Nested reference of URL’S in sitemap.xml good or bad for SEO?

I am having thousands of URL’s in the website, If I put all URL’s in sitemap.xml it’s getting too large in size. There is some suggestion to split those URLs into different files and referring in main sitemap.xml

eg

<?xml version="1.0" encoding="UTF-8"?>
<sitemapindex xmlns="http://www.sitemaps.org/schemas/sitemap/0.9">
<sitemap>
<loc>https://www.example.com/rootpages-sitemap.xml</loc>
</sitemap>
<sitemap>
<loc>https://www.example.com/detailpages-sitemap.xml</loc>
</sitemap>
...
</sitemapindex> 

And in the reference file detailpages-sitemap.xml defining URLs

<urlset xmlns="http://www.sitemaps.org/schemas/sitemap/0.9"> 
<url>
<loc> https://www.example.com/detail/Universal-Studios-Hollywood/</loc>
</url>
.....
</urlset>

Does this is a better way to implement ? or suggest some different methods

linear algebra – Reference on classifying real subspaces of complex vector spaces (based on restricted complex structure)

Every complex vector space can also been seen as real vector space. If we now choose a real subspace, it may not be a complex subspace (in particular, if it is of odd real dimension).

If the complex vector space was equipped with an inner product (for example, a Hilbert space), we can restrict the imaginary unit (also known as linear complex structure) to any real subspace using the orthogonal projection. We can then classify the types of real subspaces based on the spectrum of this “restricted complex structure”. In particular, if the restricted complex structure squares to minus identity, i.e., is itself a complex structure, the real subspace is also a complex subspace. In general, the spectrum encodes how being a complex subspace is violated.

I worked this out for myself, but I’m confident that this is standard material in linear algebra of complex vector spaces. However, the standard introductory text books that I checked do not discuss real subspaces of complex vector spaces and their classification in the above way.

Do you know of a standard reference that I could cite when discussing this (in particular, the above mentioned classification based on the spectrum of the restricted complex structure)?

reference request – Does $pi_k(M)neq 0$ implies $operatorname{ind}(gamma)

Cross post from MSE. and sorry if this is an obvious question.

Here is a line of proof of Theorem 1.15 from Ricci Flow and the Sphere Theorem
by Simon Brendle

Let us fix two
points $p, q in M$ such that $d(p, q) = operatorname{diam}(M, g) > 2$. Since $pi_k(M)neq 0$, there
exists a geodesic $gamma : (0,1) to M$ such that $gamma(0) = gamma(1) = p$ and $operatorname{ind}(gamma) < k$.

Q: Why $pi_k(M)neq 0 implies operatorname{ind}(gamma) < k$? Is this a general fact?

Note: $operatorname{ind}(gamma):=$ Morse index of $gamma$.

reference request – Grothendieck categories are locally presentable

The way I’ve read it, many fundamental facts about Grothendieck categories, such as completeness, are special cases of those about locally presentable categories (see, for example, this answer).

However, it doesn’t seem that obvious that Grothendieck categories are locally presentable. Is there a reference proving that? Wikipedia page on Grothendieck categories says that it is a consequence of Gabriel-Popescu theorem. Surely, there must be an easier way to show that?

algorithm analysis – Analyzing space complexity of passing data to function by reference

I have some difficulties with understanding the space complexity of the following algorithm.
I’ve solved this problem subsets on leetcode. I understand why solutions’ space complexity would be O(N * 2^N), where N – the length of the initial vector. In all those cases all the subsets (vectors) are passed by value, so we contain every subset in the recursion stack. But i passed everything by reference. This is my code:

class Solution {
public:
vector<vector<int>> result;
void rec(vector<int>& nums, int &position, vector<int> &currentSubset) {
    if (position == nums.size()) {
        result.push_back(currentSubset);
        return;
    }
    
    currentSubset.push_back(nums(position));
    position++;
    rec(nums, position, currentSubset);
    currentSubset.pop_back();
    rec(nums, position, currentSubset);
    position--;
}

vector<vector<int>> subsets(vector<int>& nums) {
    vector <int> currentSubset;
    int position = 0;
    rec(nums, position, currentSubset);
    return result;
}
};

Would the space complexity be O(N)? As far as i know, passing by reference doesn’t allocate new memory, so every possible subset would be contained in the same vector, which was created before the recursion calls.

I would also appreciate, if you told me how to estimate the space complexity, when working with references in general. Those are the only cases, where i hesitate about the correctness of my reasonings.

Thank you.

What’s the equivalent of Windows F4 to make a cell reference absolute (e.g. $A1$1) in Google sheets?

What’s the equivalent of Windows F4 to make a cell reference absolute (e.g. $A1$1) in Google sheets?

Online searchers tell me it’s apple (command) + T but this just opens up another tab in Chrome. I guess they mean Excel.

Anyone know the shortcut for this is for Sheets?

8 – Migrating content from RSS feed to populate multiple Entity reference media field

In the Drupal 8 site I’m working on, I’ve currently set up some migration configurations which import content from an external RSS feed. The file urls references in this RSS feed are imported into the site as media entities and then referenced in the generated node. All is well, except for when there are multiple file urls.

So here is the configuration for the node import:

id: rss_innovations
label: 'Import Innovations feed'
status: true

source:
  plugin: url
  data_fetcher_plugin: http
  urls: 'https://www.innovationagencyexchange.org.uk/feeds/innovations'
  data_parser_plugin: simple_xml

  item_selector: /rss/channel/item
  fields:
    -
      name: guid
      label: GUID
      selector: guid
    -
      name: title
      label: Title
      selector: title
    -
      name: pub_date
      label: 'Publication date'
      selector: pubDate
    -
      name: link
      label: 'Origin link'
      selector: link
    -
      name: description
      label: Description
      selector: 'description'
    -
      name: image
      label: Image
      selector: 'featured_image'
    -
      name: content
      label: Content
      selector: 'content'
    -
      name: organisation
      label: Organisation
      selector: 'organisation'
    -
      name: ahsnid
      label: AHSN ID
      selector: 'ahsn'
    -

  ids:
    guid:
      type: string

  constants:
    file_destination: 'public://images/'

destination:
  plugin: 'entity:node'

process:
  title: title
  field_remote_url: link
  body/value: content
  body/format:
    plugin: default_value
    default_value: basic_html
  field_ahsn: ahsnid
  field_company: organisation
  field_introduction: description
  field_image:
    plugin: image_import
    source: image
    destination: 'constants/file_destination'
    alt: !title
  uid:
    plugin: default_value
    default_value: 17
  created:
    plugin: format_date
    from_format: 'D, d M Y H:i:s O'
    to_format: 'U'
    source: pub_date
  status:
    plugin: default_value
    default_value: 1
  type:
    plugin: default_value
    default_value: innovation
  field_media:
    plugin: migration_lookup
    migration: rss_resources_files
    source: guid
    no_stub: true

migration_dependencies:
  required:
    - rss_resources_files

And here is the configuration for the file importing:

id: rss_resources_files
label: 'Import Innovation files'
status: true

source:
  plugin: url
  data_fetcher_plugin: http
  urls: 'https://www.innovationagencyexchange.org.uk/feeds/innovations'
  data_parser_plugin: simple_xml

  item_selector: /rss/channel/item
  fields:
    -
      name: guid
      label: GUID
      selector: guid
    -
      name: resourcefile
      label: Resource file
      selector: 'file'

  ids:
    guid:
      type: string

  constants:
    file_destination: 'public://resources/'

process:
  field_media_file:
    -
      plugin: skip_on_empty
      method: row
      source: resourcefile
      message: 'No file found'
    -
      plugin: explode
      source: resourcefile
      delimiter: '|'
    -
      plugin: file_import
      destination: 'constants/file_destination'
destination:
  plugin: 'entity:media'
  default_bundle: file

So these both work at the moment in terms of importing all the content and all the files. All the files are imported files as file entities (using the plugin: file_import after the explode) but then only one media entity is generated per RSS item, so only one media entity per RSS item / node. Which makes sense as the file import is running separately to the entity media generation. I guess I need to use the sub_process plugin to generate the media entities? However when I try with that it only accepts associative arrays and the array from the explode plugin does not seem to be accepted by it. If someone could point me in the right direction I’d be ever so grateful!

This is an example of the RSS feed if needed:

<?xml version="1.0" encoding="utf-8" ?><rss version="2.0" xml:base="https://www.healthinnovationexchange.org.uk/feeds/innovations" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:atom="http://www.w3.org/2005/Atom">
  <channel>
    <title>Innovations</title>
    <link>https://www.healthinnovationexchange.org.uk/feeds/innovations</link>
    <description></description>
    <language>en</language>
     <atom:link href="https://www.healthinnovationexchange.org.uk/feeds/innovations" rel="self" type="application/rss+xml" />
      <item>
    <title>Intelligent workforce solution and indoor location technology</title>
    <link>https://www.healthinnovationexchange.org.uk/%3Ca%20href%3D%22/solutions/intelligent-workforce-solution-and-indoor-location-technology%22%3Eview%3C/a%3E</link>
    <description><!(CDATA(Many have tried to change the way clinical teams work to be more efficient; but few have focused on optimising the supporting teams that provide the logistics which underpin the flow of patients throughout the hospital.&nbsp;Navenio has done just that. By looking at the teams working within a hospital, they have proven that knowing where people are, indoors in real-time, unlocks significant improvements in their workflow and efficiency. This improves patient flow and patient care. &nbsp;))></description>
     <pubDate>Wed, 10 Jun 2020 10:29:37 +0100</pubDate>
 <dc:creator />
 <guid isPermaLink="true">https://www.healthinnovationexchange.org.uk/%3Ca%20href%3D%22/solutions/intelligent-workforce-solution-and-indoor-location-technology%22%3Eview%3C/a%3E</guid><featured_image>https://www.healthinnovationexchange.org.uk/sites/default/files/FB6E45F5-4557-4027-9517-4E48C704E6A6_1.png</featured_image>
        <content><!(CDATA(<p style="text-align:justify"><span style="font-size:12pt"><span style="font-family:Calibri,sans-serif"><span style="font-size:14.0pt"><span style="color:black">Navenio has pioneered frictionless, accurate and robust indoor location solutions, built on award-winning science from the University of Oxford – enabled simply using sensors in existing smartphones. Unlike other RTLS, RFID, Bluetooth and Wi-Fi solutions, the Navenio technology </span></span><span style="font-size:14.0pt">requires <span style="color:black">no new investment in infrastructure</span> at all; is easily scalable and accurate to within 1 to 3 metres.</span></span></span></p><p style="text-align:justify"><span style="font-size:12pt"><span style="font-family:Calibri,sans-serif"><span style="font-size:14.0pt">The Navenio solution is available in three forms:</span></span></span></p><ul><li style="text-align:justify; margin-left:8px"><span style="font-size:12pt"><span style="font-family:Calibri,sans-serif"><span style="font-size:14.0pt">Intelligent Workforce Solution (IWS)</span></span></span><ul style="list-style-type:circle"><li style="margin-left:8px; text-align:justify"><span style="font-size:12pt"><span style="font-family:Calibri,sans-serif"><span style="font-size:14.0pt">automates the prioritisation and allocation of tasks to ensure </span><span style="font-size:14.0pt">the right person is helping in the right location every time</span></span></span></li></ul></li><li style="text-align:justify; margin-left:8px"><span style="font-size:12pt"><span style="font-family:Calibri,sans-serif"><span style="font-size:14.0pt">Location only solution</span></span></span><ul style="list-style-type:circle"><li style="margin-left:8px; text-align:justify"><span style="font-size:12pt"><span style="font-family:Calibri,sans-serif"><span style="font-size:14.0pt">provides details of current and past movements of staff via their smartphones </span></span></span></li></ul></li><li style="text-align:justify; margin-left:8px"><span style="font-size:12pt"><span style="font-family:Calibri,sans-serif"><span style="font-size:14.0pt">as a fully integrated location solution that feeds into other clinical/non-clinical solutions/applications</span></span></span><ul style="list-style-type:circle"><li style="margin-left:8px; text-align:justify"><span style="font-size:12pt"><span style="font-family:Calibri,sans-serif"><span style="font-size:14.0pt">can provide valuable data to aid and improve patient consultations, discharge and referrals; and provide confirmation of where a staff member at infection risk has travelled between over a period of time</span></span></span></li></ul></li></ul>))></content>
    <organisation>Navenio Limited</organisation>
    <ahsn>2</ahsn>                                                                                                                                                                                                                                                                                     <video>https://www.navenio.com/dr-harpreet-sood</video>                        <file>https://www.healthinnovationexchange.org.uk/sites/default/files/Navenio%20Briefing%20Doc%20-%20Covid-19%20Assistance%20Briefing%20Doc%20-%2027mar20.pdf|https://www.healthinnovationexchange.org.uk/sites/default/files/AHSNsubmission%5B1%5DMT.pdf|https://www.healthinnovationexchange.org.uk/sites/default/files/Navenio%20IWS%204pp%20June%202020.pdf|https://www.healthinnovationexchange.org.uk/sites/default/files/Hospital%20Impact%20Study-MT-11.pdf</file>
</item>  
<item>
    <title>MediShout: A Logistical Brain For Healthcare </title>
    <link>https://www.healthinnovationexchange.org.uk/%3Ca%20href%3D%22/solutions/medishout-logistical-brain-healthcare%22%3Eview%3C/a%3E</link>
    <description><!(CDATA(www.MediShout.co.ukMediShout uses digital and AI technology to provide a “logistical brain” to health and social care organisations. Currently, logistical issues (e.g. faulty equipment, no PPE, broken IT, estates and facilities issues) delay staff and prevent best care. MediShout solves this problem by integrating all logistical departments onto one App, where a single-interface lets staff instantly report any non-clinical issue. Staff can track the progress of their report whilst organisations get operational oversight of all issues. AI-algorithms allows organisations to predict future problems, like broken equipment.))></description>
     <pubDate>Sat, 30 May 2020 08:32:37 +0100</pubDate>
 <dc:creator />
 <guid isPermaLink="true">https://www.healthinnovationexchange.org.uk/%3Ca%20href%3D%22/solutions/medishout-logistical-brain-healthcare%22%3Eview%3C/a%3E</guid>
        <content><!(CDATA(<p style="margin-bottom:11px"><strong>THE STORY:&nbsp;</strong><br>MediShout's founder is a surgeon and one afternoon, had to cancel three operations as a theatre lightbulb was broken. Staff had known for days but not reported it because no effective communication channels existed.</p><p style="margin-bottom:11px"><br><strong>THE HEALTHCARE PROBLEM:&nbsp;</strong><br>All clinicians are delayed daily by similar problems because healthcare buildings are poorly automated and not digitally connective. Staff get delayed by logistical and infra-structure problems e.g. forgotten passwords, broken equipment, low stock, lack of PPE.</p><p style="margin-bottom:11px"><br><strong>THE IMPACT IS HUGE:&nbsp;</strong><br>1. Journal of Nursing Times reported a third of NHS Nurses waste two hours per shift looking for equipment, costing the NHS almost £1billion annually.<br>2. There's been a 32% increase in cancelled NHS procedures due to equipment and staffing issues</p><p style="margin-bottom:11px"><br><strong>THE SOLUTION:&nbsp;</strong><br>MediShout is on the NHS Innovation Accelerator and provides the first platform in healthcare to integrate all logistical departments e.g. IT, estates, facilities, stock, equipment, suppliers. The MediShout App provides a single-interface for staff to instantly report any non-clinical issue. Staff can track the progress of their report whilst organisations get operational oversight and can see what issues are most impacting patient care and need fixing first. Artificial intelligence (AI) allows organisations to predict future problems, like broken equipment.</p><p style="margin-bottom:11px"><br><strong>BENEFITS:&nbsp;</strong><br>Health economists have shown MediShout can save NHS Trusts £1million annually (see attached report) and save 15 minutes per clinician daily. By sending staff reports directly to equipment suppliers, MediShout can improve output of surgical theatres and endoscopy departments.</p>))></content>
    <organisation>MediShout</organisation>
    <ahsn>2</ahsn>                                                                      <file>https://www.healthinnovationexchange.org.uk/sites/default/files/MediShout%20-%20Health%20Economic%20Impact%20Report%20%28HEE%29.pdf</file>
          </item>  </channel>
</rss>

reference request – Title: Élie Cartan’s paper “Les groupes réels simples, finis et continus” of 1914

Question 1.
Does Élie Cartan’s paper
Les groupes réels simples, finis et continus,
Ann. Sci. École Norm. Sup. (3) 31 (1914), 263–355

contain a classification of $Bbb C$-linear involutions of simple complex Lie algebras?

Question 2.
If not, what kind of a similar/related classification does it contain?

Question 3.
In what book/paper is this Cartan’s paper discussed?

MathSciNet contains only the title, while zbMATH
contains a review: a translation into German of a few lines from the introduction.

office 365 – Can i reference a user/group inside SharePoint if our admin hide them from the AD global address list

Our system admin wants to hide some users/groups from the AD global address list to prevent those users from showing when sending emails through outlook. so my question is if we can still reference (add inside SharePoint group + assign the user inside a people/group column) users/groups inside SharePoint online sites, if our admin hide them from the AD global address list?

reference request – Is realization of unit disk graphs hard?

It is known that recognizing a unit disk graph is NP-hard (1).

However, the paper does not mention how hard is the realization problem.

I have looked up several references (2)(3)(4). None of the papers answer whether the following problem is NP-hard:

Given a unit disk graph $G = (V,E)$, find a configuration of a set
$mathcal{D}$ of disks, such that the intersection graph
$G(mathcal{D})$ of $mathcal{D}$ is isomorphic to $G$.

The difference between this problem and the recognition problem is that the input of this problem is guaranteed to be a unit disk.

Is there any study that shows the complexity of the above problem? I expect it to be NP-hard, but I am yet to find a full proof.