@tao @christianp I have a problem for you in Number Theory

The Bertrand postulate which states that there is a prime between (n, 2n) for all n > 2. I wanted to improve this result.

So I defined \( \delta(n) = \sum_i p_i \) for \( n = \prod_i p_i \) the prime descomposition of n.

I want to prove that for all n, there is a prime between \( n, n + \delta(n) \) which is false: 5120 is the first of such number which has no primes in this interval.

Let's define a "refinate number" a number which has prime in the interval \( n, n + \delta(n) \) and "irrefinate" else.

I want to prove that irrefinate number are very "rare".

As a consequence of Prime Number Theorem, we have that for fixed m, mp for p prime large enough.

And if irrefinate numbers are infinite, then \( \delta(n)/n \) tends to 0.

But I don't know nothing.

It could be interesting knowing the counting function of irrefinate is.

Link to unsolved problems: "for all n, there is a prime number between \( n^2 , (n+1)^2 \) .

In general, \( \delta(n^2) < 2n +1 \) but I don't know how frequently.

It connects #addivite function to #prime #number #gaps.

It was just a divertimento in my graduate days....

Thanks in advance and regards

@tecnotestering se les conoce como las #gaps o algo así, Google apps.
Yo las tengo deshabilitadas casi todas, capadas le digo yo.

Son un fastidio.

Y te meten miedo antes de hacerlo.
(ver capturas)

Goedemorgen, de #AEX & #Dax beginnen rustig aan de nieuwe week. Na de lagere opening zijn de #Gaps inmiddels gevuld.
Voor meer info lees de dag analyses, of neem een abonnement op de signalendienst.
https://www.beurspraatje.nl/dag-analyses

(#AEX 15M)

Attackers have advanced their #techniques for leveraging the "search-ms" uniform resource identifier (#URI) #protocol from #malicious #documents to direct users to websites that exploit #search-ms functionality using #JavaScript hosted on the page.

The search-ms protocol lets Windows users conduct search operations via a URI. Normally, it’s a #benign operation, but if combined with another vulnerability such as within #Windows documents, #attackers can potentially use it as a part of a broader #phishing or #malware campaign.

This attack requires #gaps at multiple layers of an organization’s defenses. First, properly leveraging email filters with URL rewriting and malicious content controls will limit the impact of a search-ms attack. Second, it relies on limited restrictions on outbound internet browsing — both at the firewall and internet proxy level. Once again, outbound controls are critical.

https://www.scmagazine.com/news/attackers-exploit-windows-based-search-ms-protocol

Full blog post with technical details available here: https://www.trellix.com/en-us/about/newsroom/stories/research/beyond-file-search-a-novel-method.html

Paper by Ueda et al "Rap1 organizes lymphocyte front-back polarity via RhoA signaling and talin1" in iScience @iScience
https://www.cell.com/iscience/fulltext/S2589-0042(23)01369-X
The role of talin1 in cell polarization, downstream of Rap1, seems to be independent of talin binding to integrins and of integrin adhesion
#Rap1 #talin #cytoskeleton #GEFs #GAPs

The reviews are in and we are really going towards a second edition of "Managing Previously Unmanaged Collections".
If there are #gaps in the first edition, please let me know.
Especially looking for real-world examples from #native and #digital #collections

Re-toots appreciated!

#museum #museums #archive #archives #RegistrarLife #MuseumDocumentation #CollectionsManagement #databases #CollectionCare #Conservation #Documentation #UnmanagedCollections #MuseumStudies

Now at 2023 #SthlmForum: Women’s participation & gender-responsive leadership in #peacebuilding, organized by @fbafolke & @GAPS_Network
📢
@FlorenceWallerC , #GAPS
Nathali Rativa @WeAreNIMD
Ambassador Kilian Wahl, Head of @OSCE_Skopje
Moderated by @ThinkPer, GD of @fbafolke https://nitter.net/FBAFolke/status/1658759293569564672#m

#Mucosal #vaccines for #SARS-CoV-2: scientific #gaps and opportunities — #workshop report https://www.nature.com/articles/s41541-023-00654-6

Relevant to competition authorities & co. 👇🏼
---
RT @FLCalv
A polarised adoption, mainly by larger and more productive firms, combined with a role of AI strengthening their advantages, may imply that in the future existing #gaps 📏 between leaders and other firms may widen, with relevant implications for #social outcomes

[9/n]
https://twitter.com/FLCalv/status/1645855312488853504

I’m a software engineer. I’m not intelligent enough to understand how to properly align #Ikea #Bestå #doors and #drawers. No matter how much I try, I can’t seem to get it right.

#Frustated #Gaps #Imperfect

#Photographs are becoming more important for documenting #biodiversity #baselines and even potentially for #conservation planning. However there are #gaps & #biases in the developing #photographic #record.

E.g., from #Australia: “ #Herbs and #graminoids have disproportionately more unphotographed species relative to their total #diversity; the latter constitute 16.1% of unphotographed #species despite making up just 8.2% of all species.”

🔗 https://nph.onlinelibrary.wiley.com/doi/10.1111/nph.18813

ChatGPT is so bad at providing information about Nazi art cases that I asked if it blacklisted certain words or phrases and it does

#openai #gaps #erasure #artlaw #caselaw #restitution #claims #lootedart #arthistory #law #disinformation #opendata #publicaccess #information #histodon #archives #knowledgegraph #filters #museums

@benjaminhollon

I use 14px by default (20px on the #PinebookPro because it's fairly high-res)

To me, the gaps are a very #EnvPsych kind of thing. They don't do much *aesthetically*, but I find them very relaxing in a visceral sense, like an office with a small and out-of-the-way window vs. none at all

~ $ grep -m4 gaps ~/.config/i3/config
### settings for i3-gaps: ###
# Set inner/outer gaps
#gaps inner 14
gaps inner 20

Door de #Gapfill van #Wallstreet zijn de #AEX & #Dax #futures fors opgelopen waardoor er nu ook bij ons weer flinke #Gaps zijn onstaan. Hoe nu verder?

Check de dag analyses van zowel de #AEX als de #Dax nu op de site.
Beurspraatje.nl

The Dorset Gap

#gaps

#Lab That Created Risky Avian #Flu Had “Unacceptable” Biosafety #Protocols

Documents obtained by The Intercept reveal disturbing #biosafety lapses and troubling #gaps in oversight by #government agencies.

https://theintercept.com/2022/11/01/biosafety-avian-flu/

The @EU_Commission has adopted its proposal to make 2️⃣0️⃣2️⃣3️⃣ the #EuropeanYearofSkills.

Addressing skills #gaps will boost #innovation, #productivity & #growth.

This is particularly relevant for #DigitalSkills.

Read the proposal
👉 https://europa.eu/!VHk4wX

🐦🔗: https://nitter.eu/EU_opendata/status/1584107377187770369

#Xvectors.pt project has just kicked-off tody! more studies on #spittlebus on #Xylella vectores and putative vectors in #Portugal. #knowledge #gaps #filled by #EFSA_EU & #grants

🐦🔗: https://nitter.eu/Plants_EFSA/status/1576875321243992064

[ 🔄 ]

@FRA 🔗 https://social.network.europa.eu/users/FRA/statuses/108515072494520645
-
#Governments should use our #safeguards for #children in criminal #proceedings’ report to identify #gaps, potential #remedies & existing solutions, says #FRA’s @MichaelCJT@twitter.com.

This will help ensure that #ChildRights are effectively upheld in practice.

Get it here:
https://fra.europa.eu/en/publication/2022/children-criminal-proceedings

https://mstdn.jp/media/ykDA2ABxsCUBkjDHSqA

Understanding persistent #gender #gaps in #STEM

Gender gaps in #science, #technology, #engineering, and #math (STEM) college majors receive considerable #attention, and it is increasingly recognized that not all STEM #majors are equal in terms of gender #disparities.

https://science.sciencemag.org/content/368/6497/1317

https://mstdn.jp/media/kGgbSdB65Pia23zsZYw