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Author: Subject: On the usefulness of amateur chemistry to society
Harristotle
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On the usefulness of amateur chemistry to society

Greetings to all.
I have wanted to put something on record for a while. That is, to acknowledge what I see as the substantial contribution of the amateur chemistry community to public education, and to the enrichment of school curricula.

In large part, due to the sometimes active, but often passive via following very interesting threads and discussions, Science Madness has made the following direct and substantial contributions to my work, and through that to the Western Australian curriculum.

1. Assistance, and information from the Readily Available Chemicals thread gave me the means to produce a colloidal gold nanoparticle practical for which I have received over 50 requests resulting in this lab being accessible to many high school students at a cost of approximately $2 per group of 4. This has resulted in students getting the "oh wow" of seeing beautiful gold nps form from a pale yellow solution. The Sigma-Aldrich cost of$180 per bottle of reagent meant that most schools in my area used to just show a youtube video.

2. Some of the great discussions on TLC (eg http://www.sciencemadness.org/talk/viewthread.php?tid=6690#p... and others), have helped me develop a microscope slide/talc system that can be cheaply made in schools, and when our curriculum expanded for Y11, allowed chemistry classes to cheaply explore this technology, which gives the students the insights necessary to understand many modern analytical techniques. It is important to note that if you want to produce future chemists (not just GMAT/GAMSAT students who are interested in chemistry as compliance), you have to let them get their hands dirty. I received much of my initial support from this forum. In addition to the general Y11 chem support, this has helped a group of my students develop a quantitative assay for paracetamol using an iphone and this technique. We are hopeful that they may win a science talent quest with it.

3. The introduction that this forum gave me to Soxhlet condensers, and their techniques has been most useful. Another group of my students have extracted germination-suppressing compounds from an Australian native plant, and are starting the work of pinning the compound down. I have never used one of these in my own undergrad degree many years ago (as a biologist/biochemist it didn't cross my path), and the discussions in these threads have been important in forming the understanding that enabled my students to do this research.

4. The discussion on Rochelle's salt and its preparation, as well as the Readily Available Chemicals list led me to develop and write a lab activity on measuring proteins using the old Biurette reagent. It was the help in "porting" to the otc format, and making this cheap and affordable for underfunded schools that I owe thanks to this forum too. Bunnings, baked baking soda, and crystalisations of cream of tartar/tartaric acid on the summer holidays led to a published student lab manual, which is used by most Y12 schools in my state.

5. The threads on making gallinstan, used on conjunction with the 2015/2016? paper on reversably oxidising its surface to make a microfluidic pump have lead to a "liquid robot" that a bunch of my students are building and coding in an advanced STEM/ robotics class.

In these times where everything that is chemistry seems in the public arena to be related to bombs, poisons or terrorism, I feel that it is important to acknowledge the huge public good that this forum has helped me achieve.

So what public good has the amateur chemistry community (this or other) helped you to do? Let us know, I think we should highlight the good too, and not just led poorly informed press define us.

Cheers,
Harristotle.
j_sum1
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Mood: Undergoing decantation and leaving all the crap behind.

Thanks H.

We should talk. It seems we have much similar experience.
However it is late here and I am off to bed. I'll send a U2U soon.
J.
Lillica
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This is a good thread idea. It's worth keeping in mind that a significant amount of the individuals in the amateur chemistry community are in fact professional chemists in their day life, or just in general very skilled chemists (even if "amateurs"). For this reason, I personally don't feel like the amateur chemistry label is a very accurate one for the community, but either way, this online chemistry community in general is quite incredible for all of the reasons you mentioned. Anytime people can come together, experiment, and share their thoughts and opinions in an open forum type format is very valuable to the scientific community as a whole, in my opinion.
NEMO-Chemistry
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 Quote: Originally posted by Harristotle Greetings to all. I have wanted to put something on record for a while. That is, to acknowledge what I see as the substantial contribution of the amateur chemistry community to public education, and to the enrichment of school curricula. In large part, due to the sometimes active, but often passive via following very interesting threads and discussions, Science Madness has made the following direct and substantial contributions to my work, and through that to the Western Australian curriculum. 1. Assistance, and information from the Readily Available Chemicals thread gave me the means to produce a colloidal gold nanoparticle practical for which I have received over 50 requests resulting in this lab being accessible to many high school students at a cost of approximately $2 per group of 4. This has resulted in students getting the "oh wow" of seeing beautiful gold nps form from a pale yellow solution. The Sigma-Aldrich cost of$180 per bottle of reagent meant that most schools in my area used to just show a youtube video. 2. Some of the great discussions on TLC (eg http://www.sciencemadness.org/talk/viewthread.php?tid=6690#p... and others), have helped me develop a microscope slide/talc system that can be cheaply made in schools, and when our curriculum expanded for Y11, allowed chemistry classes to cheaply explore this technology, which gives the students the insights necessary to understand many modern analytical techniques. It is important to note that if you want to produce future chemists (not just GMAT/GAMSAT students who are interested in chemistry as compliance), you have to let them get their hands dirty. I received much of my initial support from this forum. In addition to the general Y11 chem support, this has helped a group of my students develop a quantitative assay for paracetamol using an iphone and this technique. We are hopeful that they may win a science talent quest with it. 3. The introduction that this forum gave me to Soxhlet condensers, and their techniques has been most useful. Another group of my students have extracted germination-suppressing compounds from an Australian native plant, and are starting the work of pinning the compound down. I have never used one of these in my own undergrad degree many years ago (as a biologist/biochemist it didn't cross my path), and the discussions in these threads have been important in forming the understanding that enabled my students to do this research. 4. The discussion on Rochelle's salt and its preparation, as well as the Readily Available Chemicals list led me to develop and write a lab activity on measuring proteins using the old Biurette reagent. It was the help in "porting" to the otc format, and making this cheap and affordable for underfunded schools that I owe thanks to this forum too. Bunnings, baked baking soda, and crystalisations of cream of tartar/tartaric acid on the summer holidays led to a published student lab manual, which is used by most Y12 schools in my state. 5. The threads on making gallinstan, used on conjunction with the 2015/2016? paper on reversably oxidising its surface to make a microfluidic pump have lead to a "liquid robot" that a bunch of my students are building and coding in an advanced STEM/ robotics class. In these times where everything that is chemistry seems in the public arena to be related to bombs, poisons or terrorism, I feel that it is important to acknowledge the huge public good that this forum has helped me achieve. So what public good has the amateur chemistry community (this or other) helped you to do? Let us know, I think we should highlight the good too, and not just led poorly informed press define us. Cheers, Harristotle.

just an aside really, you mentioned germination suppressant from a native plant. From something i have been reading tomato seeds also have one on the seed coat, i dont remember much but apparently the brown substance under the gel on the tomato seed is the suppressant.

Thought i would mention it in case you wanted some other seed to look at.
Harristotle
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Thanks Nemo,
there are a few. This was present in the leaves, and resulted in fairly bare ground underneath the plant involved. Apparently acetates and acetic acid is a known suppresser found in decomposing leaves. Soxhlet extraction of fresh leaves suggests that this agent might be something different.

Over the next year we will look into it more, probably starting with acidic, basic and neutral extraction into organic solvent, and then perhaps a column separation with fractions dried and fed into a germination bioassay.

It is a great science project for a kid: the extractions can be done at school, the fractions dried onto paper and the bioassay done at home. The plant, incidently, is not toxic and in fact suffers from the fact that it is eaten by feral goats and camels !

Cheers,
H.
NEMO-Chemistry
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 Quote: Originally posted by Harristotle Thanks Nemo, there are a few. This was present in the leaves, and resulted in fairly bare ground underneath the plant involved. Apparently acetates and acetic acid is a known suppresser found in decomposing leaves. Soxhlet extraction of fresh leaves suggests that this agent might be something different. Over the next year we will look into it more, probably starting with acidic, basic and neutral extraction into organic solvent, and then perhaps a column separation with fractions dried and fed into a germination bioassay. It is a great science project for a kid: the extractions can be done at school, the fractions dried onto paper and the bioassay done at home. The plant, incidently, is not toxic and in fact suffers from the fact that it is eaten by feral goats and camels ! Cheers, H.

I really like plant chemistry, i do alot of plant extractions and TLC plates of the compounds. I couldnt afford column Chromatography because the silica was really expensive.

Then i found a cat litter online that is really similar but needs some ball milling first. But i cant moan as the cat litter is £4.50 for 10Kg, a fraction of the price for the real stuff.

Messing with mint plants at the moment and goats seem to like those as well lol. Not too many camels roaming wild in the UK so that isnt an issue. Rabbits however are fast becoming my number 1 source of frustration

[Edited on 8-8-2017 by NEMO-Chemistry]
Loptr
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My question is why does everyone seem to think that Sigma-Aldrich is a good idea to buy from, especially at the grade school level? They are RIDICULOUSLY expensive.

There are also so many chemical suppliers that mainly cater to schools, and other cheaper supplies like Oakwood Chemical.

EDIT: This is also highly dependent on where the OP is located. Oakwood Chemical is in the USA.

[Edited on 8-8-2017 by Loptr]

"Question everything generally thought to be obvious." - Dieter Rams
Harristotle
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Sigma is expensive. (I did love their catalogues though!)

No matter, I can figure around most things.

For silica, I was thinking magnesium silicate aka talc. Fine particles, no milling, no toxicity (although in the old days, talc deposits were sometimes contaminated with asbestos, this doesn't happen now).

I'm in Australia, it has been pretty good here for me. There are some restrictions on glassware, and we are watched, but good notebooks, a reasonable reason, and sensible safety/ no recklessness means no trouble. Anything that is reasonable to use in a school is accessible, and while the OHS regime (as everywhere) stops kids from having as interesting an experience as we did at school, you can do a surprising amount.

The big problem though is the continuing slide into chemophobia. This is true across the western world.
My concern is to avoid a kind of "cultural death", in which we as a country just lose the capacity to do chemistry, and to use chemical tools to solve problems. In the end, I don't want to see my country weakened and totally dependent on outside technology, bought in at huge cost, and without the skilled people to use it. We are sitting on an ancient biodiversity hotspot, as diverse as any tropical rainforest. If we knew all the chemical tricks that all that life uses, we would have the best pharmaceutical industry in the world, no foreign debt, and a guaranteed top lifestyle for many generations to come!

Hence my interest in recording and emphasising some of the positives of hobby chemistry (taking on board that some don't like it called amateur chemistry).

Cheers,
H
NEMO-Chemistry
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Talc!!!! Never occurred to me at all. Thanks alot for that, it opens other doors for me .
AJKOER
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On the usefulness of amateur chemistry to society, I would say the ability, through advanced and diverse scientific bodies of knowledge to circumvent restrictions with respect to equipment or reagents, and be able to move forward.

Some of just my more recent commentary involve such areas as magnetic field effects on chemistry, sonolysis, photolysis, radical chemistry, surface chemistry, chemistry of aerosols, Fenton and Fenton-type reactions, electrochemistry include the chemistry of corrosion, electrochemical (battery) cells,.....

[Edited on 23-9-2017 by AJKOER]
Texium (zts16)
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 Quote: Originally posted by AJKOER On the usefulness of amateur chemistry to society, I would say the ability, through advanced and diverse scientific bodies of knowledge to circumvent restrictions with respect to equipment or reagents, and be able to move forward. Some of just my more recent commentary involve such areas as magnetic field effects on chemistry, sonolysis, photolysis, radical chemistry, surface chemistry, chemistry of aerosols, Fenton and Fenton-type reactions, electrochemistry include the chemistry of corrosion, electrochemical (battery) cells
And yet,
"Commentary" is all that it is. Where have you actually tried any of these things that you claim will work? Are you expecting others to do it for you? You're not really a scientist if you just make claims without backing them up by experimenting, or at least reference experiments that back up your exact claims.

Come check out the Official Sciencemadness Wiki
Have a particular topic you're really interested in currently? Why not make a page for it? The wiki can always benefit from more contributors.

My (now defunct) YouTube Channel: Texium
My blog: Texium
VSEPR_VOID
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The usefulness of amateur chemistry is irrelevant to in the bigger picture: It is every users basic rights to be able to do as they please in the comfort of their own labs, in their own home, in the country they live in. I just want to put that out their because it this thread could lead to a the discussion of potential the justification of amateur chemistry. That being said I would like to ask what people think of the following: Is the time of amateurs contributing to major advances/discoveries over? Has science at home lost its potential for say? I hope this post contributes to the discussion.

“Keep a goverment poor and weak and it's your servant; when it is rich and powerful it becomes your master.”
―H. Beam Piper

"Well thats funny" is the most important phrase in science.
AJKOER
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Zts16:

See my thread on a photolysis path to chlorate at https://www.sciencemadness.org/whisper/viewthread.php?tid=34... with 11 pictures and lots of science too!

Be careful, that thread alone could give anyone a real big bang!!

But my most scary experiment was when I microwaved N2O and NaOH on a porclean dish in an plastic vessel. The sparks were so intensely hot that the dish violently broke apart. See https://www.sciencemadness.org/whisper/viewthread.php?tid=74... .Now, that was hot!

Alas, I do not report all my experiments, even the cool curious ones. Most recently, one of my threads (in Energetic Materials) required ZnO as a photo catalyst. I decided to test a new approach following the steps of a bleach battery (NaOCl (aq), Al and Cu, a touch of sea salt), but replace the aluminum with zinc. This was, in essence, an electrosynthesis of ZnO in a galvanic (or electrochemical) cell. The target product of ZnO was hopefully produced by jumping the reaction in a microwave. The heating also served to hopefully form ZnO and not Zn(OH)2. The results were somewhat successful (there was a flow of ZnO/Zn(OH)2 off of the zinc sheet going to the top and bottom of the vessel and onto the Zn sheet), but upon adding more (now an excess of bleach, a bad idea reducing yield), I witness a curious green color develop in the alkaline solution. I removed the zinc metal sheet, and saw what looked like a greenish colored spherical zone in the center of the solution. Remember no acid added, but perhaps some amphoteric Zn(OH)2 produced H+. The latter with NaCl and OCl- could have created some chlorine. But why centered in the solution? Also possible is, from created current in this battery cell, e- + H+ = .H and .H + OCl- = OH- + .Cl . The latter chlorine radical, centered in the cathodic zone, residing where the Zn metal was, could further have produce species like .Cl + .Cl = Cl2 or .Cl + Cl- = -.Cl2 or Cl2 + Cl- = Cl3-. Cool nevertheless. Will repeat and better document.

[Edited on 24-9-2017 by AJKOER]
Quaff
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US Patent 7,300,957 was the result of what I did in my garage. I know of at least one company that is using the material, which is basically, soaps.

The problem the amateur chemist has, is that the loser drug makers have caused public perception to be that just because someone is holding a beaker, they are a suspect. For this reason, I got rid of a small fortune's worth of glassware a decade ago. I didn't want to be accused of something I didn't do merely because of appearances, and spend \$50k defending myself to prove I wasn't doing anything unlawful.

Another issue is hazardous waste generation. Most chemistry will involve producing some unwanted by-product that cannot be dumped down the drain.

Probably the safest things to work with would be soaps, and simple metals chemistry, like recovering gold and other precious metals. I did US Patent 5,156,721 in my basement.

There are a lot of beneficial projects which can be undertaken in a micro lab, as Charles Hall had when he invented his aluminum process.

Right now, one interest is in separating enantiomers of esters, I'd like to resolve the d and l isomers of glycerly monoesters, such as glyceryl mono oleate, in a clean way at high yield, anything over 30% would make me happy.

Another fruitful area for the "home chemist" could well be in the field of magneto-calorics. This is where an alloy is subjected to a magnetic field whereby the alloy loses heat and is then removed from the magnetic field to once again absorb heat. discovering the next generation materials could be the answer for air conditioning in electric vehicles.

Another potential fruitful area is in metals chemistry, to cause dissloution of noble metals while using no noxious chemical materials.

For several years I've searched also for superconducting materials, using mixed oxides of transition metals. Each sample I prep'd was less than a gram, so after several years I had generated less than one pound of "waste". The closest I came were the Lanthanum manganates series. Strangely, somehow, my lab notes went missing, I don't know where that book is. About 4 years later, some group in China published a paper that contained a lot of what I had been working on.

There is also opportunity for developing air conditioner units which employ water as the primary refrigerant. The enthalpy of vap. for water being 44 kJ/mol is a godsend.

I see on the internet lots of folks talking about doing organic chemistry in a home lab. With the exception of soaps, I think the home organic chemistry lab is a very very very bad idea. There are simply too many other areas of investigation one can keep busy with that do not arouse unnecessary suspicion. I've profited from the two patents above, and you can also profit if you find a "need in the marketplace" for what you anticipate doing. Good luck to all.

WangleSpong5000
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Long story short. Don't believe the hype... but far far more important than this is issue of Liberty. Pursuit of knowledge is life's greatest virtue and I'll be damned if any one tries to stop me... I am in the process of delving deep into Australian law regarding this subject... so many chemicals are restricted... fucking GABA is restricted! L tyrosine and 5HTP are apparently illegal to import! Unless you can prove you need it for a medical condition which I do but that's not the point...

I understand why drug manufacture is illegal... I think it's wrong but I'm not prepared to give up my freedom for it. Iodine, Lithium, red phosphorus, HI, hypo phosphoric acid, phenylalanine, formic acid, methylamine, pretty much anything that scarcely resembles a phenethlyamine and by that I mean a benzene ring with bits on it... Forget organometallics and Grignard reagents... acetic anhydride? Fuck no but what about Metallic hydrides... Nope... Borane? Nope... People are scared to order basic acids and solvents in Australia...

Basically anything useful is vertboten or at least extremely suspicious... well I'm not doing anything wrong and they don't have the right to to harass, intimidate and profile chemists... If they come to my door... and they will... I will co operate but if they fuck with me I will have them fired or worse for vilifying a citizen with a severe disability... the Drs with write thier letters and fuck me does a Psych hold sway in this society...

TLDR

Fuck draconian laws re chemistry. It's not drug cooks that have ruined it for the rest of us... It's the lawmakers and the law enforcers... now if you'll excuse me I have to finish registering my business so I can order some fuck off glassware and order chemicals which may be on a list somewhere... you yanks have it made it seems... at least your laws seem to explicitly outline exactly what you can and can't do...

Straya innit?

[Edited on 1-12-2017 by WangleSpong5000]
LearnedAmateur
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 Quote: Originally posted by WangleSpong5000 The fact of the matter is chemistry has a stigma to it. Personally I don't think the problem is drug cooks ruining it for the rest of us, the problem is that the powers that be; and your average ignorant normie civilian

Yeah but in my opinion, it's because of not just the 'drug cooks' (the common person knows that illicit street drugs are made by 'amateur chemists', which I use ambiguously because they are mostly just following a recipe, and is too uneducated to see the differences), but also because of terrorism potential. Think about it, TATP can be made from chemicals found under a lot of kitchen sinks or in garage cupboards, chlorine gas can be made from bleach and a household acid, and reagents commonly used by home chemists can be readily used as weapons. As for that last point, there have been very popular petitions here in the UK for sulphuric and hydrochloric acids to be banned for those who do not hold a license! This has come because of physical attacks on people (albeit extremely rare compared to hit and run, knife crime, and GBH for example), and ignorance on the part of the layperson. Like with drug use in general, harsh legislation comes as a result of the few instances in which people are, or at least have a strong risk of being harmed/killed and the media certainly doesn't help in containing the issue(s) at hand since chemistry related instances are so sparse that they're milked for every penny to be made. From governments' points of view, there is no reason why any old person should be able to obtain 'specialised' chemicals without holding proof that they require it. Acetic anhydride for instance has no use in a domestic setting, nor does lithium aluminium hydride, benzaldehyde, phosphorus, or any of the like, but others like sodium hydroxide, hexamine, toluene, and potassium nitrate do have their domestic uses and are not frowned upon because of that. Governments simply see these regulations as a way to decrease drug/weapon production, because it doesn't affect >90% of the population where the majority of these wouldn't even realise that these bans are in place.

[Edited on 1-12-2017 by LearnedAmateur]

In chemistry, sometimes the solution is the problem.
WangleSpong5000
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Quote: Originally posted by LearnedAmateur
 Quote: Originally posted by WangleSpong5000 The fact of the matter is chemistry has a stigma to it. Personally I don't think the problem is drug cooks ruining it for the rest of us, the problem is that the powers that be; and your average ignorant normie civilian

Yeah but in my opinion, it's because of not just the 'drug cooks' (the common person knows that illicit street drugs are made by 'amateur chemists', which I use ambiguously because they are mostly just following a recipe, and is too uneducated to see the differences), but also because of terrorism potential. Think about it, TATP can be made from chemicals found under a lot of kitchen sinks or in garage cupboards, chlorine gas can be made from bleach and a household acid, and reagents commonly used by home chemists can be readily used as weapons. As for that last point, there have been very popular petitions here in the UK for sulphuric and hydrochloric acids to be banned for those who do not hold a license! This has come because of physical attacks on people (albeit extremely rare compared to hit and run, knife crime, and GBH for example), and ignorance on the part of the layperson. Like with drug use in general, harsh legislation comes as a result of the few instances in which people are, or at least have a strong risk of being harmed/killed and the media certainly doesn't help in containing the issue(s) at hand since chemistry related instances are so sparse that they're milked for every penny to be made. From governments' points of view, there is no reason why any old person should be able to obtain 'specialised' chemicals without holding proof that they require it. Acetic anhydride for instance has no use in a domestic setting, nor does lithium aluminium hydride, benzaldehyde, phosphorus, or any of the like, but others like sodium hydroxide, hexamine, toluene, and potassium nitrate do have their domestic uses and are not frowned upon because of that. Governments simply see these regulations as a way to decrease drug/weapon production, because it doesn't affect >90% of the population where the majority of these wouldn't even realise that these bans are in place.

[Edited on 1-12-2017 by LearnedAmateur]

You are right in regards to the issue of terrorism and I have no problem whatsoever when it comes to strict controls on reagents that can be easily used to create high explosives. The IRA got by just fine using ammonium nitrate to fuck shit up. I can't imagine plastic explosives being simple to make and the list of restricted chemicals in Oz relating to explosives consists of things I've never heard of or can be inferred by their nomenclature...

I guess for me this is more about Liberty than anything else. We don't even have free speech in my country... nothing explicitly stated only 'implied' by old connections to the commonwealth. Implied free speech? The true implication in this matter is the fact that it can be taken away at will, and it's happening... and no one cares in Oz...

Chemistry is something I've only got back into very recently and for the first time ever I have the means to do actual chemistry outside of a uni lab and as I fucked that up my meagre home lab is all I've got... and I prefer it if I'm honest! The thing that shits me is just figuring out what ones rights are re chemistry in Oz is almost impossible and no one seems to know including law enforcement and the law makers... I'm beginning to suss it out and and it's doable most definitely.

AJKOER
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Those with the knowledge of chemistry should be thankful for the currently limited and generally ineffective regulations!

After all, if I was a dictator who should I fear the most as potentially disseminating knowledge that could change the balance of power for the masses? Teachers, not so much, but does explain there low pay in some countries. Doctors, not likely. Religious leaders, more annoying, but not a direct source of power (they will need many followers). But chemists and even just those with knowledge in the field, now they could present so definite problems.

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# Search for charged Higgs bosons decaying into a top and a bottom quark in the all-jet final state of pp collisions at $\sqrt s$ = 13 TeV

## Statistics

### Citations

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text:
Triangle type
▲ base and height

Base (b)
in
Height (h)
in
Prism length (L)
in
Prism volume
cu in

# Triangular Prism Calculator

By Hanna Pamuła, PhD candidate and Jasmine J Mah

If you ever wondered how to find the volume of a triangular prism, this triangular prism calculator is the thing you are looking for. Not only can it calculate the volume but also may be helpful if you need to determine the triangular prism surface area. Choose the option which fits your needs and experiment with the tool! If you are curious about triangular prism formulas behind the calculator, scroll down to find out more.

## Triangular prism - what's that?

What is a prism? It's a solid object with:

• identical two bases
• three rectangular faces (right prism) or in parallelogram shape (oblique prism)
• the same cross section along its whole length

We are using the term triangular prism to describe the right triangular prism, what is quite a common practice. If you are looking for other prism type, check our rectangular prism calculator.

## Triangular prism formulas

Usually what you need to calculate are the triangular prism volume and its surface area. The two most basic equations are:

• `volume = 0.5 * b * h * length`, where `b` is the length of the base of the triangle, `h` is the height of the triangle and `length` is prism length

• `area = length * (a + b + c) + (2 * base_area)`, where `a, b, c` are sides of the triangle and `base_area` is the triangular base area

But what if we don't have the height and base of the triangle? And how to find triangular prism surface area without all sides of the triangular base? Check out the other triangular prism formulas!

## Triangular prism volume

In the triangular prism calculator you can easily find out the volume of that solid. A general formula is `volume = length * base_area`; the one parameter you always need to have given is the prism length, and there are four ways to calculate the base - triangle area. Our triangular prism calculator has all of them implemented, isn't it awesome?

The specific formulas look as follows:

• Length * Triangular base area given triangle base and height

It's this well-known formula mentioned before:

`volume = length * 0.5 * b * h`

• Length * Triangular base area given three sides (SSS)

If you know the lengths of all sides, use the Heron's formula to find the area of triangular base:

`volume = length * 0.25 * √( (a + b + c) * (-a + b + c) * (a - b + c) * (a + b - c) )`

• Length * Triangular base area given two sides and the angle between them (SAS)

You can calculate area of a triangle easily from trigonometry:

`volume = length * 0.5 * a * b * sin(γ)`

• Length * Triangular base area given two angles and a side between them (ASA)

You can calculate that using trigonometry:

`volume = = length * a² * sin(β) * sin(γ) / (2 * sin(β + γ))`

## Triangular prism surface area

If you want to calculate the surface area of the solid, the most well-known formula is the one given three sides of the triangular base :

• `area = length * (a + b + c) + (2 * base_area) = length * base_perimeter + (2 * base_area)`

However, we don't always have the three sides given. What then?

• Triangular base: given two sides and the angle between them (SAS)

Using law of cosines, we can find the third triangle side:

`area = length * (a + b + √( b² + a² - (2 * b * a * cos(angle)))) + a * b * sin(angle)`

• Triangular base: given two angles and a side between them (ASA)

Using law of sines, we can find the two sides of triangular base:

`area = (length * (a + a * (sin(angle1) / sin(angle1+angle2)) + a * (sin(angle2) / sin(angle1+angle2)))) + a * ((a * sin(angle1)) / sin(angle1 + angle2)) * sin(angle2)`

The only option when you can't calculate triangular prism volume is having given triangle base and its height (do you know why? Think about it for a moment). All the other versions may be calculated with our triangular prism calculator.

## How to find the volume of a triangular prism with this tool?

Let's check what's the volume and surface area of a tent shaped like a triangular prism:

1. Find out what's the length of the triangular prism. Assume it's equal to 80 in, type this value into the first box of triangular prism calculator.
2. Choose the option with your parameters given. For example, given three sides of our base.
3. Enter base sides. Our tent has a = 60 in, b = 50 in and c = 50 in.
4. Triangular prism surface area and volume appear in no time. It's 96,000 cu in (55.56 cu ft) and 15,200 in² (105.56 ft²).
Hanna Pamuła, PhD candidate and Jasmine J Mah


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If the arean of circle is 56 what is radius??

Jun 4, 2018

The radius of the circle is $\sqrt{\frac{A}{\pi}} \approx 4.2$.

Explanation:

The area of a circle is given by $\pi {r}^{2}$, where $r$ is the radius of the circle. We know what the area is, and $\pi$ is a constant, so we can solve for the radius:

$A = \pi {r}^{2} \rightarrow 56 = \pi {r}^{2} \rightarrow {r}^{2} = \frac{56}{\pi} \rightarrow r = \pm \sqrt{\frac{56}{\pi}} \approx 4.2$.

(We know we have to use the positive square root because a negative radius wouldn't make sense!)

Jun 4, 2018

$r = 2 \frac{\sqrt{14 \pi}}{\pi} \approx 4.22$

Explanation:

${A}_{\text{circle}} = \pi {r}^{2}$

$56 = \pi {r}^{2}$

$\frac{56}{\pi} = {r}^{2}$

$\pm \sqrt{\frac{56}{\pi}} = \sqrt{{r}^{2}}$

We can ignore the negative solution because a radius cannot be negative.

$r = 2 \frac{\sqrt{14 \pi}}{\pi}$

$r = 2 \frac{\sqrt{14 \pi}}{\pi} \approx 4.22$


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RAVE:Imaging Data Formats

 Reproducible Analysis and Visualization of iEEG RAVE

Import volumetric MRI data and cortical surface models

RAVE imports MRI volumetric data and cortical surface models that have been processed by FreeSurfer. See the FreeSurfer website for complete information. For additional help, see the Beauchamp Lab wiki (ignore instructions for converting FreeSurfer surfaces for AFNI/SUMA; this is not required for RAVE.) Copy the FreeSurfer output folder into the RAVE subject folder, e.g.

 rave_data/data_dir/congruency/YAB/rave/fs

RAVE will read all of the files that are needed directly from this directory.

Special Cases

Note that it is not required to have any MRI data or a cortical surface model, although RAVE works best if these are available.

No cortical surface model

RAVE reads volumetric MRI data from the file

 fs/mri/brain.finalsurfs.mgz

Partial cortical surface model

If no cortical surface model is found, RAVE will display only the volumetric MRI data. RAVE requires that both the left hemisphere and right hemisphere surface files be present, in either native FreeSurfer format, ASCII format, or GIFTI format. RAVE will attempt to read fs/surf/lh.pial or (if this file is not found) fs/surf/lh.pial.asc or (if this file is not found) fs/surf/lh.pial.gii .

In some cases, FreeSurfer may reconstruct only one hemisphere; in this case a work-around is to create a "fake" model of the other hemisphere. For instance, if the right hemisphere reconstruction failed, use a text editor to create the file

 fs/surf/rh.pial.asc

containing six lines:

 3 1
0 0 0
0 0 0
0 0 0
0 1 2
{blank line}

The first line tells how many vertices and how many faces; line 2-4 create fake vertices at the origin; line 5 links these vertices. The last line of the file must be blank.


text:
Ask your own question, for FREE!
Mathematics
114583:

A rectangular window in Jim's bedroom is 36 inches wide. The diagonal of the window is 44 inches. Which measurement is closest to the height of the window?

vietress:

You would use the pythagorean theorem to find the answer to this problem. $a^2 + 36^2 = 44^2$The first step is to solve for the exponents. 36 squared is 1296 44 squared is 1936 The new equation is: $a^2 + 1296 = 1936$Next, you subtract 1296 from both sides. This gives us: $a^2 = 640$The final step is to find the square root on both sides. $\sqrt{a^2} = \sqrt{640}$This gives us an answer of $a \approx 25.29$ Hope this helped! If it did, please consider marking my answer as "Best Response"

114583:

Thanks.

Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!
Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!


text:
## Constraint Minimization of Equation using lagrange's method

OBJECTIVE

The main objective is to Minimize the given equation with respect to the given constraint.

Problem:

This function f(x,y) = 5-(x-2)^2 -2(y-1)^2 is subject to the following constraint x + 4y = 3

Solution:

Make a new function as g(x,y) = f(x,y) + lamda (x+4y-3)

g(x,y) = (5-(x-2)^2 -2(y-1)^2) + lamda (x+4y-3)

g(x,y) = 5-(x^2 - 4x + 4 ) - 2(y^2 - 2y +1 ) + lamda (x+4y-3)

g(x,y) = -x^2 +4x - 2 y^2 +4y -1 + lamda (x+4y-3)

Perform partial differential equation on this g(x,y) function w.r.t. x, y & lamda

(del g)/(del x) = 0

-2x + 4+ lamda = 0   ---------------> Eq. 1

(del g)/(del y) = 0

-4y + 4+ 4lamda =0

lamda - y+1 =0

lamda = y-1              ---------------> Eq. 2

(del g)/(del lamda) = 0

x+4y-3=0                ---------------> Eq. 3

Put eq. 2 into eq. 1, we get

-2x+4+y-1=0

-2x+y+3=0              ---------------> Eq. 4

multiply eq. 3 with 2 and solve with eq. 4, we get

9y-3=0

y=1/3

put value of y in eq. 2, we get lamda

lamda = -2/3

put value of y in eq. 3, we get  value of x

x = 5/3

CONLUSION

We get the value of x , y and lamda

x = 5/3 , y=1/3 , lamda = -2/3

### Neon Side Crash Analysis on BIW model using Hypermesh RADIOSS Jitesh Sahjwani · 2019-10-31 05:18:23

OBJECTIVE In this challenge, we check and create the properties for a Neon side crash-BIW model and run the simulation & observe results. Question: Neon side crash -BIW Check the unit system and either follow [Mg mm s] or [Kg mm ms]. Create an appropriate int Read more

### Neon frontal crash Analysis on BIW model using Hypermesh RADIOSS Jitesh Sahjwani · 2019-10-31 05:16:57

OBJECTIVE In this challenge, we check and create the properties for a Neon frontal crash-BIW model and run the simulation & observe results. Question: Frontal crash-BIW Check the unit system and either follow[Mg mm s] or [Kg mm ms]. Create an appropriate inte Read more

### Analysis on the automotive Crash box using contact interface Type-7 simulation Type-11 along with Type-7 using Hypercrash and Radioss Jitesh Sahjwani · 2019-10-21 05:15:32

OBJECTIVE In this report, we mesh a Bumper assembly.Perform simulation on Crash tube and compare the Type-7 simulation results, Type-11 along with Type-7 and different kinematic condition simulation results. Create six different cases  Run the crash tube model Read more

### Analysis of failure behavior of a plate with 3 different materials using Hypermesh Radioss Jitesh Sahjwani · 2019-09-23 19:06:35

OBJECTIVE The main objective is to analyze and compare the failure behavior of a plate using different material models LAW-1, LAW-2, LAW-27 & LAW-36 along with Johnson-cook Failure card. For LAW-2, Once use Johnson\'s Failure card along with some certain p Read more

### Comparison of Simulation results and Improve Shell Property of rail model using Hypermesh RADIOSS Jitesh Sahjwani · 2019-09-20 14:57:35

OBJECTIVE Using the crash beam file, Comparison of simulation results of the base setup and improved shell element properties. Questions: 1.Using the crash beam file and change the run time to 55 ms. 2. Change the number of animation steps during simulation to a min Read more

### Crash Worthiness Analysis of Housing and Arm Bracket using Hypermesh Radioss Jitesh Sahjwani · 2019-09-20 04:21:10

Crash Worthiness analysis of housing and arm bracket using Radioss Hypermesh OBJECTIVE The key objective is to create the 2D and 3D meshing for the given models and solve the following questions PROCEDURE & Answers 1. Material property for steel we can ch Read more

### Geometry Cleanup and Mesh on 2D SHELL Elements Using Hypermesh Radioss Jitesh Sahjwani · 2019-09-17 07:48:47

Google drive link for Hypermesh files: https://drive.google.com/open?id=1MDhngswNUUJFrXmWwMTR4jfR0R9T6PKd   OBJECTIVE The key objective is to carry out the geometry cleanup operation & ignore holes less than dia 5mm, extract mid surface and create a 2D mesh Read more

### Data analysis File parsing script using Python Jitesh Sahjwani · 2019-09-14 04:40:04

Google drive link for the \'Engine_data.out\' file: https://drive.google.com/open?id=1lIh6RdUZRex9klgtDhpQ0tmtRTBY11YC   OBJECTIVE The primary aim is to create a data visualizer tool using python and perform certain things by this code is: The scri Read more

### Curve Fitting for Temperature and specific heat values using Python Jitesh Sahjwani · 2019-09-13 18:38:15

OBJECTIVE The key objective of writing this program is to perform curve fitting with the help of a linear and cubic polynomial for the Temp. & Cp data. #1. What does popt and pcov mean? #2. What does np.array(temperature) do? #3. What does the * in *popt Read more


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Share
Reservoir characterization

# Hopes of Basement Bonanza Drowned by Bad Modeling

## The UK offshore Lancaster field was to prove that complex basement formations could be profitably developed. Instead, it is a reminder of how a long-term production test can drastically alter a reservoir model built upon years of exploration work.

A British independent bet its future on proving that fractured basement formations could produce large amounts of oil and gas.

Based on its first two wells, the proposition that these highly fractured layers of awful-quality reservoir rock can produce billions of barrels of oil is looking very unlikely, but there might be something of value down there.

Last April, Hurricane Energy predicted those two development wells could easily produce 17,000 B/D of oil from rock it said held “half a billion barrels of oil.”

Now Hurricane’s ambitious plans and its identity as “basement reservoir specialists” are in tatters.

The initial wells were productive but much of what was coming out of the lower one—205/21a-7z—was water. After 8 months of production the water cut reached 46% from a well that was supposed to be hundreds of meters above the boundary between the oil and water aquifer.

That was not the only evidence suggesting there was something wrong with the plan to develop discoveries in the Lancaster field along Rona Ridge in the West of Shetland area.

On 8 June, Hurricane’s founder and Chief Executive Officer Robert Trice, a geologist with a keen interest in fractured basement rock, resigned, and the company launched a review of the technical work underlying the plan.

Experts were added to the subsurface team, which then made major changes. The most significant change pushed up the depth of the contact point between the oil and water levels by around 300 m, within 1 m below the toe of the lower well.

In other words, three-quarters of the reservoir in the original plan was under water.

The presentation by Beverley Smith, the company’s interim chief executive officer, was a reminder of how a long-term production test can change a reservoir model, even one based on years of work and the drilling of multiple wells.

“Let me start by reminding everyone that we are dealing with a unique and challenging reservoir that was always subject to great uncertainty and where data acquisition has long been problematic,” Smith said.

## Lowered Expectations

Hurricane’s remaining Lancaster well (205/21a-6) is producing more than 12,000 B/D, providing critical cash flow for the company, whose future looks altogether different than it did in the days when it predicted its discoveries could potentially produce 2.6 billion bbl of oil, making it the largest undeveloped resource base in the UK Continental Shelf (UKCS).

Based on Hurricane’s technical review, Rystad Energy recently downgraded its production outlook of the UKCS by 300,000 B/D to 1.7 million B/D by the mid-2030s.

“The entire UKCS long-term production forecast has been impacted quite significantly. The main takeaway here is that we may never again see any significant production upsurge in UKCS production,” said Olga Savenkova, an upstream analyst for the data and consulting firm.

It is hard to imagine that a small UK independent whose stock price recently traded at 4 cents a share, down from 40 cents at the start of this year, could alter the outlook for the UK.

But one thing that Trice accomplished as Hurricane’s CEO was to make a convincing case that fractured basement rock could allow the shrinking UK offshore sector to grow again.

It was enough to inspire predictions such as Rystad’s earlier call that basement rock could help push UK offshore output up to 2 million B/D in the future.

There is a lot of oil in offshore basement rock; profitably producing it is the hard part.

The upside is huge—basement rock holds about 20% of the potential production left in the world, according to an SPE technical paper by Petronas and Halliburton, a figure in line with what is thought to be present in the UKCS.

Paper SPE 176332 analyzed a Malaysian offshore prospect and concluded that the volume of oil stored in fractures, plus the thinness of those cracks, would mean the ultimate production at that location would not justify developing it.

Like shale, fractured basement rock production initially flows from the fractures, but the volume is limited. Classic basement rock is ultratight like shale, but unlike shale, it does not have the same carbon-rich composition to make it a source of oil and gas.

Real basement reservoirs, however, are an unpredictable mix, which in Lancaster includes productive conventional rock. There are successful examples of basement rock development around the globe, but as Lancaster showed, it can be hit or miss.

Hurricane’s report cut the potential production from Lancaster by 80%, to about 45 million bbl of oil likely to be produced (best estimate of contingent resources, or 2C, as defined in the SPE Petroleum Resources Management System). It also moved up the oil/water contact level in its Lincoln field by 370 m, which is likely to have a similar impact on potential production.

A spokesperson for the company said it would not go beyond the statement which did not offer estimates of its other fields. Savenkova said the story should be much the same at Hurricane’s nearby Halifax discovery.

All of Hurricane’s currently held discoveries have been made in basement rocks of the Rona Ridge. “Lancaster field and associated discoveries in the southwest Rona Ridge are hosted almost entirely within this fractured basement, so the reservoir properties are cognate [related],” she said.

## Rising Tide

The changes in Hurricane’s reservoir model were not small ones.

The potential production has sunk from about 500 million bbl to maybe more than 100 million bbl, if the company can install an effective injection system to maintain the reservoir pressure.

The higher contact level means the reservoir now is mostly less than 100 m thick—far less in some spots and a bit more in others.

Fast-rising water production from the lower well suggested the water was far higher than originally expected by the company, which said the wells were about “430 m above the oil/water contact” in a 2018 presentation.

The rapidly rising water cut in the lower well was an obvious clue—it reached 57% during a few days of production in August, compared to a 15% cut for the upper well located less than 100 m higher.

A surge in water production was a concern, but it did not seem like a big one going into the test. One of the presentation slides noted “an absence of sustained formation water during the first 12 months will remove extreme negative cases from consideration.”

Adding to the evidence was the 120‑psi pressure drop measured over the first year of production. Before the review, slides from Hurricane presentations said a pressure drop of 75 psi was its biggest expected drop in a year. Removing the same volume of fluids and gas from a smaller reservoir will have a larger pressure effect than a space several times larger.

Also, the revised view of the reservoir based on the extended production data analysis was supported by comparable fields in the area, including BP’s Clair field where basement rock is present, though not developed.

The errors were blamed on the methods used to measure and analyze pressure gradients. The changes per meter of depth vary depending on whether water or oil is present.

Smith noted that pressure data are “notoriously difficult to collect in fractured reservoirs and interpretation can be problematic.” She was addressing financial analysts, one of whom bluntly asked if the massive overestimates of reserves were strictly a technical matter.

“To what extent, do you believe that the errors in the previous estimates have only become obvious with the production data you’ve now gathered? Or is it likely the previous management were misrepresenting the size and risk of the project to the board and other stakeholders?” asked James Hosie, director of oil and gas equity research at Barclays.

Smith replied that conventional data used for well planning have their limits, and the production-testing system was installed to provide a long-term production measure “of a hitherto undeveloped reservoir type.

“I think it’s to be expected, therefore, that our understanding of fractured basement would evolve as the production data was accumulated and analyzed,” she said.

## Modest Expectations

The mistakes in the original Lancaster evaluation included a few in the company’s favor.

After the technical team downsized the reservoir, the pressure drop still seemed off. The pressure dropped less than would have been likely if the rock was mostly basement rock. The ancient rocks lack the pores and permeability that allow good-quality reservoirs to release more oil and gas as the pressure drops, which limits the declines in the reservoir pressure.

“Preliminary analysis suggests that rather than being primarily a basement reservoir, Lancaster has important oil-bearing sandstones onlapping the basement flanks, which may contain significant volumes of oil,” according to the company’s financial report in September.

That would help explain the strong production from the two wells, both of which ended near the sandstone formation along the upper edges of the basement rock.

Even with all that has gone wrong—Hurricane reported a $308-million loss for the first half of the year because of a charge due to the reduced value of its reserves—its two operations brought in some cash. During that period the wells generated$82 million in revenues despite an average oil price of less than $30/bbl. The$18/bbl cash production cost per barrel allowed it to generate \$22 million in free cash flow, according to the report.

Sustaining Lancaster production will require the new management team to raise the money needed to add a water-injection system to sustain that production.

Hurricane likely produced nearly half of the 14.3 million bbl of its reserves (1P and 1C reserves using the SPE system). It estimated that an injection system that sustains the pressure in the field could add from 26 to 90 million barrels of contingent resources.

“We have identified real potential in the onlapping Mesozoic sands, and there is a robust technical case to provide pressure support in the basement reservoir from water injection,” said Antony Maris, the new CEO.

Analysts quoted in stories about Hurricane’s woes question whether it can afford to do the water injection. Savenkova said the company’s lean development approach is up to the task.

“Hurricane’s portfolio remains economically viable, even with much fewer resources involved, due to a phased, risk-averse, and low-cost approach toward field development,” she said.

Its mix of conventional and basement rock production could provide a model for future development, where the basement might add barrels for platforms built to produce from conventional reservoirs.

The Hurricane story points to the need for better methods to accurately evaluate and identify the value in producing from fractured basement rock.

“The game-changer here might be technical-skills development in producing from fractured basement reservoirs, which could potentially increase the recovery factor,” she said. That might create “interest for this type of project going forward.”


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# Configuration spaces of products

-
Kathryn Hess, École Polytechnique Fédérale de Lausanne
Fine Hall 314

For any topological space $X$, the configuration space $\operatorname{Conf}_{n}(X)$ of $n$ points in $X$ is the subspace of the iterated product $X^{\times n}$ consisting of $n$-tuples of distinct points in $X$.  Configuration spaces play an important role in many areas of mathematics, in particular low-dimensional topology and homotopy theory.  For example, the fundamental group of $\operatorname{Conf}_{n}(\mathbb R^{2})$ is the pure $n$-stranded braid group, while the orbit space of the natural action of the symmetric group, $\operatorname{Conf}_{n}(\mathbb R^{2})/\Sigma_{n}$, has fundamental group isomorphic to the entire $n$-stranded braid group.  Moreover, $\operatorname{Conf}_{n}(\mathbb R^{2})/\Sigma_{n}$ is homeomorphic to the space of complex monic polynomials of degree $n$ with exactly $n$ roots.

In this talk I will provide a brief overview of the theory of configuration spaces, then describe the connection between configuration spaces and little disks operads, which encode operations and relations among operations in iterated loop spaces.  To conclude I will explain a new method for computing homotopy invariants of the configuration space of a product of two closed manifolds in terms of the configuration spaces of each factor separately that exploits this relationship with operads.

Joint work with Bill Dwyer and Ben Knudsen.


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Problems

The number of even divisors

Find the number of even divisors for number n.

Input

One positive integer n (n < 10000).

Output

Print the number of even divisors for number n.

Time limit 1 second
Memory limit 128 MiB
Input example #1
6

Output example #1
2


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# ISO open source software

##### 标签: cacticactiezisoNagiosnessusntopossimsnort

There are some projects do have ISO file for downloading. That means you could run this solution with in 20 minutes on a physics machine or a vmware session. You can just download this ISO image file and burn it on a blank cd; then you will insert it into DVD/CD driver of your target machine, after press few enter keys; You finally got all software on this box. Reboot this machine, you get everything up an running on it; including a Linux OS and everything which the solution depends on.

I had tested out only few of ISO open source software.

* CactiEZ

* OSSIM

It looks like actually two open source software collections. Let’s look inside those ISO files, it is a bootable Linux install disk with all necessary software.

CactiEZ has following parts:

1. Cacti and plugins (Discovery, flowviewer, mac Track, nTop, syslog, Thold, etc..)

2. Nagios

CactiEZ is focusing on Cacti. Now it does not provide free download. You will pay few \$; it’s a great ISO open source software and worthy to pay for Jimmy’s effort. I have a old version for you to download. click here. 下载 cactiez

There is architecture picture of OSSIM. OAAIM use sensor for collecting data over network. A typical OSSIM Sensor configuration would do the following functions:

1. IDS (Snort)

2. Vulnerability Scanner (Nessus)

4. Network Monitoring and Profiling (Ntop)

5. Collecting from local routers, firewalls, IDS’s, etc

6. It could even act as a Firewall

I love ISO open source software, for the following reasons:

* Easy to install on a physic machine.

* Time Saving. You just use it right away after you load everything and reboot that machine.

Linux is basically a ISO based open source software. If you know more others, not Linux; please let me know.


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## Why is the slope of a vertical line undefined?

The slope of a vertical line is its “rise over run.” Given any “slanting” line, we can take any two points and form an right triangle. The rise of the line is the length of the vertical side of the right triangle and its run is the length the horizontal side. Of course, we have learned that the slope of a line slanting on the left hand side is negative, and the slope of a line slanting to the right hand side is positive.

For a horizontal line, we only have the run and we have 0 rise. So, we divide 0 by the run which equals 0. » Read more

## Slope Concept 3 – Slopes of Vertical and Horizontal Lines

Note: This is the third part of the Slope Concept Series.

Part I: Basic Understanding of Slope

In the Understanding the Basic Concepts of Slope post, we have discussed that the slope of a line in the coordinate plane is described as the change in y over the change in x. When we say change in x, or change in y, we talk about the ‘change distance.’ To determine a distance we need two points.  If we are in the coordinate plane, and we have two points with coordinates $(x_1,y_1)$ and $(x_2,y_2)$, then the rise is $y_2 - y_1$ and the run is $x_2 - x_1$. Thus, the slope of the line containing the two points is $\displaystyle\frac{y_2-y_1}{x_2-x_1}$.

Fiigure 1 - Slope of a line containing points with coordinates (x1,y1) and (x2,y2).

We also have discussed that the slope of a horizontal line is 0 by rotation. Here, we will show the same fact using coordinates as shown.

A horizontal line has the same y-coordinates everywhere. Let us consider line l in Figure 2 with equation $y = a$.   Let us pick two points with coordinates $(x_1,a)$ and $(x_2,a)$. Using the formula above, calculating for the slope we have $\displaystyle\frac{a -a}{x_2 - x_1} = \frac{0}{x_2 - x_1 }= 0$. Hence, the slope of a horizontal line l is $0$.

Figure 2 - A horizontal line containing points with coordinates (x_1,a) and (x_2,a)..

Similarly, a vertical line has the same x-coordinate everywhere. Let us consider line m in Figure 3 with equation $x = b$.   Let us pick two points with coordinates $(b,y_1)$ and $(b,y_2)$. Using the formula above, calculating the slope, we have $\displaystyle\frac{y_2 - y_1}{b - b} = \frac{ y_2 - y_1}{0}$ which is undefined.

Figure 3 - A horizontal line containing points with coordinates (b,y2) and (b,y1).

In the sequel of this post, we will discuss the lines with positive and negative slopes.

## Slope Concept 1 – Understanding the Basic Concepts of Slope

Note: This is the first part of the the Slope Concept Series. The sequels of this article are Part II – Slope of the Graph of a Linear Function and Part III – Slopes of Vertical and Horizontal Lines.

***

The slope is known to be the steepness of a line.  Sometimes it is described as “rise over run,” If we are on point A, we go up 4 units and we go right 5 units (see Figure 1) then our rise is 4 and our run is 5. Let us mark our new location B. Notice that the order of movements does not matter. We can also go 5 units right and 4 units up and you will still be in B (see Figure 2).

If we do our movement in the coordinate plane starting from the origin, our rise would be our vertical movement (change of movement with respect to the y-axis) and our run would be our horizontal movement (change of movement with respect to the x-axis). In Figure 2, segment AB has rise 4 and run 5.  Thus, the slope of segment AB is $\displaystyle\frac{4}{5}$.  In general, slope in the coordinate plane is described as the change in y over the change in x.

Figure 1 - Segment AB with rise 4 units and run 5 units.

The slope of a line (or a segment) may also be described as the angle it makes with a horizontal line.  Technically speaking, it is a counterclockwise rotation with the line starting from a horizontal position about a point which is located on that line, or the origin our case.  In Figure 2, $\theta$ is the angle measure AB makes with the horizontal axis of the rectangular coordinate plane, or the amount of rotation from AB’ to AB about A.

Figure 2 - Counter-clockwise rotation of AB to AB' about A.

Looking at triangle ABC, since the given sides are the side adjacent and the side opposite to $\theta$, we can use the definition of tangent to compute for the value of $\theta$. Recall from trigonometry that the definition of a tangent of an angle of a right triangle is equal to the quotient of the length of the side opposite to it (change in y) and the length of the side adjacent to it (change in x). Now, this is precisely the definition of slope. From here, we can conclude that the angle that a line makes with a horizontal line is the same as the slope of that line. As a consequence $\tan(\theta) = \displaystyle\frac{4}{5}$ in radian measure (or approximately 38 degrees) is the slope of the line.

Figure 3 - Triangle ABC with Slope 4/5.

If we examine the value of $\theta$, it is clear that when $\tan(\theta)$ is $0$ degrees, the line is horizontal since there is no (zero) change in y. Algebraically, this makes the numerator of the fraction change in y $0$ which implies that the slope of any horizontal line is $0$.

If the line is vertical, there is no (zero) change in x. That makes the denominator of the fraction change in x $0$. Of course, we know that anything divided by $0$ is not defined. As a consequence, slope of a vertical line is undefined.

In the continuation of this article, we will discuss further about the properties of slope. We will discuss why the slope of a straight line is constant. We will further discuss zero, undefined, negative and positive slopes. We will also discuss how the concept of slope helps in solving calculus problems and how it is used to determine the behavior functions.


text:
› Electronic Theses and Dissertations

# Asymptotic Behavior of Solutions to Difference Equations Involving Ratios of Elementary Symmetric Polynomials

## Electronic Theses and Dissertations

### Item Details

abstract
This thesis studies the behavior of positive solutions of the recursive equation $y_n=\left(\frac{e_{i,k}}{e_{j,k}}\right)(y_{n-t_1},y_{n-t_2},\dots,y_{n-t_k}), 0\leq i, j \leq k$, where $e_{m,k}$ is the $m^{th}$ elementary symmetric polynomial on $k$ variables, $t_l \geq 1$ for $1\leq l\leq k$, $\gcd(t_1,t_2,\dots,t_k)=1$ and $y_{-s},y_{-s+1},\ldots, y_{-1} \in \mathbb{R^+}$, with $s=\max\{t_1,t_2,\dots,t_k\}$. A variant of Newton's inequalities is employed. Included amongst the results is a generalization of a particular case of Theorem 4.11 in E. A. Grove and G. Ladas, {\em Periodicities in Nonlinear Difference Equations}, Chapman \& Hall/CRC Press, Boca Raton (2004).
subject
difference equation
elementary symmetric polynomial
recursive equation
contributor
Berenhaut, Kenneth S (committee chair)
Rouse, Jeremy A (committee member)
date
2011-07-14T20:35:35Z (accessioned)
2011 (issued)
degree
Mathematics (discipline)
10000-01-01 (liftdate)
embargo
forever (terms)
identifier
http://hdl.handle.net/10339/33456 (uri)
language
en (iso)
publisher
Wake Forest University
title
Asymptotic Behavior of Solutions to Difference Equations Involving Ratios of Elementary Symmetric Polynomials
type
Thesis


text:
geom3d - Maple Help

Home : Support : Online Help : Mathematics : Geometry : 3-D Euclidean : Transformations : geom3d/inversion

geom3d

 inversion
 find the inversion of a point, plane, or sphere with respect to a given sphere.

 Calling Sequence inversion(Q, P, s)

Parameters

 Q - the name of the object to be created P - point, line, or sphere s - sphere

Description

 • If P is a point that is not the same as the center O of sphere $s\left(r\right)$, the inverse of P in, or with respect to, sphere $s\left(r\right)$ is the point Q lying on the line OP such that $\mathrm{OP}\mathrm{OQ}={r}^{2}$.
 • Sphere $s\left(r\right)$ is called the sphere of inversion, point O the center of inversion, r the radius of inversion, and ${r}^{2}$ the power of inversion.
 • For a detailed description of Q the object created, use the routine detail (i.e., detail(Q))
 • The command with(geom3d,inversion) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{geom3d}\right):$

Define the sphere s with center (0,0,0), radius 1

 > $\mathrm{sphere}\left(s,\left[\mathrm{point}\left(o,0,0,0\right),1\right]\right)$
 ${s}$ (1)

Define a plane passing through A, B, C

 > $\mathrm{plane}\left(p,\left[\mathrm{point}\left(A,1,0,-1\right),\mathrm{point}\left(B,0,0,-1\right),\mathrm{point}\left(C,0,1,-1\right)\right]\right)$
 ${p}$ (2)

Find the inversion of the plane with respect to the sphere s

 > $\mathrm{inversion}\left(\mathrm{s1},p,s\right)$
 ${\mathrm{s1}}$ (3)

Sine the plane p does not pass through the center of inversion, its inversion is a sphere through the center of inversion.

Checking:

 > $\mathrm{detail}\left(\mathrm{s1}\right)$
 Warning, assume that the name of the axes are _x, _y and _z
 $\begin{array}{ll}{\text{name of the object}}& {\mathrm{s1}}\\ {\text{form of the object}}& {\mathrm{sphere3d}}\\ {\text{name of the center}}& {\mathrm{center_s1_1}}\\ {\text{coordinates of the center}}& \left[{0}{,}{0}{,}{-}\frac{{1}}{{2}}\right]\\ {\text{radius of the sphere}}& \frac{{1}}{{2}}\\ {\text{surface area of the sphere}}& {\mathrm{\pi }}\\ {\text{volume of the sphere}}& \frac{{\mathrm{\pi }}}{{6}}\\ {\text{equation of the sphere}}& {{\mathrm{_x}}}^{{2}}{+}{{\mathrm{_y}}}^{{2}}{+}{{\mathrm{_z}}}^{{2}}{+}{\mathrm{_z}}{=}{0}\end{array}$ (4)
 > $\mathrm{IsOnObject}\left(o,\mathrm{s1}\right)$
 ${\mathrm{true}}$ (5)

Plotting:

 > $\mathrm{draw}\left(\left[s,\mathrm{s1},p\left(\mathrm{style}=\mathrm{patchnogrid},\mathrm{color}=\mathrm{maroon}\right)\right],\mathrm{style}=\mathrm{wireframe},\mathrm{view}=\left[-1..1,-1..1,-2..1\right],\mathrm{title}=\mathrm{inversion of a plane with respect to a sphere}\right)$


text:
WORKING DRAFT authorea.com/7062

# BETYdb Data Access

• Overview \ref{sec:overview}
• Search Box \ref{sec:searchbox}
• Details \ref{sec:searchdetails}
• Basic Search \ref{sec:basicsearch}
• Example \ref{sec:searchexample}

# Guide to accessing data from BETYdb \label{sec:overview}

## What is covered here:

There are many ways to access data in BETYdb. This document is written for people who want to get data from BETYdb through either 1) the web interface search box or 2) the more powerful url-based methods of submitting queries. This url-based query is the basis of the rOpensci 'traits' package that allows users to retrieve data in R.

## What is not covered:

While these methods allow users to access these data, some users may wish to use BETYdb actively in their research. If you want to contribute to BETYdb, see the Data Entry documentation. That document teaches users how they can curate their own data using BETYdb—either betydb.org or as a distributed node on the BETYdb network that enables data sharing.

Many people who contribute data—and others who want to submit more complex queries—can benefit from accessing a PostgreSQL server. Users who want to install a a BETYdb PostgreSQL database (just ask!) are able to enter, use, and share data within and across a network of synced instances of BETYdb (see wiki "Distributed BETYdb"). This network shares data that has not necessarily been independently reviewed beyond the correction of extreme outliers. In practice, data sets in active use by researchers have been evaluated for meaning by researchers. Expert knowledge encoded in the 'priors' table, in the PEcAn meta-analysis models and the Ecosystem models parameterized by the meta-analysis results.
Users with access to a BETYdb PostgreSQL database can access data through R packages, in particular PEcAn.DB which is designed for use in PEcAn or 2) any programming language a scientist is likely to use. When not using PEcAn, I recommend the R package dplyr unless you prefer joins in SQL.

## Data Sharing

Data is made available for analysis after it is submitted and reviewed by a database administrator. These data are suitable for basic scientific research and modeling. All reviewed data are made publicly available after publication to users of BETYdb who are conducting primary research.

If you want data that has not been reviewed, please request access. There are many records that are not publicly available through the web API, but that can be installed as a PostgreSQL database.

## Access Restrictions

All public data in BETYdb is made available under the Open Data Commons Attribution License (ODC-By) v1.0. You are free to share, create, and adapt its contents. Data with an access_level field and value <= 2 is is not covered by this license, but may be available for use with consent.

## Quality Flags

The checked value indicates if data has been checked (1) is unchecked (0) or identified as incorrect (-1). Checked data has been independently reviewed. By default, only checked data is provided through the web interface and API; as of BETYdb 4.4 (Oct 14 2015) users can opt-in to download unchecked data from the web search interface and API. Unchecked data (0) is also available as a PostgreSQL database (as easy as ./load.bety.sh).

Please cite the source of data as:

LeBauer, David; Dietze, Michael; Kooper, Rob; Long, Steven; Mulrooney, Patrick; Rohde, Gareth Scott; Wang, Dan; (2010): Biofuel Ecophysiological Traits and Yields Database (BETYdb); Energy Biosciences Institute, University of Illinois at Urbana-Champaign. http://dx.doi.org/10.13012/J8H41PB9

Most tables in BETYdb have search boxes, for example betydb.org/citations and betydb.org/sites. We describe below how to queried and downloaded these pages as .csv, .json, or .xml. The advanced search box is the easiest way to download summary datasets designed to have enough information (location, time, species, citations) to be useful for a wide range of use cases.

## Search Box \label{sec:searchbox}

On the welcome page of BETYdb there is a search option for trait and yield data (Figure \ref{fig:textsearch}). This tool allows users to search the entire collection of trait and yield data for specific sites, citations, species, and traits.

The results page provides a map interface (Figure \ref{fig:mapsearch}) and the option to download a file containing search results.

The downloaded file is in CSV format. This file provides meta-data and provenance information, including: the SQL query used to extract the data, the date and time the query was made, the citation source of each result row, and a citation for BETYdb itself (to be updated on publication) (Figure \ref{fig:excelresults}).

Instructions: Using the search box to search trait and yield data is very simple: Type the site (city or site name), species (scientific or common name), citation (author and/or year), or trait (variable name or description) into the search box and the results will show contents of BETYdb that match the search. The number of records per page can be changed to viewer preference and the search results can be downloaded in the Excel-compatible CSV format.

(Figure \ref{fig:textsearch})

The search map may be used in conjunction with search terms to restrict search results to a particular geographical area or even a specific site by clicking on a map. Clicking on a particular site will restrict results to that site. Clicking in the vicinity of a group of sites but not on a particular site will restrict the search to the region around the point clicked. Alternatively, if a search using search terms is done without clicking on the map, all sites associated with the returned results are highlighted on the map. Sites, species and traits can be searched further by clicking on or near highlighted locations on the map (Figure \ref{fig:accessmaps}). The color of each site indicates which sites match the search terms. Results can be downloaded by clicking the "Download Results" button on the upper right hand corner of the page.

(Figure \ref{fig:mapsearch})

## Details\label{sec:searchdetails}

2. Enter one or more terms in the search box. The search will succeed if (and only if) each term in the search box matches one of the following columns of the traits_and_yields_view: sitename, city, scientificname, commonname, author, trait, trait_description, or citation_year. Thus, the more terms entered, the more restrictive the search. Note that a search term matches a column value if it occurs anywhere within the text of that column value and that matches are case-insensitive. Thus, the term "grass" would match a row with commonname column value "switchgrass" or "tussock cottongrass", a row with site name "Grassland Soil & Water Research Laboratory", or a row with trait description "for grasses, stem internode length". There is no way to restrict which of the eight match columns a given term is matched against except perhaps by makeing the term itself more specific; in the example just given, typing "cottongrass" rather than just "grass" would make in more likely that only the match against the commonname column would succeed.
3. Click the search icon next to the search box (or press the ENTER key). This will take one to the search results/advanced search page and show the result of the search.

1. From the home page, you can get to the advanced search page simply by typing search terms into the search box and clicking on the search icon. (Or just click the search icon without entering any terms. Or enter the URL for the advanced search page directly: www.betydb.org/search)
2. The search will return results for both traits and yields.
3. Enter one or more terms in the main search box. As with basic searches, each term must match one of the eight searched columns.
4. Search results are updated as you type, but you may press the Enter key to do a formal search form submission; this will reload the page and update the URL in the browser address box to include all of the parameters of your search.

### Example\label{sec:searchexample}

1. Go to betydb.org
2. Task 1 (simple search): Search for sugarcane yields — Enter the search string "sugarcane Ayield" in the search box.
3. You will see a new page with a table of results showing data about sugarcane yields.
4. Task 2 (advanced search): Limit results to a specific site — We just want to see the results for the 'Zentsuji' site. Add a space and the word 'Zentsuji' to the search box.
5. You will see only the sugarcane yields for the 'Zentsuji' site.
6. Task 3 (advanced search): Limit results to a specific trait — We only want to see the results concerning stem_biomass instead of annual yield. Replace the word 'Ayield' with the word 'stem_biomass' in the search box.
7. The resulting table rows all concern stem biomass data for sugarcane at the Zentsuji site.


text:
Next: Impossible possible worlds Up: Logics for non-omniscient agents Previous: Logics for non-omniscient agents   Contents

## Weak deduction mechanisms

The obvious strategy to solve the logical omniscience problem is to weaken epistemic logic. One denies the universal validity of the mentioned inference rules (NEC), (MON), and (CGR), or one of the essential axioms like (K). In fact, almost all attempts to solve the LOP have in common that they consider (families of) systems that are weaker than the standard modal epistemic logics in the following sense. Firstly, not all theorems of modal epistemic logic are provable in those systems. Secondly, the set of formulae known by an agent at a state is not necessarily closed under the laws of the propositional calculus: a formula may be provable from by using axioms and inference rules of the propositional calculus, but cannot be derived from within the epistemic logic under consideration.

To construct such weak systems we can postulate, for example, that the agent only knows some obvious'' logical truths, but not necessarily the more complicated'' ones. We can assume that the agent can draw all obvious'' consequences, but not any arbitrary consequence of a certain sentence. This is achieved by postulating that the deduction mechanism of the agents is not complete, that is, it is not powerful enough to allow the agents to draw all logical consequences of their knowledge ([Hin70], [Ebe74], [Ste84], [Kon86], [Wut91], [GG93]). If an agent's inference mechanism is kept very weak, then logical omniscience could be avoided.

Certain systems of modal logic are able to characterize agents whose inference mechanisms are weaker than propositional consequence. For example, non-normal systems can be used for describing an agent who does not know all logical truths, and non-monotonic modal logics can model agents whose knowledge is not closed under logical consequence3.1. If a very weak modal logic (e.g., a classical system) is employed to model knowledge, then most versions of the LOP are solved: neither the necessitation rule (NEC), nor the monotony rule (MON), nor the axiom schema (K) is valid in a weak classical system. However, some weaker versions of the LOP still remain unsolved. All classical modal logics are closed under the congruence rule (CGR), so an agent described by such a modal system knows all logical equivalences of a sentence that he knows. Such a closure property is obviously too strong for real agents.

Another group of attempts to gain control over the LOP is to consider nonstandard logics to model agents' reasoning. The intuitive idea is as follows. Modal epistemic logic assumes that agents use classical logic (or more accurately, some extension of classical logic) in their reasoning. This causes logical omniscience because the notion of logical consequence defined by classical logic is too powerful, i.e., too much can be inferred from some base of knowledge. In particular, all tautologies are known because classical logic allows to derive them from the empty set. Hence, if the notion of logical consequence is restricted so that not all classical consequences can be drawn then certain forms of omniscience can be avoided. Such a restriction can be achieved by employing a nonstandard logic. Among the non-classical logics that have been employed for that purpose are several variants of relevance logic ([Lev84], [FHV95]) and many-valued logics ([Ho93]).

Although the approaches based on nonstandard logics solve certain forms of the LOP, they cannot eliminate the LOP completely. The agents described by those logics are not logically omniscient wrt classical logic, but they are omniscient wrt to some (nontrivial) non-classical logic. Such attempts cannot be considered satisfactory solutions to the LOP. Consequently, they are not suitable for characterizing explicit knowledge. In general, any logic that cannot model what is explicitly available to the agents but only information that must be inferred using some -- possibly incomplete -- deduction mechanism must be viewed as a logic of implicit knowledge3.2.

Next: Impossible possible worlds Up: Logics for non-omniscient agents Previous: Logics for non-omniscient agents   Contents
2001-04-05


text:
Gabriele Puppis

According to our database1, Gabriele Puppis
• authored at least 43 papers between 2003 and 2017.
• has a "Dijkstra number"2 of five.

Book
In proceedings
Article
PhD thesis
Other

Bibliography

2017
Regular Languages of Words over Countable Linear Orderings.
CoRR, 2017

One-way definability of two-way word transducers.
CoRR, 2017

Untwisting two-way transducers in elementary time.
CoRR, 2017

On the Decomposition of Finite-Valued Streaming String Transducers.
Proceedings of the 34th Symposium on Theoretical Aspects of Computer Science, 2017

Untwisting two-way transducers in elementary time.
Proceedings of the 32nd Annual ACM/IEEE Symposium on Logic in Computer Science, 2017

2016
Bounded Repairability for Regular Tree Languages.
ACM Trans. Database Syst., 2016

Walking on Data Words.
Theory Comput. Syst., 2016

Querying Visible and Invisible Information.
Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science, 2016

Minimizing Resources of Sweeping and Streaming String Transducers.
Proceedings of the 43rd International Colloquium on Automata, Languages, and Programming, 2016

2015
Which XML Schemas are Streaming Bounded Repairable?
Theory Comput. Syst., 2015

Games, Automata, Logics, and Formal Verification (GandALF 2013).
Inf. Comput., 2015

The complexity of higher-order queries.
Inf. Comput., 2015

A decidable weakening of Compass Logic based on cone-shaped cardinal directions.
Logical Methods in Computer Science, 2015

Logics with rigidly guarded data tests.
Logical Methods in Computer Science, 2015

Querying Visible and Invisible Tables in the Presence of Integrity Constraints.
CoRR, 2015

One-way Definability of Sweeping Transducer.
Proceedings of the 35th IARCS Annual Conference on Foundation of Software Technology and Theoretical Computer Science, 2015

2014
The per-character cost of repairing word languages.
Theor. Comput. Sci., 2014

Decidability of the Interval Temporal Logic $\mathsf{A\bar{A}B\bar{B}}$ over the Rationals.
Proceedings of the Mathematical Foundations of Computer Science 2014, 2014

2013
Bounded repairability of word languages.
J. Comput. Syst. Sci., 2013

Which DTDs are streaming bounded repairable?
Proceedings of the Joint 2013 EDBT/ICDT Conferences, 2013

Walking on Data Words.
Proceedings of the Computer Science - Theory and Applications, 2013

2012
Bounded repairability for regular tree languages.
Proceedings of the 15th International Conference on Database Theory, 2012

2011
On the Use of Guards for Logics with Data.
Proceedings of the Mathematical Foundations of Computer Science 2011, 2011

Regular Repair of Specifications.
Proceedings of the 26th Annual IEEE Symposium on Logic in Computer Science, 2011

Regular Languages of Words over Countable Linear Orderings.
Proceedings of the Automata, Languages and Programming - 38th International Colloquium, 2011

The Cost of Traveling between Languages.
Proceedings of the Automata, Languages and Programming - 38th International Colloquium, 2011

2010
Decidability of the Interval Temporal Logic ABB over the Natural Numbers.
Proceedings of the 27th International Symposium on Theoretical Aspects of Computer Science, 2010

Positive higher-order queries.
Proceedings of the Twenty-Ninth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, 2010

Maximal Decidable Fragments of Halpern and Shoham's Modal Logic of Intervals.
Proceedings of the Automata, Languages and Programming, 37th International Colloquium, 2010

Automata vs. Logics on Data Words.
Proceedings of the Computer Science Logic, 24th International Workshop, 2010

What You Must Remember When Processing Data Words.
Proceedings of the 4th Alberto Mendelzon International Workshop on Foundations of Data Management, 2010

Automata for Branching and Layered Temporal Structures: An Investigation into Regularities of Infinite Transition Systems
Lecture Notes in Computer Science 5955, Springer, ISBN: 978-3-642-11880-7, 2010

2009
Decidability of the interval temporal logic ABBar over the natural numbers
CoRR, 2009

A theory of ultimately periodic languages and automata with an application to time granularity.
Acta Inf., 2009

A Decidable Spatial Logic with Cone-Shaped Cardinal Directions.
Proceedings of the Computer Science Logic, 23rd international Workshop, 2009

2007
Compact and tractable automaton-based representations of time granularities.
Theor. Comput. Sci., 2007

On the Equivalence of Automaton-Based Representations of Time Granularities.
Proceedings of the 14th International Symposium on Temporal Representation and Reasoning (TIME 2007), 2007

A Contraction Method to Decide MSO Theories of Deterministic Trees.
Proceedings of the 22nd IEEE Symposium on Logic in Computer Science (LICS 2007), 2007

2006
On the relationships between theories of time granularity and the monadic second-order theory of one successor.
Journal of Applied Non-Classical Logics, 2006

2004
Decidability of the Theory of the Totally Unbounded omega-Layered Structure.
Proceedings of the 11th International Symposium on Temporal Representation and Reasoning (TIME 2004), 2004

Time Granularities and Ultimately Periodic Automata.
Proceedings of the Logics in Artificial Intelligence, 9th European Conference, 2004

Decidability of MSO Theories of Tree Structures.
Proceedings of the FSTTCS 2004: Foundations of Software Technology and Theoretical Computer Science, 2004

2003
Towards Compact and Tractable Automaten-Based Representations of Time Granularities.
Proceedings of the Theoretical Computer Science, 8th Italian Conference, 2003


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## Chemistry and Chemical Reactivity (9th Edition)

a) Since $c=\lambda\times\nu$ and $E=h\times\nu$, green light has a higher energy per photon because it has a smaller wavelength. b) Red light has a wavelength close to the maximum in the visible spectrum (700 nm), so it's the 680 nm one and the green light is the 500 nm one. c) The green light has a higher frequency because it has a smaller wavelength.


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# Wydawnictwa / Czasopisma IMPAN / Annales Polonici Mathematici / Wszystkie zeszyty

## Regularity of certain sets in ${\Bbb C}^n$

### Tom 82 / 2003

Annales Polonici Mathematici 82 (2003), 219-232 MSC: 32U15, 32U35. DOI: 10.4064/ap82-3-3

#### Streszczenie

A subset $K$ of ${{\mathbb C}}^n$ is said to be regular in the sense of pluripotential theory if the pluricomplex Green function (or Siciak extremal function) $V_K$ is continuous in ${{\mathbb C}}^n$. We show that $K$ is regular if the intersections of $K$ with sufficiently many complex lines are regular (as subsets of ${{\mathbb C}}$). A complete characterization of regularity for Reinhardt sets is also given.

#### Autorzy

• Nguyen Quang DieuDepartment of Mathematics
University of Education of Hanoi (Dai Hoc Su Pham Hanoi)
Cau Giay, Tu Liem, Hanoi, Vietnam
e-mail

## Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek


text:
# Levy's isoperimetric inequality for sphere

Let me recall subj:

If $s>0$, $A$ and $B$ are two subsets of $\mathbb{S}^{n}$, $|A|=|B|$ ($|\cdot|$ stands for the Lebesgue measure on the sphere) and $B$ is a cup $B=\{ (x_1,x_2,\dots,x_n)\in \mathbb{S}^n, x_n\leq t \}$ (for some $t\in [-1,1]$), then $|A_s|\geq |B_s|$, where $A_s$ means $s$-neighborhood of the set.

It leads to measure concentration inequalities for the sphere and so has numerous applications. So I guess that Levy's initial proof was simplified, maybe not once. What is the easiest proof of the inequality and where to read it?

The shortest and most amazing proof (in my opinion) is by Steiner symmetrization around half of a great circle. Given $A$, and given a half great circle $\gamma$, rotate the sphere so that $\gamma$ is a meridian arc. Then for each latitude sphere $H$, you can replace $A \cap H$ by the spherical cap in $H$ centered at $H \cap \gamma$. Let $A'$ be the result. Then it is not hard to show that $|A'_s| \le |A_s|$ for all $s > 0$; in fact even each $|A'_s \cap H| \le |A_s \cap H|$. And you can show that you can pick a sequence of half great circles such that $A$ converges to $B$ under symmetrization, and that some of the inequalities are strict unless $A$ is congruent to $B$.

Of course this is just an outline, but it is an accurate summary (I hope) of the Steiner symmetrization argument. It also works in Euclidean or hyperbolic space using a line rather than half of a line.

• $|A'_s\cap H|\leq A_s\cap H$ is induction propose if we use induction on dimension, right? Oct 26, 2010 at 10:40
• ah, no, $A_s\cap H$ does not depend only on $A\cap H$, but on close lattitudes too... Oct 26, 2010 at 10:43
• Yes, it's a proof by induction, even though $A_s \cap H$ depends on nearby latitudes. Oct 26, 2010 at 10:55
• Ah, for $A'$ it depend only on one latitude (though maybe different from $H$), so here everything is OK. It remains to show that a sequence of symmetrizations converge to a hat, It should be standard. Oct 26, 2010 at 13:32
• Although it's been a long time, I think I learned it from Figiel, Lindenstrauss, Milman. I'm also not sure whether this proof is essentially different from the ones that you have seen. It may mainly be a matter of abbreviated vs detailed explanation. Mar 6, 2017 at 14:54

A different symmetrization-based proof is given in this review article by Schechtman (pp. 7-8); see the previous page for references.

• Sorry, is a link OK? It downloads some file of 1.1kb size. Oct 26, 2010 at 19:01
• It's a PostScript file. If you have a Mac and double-click on the file, it will automatically be converted into a PDF file. For Windows, it's a bit more difficult. Oct 27, 2010 at 1:24
• I may read .ps files, but not of 1kb size Oct 27, 2010 at 7:27
• The .ps file is actually 700kB. The link works for me, on two different computers. Oct 27, 2010 at 11:16


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# Work with parameters¶

‘circuit parameters’ are symbolic variables found in expressions in the netlist. They can be assigned a value using the SPICE ‘.PARAM’ directive in the netlist. These values may again be given in the form of expressions with symbolic variables. When SLiCAP is working in numeric simulation mode, parameter values will recursively be substituted in expressions.

## Get all circuit parameters¶

A symbolic list of all circuit parameters can be obtained with the function params.m: In the following example we assing the list with parameter definitions to the variable allParams:

allParams = params();

## Get all parameter definitions¶

A symbolic list with all circuit parameters that have been assigned a value can be obtained with the function parDefs.m. In the following example we assign this list to the variable allParamsAssigned:

allParamsDefined = parDefs();

## Assign a definition to a parameter¶

A parameter can be given a value with the function defPar.m. Below three diferent ways in which way the MATLAB® variable R_pi will obtain the value of the circuit parameter R_pi, while the latter will be assigned a new value in the same statement.

R_pi = defPar('R_pi','2.5k');
R_pi = defPar('R_pi', 2500);
R_pi = defPar('R_pi', 'beta_DC/I_c/40');

## Get the definition or value of a parameter¶

The function getParValue.m returns the value of a parameter. If the simulation type (simType) has been set to ‘symbolic’ it returnsthe symbolic definition of the parameter. If the simulation type has been set to ‘numeric’ it returns its value after recursive substitution of all parameter definitions:

defPar('r_pi', 'beta_DC/I_c/40');
defPar('beta_DC', 100);
defPar('I_c', '1m');
getParValue('r_pi');

This returns 2500. If the parameter does not have a numeric value, the function returns the definition of the parameter with as many numeric subsitutions as possible.

## Assign definitions to multiple parameters¶

Multiple parameter definitions can be passed with the function defPars.m. The instruction below assigns 100 to the parameter R_f and 10e-12 to the parameter C_ell. The return value is similar as that of the parDefs() instruction, it will be assigned to allParams:

syms('R_f', 'C_ell');
allParams = defPars([R_f == 500, C_ell == 10E-12]);

Please notice that the use of metric prefixes, such as, k for kilo and M for mega, is not allowed in the argument of the defPars() function. The function arguments should be symbolic equations and cannot contain character strings.

## Delete a parameter definition¶

You can delete a parameter definition using the function delPar.m. This function does not delete the circuit parameter itself. It only clears its definition so that it can be used as a symbolic variable in numeric simulations.

delPar('r_pi');


text:
# How do you multiply (x + ½) (x + ½)?

Aug 30, 2015

#### Answer:

${x}^{2} + x + \frac{1}{4}$

#### Explanation:

${\left(x + a\right)}^{2} = {x}^{2} + 2 a x + {a}^{2}$

Substituting $\left(\frac{1}{2}\right)$ for $a$ gives the result in the "Answer"