Compute the $g_Y$-parallel part of a $(0,1)$-form

Let $ Y$ be a compact (without boundary) Calabi-Yau manifold, i.e., $ c_1(Y)=0$ in $ H^2(Y, \mathbb{R})$ . Let $ \omega$ be a Kähler form on $ \mathbb{C}^m \times Y$ and let $ \omega_P = \omega_{\mathbb{C}^m} + \omega_Y$ . Assume that $ \zeta = \omega Р\omega_P$ is an exact $ (1,1)$ -form, i.e., $ \zeta = d\xi$ for some real $ 1$ -form $ \xi$ on $ \mathbb{C}^m \times Y$ . By the Leray spectral sequence of the projection $ \pi_{\mathbb{C}^m} : \mathbb{C}^m \times Y \to \mathbb{C}^m$ , there is an isomorphism $ \Phi : H^{0,1}(\mathbb{C}^m \times Y) \to \mathcal{O}(\mathbb{C}^m, H^{0,1}(Y))$ with $ $ \Phi[\xi^{0,1}](z) = [\xi^{0,1} \vert_{\{ z \} \times Y}].$ $ Set $ \Phi[\xi^{0,1}]=f$ and identify $ H^{0,1}(Y)$ with the space of $ g_Y$ -parallel $ (0,1)$ -forms.

Q: I want to show that $ $ \frac{\partial f }{\partial \overline{z}^j}=0.$ $

Moreover, I want to show that $ \dfrac{\partial f}{\partial z^j}$ is the $ H^{0,1}$ -class, or the $ g_Y$ -parallel part of the $ (0,1)$ -form $ $ (\partial_{z^j} \llcorner \zeta) \vert_{\{ z \} \times Y},$ $ where $ \llcorner$ denotes the interior product.

Sharepoint Online – Custom CSS in Content Editor web part saves are overwritten

I’m fairly new to sharepoint customisation so have been struggling reading over some threads. I have looked at the following Posts by have been unable to figure out where / what needs to be edited to get this working.

I’m trying to add custom CSS to edit my home page where promoted links are stored in order to make them smaller (This is so that it scales better when viewing on an ipad).

I’m following this process but I can not seem to get my customisation to save after pressing the save button – It just reverts back to how it was.

  • Navigate to Home page
  • Press the Edit button
  • Add My promoted links web parts to the page
  • Save the page

At this stage the site is fine – I now want to make further customisation in order to resize the promoted links I have just added to the home page.

  • Press Edit to edit the home page
  • Add a Content Editor Webpart at the top of the page (Insert > Media and Content > Content Editor > Add
  • Click onto the Content editor web part I have just added
  • Click ‘Edit Source’
  • Add the code between the and Tags – (Link to the CSS I’m added is in the comment below)
  • Press ‘OK’ to save the source code I have entered
  • Looking at the site the Promoted links have now been resized to the size I want them

    • Press the Save button

    • After pressing save and viewing my home page the promoted links have gone back to the same size as they were before?

Does anyone know why this isn’t saving?

Please let me know if you need any further information or screenshots.

Kind regards Steven

Sharepoint Online – Custom CSS in Content Editor web part saves are overwritten

I’m fairly new to sharepoint customisation so have been struggling reading over some threads. I have looked at the following Posts by have been unable to figure out where / what needs to be edited to get this working.

I’m trying to add custom CSS to edit my home page where promoted links are stored in order to make them smaller (This is so that it scales better when viewing on an ipad).

I’m following this process but I can not seem to get my customisation to save after pressing the save button – It just reverts back to how it was.

  • Navigate to Home page
  • Press the Edit button
  • Add My promoted links web parts to the page
  • Save the page

At this stage the site is fine – I now want to make further customisation in order to resize the promoted links I have just added to the home page.

  • Press Edit to edit the home page
  • Add a Content Editor Webpart at the top of the page (Insert > Media and Content > Content Editor > Add
  • Click onto the Content editor web part I have just added
  • Click ‘Edit Source’
  • Add the code between the and Tags – (Link to the CSS I’m added is in the comment below)
  • Press ‘OK’ to save the source code I have entered
  • Looking at the site the Promoted links have now been resized to the size I want them

    • Press the Save button

    • After pressing save and viewing my home page the promoted links have gone back to the same size as they were before?

Does anyone know why this isn’t saving?

Please let me know if you need any further information or screenshots.

Kind regards Steven

A SpamAssassin filter for empty HTML part

A new kind of spam’s been getting through my defenses lately with the following common characteristics:

  1. The message itself is of type multipart/mixed with two parts.
  2. The body of the spam is in the first part, of type text/plain.
  3. The second part is of type text/html and is empty:
----f3c31d93219a26172136ed0487d80041 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: base64  ----f3c31d93219a26172136ed0487d80041-- 

How can I add a rule for recognizing such messages so SA can reject them?

Normal colorings of cubic graphs (part 1)


Definition A normal $ k$ -coloring of a cubic graph (3-regular graph) is a proper coloring of the edges with $ k$ colors such that each edge an its adjacent edges are colored with either five colors, or with three.

There is also the following

Conjecture Every bridgeless cubic graph (that is, a cubic graph without a cut edge) can be normally 5-colored.

We are looking for algorithms to normally color cubic graphs

Questions

  1. Could you suggest an algorithm to find normal $ k$ -colorings of cubic graphs that is efficient and simple. It is known that 9 colors should suffice. It is my understanding that it is possible to do this with a linear time algorithm, although the publication of this algorithm is unknown to me.

  2. Could you suggest an algorithm to find normal 5-colorings of cubic graphs if they exist?

If there is a better site where this question could be posted, please indicate this. If this site is not for questions requesting information about algorithms, please notify and it will be removed immediately. I have never posted in this site.

Page scrolls down automatically to a list web part

I have created a modern page with a few elements on it (hero webpart, a forms web part, weather web parts…). I work with SharePoint Online. At the bottom of the page, I added a regular list webpart as well. When this page loads, instead of staying at the top, it automatically scrolls down to the list view webpart, no matter where it is. It seems that it is calling the attention to it automatically.

Is there anyway to keep the page scrolled to the top and let the user scroll down when he/she wants?

How do I introduce magic to my PCs part way through an adventure

I am playing through a slightly modified version of the Pathfinder adventure Rise of the Runelords with a group who are all brand new to any form of RPG.

After around ten sessions, I still haven’t covered magic with them – my fault as a GM but the adventure path hasn’t really called for it yet…

There are a Druid and a Bard in the party, so obviously it will benefit us all greatly, but I’m trying to think of a way of working in teaching about magic after ten sessions and not just say “OK, by the way, you can cast spells, I’ll take you through it”.
I’m thinking maybe an NPC can teach them?

I would like to use the Content Search Web Part to only display Document Libraries

So I been using advanced query builder to accomplish to only display document libraries because I have a workflow that generates numerous packages.

path:”Site URL” (contentclass:STS_List_DocumentLibrary)

This only displays a couple of libraries, but also includes the general document libraries, how can I narrow my query to search only “FY” in the title of the document libraries thanks.

Is CPU Registers part of Primary Memory?

A friend of mine appeared in an exam recently, and one of the question asked was regarding CPU Registers, which has two points:

  • (a) CPU Registers are part of Primary Memory
  • (b) They are volatile

And the choices given were:

  1. Both (a) and (b) are true
  2. Only (a) is true
  3. Only (b) is true
  4. None of the above

They are volatile. So the second and forth options can be avoided. The confusion was regarding whether it was part of Primary Memory. To my knowledge, CPU Caches, RAMs and ROMs can be called as primary memory. But will CPU registers would be called as part of primary memory? Or will it be considered as Level0 caches?

Authentication Mechanism for Third Part Apps

I have an WebAPI application which is consumed in our native apps. The implemented auth grant type is ‘password’. It is working fine.

Currently we are creating a native library instead of native apps so that third party users can integrate this library into their native apps.

All API communications will be done thorough our library only. Our server have users in addition to client. Third party app have their own users.

Here my aim is we need to integrate library into their apps so that

  1. We need to validate the app
  2. Need to take user level resource based on app user.

Please suggest best authentication approach for this.

Simply telling i need to authenticate client credentials + end user id. Client is authenticated so that don’t want to authenticate against end user with password.