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# 3.3 Nonstandard interpretations (optional)

 Page 1 / 2
How non-standard interpretations can provide insight into tough problems.

## Prime factorization

Note that there are other possible interpretations of $\mathrm{prime}$ . For example, since one can multiply integer matrices,there might be a useful concept ofprime matrices.

For example: Consider only the numbers $F=\{1, 5, 9, 13, \}$ that is, $F=\{k\colon k\in \mathbb{N}\}$ . It's easy to verify that multiplying two of these numbers still resultsin a number of the form $4k+1$ . Thus it makes sense to talk of factoring such numbers:We'd say that 45 factors into $59$ , but 9 is consideredprime since it doesn't factor into smaller elements of $F$ .

Interestingly, within $F$ , we lose unique factorization: $441=9\times 49=21\times 21$ , where each of 9, 21, and 49 are prime, relative to $F$ ! (Mathematicians will then go and look for exactly whatproperty of a multiplication function are needed, to guarantee unique factorization.)

The point is, that all relations in logical formula need to be interpreted. Usually, for numbers, we usea standard interpretation, but one can consider those formulas in different, non-standard interpretations!

## The poincarDisc

A long outstanding problem was that of Euclid's parallel postulate: Given a line and a point not on the line,how many lines parallel to the first go through that point? Euclid took this as an axiom(unable to prove that it followed from his other axioms). Non-Euclidean geometries of Lobachevsky and Riemann took differentpostulates, and got different geometries. However, it was not clear whether these geometrieswere sound whether one could derive two different results that were inconsistent with each other.

Henri Poincardeveloped an ingenious method for showing that certain non-Euclidean geometries are consistentor at least, as consistent as Euclidean geometry.Remember that in Euclidean geometry, the conceptspointandlineare left undefined, and axioms are built on top of them ( e.g. ,two different lines have at most one point in common). While it's usually left to common sense to interpretpoint,line, anda point is on a line, any interpretation which satisfies the axiomsmeans that all theorems of geometry will hold.

The Poincardisc is one such interpretation:pointis taken to meana point in the interior of the unit disc, andlineis taken to meana circular arc which meets the unit disc at right angles. So a statement liketwo points determine a linecan be interpreted as

[*] For any two pointsinside the disc, there is exactly one circular arc which meets the disc at right angles.
Indeed, this interpretation preserves all of Euclid's postulates except for the parallel postulate. You can see thatfor a given line and a point not on it, there are an infinite number of parallel (that is, non-intersecting) lines.

(Note that the distance function is very different within the Poincardisc; in fact the perimeter of the disc is off at infinity.Angles, however, do happen to be preserved.)

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abeer
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What is a client engineer
A Customer Engineer (CE) is a worker whose primary job scope is to provide a service to customers who have signed a contract with the company.
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ahly
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Suraj
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abang
may be it has a problem
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gabriel
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shittu
wht teacher u need?
HANAN
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is software
RITESH
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good morning all
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Ultimate
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HANAN
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Amissah
hi
Sunday
gud morning oo
Sunday
kk
Sunday
the benefits are life changing
Louis
Louis
an ai system
Louis
is studying software engineer needs to be math expertise?
Carmela
Louis
grasp the whole field by being a problem solver
Louis
mathematics is the language of computing
Louis
but also its the language of the universe
Louis
before you start typing code please plan on pen and paper first with a goal in mind.
Louis
Thank you !!
Carmela
Are you a software engineer already?
Carmela
mathematics is not compulsory for coding
just needed basic Nexus calculations
what programming language ?
Louis
Louis
engineering in process student of software engineering
Louis
couple of languages are there not bounded specifically to single one
python, Java, Java script, php, swift, go, c# and many more are trending in
Java is now superseding his popularity but still the one of the most used coding language
I want to be a software engineer too ...
Carmela
best of luck
python is now
Louis
python is used by nasa and for data science aswell for live coding and hacking
Louis
it is the fastest growing language to date
Louis
but being efficient at math is a general stand point if your not language specific
Louis
but c++ can't be beat
Louis
especially with the new c++20 coming
Louis
swift for apple
Louis
swift is made by c code
Louis
c++ is > c
Louis
yes pathon is invented in 1991 by guido van rusom it's popular now a days but it's literally used now as much a Java and Java script php but still most popular python
Louis
java is still convenient though
Louis
c made by bell laboratories one of the basic coding languages
windows also used it
it just depends on what goal you have in mind to you have in mind to use programming language as a conversion
Louis
mathematics > any programming language
Louis
😊
Louis
sorry I've accidentally placed a question mark lol
Louis
😂
Louis
sorry I couldn't get your point
no i was saying my device placed 2 question marks accidentally
Louis
Louis
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awesome im from united states my friend nice to meet you lol
Louis
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Louis
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Thats awesome im a defcon spy
Louis
white hat
Louis
im a good guy 😊
Louis
nice to hear
coding phenomena practice practice and practice
yeah same
Louis
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Louis
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I like to be software engineer
Toheeb
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HANAN
I have mentioned the names above
@HANAN
Louis
HANAN
HANAN
yes Java is also but not we could limitize the premises
there are many others also
HANAN
@HANAN THE PROGRAMMER IS THE LEADING PROGRAMMING LANGUAGE OF THE WORLD IG YOU KNOW WHAT I MEAN
Louis
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Louis
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HANAN
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go for formal education
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HANAN
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Louis
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Louis
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HANAN
I'm a Human lol
Louis
make your basic concepts through c and C ++
but yes im a core engineer
Louis
you can say Engineering scientist
Louis
it is the sole centre and Nexus of coding
hi
Md
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Ultimate
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mubarek
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books or teacher
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both of
Hemant
both
ben
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Louis
Louis
Ogunrinde
well honestly it would be too large to explain everything in chat but, pick the programming language of choice your most comfortable with, learn that language, make it yours, use it as a primary language to learn in parallel any other language of object oriented programming,
Louis
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Louis
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Louis
have math be your way of translation of human to computer interaction because you can solve any problem in the universe with mathematics
Louis
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Louis
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Louis
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Louis
Be alittle greedy to learn any and all about any language you use.
Louis
Another important thing is not to rush through learning
Louis
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Louis
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Emmanuel
if you like graphics and games you can use a language that have graphics libraries such as C++, Python, or Java as an example
Louis
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Emmanuel
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Louis
grasp
Louis
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Louis
Emmanuel
be an android who's drug is "addicted to information" related to the field.
Louis
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Louis
learn console applications
Louis
how does your languge relate to databases
Louis
and web programming
Louis
i know just throwing some things your way to open mind
Louis
im certi at c++
Louis
it is a general programming language used to build many infrastructure
Louis
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Louis
excellent
Ogunrinde
Thanks
Louis
Suppose we are faced with developing a system that we expect to have 100000LOC. Compute the effort and the effort development time for each of the three development modes i.e. Organic, semi - detached and embedded .
c++ or python or java
Louis
Got questions? Join the online conversation and get instant answers!


text:
# Sum of normally distributed variables is a normally distributed variable?

Consider two Wiener processes: \begin{aligned} X_a &\sim\mathcal N(0,a) \\ X_{a-b} &\sim\mathcal N(0,a-b) \end{aligned} How do I show that: $$X_a - X_{a-b} \sim\mathcal N(.,.)$$ That is, how do I show that $X_a - X_{a-b}$ is Gaussian?

I know that $E(X_a - X_{a-b}) = 0$

and \begin{aligned} \text{Var}(X_a - X_{a-b}) &= E(X_a^2) - E(X_{a-b}^2) \\ &= \text{min}(a,a) -\text{min}(a-b,a-b) \\ &= a - a - b \\ &= b \end{aligned}

Note that both $X_a$ and $X_{a-b}$ have the following properties:

• They are normally distributed with mean $0$.
• Their sample paths are continuous.
• Its covariance function is $\rho(s,t) := \text{Cov}(X_s,X_t)=E(X_sX_t)=\text{min}(s,t)$.
-
What definition/construction of a Wiener process are you using? From that you should know much more about it than just the marginal distribution at a fixed time. –  cardinal Nov 7 '12 at 14:26
@cardinal Fixed. –  user14281 Nov 7 '12 at 14:30
Hi, Jase. Hmm. What is the source of this "characterization" that you've listed? (The properties are correct, but it is not a complete definition of a Wiener process.) –  cardinal Nov 7 '12 at 14:43
@cardinal It is presented in my lecture slides for "one-dimensional standard scalar BM". I left out the stuff about the filtration satisfying the usual conditions and the process $X$ being adapted to this filtration. –  user14281 Nov 7 '12 at 15:03

$X_a = X_{a-b} + \int_{a-b}^a dX_s$

$\Rightarrow X_a - X_{a-b} = X_{a-b} + \int_{a-b}^a dX_s - X_{a-b}$

$= \int_{a-b}^a dX_s$

$= X_{a - (a-b)} = X_b$.

Since $\{X_t\}_{t \in [0,T]}$ is a Wiener process and $b \in [0,T]$, then $X_b$ is Gaussian by the fact that $X_b \sim N(0,b)$ (from the definition of a Wiener process).

-
Unfortunately, this is not correct, as written. –  cardinal Nov 7 '12 at 14:41
@cardinal Which line is wrong? I stole the first line from the bottom of page 7 here: http://www.maxmatsuda.com/Papers/Intro/Intro%20to%20Brownian%20Matsuda.pdf, then the rest seems to follow. –  user14281 Nov 7 '12 at 15:02

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## Calculus 10th Edition

Published by Brooks Cole

# Chapter 2 - Differentiation - 2.3 Exercises: 19

#### Answer

Rewrite:$\frac{1}{7}(x^2+3x)$ Differentiate :$\frac{1}{7}(2x+3)$ Simplify: $\frac{2x+3}{7}$

#### Work Step by Step

Rewrite: Factor out the $\frac{1}{7}$ to get a constant times an expression. Differentiate: Using the Constant Multiple Rule and The Power Rule, find the derivative of the expression. Simplify: Multiply $\frac{1}{7}$ back to form one fraction.

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.


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## Equipartition theorem

$\Delta U=q+w$

Michelle Dela Rosa 1D
Posts: 25
Joined: Fri Sep 25, 2015 3:00 am

### Equipartition theorem

Just out of curiosity, how high does the temperature have to be to use the equipartition theorem in calculations of vibrational motion? Thank you in advance!

Chem_Mod
Posts: 18400
Joined: Thu Aug 04, 2011 1:53 pm
Has upvoted: 435 times

### Re: Equipartition theorem

The vibrational modes start to have an effect when kbT becomes greater than the vibrational energy gap. The size of this gap depends completely on the specific molecule but it can be approximated easily by quantum mechanics. Just for example, the vibrational gap in HCl is about 5.7*10^-20 J per molecule (35 kJ/mole). Dividing by kb gives about 4000 K. So you need a very high temperature to get the vibrational modes.


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# Difference between Turing machine and Universal Turing machine

I've read what a Turing machine and a UTM are, but I don't get the difference. What can a UTM do which a normal Turing machine can not?

A universal Turing machine is just a Turing machine whose programming simulates other Turing machines. That is, the input to the UTM is a description of a Turing machine $T$ and an input for $T$, and the UTM simulates $T$ on that input.

It's universal in the sense that, for any problem that can be solved by Turing machines, you could either use a Turing machine that directly solves that problem, or you could use a UTM and give it the description of a TM that directly solves the problem.

If you like, a UTM is an interpreter for (all) Turing machines.

• It is also (one of) the first description(s) of a stored-program computer. Jan 24 '17 at 11:18
• @JörgWMittag Good point. Was it thought of in those terms in the 1930s? Jan 24 '17 at 11:22
• I don't think so. After all, it wasn't even thought of as a computer at all. Or rather, it was thought of as what was at that time called a computer, namely a human who computes logarithm tables etc. by hand. That's how Turing came up with his model: a pen, a piece of paper, a (limited) vocabulary, a (limited) memory, and a (limited) set of rules. Jan 24 '17 at 12:03

A UTM can run any Turing machine on some input.

A Turing machine can be compared to a program. It takes some input and generates some output.

A UTM can be compared to a computer. It can take any program and run it with some input and generates some output.

The UTM is a Turing machine in itself, so the interesting idea here is that any Turing machine can be encoded as input understood by another Turing machine.

• I think you have to be careful with this analogy. A Turing machine feels more like a special-purpose computer, to me: it's a "physical" device. But I suppose that part of the point is that these devices can be described as something like programs. Jan 23 '17 at 20:00

Every TM does just one task. It sums two input numbers, or it scans the input for some symbol, or it looks for a counterexample of Goldbach's conjecture ...

... or it (let us call it TM#1, since we will have a 2nd one shortly) gets two parts of input, where the first describes a TM, TM#2 (think of a (fixed) TM as a finite number of states and transitions and stuff like head directions) and next to the description of TM#2 a description of input to TM#2.

So TM#1 receives the pair ("TM#2" "input#2") as its input#1. And then TM#1 runs on this input#1 and behaves (to the outside, after termination!) as if it was TM#2 working on input#2. In case TM#2 would not halt, TM#1 won't do either.

Such a TM#1 is called a UTM, since it can behave like/fake/simulate any other TM you give it as TM#2. Think of a virtual machine (TM#1), a simulated program (TM#2), and an input to the simulation (input#2). The VM takes longer, but the results are the same.

Even TM#2 = TM#1 is possible ... then input#2 = ("TM#3" "input#3") and TM#1 is a UTM and now simulates another UTM (TM#2) which in turn meta-behaves as TM#3 on input#3, in symbols:

TM#3(input#3) = TM#2("TM#3 input#3") since we took TM#2 to also be a UTM = TM#1("TM#2 'TM#3 input#3'")

Again: Behaviour is in terms of eventual final output, if and when halting, certainly not in terms of tape contents at any time, number of time steps etc., simulation takes (much) more time than doing it directly.


text:
# Hierarchical beta regression

#1

I’m trying to fit a hierarchical model using rstanarm, and since my outcome variable is a proportion, I’m trying to use beta regression.

So I initially tried to just specify “Beta” in the family argument in stan_glmer:

``````library(rstanarm)
stan_glmer(p~ (1|group),family=Beta,data=plot.data)
``````

This produced the following error message:

``````Error in stan_glm.fit(x = X, y = y, weights = weights, offset = offset,  :
'family' must be one of binomial, gaussian, Gamma, inverse.gaussian, poisson, neg_binomial_2, Beta regression
``````

This error message made me think I could just change the argument to “Beta regression” and then fit my model. However, this still didn’t work (error message included below):

``````> stan_glmer(p~ (1|group),family="Beta regression",data=plot.data)
Error in get(f, mode = "function", envir = parent.frame(2)) : object 'Beta regression' of mode 'function' was not found
``````

I even tried all of the following iterations with no success:

``````stan_glmer(p~ (1|group),family="Beta.regression",data=plot.data)
stan_glmer(p~ (1|group),family="Beta_regression",data=plot.data)
stan_glmer(p~ (1|group),family="Betaregression",data=plot.data)
``````

Finally, I ruled out the possibility that none of the distributions named my initial error message would work when plugged into the family argument. I know that this cannot be the case because this worked fine:

`stan_glmer(p~ (1|group),family="gaussian",data=plot.data)`

Despite the fact that the error message from my initial code suggested that I could specify a beta distribution with stan_glmer, is this actually not possible?

#2

The error message is messed up, but you should call it with `family = mgcv::betar`.

#3

Great, thanks. Problem solved.


text:
Calculating drop chance over several hours is very similar: $\text{Total Chance} = 1 - (1 - \text{Per Kill Drop Chance})^{(\text{Kills Per Hour} \times \text{Hours})}$, $0.05 \times \frac{101}{500\;000} = 0.00101\%$, $1 \times \frac{100}{500\;000} = 0.02\%$, https://wiki.melvoridle.com/index.php?title=Signet_Ring_Half_(b)&oldid=42789. Recommendations on best consumables, food, gems, and enchants. We also give budget alternatives. Defeat Vindamea Drethan, and recover the artifact from her corpse. The difference is about 20 spell damage in favor of 1h+offhand, BUT there will be a lot of quest items for the 2h, so if you're bottom of the list for a weapon combo, then its worth to consider just grabbing one of the many quest items. Namespaces. Hellbringer is the Warlock DPS build, but they can also heal as a Soulweaver. Affliction Warlock Enchants and Gems. Killing a  Fierce Devil, which has a 100% chance to drop loot and a Combat Level of 100 would give a $1 \times \frac{100}{500\;000} = 0.02\%$. At the time, it weighed 0.0 kg. Gearing Early on in Shadowlands as Affliction Warlock. The Cenarion Cirlce sets are a 3-piece set originating from the Ruins of Ahn'Qiraj, or simply AQ20, raid.These set pieces are acquired from quest rewards from tokens and other items found inside Ruins of Ahn'Qiraj, and also through Cenarion Circle reputation. Welcome to our Gearing Page for Destruction Warlock, this section will cover everything you need to know about equipping your character correctly. For example, the  Rune Knight has a Combat Level of 101 and a 5% chance to drop loot so the chance per kill of getting the Signet Ring Half (b) is $0.05 \times \frac{101}{500\;000} = 0.00101\%$. Incendosaurs? From Melvor Idle. Last Database Update : 20 Dec 2019 - Players with 1800 rating or higher - Add a character. Travel to the cave, and fight your way through to the last mage, Vindamea Drethan. Recommended Gear for Affliction Warlocks in Shadowlands What is the BiS Affliction Warlock gear? Simply type the URL of the video in the form below. If you have a new piece of gear that you need gems and enchants advice for, you can find everything you need on our dedicated page below. Warlock's Ring may refer to: Warlock's Ring (Arena) Warlock's Ring (Daggerfall) Warlock's Ring (Morrowind) Warlock's Ring (Quest) Warlock's Ring (Blades) This set is meant to provide the user with more offensive capabilities by not only giving large amounts of spell power, but also have critical strike rating, hit rating, and even spell penetration to deal with pesky resistances! By playing and progressing within Melvor Idle, you agree to accept that: 1) You will encounter bugs and unexpected behaviour that may directly affect your experience. Comment by 6by6n6 Memory of Wilfred's Sigil of Superior Summoning drops from Millificent Manastorm, the second boss in the dungeon De Other Side.Am definitely going to choose this legendary for m+ even if it's a single target loss.. just because destro feels sad with a 3 minute infernal. We will not be able to maintain full hit% with this setup, because various items are just too good to pass up. Sandstorm Ring No Description Item ID: 921 Category: Combat: Type: Ring Sells For: 62,400 Equipment Slot: Ring Special Attack: 20% chance for Sandstorm: An unavoidable attack that deals 1-5% of the Player's current Hitpoints as dmg 10 times over 5 seconds. 7437 relations. Armour Stats Offensive Stats Defensive Stats Strength Bonus 0 Defence Bonus 0 Stab Bonus 0 … Page; Discussion; More. and 3 of any of these: +5 to Absorb +5 to Adrenaline Dodge +5 to Blizzard Armor. The easiest way to compare monsters is through killing several (or using a combat simulator Extension) to establish an average number of kills per hour and then using the following formula: $\text{Chance Per Hour} = 1 - (1 - \text{Per Kill Drop Chance})^\text{Kills Per Hour}$. Some variations of the 3-piece bonus can be used in PvE gear setups! Perfect Ring Enchant would be: 4/5/6 Health Absorb +126 Armor Piercing. 5 out of 5 stars (1,048) 1,048 reviews $22.00. Touch of Chaos | Drops from Nefarian | Raid Blackwing Lair. The ring is currently held by Vindamea Drethan in Ashirbadon, a cave on a small island east of the ruins of Bal Fell, just east of the city of Vivec at the bottom of the map. More; Page actions. The pieces themselves have phenomenal stats for the most part as well. You can also use it to keep track of your completed quests, recipes, mounts, companion pets, and titles! Warlock Tier 3, Plagueheart Raiment is perhaps one of the most iconic Warlock sets of all time, and is excellent for Warlocks in WoW Classic. Schau dir unsere Auswahl an warlock ring an, um die tollsten einzigartigen oder spezialgefertigten handgemachten Stücke aus unseren Shops für ringe zu finden. Warlock Ring, Witchcraft, Horror, Gothic Jewelry, Aluminum Cuff Ring TheGrimHerald. Whateverosaur is More Like It, filter of all Cloth Armor added in Phase 5 (Ahn'Qiraj), https://classic.wowhead.com/gear-planner/warlock/orc/ATwBN_wCL0cDN_8FN0kGLY4HM3IIN_kJN_oKKiMLMskMMP8NMoIONpAPN_sQNowRKiwSNFQ. From shop TheGrimHerald. With proper gearing you will finally be able to make hit cap. Namespaces. Skull Ring, Skull Jewelry, Warlock Ring, Biker Ring, Goth Ring, Statement Ring, Witch Jewelry, Pagan Jewelry, Alternative jewelry wickedworld. Best Warlocks rankings (PvE) Last Database Update : 20 Dec 2019 - Players with 1/8 or more bosses killed in Mythic mode - Add a character. Warlocks have pact magic, something that counts differently with spell slots, but has the same concept. More; Page actions. The 2h options are still quite strong and should not be ignored. From shop wickedworld. The Warlock table shows how many spell slots you have. Keep in mind that Shadowlands is still undergoing tuning and that these may change without notice. Screenshots containing UI elements are generally declined on sight, the same goes for screenshots from the modelviewer or character selection screen. Destruction can deal a lot of burst to a single target, and also efficiently cleave and AoE several targets at once. The band gained popularity and some commercial success in Europe in the mid-1980s, due to the personality and stage presence of lead vocalist Doro Pesch.Warlock supported successful heavy metal bands on tour, such as W.A.S.P., Judas Priest, Dio and Megadeth. A complete searchable and filterable list of all Warlock Campaign Quests in World of Warcraft: Shadowlands. Item Sources. Download the client and get started. From Melvor Idle. 2. The table also shows what the level of those slots is; all of your spell slots are the same level. Atiesh Questline This legendary quest line is available for the Priest, Mage, Warlock and Druid classes. Ajira tells you you can recover the Warlock's Ring from the Ashirbadon cave. The Wowhead Client is a little application we use to keep our database up to date, and to provide you with some nifty extra functionality on the website! Notes . Especially because unlike tier 1, tier 2 has significant offensive stats as well. This banner text can have markup.. web; books; video; audio; software; images; Toggle navigation I would take a ring with even 2 of these and 126 Armor piercing and Absorb over this Warlock ring since you can't enchant it. The Warlock's Ring is an artifact originally owned by the Arch Mage Syrabane, an Aldmeri god-ancestor. Always up to date with the latest patch (9.0.2). This is a disambiguation page—a navigational aid which lists other pages that might otherwise share the same title. Warlocks get an ability called "mystic arcanum" which allows them to learn 6, 7, 8, and 9th level spells. Our Warlock DPS Pre-Raid Best in Slot gear page will explain the best items from dungeons, reputations, crafting, and early PvP to acquire so you are as effective as possible before stepping foot in your first raid. Namespaces. More; Page actions. If an article link refers here, consider backtracking and fixing it, so that it points directly to the intended page. This set also makes your pets much more difficult to kill. Simply browse for your screenshot using the form below. On this page, we list the best gems, enchants, flasks, potions, and food you can get for your Affliction Warlock, based on your stat priority. As with last time, the 2h vs 1h debate comes down to if you actually have the ability to get 2 item drops. The purpose of our class guides is not just to show you a build that you can copy and use on your character, but to show you a base build and teach you the mechanics and stats of the game, so you can understand and play your class to its fullest capabilities. Pick going ether 1h + offhand or 2h to get a quick staff from the AQ quest. The chance for a Signet Ring Half (b) roll to succeed is X in 500,000, where X is the combat level of the monster defeated. There is no best warlock subclass. View; View source; History; This page is up to date . Also keep in mind that "Best" can be both pretty subjective and, in many cases, a very close call. The Eternal Champion discovered this ring in either Morrowind or Elsweyr. Favorite Add to Vertebrae Ring - Brass LiquidFireMantra. In appearance, it is a ring with a large gemstone, either red or green in color. We will NOT be going for the full 8/8 t4. Gearing Early on in Shadowlands as Destruction Warlock. Warlock were a German heavy metal band, founded in 1982 by members of the underground bands Snakebite and Beast. Especially to different schools of magic. From a raiding warlock's PoV, this set is barely a sidegrade to a mix of T2.5 (Doomcaller), 2 pieces Plagueheart for the set bonus and C'Thun's gloves (Dark Storm Gauntlets). The longer any boss encounter takes the more and more value this 4-piece bonus gains. Rank Class Spec Race Name Guild Normal bosses Mythic bosses Score Realm; 1. Armour Stats Offensive Stats Defensive Stats Strength … This page is updated for World of Warcraft — Shadowlands 9.0.2. If you have a new piece of gear that you need gems and enchants advice for, you can find everything you need on our dedicated page below. … All information you need to have your Destruction Warlock ready to enter Raiding, Mythic Dungeons, and PvP. A wizard - warlock can't get 10 ability score improvements. Page; Discussion; More. Shortens stuns by 25%. So, what are you waiting for? See our Warlock Soulweaver build here. Page; Discussion; More. Go be a fighter if you want that. Destruction Warlock Enchants and Gems. Check out our warlock ring selection for the very best in unique or custom, handmade pieces from our rings shops. Please keep the following in mind when posting a comment: Your comment must be in English or it will be removed. Retrieved from "https://wiki.melvoridle.com/index.php?title=Water_Chest&oldid=41059" As the roll is only made on a loot-generating drop, the chance of a given kill giving the ring half is, $\text{Drop Chance} = \text{Monster Loot Chance} \times \frac{\text{Monster Combat Level}}{500\;000}$. The Signet Ring Half (b) can be found by killing monsters in combat and slayer areas, or by killing dungeon bosses while the player has a Gold Topaz Ring currently equipped in either the passive or ring slot of their active equipment set, and the enemy dropped an item other than Bones or another similar guaranteed drop. You might want to proof-read your comments before posting them. Our Warlock class writers have recommended the best legendary powers and item slots for Shadowlands content, as well as highlighting which legendaries are not worth crafting. While you will not ultimately use all 8 pieces, the 3 and 4-piece bonuses are quite strong and definitely worth using. View; View source; History; This page is up to date . However, unlike the previous sets, the tier 2.5 set bonuses do not make you or your pet harder to kill. Welcome to our Gearing Page for Affliction Warlock, this section will cover everything you need to know about equipping your character correctly. 2. Similarly to the first tier set, tier 2 high large amounts of stamina and some elemental resistances making it great for PvP. Destruction is almost always a viable candidate for progression fights, as it has the least ramp up time of any Warlock specialization. The Warlock's Ring is a legendary ring which Ajira, in the Balmora Guild of Mages, will tell you about, but only after you have found the Staff of Magnus. You regain all expended spell slots when you finish a short or long rest. Warlock Ring No Description Item ID: 792 Category: Combat: Type: Ring Sells For: 420,000 Equipment Slot: Ring Item Sources: Opening: Item Uses: Combat; Stats. Although immolate is not used too frequently in raids making the 3-piece bonus not significantly impactful, the 4-piece bonus is great. It is best known for its ability to reflect spells cast at its wearer and to fortify the wearer's speed and health, though it may have additional powers. 1922 est une année commune commençant un dimanche. Updated with the latest Shadowlands Pre-Patch 9.0.1 info. Players seeking to optimize their drop chance should find a monster that always drops loot and is a good balance between high combat level and short kill time. Although you are able to play and progress in this game, Melvor Idle is not a finished product. The Signet Ring Half (b) can be found by killing monsters in combat and slayer areas, or by killing dungeon bosses while the player has a Gold Topaz Ring currently equipped in either the passive or ring slot of their active equipment set, and the enemy dropped an item other than Bones or another similar guaranteed drop. Bosses inside Naxxramas have a chance to drop Splinter of Atiesh.Collecting these splinters is the first step in forming Atiesh, Greatstaff of the Guardian.Once you have 40 splinters you will be able to create the Frame of Atiesh, which provides you with the quest Frame of Atiesh. Return the ring to Ajira, and she will let you keep it. Warlock Amulet Passive: Magic spells heal you for 20% damage dealt Item ID: 793 Category: Combat: Type: Amulet Sells For: 420,000 Equipment Slot: Amulet Item Sources: Opening: Item Uses: Combat; Stats. View; View source; History; This page is up to date . A fine example of this is tier 1, found in. The items are just not as good as other pieces, However many items are listed here as optional, so if you run DKP or loot list, you can probably pick up some nicer upgrades for pretty cheep if you do not have a better item on hand. Best Warlocks rankings . For example, when you are 5th level, you have two 3rd-level spell slots. Destruction Warlock is a very flexible specialization that can find ways to excel in a variety of environments. From Melvor Idle. To cast one of your warlock spells of 1st level or higher, you must expend a spell slot. Resistance reduction is a neet stat that is coming into phase 5, but overall it will be completely useless after, Unlike a mage who typically has high amount of intellect on their tier gear, warlocks' tier gear typically has large amounts of stamina. Hyöka : 2941 : 2817 - 2389: 21457 : EU-Ravencrest : 6. Rank Class Spec Race Name 2v2 3v3 5v5 BG Score Realm; 5. Warlock DPS Pre-Raid Best in Slot Gear (BiS) - WoW Classic Before you start raiding in WoW Classic, you must prepare your character by gearing up through dungeons. The Signet Ring Half (b) is a rare drop that can be combined with Signet Ring Half (a) to create Aorpheat's Signet Ring. When found, the Signet Ring Half (b) will be added automatically to the Bank rather than appearing in the 'Loot to Collect' panel. The sets become available in Phase 5 with the release of Ruins of Ahn'Qiraj. Following the same trends set by the earlier tier sets, the Doomcaller set also has quite high stamina on each piece of gear. This page was last edited on 15 January 2021, at 01:28. , Mage, Warlock and Druid classes high stamina on each piece of gear,! Keep in mind that  best '' can be used in PvE gear setups is available for the full t4... Race Name 2v2 3v3 5v5 BG Score Realm ; 5 and more value this bonus! 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warlock ring melvor 2021


text: ## Representation Invariants and Abstraction Functions Review the [stack and queue code](../08-modules/code.ml) that accompanies the modules lecture. Each of the 4 modules defines an abstract data type. **Exercise**: The two Queue implementations document the abstraction function and rep. invariants, but these are not clearly identified as such. Modify the comments to identify the abstraction functions and rep. invariants (if any). **Exercise**: Describe the abstraction functions and rep. invariants (if any) for the two Stack implementations. **Exercise**: Write a rep_ok function for the TwoListQueue module. Modify the public functions so that they check rep_ok before returning. ## The specification game An interface designer writes the following specification for a function called reverse:  (** returns a list *) val reverse : 'a list -> 'a list  This spec is clearly incomplete. For example, a devious programmer could meet the spec with an implementation that gives the following output:  utop# reverse [1;2;3];; - : int list = []  The designer, upon realizing this, refines the spec as follows:  (** reverse l returns a list that is the same length as l *) val reverse : 'a list -> 'a list  But the devious programmer discovers that the spec still allows broken implementations:  utop# reverse [1;2;3];; - : int list = [0;0;0]  Finally, the designer settles on a third spec:  (** reverse l returns a list m satisfying * - length l = length m * - for all i, nth m i = nth l (n - i - 1) where n is the length of l *) val reverse : 'a list -> 'a list  With this spec, the devious programmer is forced to provide a working implementation to meet the spec, so the designer has successfully written her spec. **Partner exercise**: This example can be made into a game: one player (the "clever specifier") writes a specification for a function. The other player (the "devious programmer") tries to find holes in the specification by coming up with an input/output pair for the function that meets the specification but violates the intent of the function. If the programmer can't come up with a bad example, then the specifier wins. If not, the roles reverse and the other player makes an attempt to write a specification. Play this game with a partner to write precise specifications for the following functions (alternate who goes first): - is_sorted : 'a list -> bool - sort : 'a list -> 'a list - max : 'a list -> 'a ## Specification tests Precise specifications for functions can be tested for any particular input. For example, here is the spec we wrote for reverse above:  (** reverse l returns a list m satisfying * - length l = length m * - for all i, nth m i = nth l (n - i - 1) where n is the length of l *) val reverse : 'a list -> 'a list  And here is some code to test it:  (** range i n outputs the list [i; i+1; ...; n] *) let rec range i n = if i >= n then [] else i::(range (i+1) n) (** check_reverse_spec l returns true if reverse implements its spec on input l. *) let check_reverse_spec l = let open List in let m = reverse l in length l = length m && let n = length l in for_all (fun i -> nth m i = nth l (n - i - 1)) (range 0 n)  **Exercise**: write a similar function for your specification for is_sorted, max, and sort. These functions will check that the function has the correct behavior on any given input. To turn them into tests, you can simply run them on a list of example inputs:  TEST "reverse spec" = List.for_all check_reverse_spec [[1;2;3]; []; [1]; [2;2;2;3;3;3]];; TEST "sort_spec" = List.for_all check_sort_spec [[1;2;3]; []; [1]; [2;2;2;3;3;3]];;  ### Quick check For some data types, coming up with a good list of examples to use as tests can be difficult. An alternative approach is use randomized tests. The qcheck library makes this fairly easy. The Assertions module (which is part of the cs3110 tools) contains the assert_qcheck function:  val assert_qcheck : 'a QCheck.Arbitrary.t -> ('a -> bool) -> unit  The first argument is an 'a QCheck.Arbitrary.t, which gives a way to generate a random value of type 'a (more on this type below). The second argument is a test function, something like check_reverse_spec above. assert_qcheck will generate a large number of tests, and check the property on all of them. If any of them fail, it will raise an exception that contains the failing instances. You typically use assert_qcheck with TEST_UNIT, like so:  TEST_UNIT "reverse spec" = Assertions.assert_qcheck arbitrary_list check_reverse_spec  How does one create an 'a QCheck.Arbitrary.t? The [QCheck.Arbitrary](http://cedeela.fr/~simon/software/qcheck/QCheck.Arbitrary.html) module contains a large number of functions for building Arbitrary.ts. For example: - Arbitrary.alpha is a char Arbitrary.t: it generates a random alphabetic character. - Arbitrary.int n is a int Arbitrary.t: it generates a random number between 0 and n. - Arbitrary.(n -- m) is an int Arbitrary.t: it generates a random number between n and m - Arbitrary.list takes an 'a Arbitrary.t and produces an ('a list) Arbitrary.t. For example, Arbitrary.(list (40 -- 100)) generates a random list of numbers, each between 40 and 100. Arbitrary.(list alpha) generates a random list of characters. - Arbitrary.pair takes two arbitrary values and generates an arbitrary pair of values. For example, Arbitrary.(pair (0 -- 100) alpha) generates pairs where the first element is a number between 0 and 100, and the second element is a character. **Exercise**: Give a value of type ((int * (char list)) list * bool) Arbitrary.t:  open QCheck let arbitrary_thing : ((int * (char list)) list * int) Arbitrary.t = Arbitrary.( FILL IN )  **Exercise**: Use assert_qcheck to write TESTs for your is_sorted, max, and sort specifications.


text:
zbMATH — the first resource for mathematics

A 2-D Vlasov-Maxwell solver on unstructured meshes. (English) Zbl 0874.76061
Cohen, Gary (ed.), Mathematical and numerical aspects of wave propagation. Proceedings of the third international conference, Mandelieu-La Napoule, France, April 24–28, 1995. Philadelphia, PA: Society for Industrial and Applied Mathematics. 355-371 (1995).
Summary: We present a method for solving the Vlasov-Maxwell system. We propose a new constrained formulation of the Maxwell equations in order to better satisfy the divergence conditions $$\text{div} B=0$$, $$\text{div} {\mathbf E} ={\rho\over \varepsilon_0}$$. The electromagnetic field is approximated using a finite volume method, and the Vlasov equation is solved by a particle method. Some numerical test cases are presented.
For the entire collection see [Zbl 0846.00038].

MSC:
 76M25 Other numerical methods (fluid mechanics) (MSC2010) 76X05 Ionized gas flow in electromagnetic fields; plasmic flow


text:
## Mathematics Behind The Triangle Offense

It was pointed out to me recently that a few of the articles I have written describing the detailed geometric structure behind the triangle offense is scattered in various places around my blog, so here is a list of the articles in one convenient place:

• The Mathematics of Filling the Triangle (First article)
• Group Theory and Dynamical Systems Theory Behind The Triangle Offense
• A Demonstration That The Triangle Offense is the most efficient/optimal way for 5 players to space the floor.
• By: Dr. Ikjyot Singh Kohli (About the Author)

By: Dr. Ikjyot Singh Kohli (About the Author)

## Basketball – A Game of Geometry

In a previous post, I described the most optimal offensive strategy for the Knicks based on developing relevant joint probability density functions.

In this post, I attempt a solution to the following problem:

Given 5 players on the court, how can one determine (x,y) coordinates for each player such that the spacing / distance between each player is maximized. Thus, mathematically providing a solution in which the arrangement of these 5 players is optimal from an offensive strategy standpoint. The idea is that such an arrangement of these 5 players will always stretch the defense to the maximum.

The problem is then stated as follows. Let $(x_i, y_i)$ be the x and y coordinates of player $i$ on the court. We wish to solve:

Problems of this type are known as multi-objective optimization problems, and in general are quite difficult to solve. Note that in setting up the coordinate system for this problem, we have for convenience placed the basket at $(x,y) = (0,0)$, i.e., at the origin.

Now, for solving this problem we used the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) in the MCO package in R.

In general, what I found were that there are many possible solutions to this problem, all of which are Pareto optimal. Here are some of these results.

Here are some more plots of of player coordinates clearly showing the origin point (which as mentioned earlier, is the location of the basket):

Each plot above shows the x-y coordinates of players on the floor such that the distance between them is a maximum. Thus, these are some possible configurations of 5 players on the floor where the defense of the opposing team would be stretched to a maximum. What is even more interesting is that in each solution displayed above, and indeed, each numerical solution we found that is not displayed here, there is at least one triangle formation. It can therefore be said that the triangle offense is amongst the most optimal offensive strategies that produces maximum spacing of offensive players while simultaneously stretching the defense to a maximum as well. Here is more on the unpredictability of the triangle offense and its structure.

Based on these coordinates, we obtained the following distance matrices showing the maximum / optimal possible distance between player $i$ and player $j$:

Above, we show 5 possible distance matrices out of the several generated for brevity. So, one can see that looking at the fifth matrix for example, players are at a maximum and optimal distance from each other if for example the distance between player 1 and 2 is 9.96 feet, while the distance between player 3 and 4 is 18.703 feet, while the distance between player 4 and 5 is 4.96 feet, and so on.

## The Mathematics of “Filling the Triangle”

I’ve been fascinated by the triangle offense for a long time. I think it is a beautiful way to play basketball, and the right way to play basketball, in the half-court, a “system-based” way to play. For those of you that are interested, I highly recommend Tex Winter’s classic book on the topic.

There is this brief video as well where Tex Winter explains how the triangle offense and a basketball are grounded in geometric principles:

I don’t think people recognize though how deep of a geometry problem this is actually. Looking at when the triangle is filled, as in the video above, we have the following situation:

The problem I wanted to study was given 5 players’ random positions on the court, could a series of equations be solved yielding (x,y) coordinates that would yield where players should “go” to fill the triangle?

Using simple geometry, from the diagram above, we see that each player’s position in the triangle offense is governed by the following system of nonlinear equations:

$\left(x_4-x_2\right) \left(x_4-x_5\right)+\left(y_4-y_2\right) \left(y_4-y_5\right)=\cos (a) \sqrt{\left(x_2-x_4\right){}^2+\left(y_2-y_4\right){}^2} \sqrt{\left(x_4-x_5\right){}^2+\left(y_4-y_5\right){}^2}$

$\left(x_4-x_2\right) \left(x_2-x_5\right)+\left(y_4-y_2\right) \left(y_2-y_5\right)=\cos (b) \sqrt{\left(x_2-x_4\right){}^2+\left(y_2-y_4\right){}^2} \sqrt{\left(x_2-x_5\right){}^2+\left(y_2-y_5\right){}^2}$

$\left(x_2-x_5\right) \left(x_4-x_5\right)+\left(y_2-y_5\right) \left(y_4-y_5\right)=\cos (c) \sqrt{\left(x_2-x_5\right){}^2+\left(y_2-y_5\right){}^2} \sqrt{\left(x_4-x_5\right){}^2+\left(y_4-y_5\right){}^2}$

$\left(x_2-x_1\right) \left(x_2-x_5\right)+\left(y_2-y_1\right) \left(y_2-y_5\right)=\cos (d) \sqrt{\left(x_1-x_2\right){}^2+\left(y_1-y_2\right){}^2} \sqrt{\left(x_2-x_5\right){}^2+\left(y_2-y_5\right){}^2}$

$\left(x_2-x_1\right) \left(x_1-x_5\right)+\left(y_2-y_1\right) \left(y_1-y_5\right)=\cos (e) \sqrt{\left(x_1-x_2\right){}^2+\left(y_1-y_2\right){}^2} \sqrt{\left(x_1-x_5\right){}^2+\left(y_1-y_5\right){}^2}$

$\left(x_1-x_5\right) \left(x_2-x_5\right)+\left(y_1-y_5\right) \left(y_2-y_5\right)=\cos (f) \sqrt{\left(x_1-x_5\right){}^2+\left(y_1-y_5\right){}^2} \sqrt{\left(x_2-x_5\right){}^2+\left(y_2-y_5\right){}^2}$

$\left(x_1-x_3\right) \left(x_1-x_5\right)+\left(y_1-y_3\right) \left(y_1-y_5\right)=\cos (h) \sqrt{\left(x_1-x_3\right){}^2+\left(y_1-y_3\right){}^2} \sqrt{\left(x_1-x_5\right){}^2+\left(y_1-y_5\right){}^2}$

$\left(x_1-x_3\right) \left(x_3-x_5\right)+\left(y_1-y_3\right) \left(y_3-y_5\right)=\cos (i) \sqrt{\left(x_1-x_3\right){}^2+\left(y_1-y_3\right){}^2} \sqrt{\left(x_3-x_5\right){}^2+\left(y_3-y_5\right){}^2}$

$\left(x_1-x_5\right) \left(x_3-x_5\right)+\left(y_1-y_5\right) \left(y_3-y_5\right)=\cos (g) \sqrt{\left(x_1-x_5\right){}^2+\left(y_1-y_5\right){}^2} \sqrt{\left(x_3-x_5\right){}^2+\left(y_3-y_5\right){}^2}$

Further, the angles obviously must satisfy the following constraints:

$a + b + c = \pi, \quad d + e + f = \pi, \quad g + h + i = \pi$

Finally, we require that each player be about 15-20 feet apart in the triangle offense (because the offense is predicated on spacing), and thus have some additional constraints:

$15\leq \sqrt{\left(x_2-x_4\right){}^2+\left(y_2-y_4\right){}^2}\leq 20$

$15\leq \sqrt{\left(x_4-x_5\right){}^2+\left(y_4-y_5\right){}^2}\leq 20$

$15\leq \sqrt{\left(x_2-x_5\right){}^2+\left(y_2-y_5\right){}^2}\leq 20$

$15\leq \sqrt{\left(x_1-x_2\right){}^2+\left(y_1-y_2\right){}^2}\leq 20$

$15\leq \sqrt{\left(x_1-x_5\right){}^2+\left(y_1-y_5\right){}^2}\leq 20$

$15\leq \sqrt{\left(x_1-x_3\right){}^2+\left(y_1-y_3\right){}^2}\leq 20$

$15\leq \sqrt{\left(x_3-x_5\right){}^2+\left(y_3-y_5\right){}^2}\leq 20$

Solving this highly nonlinear system of equations with constraints is not a trivial problem! It fact, because of the high degree of nonlinearity and dimension of the problem, it is safe to assume that no closed-form solution exists, and therefore, must be solved numerically.

For this task, we used MATLAB, and experimented with the lsqnonlin() and fsolve() commands. The only issue is that (as with all such numerical algorithms) convergence depends very highly on the choice of initial conditions. It is very difficult to choose a priori this many initial conditions, so I wrote a script that randomized initial conditions. I then ran several numerical experiments and obtained the following results:

In the plot above, I have labeled the plots that converged to the triangle formation with the title “this one”. In addition, the five black circles denote the initial positions of the players on the court before they fill the triangles in the offense. One sees just by the diagram above, how difficult such a problem is to solve mathematically, even through a numerical approach. Running more trials would perhaps yield better results, but, it works! I am truly fascinated by this. In the coming days, I will work on optimizing the numerical algorithm, and post my updates as they come.

Here is an animation of one of the scenarios above when the algorithm converges correctly:

In this animation above, the black dots represent the positions of the players on the court. They begin at initial (random) positions and attempt to fill the triangles as described above.


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# How do you solve the system 4x+4y+z=24, 2x-4y+z=0, and 5x-4y-5z=12?

Jan 15, 2018

Add the equations to eliminate variables and solve.

#### Explanation:

$4 x + 4 y + z = 24$
$2 x - 4 y + z = 0$
$5 x - 4 y - 5 z = 12$

Choose two equations that will easily cancel out.
$4 x + 4 y + z = 24$
$2 x - 4 y + z = 0$
The y's cancel out, leaving you with $6 x + 2 z = 24$. This can be simplified to $3 x + z = 12$.

Choose another two equations to get another binomial.
$4 x + 4 y + z = 24$
$5 x - 4 y - 5 z = 12$
Again, the y's cancel out, leaving you with $9 x - 4 z = 36$.

Use substitution, making $3 x + z = 12$ into $z = 12 - 3 x$. Plug this into $9 x - 4 z = 36$ to get $9 x - 4 \left(12 - 3 x\right) = 36$. Distribute to get the equation $9 x - 48 + 12 x = 36$. Combine like terms, making the equation $21 x = 84$. Divide both sides by $21$ to get $x = 4$.

You can then use this value in the equation $z = 12 - 3 x$. Plug it in to get $z = 12 - 3 \left(4\right)$, which simplifies to $z = 0$.

With these two values you can use any of the original equations to find the remaining value. $2 \left(4\right) - 4 y + \left(0\right) = 0$. Simplify to get $8 - 4 y = 0$. Add $4 y$ to both sides to get $8 = 4 y$, and divide both sides by $4$ to get $y = 2$.

The final values are $x = 4$, $y = 2$ and $z = 0$.
This can be checked by plugging these values into the two remaining original equations.


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A Kirchhoff Voltage and Current Law problem.

Electricity and Magnetism Level 2

Find the voltage across the 40 ohm resistor.

Following values are to be used: $$R_1=10 \Omega, R_2=20 \Omega, R_3 = 40 \Omega, V_1 = 10 V,V_2 = 20V$$.

Answer is to be given in volts.

×


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# Thread: Can anyone help with this problem on Force??

1. ## Can anyone help with this problem on Force??

A circulur column has a diameter of 80mm outside edge and 60mm inside edge.
Both ends are fixed with equal force being applied top and bottom.
Young's Modulus E = 200GN m-2
Yield Stress deltay = 140 MN m-2

What is the minimum length of column at which buckling is likely to happen?
If the column is half this length what load would you expect failure to occur?

Really struggling with this one if anyone can help id really appreciate it

2. ## Re: Can anyone help with this problem on Force??

Are you familiar with Euler's equations for column critical load?

$F_{crit} = \frac {\pi ^2 EI}{(KL)^2}$

where the factor K depends on how the column is secured. For a column with both ends fixes K = 0.5. You asked for the "minimum length" under which buckling is likely to happen - that's where the length is sufficient to makes this a "long" or "slender" column, which generally means L is ten times the diameter. To find the force that can cause buckling for that length use the Euler equation above - you have the value for E, and can calculate I from the dimensions you were given. The answer to the third question may seem evident from the fact that F is inversely proportional to L^2, so if you halve L the force F that causes buckling will go up by a factor of 4. However I think this is a trick question, because if the length is now only 5 times the diameter the failure mode will be crushing of the material, not buckling. So for this you already have the value for the maximum stress it can withstand, and you simply multiply that stress by the cross-sectional area of the column to get the force.

3. ## Re: Can anyone help with this problem on Force??

thanks ill try it again tonight when ive got kids in bed and let you know


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The Knowledge Bank is scheduled for regular maintenance on Thursday, August 13th through Friday, August 14th. During this time, users will not be able to register, login, or submit content.
 dc.creator Monje, Raquel R. en_US dc.creator Lis, Darek C. en_US dc.creator Phillips, Thomas G. en_US dc.creator Goldsmith, Paul F. en_US dc.creator Emprechtinger, Martin en_US dc.creator Neufeld, David A. en_US dc.date.accessioned 2011-07-12T17:24:50Z dc.date.available 2011-07-12T17:24:50Z dc.date.issued 2011 en_US dc.identifier 2011-FA-11 en_US dc.identifier.uri http://hdl.handle.net/1811/49249 dc.description Author Institution: California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125-4700, USA; Johns Hopkins University, USA en_US dc.description.abstract We present Herschel/HIFI observations of interstellar hydrogen chloride (HCl) and hydrogen fluoride (HF) along the line-of-sight towards Galactic sources with strong submillimeter continuum emission from the PRISMAS and HEXOS GT KP. The halogen-containing molecules are of special interest because of their unique thermochemistry and their important role as tracers of the neutral ISM. The detection of foreground absorption by HF J = 1--0 transition line in each source probes the distribution of HF throughout the Milky Way, in diffuse clouds with varying values of the visual extinction, as a potential valuable surrogate for molecular hydrogen. For the optically thin absorption components we calculate the column densities of HF. We find that, in many of the background clouds, the abundances of HF with respect to H$_2$ is consistent with the theoretical prediction that HF is the main reservoir of gas-phase fluorine for these clouds. Observations of hydrogen chloride isotopologues, H$^{35}$Cl and H$^{37}$Cl J = 1--0 transition line at different galactocentric distances provide insights of how elemental abundances change with location in the Galaxy. We model the HCl observations with a non-LTE radiative transfer model to derive gas densities and HCl column densities for sources with HCl emission. Interstellar HCl abundances and isotopic ratios [$Cl^{35}$/$Cl^{37}$] are essential for improving our understanding of stellar nucleosynthesis and global chemical enrichment and evolution in the Galaxy. en_US dc.language.iso en en_US dc.publisher Ohio State University en_US dc.title OBSERVATIONS OF INTERSTELLAR HYDROGEN FLUORIDE AND HYDROGEN CHLORIDE IN THE GALAXY en_US dc.type Article en_US


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# 8. Security¶

The DDS Security specification includes five security builtin plugins.

1. Authentication plugin: DDS:Auth:PKI-DH. This plugin provides authentication for each DomainParticipant joining a DDS Domain using a trusted Certificate Authority (CA). Support mutual authentication between DomainParticipants and establish a shared secret.

2. Access Control plugin: DDS:Access:Permissions. This plugin provides access control to DomainParticipants which perform protected operations.

3. Cryptographic plugin: DDS:Crypto:AES-GCM-GMAC. This plugin provides authenticated encryption using Advanced Encryption Standard (AES) in Galois Counter Mode (AES-GCM).

4. Logging plugin: DDS:Logging:DDS_LogTopic. This plugin logs security events.

5. Data Tagging: DDS:Tagging:DDS_Discovery. This plugin enables the addition of security labels to the data. Thus it is possible to specify classification levels of the data. In the DDS context it can be used as a complement to access control, creating an access control based on data tagging; for message prioritization; and to prevent its use by the middleware to be used instead by the application or service.

Note

Currently the DDS:Tagging:DDS_Discovery plugin is not implemented in Fast DDS. Its implementation is expected for future release of Fast DDS.

In compliance with the DDS Security specification, Fast DDS provides secure communication by implementing pluggable security at three levels: a) DomainParticipants authentication (DDS:Auth:PKI-DH), b) access control of Entities (DDS:Access:Permissions), and c) data encryption (DDS:Crypto:AES-GCM-GMAC). Furthermore, for the monitoring of the security plugins and logging relevant events, Fast DDS implements the logging plugin (DDS:Logging:DDS_LogTopic).

By default, Fast DDS does not compile any security support, but it can be activated adding -DSECURITY=ON at CMake configuration step. For more information about Fast DDS compilation, see Linux installation from sources and Windows installation from sources.

Security plugins can be activated through the DomainParticipantQos properties. A Property is defined by its name (std::string) and its value (std::string).

Warning

For the full understanding of this documentation it is required the user to have basic knowledge of network security since terms like Certificate Authority (CA), Public Key Infrastructure (PKI), and Diffie-Hellman encryption protocol are not explained in detail. However, it is possible to configure basic system security settings, i.e. authentication, access control and encryption, to Fast DDS without this knowledge.

The following sections describe how to configure each of these properties to set up the Fast DDS security plugins.


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# Solution - Arithmetic Progression

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Books Shortlist
ConceptArithmetic Progression

#### Question

If the mth term of an A.P. be 1/n and nth term be 1/m, then show that its (mn)th term is 1.

#### Solution

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Is there an error in this question or solution?

#### Similar questions VIEW ALL

If m times mth term of an A.P. is equal to n times its nth term, show that the (m + n) term of the A.P. is zero

view solution

The 10th term of an A.P. is 52 and 16th term is 82. Find the 32nd term and the general term

view solution

Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.

0, - 4, - 8, - 12 …

view solution

Determine the general term of an A.P. whose 7th term is –1 and 16th term 17

view solution

Write the first five terms of the sequence defined by a_n = (–1)^(n-1) . 2^n

view solution

#### Reference Material

Solution for concept: Arithmetic Progression. For the course 8th-10th CBSE
S


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# Is one form of the answer more right than the other

#### find_the_fun

##### Active member
A committee of 12 is to be selected from 10 men and 10 women. In how many ways can the selection be carried out if there must be an even number women?

I answered $$\displaystyle {10 \choose 2}{10 \choose 10}+{10 \choose 4}{10 \choose 8}+{10 \choose 6}{10 \choose 6}+{10 \choose 8}{10 \choose 4}+{10 \choose 10}{10 \choose 2}$$

$$\displaystyle \sum\limits_{i=1}^5 {10 \choose 12-2i}{10 \choose 2i}$$

I can see how the two are equivalent but is one more correct than the other? I found the first answer just by thinking about it; was the second answer arrived at by applying a formula I'm unaware of? i.e. does the second answer imply a certain approach?

Last edited:


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The open source CFD toolbox
Wall modelling

Note
Under construction - please check again later

# Momentum

Momentum wall functions are imposed by setting the turbulence viscosity at the wall. By combining the dimensionless velocity

$u^+ = \frac{u}{u_t}$

dimensionless wall distance

$y^+ = \frac{\rho y u_t}{\mu}$

and friction velocity

$u_t = \sqrt {\frac{\tau_{wall}}{\rho}}$

the wall shear stress can be described according to:

$\tau_{wall} = \mu \frac{y^+}{u^+} \frac{u}{y} = (\mu + \mu_t) \frac{u}{y}$

where

$\mu_t = \mu\left(\frac{y^+}{u^+} - 1\right)$

# High Reynolds number

 Would you like to suggest an improvement to this page? Create an issue


text:
Contact The Learning Centre

# Drawing graphs

### Important features of linear graphs

Key features of graphs include:

• $$x$$ and $$y$$-intercepts — where the graph crosses each axis.
• Slope or gradient (especially important for linear/straight line graphs).

$\mbox{gradient} = \frac{\mbox{change is height ($$\Delta y$$)}}{\mbox{change in width ($$\Delta x$$)}}$

For example:

\begin{eqnarray*}
• The $$y$$-intercept is at $$(0,0.5)$$.
• The $$x$$-intercept is at $$(-1,0)$$.


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# Temperature of filler for multi-core cables type SS with sheath

The filler temperature is calculated in the middle between the sheath (which is separate for each core) and the armour bedding (or innermost layer over the filler).

Symbol
$\theta_{f}$
Unit
$^{\circ}$C
Formulae
$- T_{1} \left(W_{c} + \frac{W_{d}}{2}\right) - \frac{T_{2_{f}} n_{c} \left(W_{c} \left(\lambda_{1} + 1\right) + W_{d}\right)}{2} + \theta_{c}$
$T_{1}$
$T_{2_{f}}$
$\theta_{c}$
$W_{c}$
$W_{d}$


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### Archive

Archive for October, 2010

## Converting from binary to integer

26 October 2010 1 comment

The following is an updated and edited version of my posts to this sage-support thread.

Problem

You have a bitstring as output by

sage.crypto.stream.blum_blum_shub

and you want to convert that bitstring to an integer. Or in general, you want to convert a bit vector to its integer representation.

Solution

Here are two ways, assuming that you want the bits in little-endian order, i.e. you read the bits from right to left in increasing order of powers of 2.

sage: version()
'Sage Version 4.5.3, Release Date: 2010-09-04'
sage: from sage.crypto.stream import blum_blum_shub
sage: b = blum_blum_shub(length=6, lbound=10**4, ubound=10**5); b
100110
sage: type(b)
<class 'sage.monoids.string_monoid_element.StringMonoidElement'>
sage: # read in little-endian order
sage: # conversion using Python's built-in int()
sage: int(str(b), base=2)
38
sage: # conversion using Sage's built-in Integer()
sage: Integer(str(b), base=2)
38

Now assume you read the bitstring as output by blum_blum_shub in big-endian order, i.e. from left to right in increasing order of powers of 2. You simply convert the bitstring to a string, reverse that string, and apply any of the above two methods.

sage: # reversing a string
sage: str(b)
'100110'
sage: str(b)[::-1]
'011001'
sage: # read in big-endian order
sage: int(str(b)[::-1], base=2)
25
sage: Integer(str(b)[::-1], base=2)
25

Or you can do as follows:

sage: b = "100110"
sage: sum(Integer(i) * (2^Integer(e)) for e, i in enumerate(b))
25
sage: sum(Integer(i) * (2^Integer(e)) for e, i in enumerate(b[::-1]))
38

Another way is to use Horner’s method. Here’s a Sage function that computes the integer representation of a bit vector read using big-endian order. A usage example is also shown.

sage: def horner(A, x0):
...       # Evaluate the polynomial P(x) at x = x_0.
...       #
...       # INPUT
...       #
...       # - A -- list of coefficients of P where A[i] is the coefficient of
...       #   x_i.
...       # - x0 -- the value x_0 at which to evaluate P(x).
...       #
...       # OUTPUT
...       #
...       # An evaluation of P(x) using Horner's method.
...       i = len(A) - 1
...       b = A[i]
...       i -= 1
...       while i >= 0:
...           b = b*x0 + A[i]
...           i -= 1
...       return b
sage: A = [1, 0, 0, 1, 1, 0]
sage: horner(A, 2)
25

As an exercise, modify the function horner to output the integer representation of a bit vector that is read using little-endian order.

## Number theory & RSA public key cryptography

I have released version 1.1 of the Sage tutorial “Number theory and the RSA public key cryptosystem”. There is little change in terms of content. However, note that I now use the GNU Free Documentation License v1.3+ for the tutorial. Here are the relevant files you can download for your reading pleasure.

All versions of the tutorial are available from the download page on its website. For the adventurous of heart, I have also made the full $\LaTeX$ source of the document available.

The tutorial is meant to be educational. I don’t pretend that it is complete in any way. Any suggestions and/or criticisms for improving the tutorial are more than welcome. Enjoy and happy Sage’ing.

## Numbering exercises/problems using chapter numbers

9 October 2010 1 comment

To typeset a list of exercises or problems in $\LaTeX$, you could use the enumerate environment. By default, this would only produce numbers of the form n. where n is a positive integer. You could number an exercise using the chapter number to produce numbering of the form c.n. where c is the chapter number. Put the following macro definition in your preamble to get the chapter number to appear.

%% For listing problem sets. Each problem is numbered according to the
%% format
%%
%% chapterNumber.problemNumber.
\newcounter{problemcounter}
\newenvironment{problem}{%
\setcounter{problemcounter}{1}
\begin{list}
{\thechapter.\arabic{problemcounter}.}
{\usecounter{problemcounter}}
\let\olditem\item}{%
\end{list}
}

This could easily be customized to insert the section number instead of the chapter number.

Categories: documentation, LaTeX Tags: ,


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# Limit n approaches infinity of (1 + n)^(1/n)

1. lim (1 + n)^(1/n)
n→∞

2. I was able to figure out that the limit goes to 1 only after I substituted larger and larger values in place of n in my calculator.

Since I cannot use a calculator on my test, is there another way to know what the limit goes to?

Thanks.

## Answers and Replies

Related Calculus and Beyond Homework Help News on Phys.org
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
1. lim (1 + n)^(1/n)
n→∞

2. I was able to figure out that the limit goes to 1 only after I substituted larger and larger values in place of n in my calculator.

Since I cannot use a calculator on my test, is there another way to know what the limit goes to?

Thanks.
Take logarithms.

AGH! Taking logarithms seems harder than it should be...

Just setting up a log would look like this, right? log1+nx = 1/n

...Don't even know how to solve that.

But isn't there an intuitive way to figure out the right answer?

Mark44
Mentor
AGH! Taking logarithms seems harder than it should be...

Just setting up a log would look like this, right? log1+nx = 1/n
Not a very convenient log base. Try loge (AKA ln).
...Don't even know how to solve that.

But isn't there an intuitive way to figure out the right answer?

AGH! Taking logarithms seems harder than it should be...

Just setting up a log would look like this, right? log1+nx = 1/n

...Don't even know how to solve that.

But isn't there an intuitive way to figure out the right answer?
I would start approaching this by considering that: lim_(x→∞) for (1/x) = 0

Curious3141
Homework Helper
1. lim (1 + n)^(1/n)
n→∞

2. I was able to figure out that the limit goes to 1 only after I substituted larger and larger values in place of n in my calculator.

Since I cannot use a calculator on my test, is there another way to know what the limit goes to?

Thanks.
Are you sure you wrote the limit correctly? There's a much more interesting limit that goes ##\displaystyle \lim_{n \to \infty} (1 + \frac{1}{n})^n## or, equivalently, ##\displaystyle \lim_{n \to 0} (1 + n)^{\frac{1}{n}}##.

As written, the limit is easily seen to be equivalent to ##\displaystyle \lim_{n \to \infty} n^{\frac{1}{n}}## since the "1" can be ignored at the limit. This limit can be resolved by taking the natural logarithm, and then using L' Hopital's Rule.

Okay, thanks, you guys! :)

So I take the ln to bring down the fraction.

ln[(1+n)1/2]

= 1/2ln(n+1) →L'Hospital's→ (1/2)(1/(n+1))(1) = 1/(2n + 2)

When I substitute infinity for n here, it seems that it goes to 0, not 1...

Am I doing something wrong here...?

Dick
Science Advisor
Homework Helper
Okay, thanks, you guys! :)

So I take the ln to bring down the fraction.

ln[(1+n)1/2]

= 1/2ln(n+1) →L'Hospital's→ (1/2)(1/(n+1))(1) = 1/(2n + 2)

When I substitute infinity for n here, it seems that it goes to 0, not 1...

Am I doing something wrong here...?
Where did the (1/2) power come from? And if the log goes to 0 what does the original sequence go to?

oh, man. I was looking at another problem and wrote down 1/2 instead of 1/n!

ln(1+n)1/n = ln(1+n)/n →L'Hospital's→ 1/(1+n)

1/(1+infinity) = 0

Oh, so you mean that since we used the ln, and it went to zero, then the original expression must have gone to 1.

Because ln(1) = 0

Is this right?

Thanks! :)

Curious3141
Homework Helper
oh, man. I was looking at another problem and wrote down 1/2 instead of 1/n!

ln(1+n)1/n = ln(1+n)/n →L'Hospital's→ 1/(1+n)

1/(1+infinity) = 0

Oh, so you mean that since we used the ln, and it went to zero, then the original expression must have gone to 1.

Because ln(1) = 0

Is this right?

Thanks! :)
Pretty much right, except that I think you should use limit notation instead of writing things like 1/(1+infinity) = 0.


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in 📓 Notes

# URI

Table of Contents

1 min read

A Uniform Resource Identifiers (URI) is a string of characters that identifies unambiguously a resource. It is a standard in the WWW world.

The syntax:

uri = scheme:[//authority]path[?query][#fragment]
authority = [[email protected]]host[:port]
`

Examples:

## URL

A Uniform Resource Location (URL) is an URI type used to identify a resource on the Internet. It provides the

## URN

A Uniform Resource Name (URN) is an URI type that identifies a given resource by name on a given namespace. For example, a book’s isbn.

Or if you don't know what a response is, you can always write a webmention comment (you don't need to know what that is).


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# managed: A monad for managed values

[ bsd3, control, library ] [ Propose Tags ]

In Haskell you very often acquire values using the with... idiom using functions of type (a -> IO r) -> IO r. This idiom forms a Monad, which is a special case of the ContT monad (from transformers) or the Codensity monad (from kan-extensions). The main purpose behind this package is to provide a restricted form of these monads specialized to this unusually common case.

The reason this package defines a specialized version of these types is to:

• be more beginner-friendly,

• simplify inferred types and error messages, and:

• provide some additional type class instances that would otherwise be orphan instances

## Modules

[Index] [Quick Jump]


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## anonymous 3 years ago Convert the radian measure to degree measure. Use the value of π found on a calculator and round answers to two decimal places. (9π)/4 Here are the answer choices: 200π° 405° 160° 324°

1. UnkleRhaukus

|dw:1352806872068:dw|

2. UnkleRhaukus

|dw:1352806935712:dw|

3. anonymous

Thank you for replying! But, I found the answer myself!! (: I got 405! (: Thank you, though!

4. UnkleRhaukus

|dw:1352807151094:dw|

5. anonymous

Thank you!! (:

6. UnkleRhaukus

$\frac{9\pi}4=\frac{9\times180°}{4}=9\times45°=\color{grey}{(10-1)\times45°=450°-45°}=405°$

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