## google sheets – Return a blank when cell reference is blank

This formula will work to keep blank cells from returning “0” to another cell.

``````=IF( AND( ISBLANK(A1)=true , isblank(B1)=true ) , "dontsayzero")
``````

Then, you can just remove the dontsayzero after you’ve tested it, but LEAVE THE QUOTES! Also, you can make things more sophisticated adding more “IF” and “OR” statements. Check this one out (remove carriage returns but not commas)

``````=
IF( AND(ISBLANK(A1)=true,ISBLANK(B1)=true) , "bothblank",
IF( OR(ISBLANK(A1)=true,ISBLANK(B1)=true) , "atleastoneblank" ,
IF( AND(ISBLANK(A1)=false,ISBLANK(B1)=false) , "neitherblank")))
``````

This formula looks at the two cells and tells you their status. Should be pretty straightforward. This could be used if you had some data, but not enough to make the final calculation and didn’t want the zeroes or errors to mess with your further analysis. Just remove the stuff inside, leave the quote signs, and you’ve got a blank cell for any of the three situations. Moving further, if you want a different operation done in those three situations, remove the quote signs and insert your operation after the comma. There’s probably something more sophisticated out there as well. Good luck!

## google sheets – Return a blank when cell reference is blank

This formula will work to keep blank cells from returning “0” to another cell.

``````=IF( AND( ISBLANK(A1)=true , isblank(B1)=true ) , "dontsayzero")
``````

Then, you can just remove the dontsayzero after you’ve tested it, but LEAVE THE QUOTES! Also, you can make things more sophisticated adding more “IF” and “OR” statements. Check this one out (remove carriage returns but not commas)

``````=
IF( AND(ISBLANK(A1)=true,ISBLANK(B1)=true) , "bothblank",
IF( OR(ISBLANK(A1)=true,ISBLANK(B1)=true) , "atleastoneblank" ,
IF( AND(ISBLANK(A1)=false,ISBLANK(B1)=false) , "neitherblank")))
``````

This formula looks at the two cells and tells you their status. Should be pretty straightforward. This could be used if you had some data, but not enough to make the final calculation and didn’t want the zeroes or errors to mess with your further analysis. Just remove the stuff inside, leave the quote signs, and you’ve got a blank cell for any of the three situations. Moving further, if you want a different operation done in those three situations, remove the quote signs and insert your operation after the comma. There’s probably something more sophisticated out there as well. Good luck!

## google sheets – Return a blank when cell reference is blank

This formula will work to keep blank cells from returning “0” to another cell.

``````=IF( AND( ISBLANK(A1)=true , isblank(B1)=true ) , "dontsayzero")
``````

Then, you can just remove the dontsayzero after you’ve tested it, but LEAVE THE QUOTES! Also, you can make things more sophisticated adding more “IF” and “OR” statements. Check this one out (remove carriage returns but not commas)

``````=
IF( AND(ISBLANK(A1)=true,ISBLANK(B1)=true) , "bothblank",
IF( OR(ISBLANK(A1)=true,ISBLANK(B1)=true) , "atleastoneblank" ,
IF( AND(ISBLANK(A1)=false,ISBLANK(B1)=false) , "neitherblank")))
``````

This formula looks at the two cells and tells you their status. Should be pretty straightforward. This could be used if you had some data, but not enough to make the final calculation and didn’t want the zeroes or errors to mess with your further analysis. Just remove the stuff inside, leave the quote signs, and you’ve got a blank cell for any of the three situations. Moving further, if you want a different operation done in those three situations, remove the quote signs and insert your operation after the comma. There’s probably something more sophisticated out there as well. Good luck!

## reference request – English translation of von Neumann’s Algebra der Funktionaloperationen (1930)

Does anyone know if there exists an English translation of von Neumann’s early work in operator theory, in particular the paper Zur Algebra der Funktionaloperationen und Theorie der normalen Operatoren?

The full citation is Mathematische Annalen volume 102, pages 370–427(1930).

If not, are there any expository works in English from around that time period covering von Neumann’s work, maybe say pre-1950?

## reference request – Unavoidable chords

A positive number $$x$$ is called an unavoidable chord, if it has this property:
For every continuous complex-valued function $$gamma:(0,1)to C$$ with $$gamma(0)=0,gamma(1)=1$$,
there exist $$t_1neq t_2$$ in $$(0,1)$$ such that $$gamma(t_1)-gamma(t_2)=x$$.

My colleague Mario Bonk proved
the following Theorem:
Unavoidable chords are exactly the numbers $$1/n: n=1,2,3,ldots.$$

He is curious whether this is a new result, and he sent his manuscript to several friends.
I am sure that I have seen this (or an equivalent statement) somewhere, don’t remember where, and my question is what is a reference.

## reference request – Kernels with finite dimensional feature spaces

Suppose $$x,y in mathbb{R}^n$$ for some given fixed n.

Consider a kernel $$K(x,y) = f(langle x, y rangle)$$, I’d like to know which functions $$f$$ admit a finite dimensional feature map. In other words, for $$x,y in mathbb{R}^n$$, what functions $$f$$ does there exist an $$m$$ and $$phi: mathbb{R^n} rightarrow mathbb{R}^m$$ with

$$f(langle x, y rangle ) = langle phi(x), phi(y)rangle?$$

I can show that $$f$$ must be polynomial if $$m < 2^n$$, but I’m sure there must exist a more comprehensive result.

## entropy – English reference of an article

I wonder if anyone has a copy of the famous article “Entropie geometrique des feuilletages” in English. I unfortunately don’t understand French very well, and I would like to know if there is an English version of it.

The article can be found at this link, from the Ghys personal page.

## nt.number theory – Reference for behavior of Artin \$L\$-functions at \$Re(s) = 1\$

Would anyone know a reference that proves the basic facts about Artin $$L$$-functions at $$Re(s) = 1$$? Namely, the non-vanishing and holomorphicity for non-trivial characters.

I assume this was done in Artin’s original paper, but a modern source would be most welcome.

## sharepoint online – Context.ExecuteQuery() will raise this error:- “System.NullReferenceException: ‘Object reference not set to an instance of an object.”

I have the following CSOM code inside my asp.net core console application:-

`````` TaxonomySession txSession = TaxonomySession.GetTaxonomySession(context);
TermStore tc = txSession.TermStores.GetByName(termstorename);
TermGroup g = tc.Groups.GetByName(groupname);
try
{
var technician = context.Site.RootWeb.EnsureUser(SQLitem.Technician);
context.ExecuteQuery();
NewUFSlistItem("UserFeedbackEngineer") = technician;

}
catch (Exception e)
{

}

TermSet ts = g.TermSets.GetByName(termsetname);
var customername = ts.Terms.GetByName(SQLitem.Account);
context.ExecuteQuery();
``````

now if the first `context.ExecuteQuery();` raise an exception (mainly when the `context.Site.RootWeb.EnsureUser(SQLitem.Technician)` raise an error when the user can not be found), the second `context.ExecuteQuery();` will raise this error:-

``````System.NullReferenceException: 'Object reference not set to an instance of an object.'
``````

so i am not sure why this is happening? any advice?
Thanks

## reference request – minimum ratio between the shortest and longest distances between \$m\$ points in \$mathbb R^n\$

Let there be $$m$$ points in $$mathbb R^n$$. Let $$D$$ be the longest distance between two of these points and let $$d$$ be the smallest. What is the smallest possible value of $$frac{D}{d}$$ for each value of $$n$$ and $$m$$, and which configurations reach it?

It is clear when $$n$$ is $$1$$ the solution is reached when the points are evenly spaced in a line.

For $$n=2$$ I think the answer may be the regular polygons. For higher dimensions maybe it is reached by setting all the points in a sphere and trying to spread them out as best possible?