text:
Sciencemadness Discussion Board » Fundamentals » Chemistry in General » sassafras extraction from roots - anyone have experience or know yeilds? Select A Forum Fundamentals   » Chemistry in General   » Organic Chemistry   » Reagents and Apparatus Acquisition   » Beginnings   » Responsible Practices   » Miscellaneous   » The Wiki Special topics   » Technochemistry   » Energetic Materials   » Biochemistry   » Radiochemistry   » Computational Models and Techniques   » Prepublication Non-chemistry   » Forum Matters   » Legal and Societal Issues   » Detritus   » Test Forum

Pages:  1
Author: Subject: sassafras extraction from roots - anyone have experience or know yeilds?
RogueRose
International Hazard

Posts: 1443
Registered: 16-6-2014
Member Is Offline

sassafras extraction from roots - anyone have experience or know yeilds?

I have the opportunity to buy some fresh roots, IDK if fresh is best or not, but it's a few lbs and I've been wanting to do some extractions and this is a good thing to try it on IMO. I tried on basil, sage and different mints and it created a mess and yeild was really low (I think my fault for drying too much) so I thought this might be worth a try.

I plan on using the extract as an essential oil and try some soaps or similar products, or maybe even make some real authentic root beer! (a couple bottles won't hurt I don't think!!).

So I'm wondering if it is worth trying to extract from a few lbs and how much I might be able to expect. Also, is their oil in the wood, bark (non-root) or anywhere else?
B(a)P
National Hazard

Posts: 260
Registered: 29-9-2019
Member Is Offline

Mood: Confined

I think safrole has gone out of fashion as a flavouring due to the carcinogenic nature of the compounds formed when it is oxidised.
It is also regulated in my country due to its use as a precursor to illicit substances.
Now I feel like the fun police.....
SWIM
International Hazard

Posts: 690
Registered: 3-9-2017
Location: 26 Ancho street
Member Is Offline

Mood: fractious

There is oil in the bark as well.

Steam distillation is popular for sassafras, and that's what gives you sassafras essential oil.

I guess you could find way to get to more or less the same thing with extraction, but it wouldn't be a simple one step process.

Only time I ever saw somebody try it the yields were terrible, but maybe it was the sassafras material.
It had little smell, and I bet it was old.

This was back when there weren't restrictions in the US on sassafras oil so roots were in little demand and these might have been rather old. They were also bought from a bin in a health food store which was not sealed so they may have been in the fresh air for quite some time.

The small amount of oil they gave off did certainly smell right though.

EDIT: It's worth mentioning that it usually takes an awful lot of plant material to distill an essential oil.

Anise is a bit of an exception, and there are probably others, but in most cases it seems to take about 10 times as much boiling as you'd think to get an ounce of oil.

[Edited on 20-5-2020 by SWIM]

@CharlieA below: Last time I checked the essential oil can be bought (expensive) by the 1/2 ounce.
The restrictions were, at least then, on quantities over 1/2 ounce.

Aromatherapy essential oils are probably your best bet for getting the real thing.

But you'll have to look a bit as many aromatherapy suppliers won't sell it in any quantity.

At least that's how it was in California.

EDIT: And oh yeah, recipes can probably be found in old cookbooks and formularies.
I'd try Dick's formulary first as it's easy to find. Might be in there.

Sarsaparilla's pretty good too though, and you don;t need any ecstasy precursors to make it.

Birch beer's too sweet for me.

[Edited on 20-5-2020 by SWIM]

[Edited on 20-5-2020 by SWIM]

Ebay says they need to get their hands on my bank account if I want to keep selling there.
This sounds like the best idea since putting ortho tricresyl phosphate in Ginger Jake.
I'm walking while I can still walk straight.

CharlieA
International Hazard

Posts: 521
Registered: 11-8-2015
Location: Missouri, USA
Member Is Offline

Mood: No Mood

I'd rather make root beer from sassafras...if I knew how!
G-Coupled
National Hazard

Posts: 284
Registered: 9-3-2017
Member Is Offline

Mood: Slightly triturated

'Rootbeer' - lol
karlos³
International Hazard

Posts: 714
Registered: 10-1-2011
Location: yes!
Member Is Offline

Mood: verrückt & wissenschaftlich

I know a detailed anecdotal report.
Just took a look at it, and the plant matter amounted to 20 pound of freshly dug up roots.
After they were deepfrozen for 24h to damage the plant cells, he cut it all small, the small ones were used simply completely and the larger roots were peeled to their core of hard wood.
For this job, he used a potato peeler apparently, which probably reduced the overall weight of the roots at the start maybe to a quarter at most, maybe even just a tenth, with all the rootbark separated from the wood, who knows, he did not say that.
Anyway, it was steam distilled and the total amount of crude sassafras oil amounted to 320ml.

This oil was simply separated out of the distillate, not extracted.
It was fractionated and the safrole obtained was then again vacuum distilled twice.
The quantity of pure safrole amounted to 240ml at this point.

And then it went on, etc, etc, everybody knows that, he was successful and it was a respectable job he did all in all with this project.
Pretty cool, I wish sassafras would grow here in europe too... its just so cool to make such a substance out of a precursor that grows wild, and its price is only hard work and time.

Sooo... in conclusion, if it is done right and well, then one can even with the material that grew just a few years ago, still get acceptable quantities of safrole from this tree, rather only his root bark, its hard work, but it does pay off obviously.
draculic acid69
International Hazard

Posts: 850
Registered: 2-8-2018
Member Is Online

 Quote: Originally posted by B(a)P I think safrole has gone out of fashion as a flavouring due to the carcinogenic nature of the compounds formed when it is oxidised. It is also regulated in my country due to its use as a precursor to illicit substances. Now I feel like the fun police.....

I know that the oil is banned but I'm not sure if buying the roots is banned.
RogueRose
International Hazard

Posts: 1443
Registered: 16-6-2014
Member Is Offline

Thanks for all the responses. I found that I can get the entire tree, so maybe I can strip the bark off, cut it down the length of the tree with a very sharp knife and peel. The tree is 3-4" diameter and 20-25ft tall, so not real big.

I also have a wood chipper that can cut very fine, so I'm thinking that is the best option but I also have some good chain saws that can make some serious chips, even smaller than the wood chipper, so maybe that's a last resort, giving them more surface area (1/8" x 3/16") and the shredder is about 1/4" x 1/4" x 1/16-1/8", so all are pretty small chips. I'm guessing either would be fine, or is there a major advantage to more surface area.

I have a 1L Soxhlet extractor that I've never had the need to use, so would this be best done in here or would normal boiling then steam distillation be adequate. I was thinking of boiling the wood in a pressure cooker and putting all the escaping vapor through a condenser.

Finally, I found a large grove of these trees, not to far, and they are old, probably pushing 75-100 years old and maybe 40-60 of them in this lot. What this means is that there are going to be maybe 100-150, 35-44 gallon bags, of shredded leaves in the fall which would be fine b/c I have a 6gal and 16gal still that could be used for this but I'm not seeing alot of sites mention that there is safrol in the leaves, maybe at a certain time of year?
I was planning on planing a bunch of tree's this year, I have 1000's of oak sprouts that came from some AMAZING stock (the acorns did at least) so now I'm thinking of adding a couple hundred Sassy trees to the planned forest (starting in a green house for first 1-3 years)
karlos³
International Hazard

Posts: 714
Registered: 10-1-2011
Location: yes!
Member Is Offline

Mood: verrückt & wissenschaftlich

The leaves contain other unwanted stuff, and only a minute quantity of safrole, they make a rather dirty oil with little valuables in there.

As for using the woodchipper, I wouldn't recommend that either.
If you remove the bark properly, you can reduce the total volume of plant matter to steam distill much, meaning you don't have the worthless inner wood taking place away in the still pot.
Everything else besides the root bark(and actually the aerial parts of the bark aren't very good either), is not of much value.

You should better do a good pre-selection of the most valuable material only, and process that first.
If you then still are motivated to repeat the same for a small number of dirtier oil, compared to your first batch in high quality where only the good rootbark is used, it also gives you a very visual impression on this matter.
And you will see with your own eyes how much more, and how much of a better oil the rootbark gives and how much worse and less every part else.
The qualitative differences will be very impressive as well.

This way you also don't ruin the good oil out of the best parts with the low quality plant matter, something you will be happy about later, thats for sure.
G-Coupled
National Hazard

Posts: 284
Registered: 9-3-2017
Member Is Offline

Mood: Slightly triturated

 Quote: Originally posted by karlos³ The leaves contain other unwanted stuff, and only a minute quantity of safrole, they make a rather dirty oil with little valuables in there.... Everything else besides the root bark(and actually the aerial parts of the bark aren't very good either), is not of much value.. You should better do a good pre-selection of the most valuable material only, and process that first.... This way you also don't ruin the good oil out of the best parts with the low quality plant matter, something you will be happy about later, thats for sure.

Great post which if followed will greatly improve any extraction - it seems you don't get very much Safrole to begin with.

[Edited on 20-5-2020 by G-Coupled]
RogueRose
International Hazard

Posts: 1443
Registered: 16-6-2014
Member Is Offline

 Quote: Originally posted by karlos³ The leaves contain other unwanted stuff, and only a minute quantity of safrole, they make a rather dirty oil with little valuables in there. As for using the woodchipper, I wouldn't recommend that either. If you remove the bark properly, you can reduce the total volume of plant matter to steam distill much, meaning you don't have the worthless inner wood taking place away in the still pot. Everything else besides the root bark(and actually the aerial parts of the bark aren't very good either), is not of much value. You should better do a good pre-selection of the most valuable material only, and process that first. If you then still are motivated to repeat the same for a small number of dirtier oil, compared to your first batch in high quality where only the good rootbark is used, it also gives you a very visual impression on this matter. And you will see with your own eyes how much more, and how much of a better oil the rootbark gives and how much worse and less every part else. The qualitative differences will be very impressive as well. This way you also don't ruin the good oil out of the best parts with the low quality plant matter, something you will be happy about later, thats for sure.

Thank you, I think that will save me from making a rather large mess had I done that. on a side note, the guy wants $30 for 3lbs of roots, which is now sounding like too much if only the root bark produces the oil... karlos³ International Hazard Posts: 714 Registered: 10-1-2011 Location: yes! Member Is Offline Mood: verrückt & wissenschaftlich 1,5kg of wood for 30 bucks? Hmm... I mean it has to pay off for you, but in this case nothing will pay off because you are willing to pay instead of investing an afternoon of hard work to obtain much more material. I can't provide you with useful or even exact numbers though, and that obviously varies a lot. I don't know, if a few ml's are sufficient and you think this is ok to buy...? But honestly, I would feel that is taking advantage off me, I could have digged them up myself, I know how to use a shovel too. Its fresh and has much higher amoúnts of a better oil, it doesn't involves giving money away, especially not for something thats likely not fresh and worth that price at all, and lastly, you're doing some great excercise for your health RogueRose International Hazard Posts: 1443 Registered: 16-6-2014 Member Is Offline Well the roots were$30, I was thinking this might be OK if I got the whole tree with it. now I just think he is out of his mind. I'll tell him I'll give him $5 (for everything) if he has no other offers. The roots are only 2 days old he says. I think he cut them like 12-16 hours b/4 I posted. I wish I could find these on our property, you'd' think with 20 acres of woods (old farm field that grew up), there's bound to be some in there, but I never saw it. I'll need to look in spring again when leaves are more easily identifiable. I did find a wood shop not far that specializes in strange lumbers, sassafrass being one of them. he's always getting in new logs and milling them, so I'm guessing he has to deal with the bark. I'm thinking THIS might be the avenue to pursue. get all the scrap boards and where they trim the bark off, then use a bandsaw to cut it very close to the wood. If they are cutting the trees completely down, maybe I can find out where and get access to the roots. IDK if you can coppice sassy or not, where you cut it down and new trees (staves) sprout up. This is an awesome method of lumber management if you need certain types of wood, like fence posts or other 2-6" diam timber. Oak does this very well, as far as some poplar, locust and I think hickory among many others. It takes advantage of the established root system so the new growth grows like 3-10x faster than it would if it was a new tree. You usually have to wait until the tree is 40-80 years old, depending on species and climate. sorry for the tangent! S.C. Wack bibliomaster Posts: 2116 Registered: 7-5-2004 Location: Cornworld, Central USA Member Is Offline Mood: Enhanced  Quote: Originally posted by karlos³ Pretty cool, I wish sassafras would grow here in europe too... its just so cool to make such a substance out of a precursor that grows wild, and its price is only hard work and time. Yes it's great to make piperonal from the plant since the smell of piperonal is almost unknown here (definitely not OTC), unlike Europe. Tons of oil were taken there starting from the 1600's; how many more centuries before someone plants seeds or live roots. Before the ban on safrole flavor, distilleries chipped down whole roots and never bothered separating the bark. The yield was 1-2%. For 15 years now, nothing sold here as sassafras oil contains safrole. "You're going to be all right, kid...Everything's under control." Yossarian, to Snowden draculic acid69 International Hazard Posts: 850 Registered: 2-8-2018 Member Is Online The poor man's chemist on YouTube has a video on sassafras steam distillation to get the oil.its a great channel.you should check it out if you want to see it done. Amos International Hazard Posts: 1245 Registered: 25-3-2014 Location: Yes Member Is Offline Mood: No I filled a 500 mL flask about halfway with sassafras root bark and obtained about 4mL of sassafras oil to show for it. Digging up the roots probably took 2 hours :| RogueRose International Hazard Posts: 1443 Registered: 16-6-2014 Member Is Offline Quote: Originally posted by S.C. Wack  Quote: Originally posted by karlos³ Pretty cool, I wish sassafras would grow here in europe too... its just so cool to make such a substance out of a precursor that grows wild, and its price is only hard work and time. Yes it's great to make piperonal from the plant since the smell of piperonal is almost unknown here (definitely not OTC), unlike Europe. Tons of oil were taken there starting from the 1600's; how many more centuries before someone plants seeds or live roots. Before the ban on safrole flavor, distilleries chipped down whole roots and never bothered separating the bark. The yield was 1-2%. For 15 years now, nothing sold here as sassafras oil contains safrole. Piperonal comes from peppers, correct? I have a 2 HUGE bags of ground black and a bag of white pepper that had gotten contaminated with some aluminum oxide powder and maybe some small parts of aluminum. Probably about 10-15kg of each. The bags were above a stove vent (made of very thin aluminum mesh) that corroded over a cople days and all the vent material fell down into the open bag/container. It also has a very slight bit of orange something that is sticky, I think a grease from the vent. Someone had left a bottle of toilet bowl cleaner or something similar that had volatile HCl and a the fan drew air up into it, it turned the grate into powder and fell down. I've been hesitant to do anything with it, I was thinking of an extraction but don't know what I would do with the product. This stuff is only a year or so old and was very fresh when it was ordered. Maybe this is a better experiment than the sassy bark considering it's free and doesn't cost me$30 for a few ml.
G-Coupled
National Hazard

Posts: 284
Registered: 9-3-2017
Member Is Offline

Mood: Slightly triturated

Extract the pepper and use any extracts in future endeavours - you might as well IMO.
S.C. Wack
bibliomaster

Posts: 2116
Registered: 7-5-2004
Location: Cornworld, Central USA
Member Is Offline

Mood: Enhanced

 Quote: Originally posted by RogueRose Piperonal comes from peppers, correct?

Fairly pure safrole, piperine, and piperonal (from piperine or isosafrole) are all easy.

"You're going to be all right, kid...Everything's under control." Yossarian, to Snowden
morganbw
International Hazard

Posts: 523
Registered: 23-11-2014
Member Is Offline

Mood: No Mood

Even though it is watched, I plan to synthesis some Piperonal this year or next.
I really desire to smell this before my end.
karlos³
International Hazard

Posts: 714
Registered: 10-1-2011
Location: yes!
Member Is Offline

Mood: verrückt & wissenschaftlich

 Quote: Originally posted by morganbw Even though it is watched, I plan to synthesis some Piperonal this year or next. I really desire to smell this before my end.

It has a very nice smell, a warm flowery smell with an undertone of vanilla, its really good!
And not the least bit artificial or synthetic like some other isolated substances do smell, despite being natural.
No, piperonal is really a good and nice smell and not even overwhelming as other fragrances easily get in larger amounts.

And, I've heard quite a few claims from others that went like: "I couldn't stop smelling it, its so good"
Whenever I have a little of it, I put a few grams on the side for my partner, she loves the smell too

In turn, I really desire to smell sassafras oil some time!
I can't even imagine what it is like, I have no idea.
Maybe it smells obviously related to piperonal?
Then again, eugenol doesn't smell like vanillin either...
Wiki says it has a "sweet-shop smell", our wiki say it has an unique and complex smell... I'm really curious about this!
So far never had an opportunity to smell the real deal ever.

Only a few months ago I found US-imported root beer in the supermarket, and I bought a can to have a taste of it, I was motivated by the connection of it with sassafras oil.
It tasted, hmm, I have to say I was warned in advance about it, that europeans will find that its taste "dentist-ry"-like... and I had the same impression, it was still good though but it tasted not much like anything else except methyl salicylate.
Well, they use some artificial sassafras flavor nowadays, so it isn't the real thing anymore todays.
I'd like to taste the real thing some time, flavored with the real sassafras extract and not some stupid substitute.
draculic acid69
International Hazard

Posts: 850
Registered: 2-8-2018
Member Is Online

All root beer flavouring is now just methyl salicylate.i tried some a few hrs ago,took a sip then handed the can back to the girl behind the counter and said get rid of that for me please.ive had a shit load of camphor timber once that instead of smelling like Vicks vapour rub smelled like a candy store so I think I know what safrole smells like
and if it taste as good as it smells it should be pretty awesome.

[Edited on 22-5-2020 by draculic acid69]
S.C. Wack
bibliomaster

Posts: 2116
Registered: 7-5-2004
Location: Cornworld, Central USA
Member Is Offline

Mood: Enhanced

There might be some perfume with piperonal in it, and it used to be available for this in more and more restricted ways, but lets not go on a sourcing rant.

 Quote: Originally posted by karlos³ In turn, I really desire to smell sassafras oil some time! I can't even imagine what it is like, I have no idea. Maybe it smells obviously related to piperonal? Then again, eugenol doesn't smell like vanillin either... Wiki says it has a "sweet-shop smell", our wiki say it has an unique and complex smell... I'm really curious about this! So far never had an opportunity to smell the real deal ever. Only a few months ago I found US-imported root beer in the supermarket, and I bought a can to have a taste of it, I was motivated by the connection of it with sassafras oil.

A grandfather often took me to the A&W (best big fast food chain ever) in the 70's, and he never mentioned the root beer being really different now and of course after I find out about the change everyone to ask is dead.

Do not try root beer flavored candy. Maybe at one time it was OK.

The only root beer worth drinking is A&W. Sassafras root smells like safrole and it seems odd that people want to make teas from it. It's rather antiseptic to me. Sweet yes but not like candy. More like somewhere between limonene and pinene. Nowhere near piperonal. Not what you'd expect from a tree root or any other part. But, like piperonal, it's a strong, unique odor that people are drawn to. IIRC most oil not for piperonal or safrole was used in soaps.

That which is sold as sassafras oil smells and tastes nothing like sassafras, and neither does root beer.

"You're going to be all right, kid...Everything's under control." Yossarian, to Snowden
morganbw
International Hazard

Posts: 523
Registered: 23-11-2014
Member Is Offline

Mood: No Mood

I have has sassafras tea off and on my entire life.
My mother would make some on occasion when I was growing up.
I have never gone looking for the roots myself but sometimes I come across a bit and will still make the tea.

The rarity of it makes it nice. I would not use it as a continuous part of my diet but on occasion it is nice.
arkoma
Forum Redneck

Posts: 1232
Registered: 3-2-2014
Location: The Boondocks
Member Is Offline


text:
# What is image file: Huffman Coding

In previous post, the introduction about JPEG, we introduced the compression algorithm “Huffman Coding”, this post is about it.

Huffman coding is widely used in:

• File compression: zip / gzip
• Image compression: jpeg / png
• Text compression: word2vec

A slight note about word2vec, which treats words in corpus as leaf nodes, based on words’ frequency as weights, to build corresponding huffman tree.

Now as you could see, we need to understand huffman coding because it was adopted in NLP and CV domains.

There was said huffman coding was invented by David A. Huffman in 1952 while he was attending exam in MIT.

The description in detail wiki.

Key points:

• Lossless data compression.
• Optimal prefix code.
• Variable length code for different symbols.
• Greedy approach upon frequency of characters.
• Complexity of nlogn to #n unique characters.
• Length of code of character is inverse to its frequency.

Pesudo codes:

 begin
count frequency of each character
sort into ascend sequence
make each char a leaf node (character, frequency, left_son, right_son)
put nodes into queue Q
while (Q >= 2) do
begin
pop the first/smallest two nodes (n1, n2)
create a new node with sum of chosen nodes
insert new node into sorted Q
end
append 0 to left_son and 1 to right_son from the root
make output for each input character
end

Implementation:

# Huffman Coding

class Node():
def __init__(self,name=None,value=None):
self._name = name
self._value = value
self._left = None
self._right = None

class HuffmanTree():
# based on leaf node, grow the tree
def __init__(self,char_weights):
# create node for each char
self.a = [Node(part[0], part[1]) for part in char_weights]

while len(self.a) != 1:
self.a.sort(key = lambda node : node._value,reverse = True)
c = Node( value = (self.a[-1]._value + self.a[-2]._value))
c._left = self.a.pop(-1)
c._right = self.a.pop(-1)
self.a.append(c)
self.root=self.a[0]
# save huffman code into b, range 10 is the tree depth
self.b = list(range(10))

# create code recursively
def pre(self,tree,length):
node = tree
if (not node):
return
elif node._name:
print(node._name + ' : ', end='')
for i in range(length):
print(self.b[i], end='')
print('\n')
return
self.b[length] = 0
self.pre(node._left, length+1)
self.b[length] = 1
self.pre(node._right,length+1)

# create huffman code
def get_code(self):
self.pre(self.root, 0)

if __name__ == '__main__':
# take inputs of char & frequency
char_weights = [('i',3), ('p',7), ('h',6), ('o',5), ('n',1), ('e',2)]
tree = HuffmanTree(char_weights)
tree.get_code()

Let’s consider another scenario, which explains the usage of Huffman coding well. Assume we have scores of a great amount of students’ exams, which range from 0 to 100, and we want to level them from A to E.

One common approach is the if / else if / else statement, something like:

if score < 61
else if score < 71
else if score < 81
else if score < 91
else:

In a first looking, this approach would work, but if take the score distribution into consideration, i.e. majority of the scores are in between 70 ~ 80, we will know this approach is not efficient.

This is the place where Huffman coding works, if we know the distribution as following:

score A B C D E
91 ~ 100 81 ~ 90 71 ~ 80 61 ~ 70 0 ~ 60
10% 20% 40% 16% 14%

How would we rewrite the conditional statement?

if score >=71 and score <81:
else if score >=81 and score < 91:
else if score score >=61 and score < 71:
else if score if score <61:
else:

Now, let’s talk about encoding and its reverse operation of decoding. Say a string of “abcc”, what will its huffman coding looks like?

We could easily figure out in this example:

a: 00

b: 01

c: 1

But wait, what will the coding looks like towards “bacc”?

It may still be:

a: 00

b: 01

c: 1

Or a: 01, b: 00, c: 1

Towards 2 characters share same frequency, it doesn’t matter to sort in alphabetical sequence or not, during preparation for huffman tree construction, as long as the code could be generated and decoded properly.

Secret to decode a encoded huffman content without ambiguity lies in the “prefix code”. To understand prefix code, let’s see what is none-prefix code first.

Still, take the “abcc” example, if we have:

a: 00, b: 10, c: 001

This is not a prefix, because given a encoded string like: 0010001001, we would have problem to tell what 00 means, it could be an “a” or the prefix to “c”, which brings ambiguity.

So, a prefix property means, each of prefix code is unique, and, starts looking up from each code’s first position, it won’t be contained in any other codes start from their first positions.

If we have the following encoding string: 000111 and huffman man tree: a: 00, b: 01, c: 1, we may start interpret from its beginning and get out: a b c c.

If we have the same encoding string: 000111 and huffman man tree: b: 00, a: 01, c: 1, we may start interpret from its beginning and get out: b a c c.

[post status: half done]

format: plain


text:
# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2007 | May-Jun | (P2-9709/02) | Q#7

Question The diagram shows the part of the curve y=ex cos x for . The curve meets the y-axis at the  point A. The point M is a maximum point. i. Write down the coordinates of A. ii. Find the x-coordinate of M. iii. Use the trapezium rule with three intervals to estimate […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2007 | May-Jun | (P2-9709/02) | Q#6

Question      i.       Express cos2 x in terms of cos 2x.    ii.       Hence show that   iii.       By using an appropriate trigonometrical identity, deduce the exact value of Solution      i.   We are required to show   in terms of . From this we can write; Therefore;    ii.   […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2007 | May-Jun | (P2-9709/02) | Q#5

Question      i. By sketching a suitable pair of graphs, show that the equation Where x is in radians, has only one root in the interval .    ii. Verify by calculation that this root lies between 1.0 and 1.2.   iii. Show that this root also satisfies the equation   iv. Use the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2007 | May-Jun | (P2-9709/02) | Q#3

Question The parametric equations of a curve are for t > 1.      i.       Express in terms of t.     ii.       Find the coordinates of the only point on the curve at which the gradient of the curve is equal to 1. Solution      i.   We are required to find […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2007 | May-Jun | (P2-9709/02) | Q#4

Question The polynomial , where a and b are constants, is denoted by . It is given that   is a factor of , and that when  is divided by    the remainder is −20. i.       Find the values of  and . ii.       When  and  have these values, find the remainder when  is […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2007 | May-Jun | (P2-9709/02) | Q#2

Question The variables x and y satisfy the relation .      i.       By taking logarithms, show that the graph of y against x is a straight line. Find the exact value  of the gradient of this line.    ii.       Calculate the x-coordinate of the point of intersection of this line with the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2007 | May-Jun | (P2-9709/02) | Q#1

Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let, . We can write it as; We have to consider both moduli separately and it leads to following cases; When If then above four intervals translate to following with their corresponding inequality; When When When If then above four intervals translate to following […]


text:
# An embedding of the Bannai-Ito algebra in $U(osp(1,2))$ and −1 polynomials

Abstract : An embedding of the Bannai-Ito algebra in the universal enveloping algebra of osp(1,2) is provided. A connection with the characterization of the little −1 Jacobi polynomials is found in the holomorphic realization of osp(1,2). An integral expression for the Bannai-Ito polynomials is derived as a corollary.
Keywords :
Type de document :
Pré-publication, Document de travail
2017
Domaine :

https://hal-cea.archives-ouvertes.fr/cea-01529434
Contributeur : Pascal Baseilhac <>
Soumis le : mardi 30 mai 2017 - 18:14:55
Dernière modification le : mercredi 31 mai 2017 - 01:04:28

### Identifiants

• HAL Id : cea-01529434, version 1
• ARXIV : 1705.09737

### Citation

Luc Vinet, Alexei Zhedanov, Vincent Genest. An embedding of the Bannai-Ito algebra in $U(osp(1,2))$ and −1 polynomials. 2017. 〈cea-01529434〉

### Métriques

Consultations de la notice


text:
As you may remember, an access modifier describes who can use your piece of code. There are 4 of them in Java:

• private: available only for the class itself;
• default: available for classes from the same package (= package-private);
• protected: available for classes from the same package and the extending classes.
• public: available from everywhere;

We’ve already considered most of them, but there’s the most interesting one left: the protected access modifier. Let’s place it among the modifiers you already know:

This modifier determines that only subclasses and any classes from the same package can use a class member. A top-level class, which is a non-nested independent class defined in a .java file, cannot be protected, but an inner one can be declared this way. This is where the importance of a proper package decomposition comes in.

Now let’s discuss the difference between protected and its scale neighbors, private and package-private” (default).

## Protected vs default

You can think of classes from the same package as the neighbors and subclasses as the children of a particular class. There are some things you can share or do with your neighbors, for example, discuss a maintenance plan or share the basement. These things and actions would be package-private (default).

There are also things you can do for children and close friends, like borrow some money or go for a walk in a park on Sunday. These things will be protected.

## Protected vs private

This distinction is even easier: if a variable, a method, or an inner class is used only by the class itself, then it is private, otherwise, it is protected. Following the main rule:

Use the most restrictive access level that makes sense for a particular member.

If you’re not sure whether the method is useful for other classes, it’s better to first make it private and expand its availability later if needed.

## Example

Now let’s see how all of this works in practice. In the example below, the package com.codeyz.bluetooth has three classes: LaptopSmartPhone, and SmartWatch. All the gadgets in the package can be connected via Bluetooth. Laptop has a method receiveInfo(), responsible for getting any information from connected gadgets.

package com.codeyz.bluetooth;

public class Laptop {

private String info;

this.info = info;
}

}

The Laptop class has only a single field info which is not directly accessible since it is declared as private. But all classes from the same package can access it invoking the receiveInfo method which is declared as package-private (no modifier).

We consider that SmartPhone and SmartWatch classes extend the same MobileGadget class with the printNotification method:

package com.codeyz.bluetooth;

System.out.println(data);
}
}

The printNotification method is accessible for all subclasses of this class as well as for all classes in the same package (including the Laptop class).

The SmartPhone class can access the receiveInfo method of the Laptop class and the printNotification method of the MobileGadget class.

package com.codeyz.bluetooth;

public class SmartPhone extends MobileGadget {

private Laptop connectedLaptop;

public SmartPhone() {
this.connectedLaptop = new Laptop();
}

private void sendInfoToLaptop(String data) {
printNotification("Sending data to laptop : "  + data);
}
}

The SmartWatch class has a private method countHeartRate, which is not available from other classes (even from a “brother” class SmartPhone). It also uses the Laptop‘s method of receiving data and a parent’s method to print the notification:

package com.codeyz.bluetooth;

public class SmartWatch extends MobileGadget {

private int avgHeartRate;
private Laptop connectedLaptop;

public SmartWatch() {
this.avgHeartRate = 75;
this.connectedLaptop = new Laptop();
}

private int countHeartRate() {
System.out.println("Counting heart rate");
return avgHeartRate;
}

private void sendInfoToLaptop(String data) {
printNotification("Sending data to laptop : "  + data);
}
}

We hope all modifiers are clear now!

## Let’s recap

Now, it’s time to put all the access modifiers together:

The scheme is the same as it was earlier, but the questions now are specified with regard to inheritance.

##### Conclusion

In this topic, you learned about the protected access modifier, its position among the other access modifiers, and how it differs from private and package-private” (default) modifiers. We also saw how the modifiers work in an example and how to choose between them. Now, it’s time to practice!


text:
### vintage_Petr_Mitrichev's blog

By vintage_Petr_Mitrichev, history, 22 months ago,

suppose u have to find a % b , i see many red coders solution instead of using directly a%b they do like ..

if (a >=mod) a-=mod ??

why so ?

• +28

 » 22 months ago, # | ← Rev. 2 →   +5 Its faster(if you do addition like 1e6(1,000,000) or more times in a program, writing an addition function using this if instead of % will save a lot of time),but this can be used only for addition and a similar if for subtraction. It can not be used for multiplication.
 » 22 months ago, # | ← Rev. 3 →   +18 The plausible reason should be that the execution time of the statement if(a >= b) a -= b; is more likely to be less than the execution time of the statement a %= b; when it is guaranteed that the expression a < 2*b is true. You may write a short C++ program to compare the average execution time of both statements so as to confirm or refute this hypothesis.
•  » » 22 months ago, # ^ |   +10 Yes , i checked in c++14 , its 3.6 times faster than % .. thanks nikolapesic2802 , CodingKnight
•  » » » 22 months ago, # ^ |   0 With pleasure. Thanks for sharing the result of the experiment.
 » 22 months ago, # |   +21 because  const uint64_t maxn = 1000000009; uint64_t ans = 0; for (int i = 0; i < maxn; ++i) { ans += i; if (ans >= maxn) ans -= maxn; } 1000 ms  const uint64_t maxn = 1000000009; uint64_t ans = 0; for (int i = 0; i < maxn; ++i) { ans = (ans + i) % maxn; } 8700 ms


text:
Relazione su invito

# Neutrinoless double beta decay.

##### Bellini F.
Giovedì 15/09   09:00 - 13:00   Aula T - Caterina Scarpellini   III - Astrofisica
Neutrinoless double beta decay is a hypothesised nuclear process in which two neutrons simultaneously decay into protons with no neutrino emission. The prized observation of this decay would point to the existence of a process that violates a fundamental symmetry of the Standard Model of particle physics, and would allow to establish the nature of neutrinos. Today, the lower limits on the half-life of this process exceed $10^{25}\mbox{--}10^{26} {yrs}$. I will review the current status of the searches for double beta decay and the perspectives to enhance the experimental sensitivity in the next years.


text:
# Partitioning a segmented stick

Problem :

We are given a stick partitioned into n - equal parts. Each of these parts has a weight, let's say x. Number of times x appears as weight of some part is guaranteed to be even.

For example consider the following stick with 6 parts -

1 2 2 1 3 3

So the stick has n parts, with weight of first part being 1, of second being 2, and likewise. Note that each weight appears even number of times.

Now, we need to cut the stick across these n partitions, and divide the parts into two users, and those two should have same weight in the end.

We divide the parts as follows -

Let's say I made first cut at y1, then from starting till y1 - this part goes to user1. Now, we make another cut at y2. Then from y1 to y2 goes to user 2. And so on alternatively.

So we need to find the minimum number of cuts in which we can do this fair division.

I couldn't find a polynomial time algorithm. And, problem appears to be NP - Hard. So, any good approximation algorithm for this problem ?

• I think the question is stated adequately. It would be nice with some motivation though! – Kristoffer Arnsfelt Hansen Jan 5 '11 at 15:05
• I agree with Kristoffer, could you please explain why this problem is interesting and what is the motivation behind this problem? – Kaveh Jan 6 '11 at 0:38
• I cannot understood the precise problem even after I read your additional post (which should not have been an answer). When you say that the two users “should have same weight,” do you mean that they have the same total weight or the same multiset of weights? In the case of latter interpretation, Yoshio’s answer gives a reference to an NP-completeness result. – Tsuyoshi Ito Jan 6 '11 at 0:47
• By using the appropriate set of weights $(4^i)$, $i=1 \ldots n$, the reference in Yoshio's answer gives an NP-completeness results for the earlier problem, too. – Peter Shor Jan 6 '11 at 17:26
• @Peter: Nice! - – Tsuyoshi Ito Jan 7 '11 at 0:37

I'm not sure if I understand the problem specification correctly, but the problem looks a special case of the paint shop problem. In that context, there is an NP-hardness result.

The main reference is: P. Bonsma, Th. Epping, and W. W. Hochstättler, Complexity results on restricted instances of a paint shop problem for words. Discrete Applied Mathematics 154 (2006) 1335-1343. http://dx.doi.org/10.1016/j.dam.2005.05.033

The abstract says as follows.

We study the following problem: an instance is a word with every letter occurring twice. A solution is a 2-coloring of its letters such that the two occurrences of every letter are colored with different colors. The goal is to minimize the number of color changes between adjacent letters.

This is a special case of the paint shop problem for words, which was previously shown to be NP-complete. We show that this special case is also NP-complete and even APX-hard. Furthermore, derive lower bounds for this problem and discuss a transformation into matroid theory enabling us to solve some specific instances within polynomial time.

This is the partition problem, here's a starting point.

• Not Exactly I guess. Sounds like partitioning but I don't think this is any where equivalent to it. Here we know that every weight will come out even number of times. Here it matter how you place the cuts ? While in that it doesn't at all. Here it is all about where to place the cuts. (and how?) – Prof. Cees Duke Jan 5 '11 at 14:44
• @Daniel: No! For these instances we are guaranteed to be able to patition, since each weight occurs an even number of times. – Kristoffer Arnsfelt Hansen Jan 5 '11 at 15:04
• @Kristoffer, good call! The grammar threw me off. :/ – Daniel Apon Jan 5 '11 at 15:08

I missed one point in the problem statement perhaps - Yes, the weight should be equal. But, we also add this extra constraint that both should have same number of weighted cuts that is -

consider the given example - 1 1 2 2 3 3

Then it is necessary for both to have stick parts with weight (1,2 and 3) in the end. Weight will automatically be the same.

@Oleksandr - Your algorithm is suboptimal. Let's just consider the example give by Suresh - 2 2 2 2 2 2 4 4 4 4 2 2. Here the greedy algorithm will give 3 cuts , at 4,8, and 10. But it is not optimal. We can solve it in two cuts, one at 2 and other at 8.

• Please, add the first part to your post. You mean both players should have the same number of parts of the stick? – Oleksandr Bondarenko Jan 5 '11 at 21:16
• So there should be even number of cuts? – Oleksandr Bondarenko Jan 5 '11 at 21:22
• I agree. please add this to the problem specification. – Suresh Venkat Jan 5 '11 at 22:25