Last time I received a lot of help, so I guess I'll try again.

There is this problem I can't solve: https://math.stackexchange.com/questions/3698523/on-the-resolvent-set-of-an-unbounded-operator

Now, usually you have some information of A* (like A selfadjoint/normal/such that D(A)=D(A*)) or you know that A is bounded. In this general case however, I have no idea how to prove that the image of \lambda I - A is the whole X.

Thanks for all the help!

Suppose T is a self-adjoint positve unbounded operator on a Hilbert space. I know there exists T^(1/2) self-adjoint and positive such that T=T^(1/2) T^(1/2), but I also know that I can define T^(1/2) via spectral theorem. Do the two definition give the same operator? If yes, why?

Thanks to anyone who'll answer.

Hey there. I'm having a problem with proving the last step in the spectral theorem. Here's where I'm at:

For a self adjoint operator A, I have constructed a projection valued meassure (i.e., a map P from the Borel sets to the bounded operators on my Hilbert space, P(M) is a projection which additive on disjoint sets).

The projection satisfies for [; \phi, \psi \in H ;], [; \Omega \in B(R);]

[;<\phi,;][;R;]A[;(z)\psi>;]= [;\int_R;][;\frac{1}{\lambda -z};] d[;\mu_{\phi,\psi}(\lambda);]

where [;R;]A (z) is the resolvent of A in the point z, and [;\mu{\phi,\psi} ;] is the unique complex meassure (this is proven earlier) that makes this equation true.

Now I want to prove that

[; <\psi, A\psi>=\int_R \lambda d\mu_{\psi}(\lambda) ;]

where [;\mu_{\psi}=\mu_{\psi,\psi} is non negative.

If it should help, the book I'm using is Mathematical methods in quantum mechanics by G. Teschl.

Okay, I can't get latex to work, each time I try to make a subscrict (fx. R_A) it fucks up -.-.

Feeling pretty stupid but wow the operator is much better now!

FRange (GitHub, NuGet) is a new .NET library for working with ranges of values. If you have a sortable type (e.g. int, DateTime, string, etc.), you can create ranges of its values, and then compute unions, intersections, etc. of those ranges.

Ranges can be bounded or unbounded on both sides, and bounds can be either inclusive or exclusive. For example x < 3 has an exclusive upper bound and no lower bound, while 0.0 <= x <= 1.0 is bounded inclusively on both sides.

Let's say Alice has the following schedule:

let parse = DateTime.Parse
let aSchedule =
    [|
        parse "11:30am" +-* parse "1pm"
        parse "2:30pm" +-* parse "4:30pm"
    |]

The +-* operator creates a range that has an inclusive lower bound (symbolized by +) and an exclusive upper bound (symbolized by *).

Using this same pattern, we can also create a schedule for Bob:

let bSchedule =
    [|
        parse "10am" +-* parse "11am"
        parse "11am" +-* parse "3pm"
    |]

If the workday goes from 9am to 5pm, what times during the day are both Alice and Bob free? We can determine this as follows:

let day = parse "9am" +-* parse "5pm"
let free =
    Range.difference [day]
        (Range.union aSchedule bSchedule)

Range.union determines the union of two schedules, and then Range.difference determines what times during the day are not occupied by either schedule. The result is:

[12/1/2021 9:00:00 AM <= x < 12/1/2021 10:00:00 AM;
 12/1/2021 4:30:00 PM <= x < 12/1/2021 5:00:00 PM]

So the mutually free times are 9-10am and 4:30-5pm.

Edit4: All keys have been sent to the winners except for these three users who I could not contact via message or chat. If this is you then send me a message somehow.

u/ddestiny_kb

u/AcrillixOfficial

u/Collectable6

Edit3: Fun fact, Reddit doesn't like it when you rapidly send out PMs so while all winners have been selected notifying them is taking some time, sorry for the delay!

Edit2: Entries are now closed! I have generated winners and keys will start going out tonight, thanks everyone for participating and congrats to the winning comments!

Edit: Wow, this blew up! Thank you to the many generous award givers (my first gold!) and awesome commenters having fun here, can't wait to start dishing out keys tomorrow!

Hi Friends!

I have too many games in the backlog already, so I went through and culled my various bundles of unused Steam keys which are now going to be yours.

How do I get a game?

Make a post below, one per person please. List what games (max 10) you would be interested in and if you'd like a random key if your top choices are gone. If you are picked you will get your topmost remaining pick. If you don't list any games in your post you will get a random game. I will be picking winners after the giveaway closes until keys are gone and then PMing them their new keys.

Not necessary to win but feel free to include your proudest gaming achievement in your post.

Giveaway will close at 9PM EST on July 1st, my goal would be to get all the keys out that night but it may take a bit. Winners will be posted in this thread.

The Big Ol' List of Games:

(VR) Archangel Hellfire - Fully Loaded : azyru

(VR) Paper Fire Rookie : LonkOfHairool

11-11 Memories Retold : calamitysir

198X : camdog215

1993 Space Machine : josephjosephson

911 Operator : kremeyy

A Wizard's Lizard : TPForCornholio

Ace Combat Assault Horizon Enhanced Edition : redditor1101

Age of Wonders III : gamerongames

Ageless : Bonelawz

Angry Video Game Nerd II: Assimilation : Skullboy99

Annas Quest : Blirup

Armello : purplecannon

Atari Vault : cringy_flinchy

Autonauts : 5dmg

Avadon: The Black Fortress : KevinManly

Avalanche 2 Super Avalanche : BreehJah

Bards Tale IV: Director's Cut : mcnicol77

Basement : tungmapu

Battle vs Chess : poopcanalstreet

Battle vs Chess : SGLover28

Beware Planet Earth! : Threshandstuff

Boomerang Fu : Twizzee

Boreal Blade : Mirp01

Call of Juarez Gunslinger : doncornicopia

Canabalt : shotbyabhi

Capitalism 2 : OttoXV

Cast

https://preview.redd.it/2z90ch0vuv781.jpg?width=1200&format=pjpg&auto=webp&s=f825ab1124d5598e4a759c8cba144b8761b56806

WELCOME, AND HAPPY HOLIDAYS!

Hello all, and welcome to the 2021 Holiday MegaSale brought to you by Wraithmarked Creative, Mountaindale Press, Aethon Books, Shadow Alley Press, and Portal Books!

If you didn't know, this year we've turned the sale into a charity event to support St. Jude Children's Research Hospital!

ST. JUDE & DONATION BY AUTHORS:

While last year this was only a holiday sale, this year:

• Each of our 150+ participating authors has agreed to donate at least $0.01 per book they sell or give away!

AND:

• All five sponsoring publishers have agreed to each donate at least $0.01 per book sold or given away SALE-WIDE.

That means every book you buy/pick up for free net's St. Jude at least $0.05 in donations! If we only do as well as last year, we are likely to raise over $10,000 USD for the Hospital!

For those of you who aren't familiar with the organization, St. Jude's mission statement reads as follows:

The mission of St. Jude Children’s Research Hospital is to advance cures, and means of prevention, for pediatric catastrophic diseases through research and treatment. Consistent with the vision of our founder Danny Thomas, no child is denied treatment based on race, religion or a family's ability to pay.

So, every book you pick up helps further R&D of pediatric disease prevention and treatment!

(If you'd like to donate directly, check it out here!)

MEGASALE INFO:

Nothing excessive here, just a bit of information!

1. This event will run for 48hrs, through December 26th and 27th, 2021.
   1. If you missed the sale, but are reading this within a few days of this post, still check the links below. Many of the books are discounted through the new year.
2. All 400+ books listed below should be free or $0.99 in the US and free or £0.99 in the UK at LEAST.
   1. If any book is NOT listed for these prices, please ping me (u/BryceOConnor) and I will see it removed. With so many books in this MegaSale, there's bound to have be

Credits to u/JG-at-Prime for sharing this in the other sub. Crossposting for visibility:

Link to the audio: https://www.youtube.com/watch?v=v9WLziFGmng

The text was autogenerated and I just split it up according to the persons - please let me know the mistakes so I can change them.

Interviewer:

one is how do you think about the you

know why if you could be so great at

asset management why do this other thing

as well and the other is i mean what has

been the secret to to success and i know

it's technology but if you can go into a

little bit more that would be great

KG:

so first of all i think it's important

to be clear that our that our asset

management business

is driven mostly by our

our performance fees which are our

profit sharing with our investors

when our investors make money we make

money and when our investors don't make

money we get paid very little

and this alignment with our clients

puts us in a position to be laser-like

focused

on both identifying opportunities and

managing the risks of the portfolio

so unlike

most of your traditional asset managers

we're in a very different business in

terms of having to be just continually

focused

on how do you have in the marketplace

a competitive advantage in identifying

mispriced assets and opportunities

around the world

so that brings us back to the core of

our market making business which is

around predictive analytics

in the hedge fund we spend an incredible

amount of time forecasting

where we think for example the price of

natural gas will be in the united states

where the 10-year bond yield will be a

month forward think about that mindset

of forecasting

future prices

and bring it into a very short-term

horizon say the next

and then apply those forecasts

and thinking about how you manage the

risk inherent

in a portfolio that is given to you in

your capacity of providing liquidity to

the marketplace

so at 100 000 feet we're in the

forecasting business

and in the hedge fund our forecasts tend

to be

forecast that are measured over weeks or

months

and in the market making business those

forecasts are thought of as being

measured in the course of of minutes

hours or days

but at the core of both of these

businesses is very much a focus on

predicting what the future will be

so for example in the market making

business you'll see technologies like

machine learning being used

to b

I don't want to step on anybody's toes here, but the amount of non-dad jokes here in this subreddit really annoys me. First of all, dad jokes CAN be NSFW, it clearly says so in the sub rules. Secondly, it doesn't automatically make it a dad joke if it's from a conversation between you and your child. Most importantly, the jokes that your CHILDREN tell YOU are not dad jokes. The point of a dad joke is that it's so cheesy only a dad who's trying to be funny would make such a joke. That's it. They are stupid plays on words, lame puns and so on. There has to be a clever pun or wordplay for it to be considered a dad joke.

Again, to all the fellow dads, I apologise if I'm sounding too harsh. But I just needed to get it off my chest.

Disclaimer: This post is driven by frustration with the overall state of the game over the past 12 months, and not all ideas are mine, some are blatantly stolen from posts made here.

Collection & Loadout

1. Added a number of additional voice lines using already recorded, but unused social voice lines to most Heroes

2. You may now equip up to 5 voice lines, and when more than 1 voice line is equipped, pressing the voice line hotkey will open a radial menu displaying the options

3. It is now possible to unequip or equip a lower tier for hero mastery ring

4. The loadout now features 3 additional slots to save loadouts to

5. Added a new button to copy the loadout settings from one loadout to another

6. Added a randomise loadout button

7. Almost all Heroes have received pricing adjustments

8. All Heroes currently worth 2,000 Gold are free to everyone. If you have purchased a hero in this price tier within the past 8 weeks, that gold will be refunded to you

9. Zarya is now available for free to everyone. If you have purchased Zarya within the past 8 weeks, that gold will be refunded to you

10. All Heroes worth 4,000 Gold have been reduced to cost 2,000 Gold

11. All Heroes worth 7,000 Gold have been reduced to cost 5,000 Gold, with the exception of Zarya, who is now available to all players at no cost

12. All Heroes except for the last 4 released worth 10,000 Gold have been reduced to cost 7,000 Gold

13. The past 4 Heroes released priced 10,000 remain priced at 10,000

14. Deathwing remains in his own tier, costing 15,000 Gold

15. The free rotation system has been reworked

16. As above, Azmodan, Diablo, E.T.C., Gazlowe, Li Li, Malfurion, Raynor, Valla, Zarya are now all available permanently for free to all players.

17. The number of free hero rotation slots have been reduced from 14 to 8

18. With the addition of this fixed availability, all potential quests that require a certain role or universe are now available at all times, and so now hero rotations will no longer be made to fulfil that requirement

19. Hero rotations will now only update once every 2 weeks

20. A number of heroes now features split-hero pages, to display a second set of abilities they may have available to them

21. Abathur now features a split-hero page, displaying both the Symbiote and Abathur

22. Tychus now features a split-hero page, displaying both Odin and Tychus

23. Chen now features a split-hero page, displaying both the Spirits from Storm, Earth, Fire

At work BASH was upgraded from 4.2-77.1 to 4.3-82.1, and we started getting errors in old scripts.

Here is a minimal working example:

set -u
func () { local TEST1; local TEST2=$(( TEST1  ))  ; }
func

On 4.2-77.1 nothing is printed out. No error. On 4.3-82.1, we get:

-bash: TEST1: unbound variable

I can't find anything online about operator $(( )) changing its behavior when dealing with unset variables while having option "-u" set.

Can anyone explain what is going on here? Or point me to relevant documentation.

This feels like an old bug that was exploited in our scripts, but was finally fixed sometime in 4.3 cycle.

Thanks

Index

• Part 1: BTC
• Part 2: ETH
• Part 3: BNB - Binance Chain

ETH: Ethereum

Ethereum was the first blockchain to be developed (circa 2014) supporting Turing complete smart contracts: That is, blockchain native programs which can do any arbitrary computation on the current contents of and inputs to the blockchain. Ether ("ETH") is the native token of the Ethereum blockchain.

Blockchain Contents

Ethereum blocks consist of a block header, followed by the following items:

• Uncle header list
• Transaction list
• Receipt list

To briefly summarize the items other than the transactions: The uncle header list is composed of the headers of other blocks which were mined but didn't end up forming the true chain. The receipt list doesn't strictly have to be part of the block chain because it is computed from the transaction list, but it is present to allow programs inspecting the blockchain to more efficiently find the transactions they're interested in.

There is no maximum size of an Ethereum block in terms of bytes, but rather a maximum block size in terms of gas. The network targets an average value of 15 million gas per block in the long run, and there is an additional hard limit of 30 million gas on any particular block. Depending on what kinds of transaction end up in the block, how many bytes that gas total ends up being is widely variable, but there is an upper limit, which we will calculate later.

Consensus Model — ASIC Resistant Mining

Just like BTC in the previous part, Ethereum also uses a proof of work model. The Ethereum chain is planning to move to a proof of stake model soon™, but in this series I'm strictly looking at what each blockchain currently does and the date of transition isn't fixed yet, so Ethereum may end up continuing to use a PoW consensus for the foreseeable future if delays happen.

Ethereum uses the typical blockchain proof of work model, involving finding a nonce (arbitrary number) to include in the block header, such that the total block header satisfies some algorithmic property. Miners have to guess nonces repeatedly to find one that works given the transactions they have included

Consider the following LP in standard form

[;\max ~\sum_{j=0}^n c_j x_j ;]

[;\text{s.t.}~ \sum_{j=1}^n a_{ij}x_j\leq 0,~i=1,2,\ldots, m;]

[;x_j\geq 0~j=1,2,\ldots, n;]

The claim is that either x_j = 0 for all j is optimal or else the problem is unbounded. However, I'm not seeing how to prove this.

Some general facts that I know:

• Clearly the LP is degenerate, since b_j=0 for all j, but we know that Bland's rule prevents cycling, so the Simplex method will terminate.

• The fundamental theorem of LP states that if there is no optimal solution, then the problem is either infeasible or unbounded.

It is easy to see x_j=0 for all j is feasible, but how could it be optimal?

Secondly, If x_j=0 is not optimal, then I know the condition that max(a_ij/b_j)=0 implies the problem is unbounded, and we are done.

Can someone help pull this together?

Do your worst!

There are thousands of statues in the Memorial Hall on Convergence, the galactic capital, where the heroes of a hundred species stand triumphant and proud. They are soldiers, commanders, diplomats, reformers and researchers who have left their mark on the galaxy in times of peace and in war. But there is one statue that stands out among all of them as there are no other statues of its species. This sole statue is among the largest ever created and sits on a pedestal of walls and tombstones yet it wields no weapons, wears no armor and carries no banner of any spacefaring nation. In fact, said species can't be found on Convergence or even in space for they are a people still bound to their home world: Humans.

The Humans are a primitive people inhabiting what the is known to official records as System 3871-A3 who still fight among themselves and believe their crude nuclear ordinance to be "weapons of mass destruction". Their spacefaring development is equally as slow and unimpressive, counting simply "going to their moon" as a huge achievement and seeing their glorified orbital closet they call the "International Space Station" as the peak of their scientific endeavors. Silly ideas but pre-spaceflight primitives often have such delusions so the Humans are hardly unique in that regards which might cause some to question why they are even represented on Convergence let alone the hallowed Memorial Hall. And that is because Humans do the galaxy an impossible service without even realizing it.

Hundreds of thousands of cycles ago, psionic beings of pure energy and thought tore their way into our reality, burning planets and shattering empires. They were an insidious invader as they not only attacked through conventional military means, but where capable of filling the mind with thoughts of despair, of paranoia, of treachery, of ambition and of hopelessness. To some they promised their greatest, selfish wishes of power and wealth and to others they crafted a bleak, hopeless future that makes their lives meaningless. It took the greatest effort the galaxy had seen to that point and the sacrifice of untold trillions to simply contain them as great leaders stepped up and took charge of the fight against invaders on the front lines and on the home front, their legendary efforts and deeds forever immortalized in the Memorial Hall.

The galaxy had finally won after hundreds of cycles of bitter conflict and desperate struggles, the psionic invaders from beyond the veil w

I'm surprised it hasn't decade.

For context I'm a Refuse Driver (Garbage man) & today I was on food waste. After I'd tipped I was checking the wagon for any defects when I spotted a lone pea balanced on the lifts.

I said "hey look, an escaPEA"

No one near me but it didn't half make me laugh for a good hour or so!

Edit: I can't believe how much this has blown up. Thank you everyone I've had a blast reading through the replies 😂

It really does, I swear!

All timestamps refer to this version that should be watched with captions on.

BLACK HOLE is not on that same Spotify playlist Sayonakidori also isn’t, so I heard it for the first time at the end of my run through Unseen World. And so did mostly everyone else who got to experience it, I believe. Which is a good thing, because this song needs the context.

In its most available version, Unseen World starts with a very modern read of a Purcell-like chamber music piece, with a very haunting interplay of three different melodies by plucked and bowed violins, and a glockenspiel, woven into each other and punctuated by timpani and distant cymbal crashes, all of which very loosely support a tension-building tuba that’s constantly descending in pitch to the point where the song seems to start just because the tuba can’t get any lower. Some sort of unnatural noise fades in from nowhere then takes over...

That is the opening of this absolute contemporary masterpiece of an album. An album that is hopeful and positive but also filled with all the anger and frustration of a tightly knitted group of people who used to be with each other 300 out the 365 days of the year. And BLACK HOLE is its the closing argument. When I talked about Sayonakidori I said it was “the romantic love poem ballad 2021 deserves”. Well, BLACK HOLE is this year’s theme song!

It almost got called “CHAOS” and it is often described by fans as “controlled chaos”, but to me this tune is more akin to turbulence - chaos in motion. Kanami, taking hints from Dadaism and Futurism, wrote an impossible song that feels almost like a Force of Nature. All its interacting moving parts feel uncontrollably powerful and unpredictable, almost unquantifiable. And yet, there’s a point to it. It is chaotic, for sure, but it also flows very deliberately in a certain direction.

A black hole is a real thing. It is an infinitesimal point in space with infinite density (i.e. super small, super heavy), which makes it a hard thing to describe or measure and an impossible thing to escape from ([Hawking radiation](ht

They’re on standbi

The Great Khan has fallen taking with him the Lord of Decay, Mortarian

Through the Lion's Gate Space Port, the sons of Jaghatai feel his loss as a hammer blow to their hearts, whilst the Death Guard suddenly feel the true nature of their bargain with Grandpa Nurgle.

The below was an experience on audiobook. It shows what it means for a legion to lose their father. What it means for even the most wild of legions to lose their leader, their father; their Khan.

>He heard cries ring out across the battlefield, unlocked howls of disbelief and horror, and dimly realised that every White Scar across every rotten chamber and miasmatic cavern was experiencing what he was experiencing. A warrior of the Legions was not just an inducted soldier, given the Emperor's coin and handed a bolter. He was connected through warp-craft and gene-tech to his primogenitor, indelibly linked both temperamentally and psychically to the archetype. The bond was more than loyalty, more than filial duty. It was everything.
>
>He wanted to vomit. He wanted to scream. He wanted to throw his head back and empty that unbearable grief out up at the shrouded stars.
>
>But he was also a khan of the ordu, the one the others looked to, the carrier of the flame.
>
>You are Tachseer.
>
>You are the Restorer.
>
>It could not go on. He could not indulge himself. He forced himself to stand again, shakily, and opened his eyes, and it was as if the night around him had become as black as bloody pitch, more hateful than before, emptier and colder.
>
>He took up his blade again, ramming it firmly aloft, just as he had done when the Khagan had breached the first wall, when his ecstasy had been as profound as his loss was now.
>
>'Damarg!' he roared.
>
>That word had only one meaning in Khorchin. It only had one sacred use. Death. Not the death of old age or sickness, but the death of the fighter, slain in battle against an enemy; the death that had to be avenged lest destruction overcome all things. That grief-curse had been heard on the grasslands of Chogoris since the time before memory, a paean of defiance and honour and fealty, one that every sword-bearer knew and understood and venerated. They had cried it aloud when Giyahun had died, when Qin Xa had died, when Yesugei had died, and now they cried it for the greatest of them all.
>
>'Damarg!' Shiban thundered again, his powerful voice hurling the

Pilot on me!!

Because she wanted to see the task manager.

Nothing, he was gladiator.

Dad jokes are supposed to be jokes you can tell a kid and they will understand it and find it funny.

This sub is mostly just NSFW puns now.

If it needs a NSFW tag it's not a dad joke. There should just be a NSFW puns subreddit for that.

Edit* I'm not replying any longer and turning off notifications but to all those that say "no one cares", there sure are a lot of you arguing about it. Maybe I'm wrong but you people don't need to be rude about it. If you really don't care, don't comment.

When I got home, they were still there.

What did 0 say to 8 ?

" Nice Belt "

So What did 3 say to 8 ?

" Hey, you two stop making out "

I won't be doing that today!

[Removed]

Where ever you left it 🤷‍♀️🤭

This morning, my 4 year old daughter.

Daughter: I'm hungry

Me: nerves building, smile widening

Me: Hi hungry, I'm dad.

She had no idea what was going on but I finally did it.

Thank you all for listening.

You take away their little brooms

It was about a weak back.

There hasn't been a post all year!