text:
# What can an algebraic geometer do outside academia? [closed]

This question is inspired by this and this. But it is not a duplicate, read on. Please don't close it: I choose to be anonymous just not to be identified.

About to be on the job market, disenchanted with academia, bored by the teaching load in grad school, I have to make ends meet (by, say, finding a job somewhere). I've seen math people finding non-math jobs. But they seem to know some math that can be applied'', e.g. stochastic process or combinatorics. Trained as an algebraic geometer, I don't have a strong background on those stuff or anything that helps job hunting ---- knowing things about the Weil conjecture doesn't seem to be a plus. I don't think I will enjoy a teaching job in college much either.

I would guess I'm not the only one in this situation.

Question: Can anyone here give some career suggestions?

(P.S. I'm in US now but not a US citizen, so National Security Agency or similar jobs appear in answers to similar posts are really not in my list.)

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## closed as off topic by Tom Leinster, Vladimir Dotsenko, Chris Godsil, Harry Gindi, Daniel MoskovichAug 27 '12 at 5:17

Questions on MathOverflow are expected to relate to research level mathematics within the scope defined by the community. Consider editing the question or leaving comments for improvement if you believe the question can be reworded to fit within the scope. Read more about reopening questions here.If this question can be reworded to fit the rules in the help center, please edit the question.

Anything a Banach algebraist can? By which I mean, it may be best to try and make use of the experience you have gained as a graduate student rather than the content you have learned over that time. – Yemon Choi Aug 26 '12 at 5:51
Algebraic geometry does have applications to robotics, error-correcting codes and various other areas. Do any of these interest you? Not that this is a guarantee of work by any means, but it might suggest a direction in which to focus. On the other hand, beware of focusing too narrowly. – J W Aug 26 '12 at 7:06
An algebraic geometer would, I assume, be someone who is smart, can analyze problems, and articulate their solution in either verbal or written form, or, even better, both. Such a person should be able to make their way in the world without too much difficulty. – Geoff Robinson Aug 26 '12 at 16:49
Frankly, I was surprised this question stayed open as long as it did (as I am about a number of recent questions). Nothing to do with algebraic geometry, which is one of the most popular topics at this site. But like many other questions where an anonymous somebody is seeking advice from people who don't know him/her, it's really off-topic (and there have been many precedents for that judgment). But seeing as this is probably going to be reopened, it seems wise to bring the discussion to meta (please vote this up so people can see). – Todd Trimble Aug 26 '12 at 20:46
Sorry, meta: tea.mathoverflow.net/discussion/1434/career-advice-question/… Please vote up so people can see. – Todd Trimble Aug 26 '12 at 21:09

I voted to close this question earlier, but on the principle "if you can't beat 'em, join 'em", I'll say this. I know of any number of former academic mathematicians who decided to leave academe to pursue a career as an actuary. They come from all over: algebraic geometry, number theory, logic, quantum field theory, you name it. The bit about having to have some iron in applied mathematics here just doesn't hold true: what counts to prospective employers is being able to think clearly and precisely and have good mathematical sense. Being able to pass actuarial exams (the first few of which are math-y but doable with little sweat by an ex-mathematician) goes a long way towards establishing your cred.

The pay tends to be pretty good, and actuarial work tends to be stable, certainly compared to what struggling academics put up with. (I am not an actuary myself but I am married to one.) A lot of mathematicians I know are very happy with this career choice and have never looked back.

Perhaps the real point is that this is merely an example. I support what Angelo said: "a PhD in mathematics is highly regarded in the 'real world', even when it is in pure mathematics." Your prospects are probably very bright.

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People not originally from the US (or at least not from an English speaking country) tend to have a little more trouble with this question, because they have more difficulty understanding the following:

Traditionally in the United States, higher education is not specific training for a career. Rather, it is training to be a thoughtful contributing citizen. Skills necessary for being a thoughtful contributing citizen tends to be useful in all kinds of intellectual and non-intellectual work. Companies looking for intelligent employees therefore look for intelligent, hard-working people who have done well at studying something, not necessarily anything related to what they do.

As a graduate of a liberal arts college, I saw music majors and English majors get all kinds of jobs. What were the most common?

1) Sales. Plenty of companies need people to sell something. One might sell large software packages to businesses. One might sell re-insurance to insurance companies. One might sell medical devices to doctors. Since salespeople generally are mostly paid on commission, hiring a salesperson is low risk. Traditionally, salespeople know almost nothing about what they are selling; they are just good at convincing people to buy whatever they are selling.

2) Technical sales support. Someone has to understand what they are selling. Except technical sales support people are not actually experts in what is being sold. They've just had a little more training so they can answer the 98% of questions that aren't actually that technical.

3) Software. If you've learned how to program, the vast majority of jobs in the software industry don't require that much software engineering knowledge, and you've probably learned enough. We are not talking about making a database or operating system run faster; we're talking about changing the interface of MathOverflow to move the answer box 5 pixels to the right, or just making sure this webpage is displaying the answers to this question and not some other random question.

4) Consulting. There is both software consulting (see software) and management consulting. This involves being in a group that is hired to look at a company's operations, gather qualitative and quantitative data, and make recommendations. The whole point is that you are mostly not experts and therefore (at least supposedly) have a fresh view on what they are doing and can recommend the obvious stupid things they are missing.

5) Investment banking. See Sales, except you're selling financial products to companies. Except that in this industry, sales is frequently done in teams, so your role might be closer to that of a consultant (assembling data to support the sale) than an actual salesperson.

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Although not an algebraic geometer, I recently went through a similar experience (I actually posted one of the questions to which you linked.) One of the reasons I became disenchanted with academia was that I struggled to learn algebraic geometry for many years but failed. So I hope you appreciate that this advice is coming from someone who is not as smart as you!

After returning to my own country following an unsatisfactory year teaching at a liberal arts college, I did some part-time teaching at my old university while I researched possible careers. Attracted by the idea of earning a lot of money, my first thought was finance and I read several books about the stock market and the history of money. By the way, it's very hard to find textbooks about finance which don't "take sides". The very best book I found, coming from zero knowledge of economics, was "Introduction to Money" by Honor Croome.

We don't have quants in this country, but the career which appealed to me most was actuary, and I contacted some actuaries via the University Careers Service. The main actuarial recruiter in my city was not interested in me, saying that I was "over-qualified" (an expression you will probably soon be hearing a lot) and would find the job boring. Most of the actuaries I talked to were very friendly but were baffled that someone who had a PhD in mathematics would want to start a new career from the beginning.

Meanwhile, I realised that any job involving maths was going to require some knowledge of programming, so I began to learn Python. This was quite fun, although I did not get very far before switching to Javascript, because I wanted to be able to share my code more easily. An excellent resource is a free book called "Eloquent Javascript". I really recommend this if you have no programming experience. I didn't get very deeply into programming, but learned enough to do simple calculations and talk about things like "APIs", "dynamic typing" and other jargon.

I attempted to get a full-time teaching job at my old university but failed. However, everyone was very impressed by my lecture. I decided that I wanted to make a positive contribution to the world and so began to consider mathematical ecology, especially fisheries. I talked to some people and they recommended that I learn Bayesian Statistics, so I got a book and started to work on this. I rapidly became starstruck by the beauty and power of the Bayesian approach. It was also a source of helpful programming exercises (Gibbs samplers etc.) and motivated me to learn R, which is the industry standard among academically-oriented statisticians.

Around this time, I failed to get a job in fisheries. It turns out that people don't really care about whether you are capable of doing the job; they want you to "demonstrate an interest" in it. It's a bit like how, when applying for a liberal arts position from a research university, you have to harp on about how committed you are to the liberal arts philosophy. Otherwise your application goes directly into the trash.

I was at a loose end and a new semester was starting, so I sat in on two courses, one on Bayesian stats and the other in data mining. The data mining was helpful for learning R, because it's a very scatty language and there are all kinds of little tricks you need to know. The Bayesian stats was an opportunity to work through more Bayesian stats, with exercises.

Around this time, I contacted an ecologist in the statistics department who happened to have a problem to work on, so I started working on this. After a couple of months I was able to amke progress on it and I'm hoping we will eventually get a publication out of it, which will certainly boost my credibility with the ecology crowd.

Anyway, at this point (about a year after my search started) I suddenly got a job in the tax department. The reason why I got this was because my boss is a mathematician. It turns out that there are lots of mathematicians in industry who were once in the same position as I was, and you now are. They like to hire mathematicians, just like how people who have emigrated to a different country like to hire people from the same country as them. Another mathematician was hired at the same time as me. I don't view the new job as a permanent thing that will go on forever, but I really like my colleagues. I do have to deal with meetings and people blathering about "going forward", "taking the first cab off the rank", "passing the ball" and all manner of similar phrases. On the other hand, I can bask in the feeling that I am helping to stick it to those nasty finance people who care about nothing but money ...

Ultimately I am hoping to return to academia (as a statistician) or become a statistical consultant if I can, and I want to move to Canada one day.

I guess the most useful pieces of advice for someone in this position are probably the following:

1. The only way to get a job is via personal connections.
2. Appearances are very important.

and (more an obervation than a piece of advice)

1. Every real-world problem is ultimately about maximising some hideously complicated function.

I am sorry if you didn't find this too helpful, but I thought it might be useful to hear from someone who has very recently been in a similar position. It took me a year to find a job, so don't lose heart!

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Wait, you wanted to used your power for good and you went to the tax department? That sounds ironic... (Oh, I forgot you are not in U.S.) – temp Aug 27 '12 at 6:58
BTW, "use my power for good" seems to be a much better title then this post, which is kind of like "algebraic geometer is useless outside academia". – temp Aug 27 '12 at 7:00

First I wish you good luck and second I think this is appropriate question for forum.

About 3 years ago I transferred from academia to industry, so I can partly understand yours difficulties.

Algebraic geometry is of some use in some industry. On the other hand I am not sure it that it is easy (or even possible) to find such jobs.

Example 1. Cryptography. Some private companies also research it e.g. for the purpose of cloud computing (popular topic now). Modern schemes to secure data involve Weil pairing.

Example 2. Error correcting codes. There are Goppa codes built on algebraic-geometry ideas. There is also current research how to use algebraic number theory in space time codes Perfect Space Time Block Codes.

Example 3. There are applications to robotics. They are described in book Ideals, Varieties, and Algorithms by David A. Cox, John B. Little, Don O'Shea,

Well, I think the situation with research jobs in US, is better than in Russia, so if I was able find one in Russia, you have more chances there:) As another advise let me tell a bit of my story - I applied to some vacancy and was sure that they will not even interview me, cause there was big list of requirements and I knew nothing about it, except small item at the end about matrix calculations, which also was not my strong point, nevertheless to my great surprise I was hired by them. Actually I was lucky since in Russia it is difficult to find experts which they wanted to find, so they weaken the requirements. The moral of this story - just apply everywhere, does not matter it seems very related to yours experience or not.

PS

May be it is good to allow math job advertisement on MO ? On MSE there some kind of banners at the right side of the screen, sometimes they inform about existence of arXiv. May be it would be good for community ? People can learn what kind of jobs are of use in industry... I am not sure by my feelings are that there are not so many bridges between math and real world it would be great to built as more as possible...

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@Alexander: there are already other websites that focus on advertizing jobs such as www.mathjobs.org. – Patricia Hersh Aug 26 '12 at 19:25
@Patricia Hersh Well, you are right, on the other hand why not to have one more ? Competition makes everything better. Also currently I visit MO almost everyday and the day when I visited ams site is about 5 years ago... Why not to combine fun (MO) with use (jobs) ? – Alexander Chervov Aug 26 '12 at 19:31
@Alexander: I'm actually in favor of allowing a little bit of career advise on MO, provided it is of general interest, somewhat math specific, not likely to lead to arguments, and on a topic where the community could say something intelligible without specific knowledge of the OP. People who don't want to participate in such things can stay out of such questions. But that said, to me it seems like there are better places for job ads. – Patricia Hersh Aug 26 '12 at 19:38
@Patricia The existence of the question mathoverflow.net/questions/23525/… might be considered as a sign that something can be improved, there is demand on this :) I mean if you have a permanent job - are you often on job hunting site ? But when someone teach students does not he/she should be somewhat responsible for trying to adapt his course for something which might be useful for students ? How can one now this if he/she does not visit job sites ? – Alexander Chervov Aug 26 '12 at 19:51
Example - when people teach alg.geom. do they include applications to cryptography or error-correcting codes or anything else ? CLassical textbooks - Hartshorne, Griffiths Harris, Shafarevich - do not do this... – Alexander Chervov Aug 26 '12 at 19:53

Should you be interested in applying algebraic geometry, IMA Thematic Year on Applications of Algebraic Geometry may give you some inspiration, as can searching for "algebraic geometry applications" or similar. You may also wish to take a look at the Society for Industrial and Applied Mathematics's Activity Group on Algebraic Geometry SIAM Algebraic Geometry group or visit their wiki SIAM Algebraic Geometry wiki.

Of course, you may need to take courses or do self-study in certain application areas, if they appeal to you. You may also need to develop skills in algorithms or computational techniques, assuming your background does not already include these.

All advice is perilous, but I suspect that you could increase your employment options if you know at least something of programming, statistics and optimization techniques. Perhaps there are opportunities to work for government institutions in areas such as planning or infrastructure for instance. You may find areas such as complex networks or machine learning quite accessible with your advanced background and ability to cope with abstraction.

Whatever you decide to do, the very best of luck!

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I think first you have to answer the following question:

Do you wish to continue doing some kind of algebraic geometry or are you willing to adapt?

If you are willing to adapt, then several choices open up:

1. Search out which jobs might interest you (ok, this question on MO is a start)
2. Learn at least some of the skills needed to get those jobs (e.g., an additional degree or qualification)
3. Become a consultant --- easier said than done!

If you are unwilling to adapt, or wish to only partially adapt, then:

1. Maybe do some algebraic statistics --- you'll profitably use your AG skills there
2. Some research lab might be interested
3. Do a postdoc in a related yet different enough field to give you wider perspective
4. Take a month off to discover yourself, and figure out what is it that you really want? The benefit of asking, and perchance answering this last question will be greater clarity, and confidence. Disillusionment might evoke a cynical response, but really, in the long-run, you should answer this question to yourself.

I wish you luck and above all clarity

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I believe that mathematics training (of any type) is excellent preparation for work as a software engineer and, incidentally, for solving typical software engineering interview problems.

If you have a little proficiency in computer programming, or could teach yourself a little, you might land an engineering internship position. An internship working closely with one or two highly experienced engineers would be ideal. In any event the habits of thinking you've practiced as a mathematician would greatly accelerate your development in this field.

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Will you please mention the software engineering problems which a mathematician ( who is skilled in algebraic geometry ) may attack them. – Aurora Aug 26 '12 at 9:12
I think companies that make math software like wolfram, mathworks, waterloo maple etc. may be interested in such a mathematician.... – Suvrit Aug 26 '12 at 10:06

The "Software Perception Engineer" position could be appropriate depending on your background: http://bostondynamics.com/bd_jobs.html

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Steven M. LaValle's "Planning Algorithms" could be worth taking a look at if you're interested in motion planning. It's kindly made available online by the author at planning.cs.uiuc.edu. Some of the material in chaps 3, 4 and 6 touches on (real) algebraic geometry. There's also Jon M. Selig's "Geometric Fundamentals of Robotics," which draws on topics such as Lie groups, algebraic geometry and differential geometry. – J W Aug 26 '12 at 14:53
From the ad: "should have a strong software engineering background ....Must have: Experience with perception or motion planning on real-world robots." The job sounds fascinating, but I don't think the OP is who they're looking for. – M T Aug 26 '12 at 17:10
@mt: many mathematicians have a far more diverse background than a vanilla Ph.D on some sanitised, isolated subject that civilians have never heard of. And a lot of companies overlook imperfections in applications if the applicant is well-rounded enough in the general area they're looking for. – Ryan Budney Aug 26 '12 at 18:43
He is an algebraic geometrer. What makes you think, the manager is going to pay money to bring him on board for an interview? – Turbo Aug 28 '12 at 3:57

Your situation with algebraic geometry is probably more similar to that of humanities graduate students than to that of students of applied math or engineering.


text:
## Stream: new members

### Topic: type vs set for finite measure

#### Iocta (Sep 02 2020 at 01:02):

I'm not sure if I want

def F (X: Ω → ℝ): ℝ → {x : nnreal | x ≤ 1} :=
λx,
let y := p {ω | X ω ≤ x}
in ⟨ y.to_nnreal, sorry ⟩

or to define a type {x : nnreal // x ≤ 1} and use that instead. Either way I don't know how to use the definition to show that p <=1.

Context is

import algebra.big_operators
import algebra.big_operators.intervals
import measure_theory.measure_space

open measure_theory

open_locale big_operators

noncomputable theory

variables {Ω : Type*} [measurable_space Ω] (p : measure Ω) [probability_measure p]

def F (X: Ω → ℝ): ℝ → {x : nnreal | x ≤ 1} :=
λx,
let y := p {ω | X ω ≤ x}
in ⟨ y.to_nnreal,
begin
simp at *,
-- y: ennreal := ⇑p {ω : Ω | X ω ≤ x}
-- ⊢ y.to_nnreal ≤ 1
end
⟩

#### Iocta (Sep 02 2020 at 01:05):

e.g. unfold doesn't seem to work on structures so idk how to expand the set.univ = 1

#### Kevin Buzzard (Sep 02 2020 at 06:35):

There is Icc 0 1 for the interval [0,1].

#### Iocta (Sep 02 2020 at 06:36):

How should I think about "do I want a type or a set"?

You want a type

#### Kevin Buzzard (Sep 02 2020 at 06:37):

They're a more primitive notion

#### Kevin Buzzard (Sep 02 2020 at 06:38):

Of course I'm being a bit silly here. You want a set if you want to do intersections, unions etc

#### Kevin Buzzard (Sep 02 2020 at 06:39):

But the target of a function had better be a type. There's a coercion from sets to types though, and if you keep your head it's not hard to use. A term of type weird up arrow s is a pair consisting of a term of type X and a proof that it's an element of s

#### Iocta (Sep 02 2020 at 06:49):

def probability : Type :=
let interval : set _ := (Icc 0 1)
in {x : _ // x ∈ interval }

Do I want in the _ real/nnreal/ennreal/complex/doesn't matter?

#### Iocta (Sep 02 2020 at 07:00):

anyway that leaves me with

y: ennreal := ⇑p {ω : Ω | X ω ≤ x}
⊢ ↑(y.to_nnreal) ≤ 1

but I can't unfold probability_measure at p to get the <= 1, is there a similar thing to unfold but for structures?

#mwe (sorry)

see above

#### Iocta (Sep 02 2020 at 07:04):

(updated)

import algebra.big_operators
import algebra.big_operators.intervals
import measure_theory.measure_space

open measure_theory set

open_locale big_operators

noncomputable theory

variables {Ω : Type*} [measurable_space Ω] (p : measure Ω) [probability_measure p]

def probability : Type :=
let interval : set ℝ := (Icc 0 1)
in {x // x ∈ interval }

def F (X: Ω → ℝ): ℝ → probability :=
λx,
let y := p {ω | X ω ≤ x}
in ⟨ y.to_nnreal,
begin
simp,
end
⟩

#### Scott Morrison (Sep 02 2020 at 07:09):

The API for probability_measure seems to be basically nonexistent. Someone should fix this!

#### Scott Morrison (Sep 02 2020 at 07:09):

At the moment it looks like you have argue that the measure is at most the measure of set.univ, which is then equal to one.

#### Scott Morrison (Sep 02 2020 at 07:10):

Obviously there should be a one-step lemma saying exactly that.

#### Sebastien Gouezel (Sep 02 2020 at 07:15):

Note that it is probably a bad idea to let the probability take value in the set [0, 1], because we keep adding or subtracting probabilities in proofs, and this type doesn't have an addition nor a subtraction. Why not simply use the real-valued function?

#### Iocta (Sep 02 2020 at 07:18):

sometimes I will want to use that the value is <= 1, so I could put that into the type and then it would be readily available

#### Iocta (Sep 02 2020 at 07:20):

e.g. next I want to say the right-hand limit of the distribution function is 1. it seems convenient to know that it's increasing and <=1. Is that the wrong way to go?

#### Scott Morrison (Sep 02 2020 at 07:24):

Just have a separate lemma that it is at most one. Bundling that into a subtype doesn't seem to gain much.

#### Iocta (Sep 02 2020 at 07:51):

What do h and H mean?

import algebra.big_operators
import algebra.big_operators.intervals
import measure_theory.measure_space

open measure_theory set

open_locale big_operators

noncomputable theory

variables {Ω : Type*} [measurable_space Ω] (p : measure Ω) [probability_measure p]

lemma probability_1 : p univ ≤ 1 :=
begin
sorry,
end

def F (X: Ω → ℝ) : ℝ → ennreal :=
λx, p {ω | X ω ≤ x}

lemma F_le_1 (X : Ω → ℝ) : F p X ≤ 1 :=
begin
intros x pr h,
-- tactic failed, there are unsolved goals
-- state:
-- Ω : Type u_1,
-- _inst_1 : measurable_space Ω,
-- p : measure Ω,
-- _inst_2 : probability_measure p,
-- X : Ω → ℝ,
-- x : ℝ,
-- pr : nnreal,
-- h : pr ∈ 1 x
-- ⊢ ∃ (b : nnreal) (H : b ∈ F p X x), b ≤ pr
end

#### Iocta (Sep 02 2020 at 20:08):

How can I solve this using measure_univ?

import algebra.big_operators
import algebra.big_operators.intervals
import measure_theory.measure_space

open measure_theory set

open_locale big_operators

noncomputable theory

variables {Ω : Type*} [measurable_space Ω] (p : measure Ω) [probability_measure p]

example : p univ = 1 := sorry

#### Sebastien Gouezel (Sep 02 2020 at 20:11):

example : p univ = 1 := measure_univ

#### Sebastien Gouezel (Sep 02 2020 at 20:15):

You can find this by trying by library_search and following whatever advice it gives you, or by looking at the type of measure_univ and noticing it has no explicit argument: the fact that the measure is a probability measure is an assumption written between [...], which means that Lean will check this assumption all by itself (through a process called typeclass inference that you don't need to understand when you start with Lean).

#### Iocta (Sep 02 2020 at 20:17):

Oh oops, not sure how I missed that.

#### Iocta (Sep 02 2020 at 20:20):

any idea what h : pr ∈ 1 x means in the above snippet? what is 1 x? it looks like 1 is somehow a set-returning function...

#### Reid Barton (Sep 02 2020 at 20:23):

What made you think intros x pr h was a good idea?

#### Reid Barton (Sep 02 2020 at 20:23):

It looks like you've opened up the definition of ennreal

#### Iocta (Sep 02 2020 at 20:24):

I didn't know what else to do, and hint suggested it

#### Reid Barton (Sep 02 2020 at 20:24):

I would unsuggest it

ok

#### Reid Barton (Sep 02 2020 at 20:25):

Your goal is to prove an inequality--intros isn't a logical step unless you know what that inequality really means.

#### Reid Barton (Sep 02 2020 at 20:27):

presumably the argument you want is that whatever set we're taking the probability of, it's contained in univ, which has measure 1, so the original probability is at most 1

#### Reid Barton (Sep 02 2020 at 20:27):

really, it should be a lemma that already exists

#### Iocta (Sep 02 2020 at 21:35):

Is that lemma measure_lt_top?

Last updated: May 08 2021 at 03:17 UTC

format: plain


text:
University Chemistry ›› 2020, Vol. 35 ›› Issue (8): 129-134.

Special Issue: 无机化学课程教学

• Self Studies •

### The Quantitative Calculation of pH in Monoacid/Monobasic Solution in Teaching of Inorganic Chemistry

Ting Wang, Zongpei Zhang, Zhanhang He(), Kai Li()

• Received:2020-03-24 Accepted:2020-04-09 Published:2020-05-18
• Contact: Zhanhang He,Kai Li E-mail:hezhanhang@139.com;likai@zzu.edu.cn

Abstract:

The quantitative calculation of pH of monoacid/monobasic solution is a basic problem for inorganic chemistry teaching. The qualitative description and quantitative calculation of pH are connected by approximation conditions. It is very important for the students to understand these approximation conditions, which will help them solve problems about ionic equilibrium in aqueous solution. However, how to use these approximation conditions correctly in solution of low concentration and weak acids is often difficult. Even in some textbooks, the description of concepts is not accurate and not consistent with the associated courses. Thus, to solve the problems mentioned above, the derivations of the approximation conditions are introduced and examples are analyzed in detail in this paper. The problems of quantitative calculation of pH of monoacid/monobasic solution which should be paid attention to in the course teaching of inorganic chemistry are discussed.

MSC2000:

• G64


text:
# Calculating implied volatility from moneyness/volatility values for date

For an option expiring at a particular date I have

Moneyness 0.4,0.7,0.85,0.95,1,1.05,1.15,1.3,2.5
Vol       0.105,0.075,0.045,0.045,0.202,0.045,0.045,0.075,0.085

How do I get the volatility for an option with a particular moneyness? Do I interpolate with an 8th degree polynomial? How would I then handle cases where moneyness is outside the range? Or do I need to do curve fitting?

The interpolation of the implied vol surface is no easy task unfortunately and it is subject of extensive research.

This is because you want the vol surface to have some nice characteristics, e.g.: be smooth, non arbitrable, etc.

Two approaches exist:

• Assuming a parametric form for the volatility surface and calibrating it on the quoted implied volatilies.
• Interpolation of the quoted implied volatilities. In this case, linear or polynomial might not be a good idea (not smooth), try cubic splines instead.

I will just add that everthing depends on what you want to do with this volatility afterwards.

• I will use them to calculate greeks. I am going with cubic spline but it doesn't work for values oustide abscissa's range. I don't know If i should just clamp it – Ivan Anatolievich May 18 '18 at 10:09

I would say the best solution will be curve fitting, which is definitely not an easy solution.

Depends on whether you are fitting interest rates or stocks/commodities. You might try SABR for the former and SVI for the letter. There are lots of papers about them that you should easily find online.

However, it also depends on you are doing research or developing production-level. If the former, you can easily find open source old in R or python to quickly play and visualize. If the latter, you might need to spend more time to handle edge cases solving nin-converging issues. Fittings always have many tricky things you need to figure out.


text:
Saltar al contenido principal

# 5.4: Integrales impropias

5.4: Integrales impropias is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.


text:
# Cylindrical optimization problem

A closed cyliindrical container has a volume of 5000in^3. The top and the bottom of the container costs 2.50$in^2 and the rest of the container costs 4$in^2. How should you choose height and radius in order to minimize the cost?

v=pi(r)^2

Unfortunately my attempt at this problem is feeble.
I have trouble finding two equations.
past that, i can derive them and solve.
any help would be most appreciated,
thankss

Related Calculus and Beyond Homework Help News on Phys.org
Write an equation using the fact that the volume of the cylinder is known.
Use this in the expression to be minimized.


text:
# Lab 5: The Drowning of Sacramento

## Learning Objectives

After completing this lab you will be able to:

• translate ordinary differential equations into a computer function that evaluates the equations at any given point in time
• numerically integrate ordinary differential equations with Octave/Matlab's ode45
• create complete and legible plots of the resulting input, state, and output trajectories
• create a report with textual explanations and plots of the simulation
• use a simulation to design surge tanks for a hydraulic system

## Introduction

Sacramento has built a new hydroelectric power plant. A previous company designed the plant without performing a simulation before the construction. After the plant was completed, and the California monsoonal rains came, the surge tanks could not withstand the dynamics of the flow and the city flooded. Fortunately, the people of Sacramento are great swimmers. Later it was found that the company was staffed with graduates from some junior university from the bay area. The reputation of your fine UC Davis education has gained the confidence of Sacramento's city council, which has refused to pay the bad company, and has hired you to redesign the surge tanks so the town won't have to hire as many lifeguards this spring.

Surge tanks act as hydraulic "springs", absorbing the pressure increase associated with stopping the momentum of the fluid in the pipe. However, because of the reconstruction, our surge tanks must be drilled in stone and this is very expensive for large diameter holes.

## Model Description

Figure 1 provides a hydraulic schematic of a reservoir that feeds a hydroelectric turbine. There are two surge tanks that store and release hydraulic energy to help provide a steady flow through the turbine.

For this system assume that the tank areas $$A_t$$ will be significantly larger than the pipe area, $$A_p$$, e.g. $$A_t > 5 A_p$$, so that there is negligible tank inertia compared to the pipe inertia. Also assume that the tank and reservoir inlets have negligible resistance compared to the pipe resistances.

The bond graph for this system is shown below in figure 2.

The pipe resistances in this system are nonlinear and behave according to the constitutive law:

\begin{equation*} \Delta P = C_f Q \left| Q \right| \end{equation*}

which is shown graphically in Figure 3.

You will need to assign causality to the bond graph, number the bonds, and derive the system equations. You should end up with four differential equations. You will have two fluid momentum state variables (one for each section of the pipe) and two volumetric displacement state variables (one for each tank).

### Constant parameters

Symbol Description Value Units
$$\rho$$ Density of water 1000 $$\frac{\textrm{kg}}{\textrm{m}^3}$$
$$g$$ Acceleration due to gravity 9.81 $$\frac{\textrm{m}}{\textrm{s}^2}$$
$$A_p$$ Cross sectional area of the pipe from the reservoir to the turbine 0.1 $$\textrm{m}^2$$
$$P$$ Hydrostatic pressure (note that the pressure heights between nodes are relative). $$\rho g \Delta h$$ $$\frac{N}{m^2}$$
$$C_f$$ Fluid pipe resistance constant (see figure 3 for $$\Delta P$$ vs $$Q$$) 49000 $$\frac{kg}{m^7}$$
$$L$$ Pipe section lengths 50 $$\textrm{m}$$
$$I_p$$ Fluid inertia of pipe sections $$\frac{\rho L}{A_p}$$ $$\frac{kg}{m^4}$$
$$A_t$$ Tank areas (you will find the maximum tank area by simulating different values of $$A_t$$. Use increments of 0.05 $$\textrm{m}^2$$. To be determined $$m^2$$
$$C_t$$ Fluid capacitance of each tank $$\frac{A_t}{\rho g}$$ $$\frac{m^5}{N}$$

Remember that in fluid systems, we use Q for volumetric flow (not displacement) and V as volume (not velocity).

### Initial Conditions

Determine the initial conditions from the equations of motion. The system will begin in equilibrium (all state derivatives are equal to zero), with an initial turbine flow of $$Q_0=1.5\frac{\textrm{m}^3}{\textrm{s}}$$. You will need to find initial conditions for every state variable. None of the initial conditions will be zero. Develop the initial conditions equations in terms of the system parameters and let Matlab calculate the exact values. Include how you determined the initial conditions in your lab report.

### Inputs

Define all system inputs for the effort and flow sources. The effort sources are the pressures due to gravity and are constant with respect to time. The flow source is the turbine flow $$Q_0$$. When the turbine is delivering power the steady state flow $$Q_0$$ out of the pipe is $$1.5\frac{m^3}{s}$$. The turbine flow begins as $$Q_0=1.5\frac{m^3}{s}$$ at $$t = 0$$. At some time of your choosing, the turbine will begin to turn off. Over the next 0.15 seconds, the turbine shuts down and flow $$Q_0$$ decreases linearly to zero. Define $$Q_0$$ before, during, and after the shut-down period in an input function file.

### Outputs

You will also likely need to take turbine flow ($$Q_0$$) as an extra variable. You may find it useful to define the tank heights as extra outputs as well.

## Simulation

Your goal is to find the minimum cross-sectional area of the surge tanks, so that the flow to the turbines can be shut off quickly without overflowing the tanks and drowning the people of Sacramento.

Choose a starting tank area $$A_t$$ and simulate the system. Determine the height of the water in the tanks and plot the heights as a function of time. Plot the height of the water in the tank. Increase or decrease the tank area by increments of 0.05 $$\textrm{m}^2$$ until you find the smallest possible tank area that does not cause the tanks to overflow when the turbine is shut off Refer to Figure 1 to find the maximum water height in either tank.

Determine your simulation time parameters. In order to gauge how long and what time step to use to simulate the system you will need an idea of the natural frequencies. Since the system is nonlinear, a straight forward frequency analysis is not possible. But since the non-linearity of the system is in the resistance, a rough estimate can be calculated using only the compliance and inertial properties of the system. Here is a hint:

\begin{align*} T = \frac{1}{f_n} \\ f_n = \frac{\omega_n}{2\pi} \\ \omega_n = \sqrt{\frac{1}{\textrm{compliance} \times \textrm{inertia}}} \end{align*}

## Deliverables

1. Show the bond graph with both assigned causality and numbered bonds.
2. Show the system equations that you derive from the bond graph.
3. Include calculations and explanations for initial conditions, natural frequencies, time parameters, and any other such calculations.
4. Plots of the input and tank heights vs. time for the desired tank area (these do not have to be on the same plot).
5. Discussion of results
• Which tank came closer to overflowing? Why?
• How do the calculated natural frequencies compare to the vibration periods seen in your plotted results? Why is there a difference?
6. Matlab code for the main file, state derivatives, inputs, output functions. Code should follow the best practices form.

The report should follow the report template and guidelines.

## Assessment Rubric

Points will be added to 40 to get your score from 40-100.

Functions (10 points)

• [10] All functions are present and take correct inputs and produce the expected outputs.
• [5] Most functions are present and mostly take correct inputs and produce the expected outputs
• [0] No functions are present.

Main Script (10 points)

• [10] Constant parameters only defined once in main script(s); Integration produces the correct state, input, and output trajectories; Justified choices in number of time steps and resolution are chosen and explained
• [5] Parameters are defined in multiple places; Integration produces some correct state, input, and output trajectories; Poor choices in number of time steps and resolution are chosen or not explained
• [0] Constants defined redundantly; Integration produces incorrect trajectories; No clear choices in time duration and steps

Explanations (10 points)

• [10] Explanation of dynamics are correct and well explained; Explanation of the vibration period and frequency is correct and well explained; Plots of appropriate variables are used in the explanations
• [5] Explanation of dynamics is somewhat correct and reasonably explained; Explanation of vibration period and frequency is somewhat correctly describes results; Plots of appropriate variables are used in the explanations, but some are missing
• [0] Explanation of damping is incorrect and poorly explained; Explanation of vibration and frequency behavior incorrectly describes results; Plots are not used.

Report and Code Formatting (10 points)

• [10] All axes labeled with units, legible font sizes, informative captions; Functions are documented with docstrings which fully explain the inputs and outputs; Professional, very legible, quality writing; All report format requirements met
• [5] Some axes labeled with units, mostly legible font sizes, less-than-informative captions; Functions have docstrings but the inputs and outputs are not fully explained; Semi-professional, somewhat legible, writing needs improvement; Most report format requirements met
• [0] Axes do not have labels, legible font sizes, or informative captions; Functions do not have docstrings; Report is not professionally written and formatted; Report format requirements are not met

Contributions [10 points]

• [10] Very clear that everyone in the lab group contributed equitably. (e.g. both need to do some coding, both work on bond graph, both should contribute to writing)
• [5] Need to improve the contributions of one or more members
• [0] Clear that everyone is not contributing equitably


text:
Tag Info

12

The rationale behind the context requirements is, ultimately, that we want well-written questions. I understand what you're getting at: if you post a simple one line PSQ and a follow it up with an answer, then one might be inclined to think the answer could serve in some sense as context, especially if it is nice and detailed. But structuring things in that ...

7

Just a partial answer. In my opinion, some questions that is well-received in puzzling SE will be considered missing context when posted in MSE. Using your example: The non-negative integers are divided into three groups as follows: \begin{align*} A &= \{0,3,6,8,9, \cdots\},\\ B &= \{1,4,7,11,14,\cdots\}, \\ C &=\{2,5,10,13,\cdots\} \end{align*} ...

6

You can ask that on the main site. But I suggest First you search the site for similar questions. The topics that you are interested in are very standard and you can find a lot of these questions under the tag "book-recommendation" (This is what I found under the tags [book-recommendation] and [linear-algebra], ordered by votes). If you have some ...

Top 50 recent answers are included


text:
# Does same character table imply isomorphic abelianizations?

We know two finite groups with the same character table might not be isomorphic (e.g. $D_4$ and $Q_8$), but the sizes of their abelianizations are equal (in fact equal to the number of linear characters, which can be read off the character table).

Can we also say the abelianizations of these groups are isomorphic, or is this not necessarily the case?

Yes. The $1$-dimensional characters form a group under pointwise multiplication, and the abelianization is (noncanonically) isomorphic to this group. (It is canonically isomorphic to the Pontryagin dual of this group.)
• @Richard: a $1$-dimensional character is a homomorphism $G \to \mathbb{C}^{\times}$, or equivalently a homomorphism $G/[G, G] \to \mathbb{Q}/\mathbb{Z}$ (since $G$ is finite, the image of a character lands in roots of unity). If $A$ is a finite abelian group, then the group of homomorphisms $A \to \mathbb{Q}/\mathbb{Z}$ (which is one possible definition of the Pontryagin dual) is (noncanonically) isomorphic to $A$. This follows from the structure theorem for finite abelian groups, together with the observation that this is true if $A$ is cyclic. – Qiaochu Yuan Jan 5 '16 at 3:09


text:
An easy geometry-definition file generator for PENELOPE PENGEOM

# PENGEOMGEN

Python library for easy generation of PENELOPE PENGEOM geometry-definition file.

PENGEOM can describe any material system consisting of homogeneous bodies limited by quadric surfaces. Its geometry definition file is a strictly formatted text lines that define blocks of elements [1]. Write manually a geometry description file can be a long and hard task (for example, a medium complex material system may have thousands of very strictly formatted lines).

PenGeom.jar (a Java GUI application which is not part of the PENELOPE distribution package) allows the definition of the geometry and its visualization [2] through a visual interface.

pengeomgen provide a simple, light and very customizable object-oriented API for create and export the strictly formatted geometry definition file for work with PENELOPE PENGEOM. A single class allows the definition of all basic and others predefined elements.

References:

[1] F. Salvat. PENELOPE, a code system for Monte Carlo simulation of electron and photon transport. Workshop Proceedings, Barcelona, Spain. NEA/MBDAV/R(2019)1.

[2] Almansa, J., F. Salvat-Pujol, G. DÃaz-LondoÃ±o, A. Carnicer, A. M. Lallena, and F. Salvat. PENGEOM, A general-purpose geometry package for Monte Carlo simulation of radiation transport in complex material structures. Comput. Phys. Commun. 199. (2016).

## Setup

\$ pip3 install pengeomgen

## Example of usage

import pengeomgen

g=pengeomgen.GeometryDefinition("The pythonic champagne glass")

s1=g.surface(indices=( 0, 0, 0, 1, -1), zscale=9)
s2=g.surface(indices=( 0, 0, 0, 1, -1), zscale=7)
s4=g.surface_plane(zshift=-6)
s5=g.surface_plane(zshift=-6.4)
s6=g.surface_plane(zshift=-6.8)

g.surface_paraboloid("S7")
g.surface_paraboloid("S8", scale=(0.98, 0.98, 1), translation=(0, 0, 0.35))

g.surface_cone("S9", scale=(0.012, 0.012, 1), translation=(0, 0, -20))
g.surface_cone("S10", scale=(3.7, 3.7, 1), translation=(0, 0, -6))
g.surface_cone("S11", scale=(5.1, 5.1, 1), translation=(0, 0, -6.35))

g.body("B1", 2, surfaces=[(s1,-1), ("S7",-1), ("S8", 1)], comment="cup body")
g.body("B2", 1, surfaces=[("S8",-1), (s2,-1)], comment="liquid")
g.body("B3", 2, surfaces=[(s5, 1), ("S9",-1), ("S7", 1)], comment="trunk")
g.body("B4", 0, surfaces=[(s5,-1), (s6, 1), ("S11",-1)], comment="foot hole")
g.body("B5", 2, surfaces=[(s4,-1), (s6, 1), ("S10",-1)], bodies=["B3", "B4"], comment="foot body")

print(g)

# export the geometry definition file
g.export_definition("glass")

## Usage and API

The main name provided by the pengeomgen package is GeometryDefinition. This is a class name for manage the block of elements in a geometry definition file. Through its interface (methods), we can define surfaces, bodies, modules (in one line of code) using easy numeric notation and others features. Also, we can do operations like: clone, include external geometry definition, etc.

import pengeomgen

g = pengeomgen.GeometryDefinition(description="", unit="cm", angle="DEG")

• description (string): informative text
• unit (string): unit of measurement for length (translation). This parameter allows us to define the material system in the units of the schematics, as example. The current unit (see the table below) is converted to centimeter when the geometry definition file is exported
• angle (string): unit of measure for angles (rotation). This parameter can be "rad", "RAD" (radian) or "deg", "DEG" (degree)

The unit and angle parameters can be overwrite in the methods described below for construct quadric surfaces, modules and clones

Argument (string) Unit of measurement
mm, millimeter, millimeters millimeter
cm, centimeter, centimeters centimeter (default)
dm, decimeter, decimeters decimeter
m, meter, meters meter
in, inch, inches inch
ft, foot, feet foot

#### - Export geometry definition to a file

For export the constructed geometry definition to a file, we can call the export_definition method. This method has as only parameter the absolute or relative path of the output file.

g.export_definition("output_file_path")

#### - Show void inner volumes

The inner volumes can be modeled with the material value (a numeric value less or equal to zero). Itâ€™s recommended that the material value be less than zero instead of zero, Then, with the method show_void_inner_volumes we can change the sign of the materials with negative values to positive (solid material) before export it.

g.show_void_inner_volumes(show=True)

#### - Describe a material system using quadric surfaces

The methods for describe a material system using quadric surfaces, bodies and modules and make others operations are detailed in the next sections.

### Surfaces

The method surface allows the creation of quadric surfaces (reduced form by default) according to the next formatted text lines for the reduced form and implicit form respectively.

Reduced form:

0000000000000000000000000000000000000000000000000000000000000000
SURFACE (  A4) comment: reduced form
INDICES=(I2,I2,I2,I2,I2)
X-SCALE=(         E22.15       ,  I4) (DEFAULT=1.0)
Y-SCALE=(         E22.15       ,  I4) (DEFAULT=1.0)
Z-SCALE=(         E22.15       ,  I4) (DEFAULT=1.0)
OMEGA=(         E22.15       ,  I4) DEG (DEFAULT=0.0)
THETA=(         E22.15       ,  I4) DEG (DEFAULT=0.0)
PHI=(         E22.15       ,  I4) DEG (DEFAULT=0.0)
X-SHIFT=(         E22.15       ,  I4) (DEFAULT=0.0)
Y-SHIFT=(         E22.15       ,  I4) (DEFAULT=0.0)
Z-SHIFT=(         E22.15       ,  I4) (DEFAULT=0.0)

Implicit form:

0000000000000000000000000000000000000000000000000000000000000000
SURFACE (  A4) comment: implicit form
INDICES=( 0, 0, 0, 0, 0)
AXX=(         E22.15       ,  I4) (DEFAULT=0.0)
AXY=(         E22.15       ,  I4) (DEFAULT=0.0)
AXZ=(         E22.15       ,  I4) (DEFAULT=0.0)
AYY=(         E22.15       ,  I4) (DEFAULT=0.0)
AYZ=(         E22.15       ,  I4) (DEFAULT=0.0)
AZZ=(         E22.15       ,  I4) (DEFAULT=0.0)
AX=(         E22.15       ,  I4) (DEFAULT=0.0)
AY=(         E22.15       ,  I4) (DEFAULT=0.0)
AZ=(         E22.15       ,  I4) (DEFAULT=0.0)
A0=(         E22.15       ,  I4) (DEFAULT=0.0)
1111111111111111111111111111111111111111111111111111111111111111
OMEGA=(         E22.15       ,  I4) DEG (DEFAULT=0.0)
THETA=(         E22.15       ,  I4) DEG (DEFAULT=0.0)
PHI=(         E22.15       ,  I4) DEG (DEFAULT=0.0)
X-SHIFT=(         E22.15       ,  I4) (DEFAULT=0.0)
Y-SHIFT=(         E22.15       ,  I4) (DEFAULT=0.0)
Z-SHIFT=(         E22.15       ,  I4) (DEFAULT=0.0)

Method and arguments:

surface(label=None, indices=(1,1,1,1,1), scale=(1,1,1),
rotation=(0,0,0), translation=(0,0,0), starred=False, comment="", **kwargs)

• label (string): user label of the element (maximum 4 characters). This parameter is optional. If the user doesnâ€™t set it, an internal state machine assigns an unique 4-character value in the range XAAA to ZZZZ. An element without explicit label can be reference only through its instance
• indices (tuple): coefficients for the reduced form of the surface representation (I1, I2, I3, I4, I5)
• scale (tuple): scale factors for the X, Y and Z axes (X-SCALE, Y-SCALE, Z-SCALE)
• rotation (tuple): rotation values defined through the Euler angles (OMEGA, THETA, PHI)
• translation (tuple): translation values for the X, Y and Z axes (X-SHIFT, Y-SHIFT, Z-SHIFT)
• starred (boolean): if True its allow to define fixed surfaces, which will not be affected by possible translations or rotations in subsequent stages of the geometry definition
• comment (string): short text description
• return value: instance of the current Surface object

Also, we can use the assignment of a single parameter for specify the value of one compressed item in the tuples referred to the scaling, rotation and translation. The single parameters are: xscale (X-SCALE), yscale (Y-SCALE), zscale (Z-SCALE), omega (OMEGA), theta (THETA), phi (PHI), xshift (X-SHIFT), yshift (Y-SHIFT) and zshift (Z-SHIFT). In that case, the value of the single parameter overwrites the value of its respective item in the tuple, when both parameters are present.

Custom surfaces:

For grant an easy, agile and fast construction of the geometry definitions of a material system the class GeometryDefinition includes several methods that map custom and predefined reduced quadric surfaces. These surfaces are defined in the next table, with its coefficients and its method names respectively. All methods are reimplementation of the generic surface method, they just set the value of the coefficients (indices) according to the representation.

Surface Coefficients Method of the class (API)
Plane ( 0, 0, 0, 1, 0) surface_plane
Sphere ( 1, 1, 1, 0,-1) surface_sphere
Cylinder ( 1, 1, 0, 0,-1) surface_cylinder
Hyperbolic cylinder ( 1,-1, 0, 0,-1) surface_hyperbolic_cylinder
Cone ( 1, 1,-1, 0, 0) surface_cone
One sheet hyperboloid ( 1, 1,-1, 0,-1) surface_one_sheet_hyperboloid
Two sheet hyperboloid ( 1, 1,-1, 0, 1) surface_two_sheet_hyperboloid
Paraboloid ( 1, 1, 0,-1, 0) surface_paraboloid
Parabolic cylinder ( 1, 0, 0,-1, 0) surface_parabolic_cylinder
Hyperbolic paraboloid ( 1,-1, 0,-1, 0) surface_hyperbolic_paraboloid

Surfaces in implicit form:

We can use the method surface for create surfaces in implicit form setting all items of the tuple of the coefficients (indices) to zero. However, the method surface_implicit_form do this for us. There is a set of single parameters for specify the geometry of this surface: AXX, AXY, AXZ, AYY, AYZ, AZZ, AX, AY, AZ, A0 according to the model. We can set the useful values for our implementation; the others take as default value zero. For this implementation, the values of the scale are ignored in anyone of this representation (tuple or single parameter).

### Body

The method body allows the creation of homogeneous bodies limited by quadric surfaces according to the next formatted text lines:

0000000000000000000000000000000000000000000000000000000000000000
BODY    (  A4) comment
MATERIAL(  A4)
SURFACE (  A4), SIDE POINTER=(I2)
BODY    (  A4)
MODULE  (  A4)

Method and arguments:

body(label=None, material=0, surfaces=[], bodies=[], modules=[], comment="")

• label (string): user label of the element (maximum 4 characters). This parameter is optional. If the user doesnâ€™t set it, an internal state machine assigns an unique 4-character value in the range XAAA to ZZZZ. An element without explicit label can be reference only through its instance
• material (string or integer): number of the material identification conform with the convention adopted in the simulation
• surfaces (list of tuples): boundary surfaces of the current body. Each tuple contains the label (string) or the instance (surface object) of the boundary surface and its surface side pointer (integer: 1 or -1)
• bodies (list of string or body objects): boundary bodies of the current body
• modules (list of string or module objects): boundary modules of the current body
• comment (string): short text description
• return value: instance of the current Body object

### Module

The method module allows the creation of modules according to the next formatted text lines:

0000000000000000000000000000000000000000000000000000000000000000
MODULE  (  A4) comment
MATERIAL(  A4)
SURFACE (  A4), SIDE POINTER=(I2)
BODY    (  A4)
MODULE  (  A4)
1111111111111111111111111111111111111111111111111111111111111111
OMEGA=(         E22.15       ,  I4) DEG (DEFAULT=0.0)
THETA=(         E22.15       ,  I4) DEG (DEFAULT=0.0)
PHI=(         E22.15       ,  I4) DEG (DEFAULT=0.0)
X-SHIFT=(         E22.15       ,  I4) (DEFAULT=0.0)
Y-SHIFT=(         E22.15       ,  I4) (DEFAULT=0.0)
Z-SHIFT=(         E22.15       ,  I4) (DEFAULT=0.0)

Method and arguments:

module(label=None, material=0, surfaces=[], bodies=[], modules=[],
rotation=(0,0,0), translation=(0,0,0), comment="", **kwargs)

• label (string): user label of the element (maximum 4 characters). This parameter is optional. If the user doesnâ€™t set it, an internal state machine assigns an unique 4-character value in the range XAAA to ZZZZ. An element without explicit label can be reference only through its instance
• material (string or integer): number of the material identification conform with the convention adopted in the simulation
• surfaces (list of tuples): boundary surfaces of the current module. Each tuple contains the label (string) or the instance (surface object) of the boundary surface and its surface side pointer (integer: 1 or -1)
• bodies (list of string or body objects): boundary bodies of the current module
• modules (list of string or module objects): boundary modules of the current module
• rotation (tuple): rotation values defined through the Euler angles (OMEGA, THETA, PHI)
• translation (tuple): translation values for the X, Y and Z axes (X-SHIFT, Y-SHIFT, Z-SHIFT)
• comment (string): short text description
• return value: instance of the current Module object

Like the surfaces, we can use the assignment of a single parameter for specify the value of one compressed item in the tuples referred to the rotation and translation. The single parameters are: omega (OMEGA), theta (THETA), phi (PHI), xshift (X-SHIFT), yshift (Y-SHIFT) and zshift (Z-SHIFT). In that case, the value of the single parameter overwrites the value of its respective component in the tuple, when both parameters are present.

### Clone

The method clone allows the clonation of modules (bodies cannot be cloned; to clone a body that is limited only by surfaces, define it as a module) according to the next formatted text lines:

0000000000000000000000000000000000000000000000000000000000000000
CLONE   (  A4) copies one module and moves it
MODULE  (  A4) original module
1111111111111111111111111111111111111111111111111111111111111111
OMEGA=(         E22.15       ,  I4) DEG (DEFAULT=0.0)
THETA=(         E22.15       ,  I4) DEG (DEFAULT=0.0)
PHI=(         E22.15       ,  I4) DEG (DEFAULT=0.0)
X-SHIFT=(         E22.15       ,  I4) (DEFAULT=0.0)
Y-SHIFT=(         E22.15       ,  I4) (DEFAULT=0.0)
Z-SHIFT=(         E22.15       ,  I4) (DEFAULT=0.0)

Method and arguments:

clone(label=None, module="", rotation=(0,0,0), translation=(0,0,0), comment="", **kwargs)

• label (string): user label of the element (maximum 4 characters). This parameter is optional. If the user doesnâ€™t set it, an internal state machine assigns an unique 4-character value in the range XAAA to ZZZZ. An element without explicit label can be reference only through its instance
• module (string or module object): label or instance of the module to be cloned
• rotation (tuple): rotation values defined through the Euler angles (OMEGA, THETA, PHI)
• translation (tuple): translation values for the X, Y and Z axes (X-SHIFT, Y-SHIFT, Z-SHIFT)
• comment (string): short text description
• return value: instance of the current Clone object

Like the surfaces and equal to modules, we can use the assignment of a single parameter for specify the value of one compressed item in the tuples referred to the rotation and translation. The single parameters are: omega (OMEGA), theta (THETA), phi (PHI), xshift (X-SHIFT), yshift (Y-SHIFT) and zshift (Z-SHIFT). In that case, the value of the single parameter overwrites the value of its respective component in the tuple, when both parameters are present.

### Include

The method include allows the insertion of other geometry definition files according to the next formatted text lines:

0000000000000000000000000000000000000000000000000000000000000000
INCLUDE  comment
FILE=(filename.ext)

Method and arguments:

file(filename, starred=False, comment="")

• filename (string): absolute or relative path of the geometry definition file to be included
• starred (boolean): if True its allow the included file to be considered as if it were part of the main file
• comment (string): short text description
• return value: instance of the current Include object

### End

The method end cancel the reading of geometry data for the PENELOPE PENGEOM application (if this method is called in the middle of a geometry definition of some material system, all elements after this call are ignored for the application). By default this generator includes this element at the end of the geometry definition, then, its call is not mandatory.

0000000000000000000000000000000000000000000000000000000000000000
END      0000000000000000000000000000000000000000000000000000000

Method and arguments:

end()

• return value: instance of the current End object

## Project details

Uploaded source
Uploaded py3


text:
# Could we possibly have a site glossary?

This is my reply to How should abbreviations be handled?. It is here posted as a dedicated question for the site community to discuss, and hopefully (+: approve.

If the Stackexchange framework supports the process the site glossary may be a blog-post, or even simply a specific question with the title Glossary as is done here.

The answers could have relevant hyperlink, abbreviation, acronym, and description. A user could post an answer to add a term. The system would take care of the edit history, and site user sensibility would take care of the suitability of the term itself by way of upvote/downvote/flag for attention mechanism.

The glossary question itself could (assuming again the SE framework is so flexible) be made available on the 'Ask Question' page. This could allow any incoming user to refer/add to the glossary as necessary.

Of course it is moot how many people would choose to utilize/contribute to such a facility. Those who do may well be the persons who even as yet provide references/quotes. For those who do not - a 'Glossary' question may perhaps provide a visible option to do the right thing

• Thoughts please, people? If James' post remains the only reply I may just proceed with hte attempt to create the glossary question here. You have been warmed!!! (+: – Everyone Sep 7 '13 at 17:51
• It's been suggested that links to external glossaries might be helpful. Anyone have any likely candidates? – Jerard Puckett Mar 17 '14 at 17:55

Depending on what you are trying to accomplish, tag wikis might be just the thing. Most of the commonly used tags on this site have short definition (exerpts) that explain how the tag ought to be used. I'm not aware of any tags that yet have full descriptions, but these are extremely common on more mature sites. They may even take on a form resembling short Wikipedia articles. These are particularly relevant to the operation of the site and how it approaches the topic.

More general glossaries are better handled by linking to external sources within a post:

$I_{sp}$ (specific impulse)

If you can't find a succinct external resource (and you are sure the term is not generally understood) you might try asking a question on the site itself. This works especially well if you also provide an answer, if you are able.

Yes we can, it sounds from your description in your question (and linked example) that we can. All that is lacking is the creation. Barring some answer that points to a better solution then Stack Exchange Glossary - Dictionary of Commonly-Used Terms I say go for it using the existing model.

• It is unfortunate that posts do not support internal links (not even to headers). This means that for a glossary (like that linked) an entry can only reference and not link to other entries. (I asked about the existence of such on meta.writers, but apparently I was not clear that I was thinking mainly of links internal to a question+answers. [Perhaps I should be bold and make a feature request at MSO--after checking that such has not already been declined.]) – Paul A. Clayton Sep 7 '13 at 3:39
• @PaulA.Clayton - That could be solved by having an alphabetical index in the question itself, and then each answer covering at most some small number of letters in the index. Problem is, the voting on answers could shuffle their order. But the internal links could still work, at least to some degree. – TildalWave Sep 9 '13 at 2:01
• @TildalWave Even without voting, equally scored answers would be randomly arranged (I think). This also still would require some scanning to find references, but it may be the best that can be done with current constraints. – Paul A. Clayton Sep 9 '13 at 15:34
• Apparently a request has been made for internal link support over three and a half years ago. It still does not have an official status (declined, deferred, or planned). Perhaps an upvote campaign might help? :-/ (Thanks Jon Ericson for pointing this out.) – Paul A. Clayton Sep 10 '13 at 1:30

## I disagree.

My reasoning? I haven't seen it anywhere before - mSO doesn't have a list of programming terms, mSU doesn't have a list of computer terms, etc.

I am not however saying that we shouldn't just because no one else has - my main reasoning is that I have a hard time seeing people using it - it would be pretty hard for me to get in in y workflow to add an entry for every term I use in my answers.

Also, it doesn't seem like something that we should have on our Meta site - it isn't really about the site itself - and it would almost be better off as a question on the main site. However, it would be closed as too broad there, which I would take as a red flag for the entire idea.

• Your main argument against is for personal perception of other peoples use of a glossary, other then that you argument to have the glossary in main space with an exception to the overly broad rule; seems to be a thought worth considering. – James Jenkins Sep 9 '13 at 10:41


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### Seminars and Colloquiums for the week of October 7, 2019

SPEAKERS

Monday

Louis Gross, UTK
MGSC Panel
Tuesday
Xia Chen UTK
Wednesday
Marie Jameson, UTK
Thursday
Wendy Caldwell, Arizona State University
Florian Johne, Columbia
Friday
Wendy Caldwell, Arizona State University

Tea Time
3:00 pm – 3:30 pm
Monday, Tuesday, & Wednesday
Room: Ayres 401
Hosted by: Kimberlyn Eversman & Emily Campbell
Topics:    Tips for dissertation writing; Preparing for the "Big Day"; Weekly check-in

Monday, October 7

MATH BIOLOGY SEMINAR
TITLE: Overview of Catastrophe Theory from the perspective of Bifurcation Theory
SPEAKER: Louis Gross, UTK
TIME: 10:10 am
ROOM: Claxton 105

SPEAKER: Drs. Plaut, Freire, and Brodskiy
TIME: 3:35 PM
ROOM: Ayres 405

Tuesday, October 8

PROBABILITY AND STOCHASTICS SEMINAR
TITLE: Precise intermittency for the parabolic Anderson Equation with an $(1+1)$-dimensional time-space white noise
SPEAKER: Xia Chen, UTK
TIME: 2:10 PM
ROOM: Ayres 112
Abstract: The moment Lyapunov exponent is computed for the solution of the parabolic Anderson equation with an (1+1)-dimensional time-space white noise. Our main result positively confirms an open problem that originated from the observations made in the physical literature (J. Statist. Phys. 78(1995) 1377-1401) and (Nuclear Physics B290(1987) 582-602). By a link through the Feynman-Kac's formula, our theorem leads to the evaluation of the ground state energy for then-body problem.

Wednesday, October 9

COLLOQUIUM
TITLE: Modular forms and related objects
SPEAKER: Marie Jameson, UTK
TIME: 3:35 PM
ROOM: Ayres 405
Abstract: Modular forms are holomorphic functions on the upper half of the complex plane that satisfy certain transformation properties. By considering their Fourier expansions, modular forms give rise to q-series which allow us to study a variety of objects in number theory, algebra, and combinatorics, including partitions, elliptic curves, class numbers, and quadratic forms. In this talk, we will study the existence (and non-existence) of congruences satisfied by these Fourier coefficients in arithmetic progressions. We will also consider the importance of certain values of their L-functions, which give rise to newly defined objects called zeta-polynomials.

Thursday, October 10

JUNIOR COLLOQUIUM
TITLE: Hydrocode Modeling of Impact Craters
SPEAKER: Wendy Caldwell, Arizona State University
TIME: 3:35 pm
ROOM: Ayres 405
Abstract: Asteroid 16 Psyche is the largest M-type (metallic) Main Belt Asteroid (MBA). Radar albedo data indicate Psyche’s surface is rich in metallic content, but estimates for Psyche’s bulk structure vary widely. Psyche has two large impact structures in its Southern hemisphere. In this work, we present results from 2D and 3D simulations of the formation of these craters using the FLAG hydrocode, developed and maintained by Los Alamos National Laboratory. FLAG has been verified and validated for impact cratering simulations, with good agreement to theoretical and experimental results. Through quantitative comparison of the simulated crater dimensions with measured values, our models suggest that Psyche is largely composed of porous, metallic material. In addition, our work indicates that the impacts were likely oblique, with angles at least 45 degrees from vertical

GEOMETRIC ANALYSIS SEMINAR
TITLE: Surgery for an extended Ricci flow system
SPEAKER: Florian Johne, Columbia
TIME: 4:00 PM
ROOM: Ayres 113
Abstract: List flow is a geometric flow for a pair (g,u), where g is a Riemannian metric and u a smooth function. This extended Ricci flow system has applications to static vacuum solutions of the Einstein equations and to Ricci flow on warped products. The coupling in this flow induces additional difficulties compared to Ricci flow, which we overcome by proving an improved bound on the Hessian. This allows us to prove a convergence result, a singularity classification result and a surgery result in three dimensions.

Friday, October 11

COLLOQUIUM
TITLE: Understanding Asteroid 16 Psyche's Composition through 3D Hydrocode Impact Crater Models
SPEAKER: Wendy Caldwell, Arizona State University
TIME: 3:35 PM
ROOM: Ayres 405
Abstract: Asteroid 16 Psyche is the largest M-type (metallic) asteroid in the Main Asteroid Belt (MBA), and an upcoming NASA mission will be the first of its kind to visit a metallic body rather than one composed of rock or ice. Psyche is likely the remnant of a differentiated planet core from a time when planetary accretion was disrupted by frequent solid-body collisions. However, because of its distant location and the limits of available measuring techniques, basic information about Psyche is under debate. Estimates of Psyche's diameter vary considerably and typically fall in the range from 213 km to 264 km. Estimates of Psyche's bulk density typically range from 1.4 + 0.3 g/cm3 to 4.5 + 1.4 g/cm 3 . Psyche has two large impact structures in its Southern hemisphere. The goal of this work is to study the composition of Psyche by modeling its impact craters. To our knowledge, this work is the first of its kind to use impact crater simulations to determine likely material compositions as well as the first 3D models of the craters on Psyche. We study various possible material compositions and porosity levels, and we compare the crater profiles in 2D and 3D to estimate Psyche's material composition. We used a variety of materials and models for both impactor and Psyche, including iron, nickel, Monel (a nickel-copper alloy that contains titanium, aluminum, silicon, and iron), and silicon dioxide (SiO2 ). The constitutive models we used for these materials were Preston-Tonks-Wallace, Steinberg-Guinan, and perfect plasticity. For equations of state (EOS), we used the tabular SESAME EOS and the analytic Mie-Gruneisen EOS. Our 3D simulations tested impact angles of 45 and 60 from vertical. From these simulations, we predict that Psyche is indeed likely mostly metallic with a porosity of about 50%. Lower density materials resulted in craters far too large, and some highly porous materials resulted in asteroid disruption. These predictions are consistent with the idea that M-type asteroids are differentiated planet cores. Figure 1 shows crater formation 93 s after impact in our solid Monel-Monel oblique impact simulation. We will show additional simulation images and animations from 3D simulations with final crater dimensions within the expected error bars.

#### If you are interested in giving or arranging a talk for one of our seminars or colloquiums, please review our calendar.

If you have questions, or a date you would like to confirm, please contact Dr. Christopher Strickland, cstric12@utk.edu

Past notices:

Sept. 30, 2019

Sept. 23, 2019

Sept. 16, 2019

Sept. 9, 2019

Sept. 2, 2019

Aug. 26, 2019

2018-19

2017-18

###### last updated: October 2019

Department of Mathematics
College of Arts & Sciences

227 Ayres Hall. 1403 Circle Drive. Knoxville TN 37996-1320
Phone: 865-974-2461 Fax: 865-974-6576 Email: math_info@utk.edu


text:
# P-N junction voltage under polarization

1. Jul 22, 2014

### Fernsanz

All the books that deal with the p-n junction under applied bias asume that the same equations used for the equilibrium case (no bias) can be used for the biased case provided that the juntcion voltage $V_{ic}$ is substituted by $V_{ic}-V$, where $V$ is the applied bias. Although this can seem plausible I don't see any reason for why the junction voltage drop should be the $V_{ic}-V$, i.e., why the voltajes should obey a sort of superposition principle.

Is there any reason on the ground of fundamental electrostatic / thermodynamics?

Thanks.

2. Jul 28, 2014

### Greg Bernhardt

I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?

3. Aug 21, 2014

### zhanghe

First of all, you must be aware of that the built-in voltage is the one that is defined between the two edge of the depletion region, we do not care about other parts of pn-junction in our textbook for simplicity. When you have to consider bias voltage, in practice, two semiconductor-metal junction are formed at the two terminals of pn-junction, that exactly offset the built-in voltage when the bias is zero. When the bias is not zero, from the view of the depletion region, it will see a circuit where the bias voltage and the two semi-metal junctions are connected in series, that is the superposition "Vic-V". Even in an ideal case where ideal conducting wire (regardless of material, metal or not, whatever) is considered, you will find you have to face another pn-junction which is formed in opposite polarization between the two terminals when any contact is made.

Fernsanz, I wish you not be more confused by my words, :)


text:
### Home > MC2 > Chapter 11 > Lesson 11.2.1 > Problem11-30

11-30.

There are 13 diamond cards out of a deck of 52 cards.

A standard number cube has faces numbered 1 through 6.

$\frac{4}{6} \text{ or } 66.67 \%$

$\frac{3}{18} \text{ or } 16.67 \%$


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# Generating function

In mathematics a generating function is a formal power series whose coefficients encode information about a sequence an that is indexed by the natural numbers.

There are various types of generating functions - definitions and examples are given below. Every sequence has a generating function of each type. The particular generating function that is most useful in a given context will depend upon the nature of the sequence and the details of the problem being addressed.

Generating functions are often expressed in closed form as functions of a formal argument x. Sometimes a generating function is evaluated at a specific value of x. However, it must be remembered that generating functions are formal power series, and they will not necessarily converge for all values of x.

 Contents

## Definitions

A generating function is a clothesline on which we hang up a sequence of numbers for display. -- Herbert Wilf, generatingfunctionology (1994)

### Ordinary generating function

The ordinary generating function of a sequence an is

[itex]G(a_n;x)=\sum_{n=0}^{\infty}a_nx^n.[itex]

When generating function is used without qualification, it is usually taken to mean an ordinary generating function.

If an is the probability mass function of a discrete random variable, then its ordinary generating function is called a probability-generating function.

The ordinary generating function can be generalised to sequences with multiple indexes. For example, the ordinary generating function of a sequence am,n (where n and m are natural numbers) is

[itex]G(a_{m,n};x,y)=\sum_{m,n=0}^{\infty}a_{m,n}x^my^n.[itex]

### Exponential generating function

The exponential generating function of a sequence an is

[itex]EG(a_n;x)=\sum _{n=0}^{\infty} a_n \frac{x^n}{n!}.[itex]

### Lambert series

The Lambert series of a sequence an is

[itex]LG(a_n;x)=\sum _{n=1}^{\infty} a_n \frac{x^n}{1-x^n}.[itex]

Note that in a Lambert series the index n starts at 1, not at 0.

### Bell series

The Bell series of an arithmetic function f(n) and a prime p is

[itex]f_p(x)=\sum_{n=0}^\infty f(p^n)x^n.[itex]

### Dirichlet series generating functions

Dirichlet series are often classified as generating functions, although they are not strictly formal power series. The Dirichlet series generating function of a sequence an is

[itex]DG(a_n;s)=\sum _{n=1}^{\infty} \frac{a_n}{n^s}.[itex]

The Dirichlet series generating function is especially useful when an is a multiplicative function, when it has an Euler product expression in terms of the function's Bell series

[itex]DG(a_n;s)=\prod_{p} f_p(p^{-s}).[itex]

If an is a Dirichlet character then its Dirichlet series generating function is called a Dirichlet L-series.

### Polynomial sequence generating functions

The idea of generating functions can be extended to sequences of other objects. Thus, for example, polynomial sequences of binomial type are generated by

[itex]e^{xf(t)}=\sum_{n=0}^\infty {p_n(x) \over n!}t^n[itex]

where pn(x) is a sequence of polynomials and f(t) is a function of a certain form. Sheffer sequences are generated in a similar way.

## Examples

Generating functions for the sequence of square numbers an = n2 are:

### Ordinary generating function

[itex]G(n^2;x)=\sum_{n=0}^{\infty}n^2x^n=\frac{x(x+1)}{(1-x)^3}[itex]

### Exponential generating function

[itex]EG(n^2;x)=\sum _{n=0}^{\infty} \frac{n^2x^n}{n!}=x(x+1)e^x[itex]

### Bell series

[itex]f_p(x)=\sum_{n=0}^\infty p^{2n}x^n=\frac{1}{1-p^2x}[itex]

### Dirichlet series generating function

[itex]DG(n^2;s)=\sum_{n=1}^{\infty} \frac{n^2}{n^s}=\zeta(s-2)[itex]

## Another example

Generating functions can be created by extending simpler generating functions. For example, starting with

[itex]G(1;x)=\sum_{n=0}^{\infty} x^n = \frac{1}{1-x}[itex]

and replacing [itex]x[itex] with [itex]2x[itex], we obtain

[itex]G(1;2x)=\frac{1}{1-2x} = 1+(2x)+(2x)^2+\ldots+(2x)^n+\ldots=G(2^n;x).[itex]

## Uses

Generating functions are used to

• Find recurrence relations for sequences - the form of a generating function may suggest a recurrence formula.
• Find relationships between sequences - if the generating functions of two sequences have a similar form, then the sequences themselves are probably related.
• Explore the asymptotic behaviour of sequences.
• Prove identities involving sequences.
• Solve enumeration problems in combinatorics.
• Evaluate infinite sums.

## References

• Art and Cultures
• Countries of the World (http://www.academickids.com/encyclopedia/index.php/Countries)
• Space and Astronomy