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# Islam vs. the Western World: off-topic posts from a Religion thread

Discussion in 'World Events' started by kks, Oct 2, 2001.

1. ### copernicus66BannedBanned

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639
Neither did the Palestinians. One day they just woke up and 'Whoa shit, the Jews have put together an army to kick our ass!'

No, we are a distinct society.

3. ### S.A.M.uniquely dreadfulValued Senior Member

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Why use the example of Palestinians? Why not the Aboriginals?

5. ### BellsStaff Member

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24,170

They are putting together an army? You have proof of this, do you?

Documents? Photos? Anything at all?

And if they are currently putting together an army, why would they be invading us before their recruitment was complete?

Ah sweety. We are a distinct society as we are diverse. Are you going to walk through Chinatown and demand they change all the signs out the front of all the little shops and restaurants to english because asian language in Australia is not "assimilation"?

Who or what would they be assimilating into? What is the Australian society? How is it distinct? Should they be learning to say "mate" at the beginning and end of every sentence? Need to learn to love that vegemite? Dress like everyone else? Although half wear clothes with their bum cracks showing and tattoos across their lower back and then some dress like hippies.. others are going for the full on 70's look.. and then you have the ones who are stuck in the 80's..

So how exactly should they be assimilating, Pauline? How does one become a 'dinky di aussie'?

Oh God.. I just said dinky di.

7. ### Mrs.LucysnowValued Senior Member

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Bells: What are we? Borg?

Hahaha! That was sweeet!

8. ### copernicus66BannedBanned

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639
They aren't at that stage, yet. Let's not forget how the Jews retook Palestine, hmmm?

We are a distinct society of Anglo-Saxon cultural heritage. The fact that we tolerate the quirks of other cultures to a certain degree does not change that.

9. ### copernicus66BannedBanned

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639
Completely different situation. You see, the British never expressed an interest in living within Aboriginal society. They just went in and built their own civilizations on the land, and killed anyone who got in the way.

The Jews in Israel initially lived amongst the Palestinians. Then they segregated into Jewish communities, who later rose up and took their Jewish State.

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11. ### TylerRegistered Senior Member

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4,888
What? Really? Where did you read that? When did the Moslems get to North America??
Well then you haven't checked in a while. Genocide is a concerted effort to remove an entire population from existence. The Americans - as evil as they may be at times, and as stupid as these wars were - have not committed genocide. To suggest that they have is essentially to give up on rational discourse and to admit that you're interested only in satisfying yourself, not in converting others. You'll never convince someone they're wrong when you're throwing massive exaggerations their way.

When America gets to building death camps where they openly slaughter civilians by the thousand, we'll start talking genocide. When America shows a concerted effort to kill every single Iraqi, or every single Moslem, or every single Afghani of a particular tribe, then we can say it is a genocide in progress.

Until then, it's just a whole bunch of death.

Something not being a genocide doesn't make it any less terrible. Don't resort to grandiose fabrications, because you won't convince anyone.
I grew up being told "it could happen again". I still believe it most likely won't (it being the Holocaust), but I've come to think that religious and racial tensions will increase rather than decrease. Who knows, that ridiculous Clash of Civilizations shit might have held some grain of truth.

Either way, I grew up thinking that "it could never happen again" because most of the world had accepted the moral imperative to stop it whenever you see it. When I was still very young, Rwanda proved that wasn't true. Now, Sudan has cemented the fact.

Oh, and if you guys think America ruling the world has been bad... just you wait until China takes over. Remember, China is the nation currently sending planes and guns to the Sudanese government. Even America wouldn't be quite so obviously evil as to make money off of 3,000,000 people dying. Or the countless more millions that have died in DPNK thanks to the Chinese-supported Kim regime.

I'm no fan of Yankee foreign policy. But we're all going to miss them terribly once China takes hold.
No, I think it comes from any one-sided education and any country dominated by one ethnic group. Not even country necessarily. If you go to small town USA you'll hear a ton of us-versus-them rhetoric. The people have just grown up surrounded almost entirely by one viewpoint.
I'm not sure I remember the last time a cartoonist was killed by an angry Jew or Christian.
To many people, yes, they are. And to ignore that is to be as blind about the issue as the other extreme side.

If America waltzed in and (somehow) disposed of the CCP and set up an independent democracy, most Chinese would view it as a massive invasion of their sovereignty. But a good chunk would be happy, call them liberators and celebrate it as a day of freedom.

To suggest any large group would ever be so completely one-sided as you seem to like doing is bizarrely stupid. There were good Germans in Nazi Germany. There were good Russians in Stalin's Russia. There were those who liked and those who despised Hitler inside Germany.

I'm sure many Iraqi's are quite content that the country will become a democracy. Mind you, only the ones who already have food, water, electricity and such care about the political state. In fact, I've heard many interviews with Iraqis who are both proud and hopeful for their country. Both the haters and the happy exist. Some will call them liberators, some will call them tyrants.

Some called Caesar a hero.

Though, I'm not sure the same can be said at all for Afghanistan.

12. ### BellsStaff Member

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So you're prepared?

Getting ready. Stock piling the canned food, vegemite and bacon? Just in case when they invade they ban all that stuff?

Hah!

Shame about those Aboriginals, eh? Do "we tolerate" their quirky cultures too? Damn savages blowing on their didgeridoos.. That's not the Australian way at all!

Look around you my pet. We are no longer a distinct society of Anglo-Saxon's. That ended when the doors opened (aka immigration). And meals are no longer meat and three veg. We are diverse and come from all sorts of places. Get with the times..

13. ### copernicus66BannedBanned

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639
Things haven't gotten to that point. What is needed is political activism, people with the courage to call a spade a spade.

No, we don't. The British took their land and formed their own Anglo-Saxon civilization on it. You do remember that bit, right?

No, it's not. And trying to associate Anglo-Saxon Australian culture with Aboriginal culture is insulting, to both sides.

Wrong. Because, as I explained previously, partial assimilation is expected from immigrants. That means conforming to certain aspects of Australia's Anglo-Saxon culture.

Deal with it, or get out.

14. ### S.A.M.uniquely dreadfulValued Senior Member

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@ Tyler
It was an article on Malay and Arab trade with aboriginals pre colonial intervention.

I don't think it's a hidden history.

I believe there is some history of trade with the native Americans as well but I'd have to confirm it.

What if China invades the US? Or Canada? Will they be greeted as liberators too?

Last edited: Mar 8, 2009
15. ### BellsStaff Member

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People unite!

Rise and protect our bacon!

How can I forget. Neither do they.

Indeed. Damn savages.

We be civilised.

And what are they?

Can you list them?

John Howard tried to do so with disastrous results.. "mateship" and what not. He was laughed at so hard one almost felt embarrassed for him.

Right on Pauline!

/Smears vegemite on like warpaint..

/Rawr!!!

16. ### (Q)Encephaloid MartiniValued Senior Member

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20,855
You're never to busy to lie, though.

Do you give credit for Islam keeping you in the dark ages.

17. ### Mrs.LucysnowValued Senior Member

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Tyler: Oh, and if you guys think America ruling the world has been bad... just you wait until China takes over. Remember, China is the nation currently sending planes and guns to the Sudanese government. Even America wouldn't be quite so obviously evil as to make money off of 3,000,000 people dying. Or the countless more millions that have died in DPNK thanks to the Chinese-supported Kim regime.

And the Americans sent the same to Saddam so he could fight Iran, to Israel to they can fight the Palestinians and any one of their neighbors, let us also not forget to the Taliban and Osama so that they could fight the Russians. Remember the oh so liberal Shah of Iran the U.S propped up? That worked well didn't it? The Shah was so hated it paved the way for Ayatolla Khomeni as they begged for his return and cheered in the millions when he did (excuse me if the spelling is incorrect). Actually we are always fighting wars through proxy and in the process making things worse. Remember the support of south Vietnam so called 'free' government? The illegal bombing of Lao which drew communism and Cambodia which led to the strength of the Khmer Rouge and that crazy psycopath Lon nol the U.S supported, who created nothing but disaster for the Cambodian people and unwittingly strengthening the KR. The Chinese at least are not hypocrites, they don't pretend to care or interfere in sovereign issues anymore than they would want anyone interfering with their own, what they do is direct trade...quid pro quo. They don't give long speeches about democracy, freedom and all that jazz while propping up despotic leaders. They don't pretend to be 'innately good'.

Tyler: If America waltzed in and (somehow) disposed of the CCP and set up an independent democracy, most Chinese would view it as a massive invasion of their sovereignty. But a good chunk would be happy, call them liberators and celebrate it as a day of freedom.

How little you know of present day China! They would be just as happy to be 'liberated' by the U.S, as the Vietnamese were to be 'liberated' from their communist 'insurgents'. Remember it was the interference of the West which gave Mao the ammunition he needed to galvanize a nation in revolt. The chinese would fight an american invasion and propping up of a new regime in a way that would make the Vietnamese war look like a picnic. They are not always happy with their government and they protest and they speak out and they are jailed etc, etc, etc. but they are also a proud nation and they do no necessarily put the 'american' way as a better way. Maoism was nothing more than Neo-confusionism. It is an old way that has been intergrated into a new way. It always amazes me that no matter how terrible the consequences of U.S interference (back-door manipulation) they always seem to interpret it as fundamentally good. We have created the evils which now plague us but I think no matter how enlightened we seem to be its difficult for the West to admit its failures, so consequently we are doomed to make the same stupid mistakes over and over and over again...but oh yea. Don't forget we are the 'good' guys. How did Gore Vidal best describe it? Oh yes the United States of Amnesia.

Did I mention Cuba? Oh how could I forget the U.S support for a corrupt regime which gave rise to Castro who we now consider the bane of our existence. Ahh and then there was Musharaf, that military strongman. The pakistanis hate us now don't they? And they forced Musharaf to resign didn't they? And now no one knows which way the wind is blowing in Pakistan. No world dominating power whether Chinese or American or British has ever, ever given rise to a better world its simply a comedy of errors and a failure to comprehend the consequences of our own histrorical foreign policy. Yea Tyler, the world is so much better with the U.S at the helm

Last edited: Mar 8, 2009
18. ### TylerRegistered Senior Member

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4,888
Oh, I see.
This I'd be curious about. I've read a chunk of pre-Colonial Canadian history and never come across this. If you find a source, please let me know.
Well, no. Because we have a fairly satisfactory level of liberty. Presumably you mean the CCP invades us, in which case they would be reducing our liberty. And thus not be potential 'liberators'.

But if, for instance, America returned to manifest destiny ideas, invaded and took us over, and then some third country got us free and helped us restore democracy, I would consider them liberators. I can't speak for the rest of Canadians, but I would certainly think this way.
Arming Saddam and Osama can best be summed up as strategic stupidity. The government thought in the short term and was unable to think of the long term. To be fair, when they armed the Taliban they were arming it against the USSR, an equally awful power.

The Shah there is no defense for. That was horrible.

But I'm not sure it's quite the same as selling weapons to the next Hitler. They also armed the Rwandans. And the DPNK, as I said, which has most likely surpassed Hitler for deaths caused.
Are you out of your mind?
The CCP calls itself the people's government and yet does not protect or work for the people of China. Often, it does the opposite. I'm not sure what could be more hypocritical. Not to mention Maoist thought - still taught as the government's official line - to only support government's which represent the people of their nation. Clearly, Sudan and Rwanda do not quite fall into that category.
I live in China and speak Chinese.
I personally know a number of Chinese people who have openly said they would prefer to be liberated.
That is an incredibly narrow and uninformed view of Maoism. If you think "On Contradictions" is "nothing more than Neo-confusionism" you are sadly mistaken.
I'm Canadian. The last major international policy decision we affected was the Suez Canal Crisis.
For all the American examples you can cite I could cite a Chinese one equal or worse. And then there's Sudan and Rwanda and China's current colonization and buying off of murderers that tops it all off.

19. ### Mrs.LucysnowValued Senior Member

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I have also lived in China and the liberation they speak of is a self-generated, self-initiated liberation; they have a great tradition of that you know. As for Rwanda you should look to the French and the Belgians, as a Canadian I imagine you have read Dalliar's 'Shaking Hands With The Devil'. The U.S state department decidely turned their back on the situation as well as the U.N and just as Dallaire predicted it lead to the disaster we now see in the Congo. The Chinese had no involvement in that fiasco. The Chinese don't colonize they trade, now you can call it a 'buy off' if you want but what exactly are they buying off? All they care about is the oil.

We obviously agree on some matters but Sudan is a quite different situation. First of all the idea that there is a genocide as opposed to warfare killing is in question by many on the ground. Even members of the same tribe have splintered into fractions so the killing is somewhat wholesale with no one tribe being anymore innocent than the next, but don't get me wrong I feel nothing but sympathy for the people in the ground who are locked into this crises without relief BUT I have a very very difficult time looking at the situation in Rwanda as an african version of Nazi Germany. The situation in Sudan as in Somalia is incredibly complex and as usual the West likes to create neat linear lines to understand the issues which always leads to some disaster in the future anyway. As a side note I also don't consider what happened in Cambodia as a genocide, I agree with the scholar Michael Vickery who refers to it as a failed revolution.

20. ### zombieflirtRegistered Member

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They don't know what it's like to have to start out with your people in textile factories and slowly evolved through all the industrial progress to the first world state. They had oil. They had no real struggle. They inherited it from us.

21. ### spidergoatLiddle' Dick TaterValued Senior Member

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53,966
I suppose you forgot that Islam colonized the west first.

Islamic armies, of African slaves, invaded France in the 8th century, and Islam then colonized southern Italy and Spain where it created societies where the majority ethnically indigenous Christian population was discriminated against and enslaved. Then Islam colonized eastern Europe where it enslaved Slavs, then it was on to colonize central Asia and India in the 11th century. Then it was eastern Africa and areas near the west coast of Africa where Islamic empires and sultanates' invaded Africa in order to export slaves. By 1700 the Islamic empire in Africa and India, eastern Europe and the Middle East merely mirrored what the European empire of 1900 would look like. It was Islamic empire that first deported 11 million Africans for sexual and military slavery. When one blames American imperialism' for Bin Laden's terrorism, one should recall that it was first Islam that colonized Europe, it was the minaret and mosque that were first symbols of oppression, not the cross and the sword.

Islamic Imperialism : A History (Hardcover)
by Efraim Karsh

(quote paraphrased from the comments section)

22. ### Buffalo RoamRegistered Senior Member

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At least we aren't wiping our ass with our bare hands.

23. ### TylerRegistered Senior Member

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4,888
Cool. Where did you live?
I know a few people who have openly hoped for a war over the island for the sake of bringing liberation. The government's propaganda demonizing "western ideas" has a backlash whereby some over-romanticize the west and do, indeed, hope for their aid in "liberation".
Many nations acted horribly over Rwanda, and America did not do what it could have. Much as people have generally ignored Sudan for too long. But there's a difference between criminal negligence and outright murder. America also hasn't used it's military to kill a good 3,000+ of it's own citizens any time recently.
They sold Rwanda weapons. They currently sell Sudan weapons. And are the largest oil trader.
They're giving legitimization in exchange for cheap oil. In essence, China gives them defense.
I can agree with this. Though I think the west has had it's hands mostly tied on Sudan. Partially by it's own obsession with the Middle East, and partially by China and Russia's extension of protection.

There was a good article recently on China's "colonization" (though an economic form of colonization) of Africa. I'll try to find it for you.


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# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2022098
Online First

Online First articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Online First publication benefits the research community by making new scientific discoveries known as quickly as possible.

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## Evolutionary game theory analysis of supply chain with fairness concerns of retailers

 1 Institute for Logistics and Emergency Management, School of Economics and Management, Southwest Jiaotong University, Chengdu 610031, Sichuan, China 2 School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, Guizhou, China

*Corresponding author: Ying Dai

Received  November 2021 Revised  April 2022 Early access June 2022

This study focuses on evolutionary game analysis of supply chain (SC) strategies with fairness concerns. First, the equilibrium solutions under the eight combined strategies are obtained through the Stackelberg game. Subsequently, evolutionary game theory is applied to analyze the stability of these equilibrium solutions and to discuss the evolutionary stability strategy of the tripartite game. The study suggests that the effect of distributional fairness concerns on SC pricing differs from that of peer-induced fairness concerns in the short term. Implanting fairness concerns into SC pricing decisions is always detrimental to the supplier and not always beneficial to retailers. From a long-term perspective, only one evolutionarily stable equilibrium point exists. Retailers do not pay attention to the fairness of the channel profit distribution, and the supplier does not consider the fairness of retailers. The results help enterprises understand the influence of fairness preferences on pricing decisions and provide a reference for the efficient operation of SCs.

Citation: Yadong Shu, Ying Dai, Zujun Ma. Evolutionary game theory analysis of supply chain with fairness concerns of retailers. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2022098
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Yang, Wholesale pricing and evolutionary stable strategies of retailers under network externality, European Journal of Operational Research, 259 (2017), 37-47.  doi: 10.1016/j.ejor.2016.09.014. [53] R. Yoshihara and N. Matsubayashi, Channel coordination between manufacturer and competing retailers with fairness concerns, European Journal of Operational Research, 290 (2021), 546-555.  doi: 10.1016/j.ejor.2020.08.023. [54] H. S. Yu, A. Z. Zeng and L. D. Zhao, Analyzing the evolutionary stability of the vendor-managed inventory supply chains, Computers and industrial engineering, 56 (2009), 274-282. [55] L. H. Zhang, H. Zhou, Y. Y. Liu and R. Lu, Optimal environmental quality and price with consumer environmental awareness and retailer's fairness concerns in supply chain, Journal of Cleaner Production, 213 (2019), 1063-1079.  doi: 10.1007/s10651-018-0412-8. [56] N. Zhang and B. Li, Pricing and coordination of green closed-loop supply chain with fairness concerns, IEEE Access, 8 (2020), 224178. [57] R. R. Zhang, W. M. Ma, H. Y. Si, J. J. Liu and L. Liao, Cooperative game analysis of coordination mechanisms under fairness concerns of a green retailer, Journal of Retailing and Consumer Services, 59 (2021), 102361. [58] T. Zhang and X. C. Wang, The impact of fairness concern on the three-party supply chain coordination, Industrial Marketing Management, 73 (2018), 99-115. [59] Q. Zhou, Q. H. Li, X. Q. Hu, W. Yang and W. X. Chen, Optimal contract design problem considering the retailer's fairness concern with asymmetric demand information, Journal of Cleaner Production, 287 (2021), 125407. [60] H. Zou, J. Qin and B. Dai, Optimal pricing decisions for a low-carbon supply chain considering fairness concern under carbon quota policy, International Journal of Environmental Research and Public Health, 18 (2021), 556.

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SC Structure diagram with fairness concerns implanted
Tripartite Stackelberg game
The relation of $\pi_S^{l*}$ to $\lambda$
The relation of $\pi_S^{l*}$ to $\theta$
The relation of $\pi _{{R_1}}^{l*}$ to $\lambda$
The relation of $\pi _{{R_2}}^{l*}$ to $\lambda$
The relation of $\pi _{{R_2}}^{l*}$ to $\theta$
The relation of $\ u_{{R_i}}^{l*}$ to $\lambda$
The literature positioning of this paper
 Reference Number of participants Consider multiple fairness concerns Leader "actively" or "fairness" considers the fairness Stability analysis of equilibrium concerns of followers points Assarzadegan et al.[3] 2 $\times$ Passively $\surd$ Ho et al. [17] 3 $\surd$ Passively $\times$ Li et al. [29] 2 $\times$ Passively $\times$ Liu et al. [30] 3 $\surd$ Passively $\times$ Nie and Du[37] 3 $\surd$ Passively $\times$ Sharma[42] 2 $\times$ Passively $\times$ Shi and Zhu[43] 3 $\surd$ Passively $\times$ Yoshihara et al.[53] 3 $\times$ Passively $\times$ Zhang et al. [55] 2 $\times$ Passively $\times$ Zhang et al. [57] 3 $\times$ Passively $\times$ Zhang and Wang[58] 3 $\surd$ Passively $\times$ This paper 3 $\surd$ Passively and actively $\surd$
 Reference Number of participants Consider multiple fairness concerns Leader "actively" or "fairness" considers the fairness Stability analysis of equilibrium concerns of followers points Assarzadegan et al.[3] 2 $\times$ Passively $\surd$ Ho et al. [17] 3 $\surd$ Passively $\times$ Li et al. [29] 2 $\times$ Passively $\times$ Liu et al. [30] 3 $\surd$ Passively $\times$ Nie and Du[37] 3 $\surd$ Passively $\times$ Sharma[42] 2 $\times$ Passively $\times$ Shi and Zhu[43] 3 $\surd$ Passively $\times$ Yoshihara et al.[53] 3 $\times$ Passively $\times$ Zhang et al. [55] 2 $\times$ Passively $\times$ Zhang et al. [57] 3 $\times$ Passively $\times$ Zhang and Wang[58] 3 $\surd$ Passively $\times$ This paper 3 $\surd$ Passively and actively $\surd$
Notations description
 Parameter Meaning $S$ Supplier $R_{i}$ Retailer $i$, $i=1, 2$ $D_{i}$ Demand function of the retailer $R_{i}$, $D=D_{1}+D_{2}$ $Superscript$ "$\ast$" The optimal solution $\lambda_{R_{i}}$ Distributional fairness concerns coefficient of the retailer $R_{i}$, let $\lambda_{R_{1}}=\lambda_{R_{2}}$, and $0\leq \lambda \leq 1$ $\theta$ Peer-induced fairness concerns coefficient, and $0\leq \theta \leq 1$ Decision variables $p_{i}$ Selling price, and it is the retailer $R_{i}^{'}$s decision variable $\omega_{i}$ Wholesale price, and it is the supplier's decision variable Performance $\pi_{S}^{l}$ The profit of the supplier under model $l$, $l\in\left\{CCC, CCN, CNC, CNN, NCC, NCN, NNC, NNN\right\}$ $\pi_{R_{i}}^{l}$ The profit of the retailer $\pi_{R_{i}}$ under model $l$, $l\in\left\{CCC, CCN, CNC, CNN, NCC, NCN, NNC, NNN\right\}$ $\pi_{SJ}$ The supplier's profit in the $j$-th round of the game, $j=1, 2$ $\pi_{J}$ The profit of the SC in the $j$-th round of the game, $j=1, 2$ $\bar{\pi}_{R_{i}}$ Nash bargaining solution of the retailer $R_{i}$ $\bar{\pi}_{S}$ Nash bargaining solution of the supplier $u_{R_{i}}^{l}$ The utility of the retailer $R_{i}$ under model $l$, $l\in\left\{CCC, CCN, CNC, CNN, NCC, NCN, NNC, NNN\right\}$
 Parameter Meaning $S$ Supplier $R_{i}$ Retailer $i$, $i=1, 2$ $D_{i}$ Demand function of the retailer $R_{i}$, $D=D_{1}+D_{2}$ $Superscript$ "$\ast$" The optimal solution $\lambda_{R_{i}}$ Distributional fairness concerns coefficient of the retailer $R_{i}$, let $\lambda_{R_{1}}=\lambda_{R_{2}}$, and $0\leq \lambda \leq 1$ $\theta$ Peer-induced fairness concerns coefficient, and $0\leq \theta \leq 1$ Decision variables $p_{i}$ Selling price, and it is the retailer $R_{i}^{'}$s decision variable $\omega_{i}$ Wholesale price, and it is the supplier's decision variable Performance $\pi_{S}^{l}$ The profit of the supplier under model $l$, $l\in\left\{CCC, CCN, CNC, CNN, NCC, NCN, NNC, NNN\right\}$ $\pi_{R_{i}}^{l}$ The profit of the retailer $\pi_{R_{i}}$ under model $l$, $l\in\left\{CCC, CCN, CNC, CNN, NCC, NCN, NNC, NNN\right\}$ $\pi_{SJ}$ The supplier's profit in the $j$-th round of the game, $j=1, 2$ $\pi_{J}$ The profit of the SC in the $j$-th round of the game, $j=1, 2$ $\bar{\pi}_{R_{i}}$ Nash bargaining solution of the retailer $R_{i}$ $\bar{\pi}_{S}$ Nash bargaining solution of the supplier $u_{R_{i}}^{l}$ The utility of the retailer $R_{i}$ under model $l$, $l\in\left\{CCC, CCN, CNC, CNN, NCC, NCN, NNC, NNN\right\}$
The relation between the supplier's profits and distributional fairness concerns
 $\frac{\partial \pi_{S}^{CCC\ast}}{\partial \lambda}$ $\frac{\partial \pi_{S}^{CCN\ast}}{\partial \lambda}$ $\frac{\partial \pi_{S}^{CNC\ast}}{\partial \lambda}$ $\frac{\partial \pi_{S}^{CNN\ast}}{\partial \lambda}$ $\frac{\partial \pi_{S}^{NCC\ast}}{\partial \lambda}$ $\frac{\partial \pi_{S}^{NCN\ast}}{\partial \lambda}$ $\frac{\partial \pi_{S}^{NNC\ast}}{\partial \lambda}$ $\frac{\partial \pi_{S}^{NNN\ast}}{\partial \lambda}$ $-$ $-$ $-$ $-$ $-$ $-$ $-$ $/$
 $\frac{\partial \pi_{S}^{CCC\ast}}{\partial \lambda}$ $\frac{\partial \pi_{S}^{CCN\ast}}{\partial \lambda}$ $\frac{\partial \pi_{S}^{CNC\ast}}{\partial \lambda}$ $\frac{\partial \pi_{S}^{CNN\ast}}{\partial \lambda}$ $\frac{\partial \pi_{S}^{NCC\ast}}{\partial \lambda}$ $\frac{\partial \pi_{S}^{NCN\ast}}{\partial \lambda}$ $\frac{\partial \pi_{S}^{NNC\ast}}{\partial \lambda}$ $\frac{\partial \pi_{S}^{NNN\ast}}{\partial \lambda}$ $-$ $-$ $-$ $-$ $-$ $-$ $-$ $/$
The relation between the supplier's profits and peer-induced fairness concerns
 $\frac{{\partial\pi_S^{CCC*}}}{{\partial\theta}}$ $\frac{\partial \pi_{S}^{CCN\ast}}{\partial \theta}$ $\frac{\partial \pi_{S}^{CNC\ast}}{\partial \theta}$ $\frac{\partial \pi_{S}^{CNN\ast}}{\partial \theta}$ $\frac{\partial \pi_{S}^{NCC\ast}}{\partial \theta}$ $\frac{\partial \pi_{S}^{NCN\ast}}{\partial \theta}$ $\frac{\partial \pi_{S}^{NNC\ast}}{\partial \theta}$ $\frac{\partial \pi_{S}^{NNN\ast}}{\partial \theta}$ $+$ $+$ $+$ $+$ $+$ $/$ $+$ $/$
 $\frac{{\partial\pi_S^{CCC*}}}{{\partial\theta}}$ $\frac{\partial \pi_{S}^{CCN\ast}}{\partial \theta}$ $\frac{\partial \pi_{S}^{CNC\ast}}{\partial \theta}$ $\frac{\partial \pi_{S}^{CNN\ast}}{\partial \theta}$ $\frac{\partial \pi_{S}^{NCC\ast}}{\partial \theta}$ $\frac{\partial \pi_{S}^{NCN\ast}}{\partial \theta}$ $\frac{\partial \pi_{S}^{NNC\ast}}{\partial \theta}$ $\frac{\partial \pi_{S}^{NNN\ast}}{\partial \theta}$ $+$ $+$ $+$ $+$ $+$ $/$ $+$ $/$
The relation between the retailer ${R_1}$'s profits and distributional fairness concerns
 $\frac{{\partial \pi _{{R_1}}^{CCC*}}}{{\partial \lambda }}$ $\frac{{\partial \pi _{{R_1}}^{CCN*}}}{{\partial \lambda }}$ $\frac{{\partial \pi _{{R_1}}^{CNC*}}}{{\partial \lambda }}$ $\frac{{\partial \pi _{{R_1}}^{CNN*}}}{{\partial \lambda }}$ $\frac{{\partial \pi _{{R_1}}^{NCC*}}}{{\partial \lambda }}$ $\frac{{\partial \pi _{{R_1}}^{NCN*}}}{{\partial \lambda }}$ $\frac{{\partial \pi _{{R_1}}^{NNC*}}}{{\partial \lambda }}$ $\frac{{\partial \pi _{{R_1}}^{NNN*}}}{{\partial \lambda }}$ $+$ $+$ $+$ $+$ $-$ $-$ $/$ $/$
 $\frac{{\partial \pi _{{R_1}}^{CCC*}}}{{\partial \lambda }}$ $\frac{{\partial \pi _{{R_1}}^{CCN*}}}{{\partial \lambda }}$ $\frac{{\partial \pi _{{R_1}}^{CNC*}}}{{\partial \lambda }}$ $\frac{{\partial \pi _{{R_1}}^{CNN*}}}{{\partial \lambda }}$ $\frac{{\partial \pi _{{R_1}}^{NCC*}}}{{\partial \lambda }}$ $\frac{{\partial \pi _{{R_1}}^{NCN*}}}{{\partial \lambda }}$ $\frac{{\partial \pi _{{R_1}}^{NNC*}}}{{\partial \lambda }}$ $\frac{{\partial \pi _{{R_1}}^{NNN*}}}{{\partial \lambda }}$ $+$ $+$ $+$ $+$ $-$ $-$ $/$ $/$
The relation between the retailer ${R_2}$'s profits and distributional fairness concerns
 $\frac{{\partial \pi _{{R_2}}^{CCC*}}}{{\partial \lambda }}$ $\frac{{\partial \pi _{{R_2}}^{CCN*}}}{{\partial \lambda }}$ $\frac{{\partial \pi _{{R_2}}^{CNC*}}}{{\partial \lambda }}$ $\frac{{\partial \pi _{{R_2}}^{CNN*}}}{{\partial \lambda }}$ $\frac{{\partial \pi _{{R_2}}^{NCC*}}}{{\partial \lambda }}$ $\frac{{\partial \pi _{{R_2}}^{NCN*}}}{{\partial \lambda }}$ $\frac{{\partial \pi _{{R_2}}^{NNC*}}}{{\partial \lambda }}$ $\frac{{\partial \pi _{{R_2}}^{NNN*}}}{{\partial \lambda }}$ $+$ $+$ $+$ $+$ $-$ $/$ $-$ $/$
 $\frac{{\partial \pi _{{R_2}}^{CCC*}}}{{\partial \lambda }}$ $\frac{{\partial \pi _{{R_2}}^{CCN*}}}{{\partial \lambda }}$ $\frac{{\partial \pi _{{R_2}}^{CNC*}}}{{\partial \lambda }}$ $\frac{{\partial \pi _{{R_2}}^{CNN*}}}{{\partial \lambda }}$ $\frac{{\partial \pi _{{R_2}}^{NCC*}}}{{\partial \lambda }}$ $\frac{{\partial \pi _{{R_2}}^{NCN*}}}{{\partial \lambda }}$ $\frac{{\partial \pi _{{R_2}}^{NNC*}}}{{\partial \lambda }}$ $\frac{{\partial \pi _{{R_2}}^{NNN*}}}{{\partial \lambda }}$ $+$ $+$ $+$ $+$ $-$ $/$ $-$ $/$
The relation between the retailer ${R_2}$'s profits and peer-induced fairness concerns
 $\frac{{\partial \pi _{{R_2}}^{CCC*}}}{{\partial \theta }}$ $\frac{{\partial \pi _{{R_2}}^{CCN*}}}{{\partial \theta }}$ $\frac{{\partial \pi _{{R_2}}^{CNC*}}}{{\partial \theta }}$ $\frac{{\partial \pi _{{R_2}}^{CNN*}}}{{\partial \theta }}$ $\frac{{\partial \pi _{{R_2}}^{NCC*}}}{{\partial \theta }}$ $\frac{{\partial \pi _{{R_2}}^{NCN*}}}{{\partial \theta }}$ $\frac{{\partial \pi _{{R_2}}^{NNC*}}}{{\partial \theta}}$ $\frac{{\partial \pi _{{R_2}}^{NNN*}}}{{\partial \theta }}$ $+$ $+$ $+$ $+$ $-$ $/$ $-$ $/$
 $\frac{{\partial \pi _{{R_2}}^{CCC*}}}{{\partial \theta }}$ $\frac{{\partial \pi _{{R_2}}^{CCN*}}}{{\partial \theta }}$ $\frac{{\partial \pi _{{R_2}}^{CNC*}}}{{\partial \theta }}$ $\frac{{\partial \pi _{{R_2}}^{CNN*}}}{{\partial \theta }}$ $\frac{{\partial \pi _{{R_2}}^{NCC*}}}{{\partial \theta }}$ $\frac{{\partial \pi _{{R_2}}^{NCN*}}}{{\partial \theta }}$ $\frac{{\partial \pi _{{R_2}}^{NNC*}}}{{\partial \theta}}$ $\frac{{\partial \pi _{{R_2}}^{NNN*}}}{{\partial \theta }}$ $+$ $+$ $+$ $+$ $-$ $/$ $-$ $/$
Equilibrium solutions under different strategy combination
 $w_1^{CCC*}$ $w_1^{CCN*}$ $w_1^{CNC*}$ $w_1^{CNN*}$ $w_1^{NCC*}$ $w_1^{NCN*}$ $w_1^{NNC*}$ $w_1^{NNN*}$ $416.7$ $416.7$ $416.7$ $416.7$ $500$ $500$ $500$ $500$ $w_2^{CCC*}$ $w_2^{CCN*}$ $w_2^{CNC*}$ $w_2^{CNN*}$ $w_2^{NCC*}$ $w_2^{NCN*}$ $w_2^{NNC*}$ $w_2^{NNN*}$ $437.5$ $437.5$ $437.5$ $437.5$ $500$ $500$ $500$ $500$ $p_1^{CCC*}$ $p_1^{CCN*}$ $p_1^{CNC*}$ $p_1^{CNN*}$ $p_1^{NCC*}$ $p_1^{NCN*}$ $p_1^{NNC*}$ $p_1^{NNN*}$ $750$ $750$ $708.3$ $708.3$ $800$ $800$ $750$ $750$ $p_2^{CCC*}$ $p_2^{CCN*}$ $p_2^{CNC*}$ $p_2^{CNN*}$ $p_2^{NCC*}$ $p_2^{NCN*}$ $p_2^{NNC*}$ $p_2^{NNN*}$ $750$ $718.7$ $750$ $718.7$ $785.7$ $750$ $785.7$ $750$
 $w_1^{CCC*}$ $w_1^{CCN*}$ $w_1^{CNC*}$ $w_1^{CNN*}$ $w_1^{NCC*}$ $w_1^{NCN*}$ $w_1^{NNC*}$ $w_1^{NNN*}$ $416.7$ $416.7$ $416.7$ $416.7$ $500$ $500$ $500$ $500$ $w_2^{CCC*}$ $w_2^{CCN*}$ $w_2^{CNC*}$ $w_2^{CNN*}$ $w_2^{NCC*}$ $w_2^{NCN*}$ $w_2^{NNC*}$ $w_2^{NNN*}$ $437.5$ $437.5$ $437.5$ $437.5$ $500$ $500$ $500$ $500$ $p_1^{CCC*}$ $p_1^{CCN*}$ $p_1^{CNC*}$ $p_1^{CNN*}$ $p_1^{NCC*}$ $p_1^{NCN*}$ $p_1^{NNC*}$ $p_1^{NNN*}$ $750$ $750$ $708.3$ $708.3$ $800$ $800$ $750$ $750$ $p_2^{CCC*}$ $p_2^{CCN*}$ $p_2^{CNC*}$ $p_2^{CNN*}$ $p_2^{NCC*}$ $p_2^{NCN*}$ $p_2^{NNC*}$ $p_2^{NNN*}$ $750$ $718.7$ $750$ $718.7$ $785.7$ $750$ $785.7$ $750$
Tripartite game benefit matrix
 Supplier Supplier $R_{1}$ Concerns ($y$) No concerns ($1-y$) Retailer $R_{2}$ Consideration ($x$) $A, I, q$ $b, T, r$ Concerns ($z$) No consideration ($1-x$) $c, k, s$ $d, I, B$ Consideration ($x$) $c, m, u$ $g, n, v$ (No concerns $1-z$) No consideration ($1-x$) $f, o, W$ $h, p, \varphi$
 Supplier Supplier $R_{1}$ Concerns ($y$) No concerns ($1-y$) Retailer $R_{2}$ Consideration ($x$) $A, I, q$ $b, T, r$ Concerns ($z$) No consideration ($1-x$) $c, k, s$ $d, I, B$ Consideration ($x$) $c, m, u$ $g, n, v$ (No concerns $1-z$) No consideration ($1-x$) $f, o, W$ $h, p, \varphi$
ESS stability analysis
 Equilibrium Points Eigenvalues Asymptotic Stability $\lambda_{1}$ $\lambda_{2}$ $\lambda_{3}$ $E_{1}(0, 0, 0)$ $\eta_{1}$ $\eta_{1}$ $\eta_{1}$ ESS $-$ $-$ $-$ $E_{2}(1, 0, 0)$ $-\eta_{1}$ $\alpha_{2}+\eta_{2}$ $\alpha_{3}+\eta_{3}$ Saddle-point $+$ $-$ $-$ $E_{3}(1, 1, 1)$ $-(\alpha_{1}+\theta_{1}+\eta_{1})$ $-(\alpha_{2}+\eta_{2})$ $-(\alpha_{3}+\eta_{3})$ Saddle-point $-$ $+$ $+$ $E_{4}(0, 1, 0)$ $\alpha_{1}+\eta_{1}$ $-\eta_{2}$ $\eta_{3}$ Saddle-point $+$ $+$ $-$ $E_{5}(0, 0, 1)$ $\theta_{1}+\eta_{1}$ $\eta_{2}$ $-\eta_{3}$ Saddle-point $Uncertain$ $-$ $+$ $E_{6}(1, 1, 0)$ $-(\alpha_{1}+\eta_{1})$ $-(\alpha_{2}+\eta_{2})$ $\alpha_{3}+\eta_{3}$ Saddle-point $-$ $+$ $-$ $E_{7}(1, 0, 1)$ $-(\theta_{1}+\eta_{1})$ $\alpha_{2}+\eta_{2}$ $-(\alpha_{3}+\eta_{3})$ Saddle-point $Uncertain$ $-$ $+$ $E_{8}(0, 1, 1)$ $\alpha_{1}+\theta_{1}+\eta_{1}$ $-\eta_{2}$ $-\eta_{3}$ Saddle-point $+$ $+$ $+$
 Equilibrium Points Eigenvalues Asymptotic Stability $\lambda_{1}$ $\lambda_{2}$ $\lambda_{3}$ $E_{1}(0, 0, 0)$ $\eta_{1}$ $\eta_{1}$ $\eta_{1}$ ESS $-$ $-$ $-$ $E_{2}(1, 0, 0)$ $-\eta_{1}$ $\alpha_{2}+\eta_{2}$ $\alpha_{3}+\eta_{3}$ Saddle-point $+$ $-$ $-$ $E_{3}(1, 1, 1)$ $-(\alpha_{1}+\theta_{1}+\eta_{1})$ $-(\alpha_{2}+\eta_{2})$ $-(\alpha_{3}+\eta_{3})$ Saddle-point $-$ $+$ $+$ $E_{4}(0, 1, 0)$ $\alpha_{1}+\eta_{1}$ $-\eta_{2}$ $\eta_{3}$ Saddle-point $+$ $+$ $-$ $E_{5}(0, 0, 1)$ $\theta_{1}+\eta_{1}$ $\eta_{2}$ $-\eta_{3}$ Saddle-point $Uncertain$ $-$ $+$ $E_{6}(1, 1, 0)$ $-(\alpha_{1}+\eta_{1})$ $-(\alpha_{2}+\eta_{2})$ $\alpha_{3}+\eta_{3}$ Saddle-point $-$ $+$ $-$ $E_{7}(1, 0, 1)$ $-(\theta_{1}+\eta_{1})$ $\alpha_{2}+\eta_{2}$ $-(\alpha_{3}+\eta_{3})$ Saddle-point $Uncertain$ $-$ $+$ $E_{8}(0, 1, 1)$ $\alpha_{1}+\theta_{1}+\eta_{1}$ $-\eta_{2}$ $-\eta_{3}$ Saddle-point $+$ $+$ $+$
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text:
OpenStudy (anonymous):

After picking apples, 4 friends compared the amount of apples in their buckets. Dan’s bucket was 2/3 full, Mary’s bucket was 4/5 full, Julie’s bucket was 3/4 full, and Jane’s bucket was 1/8 full. How would these amounts be arranged in order from greatest to least? Not Here 2/3, 4/5, 3/4, 1/8 4/5, 3/4, 2/3, 1/8 3/4, 4/5, 1/8, 2/3 1/8, 2/3, 3/4, 4/5

7 years ago
OpenStudy (anonymous):

second option

7 years ago


text:
# Would HTML/Unicode formatting cause troubles?

Although, as of now, this comment collected 17 upvotes, I still hope that the thought was expressed not precisely enough. (Mis)typesetting like

b^2 - a^2 = (b+a)x(b-a)

can induce vomit, many would agree. But is

b2a2 = (b + a) × (b − a)

very different from $$b^2 - a^2 = (b+a)\times(b-a)\ ?$$

In specific cases, there may be some arguments against using LaTeX, ranging from avoiding unnecessary complications ($1,729$ renders with an annoying space – do you know which code produces $1{,}729$?) to aesthetisation (“a 2 × 2 matrix” does not protuberate unlike “a $2×2$ matrix”, and I prefer 2π over $2π$, as well as 360° over either $360°$ or $360^\circ$; the last one is also not searchable due to incorrect code point). Also, it is a common practice to avoid LaTeX in titles; although they haven’t HTML, Unicode is available.

Is here some rule or prejudice against HTML/Unicode-formatted formulae? Ones similar to those I produce at various Internet sites, namely: StackExchange, Wikipedia and, very recently, Quora. Have LaTeX codes some importance but as one of formatting mechanisms?

1. I found that ISO 80000 advises against italicizing symbols of constants. Namely, ISO deems that π (for the area of unit circle) is incorrect whereas π is correct. I doubt there is a convenient way to display roman-type Greek lowercase letters, namely α β γ δ ϵ ε ζ η θ ι κ λ μ ν ξ ο π ρ ς σ τ υ ϕ φ χ ψ ω, with either TEX or MathJax.
2. A newer discussion about questionable MathJax practices, borrowed from early days plain TEX kludges, is currently hosted here.

• You bring up some good points. I think the some simple formulas look okay in Unicode, and don't need to be edited into LaTeX. But only really simple ones. As for issues, there is minor one: if one wants to save the post as a LaTeX file, the Unicode characters have to be replaced with their LaTeX analogues. – user147263 Nov 30 '14 at 18:58
• To avoid having a space after $,$ use {,} for example, $1{,}729$. – Asaf Karagila Mod Nov 30 '14 at 20:25
• Also my phone usually fails to render many unicode math characters. Since I post more and more from my phone, I prefer to let its CPU sweat with MathJax rendering and be able to actually read the question, or answers given. As for the preference of fonts, if you'll write enough papers in $\LaTeX$ you will change your mind. – Asaf Karagila Mod Nov 30 '14 at 20:27
• @Asaf Karagila: do you mean you device can do MathJax, but fails to render Unicode Mathematical Operators and similar in running text? Sorry my humour about space was so subtle that you rushed to write a spoiler instead of taking the point. – Incnis Mrsi Nov 30 '14 at 20:36
• Yes, that is what I meant. My phone can show me MathJax, but not all unicode math. – Asaf Karagila Mod Nov 30 '14 at 20:37
• Although the above form is acceptable to me, most users will still downvote it, since it shows a lack of effort in conforming with the standard everyone else has. My problem mainly lies with rendering fractions and symbols. What about matrices or piecewise defined functions? – user142198 Nov 30 '14 at 21:41
• In brief, there is definitely a prejudice against non-$\LaTeX$ formatting. Our MathJaX just looks the best, it's not hard to learn, and it reads best on a broader variety of device formats. – J. W. Perry Dec 1 '14 at 5:37
• I have added (mathjax) tag (since it is related - it discusses not using mathjax) and (unicode) tag (I am not sure about this one, but I have no idea whether we have some tag which is close to typesetting math without mathjax.) If anybody has better idea for suitable tags for this question, feel free to retag. – Martin Sleziak Dec 2 '14 at 8:01
• Related older discussion: Is there something wrong with posts avoiding mathjax? – Martin Sleziak Dec 2 '14 at 8:03
• Don't tell me you want to say you'd prefer this over Mathjax. – Aditya Hase Dec 2 '14 at 8:45
• @Integrator Don't tell me you came across that post, had 2000 rep, and did not edit it. – user147263 Dec 4 '14 at 16:11
• @WarmFuzzies I just noticed that you changed your name, but just see who is next to you when it comes to editing! – Aditya Hase Dec 4 '14 at 16:13
• @Integrator Point taken. Good job. – user147263 Dec 4 '14 at 16:17
• @WarmFuzzies I actually started to edit it but I hate HTML so... – Aditya Hase Dec 4 '14 at 16:18

Although there are some great comments above, one thing no one has mentioned is people who use assistive technology like screen readers. Having the mathematics clearly marked as mathematics (as oppose to "fake" mathematics using other HTML tricks) makes it much easier to properly voice the mathematics for screen readers. Although few screen readers currently handle mathematics, the number are growing, and the MathJax team is working with several to help improve the situation. The format used by most screen readers is MathML, and since MathJax can generate MathML from your TeX input, that means that any math that is entered in MathJax notation will be accessible to those users with special needs. The upshot is, if you use MathJax to mark up your mathematics, even when it is possible to do it using HTML, it will help out those readers who use assistive technology.

A related issue is that people who wish to reuse the content of the questions and answers, not just in LaTeX papers, as has been mentioned in the comments, but for other machine processing of the math (math aggregators, math search, analysis of mathematical content of questions, copying and pasting into other programs, etc.), will find it much easier to identify the mathematical sections of the questions if they are clearly marked as mathematics rather than marked up in HTML in other ways. MathJax can create a good machine-readable form (MathML) for the math content when it is written in TeX, and that can be used as an interchange format for other programs. For example, the MathML obtainable from MathJax's "Show Math As..." contextual menu can be pasted into programs like Mathematica, and even Microsoft Word, while retaining its mathematical meaning. That simply can't be done with HTML-formatted mathematics.

My own feeling is that anything that improves the semantics of the content (without unduly burdening the author) is a good thing. Using a mechanism (like MathJax notation) that clearly delimits the mathematics from the other text on the page is an important example of this.

• It might be worth stressing, in case you agree, that as a consequence of this MathJax should rather not be used for things that are not at all mathematics, such as $ugly slanted text$ or just "white space." Do you agree with this or is there a point that I am missing that might make that practice legitimate? – quid Mod Dec 5 '14 at 12:52
• @quid. I absolutely agree. MathJax should be used only for mathematical content, not for adding white space, or italics, or colored text, or background colors, or line breaks in comments, or other display hacks, to textual (non-math) content. – Davide Cervone Dec 5 '14 at 13:47
• @DavideCervone Recently a question about screen readers was posted here on meta: [Problem with MathJax and Screen Readers. I though it might be wise to ping you, since you are probably best qualified to say something about MathJax and Screen Readers from the people around here. (Or at least you might know where to look for further information.) – Martin Sleziak Nov 18 '15 at 16:01
• Thanks -- I've commented in the post you link to. – Davide Cervone Nov 18 '15 at 22:18


text:
#### An axiomatic approach to intrinsic dimension of a dataset

We perform a deeper analysis of an axiomatic approach to the concept of intrinsic dimension of a dataset proposed by us in the IJCNN'07 paper (arXiv:cs/0703125). The main features of our approach are that a high intrinsic dimension of a dataset reflects the presence of the curse of dimensionality (in a certain mathematically precise sense), and that dimension of a discrete i.i.d. sample of a low-dimensional manifold is, with high probability, close to that of the manifold. At the same time, the intrinsic dimension of a sample is easily corrupted by moderate high-dimensional noise (of the same amplitude as the size of the manifold) and suffers from prohibitevely high computational complexity (computing it is an $NP$-complete problem). We outline a possible way to overcome these difficulties.


text:
A train running at the speed of 72 km/ h goes past a pole in 15 s. What is the length of the train? [CDS 2013]

# Ask a Question

### Question Asked by a Student from EXXAMM.com Team

Q 1433756642.     A train running at the speed of 72 km/ h goes past a pole in 15 s. What is the
length of the train?

[CDS 2013]
A

150 m

B

200 m

C

300 m

D

350 m

#### HINT

(Provided By a Student and Checked/Corrected by EXXAMM.com Team)

#### Access free resources including

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text:
# Charge density

1. Sep 7, 2008

### kjintonic

A semicircular loop of radius a carries positive charge Q distributed uniformly over its length.?
Find the electric field at the center of the loop (point P in the figure). Hint: Divide the loop into charge elements dq as shown in the figure, and write dq in terms of the angle d\theta. Then integrate over \theta to get the net field at P.

http://i533.photobucket.com/albums/ee336/shaneji_kotoba/RW-20-72.jpg

I dunno how to start this question....

2. Sep 7, 2008

### Hootenanny

Staff Emeritus
You must have some idea how to start, have you tried using the hint?

3. Sep 7, 2008

### kjintonic

Probably I can use E= (S)dE= (S)kdq/r^2 inwhich r=a
(S) is integral sign

4. Sep 7, 2008

### Hootenanny

Staff Emeritus
You're on the right lines, how about writing dq in terms of $d\theta$?

HINT: Notice that the horizontal components will cancel so you need only consider the vertical components of the electric field.

5. Sep 7, 2008

### kjintonic

hmmm... Sorry I kinda don't understant how to write dq in terms of d[itex]d\theta[itex] :(

6. Sep 7, 2008

bump?

7. Sep 7, 2008

### Defennder

First step you should note that by symmetry, one of field components in an axial direction is 0. Now you only have to find the other component. Set this problem up in the coordinate plane with point P at the origin. Draw a triangle for E in terms of E_x and E_y and theta. What can you say about how E_x is related to x? Write down the expression for dE, the differential electric field magnitude due to dq, then try to write dq in terms of $$\lambda dr$$, where lambda is Q/length.


text:
# Cost to install a camlock?

#### JD

##### Well-Known Member
I'd concur. Some panels on the existing cabinet might have to be blanked but 4 pigtails with NEMA 14-15p plugs and 4 NEMA 14-50R Rece3ptacle s- basically an electric range set up - would seem to run in the $15-20 range each component - so under$150 for all of the parts - plus pipe and wire and qualified install. I "think" Steve Terry would concur. I agree emphasizing the necessity to find qualified personnel to do the installation and modifications. Probably not one or two useable LED units - and they require jumpers and other wiring.

The 30 amp "Dryer" plug/receptacle is about the same price as the 50 amp "Range" plug/receptacle. In fact, often it is sold as the same plug packaged with both blades. Beware of one thing- The "Range" plug/cable set, such as you would buy at Home Depot, is not suitable. This is due to the fact that the cable is a light duty plastic AND although the two hots are gauged at 6, the ground and neutral are gauged at 8. I am not sure why it is listed as UL approved, but I suspect it may come under the "whip cable" exemption. In either case, use the plug assembly with 6/4 SO cable.

As for the connectors not being permitted for stage usage, I am not aware of that and have seen plenty in use. (There may be local rules that prevent their use.) Pin and sleeve connectors are preferable as they are locking, whereas the range plugs are not. Unfortunately, pin and sleeve connectors are also !

One annoyance of the standard "Range" plugs are that they exit at a 90, so they are problematic in some cases. However, in this case, it is probably an advantage.

One last thing about cams- (This may have been covered before.) They are considered a "tool-less lug" so the same rules apply to plugging in a cam as do to a direct tap. (See- http://www.controlbooth.com/forums/lighting-electrics/18977-cam-turn-arounds.html#post173586)
This is why multi-pin connectors are the way to go.

Last edited:

#### derekleffew

##### Resident Curmudgeon
Senior Team
Can NEMA 14-50 plugs not be used in theatrical applications? ...
I don't think there's anything in the NEC forbidding it; however, the use of the range plug /stove plug / dryer plug has only two advantages (cost and ease of availability) and many more disadvantages. These include:
1. Only available in a 90° version as JD stated.
2. If the cable needs to be extended, No cable mount/inline, female, line connector version. A box containing a panel mount receptacle on the end of a jumper is unwieldy at best.
3. Not really intended for repeated connection/disconnection. How often are ranges/dryers unplugged/replugged?
4. Often flimsy construction and the strain-relief may not accept 6/4 or 4/4 type SO (and derivatives) cord.

I'd spend the extra money for the Hubbell CS-style, "California Plug". To each his own, as long as it's safe.
.

#### JD

##### Well-Known Member
The name varies somewhat from region to region, but what Derek is referring to is this:
Reliance Generator Cord Plug — 50 Amp, 120/240 Volt | Generator Cordsets Plugs| Northern Tool + Equipment

They take a lot of abuse.

They even have cable sets
http://www.northerntool.com/shop/tools/product_200596099_200596099

#### BGW

##### Active Member
I wholeheartedly agree with you- I like other connectors much more. I just thought of the 14-50 first for the two reasons you list. It's not the most elegant solution, but it sounds as though it's a mixed bag of components to begin with.


text:
# Quick tests with Riemann zeta function code in a few languages

I am a self admitted speed freak … I like fast things. I like playing with the new shiny as well, to get a feel for its utility and capabilities.
I’ll freely admit I’ve been quite excited about the Julia language. I like the concept of a language specifically designed for high performance.
I am a user of Perl for many things. It is still, IMO, one of the most powerful languages available, and is reasonably fast. I am not sure I am happy with it as a data language (for massive data processing), as this is not its core competency. I’ve been hoping Julia would be able to fill this void eventually.
Matlab and more precisely, Octave, is my go-to modeling/analysis language. Its pretty trivial to express algorithms in it, and its designed to handle data.
I really need to get better at k/q in kdb+. It is very expressive, and very compact simultaneously.
Previously, I had written the rzf (Riemann zeta function calculator) in C, Fortran, node (Javascript), rewritten the C to have hand optimized inner loops, Perl. Now I’ll show the Perl, matlab/octave, julia, python, java, and kdb+ for fixed order 2, and 1 billion (109 iterations). What I am curious about is how easy it is to express, and how fast the loop construct is, without significant hand optimization. Java, Perl and Julia use a JIT compilation system though Perl executes a mid-level set of op-codes, while Julia compiles via a LLVM based JIT, and Java compiles to optimized byte codes. Matlab/octave, python and kdb+ are strictly interpreted.
The julia code is pretty straightforward:

N        = 1000000000.0
sum	 = 0.0
pi_exact = 4.0*atan(1.0)
tic()
for i=N:-1.0:1.0
sum += 1.0/(i*i)
end
timing = toc()
println("sum reduction took ", timing  * 1000, " ms")
pi_comp	= sqrt(sum*6.0)
println("pi = ",pi_comp)
println("error in pi = ",pi_exact-pi_comp)
println("relative error in pi = ",(pi_exact-pi_comp)/pi_exact)

The time to execute this cam out to about 238.5s on my laptop
It turns out the matlab/octave version is almost identical.

format long
N		=1000000000.0
sum		= 0.0
pi_exact	= 4.0*atan(1.0)
tic()
for i=N:-1.0:1.0
sum += 1.0/(i*i);
end
timing = toc()
"timing = ",timing
pi_comp	= sqrt(sum*6.0)
"pi = ",pi_comp
"error in pi = ",pi_exact-pi_comp
"relative error in pi = ",(pi_exact-pi_comp)/pi_exact

It takes 2398s.
The kdb+/q version (serial loop)

N:1000000000
s:0.0f
i:N
\t do[N; s+:1.0%(i*i); i-:1; ]
s*:6.0f
pi_comp: sqrt s
pi_exact: 4.0f * atan(1.0f)
delta: pi_comp - pi_exact
fdelta: delta % pi_exact
pi_comp
delta
fdelta

takes 640.7 seconds.
The Perl (5.16.1) version

#!/opt/scalable/bin/perl
use Time::HiRes qw( usleep ualarm gettimeofday tv_interval nanosleep
clock_gettime clock_getres clock_nanosleep clock
stat );
use Math::Trig;
my ($i,$j,$k,$milestone,$n,$rc);
my (@array,$total,$p_sum,$sum,$delta_t,$pi,$pi_exact,@caliper);
use constant true => (1==1);
use constant false => (1==0);
my $inf=1000000000 ; my$c;
$milestone = 0;$n		= 0;
$sum = 0.0;$pi_exact	= 4.0*atan(1.0);
$caliper[$milestone] = [gettimeofday];
$sum=0.0; for($k=$inf-1;$k>=1;$k--) {$sum += 1.0/($k*$k);
}
$milestone++;$caliper[$milestone] = [gettimeofday]; printf("zeta(%i) = %-.15f \n",$n,$sum);$pi = sqrt($sum*6.0); printf("pi = %-.15f \n",$pi);
printf("error in pi = %-.15f \n",$pi_exact-$pi);
printf("relative error in pi = %-.15f \n",($pi_exact-$pi)/$pi_exact); #/* now report the milestone time differences */ for ($i=0;$i< =($milestone-1);$i++) {$delta_t = tv_interval($caliper[$i] ,  $caliper[$i+1] );
printf("Milestone %i to %i: time = %-.3fs\n",$i,$i+1,$delta_t); }  takes 152s. The python code (works in Python 3 and 2.x, though you should change range to xrange for 2.x) import math import time N = 1000000000 sum = 0.0 pi_exact = 4.0*math.atan(1.0) start = time.clock() for i in range(N,0,-1): sum += 1.0/(i*i) stop = time.clock() timing = stop - start print("timing=", timing) pi_comp = math.sqrt(sum*6.0) print("computed pi=",pi_comp) delta = pi_exact-pi_comp rerr = delta / pi_exact print("delta=",delta) print("relative error",rerr)  takes 275.1s with Python 3.3.1 The Java code is also fairly straightforward: import java.*; public class rzf { public static void main (String[] args) { long N=1000000000; long start,stop; double sum=0.0,timing,rerr,delta,pi_comp,pi_exact; pi_exact=4.0*Math.atan(1.0); start = System.currentTimeMillis(); for( long i = N; i >= 1; i--) { sum += 1.0/((double)i*(double)i); } stop = System.currentTimeMillis(); timing = (double)(stop - start)/ 1000.0; System.out.println (timing); pi_comp = Math.sqrt(6.0*sum); System.out.println (pi_comp); delta = pi_comp - pi_exact; rerr = delta / pi_exact ; System.out.println (delta); System.out.println (rerr); } }  The java code takes 11 seconds. The same code in C #include #include  takes 7.5s Whats interesting to me is that since none of these are vectorized/parallelized, we see something of raw compiler/interpreter performance. The optimization in terms of using vector operations, and exploiting parallelism is where this gets interesting. Rewriting the kdb+/q code as a blocked set of vectors (I had to adjust this as it was running the 32 bit version and I kept running out of memory) N:1000000000 M:10 s:0.0f i:0 rzfk: {[x] 1.0f % (x*x) } v: {[i;r] (i*6h$r)+1+til 6h$r } \t do [M; s+: sum rzfk 9h$(v[i;N%M]) ; i+:1; ]
s*:6.0f
pi_comp: sqrt s
pi_exact: 4.0f * atan(1.0f)
delta: pi_comp - pi_exact
fdelta: delta % pi_exact
pi_comp
delta
fdelta

we now execute this in 34.4 seconds. Within a factor of 5 of the C code, and within a factor of 3 of Java. Whats more interesting than this is that this is the pure 32 bit version of kdb+, versus 64 bit for everything else. I am not sure what sort of performance hit this would take running this way. The construction of the kernel (the rzfk function lambda) is quite interesting. It basically provides the template for the computation. The vector v is one group of vectors (M groups total). But you can see the exercise of power from this code. I am working on the same thing in Octave, but running into some curious bugs:

octave:25> V=1:10
V =
1    2    3    4    5    6    7    8    9   10
octave:26> sum(V)
error: A(I): index out of bounds; value 10 out of bound 1
octave:26> V=[1:10]
V =
1    2    3    4    5    6    7    8    9   10
octave:27> sum(V)
error: A(I): index out of bounds; value 10 out of bound 1

Cool (not).

### 2 thoughts on “Quick tests with Riemann zeta function code in a few languages”

1. Just a quick clarification — you say matlab/octave is “almost identical” to the julia code, but you list the matlab/octave time as 2398s. Do you mean 239.8s?

• The code is almost identical. The runtimes were anything but identical.


text:
# Incompleteness of Lorentzian manifolds

Let $\tilde{M}$ be a simply connected Lorentzian manifold and suppose that $\tilde{M}$ admits some Riemannian metric.

Question: What can be said about the relation between the geodesic completeness of $\tilde{M}$ as a Lorentzian manifold and the metric completion as a metric space via the Riemannian metric? In particular, if $\tilde{M}$ is already metrically complete, is it then also Lorentzian geodesically complete?

• You may find some interesting results in dimension two contained in this book by Tilla Weinstein.
– Neal
Feb 16 '16 at 1:49

Even if every Riemannian metric on $\bar{M}$ is complete (so that $\bar{M}$ is necessarily compact), the Lorentzian metric may not be complete: the Clifton-Pohl torus is an example of a compact Lorentzian manifold which is not geodesically complete. This shows that the Hopf-Rinow Theorem does not generalise to Lorentzian manifolds.
• Yes I am well aware of these results. I am currently trying to understand that completeness is guaranteed when $M$ has constant sectional curvature and is compact. The proof is rather complicated, and my question was conceptually relevant. Feb 16 '16 at 20:13


text:
# 10.4: Sampling methods

As we mentioned in a previous section, the first thing we should do before conducting a survey is to identify the population that we want to study. Suppose we are hired by a politician to determine the amount of support he has among the electorate should he decide to run for another term. What population should we study? Every person in the district? Not every person is eligible to vote, and regardless of how strongly someone likes or dislikes the candidate, they don't have much to do with him being re-elected if they are not able to vote.

What about eligible voters in the district? That might be better, but if someone is eligible to vote but does not register by the deadline, they won't have any say in the election either. What about registered voters? Many people are registered but choose not to vote. What about "likely voters?"

This is the criteria used in much political polling, but it is sometimes difficult to define a "likely voter." Is it someone who voted in the last election? In the last general election? In the last presidential election? Should we consider someone who just turned 18 a "likely voter?" They weren't eligible to vote in the past, so how do we judge the likelihood that they will vote in the next election?

In November 1998, former professional wrestler Jesse "The Body" Ventura was elected governor of Minnesota. Up until right before the election, most polls showed he had little chance of winning. There were several contributing factors to the polls not reflecting the actual intent of the electorate:

• Ventura was running on a third-party ticket and most polling methods are better suited to a two-candidate race.
• Many respondents to polls may have been embarrassed to tell pollsters that they were planning to vote for a professional wrestler.
• The mere fact that the polls showed Ventura had little chance of winning might have prompted some people to vote for him in protest to send a message to the major-party candidates.

But one of the major contributing factors was that Ventura recruited a substantial amount of support from young people, particularly college students, who had never voted before and who registered specifically to vote in the gubernatorial election. The polls did not deem these young people likely voters (since in most cases young people have a lower rate of voter registration and a turnout rate for elections) and so the polling samples were subject to sampling bias: they omitted a portion of the electorate that was weighted in favor of the winning candidate.

## Definition: Sampling bias

A sampling method is biased if every member of the population doesn’t have equal likelihood of being in the sample.

So even identifying the population can be a difficult job, but once we have identified the population, how do we choose an appropriate sample? Remember, although we would prefer to survey all members of the population, this is usually impractical unless the population is very small, so we choose a sample. There are many ways to sample a population, but there is one goal we need to keep in mind: we would like the sample to be representative of the population.

Returning to our hypothetical job as a political pollster, we would not anticipate very accurate results if we drew all of our samples from among the customers at a Starbucks, nor would we expect that a sample drawn entirely from the membership list of the local Elks club would provide a useful picture of district-wide support for our candidate.

One way to ensure that the sample has a reasonable chance of mirroring the population is to employ randomness. The most basic random method is simple random sampling.

## Definition: Simple random sample

A random sample is one in which each member of the population has an equal probability of being chosen. A simple random sample is one in which every member of the population and any group of members has an equal probability of being chosen.

## Example 7

If we could somehow identify all likely voters in the state, put each of their names on a piece of paper, toss the slips into a (very large) hat and draw 1000 slips out of the hat, we would have a simple random sample.

In practice, computers are better suited for this sort of endeavor than millions of slips of paper and extremely large headgear.

It is always possible, however, that even a random sample might end up not being totally representative of the population. If we repeatedly take samples of 1000 people from among the population of likely voters in the state of Washington, some of these samples might tend to have a slightly higher percentage of Democrats (or Republicans) than does the general population; some samples might include more older people and some samples might include more younger people; etc. In most cases, this sampling variability is not significant.

## Definition: Sampling variability

The natural variation of samples is called sampling variability.

This is unavoidable and expected in random sampling, and in most cases is not an issue.

To help account for variability, pollsters might instead use a stratified sample.

## Definition: Stratified sampling

In stratified sampling, a population is divided into a number of subgroups (or strata). Random samples are then taken from each subgroup with sample sizes proportional to the size of the subgroup in the population.

## Example 8

Suppose in a particular state that previous data indicated that the electorate was comprised of 39% Democrats, 37% Republicans and 24% independents. In a sample of 1000 people, they would then expect to get about 390 Democrats, 370 Republicans and 240 independents. To accomplish this, they could randomly select 390 people from among those voters known to be Democrats, 370 from those known to be Republicans, and 240 from those with no party affiliation.

Stratified sampling can also be used to select a sample with people in desired age groups, a specified mix ratio of males and females, etc. A variation on this technique is called quota sampling.

## Definition: Quota Sampling

Quota sampling is a variation on stratified sampling, wherein samples are collected in each subgroup until the desired quota is met.

## Example 9

Suppose the pollsters call people at random, but once they have met their quota of 390 Democrats, they only gather people who do not identify themselves as a Democrat.

You may have had the experience of being called by a telephone pollster who started by asking you your age, income, etc. and then thanked you for your time and hung up before asking any "real" questions. Most likely, they already had contacted enough people in your demographic group and were looking for people who were older or younger, richer or poorer, etc. Quota sampling is usually a bit easier than stratified sampling, but also does not ensure the same level of randomness.

Another sampling method is cluster sampling, in which the population is divided into groups, and one or more groups are randomly selected to be in the sample.

## Cluster sampling

In cluster sampling, the population is divided into subgroups (clusters), and a set of subgroups are selected to be in the sample

## Example 10

If the college wanted to survey students, since students are already divided into classes, they could randomly select 10 classes and give the survey to all the students in those classes. This would be cluster sampling.

Other sampling methods include systematic sampling.

## Systematic sampling

In systematic sampling, every $$n^{t h}$$ member of the population is selected to be in the sample.

## Example 11

To select a sample using systematic sampling, a pollster calls every $$100^{th}$$ name in the phone book.

Solution

Systematic sampling is not as random as a simple random sample (if your name is Albert Aardvark and your sister Alexis Aardvark is right after you in the phone book, there is no way you could both end up in the sample) but it can yield acceptable samples.

Perhaps the worst types of sampling methods are convenience samples and voluntary response samples.

## Convenience sampling and voluntary response sampling

Convenience sampling is samples chosen by selecting whoever is convenient.

Voluntary response sampling is allowing the sample to volunteer.

## Example 12

A pollster stands on a street corner and interviews the first 100 people who agree to speak to him. This is a convenience sample.

## Example 13

A website has a survey asking readers to give their opinion on a tax proposal. This is a self-selected sample, or voluntary response sample, in which respondents volunteer to participate.

Usually voluntary response samples are skewed towards people who have a particularly strong opinion about the subject of the survey or who just have way too much time on their hands and enjoy taking surveys.

## Try it Now 4

In each case, indicate what sampling method was used

1. Every 4th person in the class was selected
2. A sample was selected to contain 25 men and 35 women
3. Viewers of a new show are asked to vote on the show’s website
4. A website randomly selects 50 of their customers to send a satisfaction survey to
5. To survey voters in a town, a polling company randomly selects 10 city blocks, and interviews everyone who lives on those blocks.


text:
# Escaping the “^” character causes formatting error

Escaping "^" after \tt is causing formatting error in the following code. All words after \^{} is being affected by \tt.

Code:

\item Use the {\tt linspace} command to create a vector $\mathbf{x} \in \mathbb{R}^{100}$ containing 100 equally spaced points between 0 and 10 (inclusive). Use this vector to create the Vandermonde matrix $\mathbf{D} \in \mathbb{R}^{100 \times 4}$ with rows $\begin{bmatrix} 1 & x_i & x_i^2 & x_i^3 \end{bmatrix}$ for $i = 1,\dots,100$. (Hint: While using {\tt x\^{}n} will result in an error, using {\tt x.\^{}n} will return a vector where each element is raised to the $n$th power.) Save the matrix $\mathbf{D}$ as {\tt A4.dat}.

Current output:

Is there a way to resolve this issue?

• Well, now you should not use \tt at all. In this case, I think \verb fits best – JouleV Apr 26 at 4:44
• However, your code works fine for me – JouleV Apr 26 at 4:47
• Independent of your question, you might be interested in this package: matlab-prettifier. – Henri Menke Apr 26 at 5:06

Your code works file for me. However,

1. you should not use the deprecated \tt. Such commands are some of the most deprecated commands in LaTeX.

2. \verb is for that purpose. You can use something as simple as \verb|a^b| to get a^b instead of \texttt{a\^{}b}; or \verb|\cmd| to get \cmd instead of \texttt{\textbackslash{}cmd}.

Code:

\documentclass{article}
\usepackage{mathtools}
\usepackage{amssymb}
\usepackage[shortlabels]{enumitem}
\begin{document}
\begin{enumerate}[(a)]
\item Use the \verb|linspace| command to create a vector $\mathbf{x} \in \mathbb{R}^{100}$ containing 100 equally spaced points between 0
and 10 (inclusive). Use this vector to create the Vandermonde matrix
$\mathbf{D} \in \mathbb{R}^{100 \times 4}$ with rows $\begin{bmatrix} 1 & x_i & x_i^2 & x_i^3 \end{bmatrix}$ for $i = 1,\dots,100$. (Hint:
While using \verb|x^n| will result in an error, using \verb|x.^n| will
return a vector where each element is raised to the $n$-th power.)
Save the matrix $\mathbf{D}$ as \verb|A4.dat|.
\end{enumerate}
\end{document}