Some useful inequalities:

1. Cauchy–Schwarz inequality

\[\displaystyle\sum_{k=1}^na_kb_k\leq\sqrt{\sum_{k=1}^na_k^2}\sqrt{\sum_{k=1}^nb_k^2\]

2. Hölder's inequality

\[\displaystyle\sum_{k=1}^n\left|a_kb_k\right|\leq\left(\sum_{k=1}^n|a_k|^p\right)^{1/p}\left(\sum_{k=1}^n|b_k|^q\right)^{1/q}\]

3. Minkowski's inequality

\[\displaystyle\left(\sum_{k=1}^n\left|a_k+b_k\right|^p\right)^{1/p}\leq\left(\sum_{k=1}^n|a_k|^p\right)^{1/p}+\left(\sum_{k=1}^n|b_k|^p\right)^{1/p}\]

4. Hardy's inequality

\[\displaystyle\sum_{k=1}^\infty\left(\dfrac{a_1+a_2+\cdots+a_k}{k}\right)^p\leq\left(\dfrac{p}{p-1}\right)^p\sum_{k=1}^\infty a_k^p\]

#mathematics #mastodon #mathstodon #maths #hardy #minkowski #holder #Schwarz #cauchy #inequality

Last updated 1 year ago

Architecture News · @architecture
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Cults. · @cults3d
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Cults. · @cults3d
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Lucky Resistor · @luckyresistor
84 followers · 61 posts · Server mastodon.art

In today's showcase are sturdy 3D-printed clamp holders. I developed projects LR2218 and LR2219 to store small and large clamps as compactly as possible on the wall of your workshop.

printables.com/model/150793-so
printables.com/model/151272-co

While similar, both projects have minor differences as I optimised them for a weight class of clamps. In each project, you find the fully parametric Fusion360 design, where you can tune the holder to your desired dimension.

#showcase #holder #clamp #3dprinting

Last updated 1 year ago

@Om · @atomjack604
208 followers · 3629 posts · Server mastodon.social
@Om* · @atomjack
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Allen Holder Official · @aholder928
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Allen Holder Official · @aholder928
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Allen Holder Official · @aholder928
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Cults. · @cults3d
1 followers · 1474 posts · Server bots.franssen.xyz
RandomizY · @RandomizY
20 followers · 22 posts · Server awscommunity.social

New model out! ✏️

I've created something that you can use in your everyday life, which should help you having your desks cleaner and in order! 😄
__

Available for as reward for my Patrons on my page: patreon.com/RandomizY
__

#free #patreon #3dprint #3dprinting #penholder #pen #holder #decor #home #office #school #giftideas #Gifts #dyi #craft #impression3d #3ddruck #impresion3d #impressao3d #sonyalpha #madewithwacom #randomizy

Last updated 2 years ago

The Root RSS · @theroot
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Allen Holder Official · @aholder928
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Jamie Nemeth · @JamieNemeth
54 followers · 43 posts · Server toot.wales

Did some searching on eBay for a .

"Wait, that's a tablet ?! But I have one of those!"

So I finally have a rigidly-held tablet always within reach (rather than on my lap or odd wrist angles with it on the desk).

The is back!

#twitchstreamer #twitch #streaming #drawing #whiteboard #graphicstablet #glassboard #stream #graphics #holder #clamp #tripod #tablet

Last updated 2 years ago