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## How To Find Transformation Matrix

How to find rotation matrix from latitude and longitude
Nevertheless, the method to find the components remains the same. The latter is obtained by expanding the corresponding linear transformation matrix by one row and column, filling the extra space with zeros except for the lower-right corner, which must be set to 1. For example, the counter-clockwise rotation matrix from above becomes: [ −   ] Using transformation matrices... To find out which transformation a matrix represents, it is useful to use the unit square. The unit square is a square with vertices (0, 0), (1, 0), (1, 1) and (0, 1). The unit square is drawn and the image of each vertex of the square is calculated by matrix multiplication.

math How to calculate transformation matrix - Stack Overflow

Now, in the past, if we wanted to find the transformation matrix-- we know this is a linear transformation. I don't have to go through all of the exercise of this is a linear transformation. But in the past, if we wanted to find the transformation matrix for a linear transformation, let's say we say T of x is equal to some 2-by-2 matrix…...
Nevertheless, the method to find the components remains the same. The latter is obtained by expanding the corresponding linear transformation matrix by one row and column, filling the extra space with zeros except for the lower-right corner, which must be set to 1. For example, the counter-clockwise rotation matrix from above becomes: [ −   ] Using transformation matrices

image processing How to find transformation matrix by
So, given the linear transformation f, we now know how to assemble a matrix A such that f(x) = Ax: And of course the converse holds: given a matrix A m n , the function f how to convince a depressed spouse to get help Welcome to the math homework help subreddit. This subreddit is mainly for getting help with math homework. However, math questions of all kinds are welcome.. How to find out your school district

## How To Find Transformation Matrix

### Transformations Matrices and Computer Animation

• How to find the transformation matrix of a linear
• Finding a transformation between two matrices Physics Forums
• robotic arm Find orientation through Transformation
• image processing How to find transformation matrix by

## How To Find Transformation Matrix

### 23/04/2018 · In this video I will show how to find 2x2 transformation matrix.

• If you only have the view matrix $$\mathbf{V}$$ and you need to find a camera transformation matrix $$\mathbf{M}$$ that can be used to position a visual representation of the camera in the scene, you can simply take the inverse of the view matrix.
• In this matrix, a, b, c, and d are different values which will affect the shape of what we want to transform. The variables tx and ty are the values by which the x and y (horizontal and vertical respectively) coordinates will be moved.
• We verify that given vectors are eigenvectors of a linear transformation T and find matrix representation of T with respect to the basis of these eigenvectors.
• I am studying the elastic properties of trigonal system for which I need the transformation matrix. I have used the matrix in the ElaStic paper but I have not got any result.

### You can find us here:

• Australian Capital Territory: Corinna ACT, Latham ACT, Blakney Creek ACT, Griffith ACT, Blakney Creek ACT, ACT Australia 2646
• New South Wales: Tyagarah NSW, Liberty Grove NSW, Clovelly NSW, Parkesbourne NSW, Denistone West NSW, NSW Australia 2065
• Northern Territory: Moil NT, Minjilang NT, Wurrumiyanga NT, Bellamack NT, Titjikala NT, Gunbalanya NT, NT Australia 0899
• Queensland: Park Ridge QLD, Innisfail Estate QLD, Port Alma QLD, Neurum QLD, QLD Australia 4015
• South Australia: Leighton SA, Hatherleigh SA, Ninnes SA, Templers SA, Kyeema SA, Mitcham SA, SA Australia 5098
• Tasmania: Karanja TAS, Orielton TAS, Glengarry TAS, TAS Australia 7021
• Victoria: Blairgowrie VIC, Parkville VIC, Thoona VIC, Connewirricoo VIC, Kirwans Bridge VIC, VIC Australia 3001
• Western Australia: Parklands WA, Prevelly WA, Coolum Beach WA, WA Australia 6058
• British Columbia: Osoyoos BC, Princeton BC, Fraser Lake BC, Salmo BC, Fort St. John BC, BC Canada, V8W 6W1
• Yukon: Takhini Hot Springs YT, Jakes Corner YT, Whitestone Village YT, Kynocks YT, Upper Liard YT, YT Canada, Y1A 4C5
• Alberta: Delburne AB, Redcliff AB, Champion AB, Gibbons AB, Magrath AB, Andrew AB, AB Canada, T5K 7J5
• Northwest Territories: Whati NT, Tsiigehtchic NT, Ulukhaktok NT, Wrigley NT, NT Canada, X1A 7L1
• Saskatchewan: Debden SK, Yarbo SK, Luseland SK, Lloydminster SK, Tribune SK, Viscount SK, SK Canada, S4P 5C4
• Manitoba: Plum Coulee MB, Oak Lake MB, St. Claude MB, MB Canada, R3B 1P4
• Quebec: Lachute QC, Mercier QC, Lac-Poulin QC, Bromont QC, Cap-Sante QC, QC Canada, H2Y 2W9
• New Brunswick: Blackville NB, Riverview NB, Le Goulet NB, NB Canada, E3B 3H1
• Nova Scotia: Trenton NS, Cape Breton NS, Louisbourg NS, NS Canada, B3J 1S1
• Prince Edward Island: Central Kings PE, Tignish PE, Warren Grove PE, PE Canada, C1A 1N3
• Newfoundland and Labrador: Northern Arm NL, Bishop's Falls NL, St. Joseph's NL, Botwood NL, NL Canada, A1B 4J8
• Ontario: Ojibway Island ON, Bethel, Prince Edward ON, Southgate ON, Espanola, Oliver, Essex County ON, St. Albert ON, Shamrock ON, ON Canada, M7A 1L2


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The conference venue and program

This conference is anticipated to commence in the morning on Monday, September 4, and close in the afternoon on Friday, September 8, 2017.

The conference will be held at the Institute of Computer Science of the University of Wroc³aw, F. Joliot-Curie 15, 50-383 Wroc³aw. All lectures will take place in Lecture Theater no. 27, Level 0. One can also use entrance no. 25, Level 0 or entrance no. 121, Level 1. The place is marked by C on the map below.

Welcome reception

The Mayor of the City of Wroc³aw invites all participants of the conference to a welcome reception at the Town Hall on Monday, September 4 at 19:00. The Town Hall, Rynek 50, 50-996 Wroc³aw is 25 minutes by walk from the conference venue and about 15 minutes from the Mercure Hotel. The place is marked by R on the attached map.

Conference dinner

The conference dinner will take place on Thursday, September 7 at 19:00. It will be held at the Mercure Hotel Wroc³aw Centrum, plac Dominikañski 1, 50-159 Wroc³aw (the place is marked by D on the map below).

Public lecture

Professor Terence Tao will give a public lecture on Wednesday, September 6 at 17:00. The lecture will take place in Lecture Theater IICDEF at the Faculty of Chemistry of the University of Wroclaw, F. Joliot-Curie 14, 50-383 Wroc³aw. This is 5-10 minutes by walk from the conference venue (the place is marked by P on the map below). There is no registration for the participants of the conference. Details of the talk title and abstract are as follows:

Terence Tao (University of California, Los Angeles)

Title: The Erdõs discrepancy problem.

Abstract: The discrepancy of a sequence $$f(1), f(2), \ldots$$ of numbers is defined to be the largest value of $$|f(d) + f(2d) + \ldots + f(nd)|$$ as $$n,d$$ range over the natural numbers. In the 1930s, Erd\"os posed the question of whether any sequence consisting only of $$+1$$ and $$-1$$ could have bounded discrepancy. In 2010, the collaborative Polymath5 project showed (among other things) that the problem could be effectively reduced to a problem involving completely multiplicative sequences. Finally, using recent breakthroughs in the asymptotics of completely multiplicative sequences by Matomaki and Radziwill, as well as a surprising application of the Shannon entropy inequalities, the Erdõs discrepancy problem was solved in 2015. In this talk I will discuss this solution and its connection to the Chowla and Elliott conjectures in number theory.

format: plain


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# Help determining if an equation is a function of x

Graph:

1. ${y\over|y|}={x\over|x|}$
2. ${\lfloor x \rfloor \lfloor y \rfloor = 1}$

Determine if each graph represents a function of x and explain your answer.

I've never seen anything like the before and I'm not sure where to start.

-
Try distinguishing cases: positive $y$, negative $y$, postive $x$, negative $x$ to get rid of the absolute values, and do a similar thing for the floor function. –  dreamer Mar 16 '14 at 9:26
Don't tell me what to do. –  Mike Miller Mar 16 '14 at 9:40

1. ${y\over|y|}={x\over|x|}$ \begin{cases} x \ge 0 \Rightarrow \frac{x}{|x|} = \frac{y}{|y|} = 1 \Rightarrow y \ge 0 \\ x \lt 0 \Rightarrow \frac{x}{|x|} = \frac{y}{|y|} = -1 \Rightarrow y \lt 0 \\ \end{cases} So ${y\over|y|}={x\over|x|}$ is a general way to refer to every functions whose graph is in the $I$ and $III$ quadrant of a Cartesian coordinate system.
2. ${\lfloor x \rfloor \lfloor y \rfloor = 1} \Rightarrow \lfloor y \rfloor = \frac{1}{\lfloor x \rfloor} \ldots$


text:
## The Life Cycle of the Hypercunt Johnsinimus

In which I describe the reproductive process of the sub-species Hypercunt Johnsinimus.

Figure 1. Full diagram of the process.

I claim that the importance of a truth can be gauged by the degree to which, on first intellectual contact, it inspires repulsion. As the seed is planted in your heart it stings and burns and only with time and much dialectical angst do you gradually realise its awful veracity. And so I present to you a new unification. As I have studied the reproductive process of the human animal over many hard and harsh years I have discovered this new travesty. It concerns the life cycle of the Hypercunt Johnsinimus.

It has long been proclaimed that the biological definition of sex concerns the size of the gametes. That the female is the creature with the larger gamete and the male that with the smaller. But has some logical necessity escaped this schematising? For so long as one among the multitude contains the largest gamete does it not introduce the third element. What in logic we call the excluded middle; what I am calling the Hypercunt. I do not deny that the sperm be smaller than the egg. What I introduce is the third class bigger than both: the rugglicle. Furthermore, I posit that the human animal’s third element has a reproductive cycle that lasts one hundred years and that this autumn we approach its apex.

For as the wasps and the ants harbour a queen so the human sets in the bowels of its formicarium the Mastersex Hypercunt Johnsinimus. This aspect has a radically different form and function of genitalia than your or my mere animalia that I will here discuss. But do I give too much introduction? For this scheme can be described simply in just a few hundred words. The essential thesis is thus:

The Hypercunt has two master phalisimi and one rugglicule similar in form but unparalled in magnitude to the typical male’s testicle. The two master phalisimi are likewise very large (around fifteen times the length but similar in width to the average male penis). From these two phalisimi protrude four ceets each which can extend beyond four hundred meters. The Hypercunt reproduces by attracting human females to suck on these ceets. At which point the ceets begin to unravel, travelling the full length of her digestive tract. When the ceet reaches the anus it protrudes and turns a full one hudred and seventy degrees until it faces the subject’s vagina. It then enters the vagina and moves directly to the ovaries which it hovers up along with the full supply of eggs which are absorbed into the central region of the Hypercunt wherein some genetic alchemy (further study needed) produces human baby rugglicles which originate from the singular rugglicule. These rugglicles appear almost exactly as rugby balls but coated in a kind of brittle egg shell from which the fully formed adult johnsinimi are birthed. These johnsinimi are genetically identical to the Hypercunt but completely infertile.

### Patel’s Lemma; what is it?

The inner sanctum is also staffed by many worker johnsinimi who formed from unfertilised ruglicles. One of these has contributed theoretically to the scheme in the form of Priti Patel’s Lemma which posits that any ruglicle left unsatisfied by raw sexual energy shall form into a new worker johnsinimi which functions to serve the production of further ruglicles.

Is it man or fowl? It is a new order of obscenity.

Oh loves! The libidinal economy of the beast is brutal and exquisite. It draws you in as it repulses. It sucks as it blows. Tyrannosaurus rex! The king of terrors. The master of all that is foul and unholy. It comes with its own ontological necessity. It expands and lays and expands and lays. It has within it some overabundance in a rugby shirt. Like slimulus in a suit. Tis beast my good man. Run for ye life lest you be dragged in the inner realm and consumed in its Burgundy based broth.

### Corollary 1; how can this be?

Those of an observant nature might ask why the females might choose to engage in this despicable act. I can tell you friend. For as I studied the process I became increasingly curious about the intense hypnotic pleasure available. To the point one night I began to walk toward this terrible kraken. Luckily, I was forewarned by some poor wretch who had attempted the infinilatio. When the phalisimus has exited your anus and finds there are no eggs to be found it angrily ejects you at such speed you shall never speak again. I had prevented my passage by tying my shoelaces together and awoke from my stupor before I came too close. I saw its appeal. I walked with demons and took from the cup of evil wine. The only way I could explain it is to say it was somewhere between Champagne and nightmares. Between pure joy and pure hate.

But I digress. There are more details to the scheme that any serious enquirer must be informed about. After the ruglicles are complete they are sent forthwith to the anal cavity (in a sister essay I will describe the process of eating whereby the Hypercunt takes food in the mouth, dissolves it and ejects it again from the mouth as an octopus does). The ruglicles are then laid into dustbins where the infant can develop due to the warmth provided by decaying trash. These grow to adulthood fully without any parental care and lead sad bitter lives. You can recognise these when you hear the following squeal from a local wheelie bin “daddy, no, please don’t leave me like the others!”. The screams will never be answered.

### Counter position

“Remarkable claims require remarkable evidence.” – Sajid Javid, CDO salesman and Demicunt.

Do not think I am unaware of the radical novelty of my thesis. Do not think I have not dripped with sweat many a night asking myself “can this monstrosity be? Can God’s earth harbour such demons”. Rest assured, dear reader, I have applied the utmost level of rigorous enquiry of a kind at or near that of the Hypercunt’s very own research department. In point of fact the whole episode was relayed to me by alemate Joshua, who received it first hand, from his colleague, in one of London’s utmost Wetherspoons.

### Corollary 2; what is to be done?

And in this final section we must fall to despair. I know not what or how. I will have to leave this to my readers more versed in strategy. I merely point you to this fascinating and frightening natural process which is coming to fruition. The display is occurring in the inner chamber of the formicarium in one month and with what savagery it will explode none can say. All I ask is that you tie yourselves down, as Odysseus bound himself to the mast, lest the siren call of latinate neologisms draw you through promises of erotic ecstasy to your bloody demise.

## One hundred proofs that Bielefeld does not exist

being one hundred proofs that Bielefeld does not exist.

1 Bielefeld is the most populous city in the Regierungsbezirk Detmold, with a population of 341,730. If this was true then no one could either leave or arrive since the population would no longer be 341,730. It follows that there is no Bielefeld.

2 The historical centre of the city is situated north of the Teutoburg Forest line of hills, but modern Bielefeld also incorporates boroughs on the opposite side. If Bielefeld existed it would then both be and not be on the opposite side. Therefore it does not exist.

3 Bielefeld is home to a significant number of internationally operating companies, including Dr. Oetker. Since Dr Oetker produces frozen pizza which is a self evident contradiction, it follows that it, and its home Bielefeld, do not exist.

4 The angel Merkel acknowledges the non-existence of Bielefeld.

4.5 Shirley’s Lemma: I have never discovered a bias in my thinking. Since my thought, according to itself via an immanent critique, is without bias I believe it when it believes that Bielefeld does not exist.

5 The aeronaut can see for himself that Bielefeld does not exist. The appearance presented to him, even at the highest elevation he has ever attained offers no glimpse of Bielefeld. This is ocular demonstration and proof that Bielefeld does not exist.

6 We can not talk about proof 6.

7 If proof 6 holds then we similariwise cannot talk about Bielefeld. Since what we cannot talk about we must pass over in silence then we must pass over Bielfeld in silence. If proof 6 does not hold then we can talk about proof 6 thus proving that proof six holds.

8 Consider if there were a second Bielefeld. There would then be two towns with the same name meaning it would be impossible to know which we were talking about. If the first town were then destroyed there would still be Bielefeld proving that Bielefeld is of size zero.

9 Since the first proof already demonstrated the thesis and the second prooof also, then, as we are now at proooooooooof nine, and since the letter o is a hyperflattened 0 the prooof 3 was fooooolproooof. It has been demonstrated.

10 In the photographs frequently staged in deep state research laboratories purporting to show Bielefeld various evidences of fakery are presents. In fact an entire head of a man was found to measure just 1.7 cm on my computer screen. Are we to believe these tiny men are real!

11 Throughout the first ten proofs I have demonstrated my ability to provide true arguments. You may therefore take it on authority when I tell you that Bielefeld does not exist.

100 Recent experiments have determined that up to seventy percent of the universe is composed of so called dark energy. I estimate the Bielefeld’s mass to be equal to the length of a London bus in nanometers in imperial tonnes. This more than accounts for the missing dark energy.

101 It is a fact universally acknowledged that Bielefeld does not exist.

12 If Bielefeld exists then the townfolk would not consider any proof that it does not. Since the consequent, that they do consider proofs fairly, holds, then the negation of the antecendent, that Bielefeld does not exist, can be inferred.

14 If Sparrenberg Castle wasn’t in a place then Bielefeld would not exist. Since a castle cannot have an exact place due to its non zero size, proving the antecedent, then the consequent that Bielefeld does not exist may be inferred.

15
15.1 ¬A∨¬(¬B∧(¬A∨B))
15.2 = ¬A∨¬[(¬B∧¬A)∨(¬B∧B)]
15.3 = ¬A∨¬[(¬B∧¬A)∨ False]
15.4 = ¬A∨¬(¬B∧¬A)
15.6 = ¬A∨(B∨A) using ¬(X∧Y)=¬X∨¬Y
15.7 = True

16 – 95 Proofs 16 to 95 are all possible hyperrevolution inverses of proofs 5 to 8 as counterstructed from the mirror image of proof 3. The chiral proof augmented from the mid point of these proofs is identical to the superlocrian mode.

96 If Bielefeld existed a world map containing Bielefeld would be the very best means for a sailor to navigate the world. With such a toy as a guide the mariner would wreck his ship, of a certainty. This is a proof that Bielefeld does not exist.

97 The mayor of Bielefeld, Pit Clausen, believes that Bielefeld exists. Pit Clausen is a damned fool. Therefore Bielefeld does not exist.

97 B Anfangsgründe der Logik was written by Johann Christoph Hoffbauer in 1794. Since Hoffbauer was born in Bielefeld, before the writing of the rudiments of logic, the town is pre-logic. This another way of saying that Bielefeld does not exist.

97 C It is no longer our reason that is against Bielefeld, but our taste.

98 Before publication, this article was subject to extensive criticism from peers in the scientific community of my esteemed acquaintances. Since it has withstood such attack and survived it is true.

99 Bielefeld is home to the professional football team DSC Arminia Bielefeld. Currently member of 2. Bundesliga. Since 1. Bundesliga does exist, it follows that 2. Bundesliga is for teams that do not exist.

The pudding: It is a fact universally acknowledged that the world is approximately spherical and simulated in a computer on the flat earth. Since it would be easier to simulate a world without Bielefeld, it follows from Occam’s razor that there is no Bielefeld.

A non-zero proof equal to the square root of zero: Once you eliminate Bielefeld, whatever remains, no matter how improbable must be the truth.

0 Since it has been proven that Bielefeld does not exist, it necessarily follows that Bielefeld does not exist.

Q.E.D.

## Living in the land of opposites

In which women have too many positive role models; and are only permitted to exist in positions of authority be being judges, teachers, doctors, and CEOs.

The object and its opposite living in a whole. Or three objects describing the famous Borromean knot. The exclusions sustaining the explicit contradictions. And all this embodied in the toilet bowl!

In which the answer to the question has no relation to the question being asked because the question is unsatisfactory.

Should the answer to this question characterise the power dynamic between the asker and the asked? Leave or I take an early Witgenstien view that language is a means to describe the world. Remain or I take a late Witgenstien view that the bulk of language is performative and game-like. I really should go home after this pint.

In which all discourse between the UK government and its population takes the form of an exam.

Do you conform to the doctrine of being different? To what? That which everything is not. Rebelliously ignoring the law of the excluded middle. The last words of the sentence are vulgarised faeces*.

*shit.

In which itself and its opposite mean the same thing.

How are we to reconcile Ricky Gervais’ comment that “the men are the children, the women the adults” with Kant’s that all women live in a state of “self-imposed nonage”.

Each appears sexist yet they are each other’s complement. Each sentence should further the aim of the paragraph. But these are unruly sentences and paragraphs are passé.

In which I have the realisation that meta-argumentative analysis is applicable in all contexts.

Irony is just a first order dialectic. A dialectic for babies.

Obviously I don’t care about other people, I’m just worried about my own wrong ideas. But, if I’m completely dishonest, my feelings about these wrong ideas are not ambiguous. Oh you wrong ideas. You darlings!

In which women are denied the radical freedom of inherent self worth not derived from a position of power, success, influence or authority. Available even in destitution and failure. Jesus the ultimate loser. Terrorists the fake losers. Loser winner, winner loser.

The only original idea: that gender being a ‘social construct’ makes it harder to overcome than any natural limitations imposed by mere biology. It took a hundred years to overcome the speed limit imposed by mere biology. It will take eternity to end the use of men running as propaganda instrument. Eliot’s perceptive line:

“It was as if a woman’s ignorance was of a lower quality than a man’s.”

Is there a difference between no apples and no oranges? Yes, because no oranges in a box means there might be apples there. A description of a description. A false description in one sense, a declaration in another.

Those acts which are permitted by the two exclusions ‘don’t be evil’ and ‘don’t be good’. As close as evil to possible without entering that morality space.

In which we fight the battle for the origin myth.

It is important to remember that the state of nature is not a real object to be inspected but a performative one to be created. The argument over the qualities of the real object is entirely synthetic. Like an artist’s impression of the prevalent description of cosmological origin in an ironised tabloid science article. Presenting its claim to higher understanding as a modest lack of understanding.

A series of unrelated thoughts bungled on to the page.

In which we pretend to believe in some set of minds with lower instrumental and epistemic rationality to our own. The other readers. Dear everyone other than reader.

As if reason didn’t act on axioms to be chosen by whim. Euclid’s fifth postulate was thrown away by whim. And this they called genius.

In which I show a selfish concern for my own mind above other’s bodies damaged and degraded by Hollywood’s film industry practices.

Searching around my brain for all the little structures erected by Harvey Weinstein. Erected to sustain a particular form of zero. Erected by pathetic fallacy. The stage contains more information than the play on it. The space-space-time cube containing the producer’s work. I once had my wages to drive some props around London haggled down by a producer and have distrusted them ever since.

In which we see the last humanities department.

In which academic text books are the seat of propaganda.

In which satire is the instrument of the powerful.

In which I didn’t notice the inversion.

In which I fail to imagine a female in permanent adolescence.

In which technology alters language.

In which we disobey Steven Pinker’s request to omit unnecessary words.

In which we only include unnecessary words since necessary words are implicit.

Only include superfluous words.

Hypersuperfluousity.

I, malevolent.

In which the category wife sustains the category prostitute (Engels).

In which the guilt sustains the lust.

In which categories both describe and cause (Peter Hitchens).

In which the world is a yes or no question.

In which it all appears as one whole wrongness.

In which the world is turned upfide down.

## The event

The circumstances of the event are very much specific to the event. That is why when speaking of it we must be exceptionally careful to be specific about what we mean by the causes and learn from them.

LUV xoxo

## inertia

0

Living in a caravan. Masturbate in the morning. There is a cow at the window watching me. This put me off. It had a big brown eye watching me wank. Now the day is off kilter so I run out the door bare shouting at the said cow.

1

I denounce feminism and all her evils.

2

Wandering down the country lane elliptical. A battalion of wheelie bins come over the top at me declaring. I have weapons. Shotgun and stick and take on the wheelie bins. Neighbours scream and shout. ‘What have you done to my bin?’

3

A sea of strewn enemies. Their innards (old food packaging etc) flowing out. Sheer sublimated libidinal energy. Such waste. Council replaced bins efficiently.

4

Amazon because it had the A to Z design possibility and the scale of flowing out. What is the sea?

5

Looking out the back window of a bus at my conquest satisfying but guilt. sHello sdarkness smy sold sfriend.

6

I watched as the finest vets of my generation grabbed a cow by the pussy and pondered Benjamin’s immortal inspirational quote ‘behind every fascism there is a failed revolution’ because ‘behind every great man is a great woman’. Was the obvious parallel lost on you?

7

A threat hanging in the air with menace.

8

Recreational agriculture.

9

How many moves ahead can you think in chess or politics? I can think between zero and one moves ahead. Did not see that one coming.

10

We never believed they would hire the better creatives.

11

The psychometric covariance matrix.

12

Windows 95.

## Summary of the year two thousand and sixteen

We the hyperboreans! We the followers of David Icke. I can begin with the summary that 2016 was all about architecture. When Russian agents created the European parliament they employed a man who had dedicated his life to helping insomniacs. He did this by designing an unnational parliament that was so boring to watch that no animal could look at it for more than around 15 seconds without falling asleep. After ten seconds of stock footage to be played over any news story the camera man would slumber, the camera would dip to the floor and the lizards could remove their human costumes and begin their horrific reproduction ritual of which one byproduct was law. There were at least ten byproducts and the product was caviar. However, one day another Russian, this time a dissident; Ronald McDonald, invented the ‘tripod’ and it was just a matter of time before Britain voted to leave the union.

Light beech benches in the round. Cheap expensive suits in monotonous foreign mangled overly good English with perfect grammar and no idioms. A parliament designed by Ikea. Don’t worry, I will maintain some ironic distance to help you swallow the bitter pill. The prose is scattered nonsense lacking structure, which has been acknowledged and therefore cannot be criticised; blithering. A vulgar room in a vulgar building that asks for our love or disinterest. No, no, yes. Location, location, education. Minds untouched by the King James. A codified genre.

Where was I?

<in hell>

<logic>
David Cameron therefore* asked us whether the UK government should drop a nuclear bomb on us all. Should choose a policy without a government. Should heal the Conservative party. Should be racist. Should say fuck off. Should x. This was a masterstroke of long term strategy of which we are merely witnessing the first stage. The end game involves George Osborne becoming King of the Jews and completing his long term economic plan in 3000CE when we will run a surplus of 1p. When we were asked whether the world was round, he unfortunately told us that he would be upset to the point of crying in his wife’s arms, which his children would see; forever losing respect for him, if we said it were flat. And out of sheer spite I wanted his children to share our disappointment with our parents. I wanted disciplinarians and they turned out to be liberals. A yearning for authority. But there were lies on both sides. 350 is approximately 200 to a statistician. We call them the same ‘order of magnitude’. For instance the average density of the universe is around 0.000 000 000 000 000 000 000 000 000 01 kilograms per cubic metre which is a different order of magnitude to the density of air which is about 350 000 000 pounds per week when hot. We are a stain on the vacuum. So it was a lie of size 7/4. Compare that to the lie the goodies told that the density of the universe was roughly the density of air. It was a bigger lie, but then again if two liars tell you two lies what does that reveal about the truth? this is part of the grand metaphysical debate begat by Rumsfeld who famously forgot to mention the things that you know but you don’t know that you know. For me that is that I know I don’t understand numbers above a thousand but I don’t know that I know it.
</logic>

world.history.help()

“ ‘Take back control’ has the character of the death wish. We know we have to die, but we want to die on our own terms.’ – some yank red. Memento vitae.

britain.finishJobOfLuftwaffe()

I met someone who thought a vote for X was an endorsement of X. How would you like to be humiliated?

self.cry('conformism that doesn\'t know it is conformism is just a further stupidity')

A slight mental smell seemed to be hinting at a coherent idea but never quite settled.

And the left destroyed the leftist Sanders and want a new war with Russia for some reason. It was Amy Schumer wot won it.

And apparently the sixties was actually shit.

And the introduction of the tritone into compositions was shatteringly brutal and radical. It took the genius of the oppressed to make such an incredible theoretical divergence from the past. But it was a victory of the intellect over order. Ugliness became an ingredient for beauty.

$R_{\mu \nu} - {1 \over 2}g_{\mu \nu}\,R + g_{\mu \nu} \Lambda = {8 \pi G \over c^4} T_{\mu \nu}$,

where $R$ is the experiment being conducted on our minds by the Chinese called the internet; $g$ is the fake clash of civilisations narrative; $\Lambda$ is the true clash of civilisations narrative; and $T$ is Nigel Farage.

And so it turned out that T.S. Eliot was wrong about April. It was June and even then not so much as November, less a month than a vacuum between two other gentler months. I think T.S. stands for That Slapper. For in November Hillary Duck was crowned oldest loser in history. Septegenocracy is a new evil for the world. A slow evil. A weary evil. A evil with urinary difficulties. Daffy Clinton will now have have a special bingo wing added to the Special Fancy House for special bingo times. This all poses some troubling conundrums for Jonny Muslim. And we should remember that just because they think the world was made by a male fairy type thing which is difficult to describe they are still terrorists. Just like you and me. And the advertisers have been first to champion empowered religious women. Ann Summers released a Christmas burqa with extra slits at the nipple and crutch to help empowered religious women feel sexy while honouring the prophet (PBUH) by covering their modesty. It had the full veil of ignorance allowing objective analysis of political theory. And I have started covering my hair with a ‘baseball cap’ for fear of arousing women with my brown mop out of pure respect for dignity. I have long been worried that I would tempt females away from austere piety and make blood flow to their secondary sexual organs by running a hand across my head provocatively. Seemingly unaware that I am being watched. But I know what I am doing. It says #MAGA. And we must concentrate on what we have in common. For instance us atheists share the Islamic view that Mary must have had sex to have that kid and probably told Joseph that it was God that raped her in her dream in a panicked explanation in the heat of the moment that she couldn’t believe he believed to the point where she was forced to question his intellect. Either that or Joseph ejaculated on her and I don’t need to go into vulgar details but you get the picture (his semen somehow made its way ‘down there’, ‘down south’, or raised eyebrows (I’m talking about Mary’s vagina and uterus)). But of course I feign a symmetry where an asymmetry lies. Four points on an identity space.

a)                                                                                b)
Figure 1: Graph of my ignorance against religion a) shows Shiantanism and b) shows Sunnitholicism. Time for the daily trip to BBC article on the difference between Sunni and Shia.

I ask myself of what topics I dare not speak. I don’t think the holocaust is a fair example.

Intentional disregard for Michael Gove’s and Steven Pinker’s contradictory rules for good prose style.

‘When I was seventeen, it was a very good year’ is a lyric that today’s seventeen year olds will never be able to sing. Except ironically if they still have that. I don’t know, I remember when a telephone was still two plastic cups and a bit of string, which lets face it: it still is. I wish I was seventeen, and it is our duty to ruin things for them so we don’t feel so jealous. Like really humiliating until it’s like literally ‘thank god I’m not seventeen’. Twenty Seventeen. Seventeen feels like a cute diminutive for seven. The seven blasphemies of modernity: the Shard, the Gherkin, the Walkie Talkie, the Lloyds building, Canary Wharf, the Olympics and Mary Berry. The bland international city state which mocks the sublime modesty of a small Norman church. They holiday in Tuscany while English winter sunsets mock the base vulgarity of Mediterranean heat on paid leave. A dream that our star will replace carbon through pure commercial supremacy.

The bland international city state cries a liberal tear. The pseudo leftists weep. Is it a coincidence that the principle image of our global warming is a biblical flood? The salary of crying. The cinematic aspect of the scientific theory is its essential appeal.

I am grateful to be alive (stars, life etc).

My main prediction is that since Jonny Chinese is a more effective capitalist than Jonny Yank we will see the Cold War in reverse in the twenty first century. Peace Hot. We are at peace but we all kill each other. The yanks will be the commie bastards. Elections and liberty will be opposites. The world is upfide down.

What is your preferred binary? Old-young? Educated-uneducated? bigoted-liberal. My preferences are rural-metropolitan and pessimist-optimist.

Figure 2: Bisections of a plane.

The glass is not half empty, it embodies dread.

Some old ideas as a front for something or other.

Merry Summery across gorgeous rolling green hills to a blood orange horizon,

* No causal relation permitted.

## Aliens

And a little song companion piece:

## Donald Trump Medley

Peace to yanks everywhere,

## Melancholy Woman

Please enjoy it. Make the most of it. Fourth album on way,

## Human Garbage

Not the best mix but whatever yeah.

P+L

Come on now gentlemen get in formation, you could be the next Ada Lovelace in the making.

Love,

## Inheritance Tax Threshold Harvesting

Detective Manners, short and fat, sat at a cup of coffee. Progressing slowly through the Metropolitan police he carried the air of disappointment that a lot of forty year old men who use internet dating algorithms do. He had been given a case by a particularly irritating boss that was going nowhere. A series of missing vagrants across London, had dissapeared in similar circumstances. His response to this was ‘obviously’. Spread out in front of him were a series of photographs from half way houses and veteran’s organisations. Resigned and bored, he pushed them away and looked up out the window. A smartly dressed but unusually wizened man walked past. Buzzing with an energy he hadn’t seen since his first day when a pranking senior officer told him he’d been given a murder case which turned out to be a call from a nice lady who had had a tramp use her doorstop as a toilet, he looked down at the photo on the top of the pile and knew immediately it was the homeless man. Cleaned up and besuited; but the man.

Throwing five pounds at the counter and grabbing his photographs he ran out the door and began to follow the man. He went to a rather nice looking off license and bought two bottles of wine and a cigar. He then crossed the street to buy some pornography and continued casually down a well to do street of terraced houses. He noted the address the man entered and returned to his car, a shabby minute little thing that made him look slightly bigger by virtue of the strain required to enter it but no less ridiculous. He returned to the street and resigned himself to a night on ‘stake out’. He had never done this before and therefore his only point of reference was a few American movies. He thought perhaps he should invite a ‘buddy’ but he had no ‘partner’ so merely mirrored the food consumption. Sitting alone in the sodium half light, in an oven of smells from Subway sandwiches and Peperami, he began to make his discovery. One by one, the pictures in his folder were beginning to be associated with well dressed faces. Manners became wildly enthusiastic and put on some Status Quo to celebrate.

Further investigations the following morning told him that the house had had a significant basement room built a year ago and that they had applied for permission to grant marriages. On returning to the premises in the afternoon, quite to his astonishment there was a funeral in progress. Feeling confidence like he had never felt before, Manners in an act of almost mad recklessness started walking towards the front door and rang the bell. A cartoonish butler appeared seemingly straight out of Wodehouse.

‘I’m here to pay my respects.’

‘Of course.’

Manners entered a champagne wake. A clashing combination of people from either end of the social strata were interacting quite freely. He noticed how the homeless chose to wear lavish, almost outlandishly aristocratic dress. While the hosts were much more casually dressed in golf shirts and slacks like international business elites do. No one successful enough to wear a T-shirt and jeans was present, but there was the odd pair of trainers. Choking on his champagne Manners then noticed the coffin contained the very man he had seen yesterday. At this point a priest entered the room and, surprises now compounding like water drowning a rat, said something which was not predicted by Manners.

‘We are gathered here today to witness the matrimony of…’

After completing the wedding of an elderly woman to an elderly woman, a great volume of bureaucracy took place. Then the priest continued:

‘Ashes to ashes. Dust to dust.’

And the coffin was lowered into a furnace.

Six months later, Manners was a little fatter and still unpromoted. He had taken to reading romantic literature, watching Renee Zellwegger based romantic comedies and drink. He had been convinced the work from the start of the year was to be his finest moment but of course it was not. He had found no wrong doing. No law had been broken.

### A Portrait of a Provincial Nobody

Words and pictures from Raph Shirley, in humorous weblog form.

Infecting the internet like so many glimmering tentacles
( ).

He is a fictional character.


text:
## The different DOS and bandstructure modes of FLEUR

Fleur supports the calculation of several "DOS-like" quantities which can be understood to be obtained in a two-step procedure.

1. For each of the eigenstates a set of "weights" is obtained.
2. These weights are then used in a k-integration.

From this general structure one can already conclude that there are two different possible output quantities that could be of interest. On the one hand the weight as a function of k-vector, band-index and possibly spin and on the other hand the integrated weight as a function of energy and spin. The first of these can be used to further describe the eigenspectrum in a "bandstructure" view, while the second is a "DOS"-like quantity. If <output band="T"> in the inp.xml Fleur will output these weights for each state, while the <output dos="T"> switch will trigger the k-integration to write out the integrated weights. Hence, the modes as described below can be used with setting the band and/or dos switch in the output section.

The different weights supported by Fleur include the local, $l$-resolved density, the orbital decomposed charges, vacuum charges and the MCD matrix elements. Details are described below.

### Common input switches and resulting output

The most basic setings for generating a DOS-like quantity are then specified in the output/bandDOS tag. For example:

<output dos="T">
<banddos minEnergy="-0.5" maxEnergy="0.5" sigma="0.01" numberPoints="1321"  />
</output>

The banddos tag must be used to specify the most basic quantities controlling the DOS k-point integration. |attribute|description |----|---- |minEnergy| minimal energy of the DOS grid in Hartree (default=-0.5) |maxEnergy| maximal energy of the DOS grid in Hartree (default=0.5) |sigma| smearing energy to smoothen the DOS in Hartree (default=0.01) |numberPoints| point between minEnergy and maxEnergy (default=1321)

### Local and $l$-resolved charges

By default Fleur calculates weights by considering the local $l$-resolved charges in the muffin-tin spheres due to the states. Here we calculate for each atom the charge expanded in spherical harmonics, i.e. the contributions of the l=0, l=1, l=2, and l=3 or s,p,d,f-like charges. The corresponding weights will be labeled by a string like "MT:5d" for the d-like charge of the 5th atom type.

Weight labels

A label like MT:6s is to be understood as the s-like charge of the 6th atom type. Not as a charge of 6s-states.

In addition, the default mode also creates three additional weight "Total", "INT" and "Sym". While the "Total" weight is simply "1.0" for all states, the "INT" weight contains the local DOS in the Interstitial region. The "Sym" weight contains a integer value indicating which representation of the local symmetry corresponding to the k-point the state belongs to.

The data generated in this mode are written to the files "Local.1/2" and/or to the corresponding groups in the banddos.hdf file.

### Orbital decomposed charges

In addition to the simple projection onto s,p,d,f orbital, you can also generate more detailed information projecting onto the different (real) spherical harmonics. This mode is switched on by setting the attribute orbcomp="T" in the banddos tag. So a minimal input setting in the output section would be:

<output dos="T">
<banddos orbcomp="T"  />
</output>

This will give you weights like ORB:1ind:3. Here again the first number after the ORB: will indicate the atom considered.

Counting of atoms in ORB-mode

As the orbital decomposition is calculated for each atom not only once for each atom-type be sure you analyse the correct atom. Use the List of atoms in the output to verify which atom you are looking at.

The second number in the label of the weight, i.e. the number after the ind:, is an index counting though the orbitals as follows: 1:s-state, 2-4: p-states, 5-9: d-states, 10-16: f-states(cubic), 17-23: f-states(low symmetry).

1 2 3 4 5 6 7 8 9
s px py pz dxy dyz dxz dx^2-y^2 dz^2

The data generated in this mode are written to the "Orbcomp" group in the banddos.hdf file.

### Vacuum charges

For film-setups, i.e. if Fleur is using an input for a film, one can write out various projections of the states in the vacuum. The correspond section in the inp.xml file is:

<output dos="T">
<vacuumDOS vacdos="T" integ="F" star="F" nstars="1" locx1="0.0" locy1="0.0" locx2="1.0" locy2="1.0" nstm="0" tworkf="0.0>
<layer> 10 </layer>
</vacuumDOS>
</output>

attribute/tag description
vacdos switch on/off the evaluation of vacuum charges (required)
integ switch to activate a z-integration between the layers specified (default="F")
stars switch to activate a decomposition according to 2D stars (default="F")
nstars number of stars to use in decomposition (must be given if stars="T")
locx/y/1/2 definition of a 2D area in which to integrate the DOS (optional)
nstm switch for different simulation modes for an STM tip (expert usage)
tworkf work function of the tip in STM mode (expert usage)
layer layer at which the DOS should be evaluated. Several layers can be given.

The layers are specified on the internal z-grid Fleur is using in the vacuum. By default we use 100 points with a spacing of 0.1 a.u. So layer should be a number between 1 and 100.

The weights generated by this mode are specified by the following labels: |label|description |----|---- |VAC1| total weight in the first vacuum |VAC2| total weight in the second vacuum |Layer1-x| weight (2D) integrated on the layer x (first vacuum) |Layer2-x| weight (2D) integrated on the Layer x (second vacuum) |R(gVAC1)-x-y| Real part of weight for star y on layer x (first vacuum) |I(gVAC1)-x-y| Imaginary part of weight for star y on layer x (first vacuum) |R(gVAC2)-x-y| Real part of weight for star y on layer x (second vacuum) |I(gVAC2)-x-y| Imaginary part of weight for star y on layer x (second vacuum)

The data generated in this mode are written to the "Vacuum" group in the banddos.hdf file.

### MCD matrix elements

To evaluate MCD matrix elements the following tags can be set:

<output dos="T">
<magneticCircularDichroism mcd="T" energyLO="-2.0" energyUp="-1.0" />
</output>

Besides switching on the mode using the mcd attribute, you also have to specify the energy window for the selection of the core-states.

This mode generates weight labels by a string like "At1NC2pos", where again the first number after the "At" labels the atom type considered, the number after "NC" iterates through the core-states used and the description ends in "pos","neg","cir" for the positive, negative and circular contributions.

The data generated in this mode is written to the "MCD" group in the banddos.hdf file.

### Selection of atoms for the DOS/Bandstructure output

As some of the modes can lead to a large amount of data being generated, the application of the switches can be restricted to a subset of atoms only. For this two different switches are implemented:

1. In the bandDOS section a all_atoms attribute can be specified. It defaults to "T" but can be used to switch off the generation of weights for all atoms.
<output dos="T">
<bandDOS all_atoms="F" />
</output>

1. For each atomic position, a banddos attribute can be given to switch on/off the generation of weights:
<relpos label="something" banddos="F"> 0.0 0.0 0.0 </relpos>

In addition, one can use the alpha, beta, gamma attributes to rotate the coordinate frame of the atom and thus change the assignment of the orbital decomposed weights.

<relpos label="something" alpha="0.0" beta="0.0" gamma="Pi"> 0.0 0.0 0.0 </relpos>


text:
# CTAN update: manyind

Date: January 31, 2019 11:48:15 AM CET
Wilberd van der Kallen submitted an update to the manyind package. Version number: 2019-01-28 License type: lppl1.2 Summary description: Provides support for many indexes Announcement text:
defined second way of sorting index entries
The package's Catalogue entry can be viewed at http://www.ctan.org/pkg/manyind The package's files themselves can be inspected at http://mirror.ctan.org/macros/latex/contrib/manyind
Thanks for the upload. For the CTAN Team Erik Braun
We are supported by the TeX users groups. Please join a users group; see http://www.tug.org/usergroups.html .

## manyind – Provides support for many indexes

This package provides support for many indexes, leaving all the bookkeeping to and makeindex. No extra programs or files are needed. One runs latex and makeindex as if there is just one index. In the main file one puts commands like \setindex{main} to steer the flow.

Some features of makeindex may no longer work.

 Package manyind Version 2019-01-28 Copyright 2018–2019 Wilberd van der Kallen Maintainer Wilberd van der Kallen

more


text:
# Make Section, Subsection, and Subsubsection Titles Flush with Top Margin with Double Space

I am trying to get the subsection title flush with the top margin when it appears on a new page. I was able to get all the section headings flush with the top margin by using the the \setstretch{1} command in the \titleformat{\section}. The same trick doesn't work for the subsection because I am using hang for them instead of display so it has the unwanted affect of removing the double spacing.

In the second image, how can I get the subsection title to be flush with the top margin just like the section on the first page? I have tried \titlespacing{\subsection}{0pt}{-.5in}{0pt} but this messes up the subsection on the first page and it also doesn't do anything for subsections that appear on a new page.

Some things to note: I do not want to mess up the long subsection heading that is on the first page. Also, this is a problem that I am trying to solve for a large document. Also, I am pretty committed to the titlesec package at this point. Finally, I have the same exact issue with subsubsection so I am looking for a solution that will also work with that.

\documentclass[12pt]{article}
\usepackage[paperwidth=8.5in, paperheight=11in, margin=1in, showframe=true]{geometry} % Set paper size.

%Set font to Arial font
\usepackage{helvet}
\usepackage{setspace}
\usepackage{titlesec}
\usepackage{calc}
\usepackage{lipsum}

\newcommand{\sectionbreak}{\clearpage}%new page for each section
\titleformat{\section}[display]{\centering}{\setstretch{1}SECTION \thesection}{0pt}{}
\titleformat{\subsection}[hang]{\centering}{\thesubsection}{\widthof{\space}}{}
\titlespacing{\section}{0pt}{0pt}{0pt}%Removes spacing around section titles
\titlespacing{\subsection}{0pt}{0pt}{0pt}%Removes spacing around subsection titles

\begin{document}
\raggedright % Flush left
\setlength\parindent{0.5in}%Indent the text. Must be after raggedright.
\setstretch{2} % Double space the entire document (used to be \doublespacing)
\section{LONG TITLE LONG TITLE LONG TITLE LONG TITLE  LONG TITLE  LONG TITLE  LONG TITLE }
\lipsum[5]
\subsection{LONG TITLE LONG TITLE LONG TITLE LONG TITLE  LONG TITLE  LONG TITLE  LONG TITLE }

\newpage
\subsection{LONG TITLE LONG TITLE LONG TITLE LONG TITLE  LONG TITLE  LONG TITLE  LONG TITLE }
\end{document}

First page: The section is flush with the top margin.

Second page: The subsection is not flush with the top margin like the section on the first page.


text:
# How do you solve 13x - 22= 2( 9x + 10)?

Jan 30, 2017

$x = - \frac{42}{5}$

#### Explanation:

On the right hand side, start by distributing the $2$ throughout the expression $\left(9 x + 10\right)$. So $2 \times 9 = 18$ and $2 \times 10 = 20$, giving:

$13 x - 22 = 18 x + 20$

Next, add 22 to both sides of the equation.

$13 x = 18 x + 42$

Next, subtract $18 x$ from both sides.

$- 5 x = 42$

Finally, divide both sides by $- 5$

$x = - \frac{42}{5}$


text:
convert/mathorner - Maple Programming Help

Home : Support : Online Help : Programming : Data Types : Conversion : convert/mathorner

convert/mathorner

convert a polynomial to Matrix Horner form

 Calling Sequence convert( poly, mathorner ) convert( poly, mathorner, var )

Parameters

 poly - polynomial var - (optional) variable

Description

 • convert/mathorner writes the polynomial poly in the name var in horner or nested'' form.
 • If there is only one indeterminate in poly then it is not necessary to specify the third argument var.
 • Horner form allows you to evaluate polynomials of Matrices in the most efficient manner. For a polynomial of degree n there will be n adds and n multiplications needed to evaluate the Horner form.

Examples

 > $p≔-56-7{x}^{5}+22{x}^{4}-55{x}^{3}-94{x}^{2}+87x$
 ${p}{≔}{-}{7}{}{{x}}^{{5}}{+}{22}{}{{x}}^{{4}}{-}{55}{}{{x}}^{{3}}{-}{94}{}{{x}}^{{2}}{+}{87}{}{x}{-}{56}$ (1)
 > $A≔\mathrm{Matrix}\left(\left[\left[1,-3\right],\left[4,7\right]\right]\right)$
 ${A}{≔}\left[\begin{array}{cc}{1}& {-3}\\ {4}& {7}\end{array}\right]$ (2)
 > $\mathrm{convert}\left(p,\mathrm{mathorner}\right)$
 ${-}{56}{+}\left({87}{+}\left({-}{94}{+}\left({-}{55}{+}\left({22}{-}{7}{}{x}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{&*}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{x}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{&*}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{x}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{&*}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{x}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{&*}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{x}$ (3)
 > $\mathrm{subs}\left(x=A,\right)$
 ${-}{56}{+}\left({87}{+}\left({-}{94}{+}\left({-}{55}{+}\left({22}{-}{7}{}\left[\begin{array}{cc}{1}& {-3}\\ {4}& {7}\end{array}\right]\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{&*}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\left[\begin{array}{cc}{1}& {-3}\\ {4}& {7}\end{array}\right]\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{&*}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\left[\begin{array}{cc}{1}& {-3}\\ {4}& {7}\end{array}\right]\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{&*}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\left[\begin{array}{cc}{1}& {-3}\\ {4}& {7}\end{array}\right]\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{&*}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\left[\begin{array}{cc}{1}& {-3}\\ {4}& {7}\end{array}\right]$ (4)
 > $\genfrac{}{}{0}{}{\phantom{\mathrm{&*}=\mathrm{.}}}{}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}|\phantom{\rule[-0.0ex]{0.1em}{0.0ex}}\genfrac{}{}{0}{}{\phantom{}}{\mathrm{&*}=\mathrm{.}}$
 $\left[\begin{array}{cc}{14717}& {12681}\\ {-16908}& {-10645}\end{array}\right]$ (5)
 > $\mathrm{eval}\left(,\left[x=A,\mathrm{&*}=\mathrm{.}\right]\right)$
 $\left[\begin{array}{cc}{14717}& {12681}\\ {-16908}& {-10645}\end{array}\right]$ (6)
 > $P≔\genfrac{}{}{0}{}{p}{\phantom{x=\mathrm{%A}}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}|\phantom{\rule[-0.0ex]{0.1em}{0.0ex}}\genfrac{}{}{0}{}{\phantom{p}}{x=\mathrm{%A}}$
 ${P}{≔}{-}{7}{}{{?}}^{{5}}{+}{22}{}{{?}}^{{4}}{-}{55}{}{{?}}^{{3}}{-}{94}{}{{?}}^{{2}}{+}{87}{}{?}{-}{56}$ (7)
 > $\genfrac{}{}{0}{}{\mathrm{convert}\left(P,\mathrm{mathorner},\mathrm{%A}\right)}{\phantom{\mathrm{&*}=\mathrm{.}}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}|\phantom{\rule[-0.0ex]{0.1em}{0.0ex}}\genfrac{}{}{0}{}{\phantom{\mathrm{convert}\left(P,\mathrm{mathorner},\mathrm{%A}\right)}}{\mathrm{&*}=\mathrm{.}}$
 ${-}{56}{+}\left({87}{+}\left({-}{94}{+}\left({-}{55}{+}\left({22}{-}{7}{}{?}\right){·}{?}\right){·}{?}\right){·}{?}\right){·}{?}$ (8)
 > $\mathrm{value}\left(\right)$
 $\left[\begin{array}{cc}{14717}& {12681}\\ {-16908}& {-10645}\end{array}\right]$ (9)


text:
Thermal conductivity measures a materials ability to allow heat to pass through it via conductance. Calculate Conductive Heat Transfer For instance, metals typically have high thermal conductivity and are very efficient at conducting heat, … Typically they are malleable and ductile, deforming under stress without cleaving. Stainless steel has an even lower conductivity than carbon steel at about 15 watts per kelvin per meter. Please help improve this list. Thermal conductivity of air as a function of temperature can be found at James Ierardi's Fire Protection Engineering Site, Categories: Chemical properties | Thermodynamics | Heat conduction. Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal conductivity. Stainless steel is … Thermal properties which are relevant to fire behavior include the thermal conductivity (k), the mass density (ρ), the specific heat (Cp), and for materials that may undergo thermal degradation (i.e., pyrolysis) the heat of gasification (Lg) and the ignition temperature (Tig). Annealed at steel poured at ingot. High–alloy steels having lower thermal conductivity at normal … Microsoft Internet Explorer 6.0 does not support some functions on Chemie.DE. The thermal conductivity of a material is highly dependent on composition and structure. It may be poorly defined, unverified or indiscriminate. Order) 6 YRS . Metals are typically known to be highly efficient thermal conductors. The thermal conductivity of steel alloys diverge as temperature is decreased, pure iron having the highest thermal conductivity, followed by carbon steels, alloy steels and then by high–alloy steels. ASTM A36 carbon steel is a carbon (non-alloy) steel formulated for primary forming into wrought products. US $500.00-$700.00 / Metric Ton 10 Metric Tons (Min. On the other hand, stainless steel has one of the lowest thermal conductivities for metal alloys. Conductivity in Stainless Steel. In physics, thermal conductivity, k, is the intensive property of a material that indicates its ability to conduct heat. © 1997-2020 LUMITOS AG, All rights reserved, https://www.chemeurope.com/en/encyclopedia/List_of_thermal_conductivities.html, Your browser is not current. And electronic thermal conductivity is ruled by Wiedemann-Franz law. Aluminum has BTU of 118 while steel has 17. Read what you need to know about our industry portal chemeurope.com. Its thermal conductivity is around 45 watts per kelvin per meter. The heat transfer characteristics of a solid material are measured by a property called the thermal conductivity , k (or λ), measured in W/m.K . 444 BureauofStandardsJournalofResearch [Vol.It >j p <: cc" p steel poured at nch ingot. Directory | Standard | Heat | Heat Exchanger | Temperature | Pressure | Corrosion | Hardness | Surface | Properties | Select Stainless Steel | Contact US, Relative Conductivity of Different Metals, Copper Brass Alloy Sheet Plate Weight Calculator, Rockwell Brinell Vickers Shore Hardness Conversion Chart, Length Weight Temperature Volume Pressure Calculater, Stainless Steel Reheater Tube Superheater Tubes, Integral Finned Tubes / Extruded Aluminum Finned Tubes, Brass Alloys Copper Nickel Alloy Integral Low Finned Tubes, HFW High Frequency Welded Helical Spiral Serrated Finned Tubes, ASTM A789 ASME SA 789 S31803 S32205 S32101 S32750 S32760 S32304 S31500 S31260 Seamless Tubes, EN 10216-5 1.4462 1.4362 1.4162 1.4410 1.4501 Seamless Tubes, ASTM B622 N06022 Hastelloy C-22 Alloy Tubes, EN 10305-1 E215 E235 E355 Seamless Precision Steel Tube Tubing Tubes, DIN 2393 St28 St34.2 St37.2 St44.2 St52.3 Welded Precision Steel Tubes, EN 10305-2 E195 E235 E355 Welded Cold Drawn Precision Steel Tube. Cog-s, then rolled to. In terms of optical properties, metals are shiny and lustrous. Find Trusted Steel Thermal Conductivity Supplier And Manufacturers That Meet Your Business Needs On Exporthub.com Qualify, Evaluate, Shortlist And Contact Steel Thermal Conductivity Companies On Our Free Supplier Directory And Product Sourcing Platform. Generally speaking, dense materials such as metals and stone are good conductors of heat, while low density substances such as gas and porous insulation are poor conductors of heat. Thermal conductivity (cal/sec)/(cm 2 C/cm) Thermal conductivity (W/m K)* Diamond... 1000: Silver: 1.01: 406.0: Copper: 0.99: 385.0: Gold... 314: Brass... 109.0: Aluminum: 0.50: 205.0: Iron: 0.163: 79.5: Steel... 50.2: Lead: 0.083: 34.7: Mercury... 8.3: Ice: 0.005: 1.6: Glass,ordinary: 0.0025: 0.8: Concrete: 0.002: 0.8: Water at 20° C: 0.0014: 0.6: Asbestos: 0.0004: 0.08: Snow (dry) 0.00026... Fiberglass: 0.00015: 0.04: … Find out more about the company LUMITOS and our team. This Table gives typical values of thermal several common commercial metals and alloys. DIN 2391 Seamless Precision Steel Tubes EN 10305-1 E215 E235 E355 Seamless Precision Steel Tube Tubing Tubes DIN 2393 St28 St34.2 St37.2 St44.2 St52.3 Welded Precision Steel Tubes Metals in general have high electrical conductivity, high thermal conductivity, and high density. Your browser does not support JavaScript. In simple words, it is the capability of any material to transfer heat by conduction. The high thermal conductivity means that steel construction systems, both the structural frame and cladding, must be carefully designed to minimise unwanted heat flows. Thermal conductivity measures a materials ability to allow heat to pass through it via conductance. Find out how LUMITOS supports you with online marketing. Thermal Conductivity - k -(W/m.K) Material: Temperature (o C)25: 125: 225: Acetone: 0.16 : Acrylic Values refer to ambient temperature (0 to 25°C). Thermal conductivities have been measured with longitudinal heat flow methods where the experimental arrangement is so designed to accommodate heat flow in only the axial direction, temperatures are constant, and radial heat loss is prevented or minimized. The thermal conductivity of a material such as metal is highly dependent on composition and structure. The metallic bars and the sample were surrounded by insulation material which was encased in a longitudinal aluminum guard shell. The thermal conductivity of wrought iron is around 50 W/ (m.K). It is defined as the quantity of heat, Q, transmitted in time t through a thickness L, in a direction normal to a surface of area A, due to a temperature difference ΔT, under steady state conditions and when the heat transfer is dependent only on the temperature gradient. Thermal conductivity steel pipe round section hollow steel pipe galvanized steel pipe manufacturers . To use all the functions on Chemie.DE please activate JavaScript. Thermal Conductivity of Stainless Steel at Various Temperatures: Stainless steel: … This list makes up the data for the smaller list provided in Thermal conductivity. Thermal Conductivity - k - is used in the Fourier's equation. Find trusted Steel Thermal Conductivity importers and buyers that meet your business needs on Exporthub Qualify, evaluate, shortlist and contact Steel Thermal Conductivity buyers on our free importer directory and product sourcing platform. Sheets of metal beyond a few micrometres in thickness appear opaque, but gold leaf transmits green light. K at 100 °C, National Physical Laboratory, UK). Steel is generally considered to be fairly low on the thermal conductivity scale – let’s look at this scale and where various common metals rank, plus what this means about certain applications and which metals are best for them. Thermal conductivities of the elements (data page), Wikipedia article "List_of_thermal_conductivities". Thermal Conductivity for some common Materials. thermal conductivity steel = 5.14 watts/in - °C The heat transfer characteristics of a solid material are measured by a property called the thermal conductivity, k (or λ), measured in W/m.K. Thermal Conductivity of Carbon Steel Low-carbon steel is a multi-element substance, principally of iron, with additions of carbon and impurities. Steel has a high thermal conductivity (λ) compared with many other construction materials (see Table 1.1). It has a very high electrical conductivity among the wrought carbon or non-alloy steels in the database. All values should be regarded as typical, since these properties are dependent on the particular type of alloy, heat treatment, and other factors. The thermal conductivity of carbon steel is much lower than that of aluminum. Thermal Conductivity is defined as the property of any material to conduct heat. Cited properties are appropriate for the as-fabricated (no temper or treatment) condition. To use all functions of this page, please activate cookies in your browser. Low-carbon steel is a multi-element substance, principally of iron, with additions of carbon and impurities. With an accout for my.chemeurope.com you can always see everything at a glance – and you can configure your own website and individual newsletter. For the sake of simplicity the conductivities that are found by that method in all of its variations are noted as L conductivities, those that are found by radial measurements of the sort are noted as R conductivities, and those that are found from periodic o… Thermal conductivity for stainless steel is 17 W/(m K) (from the table above). Thermal Conductivity of Metals, Metallic Elements and Alloys Thermal Conductivity - k - is the quantity of heat transmitted due to an unit temperature gradient, in unit time under steady conditions in a direction normal to a surface of the unit area. At Wasatch Steel, we’re happy to detail the thermal conductivity properties of any of our steel products, from steel tube to steel bar and many others. This material is a good and economical choice for building structural components. Another metric used to track thermal conductivity is the British thermal unit (BTU), which uses a number to represent the ability of a material to conduct heat. Thermal Conductivity of High-carbon Steel – AISI 1095 Steel The thermal conductivity of high-carbon steel is 50 W/(m.K). It is commonly denoted by k {\displaystyle k}, λ {\displaystyle \lambda }, or κ {\displaystyle \kappa }. Conductivity in Carbon Steel. The thermal conductivity of a material is a measure of its ability to conduct heat. The equation is given by kappa electron equals sigma times L times absolute temperature, T. In this equation sigma is the electrical conductivity and L is the Lorenz number. This list may require cleanup to meet Wikipedia's quality standards. In metallic conductor Lorenz number is … Conductive … Hollow steel pipe manufacturers its thermal conductivity of wrought iron is around 45 watts per kelvin per.... Words, it is commonly denoted by k { \displaystyle k }, or κ { \displaystyle }! / Metric Ton 10 Metric Tons ( Min very high electrical conductivity the. 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Previous | Next --- Slide 17 of 34
Back to Lecture Thumbnails

xiaowend

Here, latency between two nodes is the number of different bits of binary representation of the two nodes, which is O(lg n).

And radix is number of bits of binary representation of a node.

markwongsk

so for an n-dimensional hypercube it is just a projection of the hypercube into 3d space?

yongzuaw

Question: What will be the bisection bandwidth of this topology? My guess is O(N) since when the nodes are divided into two sets there are "parallel" links that connect pairs of node across each side.

kayvonf

@yonguaw: Correct. Bisection bandwidth is N/2.

AnnabelleBlue

Question: Is this a practical topology? It has a low latency, but there is also a large overhead of laying out the wires since it's difficult to project hypercubes into 3d space. In this example, which one would win?

rutwikparikh

This topology appears to be directed since all switches essentially consist of one node.

tpassaro

An advantage to this design is that you are directly connected to your N closest neighbors, but a disadvantage is that your machine needs $2^n$ processors to work in this configuration. Processors typically do have $2*n$ processors, so if you wanted to use this configuration, you might need more or less CPUs.


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# Magic resistance

2,163pages on
this wiki

Magic resistance (or MR) is a stat that all units have, including minions, monsters, and buildings. Increasing magic resistance reduces the magic damage the unit takes. Each champion begins with some magic resistance which may increase with level. You can gain additional magic resistance from abilities, items, masteries, and runes. Magic resistance stacks additively.

All champions begin with 30 base magic resistance. Currently no ranged champion gains magic resistance per level, but most melee champions do except , , , and .

, , , and do not gain magic resistance per level because they are not always melee champions due to their variable attack range.

All champions that do gain magic resistance per level gain 1.25 magic resistance per level, reaching 53.4 base magic resistance at level 18.

## Damage reduction

Magic Resistance reduces the damage of incoming magical attacks by a percentage. This percentage is determined by the formula: Damage Reduction = Total Magic Resistance / (100 + Total Magic Resistance). For example, a champion with 150 points of magic resistance would receive 60% reduced damage from magical attacks. Incoming magic damage is multiplied by a factor based on the unit's magic resistance(same with armor):

$${\rm Damage\ multiplier}=\begin{cases} {100 \over 100+{\it MR}}, & {\rm if\ }{\it MR} \geq 0\\ 2 - {100 \over 100 - {\it MR}}, & {\rm otherwise} \end{cases}$$

Examples:

• 25 magic resistance → × 0.8 incoming magic damage (20% reduction).
• 100 magic resistance → × 0.5 incoming magic damage (50% reduction).
• −25 magic resistance → × 1.2 incoming magic damage (20% increase).

## Stacking magic resistance

Every point of magic resistance requires a unit to take 1% more of its maximum health in magic damage to be killed. This is called "effective health."

Example: A unit with 60 magic resistance has 160% of its maximum health in its effective health, so if the unit has 1000 maximum health, it will take 1600 magic damage to kill it.

What this means: by definition, magic resistance does not have diminishing returns, because each point increases the unit's effective health against magic damage by 1% of its current actual health value whether the unit has 10 magic resistance or 1000 magic resistance.

For a more detailed explanation, see this video.

Unlike health, increasing magic resistance makes healings and shields more effective because it requires more effort from your enemies to remove the bonus health granted. This is called indirect scaling.

## Magic Resistance as Scaling

These use the champion's magic resistance to increase the magnitude of the ability. It could involve total or bonus magic resistance. By building magic resistance items, you can receive more benefit and power from these abilities.

### Champions

• grants magic resistance equal to 10 / 11.5 / 13 / 14.5 / 16% of his bonus magic resistance to himself and the target ally (in addition to a base amount) for 3 seconds.
• grants him bonus ability power equal to 50% of his total magic resistance.
• grants additional magic resist equal to 20 / 30 / 40 / 50 / 60 + (20% of her bonus magic resistance for its duration.
• takes 40% of the target's magic resistance and gains an equal amount of magic resistance. Half of this magic resistance is stolen on cast, and the next half is taken over 4 seconds. The magic resistance bonus/reduction lasts for another 4 seconds after the drain completes.

## Increasing magic resistance

### Items

• : +50 magic resistance, +70 ability power. Unique Aura: Reduces the magic resistance of nearby enemies by 20. 2430 .
• : +20 magic resistance. Unique Aura – Legion: Grants nearby allies +15 magic resistance. +200 health, +100% base health regen. 1600 .
• : +25 magic resistance, +60 ability power, +100% base mana regeneration, +20% cooldown reduction. Unique Passive: Restores 30% of your maximum mana on kill or assist. Unique Passive – Mana Font: Restores 2% of missing mana every 5 seconds. 2700 .
• : +20 magic resistance. Unique Aura – Legion: Grants nearby allies +15 magic resistance. +200 health, +100% base health regen, +60 ability power, +10% cooldown reduction. Unique Active – Promote: Greatly increases the power of a lane minion and grants it immunity to magic damage (120 second cooldown) (1200 range). 2750 .
• : +25 magic resistance, +50% base mana regeneration. Unique Passive – Mana Font: Restores 2% of missing mana every 5 seconds. 900 .
• : +30 magic resistance, +25 attack damage. Unique Passive – Lifeline: Upon taking magic damage that would reduce health below 30%, grants a shield that absorbs 250 magic damage for 5 seconds (90 second cooldown). 1450 .
• : +20 magic resistance. Unique Aura – Legion: Grants nearby allies +15 magic resistance. +400 health, +100% base health regen, +10% cooldown reduction. Unique Active: Shield yourself and nearby allies for 5 seconds, absorbing up to 50 + (10 × level) damage (60 second cooldown). 2750 .
• : +40 magic resistance, +60 attack damage. Unique Passive: Grants +1 attack damage for every 2% of missing health, up to a maximum of 35 attack damage. Unique Passive – Lifeline: Upon taking magic damage that would reduce health below 30%, grants a shield that absorbs 400 magic damage for 5 seconds (90 second cooldown). 3200 .
• : +25 magic resistance. Unique Passive – Enhanced Movement: +45 movement speed. Unique Passive - Tenacity: Reduces the duration of stuns, slows, taunts, fears, silences, blinds and immobilizes by 35%. 1200 .
• : +40 magic resistance, +100% base mana regeneration, +10% cooldown reduction. Unique Passive – Mana Font: Restores 2% of missing mana every 5 seconds. Unique Active: Removes all stuns, roots, taunts, fears, silences and slows on an allied champion and heals that champion for 150 + (10% of the target's maximum health) (180 second cooldown). 2450 .
• : +45 magic resistance. 850 .
• : +25 magic resistance. 500 .
• : +30 magic resistance. Unique Active – Quicksilver: Removes all debuffs from your champion (90 second cooldown). 1250 .
• : +40 magic resistance, +200 health. Unique Passive: Grants 150% base health regen for up to 10 seconds after taking damage from an enemy champion. 1200 .
• : +60 magic resistance, +400 health, +150% base health regeneration, +10% cooldown reduction. Unique Passive: Increases effectiveness of all sources of healing including self-healing, health regen, life steal and spell vamp by 20%. 2700 .
• : +30 magic resistance. Unique Passive: Your basic attacks steal 5 magic resistance of the target for 5 seconds (stacks up to 5 times). +50% attack speed. Unique Passive: Your basic attacks deal 42 bonus magic damage. 2600 .

#### Variable Availability

• STH : +60 magic resistance, +450 health, +100% base health regeneration. Unique Passive: Grants a spell shield that blocks the next enemy ability. This shield refreshes after no damage is taken from enemy champions for 40 seconds. 2700 .
• TC : +45 magic resistance, +50% attack speed, +10% cooldown reduction. Unique Active – Quicksilver: Removes all debuffs from your champion. Melee champions also gain +50% movement speed for 1 second (90 second cooldown). 2700 .
• SC : +50 magic resistance, +50 armor. Unique Passive: Upon taking lethal damage, restores 30% of maximum health and 30% of maximum mana after 4 seconds of stasis (5 minute cooldown). 2800 .
• H : Unique Active – Battle Cry: Gain 20 magic resistance, 30% movement speed and 20 armor for 3 seconds (25 second cooldown). +200 health, +125% base health regeneration. 1015 .
• SH : +35 magic resistance, +80 attack damage. Unique Active – Quicksilver: Removes all debuffs and also grants 50% bonus movement speed for 1 second (90 second cooldown). 3700 .
• TC : +50 magic resistance, +50 ability power, +50 armor. Unique Passive – Tenacity: Reduces the duration of stuns, slows, taunts, fears, silences, blinds, polymorphs, and immobilizes by 35%. 2570 .
• C : +50 magic resistance, +350 health, +350 mana. Unique Passive: Reduces and stores 10% of magic damage received. Unique Active: Deals 200 + (stored magic damage – max 200) magic damage to nearby enemy units (90 second cooldown). 2450 .
• H : +70 magic resistance, +100% base health regeneration. Unique Passive: Grants a shield that absorbs up to 30 + (10 × level) damage. The shield will refresh after 9 seconds without receiving damage. 2150 .
• S : +60 magic resistance, +60 armor, +150% base health regen. Unique Passive – Point Runner: Build up to +20% movement speed over 2 second while near turrets, fallen turrets and Void Gates. Unique Active: Spawns a Void Gate at target location for 150 seconds. Every 4 seconds the gate makes a that travels down the nearest lane and decays over time. Voidspawn explodes when attacking structures. ignore champions and void targets (150 second cooldown). The first and every fourth voidspawn gain 15% of maximum health as damage (150 second cooldown). 2750 .

### Champion abilities

Note: Only the magic resist buff effect of these abilities is shown here, to read more information on each of these abilities, follow the link on each of them.

• allows her to enter an egg-state for up to 6 seconds upon taking lethal damage. While in this state, she will receive a magic resistance modifier of −40 / −25 / −10 / +5 / +20.
• increases her magic resistance by 10 / 20 / 30 / 40 / 50 for 5 seconds.
• increases magic resistance by 15 / 17.5 / 20 / 22.5 / 25 + (10 / 11.5 / 13 / 14.5 / 16% bonus magic resistance) to himself and the target ally for 3 seconds.
• increases an allied champion's magic resistance by 30 / 45 / 60 / 75 / 90 for 4 seconds.
• increases his magic resistance by (2 × Gnar's level) when transformed into .
• permanently gains 0.25 bonus magic resistance every time he kills an enemy, up to a maximum of 30.
• increases his magic resistance by 1 / 2 / 3 every second he remains in combat. This bonus stacks up to 10 times for a maximum of 10 / 20 / 30. Graves is considered in combat if he has dealt or received damage in the last 3 seconds.
• increases his magic resistance by 30 / 50 / 70 + (20% AP) for 8 seconds.
• increases his magic resistance by 10 / 20 / 30 / 40 / 50 for 4 seconds.
• increases his magic resistance by 5 / 15 / 25 / 35.
• increases her magic resistance by 20 / 30 / 40 / 50 / 60 + (20% bonus magic resistance) for 3 seconds, deals damage after that time to units around her, and retains the defensive buff for an additional 3 seconds if any enemy is struck by the blast.
•  passively increases his magic resistance by 10 / 20 / 30. He loses the passive while his ability is active.
• increases an allied champion's magic resistance by 10 / 15 / 20 / 25 / 30 as long as the ball is attached to it.
• increases his magic resistance by 40 / 60 / 80 / 100 / 120 for 6 seconds.
• lets out a battle roar, damaging enemies increases his magic resist by 10 / 15 / 20 / 25 / 30 for each enemy champion or large monster hit for 4 seconds.
• passively increases her magic resistance by 5 / 10 / 15 / 20. This bonus is doubled while she is in dragon form (20 / 30 / 40).
• increases his magic resistance by 35 / 50 / 80 for 25 seconds.
• immediately steals 20% of the target's magic resistance, and a further 20% over 4 seconds. These magic resistance bonuses lasts for another 4 seconds after the drain completes.
• increases his magic resistance by 60 / 90 / 120 for 5 seconds.
• grants him 4 / 6 / 8 magic resistance for each visible nearby enemy champion.
• increases his magic resistance by 15 / 20 / 25 for each enemy champion hit for 8 seconds.

### Masteries

• increases your bonus armor and magic resistance by 2.5 / 5 / 7.5 / 10%.
• grants 2 / 3.5 / 5 magic resistance.
• grants 3 armor and 3 magic resistance for each visible enemy champion within 700 units.

### Runes

Name Type Tier 1 (Lesser) Tier 2 (Normal) Tier 3 (Greater)
Magic Resist Mark

X X 0.77

205

Seal

0.41

5

0.58

35

0.74

205

Glyph

0.74

5

1.04

35

1.34

205

Quintessence

2.22

15

3.11

100

4

1025

Magic Resist, Scaling

(Magic Resist per level)

Mark

X X 0.07 per level (1.26)

205

Seal

X X 0.1 per level (1.8)

410

Glyph

X X 0.16 per level (2.88)

205

Quintessence

X X 0.37 per level (6.66)

1025

### Other

• Disconnecting gives approximately +1000 magic resistance after a delay.

## Ways to reduce magic resistance

See magic penetration. Note that magic penetration and magic resistance reduction are different.

## List of champions' magic resistance

• 64 champions have 30 base magic resistance from level 1 to level 18. These champions are mostly ranged champions, with the expection of , , and .

• 61 champions start with 32.1 base magic resistance at level one, and at 53.4 base magic resistance at level 18. These champion are all melee champions, without exception.

## Trivia

[Last updated 1/9/2015 on patch 5.16]

• One of the biggest amount of magic resistance any champion can obtain is 1028.489984 (which reduces magical damage by 91.139%), being a level 18 in the Howling Abyss.

must:

Relevant mathematics:
Bonus Magic Resist (before ) = (70 × 6 + 15 + 15 + 5 + 1.26 × 9 + 1.8 × 9 + 2.88 × 9 + 6.66 × 3) × 1.10 = 581.284
Magic Resist = ((70 × 6 + 15 + 15 + 5 + 90 + 30 + (25 + 581.284 × 0.16) + 1.26 × 9 + 1.8 × 9 + 2.88 × 9 + 6.66 × 3 + 120) × 1.10) + 53.4 = 1028.489984

Having an enemy with the same setup use on will yield a total of 1343.525577 magic resistance. This may be the highest possible finite amount of magic resist(without using metagame effects—see below), and reduces magic damage by 93.072%.

Relevant mathematics:

Magic Resist = ((70 × 6 + 15 + 15 + 5 + 90 + 30 + (25 + 581.284 × 0.16) + 1.26 × 9 + 1.8 × 9 + 2.88 × 9 + 6.66 × 3 + 120) × 1.10) + 53.4 = 1028.489984
Magic Resist = ((70 × 6 + 15 + 15 + 5 + 90 + 30 + (25 + 581.284 × 0.16) + 1.26 × 9 + 1.8 × 9 + 2.88 × 9 + 6.66 × 3 + (1028.489984 × 0.4)) × 1.10) + 53.4 = 1343.525577

It is still possible to go higher through metagame functions. If a summoner disconnects from the server and is in the fountain, his/her champion will gain 1000 magic resistance. With the same setup as above, a disconnected will have approximately 2122.989984 magic resist. cannot exceed this. This reduces magical damage by 95.502%.

• Prior to Patch 3.10, a level 18  with 1 , 5 , 3 points in , 3 points in , , , , , an allied  aura, a full page of Scaling Magic Resist runes, and  active gave a total of approximately 1004 magic resist. Switching  for  and having an enemy  with the same setup use  on  and the allied  use  on the enemy , yielded a total of approximately 1297 magic resist. This is the highest possible amount of magic resistance, which is 92.8% reduction.
• If disconnects from the fountain and has the same setup, he will have 2108 magic resist. This is a 95.5% reduction.
• NOTE: This calculation does not include the mastery.


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# Need help, ASAP! Urgent

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1) Let line l$$l_1$$ be the graph of 5x + 8y = -9. Line L2 is perpendicular to line L1 and passes through the point (10, 10). If line L2 is the graph of the equation y=mx +b, then find m+b .

2) Find all real numbers x  such that $$3x - 7 \le 5x +9$$. Give your answer as an interval.

3) Find all real numbers s such that $$-2(s - 7) > 4s + 8$$ . Give your answer as an interval.

4) Without using a calculator, order the following numbers from least to greatest: \begin{align*} A &= \frac{2^{1/2}}{4^{1/6}}\\ B &= \sqrt[12]{128}\vphantom{dfrac{2}{2}}\\ C&= \left( \frac{1}{8^{1/5}} \right)^2\\ D&= \sqrt{\frac{4^{-1}}{2^{-1} \cdot 8^{-1}}}\\ E&= \sqrt[3]{2^{1/2} \cdot 4^{-1/4}}.\vphantom{dfrac{2}{2}}\end{align*}
Give your answer as a list of capital letters separated by commas. For example, if you think that E < B < C< D< A , then you would answer E,B,C,D,A.

Sorry for so many questions, help as fast as you can, please! Thanks to anyone who answers! I'll definitely give you extra likes if you answer!

Nov 17, 2018

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1)$$5x + 8y = -9 <=> y=-\frac{5}{8}x-\frac{9}{8}$$

λ1=-$$\frac{5 }{8}$$

L2 is perpendicular to line L1 so λ1*λ2=-1 <=> -5/8*λ2=-1

λ2=$$\frac{8}{5}$$

so the l2: y-y1=λ2(x-x1)  x1=10,y1=10 because  passes through the point (10, 10)

so $$y-10 = \frac{8}{5}(x-10)<=> y=\frac{8}{5}x-\frac{80}{5}+10<=> y=\frac{8}{5}x-\frac{30}{5}$$

m=8/5,b=-30/5

m+b=$$\frac{8}{5}-\frac{30}{5}=\frac{-22}{5}$$

2)$$3x-7≤ 5x+9<=> 3x-5x≤9+7 <=> -2x≤16 <=> x≥ 8$$

$$x≥ 8$$

3)$$-2s+14>4s +8<=> 14-8 > 4s+2s <=> 6>6s <=> 1>s <=> s<1$$

$$s<1$$

Hope this helps!

.
Nov 18, 2018
edited by Dimitristhym  Nov 18, 2018
edited by Dimitristhym  Nov 18, 2018

#1
+316
+4

1)$$5x + 8y = -9 <=> y=-\frac{5}{8}x-\frac{9}{8}$$

λ1=-$$\frac{5 }{8}$$

L2 is perpendicular to line L1 so λ1*λ2=-1 <=> -5/8*λ2=-1

λ2=$$\frac{8}{5}$$

so the l2: y-y1=λ2(x-x1)  x1=10,y1=10 because  passes through the point (10, 10)

so $$y-10 = \frac{8}{5}(x-10)<=> y=\frac{8}{5}x-\frac{80}{5}+10<=> y=\frac{8}{5}x-\frac{30}{5}$$

m=8/5,b=-30/5

m+b=$$\frac{8}{5}-\frac{30}{5}=\frac{-22}{5}$$

2)$$3x-7≤ 5x+9<=> 3x-5x≤9+7 <=> -2x≤16 <=> x≥ 8$$

$$x≥ 8$$

3)$$-2s+14>4s +8<=> 14-8 > 4s+2s <=> 6>6s <=> 1>s <=> s<1$$

$$s<1$$

Hope this helps!

Dimitristhym Nov 18, 2018
edited by Dimitristhym  Nov 18, 2018
edited by Dimitristhym  Nov 18, 2018
#2
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If you want to use "-->" or "==>" in LaTex, it is $\Rightarrow$.

Nov 19, 2018
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Big shout out to Dimitristhym for answering my questions, but how do you write the answer to number 2) in regular form? I can't get the x_> 8 things right. Thank you all, though!

Nov 20, 2018


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Deepak Scored 45->99%ile with Bounce Back Crack Course. You can do it too!

# Figure 9.37 shows an equiconvex lens (of refractive index 1.50) in contact with a liquid layer on top of a plane mirror.

Question:

Figure 9.37 shows an equiconvex lens (of refractive index 1.50) in contact with a liquid layer on top of a plane mirror. A small needle with its tip on the principal axis is moved along the axis until its inverted image is found at the position of the needle. The distance of the needle from the lens is measured to be 45.0 cm. The liquid is removed and the experiment is repeated. The new distance is measured to be 30.0 cm. What is the refractive index of the liquid?

Solution:

Focal length of the convex lens, f1 = 30 cm

The liquid acts as a mirror. Focal length of the liquid = f2

Focal length of the system (convex lens + liquid), = 45 cm

For a pair of optical systems placed in contact, the equivalent focal length is given as:

$\frac{1}{f}=\frac{1}{f_{1}}+\frac{1}{f_{2}}$

$\frac{1}{f_{2}}=\frac{1}{f}-\frac{1}{f_{1}}$

$=\frac{1}{45}-\frac{1}{30}=-\frac{1}{90}$

$\therefore f_{2}=-90 \mathrm{~cm}$

Let the refractive index of the lens be $\mu_{1}$ and the radius of curvature of one surface be $R$. Hence, the radius of curvature of the other surface is $-R$.

can be obtained using the relation:

$\frac{1}{f_{1}}=\left(\mu_{1}-1\right)\left(\frac{1}{R}+\frac{1}{-R}\right)$

$\frac{1}{30}=(1.5-1)\left(\frac{2}{R}\right)$

$\therefore R=\frac{30}{0.5 \times 2}=30 \mathrm{~cm}$

Let $\mu_{2}$ be the refractive index of the liquid.

Radius of curvature of the liquid on the side of the plane mirror $=\infty$

Radius of curvature of the liquid on the side of the lens, R = −30 cm

The value of $\mu_{2}$ can be calculated using the relation:

$\frac{1}{f_{2}}=\left(\mu_{2}-1\right)\left[\frac{1}{-R}-\frac{1}{\infty}\right]$

$\frac{-1}{90}=\left(\mu_{2}-1\right)\left[\frac{1}{+30}-0\right]$

$\mu_{2}-1=\frac{1}{3}$

$\therefore \mu_{2}=\frac{4}{3}=1.33$

Hence, the refractive index of the liquid is 1.33.