#Applications and Derivatives

[lilacandladybugs]

sometimes i ask my math professors why we're doing a certain thing and i dont know how to explain that i dont mean "this has no real world applications>:(" i mean what are the math applications?

it was such an exciting moment for me when i realized that since combinations/permutations are ways to find how things can be arranged, and probability is just the ways we can get something we're interested in over all the ways we could get something(want/all), combinations and permutations give us ways to find more complicated probabilities without being able to individually list all possible combinations by hand. so the "why are we doing this" for combinations/permutations is "so we can take more complicated probabilities later on". (It's also the basis for the binomial distribution!!)

without being able to understand the direction we're going with an idea it feels like a random exercise instead of the doorway to understanding more complex mathematical ideas and it also makes me feel like i don't understand how all the pieces of the class fit together.

[woodfrogs]

the physics nobel prize picks this year are crazyyyy

[becky-with-the-good-yield]

Dear Calculus,

Thanks for being the one math subject in school that could ever make me feel stupid.

Regards,

Lara

[thursdayg1rl]

OH MY GOD CALL ME THE CILLIT THE WAY I JUST BANGED THAT INTERVIEW. king of maths. im literally like if euler was a beautiful girl

[brionysea]

wow! this show has so many brilliant and well written female characters! surely i won't open ao3 to find that everyone has decided some white guy is actually The Most Interesting™

[philodendronplants]

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[industryoverview2025]

Global and U.S. Magnesium and Derivatives Market Outlook 2034

The global and U.S. magnesium and derivatives market, valued at US$ 33.8 Bn in 2023, is projected to grow at a CAGR of 5.1% from 2024 to 2034, reaching US$ 58.0 Bn by 2034.

[hautsreadsmarvel]

Rick Jones is NOT one of… “The Avengers” (1963; issues 8-13)

“Kang, the Conqueror”

Wow. This was. Not it.

Kang isn’t a particularly interesting or awesome villain. He’s just Rama-Tut except 1) he looks worse showing less skin, and 2) he travelled to the fortieth century to get tech that would give him an insurmountable edge against the twenty-first, but none of that tech is really that impressive. Oh no, he has a forcefield that can only be overcome by some other inventor’s tech - DOOM did that. Oh no, he has a paralysis ray - DOOM did that. He has hero-seeking missiles - the US government, Magneto, and dozens of other villains already did that. There is nothing going for this man. Even his personality is both derivative and somehow worse than other recent tech villains.

As a result, I will not be covering this one in any depth! Suffice to say that Kang the Conqueror intends to conquer the Earth; he beats our heroes; the fucking… the fucking Teen Brigade rescues them? Are you fucking kidding me!? Rick Jones is not and should not ever be insinuated to be an Avenger; the heroes beat Kang and he time travels out.

“The Coming of the… Wonder Man!”

Now this was it.

Zemo and his Asgardian compatriots return to Earth and find a guy who has it out for Iron Man. Zemo uses technology to enhance him with invulnerability, strength, and a flying rocket belt, creating Watermelon Wonder Man. Wonder Man infiltrates the Avengers, but Cap is immediately suspicious of his backstory as an escapee of Zemo, requiring him to lie with even more truth - he’s dying of the power-granting treatment he was administered and thus came to the Avengers for help. They all decide to help him, but to no avail. He then captures the Wasp and radios the Avengers for help, luring them to a battleground of Zemo’s choosing; the villains beat the heroes.

As Zemo prepares to execute the Avengers, Wonder Man foregoes his chance to obtain a life-saving antidote from Zemo, frees Thor, and buys time for the others to rally. The heroes win, Wonder Man dies, but it’s ok because we all learned our lesson about the values of honesty and goodness or something.

I’m pretty sure Wonder Man comes back at some point. I've heard his name a few times before, and it seems like he’d be a popular character that deserves to be fleshed out more.

“The Avengers Break Up!” (1963)

They did not break up.

I already did a frustrated brief post about this issue, but I’d like to reiterate my complaints. This story brings up the idea of elevating Rick Jones to an official Avenger - you know, Rick Jones, the teenager with no powers who is learning judo and karate from Captain America? Rick Jones, the kid with a radio? Those cannot possibly be sufficient criteria for Avengerhood.

Also, this issue introduces “the truly different villainy of Immortus”, but I’m 95% sure Immortus is another Kang variant so how different can he be? He can transport people thru time with a touch, which would enable him to instantly defeat any Avenger who isn’t Thor, but despite fully wanting to defeat the Avengers he doesn’t use this on anyone except Cap. He can also use his ability to summon heroes and legends from other eras, such as when he sics the mighty Hercules on Thor, but he decides to use this ability for staging one-on-one battles, and always picks the worst Avenger for his own summons to face.

Zemo & Co. are also here, I guess.

Also one of the minions Immortus summons is Merlin, but this Merlin seems to be an actual wizard as opposed to the mutant Merlin that Thor faced in his solo run.

“The Mighty Avengers Meet Spider-Man!” (1963)

The cover art was good, but I used this instead on account of it making a neat banner.

Ahahahahaha they have chairs with their noms de guerre emblazoned on them. I should really look into something like that… maybe a chair cozy…

I guess we should talk about the Iron Man series a little. I’ve been skipping over the last couple of stories for prominently featuring “the Mandarin”, an explicitly Fu Manchu-like villain who lairs in a hidden Chinese castle stocked up with technology and ten power rings he looted from the crashed ship of an ancient dragon-alien. Where we last left off, Tony realized that taking off the Iron Man suit would kill him, forcing him to stay in hero mode 24/7 and causing everyone around him to worry that Tony might be dead… and worse, that Iron Man might have killed him. While that sounds like an awesome premise, and it gave something for Happy and Pepper to do other than “““““““romance””””””” gags, nothing much has come of it so far. Anyways, Kang the Conqueror decides to take his revenge on the Avengers since they are down their tech genius.

Villains usually all speak in the same manner, but Kang has a three-page one-man vocal brainstorming session in which he exhibits a very distinct “mad genius” diction. Points to Kang for that.

Time… the final frontier… for the record, I think Kang’s first draft plan of jumping the Avengers with half a dozen supervillains would probably have been more likely to succeed. Alas.

The action’s pretty good, but getting there involves a pointlessly convoluted chain of events. Kang sends his decoy Spider-Man to apprehend decoy vagrants assaulting Captain America so he can be taken to the Avengers HQ so he can spin a false yarn about Iron Man’s whereabouts so they can go to a fictional temple in Mexico so he can teleport there to catch up so he can fight them there.

While at first it seems like the temple doesn’t provide him any situational advantages (other than an endless supply of granite blocks to launch at the Avengers), its interior has been filled with a nerve gas which affects everyone except the Spider-Robot. Spiderbot beats our heroes, but before he can hand Kang the victory…

…the only blurb I can write is “wowee!” indeed. We get a riveting battle of the Spiders and the Avengers are able to infer that only Kang could have designed the Spiderbot, so the issue ends with them shouting at Kang to leave them the fuck alone, hoping his sensors will pick that up in the next millennium.

While I think the plot on this one was pretty thin, I enjoyed it a lot.

“This Hostage Earth!”

Great title, nice cover art, but Mole Man is still deeply uncool. I think this is the first time I’ve seen Giant-Man referred to as “the Master of Many Sizes”, which is a solid title.

Nobody - not even Janet - believes the Master of Many Sizes when he warns of subterranean disturbances picked up by his ants. Doesn’t make any sense, they should know and trust his ant psionics by this point. He gets captured while alone. The Avengers go rescue him.

The surprise highlight of the issue is our surprise second villain, the Red Ghost. Turns out his hamminess is actually rather enjoyable when he's not being forced to spout demonizing propaganda, and unlike the Mole Man, he can put his money where his mouth is in a fight!

In lieu of talking about a fairly standard plot, I’d like to highlight some of the art. While I don’t like the Mole Man, his subterraneans look good.

We also have another money shot in the form of this effortless beatdown monologue orchestrated in defense of Rick Jones (grr).

“The Castle of Count Nefaria!” (1963)

The cover claims “See Rick Jones and his Teen Brigade imprisoned in the Dungeon of Doom!”. This was effective advertising on me, if perhaps not in the way the writers intended.

This issue technically introduces the Maggia, which I’m 99% sure is a recurrent crime syndicate in the Marvelverse, but they don’t really get a good showing. The Avengers are up, crime is down, and Count Nefaria (leader of the Maggia) is displeased. He’s supposed to come across as regal and intimidating - he's a Count, his hair stylist is on point, and he’s got enough money to ship his castle stone by stone from Europe to the Palisades in New Jersey - but he’s one of those “minions are disposable, shoot the messenger”-type villains, and his introduction page is just… so silly.

“Touch the sensitized electro-disc” “So! He is touching the electro-disc!” Noooo the punishment, not the punishment! C’mon. It sounds like kids playacting at being a really poor conception of gangsters.

Nefaria’s plan is cobbled together from tons of stories they’ve already done. Use of a false invitation “for charity” to lure the Avengers into a trap; subdual via paralytic device; use of false versions of the heroes to trick the public into hating them (readers will recall the long-winded litany I brought to bear about this specific trick when Spider-Man and the Torch met for the first time, and that was like a hundred issues ago, there’s way more examples now); and he uses them to do this:

Even after the Avengers escape the castle and escape the furious attack of the American military, they are all subdued by paralytic booby traps when they attempt to reenter Nefaria’s castle. Cap saves the day by being too nimble to get trapped, some junk happens with the Teen Brigade (blarg), and Nefaria unwisely confesses to his crimes in front of some random general Cap happened to catch the attention of. Except for the Teen Brigade (horf) and Nefaria being enough of a rube to leave no room for plausible deniability, the latter half of the story wasn’t that bad… until the ending, where it turns out that Janet’s been shot by a gun, leaving us on the suckiest cliffhanger so far. Not only do we know she’s not gonna die, that was literally her only contribution to the story. I’m starting to see why Rick Jones is considered at her level. Please let her be useful later. I will trade somebody’s firstborn child to any powers listening if that will make Janet not be a detriment to the team sooner.

[woodfrogs]

in another life i was a monk. or a statistician. in a third life i was the worlds first statistician monk. gregor mendel but with linear regression instead of peas or whatever

[vavaclasses]

Universal Law of Gravitation-Class 11 Physics Detailed Explanation

𝐈𝐧𝐭𝐫𝐨𝐝𝐮𝐜𝐭𝐢𝐨𝐧:

Physics is the foundation of understanding how the universe operates. One of the most fundamental concepts in this subject is Newton's Universal Law of Gravitation, which describes the gravitational force that governs the motion of planets, stars, and objects around us. In this article, we’ll break down the Universal Law of Gravitation, explore its derivation, and discuss its applications. 

𝐔𝐧𝐢𝐯𝐞𝐫𝐬𝐚𝐥 𝐋𝐚𝐰 𝐨𝐟 𝐆𝐫𝐚𝐯𝐢𝐭𝐚𝐭𝐢𝐨𝐧 - 𝐂𝐥𝐚𝐬𝐬 𝟏𝟏 𝐏𝐡𝐲𝐬𝐢𝐜𝐬 𝐍𝐨𝐭𝐞𝐬

A detailed explanation for Class 11 Physics students covering the key aspects of Newton's law of gravitation. 

𝐖𝐡𝐚𝐭 𝐢𝐬 𝐭𝐡𝐞 𝐔𝐧𝐢𝐯𝐞𝐫𝐬𝐚𝐥 𝐋𝐚𝐰 𝐨𝐟 𝐆𝐫𝐚𝐯𝐢𝐭𝐚𝐭𝐢𝐨𝐧?

Newton's law of gravitation explains that every particle of matter attracts every other particle with a force. 

𝐌𝐚𝐭𝐡𝐞𝐦𝐚𝐭𝐢𝐜𝐚𝐥 𝐄𝐱𝐩𝐫𝐞𝐬𝐬𝐢𝐨𝐧 𝐨𝐟 𝐭𝐡𝐞 𝐔𝐧𝐢𝐯𝐞𝐫𝐬𝐚𝐥 𝐋𝐚𝐰 𝐨𝐟 𝐆𝐫𝐚𝐯𝐢𝐭𝐚𝐭𝐢𝐨𝐧:

F = G m1​m2​/r^2 

F: Gravitational Force 

G: Universal Gravitational Constant 

m₁, m₂: Masses of two objects 

r: Distance between their centers 

𝐈𝐦𝐩𝐨𝐫𝐭𝐚𝐧𝐜𝐞 𝐨𝐟 𝐭𝐡𝐞 𝐆𝐫𝐚𝐯𝐢𝐭𝐚𝐭𝐢𝐨𝐧𝐚𝐥 𝐂𝐨𝐧𝐬𝐭𝐚𝐧𝐭 (𝐆):

- Value of G 

- Units of G

- Significance in calculating gravitational forces 

Applications of the Universal Law of Gravitation:

1. Explaining planetary motion 

2. Tides caused by the moon and the sun 

3. Motion of satellites 

4. Understanding star systems 

𝐃𝐞𝐫𝐢𝐯𝐚𝐭𝐢𝐨𝐧 𝐨𝐟 𝐭𝐡𝐞 𝐔𝐧𝐢𝐯𝐞𝐫𝐬𝐚𝐥 𝐋𝐚𝐰 𝐨𝐟 𝐆𝐫𝐚𝐯𝐢𝐭𝐚𝐭𝐢𝐨𝐧:

Step-by-step derivation with a simple explanation for Class 11 Physics students. 

𝐋𝐢𝐦𝐢𝐭𝐚𝐭𝐢𝐨𝐧𝐬 𝐨𝐟 𝐭𝐡𝐞 𝐔𝐧𝐢𝐯𝐞𝐫𝐬𝐚𝐥 𝐋𝐚𝐰 𝐨𝐟 𝐆𝐫𝐚𝐯𝐢𝐭𝐚𝐭𝐢𝐨𝐧:

- Assumes point masses 

- Ignores relativistic effects 

- Does not explain the behavior of subatomic particles 

𝐒𝐨𝐥𝐯𝐞𝐝 𝐄𝐱𝐚𝐦𝐩𝐥𝐞𝐬 𝐨𝐧 𝐔𝐧𝐢𝐯𝐞𝐫𝐬𝐚𝐥 𝐋𝐚𝐰 𝐨𝐟 𝐆𝐫𝐚𝐯𝐢𝐭𝐚𝐭𝐢𝐨𝐧:

1. Example: Calculate the force between Earth and a satellite. 

2. Example: Gravitational force between two masses at a distance. 

𝐂𝐨𝐧𝐜𝐥𝐮𝐬𝐢𝐨𝐧:

The Universal Law of Gravitation is a cornerstone of classical physics, explaining a wide range of natural phenomena, from planetary motion to everyday gravitational interactions. Understanding this law lays the groundwork for exploring more advanced concepts in physics. 

[adalidda]

Illustration photo: Maize kernels being processed for food manufacturing (public domain)

Unveiling the Treasure of West Africa: Maize Grains from Sahel Agri-Sol

July 5, 2024

In the heart of West Africa, where the fertile lands of Mali stretch under the warm African sun, Sahel Agri-Sol cultivates nature's bounty - maize grains that stand unrivaled in quality, flavor, and versatility. As a leading producer and exporter of agricultural commodities, we invite food and cosmetics manufacturers worldwide to discover the transformative power of our exceptional corn.

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For Food Manufacturers: Elevate Your Culinary Creations

Flavor Profile

Our maize grains boast a robust, slightly sweet flavor with nutty undertones - a testament to the unique terroir of West Africa. This distinctive taste can add depth and character to a wide range of food products, setting your offerings apart in a competitive market.

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For Cosmetics Manufacturers: Nature's Beauty Secret Unveiled

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We invite you to discover the unparalleled quality of our West African maize. Contact us today to request samples, discuss your specific needs, or arrange a visit to our facilities in Mali. Let's explore how Sahel Agri-Sol's premium maize grains can revolutionize your product line and captivate your customers.

Bring the golden essence of West Africa to your global products. Choose Sahel Agri-Sol - where quality meets tradition, and innovation embraces nature.

Sahel Agri-Sol

Hamdallaye ACI 2 000,

« BAMA » building 5th floor APT 7

Bamako

Mali

Phone: +223 20 22 75 77

Mobile:  +223 70 63 63 23, +223 65 45 38 38

WhatsApp/Telegram global marketing and sales: +223 90 99 1099

Email: sales@sahelagrisol.com

Web sites

English https://sahelagrisol.com/en

Français https://sahelagrisol.com/fr

Español https://sahelagrisol.com/es

简体中文 https://sahelagrisol.com/zh

عربي https://sahelagrisol.com/ar

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[elms-art-gallery]

hypothetical godtier abilities for dirk for combat! thinking about doing these for all the kids when i have time hehe

EXPLANATIONS FOR EACH POWER UNDER THE CUT

Soul Lightning: the very basic power that dirk canonically has and shows repeatedly in the comic itself. from what we know, he can produce a sort of lightning that tears souls out of their bodies and tears it apart (assumedly. dirk doesnt actually get to kill anyone with this power. sad!). for the rest of his hypothetical powers, i used this one as the basis: association with lightning and physical action (use of hands) and being really direct with its application. very little metaphorical bullshit hes just Doing It.

Soul Weapons: a play off of that original idea of electricity being able to sever the soul from the body, and dirk's consistent action to treat his body/self as a tool to accomplish his goals (see unite synchronization and half of the shit dirk does LOL). its an overt reference to revolutionary girl utena and the raiden shogun from genshin impact, both overtly about self weaponization, dehumanization, etc. A lot of his powers i based off of famous anime references because of his 'otaku nature'.

Sheer Presence: THIS is another anime reference! the trope when anime protagonists/antagonists gain a menace aura, but this time the aura actively attacks the soul of those in the aura. this one specifically goes from the angle of a prince "destroying through aspect" specifically. in contrast to soul weapons which physically damages his enemies with his soul while emotionally damaging his sense of self esteem/respect, it is purely his identity (or, sheer presence) that is damaging others. he is the center of gravity here, overbearing every other being with himself.

Flatline: probably one of the weakest in this set LOL but i wanted to play with the idea of being able to collapse what connects your 'self' with your 'body' into one connection and severing the line, trapping your soul outside of your body. its plays into dirk's perception of "self", being awake on derse simultaneously as his actual body probably fucked with how he connects his body with his "self". so another prince of heart who believes the self is inherent with the body wouldnt have this power, but because of dirk's perception he does.

Gunhearted: this is a sub power under soul weapons! its a reference to yuyu hakusho (+all other anime derivations from the og soul gun power LOL) and undertale. not a lot of deep thoughts on this one, its more so practicality (long ranged weapon would be useful generally) and cultural knowledge (dirk probably watched as much anime as he possibly could).

[techninja]

Unveiling the Potential: Exploring the Starch Derivatives Market

Starch derivatives, derived from native starch sources through chemical or enzymatic processes, have emerged as versatile ingredients with a wide range of applications across various industries. From the food and beverage sector to pharmaceuticals, textiles, and industrial applications, starch derivatives play a crucial role in enhancing product quality, texture, and functionality.

In the food industry, starch derivatives are extensively utilized as thickening agents, stabilizers, emulsifiers, and texturizers in a myriad of products ranging from sauces and soups to baked goods and dairy products. Modified starches, in particular, are highly sought after for their ability to improve product consistency, shelf-life, and sensory attributes while meeting the demands of modern consumers for clean label and natural ingredients.

The pharmaceutical industry also relies on starch derivatives for their binding, disintegration, and encapsulation properties in the formulation of tablets, capsules, and other dosage forms. Additionally, starch-based excipients are preferred for their biocompatibility, inertness, and compatibility with active pharmaceutical ingredients, ensuring the safety and efficacy of medicinal products.

Apart from the food and pharmaceutical sectors, starch derivatives find applications in various industrial processes, including papermaking, adhesives, textiles, and bioplastics. Modified starches, in particular, are valued for their film-forming, adhesive, and rheological properties, making them indispensable in manufacturing processes and product formulations.

The starch derivatives market is characterized by ongoing research and development efforts aimed at expanding product functionalities, improving process efficiency, and addressing emerging market trends. Innovations such as resistant starches, prebiotic fibers, and clean label starch derivatives are gaining traction, driven by increasing consumer awareness of health and sustainability issues.

In conclusion, the starch derivatives market presents vast opportunities for manufacturers, suppliers, and end-users across multiple industries. With their diverse applications, functional properties, and versatility, starch derivatives continue to play a pivotal role in driving innovation and meeting the evolving needs of a dynamic global market.

[associativeglassdesert]

gonna throw a curveball here and say fav algebraic topology least fav differential topology

Math enthusiasts of tumblr. What math subjects have you studied and which ones were your favorite? Which ones were your least favorite? Which ones were the hardest?

[prokopetz]

I'm spinning this off of the main thread about tracing the origin of the term "d66" because it's not strictly germane to the topic – none of these examples actually use the term "d66" to describe their dice-rolling methods – but I'm going to post it anyway as a matter of general interest: following a conversation with Tumblr user @notclevr, it appears that before tabletop wargames (and, nearly concurrently, tabletop RPGs) got their hands on the mechanic, the principal (though by no means exclusive) users of the old "roll a six-sided die twice, reading one die as the 'tens' place and the other die as the 'ones' place" trick may have been tabletop American baseball simulators.

The most notable example of the type – and the only well-known example still in publication today – is J Richard Seitz' APBA Baseball, first published in either 1950 or 1951 (accounts vary). In this game, a d66 roll is cross-referenced with a card representing the active player and a "board" representing the current situation on the field:

For example, with Carlton Fisk at bat, a d66 roll of 31 would yield a result of "8". Assuming for the sake of argument that the situation on the field is a runner on first and a grade C pitcher, consulting the "Runner on First Base" board, this corresponds to an outcome of "SINGLE—line drive to left; runner to third".

(This example is, strictly speaking, incorrect, as Carlton Fisk didn't have his major league debut until 1969 and I'm using the wrong lookup tables for any year in which he played, but you get the idea!)

Interestingly, APBA Baseball is not the first game to use this setup. It's heavily derived from Clifford Van Beek's National Pastime, a game whose patent was registered in 1925, though it wasn't actually published until 1930. Even at a glance, the similarities are substantial:

Indeed, though National Pastime's lookup tables are much simpler than APBA Baseball's, where they overlap they're often word for word identical. It's generally accepted that Seitz plagiarised National Pastime without credit when creating APBA Baseball (ironically, given his own famously combative stance toward alleged imitators!), though he was within his rights to do so, as National Pastime had fallen into the public domain by the time APBA Baseball was published.

We can go back even further, though. As far as I've been able to determine, the earliest known tabletop baseball simulator to use d66 lookup tables for resolving plays is Edward K McGill's Our National Ball Game, first published in 1886:

A copy of the game's 1887 US patent application can be downloaded here. This one uses an unusual 21-entry variant of the standard d66 lookup table in which the order of the rolled digits is insignificant, with doubles being half as likely as non-doubles rolls; it's unclear whether McGill was aware of this when he laid out the table. Unlike later incarnations of the genre, there are no individual player statistics, with all at-bats being resolved via the same table.

[medicaldevicesindustrynews]

Navigating the Acetone Market Landscape: Trends and Opportunities

The acetone market will grow at a compound annual growth rate of 7.4% in the years to come, to touch a value of USD 9,590.9 million by the year 2030. Acetone is water-white, volatile, combustible, and mixable in water. Due to its high rate of evaporation and excellent usability as a solvent, it is used to dissolve both synthetic and natural oils, gums, waxes, resins, and other additives. It is…