0)) :} = { ("undefined"), ("undefined"), (3), (3) :}

The domain of $f \circ g$ is that part of the domain of $g$ that yields a value in the domain of $f$.


text:
# stability of alkali metal carbonates

All the bicarbonates (except which exits in solution) exist … On decomposition, lithium nitrate gives lithium oxide. rev 2021.1.11.38289, The best answers are voted up and rise to the top, Chemistry Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. Check out a sample Q&A here. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. But carbonates of alkaline earth metals are insoluble in water. M CO → M O+C O Concatenate files placing an empty line between them, Realistic task for teaching bit operations, One likes to do it oneself. Explain giving reason. It is found that the conductivity of X2CO3:MZO film can be controlled and the thermal stability of ETLs could be improved by X2CO3 blending in MZO. Your "answer" lacks credibility otherwise. As we move down group 1 and group 2, the thermal stability of nitrate increases. Asking for help, clarification, or responding to other answers. Can an Airline board you at departure but refuse boarding for a connecting flight with the same airline and on the same ticket? @KartikWatwani sorry for the late follow-up, but I wanted to add this: so you're asking as to whether if you heat up sodium carbonate, at what temperatures does is decompose WITHOUT producing carbon dioxide? 7. Reaction – 4LiNO 3 2Li 2 O + 4NO 2 + O 2. MathJax reference. Thermal stability. That’s … Saltpetre (potassium nitrate) was used in gunpowder, which was invented in China about the 9th century ad and had been introduced into Europe by the 13th century.. The stability of group 1 and 2 carbonates increases down the group therefore you can expect that the lower the metal in the periodic table the more stable is its corresponding carbonate. asked May 27, 2019 in Chemistry by ManishaBharti ( 64.9k points) classification of elements The carbonates of alkali metals are stable towards heat. The stability of carbonates and bicarbonates increases down the group. Why doesn't IList only inherit from ICollection? Chemical Characteristics: Low solubility in water. The carbonates decompose on heating form metal oxide and CO2. MCO3 —-> MO + CO2 S - block elements - alkali and alkaline earth metals, Classification of elements and periodicity in properties, General principles and process of Isolation of metals, Purification and characteristics of organic compounds, Some basic principles of organic chemistry, Principles related to practical chemistry. Hydrogen carbonates of other alkali metals are found in solid state. Lithium does not react with ethyne. I have problem understanding entropy because of some contrary examples. (ii) Carbonates. From Li to Cs, thermal stability of carbonates increases. In Group 1, lithium carbonate behaves in the same way - producing lithium oxide and carbon dioxide.. asked Oct 2, 2020 in Alkali and Alkaline Earth Metals by Manish01 (47.4k points) alkali and alkaline earth metals; class-11; 0 votes. Other carbonates form by precipitation. Thanks for contributing an answer to Chemistry Stack Exchange! Is there any temperature where $Na_2CO_3$ doesn't give $CO_2$ on thermal decomposition? Stability of carbonates increases down group I (alkali) and group II (alkaline earth) metals. Group I cations increase in ionic radius down the group. Not getting into the energetics one can safely state that the reason for these trend is the polarising power of the metal cation. Alkali metal salts were known to the ancients. Ionic character and the … Carbonates of alkali metals are soluble in water with the exception of Li2CO 3. This makes the C-O bond weaker allowing the -CO2 group to depart easily. Since electropositive character increases from Li to Cs All carbonates and bicarbonate are water soluble and their solubility increases from Li to Cs CHEMICAL PROPERTIES Alkalimetals are highly reactive due to low ionization energy. However, the decomposition of carbonate salts (r eaction-9, where M represents alkali-metals Li, Na, or K) is suggested by other researchers, par ticularly above 700 °C [34–39]. The Old Testament refers to a salt called neter (sodium carbonate), which was extracted from the ash of vegetable matter. So, solubility should decrease from Li to Cs. Whereas bicarbonates give carbonate, water and carbon dioxide. Unstable to heat. All the carbonates in this group undergo thermal decomposition to the metal oxide and carbon dioxide gas. How can deflection and spring constant of cantilever beam stack be calculated? Use MathJax to format equations. See Answer. Solubility. Describe the thermal stability of carbonates of alkali and alkaline earth metals. The thermal stability of these hydrides decreases in which of the following order. All the Group 2 carbonates and their resulting oxides exist as white solids. These halides can also be prepared by the action of halogen acids (HX) on metals, metals oxides, hydroxides and carbonates. Want to see the step-by-step answer? Carbonates of metal: Thermal stability The carbonates of alkali metals except lithium carbonate are stable to heat. This can therefore enhance the operational lifetime of … Why does Steven Pinker say that “can’t” + “any” is just as much of a double-negative as “can’t” + “no” is in “I can’t get no/any satisfaction”? Can an electron and a proton be artificially or naturally merged to form a neutron? The alkali metals form salt like hydrides by the direct synthesis at elevated temperature. Heating the carbonates. so, the correct order of thermal stability of given carbonates is:BeCO3 < MgCO3 < CaCO3 < K2CO3Be, Mg and Ca present in second group and K … However, carbonate of lithium, when heated, decomposes to form lithium oxide. To learn more, see our tips on writing great answers. MO + 2HX → MX 2 + H 2 O . 8) While the hydroxides and carbonates of sodium and potassium are readily soluble in water, the corresponding salts of magnesium and calcium are only sparingly soluble. From Li to Cs, due to larger ion size, hydration enthalpy decreases. Most carbonates tend to decompose on heating to give the metal oxide and carbon dioxde. Thermal stability. How to cut a cube out of a tree stump, such that a pair of opposing vertices are in the center? The reaction for sodium carbonate decompositon at melting point should be: Here the comparison is highly relative(or subjective). Which of the following carbonate of alkali metals has the least thermal stability? check_circle Expert Answer. Why are alkali metals not found in nature? Na2CO3 is more thermally stable. (Who is one?). Li 2 CO 3 , however is considerably less stable and decomposes readily. Other alkali metals react with ethyne and form corresponding ethynide. Are there any alternatives to the handshake worldwide? Which of the following can not decompose on heating to give $\ce{CO_2}$? Also, for the same period the group 1 carbonate is relatively more stable. Question: S-GROUP ELEMENTS C) E) 1) Mention 3 General Characteristics Of The S-block Elements That Distinguishes Them From The Other Elements Of The Periodic Table 2) Explain Why Group 2 Elements Never Form Mion. The stability of peroxide and superoxide of alkali metals increase as we go down the group. Do rockets leave launch pad at full thrust? In chemistry, there are three definitions in common use of the word base, known as Arrhenius bases, Brønsted bases and Lewis bases.All definitions agree that bases are substances which react with acids as originally proposed by G.-F. Rouelle in the mid-18th century.. Arrhenius proposed in 1884 that a base is a substance which dissociates in aqueous solution to form hydroxide ions OH −. Chemistry Stack Exchange is a question and answer site for scientists, academics, teachers, and students in the field of chemistry. The work function of the four carbonates … What I have read till now: Lithium carbonate is not so stable to heat and bicarbonates of alkali metals decompose at approximately $\pu{300 ^\circ C}$. Group 1: Alkali Metals and Carbonates (X 2 CO 3) is the reaction between Li, Na, K, Rb and Cs with CO 3. Hence there is no reaction and carbon dioxide is not released. All except Lithium are soluble in water and stable to heat. Alkali metal carbonates blending in MZO, X2CO3:MZO, control the band-gap, electrical properties, and thermal stability. Alkali metal carbonates blending in MZO, X2CO3:MZO, control the band-gap, electrical properties, and thermal stability. Please cite references for your claims. Also, for the same period the group 1 carbonate is relatively more stable. Aside from some arcane extreme conditions (extreme pressures and temperatures combined, for example), I think that if it decomposes, it will probably produce carbon dioxide. Carbonates of alkaline earth metals are insoluble in water. They are all also mentioned on Wikipedia. This e/r decreases down the group making the compound relatively stable. 8. Appearance: white powder, fragrance-free; Sodium Carbonate (Na 2 CO 3) diodes (QLEDs) by blending various alkali metal carbonate in magnesium (Mg) doped zinc oxide (ZnO) (MZO) electron transport layer (ETL). Nitrates of both group 1 and group 2 metals are soluble in water. Can 1 kilogram of radioactive material with half life of 5 years just decay in the next minute? Alkaline earth metal carbonates decompose on heating gives carbon dioxide and oxide. Why is there no Vice Presidential line of succession? 1 answer. We know that in the carbonate ion, the charge is delocalized and is thus highly polarizable. Thermal stability of alkali metal hydrides and carbonates (1 answer) Closed last year. The carbonates of alkaline earth metals can be regarded as salts of weak carbonic acid (H2CO3) and metal hydroxide, M (OH)2. The carbonates (M 2 CO 3) of alkali metals are remarkably stable upto 1273 K, above which they first melt and then eventually decompose to form oxides. Also, the solubility increases as we move down the group. Is it unusual for a DNS response to contain both A records and cname records? T.S ∝ Ionic character (for poly atomic anion). Why do "checked exceptions", i.e., "value-or-error return values", work well in Rust and Go but not in Java? The thermal stability of carbonates increases with the increasing basic strength of metal hydroxides on moving down the group.Thus the order is The bicarbonates of all the alkali metals are known. Select correct statement (s) : (A) stability of peroxides and superoxides of alkali metals increases with increase in size of the metal ion. All the carbonates of alkaline earth metal are more soluble in the presence of CO2 due to the formation of corresponding bicarbonates. The thermal stability of alkaline earth metal carbonates–MgCO3, CaCO3, SrCO3 and BaCO3, follows the order. Alkali metal carbonates blending in MZO, X 2 CO 3 … Stability of Quantum-Dot Light Emitting Diodes with Alkali Metal Carbonates Blending in Mg Doped ZnO Electron Transport Layer Nanomaterials (Basel) . Group one and two cations have a very high charge to radius ratio(e/r) which implies that their polarizing powers are fairly high. 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## Modeling and forecasting U.S. mortality. (With discussion).(English)Zbl 1351.62186

Summary: Time series methods are used to make long-run forecasts, with confidence intervals, of age-specific mortality in the United States from 1990 to 2065. First, the logs of the age-specific death rates are modeled as a linear function of an unobserved period-specific intensity index, with parameters depending on age. This model is fit to the matrix of U.S. death rates, 1933 to 1987, using the singular value decomposition (SVD) method; it accounts for almost all the variance over time in age-specific death rates as a group. Whereas $$e_0$$ has risen at a decreasing rate over the century and has decreasing variability, $$k(t)$$ declines at a roughly constant rate and has roughly constant variability, facilitating forecasting. $$k(t)$$, which indexes the intensity of mortality, is next modeled as a time series (specifically, a random walk with drift) and forecast. The method performs very well on within-sample forecasts, and the forecasts are insensitive to reductions in the length of the base period from 90 to 30 years; some instability appears for base periods of 10 or 20 years, however. Forecasts of age-specific rates are derived from the forecasts of $$k$$, and other life table variables are derived and presented. These imply an increase of 10.5 years in life expectancy to 86.05 in 2065 (sexes combined), with a confidence band of plus 3.9 or minus 5.6 years, including uncertainty concerning the estimated trend. Whereas 46% now survive to age 80, by 2065 46% will survive to age 90. Of the gains forecast for person-years lived over the life cycle from now until 2065, 74% will occur at age 65 and over. These life expectancy forecasts are substantially lower than direct time series forecasts of $$e_0$$, and have far narrower confidence bands; however, they are substantially higher than the forecasts of the Social Security Administration’s Office of the Actuary.

### MSC:

 62P20 Applications of statistics to economics 91B84 Economic time series analysis 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62M20 Inference from stochastic processes and prediction 91D20 Mathematical geography and demography

### Keywords:

demography; forecast; life expectancy; mortality; population; projection
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### References:

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