I am trying to write a formula that updates a number in the cell if another cell is empty, and leaves the last number calculated if the other cell is not empty. I am calculating my profit, which changes until I actually collect it. So far I have this:

`=IF(ISBLANK(K2),C2-H2,())`

Obviously it is not possible to do this. Prove me wrong

# Tag: function

## beginner – GetNeighborhood function for 3D cells structure in MATLAB

I am attempting to implement a `GetNeighborhood`

function in order to get a specific region from `inputCells`

by `sizeInput`

and `centralLocation`

parameters in 3D cells structure.

**The experimental implementation**

The experimental implementation of `GetNeighborhood`

function is as below.

```
function (output) = GetNeighborhood(inputCells, sizeInput, centralLocation)
% Get neighborhood of fixed size and centered at centralLocation
output = cell( sizeInput ,sizeInput ,sizeInput );
X = centralLocation(1);
Y = centralLocation(2);
Z = centralLocation(3);
for x = -sizeInput:sizeInput
for y = -sizeInput:sizeInput
for z = -sizeInput:sizeInput
if X + x < 1
xLocation = 1;
elseif X + x > size(inputCells, 1)
xLocation = size(inputCells, 1);
else
xLocation = X + x;
end
if Y + y < 1
yLocation = 1;
elseif Y + y > size(inputCells, 2)
yLocation = size(inputCells, 2);
else
yLocation = Y + y;
end
if Z + z < 1
zLocation = 1;
elseif Z + z > size(inputCells, 3)
zLocation = size(inputCells, 3);
else
zLocation = Z + z;
end
output{sizeInput + x + 1, sizeInput + y + 1, sizeInput + z + 1} = ...
inputCells{xLocation, yLocation, zLocation};
end
end
end
end
```

**Test cases**

For testing purpose, a simple test script is created as below.

```
clear all;
clc;
close all;
set(groot,'defaultFigureVisible','on');
%% Create test cells
testCellsSize = 10;
test = cell(testCellsSize, testCellsSize, testCellsSize);
for x = 1:size(test, 1)
for y = 1:size(test, 2)
for z = 1:size(test, 3)
test{x, y, z} = (x * 100 + y * 10 + z);
end
end
end
%% Specify test parameters
NeighborhoodDist = 1;
centralLocation = (5 2 2);
%% Perform test
result = GetNeighborhood(test, NeighborhoodDist, centralLocation);
result
```

If there is any possible improvement about potential drawback or unnecessary overhead, please let me know.

## SQL function on a javascript variable

I have a javascript file that receives a number like “1345”, and in order to insert it into a table, I need to find a way to apply an specifiq SQL command on it.

This is the code that I have:

```
var stime = traffic.startTime;
var dateNow = new Date().toLocaleString('pt-BR', {
timeZone: "America/Sao_Paulo"
});
conn.executeUpdate(
'INSERT INTO "SCHEMA"."TABLE" VALUES (?,?,?,?,?,?,?,?,?)',
val1, val2, val3, val4, stime, val6, val7, new Date(dateNow), null);
```

what I need is to apply the SQL function to_time to the variable stime and then, run the insert. so `to_time(stime, HHMI)`

.

How can I do that?

Obs: I don’t wanna manipulate the number in js, it’s gotta be in SQL.

## php – WordPress schedule event function not running

I am totally new with the schedule event from WordPress.

For my theme I created a function that must run every minute.

To test my scheduler I created a test function that send me an email.

But I do not receive an email and I think my scheduler is not working.

Please who can help me a bit?

Below my code so far

```
add_action( 'my_test', 'test_scheduler');
add_filter( 'cron_schedules', function ( $schedules ) {
$schedules('per_minute') = array(
'interval' => 60,
'display' => __( 'One Minute' )
);
return $schedules;
} );
//create event after theme setup
add_action("after_setup_theme", function(){
if (! wp_next_scheduled ( 'my_test' )) {
wp_schedule_event( time(), 'per_minute', 'my_test' );
}
});
//delete event if theme is deactivated
add_action('switch_theme', function(){
wp_clear_scheduled_hook( 'my_test' );
});
```

The code above is in the functions.php file.

## How can I implement a function that is a homomorphism?

I want to do the follow: Write a function $f$ such that if I evaluate $f(ax+by)$, it returns $f(a)f(x)+f(b)f(y)$. How can I do that? I tried to look in the help for "homomorphism" but didn’t find anything. I suspect there might be another name for this kind of functions in Mathematica.

## Dataset: selectively map a function onto the nth column

I have this data, which I used the following to `Import`

.

```
c=Import("data1.csv", "Dataset", HeaderLines -> 1);
d=c(All, {1 -> ToExpression});
```

I want to convert the 1st col to `Minute`

and want to use the `dataset(All,{n->f})`

mentioned in MMA’s `Dataset`

document. My idea to operate a function on the 1st col and return a **two-col** dataset. I tried the following. Some worked, while some did not. Could you please have a check and comment on why some methods did not return what I want. Thanks.

Those worked.

```
f = UnitConvert(#, "Minutes") &;
d(All, {1 -> f})
d(All, {"t" -> f})
d(All, {"t" -> Function({x}, UnitConvert(x, "Minutes"))})
```

Those did not.

```
d(All, {1 -> UnitConvert(#, "Minutes") &}) (*I understand why this one did not work.*)
d(All, {1 -> UnitConvert(#((1)), "Minutes") &})
d(All, {"t" -> UnitConvert(#((1)), "Minutes") &})
```

This simply blowed my mind. I wanted to return the 1st col itself. However, `1`

seems to work as `#((1))`

and `2`

as `#((2))`

. It seems to me anything appears on the right hand left is treated as a `Function`

(Here, as `Part`

)?

```
d(All, {"t" -> 1})
d(All, {"t" -> 2})
```

## replacement – Apply a function to all coefficients of a polynomial

Here’s one way:

```
rules = CoefficientRules(P, {x, y})
newrules = MapAt(f, #, 2) & /@ rules
FromCoefficientRules(newrules, {x, y})
```

Or, in general,

```
CoefficientMap(f_, P_) := FromCoefficientRules(
MapAt(f, #, 2) & /@ CoefficientRules(P, Variables(P)), Variables(P))
CoefficientMap(f_, P_, vars_) := FromCoefficientRules(
MapAt(f, #, 2) & /@ CoefficientRules(P, vars), vars)
```

In general, if you replace `MapAt(f, #, 2) &`

with a function which takes `Rule(powerlist, coeff)`

to `Rule(newpowerlist, newcoeff)`

, you could build more general maps on polynomials! (Currently, `MapAt(f, #, 2) &(Rule(p, c))`

yields `Rule(p, f(c))`

.)

For the application you mention later on, though, where you change `Sin(2 x)`

to `Sin(4 x)`

it sounds like you might want to build your own version of `Variables`

or `CoefficientRules`

for that situation which would extract and encode Fourier coefficients of finite Fourier series (or something like that)â€”possibly by converting them into polynomial variables in their own right.

## google sheets – How to add arrayformula function to this formula with IF function?

I made a table that has two columns (namd & State). The 4th column(check) makes conditional formatting possible for any of these combinations: (if name is either “Ali” or “John”, AND state is “FL”), a conditional formatting rule is applied only if the cell value of E2 is “NO”.

I had to repeat this formula for all rows and I failed to wrap it in an arrayformula function.

I tried this but failed:

`=if(OR(AND(C2="John",D2="FL",$E$1="No"),AND(C2="Ali",D2="FL",$E$1="No")),1,0)`

adding arrayformula:

`=ArrayFormula(if(OR(AND(C2:C="John",C2:D="FL",$E$1="No"),AND(C2:C="Ali",D2:D="FL",$E$1="No")),1,0))`

https://docs.google.com/spreadsheets/d/17mmduo0em4PK0FDPxIRTX36CqhW6woI4jdyPSJaiGAM/edit#gid=1414263054

## fa.functional analysis – Is the graph of a Sobolev function path connected?

Let $Omega$ be a bounded, open, simply connected subset of $mathbb R^n$ with Lipschitz boundary.

Question:Does every function in the Sobolev space $W^{1,1} (Omega)$

admit a representative whose graph in $Omega times mathbb R$ is

path connected?