## Creating audience targeted ad groups

Hi,

I want to set up an experiment in Google ads. We currently aren’t really using audiences. My campaign structure is just based on keywords, so each ad group is a product type and the keywords are various keywords relating to the ad group.

But I want to try and target the ads better, so my plan is to set up ad groups based on audiences. For example, one ad group would be ‘whiteboards-architecture’. And then the ad text would relate to architects.

But my question is. If I set up the architect ad group, and target the ad group to architects in the audience section, and then have a normal ad group with the same keywords that is has no targeting, will these two ad groups clash is some way? Or will it just show the architect ads to the architects and then the normal ads to everyone else?

## Intersection Theory – Chow groups and Their Applications

I’m a beginner in the filed of $$Algebraic$$ $$Geometry$$, especially the $$Intersection$$ $$Theory$$. I came to know that the $$chow$$ $$groups$$ of schemes are analogs to the $$homology$$ $$groups$$ of manifolds. I know at least one motivation behind the study of homology groups; they provide invariants of the manifold that can be used for classification purposes. I believe there must be many such motivations/applications of chow groups but right now I am failed to find. Can any of you be kind enough to enlist few of these?

## Algorithm for factoring elements of permutation groups?

You can solve a Rubik’s cube by factoring its permutation into a sequence of “elementary” permutations (a subset of permutations that is sufficient to construct every other permutation in the group). There are several algorithms for solving Rubik’s cubes. Are there any algorithms for the general problem of factoring permutations?

## How to set the display name for group members in Google Groups?

I’m a manager on Google Groups for a group that has about 100 members. I want to be able to edit the display name so I can identify who my users are, instead of “JKL6” for example, which is the prefix for an email address. First, I can’t seem to edit the “Display Name” and second, I have deleted the list of email addresses when I was fooling around with the identity tool. I was trying to change the settings about display name vs. Google name, and now my “Members” list does not have ANY email addresses showing.

## Relationship between distances on homogeneous spaces and their Lie groups

Consider the (round) sphere $$M=\mathbb{S}^{n-1}$$ as a homogeneous $$O(n)$$-space. Then for $$x,y\in\mathbb{S}^{n-1}$$ there is $$g\in O(n)$$ such that $$y=g\cdot x$$. Denote the Riemannian distance on $$\mathbb{S}^{n-1}$$ by $$d_{\mathbb{S}^{n-1}}$$. Intuitively, if $$y$$ and $$x$$ are not far apart then $$g$$ should be almost the identity (because the $$O(n)$$-action is smooth). I am able to explicitly construct such a rotation $$g$$ so that \begin{align} \|g-\operatorname{Id_{\mathbb{R}^n}}\| \leq d_{\mathbb{S}^{n-1}}(y,x) \end{align} where $$\|\cdot\|$$ is the operator norm for matrices.

Analoguously, if $$M=\mathrm{Gr}_m(\mathbb{R}^n)$$ is the Grassmannian, then by a similar construction using principle angles I can find a rotation $$g$$ such that $$F=g\cdot E$$ for $$m$$-planes $$E,F$$ and \begin{align} \|g-\operatorname{Id_{\mathbb{R}^n}}\| \leq 2m\; d_{\mathrm{Gr}_m(\mathbb{R}^n)}(F,E) \end{align} where $$d_{\mathrm{Gr}_m(\mathbb{R}^n)}$$ is the angle metric on $$\mathrm{Gr}_m(\mathbb{R}^n)$$ (e.g. here).

However, I find these constructions rather unsatisfying and would like to understand if there is a more abstract underlying principle at play.

Here is my question: Given a homogeneous $$G$$-space $$M$$, are there always metrics on $$M$$ and $$G$$ such that there is a quantitative estimate \begin{align} d_G(g,e) \leq C \; d_M(g\cdot y, x) \end{align} for all $$x,y\in M$$ and $$g\in G$$?

Feel free to add any hypotheses (such as compactness etc) that apply to $$\mathbb{S}^{n-1}$$, $$\mathrm{Gr}_m(\mathbb{R}^n)$$ and $$O(n)$$.

## Add Azure AD users to SharePoints groups and document library permissions in bulk

I need to create Azure AD users in bulk (about 90), in order to add each of them: – To a SharePoint group present in 90 sub-sites – Authorizations from two libraries in each of these sub-sites

Example : – User: “user1@mydomain.com” – SharePoint sub-site: “https://mydomain.sharepoint.com/sites/principalsite/sub-site1” (already created) – Two document libraries: “Library1” and “Library2” (already created) for which the user “user1@mydomain.com” must be added to the authorizations of these two libraries, with a specific authorization level “Special authorization” (already created)

• User: “user2@mydomain.com”
• SharePoint sub-site: “https://mydomain.sharepoint.com/sites/principalsite/sub-site2” (already created)
• Two document libraries: “Library1” and “Library2” (already created) for which the user “user2@mydomain.com” must be added to the authorizations of these two libraries, with a specific authorization level “Special authorization” (already created)

Etc Etc Etc….. Up to 90.

The idea would be to create a PowerShel script based on a CSV file with the necessary information: UPN > Sharepoint link > Sharepoint group name > Document library names > Name of the specific authorization level.

I don’t really master scripting and I don’t know much about the powershell functions related to Sharepoint. After some research, I find information but it doesn’t really correspond to my needs.

Can you help me ?

Regards,

## User testing navigation with one or two groups

We want to test a set of five users to compare usability between our existing application navigation and our proposed next generation navigation. During the course of planning how we will do our testing. Currently our options are as follows:

1. Test both navigations with the same group
2. Test both navigations with a separate group for each

I was wondering if anyone had any advice on which has delivered a more optimal response. Option 1 has the possibility of the first test affecting the results of the second but I wanted to find out more opinions

## Nesting Email Distribution Groups into job code Groups

My company wants to create job code groups. A single group for a single job code. For example, if Bob is a courier, the only groups he will have is the “Domain User” and Courier. Couriers are part of 3 distribution groups, 1 universal and 2 global. They are also in 4 global security groups and 1 mail-enabled global security group.

Of course, no reason is given, just they want it that way.

The problem I am facing is the end user is not receiving the distribution email.

Any suggestions?

## Generators for permutation groups

Consider (e.g.) the full permutation group $$G=S_6$$. A valid set of generators and equations for $$G$$ is $$r^6=m^2=(rm)^5=1$$. I say this system has width $$3$$ (because there are $$3$$ equations), length $$10$$ (because there are $$10$$ generators in $$(rm)^5$$ – arguably, $$m$$ as a mirror causes no “load” in which case the length would be $$6$$) and height $$6$$ (for the exponent $$6$$).
What is the generator set with minimum height or length or width or (best) everything at the same time? How do I find it in the general case?

## Amenable groups with special presentations

Is there a group with a presentation

$$\left< X \mid r_i, i \in \mathbb{N} \right>$$ (where $$X$$ is finite) with

$$\left< X \mid r_i, i \in A \right>$$ is amenable if and only if $$A\subset \mathbb{N}$$ is infinite.